UK ENERGY RESEARCH CENTRE

UKERC Review of Evidence 

for the Rebound Effect 

Technical Report 2: 

Econometric studies 

Working Paper 

October 2007: REF UKERC/WP/TPA/2007/010 

Steve Sorrell and John Dimitropoulos - Sussex Energy Group (SEG), University of Sussex 

This document has been prepared to enable results of on-going work to be made available rapidly. It has not been 

subject to review and approval, and does not have the authority of a full Research Report. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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Preface 

This report has been produced by the UK Energy Research Centre’s Technology and Policy 

Assessment (TPA) function. 

The TPA was set up to address key controversies in the energy field through comprehensive 

assessments of the current state of knowledge. It aims to provide authoritative reports that 

set high standards for rigour and transparency, while explaining results in a way that is both 

accessible to non-technical readers and useful to policymakers. 

This report forms part of the TPA’s assessment of evidence for a rebound effect from 

improved energy efficiency. The subject of this assessment was chosen after extensive 

consultation with energy sector stakeholders and upon the recommendation of the TPA 

Advisory Group, which is comprised of independent experts from government, academia and 

the private sector. The assessment addresses the following question: 

What is the evidence that improvements in energy efficiency will lead to economywide reductions in energy consumption? 

The results of the project are summarised in a Main Report, supported by five in-depth 

Technical Reports, as follows: 

1. Evidence from evaluation studies 

2. Evidence from econometric studies 

3. Evidence from elasticity of substitution studies 

4. Evidence from CGE modeling studies 

5. Evidence from energy, productivity and economic growth studies 

A shorter Supplementary Note provides a graphical analysis of rebound effects. All these 

reports are available to download from the UKERC website at: www.ukerc.ac.uk/

The assessment was led by the Sussex Energy Group (SEG) at the University of Sussex, 

with contributions from the Surrey Energy Economics Centre (SEEC) at the University of 

Surrey, the Department of Economics at the University of Strathclyde and Imperial College. 

The assessment was overseen by a panel of experts and is extremely wide ranging, 

reviewing more than 500 studies and reports from around the world. 

Technical Report 2: Econometric Studies focuses upon econometric estimates of the 

elasticity of demand for different types of consumer energy service such as household 

heating. Under certain assumptions, these estimates can provide good indication of the 

magnitude of the direct rebound effect for these energy services. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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THE UK ENERGY RESEARCH CENTRE 

Operating at the cusp of research and policy-making, the UK Energy Research Centre's 

mission is to be the UK's pre-eminent centre of research, and source of authoritative 

information and leadership, on sustainable energy systems. 

The Centre takes a whole systems approach to energy research, incorporating economics, 

engineering and the physical, environmental and social sciences while developing and 

maintaining the means to enable cohesive research in energy. 

To achieve this we have developed the Energy Research Atlas, a comprehensive database of 

energy research, development and demonstration competences in the UK. We also act as 

the portal for the UK energy research community to and from both UK stakeholders and the 

international energy research community. 

Acknowledgements 

Earlier versions of Section 2 of this report were presented at the 29th IAEE International 

Conference ‘Securing energy in insecure times’, held in Potsdam, Germany on the 7-10th

June 2006 and the 6th BIEE Academic Conference, held at St. John's College, Oxford on the 

20-21st September 2006. An updated version has been accepted for publication in 

Ecological Economics (Sorrell and Dimitropoulos, 2007). The authors gratefully acknowledge 

comments from Harry Saunders, John Feather, Blake Alcott, Brenda Boardman, Mark Barrett 

and Ed Steinmuller as well as from participants at both conferences and two anonymous 

referees. A debt is also owed to Lorna Greening and David Greene for their previous 

synthesis of empirical work in this area (Greening and Greene, 1998). The usual disclaimers 

apply. 

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Executive Summary 

This report examines the evidence for direct rebound effects that is available from studies 

that use econometric techniques to analyse secondary data. The focus throughout is on 

consumer energy services, since this is where the bulk of the evidence lies. The evidence 

relevant to direct rebound effects for producers is discussed separately in Technical Reports 

3, 4 and 5. 

Direct rebound effects are sometimes estimated through quasi-experimental, or ‘evaluation’ 

studies in which the consumption of energy or useful work is measured both before and 

after an energy efficiency improvement. While a number of studies that use this approach 

are reviewed in Technical Report 1, this approach is relatively uncommon. An alternative 

approach uses econometric techniques to analyse secondary data sources that include 

information on the demand for energy, useful work and/or energy efficiency. This data can 

take a number of forms and can apply to different levels of aggregation, but is most useful 

when it applies to a single energy service. A key objective of such studies is to estimate 

elasticities, meaning the percentage change in one variable following a percentage change in 

another, holding other variables constant. Under certain assumptions, a number of these 

elasticities can be taken as estimates of either the short-run or long-run direct rebound 

effect for the relevant energy service. 

The econometric literature is dominated by studies of personal automotive transportation 

and household heating, with very few studies of other energy services. The majority of 

studies have been conducted in the United States, with the evidence for direct rebound 

effects in developing countries being particularly weak. 

This report clarifies the theoretical and methodological issues associated with such 

estimates, highlights the strengths and limitations of different approaches and summarises 

the available evidence for direct rebound effects for consumer energy services, paying 

particular attention to personal automotive transportation. 

Defining the direct rebound effect 

Direct rebound effects relate to individual energy services, such as heating, lighting and 

refrigeration and are confined to the energy required to provide that service. Improved 

energy efficiency will decrease the marginal cost of supplying that service and could 

therefore lead to an increase in consumption of the service. For example, consumers may 

choose to drive further following the purchase of energy efficient car because the price per 

kilometre has fallen. The resulting increase in energy service consumption will tend to offset 

the expected reduction in energy consumption provided by the energy efficiency 

improvement. The operation of direct rebound effects is discussed in more detail in the 

Supplementary Report. 

Energy services are provided by a combination of energy commodities and associated 

equipment, including energy conversion equipment. A defining feature of an energy service 

is the useful work obtained, which may be defined and measured in different ways (e.g. 

vehicle, passenger or tonne kilometres) and decomposed in different ways (e.g. the product 

of the number, capacity and average utilisation of energy conversion devices). Energy 

services also have associated attributes, such as comfort, acceleration and prestige. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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Different definitions of the independent variable (energy efficiency) and dependent variable 

(demand for useful work) for the direct rebound effect may lead to different conclusions 

regarding its size and importance. For example, most estimates of the direct rebound effect 

for passenger transport focus upon the increased demand for vehicle kilometres following an 

energy efficiency improvement. But this neglects changes in vehicle load factors and vehicle 

size. 

Estimating the direct rebound effect 

The econometric literature relevant to the direct rebound effect is technical and difficult to 

interpret. While this is partly a consequence of the variety of methodological approaches 

used, it also stems from a lack of clarity over basic definitions. Different studies use different 

definitions of the direct rebound effect, estimate the effect through a number of different 

measures, express these measures in a variety of ways and frequently fail to clarify the 

relationship between them. The situation is compounded by the fact that many of the 

relevant studies do not mention the rebound effect at all, since their primary focus lies 

elsewhere. These studies nevertheless provide elasticity estimates that, under certain 

assumptions, may be used as proxy measures of the direct rebound effect. A key objective 

of this report is therefore to clarify these different definitions and to develop a common 

terminology that aids interpretation of the relevant literature. 

In principle, the direct rebound effect may be estimated from the elasticity of demand for 

either energy or useful work with respect to changes in energy efficiency. However, 

relatively few studies follow this approach, either because of data limitations or because the 

limited variation in the independent variable (energy efficiency) leads to high variance in the 

parameter estimates. Instead, rather more studies estimate the own-price elasticity of the 

demand for useful work (e.g. the elasticity of demand for vehicle kilometres with respect to 

the cost per kilometre). Since the price of useful work depends upon both energy prices and 

energy efficiency, the degree of variation in the independent variable is greater - with most 

of the variation typically deriving from historical or cross-sectional variations in energy 

prices. But the validity of this approach hinges upon the assumption that consumers respond 

in the same way to decreases in energy prices as they do to improvements in energy 

efficiency (and vice versa). In many cases this assumption is likely to be flawed. 

It is also possible to estimate the direct rebound effect from the own-price elasticity of the 

demand for energy - thereby avoiding the need to collect data on the demand for useful 

work. But, unless energy efficiency is explicitly controlled for, this approach effectively 

assumes that: first, consumers respond in the same way to decreases in energy prices as 

they do to improvements in energy efficiency (and vice versa); and second, energy 

efficiency is unaffected by changes in energy prices. Both these assumptions are likely to be 

flawed, but the extent to which this leads to biased estimates of the direct rebound effect 

may vary widely from one energy service to another and between the short and long term. 

Sources of bias when estimating the direct rebound effect 

There are a number of potential sources of bias in econometric estimates of the direct 

rebound effect, several of which may lead the effect to be overestimated. The most 

important include the following: 

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 Input costs: Changes in energy prices are generally not correlated with changes in 

the costs of other inputs required to provide the relevant energy service. However, 

changes in energy efficiency may be - in particular, higher energy efficiency may 

require new equipment with higher capital costs. Hence, estimates of the direct 

rebound effect that rely primarily upon historical and cross-sectional variations in 

energy prices could overestimate the effect. 

 Asymmetry: Energy price elasticities tend to be higher for periods with rising prices 

than for those with falling prices. One explanation is that higher energy prices induce 

technological improvements in energy efficiency, which also become embodied in 

regulations. Also, investment in measures such as thermal insulation is largely 

irreversible over the short to medium-term. But the appropriate proxy for 

improvements in energy efficiency is reductions in energy prices. Since many timeseries studies incorporate periods of rising energy prices, the estimated price 

elasticities may overestimate the response to falling energy prices. Hence, estimates 

of the direct rebound effect that rely primarily upon variations in energy prices and 

do not control for asymmetry in demand responses could overestimate the effect. 

 Endogeneity: Improvements in energy efficiency may encourage consumers to 

increase their consumption of useful work (e.g. driving further after purchasing an 

energy-efficient car). But at the same time, consumers who anticipate a high demand 

for useful work may also purchase more energy efficient conversion devices (e.g. 

buying an energy-efficient car because you expect to drive further). This suggests a 

potential circularity: i.e. the demand for useful work depends on the price of useful 

work, which depends upon energy efficiency, which depends upon the demand for 

useful work. The technical term for this is endogeneity, which means that the 

relevant variables (energy efficiency and useful work) are in part determined by each 

other. This can be addressed empirically through the use of simultaneous equation 

models and related techniques, but many studies do not use these. Hence, estimates 

of the direct rebound effect that do use appropriate techniques to control for 

endogeneity could potentially lead to biased estimates of the effect. 

 Time costs: Consumers may be expected to take time costs into account when 

making decisions about the consumption of particular energy services. Time costs are 

conventionally measured by hourly wage rates, which have increased relative to 

energy prices throughout the past century. Indeed, increases in energy consumption 

in industrial societies may be partly driven by the substitution of energy for time. 

Some energy services involve trade-offs between energy efficiency and time 

efficiency, with higher (lower) energy efficiency implying lower (higher) time 

efficiency (e.g. compare rail to air travel). If wage rates continue to increase faster 

than energy prices in real terms, the rebound effect with respect to energy efficiency 

should become less important, since improvements in energy efficiency have an 

increasingly small impact on the total cost of useful work. Hence, for those energy 

services where trade-offs between energy and time costs are relevant, estimates of 

the direct rebound effect that do not control for increases in income could 

overestimate the direct rebound effect. 

Consideration of time costs also points to another issue: increasing time efficiency may lead 

to a parallel ‘rebound effect with respect to time’ (e.g. faster cars encourage longer driving 

distances). So energy consumption may be increased, first, by trading off energy efficiency 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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for time efficiency (e.g. choosing air travel rather than rail) and second, by the rebound 

effect with respect to time (e.g. choosing to travel further). 

Summarising estimates of the direct rebound effect 

The econometric literature relevant to the direct rebound effect is both relatively small and 

extremely diverse. Studies differ in their definition of independent and dependent variables, 

the methods of measuring those variables, the structural form employed, the type of data 

used and other relevant factors. Such diversity precludes a formal meta-analysis of 

quantitative results. Instead, we have simply described the methodology and approach of 

relevant studies, identified their strengths and weaknesses, highlighted key issues and 

summarised results. This leads to ‘best guess’ estimates for the long-run direct rebound 

effect for each service, in which greater weight is placed on the results from more rigorous 

studies (Table E.1). We have also reviewed estimates of the own price elasticity of energy 

consumption for different energy services, since under certain assumptions these may 

provide upper bounds for the direct rebound effect. 

Table E.1 Estimates of the long-run direct rebound effect for consumer energy services in 

the OECD 

Range of Values 

in Evidence Base

‘Best 

guess’ 

No. of 

Studies 

Degree of 

Confidence End-Use 

Personal 

automotive 

transport 

3-87% 10-30% 17 High 

Space heating 0.6-60%% 10-30% 9 Medium 

Space cooling 1-26% 1-26% 2 Low 

Other consumer 

energy services 0-39% <20% 3 Low 

Personal automotive transportation is the only area where the evidence is sufficiently strong 

to allow the magnitude of the direct rebound effect to be quantified with some confidence. 

Studies using aggregate time-series and cross-sectional data estimate the long-run direct 

rebound effect for personal automotive transport to be somewhere between 5% and 30%. 

Studies using aggregate panel data should provide more robust estimates owing to the 

greater number of observations, and these suggest direct rebound effects in the range 22% 

to 30%. Studies using disaggregate (i.e. household survey) data sources provide much less 

consistent estimates, ranging from 0% to 87%. However, the most rigorous of those 

reviewed estimates the long-run direct rebound effect to be 23%, which is consistent with 

the results of studies using aggregate data. 

Overall, the review suggests that the long-run direct rebound effect for personal automotive 

transport lies somewhere between 10% and 30%. The relative consensus on estimates, 

despite wide differences in data and methodologies suggests that the findings are robust. 

Also, the asymmetry of demand responses suggests that a value towards the lower end of 

this range is more likely. There is some evidence to suggest that the direct rebound effect 

for this energy service declines with income, but there is insufficient evidence to determine 

how it varies between different countries. 

In contrast, the available evidence does not permit the direct rebound effect for space 

heating to be quantified with much confidence. While this is partly because space heating is 

inherently more complex, it is also because the topic has received insufficient attention. The 

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studies reviewed here suggest direct rebound effects in the range 1.4 to 60%, with 

considerable variation between different countries, households, fuels and types of energy 

efficiency improvement. The strong evidence for the price asymmetry of energy demand 

responses for space heating suggests that the mean effect may be towards lower rate end of 

the above range, but rebound effects appear to be higher for low-income groups. For the 

purpose of policy evaluation, a figure of 30% would appear a reasonable assumption, which 

is consistent with the results of the evaluation studies reported in Technical Report 1. 

There are a number of reasons why direct rebound effects for most other household energy 

services should be smaller than those for household heating. However, the econometric 

evidence is very poor, owing to measurement difficulties. Two rather dated studies of space 

cooling both suggest a direct rebound effect in the range 1%-26%. However, both focus 

solely upon changes in equipment utilisation and therefore neglect the demand from 

‘marginal consumers’ acquiring space cooling equipment for the first time, as well as any 

increases in the capacity of space cooling systems among existing users. While one study 

suggests direct rebound effects of up to 39% for other energy services, this estimate 

appears suspiciously high. A more rigorous study estimates the direct rebound effect for 

energy efficient washing machines to be less than 5%. This figure is likely to be 

representative of other time-intensive energy services, such as those provided by 

dishwashers, vacuum cleaners and electronic appliances. 

The evidence therefore suggests that direct rebound effects for consumer energy services 

are likely to be low to moderate in developed economies and may decline with income. 

Therefore, direct rebound effects should not undermine the objectives of energy efficiency 

programmes aimed at reducing the energy required to deliver particular energy services. 

However, these conclusions are subject to a number of qualifications, including the relatively 

limited time periods over which the effects have been studied, the frequent neglect of 

marginal consumers and the restrictive definitions of ‘useful work’ that are commonly 

employed. 

Further research on the direct rebound effect 

The current state of knowledge on direct rebound effects is insufficient for policy purposes. 

Research on direct rebound effects therefore needs to improve in rigour and expand in 

scope. This requires both good data sets and more robust methodologies that address the 

potential sources of bias indicated above. There is scope for studies of a greater range of 

consumer energy services, provided that individual appliances can be monitored. However, 

the policy issue here is not so much changes in short-term utilisation patterns, but changes 

in the number and capacity of conversion devices over the longer term. 

Estimates of the direct rebound effect for personal automotive transport would benefit from 

more appropriate definitions of useful work. A study employing tonne-kilometres as the 

dependent variable appears feasible and could potentially capture the effect of increasing 

car sizes. Analysis is also needed of other modes of transport, including freight. There is also 

scope for more empirical work on the ‘rebound effect with respect to time’, especially in the 

area of transportation, and on the dependence of direct rebound effects on income. 

The geographical bias of the evidence base also needs to be addressed. In particular, the 

evidence for rebound effects in developing countries remains very weak. 

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Contents 

1 INTRODUCTION ..........................................................................................................................................1

2 THE DIRECT REBOUND EFFECT: DEFINITIONS, LIMITATIONS AND EXTENSIONS

 ..............................................................................................................................................................................3

2.1 INTRODUCTION...........................................................................................................................................3

2.2 UNDERSTANDING THE DEMAND FOR ENERGY SERVICES .........................................................................4

2.3 THE DIRECT REBOUND EFFECT AS AN ENERGY EFFICIENCY ELASTICITY.................................................6

2.4 THE DIRECT REBOUND EFFECT AS A PRICE ELASTICITY...........................................................................8

2.5 CORRELATION BETWEEN ENERGY EFFICIENCY AND OTHER INPUT COSTS ............................................12

2.6 ENDOGENOUS ENERGY EFFICIENCY ........................................................................................................15

2.7 ENERGY EFFICIENCY AND TIME COSTS ...................................................................................................18

2.8 SUMMARY..................................................................................................................................................21

3 ECONOMETRIC APPROACHES TO ESTIMATING THE DIRECT REBOUND EFFECT.24

3.1 INTRODUCTION.........................................................................................................................................24

3.2 IDENTIFYING THE ECONOMETRIC EVIDENCE BASE.................................................................................24

3.3 MEASUREMENT ISSUES............................................................................................................................27

3.4 TYPES OF DATA ........................................................................................................................................29

3.5 MODEL STRUCTURES................................................................................................................................31

3.5.1 Single equation models ..........................................................................................................31

3.5.2 Structural/simultaneous equation models.......................................................................33

3.5.3 Discrete/continuous models..................................................................................................35

3.5.4 Household production models..............................................................................................36

3.6 FUNCTIONAL FORMS ................................................................................................................................36

3.7 ESTIMATION TECHNIQUES.......................................................................................................................37

3.8 SUMMARY..................................................................................................................................................38

4 EVIDENCE FOR DIRECT REBOUND EFFECTS FOR PERSONAL AUTOMOTIVE 

TRANSPORTATION............................................................................................................................................40

4.1 INTRODUCTION.........................................................................................................................................40

4.2 SETTING BOUNDS ON THE DIRECT REBOUND EFFECT FOR PERSONAL AUTOMOTIVE TRANSPORTATION

 40

4.3 EVIDENCE FROM STUDIES USING AGGREGATE TIME-SERIES OR CROSS-SECTIONAL DATA................45

4.4 EVIDENCE FROM STUDIES USING AGGREGATE PANEL DATA..................................................................50

4.5 EVIDENCE FROM STUDIES USING DISAGGREGATE DATA.......................................................................55

4.6 SUMMARY..................................................................................................................................................62

5 EVIDENCE FOR DIRECT REBOUND EFFECTS FOR HOUSEHOLD HEATING ...............64

5.1 INTRODUCTION.........................................................................................................................................64

5.2 SETTING BOUNDS ON THE DIRECT REBOUND EFFECT FOR HOUSEHOLD HEATING...............................65

5.2.1 The importance of heating in household energy consumption................................65

5.2.2 Heating elasticities and overall elasticities......................................................................65

5.2.3 The price elasticity of total household electricity demand........................................67

5.2.4 The price elasticity of total household fuel demand....................................................67

5.3 ESTIMATING THE DIRECT REBOUND EFFECT FOR HOUSEHOLD HEATING..............................................68

5.3.1 Choice of households...............................................................................................................68

5.3.2 Choice of elasticity measure.................................................................................................69

5.4 EVIDENCE FROM SINGLE EQUATION MODELS.........................................................................................72

5.5 EVIDENCE FROM MULTIPLE EQUATION MODELS .....................................................................................78

5.6 SUMMARY..................................................................................................................................................82

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6 EVIDENCE FOR DIRECT REBOUND EFFECTS FOR OTHER HOUSEHOLD ENERGY 

SERVICES ...............................................................................................................................................................83

6.1 INTRODUCTION.........................................................................................................................................83

6.2 DIRECT REBOUND EFFECTS FOR SPACE COOLING..................................................................................83

6.3 DIRECT REBOUND EFFECTS FOR OTHER ENERGY SERVICES ..................................................................86

6.4 SUMMARY..................................................................................................................................................90

7 SUMMARY AND CONCLUSIONS ........................................................................................................91

ANNEX A – MATHEMATICAL DERIVIATIONS.....................................................................................94

REFERENCES.........................................................................................................................................................98

UK Energy Research Centre UKERC/WP/TPA/2007/010
1 

1 Introduction 

Direct rebound effects relate to individual energy services, such as heating, lighting and 

refrigeration and are confined to the energy required to provide that service. Improved 

energy efficiency will decrease the marginal cost of supplying that service and could 

therefore lead to an increase in consumption of the service. For example, consumers may 

choose to drive further following the purchase of energy efficient car because the price per 

kilometre has fallen. The resulting increase in energy service consumption will tend to offset 

the expected reduction in energy consumption provided by the energy efficiency 

improvement. 

While the existence of direct rebound effects is widely acknowledged, their magnitude is 

greatly disputed. Direct rebound effects are sometimes estimated through quasiexperimental, or ‘evaluation’ studies in which the consumption of energy or useful work is 

measured both before and after an energy efficiency improvement. While a number of 

studies that use this approach are reviewed in Technical Report 1, this approach is relatively 

uncommon. An alternative approach uses econometric techniques to analyse secondary data 

sources that include information on the demand for energy, useful work and/or energy 

efficiency. This data can take a number of forms and can apply to different levels of 

aggregation, but is most useful when it applies to a single energy service. A key objective of 

such studies is to estimate elasticities, meaning the percentage change in one variable 

following a percentage change in another, holding other variables constant. Under certain 

assumptions, a number of these elasticities can be taken as estimates of either the shortrun or long-run direct rebound effect for the relevant energy service. 

This report therefore examines the quantitative estimates of direct rebound effects that are 

available from studies using econometric techniques to analyse secondary data. The focus 

throughout is on consumer energy services, since this is where the bulk of the evidence 

lies.1 

The report is structured as follows. Section 2 provides an in-depth examination of the 

different definitions of the direct rebound effect, including the strength and limitations of 

those definitions and the relationship between them. It develops a number of extensions to 

the basic definition and uses these to highlight some potential sources of bias in econometric 

estimates of the direct rebound effect. A key objective is to develop a common terminology 

that aids understanding of the relevant literature. 

Section 3 sets out the criteria through which the empirical studies were selected and 

provides an overview of the various econometric approaches to estimating the direct 

rebound effect, including issues such as model structure, functional form and estimation 

techniques. This provides a useful basis for understanding and comparing the various 

studies discussed in the subsequent sections. 

Sections 4 to 6 summarise the relevant empirical literature, addressing in turn personal 

automotive transportation, household heating and other consumer energy services. Each 

section begins by summarising the evidence on own-price elasticities of energy consumption 

 

1

 The evidence relevant to direct rebound effects for producers is discussed separately in Technical Reports 3, 4 and 

5. 

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2 

for the relevant energy service, since these may provide an upper bound for the direct 

rebound effect. It then describes the methodology and approach of a number of studies that 

provide more accurate estimates of the effect, identifies their strengths and weaknesses, 

highlights key issues and summarises and compares the results. This leads to a ‘best guess’ 

estimate for the long-run direct rebound effect for each energy service, in which greater 

weight is placed on the results from more rigorous studies. Section 7 concludes. 

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2 The direct rebound effect: definitions, limitations 

and extensions 

2.1 Introduction 

The econometric literature relevant to the direct rebound effect is highly technical and 

difficult to interpret. While this is partly a consequence of the variety of methodological 

approaches used, it also stems from a lack of clarity over basic definitions. Different studies 

use different definitions of the direct rebound effect, estimate the effect through a number 

of different measures, express these measures in a variety of ways and generally fail to 

clarify the relationship between each measure. The situation is greatly compounded by the 

fact that many of the relevant studies do not mention the rebound effect at all, since their 

primary focus lies elsewhere. These studies nevertheless provide elasticity estimates that, 

under certain assumptions, may be used as proxy measures of the direct rebound effect. 

Taken together, these features inhibit understanding of the effect and the appropriate 

empirical approach to estimating its magnitude in different circumstances. They also make it 

very difficult to identify the relevance of different studies. 

Hence, when first encountered the empirical literature is extremely confusing. While 

Greening and Greene (1998) provide a comprehensive and insightful review of this 

literature, they fail to clarify the key differences between each study in terms of the 

methodological approach adopted and elasticity measures used. As a result, they overlook a 

number of potential sources of bias in the empirical estimates. 

This section seeks to address these weaknesses by identifying the different definitions of the 

direct rebound effect, clarifying the relationship between these definitions and highlighting 

some potential sources of bias in the empirical estimates. The aim is to develop a common 

terminology that aids understanding of the diverse literature discussed in the subsequent 

sections. The focus throughout is upon consumer energy services, since this is where the 

bulk of the econometric evidence lies. 

This section is structured as follows. Section 2.2 presents a general ‘household production’ 

framework for characterising the demand for consumer energy services that helps to 

illustrate the different trade-offs involved. Section 2.3 shows how the direct rebound effect 

can be represented as the elasticity of energy demand with respect to energy efficiency and 

how it may be decomposed into the sum of elasticities for the number, capacity and 

utilisation of energy conversion devices. Section 2.4 identifies the relationship between the 

direct rebound effect and the own-price elasticity of the demand for ‘useful work’, as well as 

the own-price elasticity of the demand for energy, and shows why empirical studies using 

these definitions provide a primary source of evidence for the direct rebound effect. 

Section 2.5 exposes the limitations of the above definitions, focusing on: a) the potential 

correlation between various input costs and improvements in energy efficiency; b) the 

endogeneity of energy efficiency and the implied need for simultaneous equation estimation; 

and c) the role of time costs and time efficiency in the production and consumption of 

energy services. It identifies some of the factors that need to be controlled for to obtain 

accurate estimates of the direct rebound effect and argues that the neglect of these factors 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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by several existing studies may lead the direct rebound effect to be overestimated. Section 

2.6 concludes. 

2.2 Understanding the demand for energy services 

The demand for energy (E) derives from the demand for energy services (ES) such as 

thermal comfort, refrigeration and motive power. These services, in turn, are delivered 

through a combination of energy commodities and the associated energy systems, including 

energy conversion devices. Consumers are assumed to derive utility from consuming these 

services, rather than from consuming energy commodities and other market goods directly. 

In practice, nearly all services require energy in some form, although energy may form a 

much smaller proportion of total costs for some services than for others. 

An essential feature of an energy service is the useful work (S) obtained, which may be 

measured by a variety of thermodynamic or physical indicators (Patterson, 1996).2 These 

indicators may, in turn, be decomposed in a variety of ways to reveal the relative 

importance of different contributory variables. For example, the useful work from the private 

cars owned by a group of households may be: 

 measured in vehicle kilometres and decomposed into the product of the number of 

cars and the mean driving distance per car per year: = *UTILNOS ; 

 measured in passenger kilometres and decomposed into the product of the number 

of cars (NO), the mean driving distance per car per year (UTIL) and the average 

number of passengers carried per car (LF): = ** LFUTILNOS ; or 

 measured (rather unconventionally) in tonne kilometres and decomposed into the 

product of the number of cars (NO), the mean driving distance per car per year 

(UTIL) and the mean (loaded or unloaded) vehicle weight (CAP): 

= ** UTILCAPNOS . 

In practice, the choice of indicator and associated decomposition will depend upon the 

objective of the analysis, the level of aggregation (e.g. household, sector, economy) and, 

most importantly, the availability of the relevant data. In much empirical work, measures of 

useful work are not decomposed. 

It important to recognise that energy services also have broader attributes (A) that may be 

combined with useful work in a variety of ways. For example, all cars deliver passenger 

kilometres, but they may vary widely in terms of features such as speed, comfort, 

acceleration and prestige. The combination of useful work (S) with these associated 

attributes (A) may be considered to provide the full energy service: = ASesES ),( . 

Becker’s ‘household production’ model provides a helpful framework for understanding the 

demand for energy services (Becker, 1965). In this model, individual households are 

assumed to produce energy services (ES) by combining energy commodities (E), capital 

equipment (K), other market goods (O) and some of the household’s own labour, which may 

be measured by the amount of time (T) required. For example, mobility may be produced by 

the household through the combination of gasoline, a private car, expenditure on 

 

2

 See Technical Report 5 for a comprehensive discussion of thermodynamic, physical and economic measures of 

energy and energy efficiency, including a definition of output energy or ‘useful work’. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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maintenance and driving time. Similarly, a cooked meal may be produced through the 

combination of natural gas, a gas cooker, ingredients and cooking time. 

The provision of useful work for a particular energy service may then be described by a 

production function, representing the maximum output that can be obtained from the 

currently available technology for a given level of energy and other inputs (Wirl, 1997). But 

the provision of broader attributes for a given amount of useful work is likely to require 

additional inputs; or, alternatively, for a given budget, the provision of broader attributes is 

likely to reduce the amount of useful work. To reflect this, the production function for energy 

service i may be written as: 

 (2.1) ];,,,[ = ATOKEesES iiiiiii

If a household’s utility is assumed to depend solely upon these services, the utility function 

becomes: 

 (2.2) ],....,,[ = 321 ESESESESuU n

The household may be assumed to be subject to the following income constraint: 

 (2.3) ∑=

≥+ ++

ni

WW KOPEPPTV iKiOiE

,1

( δ )

Where V represents non-wage income; PW represents the average wage rate; TW represents

the time spent in the labour market; PE and PO represent the unit price of energy and other 

goods respectively; and AKP )( δ K = δ KK represents a discount factor (so ) gives the 

annualised capital costs). Households will also be subject to a second constraint on their 

available time: 

 (2.4) ∑

Where Ti represents the time spent in producing services Si. Becker (1965) argued that, 

since money and time are partly interchangeable through decisions on TW, the income and 

time constraints can be collapsed into a single constraint. By substituting 

into the budget constraint and rearranging

∑=

−=

n

t

W TTT i

1

, we obtain: 

 (2.5) W ≥+ ∑ +++ TPKOPEPTPV iWiKiOiE ( δ )

Versions of Becker’s ‘household production’ model form the basis of a substantial volume of 

empirical research (Juster and Stafford, 1991; Gronau, 1997). This includes numerous 

applications to energy use, although these studies frequently (and importantly) neglect the 

time inputs to energy services (Dinan, 1987; Willet and Naghshpour, 1987; Davis, 2004). 

The attraction of Becker’s model for energy studies is that: first, it embodies the recognition 

that utility is derived from the consumption of energy services, rather than energy 

commodities; second it recognises that households have a joint role in both producing and 

consuming those services; and third, that time is an important (but often neglected) input 

into the production of those services. The implications that follow arguably offer greater 

insight into the determinants of energy-related behaviour than more conventional models of 

energy demand. 

=

n

t 1

+=

t

W TTT i

1

n

=

UK Energy Research Centre UKERC/WP/TPA/2007/010
6 

Becker’s model rests upon a set of behavioural and other assumptions that may be criticised 

on a variety of grounds (Pollack and Wachter, 1975; Juster and Stafford, 1991).3

Nevertheless, it offers a number of advantages over conventional models of household 

energy demand and predictions from the model appear broadly confirmed by empirical 

research (Juster and Stafford, 1991). The primary contribution of this model in the present 

context is to emphasise that consumption of an energy service involves three interrelated 

trade-offs, namely: 

 between consumption of useful work versus consumption of other attributes of an 

energy service; 

 between energy, capital, other market goods and time into the production of an 

energy service; and 

 between consumption of different types of energy service. 

This general framework forms the foundation for what follows. 

2.3 The direct rebound effect as an energy efficiency elasticity 

The energy efficiency (ε ) of an energy system may be defined as ε = / ES , where E 

represents the energy input required for a unit output of useful work (however measured).4

For example, a car may require ten litres of gasoline to drive one hundred kilometres. The 

energy cost of useful work (P /ε = PP ES S) is then given by , where PE represents the unit 

price of energy. This is one component of the generalised cost of useful work (PG), which 

also includes other input costs, such as annualised capital costs (PK), maintenance costs (PM) 

and time costs (PT) : 

 (2.6) 

Consider a situation where the energy efficiency of an energy system is improved ( ε >Δ )0 , 

but the consumption and costs of non-energy inputs remain unchanged, together with the 

consumption of other attributes of the energy service. In the absence of a direct rebound 

effect, the demand for useful work would remain unchanged (ΔS = 0) and energy demand 

would be reduced in proportion to the improvement in energy efficiency ( EE Δ−=Δ ε // ε ). 

But the energy efficiency improvement lowers the energy cost per unit of useful work 

( ) and hence also the total cost. Assuming that the energy service has a price 

elasticity in the normal range, consumers will demand more useful work ( ) and the 

proportional change in energy consumption will be less than the proportional change in 

energy efficiency (

PS <Δ 0

S >Δ 0

EE Δ−<Δ ε // ε ). 

 

P = PEG + + + PPP TMK ε )/(

3

 Including: the assumption that each market good or allocation of time is dedicated to the production of a single 

service; the notion that households are indifferent to the allocation of time, except as an input into the production 

of services; difficulties in defining what a service actually is (e.g. travel by car for a visit or the visit 

itself); the neglect of the fact that utility may be a function of producing as well as consuming a 

service; the implicit assumption of constant returns to scale in production; the difficulty in 

operationalising the model; the lack of good data on time use patterns; and the usual difficulties 

associated with models that assume ‘hyper-rational’, utility maximising individuals. 

4

 The appropriate measure of energy efficiency depends upon the objectives of the analysis and is 

generally a property of the energy system, rather than just the energy conversion device. For 

example, the amount of heat required to maintain a particular internal temperature depends upon 

both of the thermodynamic efficiency of the heating system and the thermal integrity of the building. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
7 

The change in demand for useful work following a small change in energy efficiency may be 

measured by the energy efficiency elasticity of the demand for useful work ( S)( ηε ): 

 (2.7) 

S S

In a similar manner, the change in energy demand following a small change in energy 

efficiency may be measured by the energy efficiency elasticity of the demand for energy

( E)( ηε ): 

 (2.8) 

Substituting = SE / ε in the equation for E)( ηε and taking partial derivatives we can derive 

the following relationship between these two elasticities:5

Definition 1: = SE −1)()( ηε ηε

The elasticity of demand for useful work with respect to energy efficiency ( S)( ηε ) has been 

commonly taken as a measure of the direct rebound effect (Berkhout, et al., 2000). The 

actual saving in energy consumption will only be equal to the predicted saving from 

engineering calculations when this elasticity is zero ( S = 0)( ηε ). Under these circumstances, 

the elasticity of demand for energy with respect to energy efficiency ( E)( ηε ) is equal to 

minus one. A positive direct rebound effect implies that S > 0)( ηε and E < 1)( ηε . For 

example, a positive direct rebound effect for car travel implies that improvements in vehicle 

fuel efficiency lead to an increase in vehicle kilometres driven, with the result that the 

savings in energy consumption are less than predicted from engineering calculations alone. 

If the demand for useful work is inelastic ( <ηε S <1)(0 ) improvements in energy efficiency 

should reduce energy demand ( ηε E >> −1)(0 ). But if the demand for useful work is elastic 

( S >1)( ηε ), improvements in energy efficiency will increase energy consumption. This 

somewhat counterintuitive outcome is termed ‘backfire’ in the literature (Saunders, 1992). 

Technological improvements in energy efficiency may, over time, lead to an increase in the 

number of energy conversion devices (NO), their average size (CAP), their average 

utilisation (UTIL) and/or their average load factor (LF). For example, people may buy more 

cars, buy larger cars, drive them further and/or share them less. Similarly, people may buy 

more washing machines, buy larger machines, use them more frequently and/or reduce the 

size of the average load. The equation for the energy efficiency elasticity of energy demand 

may therefore be decomposed in a variety of ways, depending upon data availability, the 

timeframe under consideration and the choice of measure for useful work (S). For example, 

if useful work is defined as the product of the number, average output capacity and average 

utilisation of energy conversion devices (S=NO*CAP*UTIL), the equation becomes: 

 (2.9) 

The relative importance of these variables may vary widely between different energy 

services and over time. For example, technological improvements in the energy efficiency of 

new refrigerators are unlikely to increase the average utilisation of the refrigerator stock 

(measured in hours/year) but could lead to an increase in both the number and average size 

 

5

 See Annex A for derivations of this and subsequent definitions and formulae. 

S

ε

ε

ηε ∂

∂ )( =

E E

E

ε

ε

ηε ∂

∂ ( ) =

= + ))) + ((([( −1)] ηε ηε NOE ηε CAP ηε UTIL

UK Energy Research Centre UKERC/WP/TPA/2007/010
8 

of refrigerators over time (since the cost per cubic metre of refrigeration has reduced). The 

majority of empirical estimates of the direct rebound effect relate to travel by private cars, 

where useful work is commonly measured in vehicle kilometres travelled and decomposed 

into the product of vehicle numbers and the mean distance travelled per car per year 

(Greene, et al., 1999b; Small and Van Dender, 2005). An important consequence of this is 

that any increases in average vehicle weight as a result of energy efficiency improvements 

(e.g. more SUVs) as well as decreases in average load factor (e.g. less car sharing) will be 

overlooked.6 

The marginal utility of energy service consumption is likely to decline with increased 

consumption, which should reduce the direct rebound effect from energy efficiency 

improvements. For example, direct rebound effects from improvements in the energy 

efficiency of household heating systems should decline rapidly once whole-house indoor 

temperatures approach the maximum level for thermal comfort. One implication, frequently 

observed in the policy evaluation literature, is that direct rebound effects will be higher 

among low income groups, since these are further from satiation in their consumption of 

individual energy services (Boardman and Milne, 2000). 

2.4 The direct rebound effect as a price elasticity 

/ε ε Since = PP ES , raising (lowering) energy efficiency ( ) when energy prices (PE) are 

constant should have the same effect on the energy cost of useful work (PS) as falling 

(rising) energy prices when energy efficiency is constant. Under the ceteris-paribus 

assumptions given above, the effect on the total cost and hence the demand (S) for useful 

work should be symmetrical. If income and the price of other inputs are held constant, we 

can write the demand for useful work solely as a function of energy prices and energy 

efficiency: ε )/( = PsS E ε /)/( ε = PsE E . The demand for energy is then given by: . Assuming 

that energy prices are exogenous (i.e. PE does not depend upon ε ), we can differentiate this 

equation with respect to energy efficiency to give an alternative definition of the direct 

rebound effect: 

Definition 2: = − SE −1)()( PS ηε η

Hence, under these assumptions, the energy efficiency elasticity of energy demand ( E)( ηε ) 

is equal to the energy cost elasticity of demand for useful work ( S)( PS η ), minus one. 

Effectively, the negative of the energy cost elasticity of demand for useful work ( S)( PS η ) is 

being used as a proxy for the energy efficiency elasticity of demand for useful work ( S)( ηε ), 

which in turn is the primary definition of the direct rebound effect. If useful work is a normal 

good, we expect that S ≤ 0)( PS η . For example, if the elasticity of vehicle km (S) with respect 

to energy cost per kilometre (PS) is estimated as -0.10, then the elasticity of gasoline 

demand with respect to fuel efficiency can be estimated from Definition 2 as –0.90. This 

implies that the demand for gasoline will fall by only 9% if the fuel efficiency of vehicles 

 

6

 The first of these rebound effects could be captured if useful work for private travel was measured in unloaded 

tonne kilometres rather than vehicle kilometres. This would be possible if data was available on the composition of 

the vehicle stock and the average unloaded weight of different types of vehicle. The second effect could be 

captured if useful work was measured in passenger kilometres rather than vehicle kilometres. This would require 

data on the average load factor of different types of vehicle. To capture both of these rebound effects, useful work 

would need to be measured in loaded tonne kilometres. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
9 

improves by 10% - or, alternatively, that 10% of the potential savings in gasoline 

consumption will be ‘taken back’ by increased distance driven. 

As with Definition 1, Definition 2 may also be decomposed in a variety of ways, depending 

upon data availability and the choice of measure for useful work. For example, if useful work 

is defined as the product of the number, average output capacity and average utilisation of 

energy conversion devices, the equation becomes: 

 (2.10) E −= NO)[) + ((( CAP) + (UTIL −1)] PS PS PS ηε η η η

A version of Definition 2 is derived by Khazzoom (1980), Berkhout et al (2000), Binswanger 

(2001) and Greene et al (1999a) and is generally used in preference to Definition 1 in 

empirical estimates of the direct rebound effect. For many energy services, the available 

data provides only limited variation in the independent variable for Definition 1 ( ε ), which 

leads to a high variance in the estimated elasticities while at the same time requiring energy 

prices to be controlled for. In contrast, the data frequently provides greater variation in the 

independent variable for Definition 2 ( ), since this reflects both variations in energy 

efficiency and variations in energy prices. For many energy services, the historical and 

cross-sectional variations in the relevant energy commodity prices tend to be much greater 

than the corresponding variations in the energy efficiency of the relevant energy systems. 

Given the assumption that consumers respond in the same way to increases (decreases) in 

energy prices as to decreases (increases) in energy efficiency, Definition 2 provides a means 

to estimate the magnitude of direct rebound effects from energy efficiency improvements 

even in circumstances where the available data provides little or no variation in energy 

efficiency. 

PS

Empirical studies based upon Definition 2 require accurate measures of the energy cost of 

useful work (PS) which depends upon both energy commodity prices and the energy 

efficiency of the relevant energy system ( /ε = PP ES ). But frequently, data on the energy 

efficiency of the relevant system is unavailable or of limited accuracy. An alternative 

approach, therefore, is to estimate the direct rebound effect from the elasticity of demand 

for useful work with respect to changes in energy prices alone ( S)( PE η ): 

Definition 3: = − SE −1)()( PE ηε η

As for Definition 2, Definition 3 relies upon the assumption that consumers respond in the 

same way to increases (decreases) in energy prices as to decreases (increases) in energy 

efficiency. In addition, unless energy efficiency is explicitly controlled for (i.e. ε η S)( PE ), 

Definition 3 implicitly assumes that energy efficiency is unaffected by changes in energy 

prices (i.e. η ε = 0)( PE ). If, instead, energy price changes induce changes in energy 

efficiency, the use of this measure to estimate the direct rebound effect could lead to bias 

since the change in the energy cost of useful work will not be directly proportional to the 

change in energy prices. However, Definition 3 is useful since it provides a means to 

estimate the magnitude of direct rebound effects even in circumstances where no data is 

available on energy efficiency. 

Empirical studies based upon Definitions 2 and 3 still require accurate measures of the 

demand for useful work (S). But, depending upon how useful work is defined, this can be 

problematic. For example, the useful work from a domestic heating system could be defined 

UK Energy Research Centre UKERC/WP/TPA/2007/010
10 

as the average internal temperature of the house and measured directly using field 

thermometers or indirectly from thermostat settings. But the latter are notoriously 

inaccurate and can be a poor proxy for the thermal comfort of the occupants, which depends 

upon other variables such as humidity, airflow and the mean temperature of radiant 

surfaces (Greening and Greene, 1998). One reason that travel by private car is the most 

widely studied area for the direct rebound effect is that relatively good data is available on 

vehicle kilometres as a measure of useful work. 

While obtaining measures of useful work (S) can be difficult, data is more commonly 

available on the energy demand (E) for the relevant energy service. For example, data may 

be available on the demand for gas for household heating. Again, if we assume that that 

energy efficiency is constant, the symmetry argument implied by the ratio /ε = PP ES leads 

to an alternative definition for the direct rebound effect based upon the own price elasticity 

of energy demand ( E)( PE η ): 

Definition 4: = − EE −1)()( PE ηε η

It is this expression, rather than Definition 2, that was originally put forward by Khazzoom 

and is also used by Wirl (1997) in his comprehensive analysis of the economics of energy 

efficiency. Definition 4 shows that under certain assumptions, the direct rebound effect may 

be approximated by the own price elasticity of energy demand for the relevant energy 

service. As with Definition 3, Definition 4 relies upon the assumption that consumers 

respond in the same way to increases (decreases) in energy prices as to decreases 

(increases) in energy efficiency and that energy efficiency is unaffected by changes in 

energy prices. 

The attraction of Definition 4 is that it avoids the need to collect data on either useful work 

or energy efficiency. It therefore provides a means for estimating direct rebound effects for 

a wider range of energy services. However, this definition is most useful when the energy 

demand in question relates to a single energy service (e.g. refrigeration). In practice, 

available measures of energy demand frequently apply to a collection of energy services 

(e.g. household electricity use), although techniques such as conditional demand analysis 

may allow the proportion of demand attributable to an individual service to be estimated 

(Parti and Parti, 1980).7 

Empirical studies of the direct rebound effect for different energy services may use any of 

the above definitions, but the differences between studies are not always made clear. For 

example, in their comprehensive literature review of the rebound effect, Greening and 

Greene (1998) cite six econometric studies of household heating, but place particular weight 

on the methodologically rigorous studies of household survey data by Klein (1987), Hseuh 

and Gerner (1993) and Schwarz and Taylor (1995) (reviewed in Section 5).8 As Table 2.1 

makes clear, these three studies use different definitions of the dependent and independent 

variable, apply different methodologies and controls and focus upon different fuels. Only one 

 

7

 For example, Haas and Biermayr (2000) unbundled energy use for space heating from that for water heating by 

assuming that the latter was constant over the year, while the former depended upon external temperature. 

8

 Greening and Greene (1998) cite 23 studies of household heating, but the majority of these are ‘evaluation 

studies’ which are discussed in Technical Report 1. Most of the heating studies are sponsored by US utilities and 

appear to be small-scale, short-term and methodologically weak. We have not been able to access these studies, 

which were originally reviewed by Nadel (1993). Greening and Greene simply reproduce Table 1 from Nadel (1993) 

and discuss a small number of additional econometric studies. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
11 

of the three studies (Schwarz and Taylor) represents an explicit investigation of rebound 

effects (the other two do not mention the term) and Greene and Greening’s estimate of 

direct rebound effects is based upon a different elasticity measure in each case. Clearly, the 

existing literature is too small and diverse to allow a consistent approach to this issue. 

Table 2.1 Varying estimates of the direct rebound effect for household heating 

Greening and 

Greene (1998) 

estimate the 

direct rebound 

effect from: 

Dependent 

variable Study Approach 

Proxy measure 

for S estimated 

from difference 

between 

thermostat 

setting and 

external 

temperature 

Simultaneous estimation of a cost 

function for S, a demand function 

for S and an equation for the 

relative share of capital and fuel 

Klein 

(1987)

S)( PG η 1

E estimated 

from energy 

bill. 

Hseuh 

and 

Gerner 

(1993)

Estimates an equation for the 

demand for E. incorporating 

engineering and other variables 

that affect the demand for S. 

E)( PE η

(No measure of 

S available) 

2

Two proxy 

measures for S:

thermostat 

setting and 

estimated 

demand for 

heat 

Estimate a equation for the 

demand for S, that incorporates a 

variable representing the thermal 

resistance of the house 

Schwarz 

and 

Taylor 

(1995)

S)( ηε

3

Notes: 

1. Space heating demand is defined as the difference between the internal thermostat setting and the external 

temperature during the heating season. Klein specifies simultaneous equations for the total cost of space heat, the 

share of energy costs in total costs and the demand for space heat (S). Simultaneous equations are required 

because S appears in both the cost function and the factor share equation and individual household attributes affect 

both the production and consumption decision. The study estimates the elasticity of demand for space heat with 

respect to the generalised cost of space heat ( S)( PG

η ), but Greening and Greene incorrectly interpret this as 

S)( PSη , thereby overestimating the direct rebound effect. The study does not mention the rebound effect 

specifically. 

2. In principle, the reduced form equation should allow E)( ηε to be estimated - where ε represents the overall 

energy efficiency of the household, including both building fabric and energy conversion devices. But Hseuh and 

Gerner only quote the change in energy consumption following a physical change in one element of the system, 

such as increasing insulation thickness by one inch. So instead of E)( ηε , Greene and Greening take the estimate of 

E)( PEη as a measure of the direct rebound effect for electricity only, but the estimate for natural gas is ignored, 

although the gas equation provides more reliable estimates owing to the larger sample size. 

3. The measure of energy efficiency is the thermal resistance of the house. The data and specification allows the 

energy efficiency elasticity of the thermostat setting and the energy efficiency elasticity of the demand for useful 

work to be estimated. The difference between each of these and -1 are taken as alternative measures of the direct 

rebound effect. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
12 

Following Definition 4, a number of authors have used new or existing estimates of the ownprice elasticity of energy demand as approximate indicators of the magnitude of the direct 

rebound effect (Zein-Elabdin, 1997; Berkhout, et al., 2000; Roy, 2000; Bentzen, 2004). This 

opens up a very large evidence base, as reviewed, for example by Espey (1998) and Dahl 

(1991). Most studies suggest that energy demand is relatively inelastic, with typical values 

ranging from -0.3 to –0.9 in the long run. Applying Definition 4, these figures suggest that 

some 30-90% of energy savings deriving from energy efficiency improvements may be 

‘taken-back’ by the direct rebound effect. However, Definition 4 is likely to significantly 

overestimate the direct rebound effect for reasons discussed below. Also, elasticity 

estimates vary widely between different energy commodities, end-uses, sectors, countries 

and levels of aggregation; as well as increasing proportionately with the price level 

(Douthitt, 1989; Berkhout, et al., 2000). 

Of particular importance is the fact that elasticities tend to be higher for periods with rising 

energy prices than for periods with falling energy prices (Gately, 1992a; 1993; Dargay and 

Gately, 1994; 1995; Haas and Schipper, 1998). For example, Dargay (1992) found that the 

reduction in UK energy demand following the price rises of the late 1970s was five times 

greater than the increase in demand following the price collapse of the mid-1980s. Two 

explanations for this are that higher energy prices induce technological improvements in 

energy efficiency that are not reversed when energy prices fall, while investment in 

measures such as thermal insulation is largely irreversible over the short to medium-term 

(Grubb, 1995). Energy efficiency requirements may also become embodied in regulations 

that ensure that new investments maintain high standards, even in the absence of a price 

incentive. As a result, estimates of price elasticities based upon time-series data are likely to 

vary according to whether energy prices were rising, falling (or both) over the period in 

question (Haas and Schipper, 1998). In the case of the direct rebound effect, the 

appropriate proxy for energy efficiency improvements is reductions in energy prices. Hence, 

empirical estimates based upon periods of rising energy prices are likely to overestimate the 

size of the effect. 

Econometric estimates based upon Definitions 2, 3 or 4 are a primary source of evidence for 

the direct rebound effect. Hence, the assumptions behind these definitions - and particularly 

the ‘symmetry’ argument - require careful scrutiny. The following three sections explore the 

limitations of these definitions in more detail, focusing on: 

 the correlation between energy efficiency and other input costs, notably capital costs; 

 the endogeneity of energy efficiency and the implied need for simultaneous equation 

estimation; and 

 the role of time costs and time efficiency in the production and consumption of 

energy services. 

2.5 Correlation between energy efficiency and other input costs 

For an individual energy service, changes in energy commodity prices are unlikely to be 

correlated with changes in other input costs or with changes in the broader attributes of the 

energy service. But the same cannot be said about changes in energy efficiency. In many 

(although by no means all) cases, energy efficient conversion devices will have a higher 

capital cost than inefficient models (i.e. ε and K will be positively correlated). For example, 

UK building regulations now require high efficiency condensing boilers to be used when 

UK Energy Research Centre UKERC/WP/TPA/2007/010
13 

installing or replacing a domestic central heating system and these have historically cost 

some £200-300 more than a conventional boiler. 

Khazzoom (1980) assumed this problem away by arguing that a more energy efficient 

appliance does not necessarily entail a greater initial cost and citing the lower cost of 

smaller and more fuel-efficient cars as an example. But in this case, the improvement in 

energy efficiency may have been achieved at the expense of other attributes of the energy 

service, such as carrying capacity and legroom (i.e. ε and A will be negatively correlated). 

In general, improvements in energy efficiency could result from energy-saving technological 

change, substitution between energy and other inputs in the production of useful work, or 

substitution between useful work and other attributes of the energy service. In practice, 

many energy services have multiple attributes (e.g. size, comfort, reliability, speed) and 

each attribute may have non-zero elasticity with respect to the energy cost of useful work. 

As Einhorn (1982) has argued, the long-term response to a reduction in energy costs will 

depend upon the trade-offs between useful work and these multiple attributes. 

Khazzoom’s neglect of capital costs has been challenged by several authors (Besen and 

Johnson, 1982; Einhorn, 1982; Henly, et al., 1988; Lovins, et al., 1988) who argue that it 

may lead empirical studies that rely upon Definitions 2, 3 or 4 to overestimate the direct 

rebound effect. Henly et al (1988) illustrate this clearly by including annualised capital costs 

(PK) in the equation for energy demand. Assuming that capital costs are a function of energy 

efficiency, the basic identity becomes: ε ε /)](,/[ ε = PPsE KE

9 . We can then derive the 

following alternative definition of the energy efficiency elasticity of energy demand: 

Extension 1: = −[ − ( )]−1)()()()( ηε E η PS η PK ηε PSS K

Compared to Definitions 2-4 there is an additional term in brackets. This is the product of 

the elasticity of demand for useful work with respect to capital costs ( S)( PK η ) and the 

elasticity of capital costs with respect to energy efficiency ( )( ηε PK ). We expect the first of 

these to be negative: higher capital costs should reduce the long-run demand for useful 

work, largely because they should reduce the number of energy conversion devices 

( NO ≤ 0)( PK η ) and/or their average size ( CAP ≤ 0)( PK η - assuming that capital costs are 

proportional to size). Under the assumption that energy efficient equipment is more 

expensive, the second term will be positive, making the product of these two expressions 

negative. The net result will be to reduce the absolute magnitude of the elasticity of energy 

demand with respect to energy efficiency ( E)( ηε ). Hence, if energy efficient equipment is 

more expensive, the direct rebound effect may be smaller than suggested by studies that 

rely primarily upon historical or cross-sectional variations in energy prices and estimate the 

direct rebound effect from Definitions 2, 3 or 4. This is because the change in energy service 

demand following a change in energy prices will be different from that following a change in 

energy efficiency. In general, such studies will tend to overestimate the direct rebound 

effect. The size of this upward bias will depend upon the relative magnitude of the three 

separate elasticities. 

The correlation between energy efficiency and capital costs may be expected to vary 

between energy services and over time. In areas such as computing, for example, 

 

9

 See Annex 1 

UK Energy Research Centre UKERC/WP/TPA/2007/010
14 

improvements in energy efficiency have long been associated with both improvements in 

service attributes and reductions in capital costs (Triplett, 1989). Also, higher capital costs 

will only reduce the direct rebound effect if the consumer faces the full cost of the purchase 

decision. If, for example, the additional cost of energy efficient conversion devices is fully 

subsidised, the higher initial cost should not affect the purchase decision. Furthermore, if 

government subsidies make energy-efficient devices cheaper than inefficient models, it is 

possible that the rebound effect will be amplified (i.e. if both S)( PK η and )( ηε PK are 

negative, their product will be positive). Moreover, the key variable may not be the initial 

cost of the equipment, but the discounted costs over the equipment lifetime, which depends 

upon consumer time preferences and the relative durability and lifetime of different models. 

Consideration of the role of capital costs further highlights the importance of distinguishing 

between the number, capacity and utilization of energy service devices when estimating 

direct rebound effects. Once an appliance is purchased, the capital cost is sunk and hence 

should be irrelevant to the utilisation decision. But higher capital costs may lead to the 

purchase of fewer, smaller and/or different conversion devices, depending upon the tradeoffs between different categories of input costs and between useful work and other output 

attributes. Holding output attributes constant, energy efficient conversion devices allow their 

owners to enjoy a greater consumer surplus in each time period, owing to the higher 

demand for useful work (Einhorn, 1982). But if the more efficient appliance is also more 

expensive than the inefficient alternative, it will only be purchased by an ‘economically 

rational’ consumer if the present value of the discounted stream of additional consumer 

surplus exceeds the present value of the additional capital cost. A mandatory requirement 

for new capital equipment to meet high standards of energy efficiency could mean that 

consumers will either: choose to delay replacing their existing equipment (if owned and if 

still working); choose to purchase smaller or different equipment; choose to purchase 

inefficient, second-hand equipment; or choose to go without the energy service altogether. 

The net effect on energy consumption for the relevant energy service over a particular 

period of time could therefore be ambiguous. But in all cases, the effect of the energy 

efficiency standard will be different from that of a change in energy prices, so an estimate of 

the direct rebound effect based upon the latter is likely to be incorrect. 

It is also possible that improvements in energy efficiency will be associated with changes in 

other input costs, such as operation and maintenance (O&M) costs. If, for example, more 

efficient conversion devices are less reliable and more costly to maintain and operate, the 

effect of energy efficiency improvements on the demand for useful work will again be 

different from the effect of changes in energy prices. However, the evidence for a positive 

correlation between energy efficiency and O&M costs is absent for most energy services, and 

for some the correlation may be negative. In general, the magnitude and direction of the 

bias in estimating the direct rebound effect using Definitions 2, 3 or 4 will depend upon the 

degree and sign of the correlation between energy efficiency and all other categories of 

input costs. If they are positively correlated, the bias will be negative and the direct rebound 

effect may be overestimated, while if they are negatively correlated the bias will be positive 

and the rebound effect may be underestimated. 

Even if improvements in energy efficiency are not associated with changes in other input 

costs, certain types of direct rebound effect may be constrained by the real or opportunity 

costs associated with increasing the demand for useful work. Two important examples are 

the opportunity cost of space (e.g. increasing refrigerator size may not be the best use of 

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15 

available space) and the opportunity cost of time (e.g. driving longer distances may not be 

the best use of available time). Both of these examples point to constraints on the demand 

for certain categories of useful work by individual households. However, space constraints 

may become less important over time if technological improvements reduce the average 

size of conversion devices per unit of useful work (e.g. computing) or if rising incomes lead 

to an increase in average living space (e.g. compare refrigerator sizes in the US and the UK) 

(Wilson and Boehland, 2005). In contrast, while technological improvements may reduce the 

time requirements per unit of useful work, the opportunity cost of time should increase with 

rising incomes. This illustrates, again, that direct rebound effects are not fixed, but vary 

over time and depend upon income and other factors. The relationship between time 

constraints and energy service consumption appears particularly important and is discussed 

further below. 

2.6 Endogenous energy efficiency 

Definitions 1-4 assume that energy efficiency is independent of the values of other 

independent variables – in other words, that it is exogenous. This follows naturally from 

Khazzoom’s original focus on the effect of mandatory energy efficiency standards for 

household appliances. In practice, however, the system-wide level of energy efficiency is 

likely to be influenced by one or more of the other dependent variables – in other words, 

energy efficiency must be considered partly endogenous. In particular, energy efficiency 

may be expected to be a function of current and historical energy prices: )(PE ε (Greene, et 

al., 1999b; Small and Van Dender, 2005). In the short term, increases in energy commodity 

prices may encourage consumers to utilise existing equipment in more energy efficient ways 

– such as increasing average load factor (e.g. car sharing), or adopting energy efficient 

operating practices (e.g. avoiding excessive speed). In the longer term, consumers may 

choose to purchase more energy efficient conversion devices, while producers may choose 

to devote expenditure to developing, improving and marketing such devices. 

[ ] / ε = PsS E If the demand for useful work depends upon the energy cost of useful work ( ) 

and energy efficiency depends upon energy prices ( ), the demand for energy for 

the relevant energy service may be represented as 

)(PE = εε

[ ] )(/)(// EE PPPsSE E == εεε . If we 

differentiate this expression with respect to energy prices and substitute the resulting 

expression for into Definition 2, we obtain an alternative definition of the direct 

rebound effect that takes into account price-induced energy efficiency improvements: 

S)( PS η

Extension 2: 1

)(1

)()( )( −

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−

+ −= εη

εηη

ηε

E

E E

P

P E P E

Where the expression in square brackets represents the energy cost elasticity of the demand 

for useful work ( S)( ). PS η

Previous versions of this equation have appeared in Blair et al (1984b), Mayo and Mathis 

(1988) and Small and Van Dender (2005). In principle, Extension 2 provides an alternative 

method of estimating the direct rebound effect. Rather than estimating the energy cost 

elasticity of the demand for useful work, one could separately estimate the own price 

elasticity of energy consumption for the relevant energy service ( E)( PE η ) and the elasticity 

UK Energy Research Centre UKERC/WP/TPA/2007/010
16 

of energy efficiency with respect to energy prices ( ). The resulting calculated value for 

the energy cost elasticity of the demand for useful work ( ) could then be used to 

estimate the direct rebound effect. 

εη )( PE

S)( PS η

It is clear from Extension 2 that the energy cost elasticity of the demand for useful work 

( ) will only be equal to the own price elasticity of the demand for energy for the 

relevant energy service (

S)( PS η

E)( PE η ) if the energy price elasticity of energy efficiency is equal to 

zero ( ). This is unlikely to be the case in practice. Annex 2 derives an expression 

for the relative magnitude of different price elasticities that should hold for all econometric 

estimates (see also Hanley et al. (2002)): 

εη = 0)( PE

 (2.11) (((( ) P P ))) ≤≤≤ ηηηη EESS PE S E PS

This relationship provides a valuable point of reference for the results from individual studies 

and is supported by evidence from recent surveys (Espey, 1998; Hanley, et al., 2002; 

Graham and Glaister, 2004). It suggests that: 

 The elasticity of demand for useful work with respect to the energy cost of useful 

work should be greater than the elasticity of the demand for useful work with respect 

to energy prices ( SS )()( PE PS ≤ ηη ). This shows that, relative to Definition 2, 

Definition 3 is likely to underestimate the magnitude of the direct rebound effect due 

to the neglect of price-induced energy efficiency improvements. 

 The elasticity of demand for useful work with respect to the energy cost of useful 

work should be smaller than the elasticity of energy demand with respect to energy 

prices ( ES )()( PS PE ≤ ηη ). This shows that, relative to Definition 2, Definition 4 is 

likely to overestimate the magnitude of the direct rebound effect due to the neglect 

of price-induced energy efficiency improvements. 

Equation 2.11 also suggests that the own price elasticity of energy demand for a particular 

energy service should provide an upper bound for the direct rebound effect for that service 

(since ES )()( PS PE ≤ ηη ). This suggests that the voluminous literature on own price 

elasticities of energy demand may be used to provide an upper bound on the likely 

magnitude of direct rebound effects. This is an important result that is used subsequently in 

Sections 4 and 5. 

It seems likely that energy efficiency will also be a function of other endogenous or 

exogenous variables in ways that could bias the results of empirical studies (Small and Van 

Dender, 2005). In particular, if consumers expect to have a high demand for useful work, 

they may be more likely to choose an energy-efficient conversion device in order to 

minimise the energy cost of useful work. For example, drivers may choose to purchase a 

more fuel-efficient car if they expect to drive long distances.10 This may create a positive 

correlation between S and ε that is in addition to the positive correlation created by the 

direct rebound effect. If this is not corrected for in empirical studies, the magnitude of the 

 

10 This is a hypothesis to be tested. A counter argument could be that drivers will purchase larger cars if they 

expect to drive long distances, since these are more comfortable. As larger cars tend to be less fuel-efficient, this 

may lead to a negative correlation between S and ε . 

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direct rebound effect will again be overestimated. Moreover, as pointed out by Small and 

Van Dender (2005), this type of endogeneity makes the logic behind Definition 2 circular: 

the demand for useful work (S) depends upon the energy cost of useful work (PS), which in 

turn depends upon energy efficiency (ε ) which in turn depends upon the demand for useful 

work (S). 

This simultaneous determination of an endogenous variable (ε ) with another endogenous 

variable (S) can be captured empirically with a simultaneous equation model. This starts 

with a set of n equations for n endogenous variables, with each equation representing either 

a causal relationship or an equilibrium condition. Such models could be formulated in a 

variety of ways, depending upon data availability. Small and Van Dender (2005), for 

example, use aggregate data for each US state and establish separate equations for the 

number (NO) of private cars in each state, their total annual mileage (S) and the average 

fuel efficiency of the state vehicle fleet ( ε ). Small and Van Dender base their model upon 

the following generic assumptions regarding consumer choices: 

 The total demand for useful work (S) is influenced by the number of energy 

conversion devices (NO), the energy cost of useful work ( / ε = PP ES ) and a number 

of exogenous variables (XS). 

 The number of energy conversion devices (NO) is influenced by the capital cost of 

those devices (PK), the anticipated demand for useful work (S), the energy cost of 

useful work ( /ε PE ) and a number of exogenous variables (XN). 

 The average energy efficiency of the stock of conversion devices (ε ) is influenced by 

the price of energy ( ), the anticipated demand for useful work (S), regulatory 

standards on the energy efficiency of new devices ( ) and a number of exogenous 

variables ( ). 

PE

Rε

X ε

This leads to the following set of ‘structural’ equations: 

 (2.12) 

),,(

)),/(,,(

)),/(,(

εε εε

ε

ε

XRSP

XPSPnoNO

XPNOsS

E

K E NO

E

=

=

= S

It is an empirical question as to whether a simultaneous equation model is appropriate for a 

particular energy service. In some cases, the joint dependence of some or all of the 

variables may either not hold or be sufficiently weak that it can be ignored. For example, 

Johansson and Schipper (Johansson and Schipper, 1997) assumed that mean driving 

distance per vehicle was a function of the number of vehicles and their average fuel 

efficiency, but argued that the latter did not depend upon mean driving distance because: 

‘.....one chooses what distance to drive for a given vehicle stock with different 

characteristics, and not the other way round’ (Johansson and Schipper, 1997). In contrast, 

Small and Van Dender (2005), Greene et al (1999b) and Wheaton (1982) all formulate 

models in which energy efficiency is a function of the number of cars and distance driven 

and each find the relevant coefficients to be statistically significant.11 

 

11 However, Small and Van Dender find no support for the endogeneity implied by the second of the equations in 

(9), since the coefficients on PS and S are not significant. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
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The key point, however, is that if joint dependence is relevant, the equations need to be 

estimated through an appropriate econometric technique, such as the use of instrumental 

variables. If, instead, one or more of the individual equations are estimated through 

ordinary least squares (OLS), the resulting coefficients will be biased and inconsistent owing 

to correlation between the endogenous variable and the error term. As an illustration, Small 

and Van Dender (2005) found that the use of OLS in their model overestimated the short 

and long-run direct rebound effects for car travel by 88% and 53% respectively (although 

factors other then endogeneity may have been involved). 

The use of a simultaneous equation model provides a clearer understanding of the 

implications of changes in energy efficiency, whether induced by regulatory intervention, 

energy price increases or other factors. For example, a mandatory standard for the energy 

efficiency of new conversion devices will have a direct effect on the energy efficiency of the 

stock, through the third of the equations in (9). However, improvements in energy efficiency 

will also tend to increase the number of conversion devices (e.g. the number of cars), which 

in turn will increase the total demand for useful work. Improvements in energy efficiency 

should also increase the demand for useful work (e.g. the distance driven by each car) by 

reducing the associated energy costs. The net increase in the demand for useful work will in 

turn encourage higher energy efficiency. Hence, a change in an exogenous variable such as 

regulatory standards for energy efficiency may trigger a complex set of changes within the 

system until a new equilibrium is reached. If the behavioural assumptions given above hold, 

the total change in system-wide energy efficiency following the regulatory intervention will 

be greater than the direct change, as will the total change in the demand for useful work. 

The structural equations may be solved to allow each of the endogenous variables to be 

written solely as functions of the exogenous variables, giving so-called ‘reduced form’ 

equations. However, many empirical estimates of the direct rebound effect use neither a 

structural equation system nor their reduced form solution. Instead, they employ what 

Small and Van Dender (2005) term a ‘partially reduced form’ equation for S, denoted here 

by the symbol . This includes energy efficiency indirectly via the energy cost of useful 

work, but does not include the number or capacity of conversion devices: 

^

s

 (2.13) ),),/(, XX SNO = sS ( ε ^

PP EK

Since energy efficiency is endogenous, estimation of this equation by OLS is likely to lead to 

biased estimates of the direct rebound effect. Moreover, the bias will be compounded if (as 

is commonly the case), capital costs (PK) or other input costs are correlated with either S or 

ε , but are omitted from the equation owing to lack of data. 

2.7 Energy efficiency and time costs 

The model summarised in Section 2.1 is based upon Becker’s work on the allocation of time 

within household production (Becker, 1965). As Binswanger (2001) has argued, time costs 

and the efficiency of time use have important implications for energy use in general and the 

direct rebound effect in particular. However, empirical work in this area remains in its 

infancy (Jalas, 2002). 

For consumers, time is a necessary input to the production and enjoyment of energy 

services. For example, it takes time to drive from one place to another; to purchase food; to 

UK Energy Research Centre UKERC/WP/TPA/2007/010
19 

prepare a meal; to wash, dry and iron clothes and so on. The total cost of time for a 

particular energy service will depend upon the opportunity cost of time and the amount of 

time required per unit of useful work. In the household production model, the cost of time is 

conventionally measured by the average hourly wage for the household (PW) and hence 

should vary from one household to another. The amount of time required per unit of useful 

work may be measured by the efficiency of time use (θ ), which depends upon the 

technology used. For example, a microwave oven is more time efficient than a conventional 

oven; a car is more time efficient than a bike;12 an aircraft is more time efficient than a 

ship; and so on. The relationship between useful work and time consumption for a particular 

energy services may then be expressed as: =θTS , while the time cost per unit of useful 

work may be expressed as = PP WT /θ . These expressions are entirely analogous to those 

used for energy consumption for a particular energy service (namely = εES and 

/ ε = PP ES ). 

Under these assumptions, the contribution of time costs to the full cost of an energy service 

should be inversely proportional to the time efficiency of the relevant technology and 

proportional to the wage rate. Similarly, the contribution of energy costs should be inversely 

proportional to the energy efficiency of the relevant technology and proportional to the 

energy price. Consumers may be able to choose between technologies with different 

combinations of energy and time efficiency in the provision of a particular energy service, 

and also between energy services with different levels of time and energy efficiency. The 

relative price of time and energy should influence the direction of technological innovation 

and encourage higher or lower levels of time/energy efficiency for individual energy 

services, as well as shifts towards the development of more or less time/energy efficient 

services. 

These considerations suggest that an increase in the cost of time (i.e. wages) relative to 

energy prices should induce a substitution away from time and toward energy in the 

production of individual services, as well as a substitution away from time-intensive services 

and towards energy intensive services.13 Since, in real terms, wages have grown faster than 

energy prices within developed countries over most of the last century, this mechanism 

could be an important driver of increased energy consumption (Binswanger, 2001). With 

time costs forming a significant proportion of the total cost of many energy services, 

consumers and producers have sought ways to improve the time efficiency, rather than the 

energy efficiency, of service provision. So travel by private car has replaced walking, cycling 

and public transport; automatic washing machines have replaced washing by hand; fast 

food and ready meals have replaced traditional cooking; supermarkets (and more recently 

e-shopping and home delivery) have replaced the trip up the high street; email has postal 

services; and so on. Increases in aggregate energy consumption could therefore have been 

driven as much by the substitution of energy for time as by the overall increases in income. 

The relative importance of time costs and energy costs may be expected to vary over time 

and between different energy services. One area where time costs are particularly important 

and relatively well researched is transport. For example, figures presented by Small (1992) 

 

12 Assuming no road congestion. As with energy efficiency, time efficiency is a function of the overall energy 

system, which could have multiple users. While congestion is given for individual decisions, it is an endogenous 

variable for the system as a whole. 

13 Note that traditional consumer theory would only capture the second of these effects and that the model implies 

that increases in non-wage income would not encourage either type of substitution. 

UK Energy Research Centre UKERC/WP/TPA/2007/010
20 

suggest that the average time costs for US car travel were more than three times total 

running costs, implying that they were more than six times the total fuel costs. If the value 

of time is proportional to the average wage, this ratio will be higher for high-income groups 

and may be expected to increase over time if real incomes continue to increase faster than 

energy prices. For other energy services, such as household heating for example, time costs 

may be a less significant determinant of demand. However, time costs for this service may 

have been much greater in the past when coal or wood fires were the norm, since time was 

required for preparing and lighting the fuel. In many developing countries, the time required 

to collect fuelwood remains an enormous burden. 

In those cases where technology permits a trade-off between the two, time efficiency may 

be represented as a function of energy efficiency (θ ε )( ) or vice versa ( ε θ )( ). By taking the 

first of these, we may write the energy demand for a particular energy service as: 

ε θ ε /))]((),([ ε = PPsE TS . This leads to an alternative definition of the direct rebound effect 

that takes into account the associated changes in time costs: 

Extension 3: η = −[η + (η η η θ )]−1)()()()()( ε E P P θ PSS T ε S T

Again, as compared to Definitions 2 and 3 there is an additional term in brackets. This is the 

product of the elasticity of demand for useful work with respect to time costs ( S)( PT η ), the 

elasticity of time costs with respect to time efficiency ( )( ηθ PT ) and the elasticity of time 

efficiency with respect to energy efficiency (η θ )( ε ). We expect the first of these to be 

negative (higher time costs should reduce the demand for useful work) and the second to be 

positive (higher time efficiency should reduce time costs). However, the sign of the last 

elasticity is ambiguous: while substitution between energy and time implies that energy 

efficiency is negatively correlated with time efficiency, technological improvements may 

sometimes improve both (e.g. microwave ovens). However, in many cases greater energy 

(time) efficiency is likely to be achieved at the expense of lower time (energy) efficiency 

(i.e. θ and ε will be negatively correlated). For example, a sports car is less energy 

efficient than a Smart car; aircraft are less energy efficient than ships; washing machines 

are less energy efficient than hand-washing; and so on. In these circumstances, the 

resulting increase in time costs will offset the saving in energy costs leading to a smaller 

direct rebound effect with respect to improvements in energy efficiency. For example, while 

greater fuel efficiency may make driving cheaper, consumers may not be willing to spend 

the time driving greater distances. This suggests that, for those energy services where 

trade-offs between time and energy efficiency are relevant, empirical estimates based upon 

Definitions 2 and 3 and relying primarily upon historical or cross-sectional variations in 

energy prices may overestimate the magnitude of the direct rebound effect. 

As with capital costs, the size of this upward bias will depend upon the relative magnitude of 

the different elasticities. One notable implication is that, for time-intensive energy services, 

direct rebound effects from improved energy efficiency may be expected to decrease over 

time. One of the few studies to show evidence for this is Small and Van Dender (Small and 

Van Dender, 2005), although their methodology was subsequently criticised by Harrison et 

al (2005). 

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21 

If energy efficiency is influenced by energy prices and if improvements in energy efficiency 

are associated with changes in both time costs and capital costs, the appropriate expression 

for the direct rebound effect incorporates all three of the extensions developed above: 

 (2.14) ( )( ) 1)()()()()( )()( )( ⎥ −

⎤ ⎢⎡ ⎟ − +

⎞

⎜

⎜

⎝

⎛ + −= θηηηηη εηη

η P ε K P θ T

P

P P PS PS

E

E K T

E

E E

)(1 ⎥⎦ ⎢⎣ ⎟

⎠ − εη ε ε

As pointed out by Binswanger (2001), the analogy between time and energy efficiency also 

suggests that there should be a parallel rebound effect with respect to time. Since 

improvements in the time efficiency associated with a particular service lower the cost of 

that service, there should be a corresponding increase in service demand that will offset the 

potential time savings. Again, transport provides a particularly good example: the potential 

time savings from faster modes of transport may be partly or wholly taken back by traveling 

greater distances. For example, in the UK, the time spent travelling increased by only 17% 

between 1975 in 2005, while the total distance travelled increased by 52% (Department of 

Transport, 2006). Similar patterns are likely to apply to other energy services (e.g. washing 

clothes more often), but may be less important if time costs form a smaller proportion of 

total costs, or if the assumptions of the simple Becker model (e.g. no joint production) do 

not apply. 

The rebound effect with respect to time may be defined as an efficiency elasticity 

( ST −= 1)()( ηθ ηθ ) or as a price elasticity ( = ST −1)()( PT ηθ η ) in a similar manner to the 

conventional direct rebound effect. Empirical investigation of this effect would similarly need 

to take into account the potential correlation between improvements in time efficiency and 

other input costs (including capital and energy costs); and the potential endogeneity of time 

efficiency (e.g. consumers may choose a more time efficient technology if they anticipate a 

high demand for the service). But in the absence of good data on time use patterns and 

time efficiency, such considerations remain academic. 

Both the substitution of energy for time in the production and consumption of energy 

services, and the subsequent rebound effect with respect to time should act to increase 

overall energy consumption. Indeed, it is possible that these processes have had a more 

important influence upon aggregate energy consumption than the conventional direct 

rebound effect with respect to energy efficiency. Moreover, if wages continue to increase 

faster than energy prices, the substitution of energy for time may be expected to increase in 

importance, while the conventional direct rebound effect decreases in importance. To date, 

however, attention has focused disproportionately on the latter. 

2.8 Summary 

This section began by clarifying the distinction between energy inputs (E) and ‘useful work’ 

outputs’ (S) and argued that ‘energy services’ (ES) comprise both useful work and other 

attributes (A). It then showed how the consumption of an energy service involved trade-offs 

between: first, the consumption of useful work and the consumption of those other 

attributes; second, the use of energy and the use of other inputs in the production of that 

energy service; and third, the consumption of different types of energy service. 

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22 

The section then introduced the four definitions of the direct rebound effect in common use, 

identified their underlying assumptions and clarified the relationship between them. It 

distinguished: 

 the ‘engineering’ definition of the direct rebound effect as the energy efficiency 

elasticity of the demand for energy or useful work (Definition 1); 

 the ‘economic’ definition of the direct rebound effect as the energy cost elasticity of 

the demand for useful work (Definition 2); 

 a first approximation to the direct rebound effect based upon the energy price 

elasticity of the demand for useful work (Definition 3); and 

 a second approximation to the direct rebound effect, based upon the own-price 

elasticity of the demand for energy (Definition 4). 

These definitions are summarised in Table 2.2. The appropriate choice for empirical work will 

depend upon the availability, accuracy and variability of the relevant data and a range of 

other considerations. In principle, in the absence of any data constraints, empirical studies 

using Definition 1 should estimate the direct rebound effect more accurately than those 

using Definition 2, while studies using Definition 2 should estimate the direct rebound effect 

more accurately than those using Definitions 3 or 4. In practice, however, there are far 

more estimates of the own price elasticity of energy demand (Definition 4) then there are of 

the other elasticities listed in Table 2.1. While Definition 4 provides a relatively poor 

approximation to the direct rebound effect, simple theoretical arguments suggest that it 

should provide an upper bound for the direct rebound effect (since, from Equation 2.11, 

ES )()( PS PE ≤ ηη ). 

Table 2.1 Definitions of the direct rebound effect 

= SE −1)()( Definition 1 ηε ηε

= − SE −1)()( PS Definition 2 ηε η

= − SE −1)()( PE Definition 3 ηε η

= − EE −1)()( PE Definition 4 ηε η

Notes: 

• Symbols in parentheses stand for elasticity numerators while subscripts represent elasticity denominators 

• S: Useful work; E: Energy; PS: Energy cost of useful work; PE: Energy price; ε: energy efficiency. 

This section has also shown how the different ways in which useful work is defined and 

measured can lead to different conclusions regarding the nature and size of the effect. For 

example, improvements in the energy efficiency of washing machines may lead to a 

different outcome in terms of weight of clothes washed per year than in terms of hours of 

use. If the demand for energy or useful work can be decomposed into its constituent 

elements, such as the number, capacity and utilisation of energy conversion equipment, the 

determinants of short and long-run direct rebound effects may be much better understood. 

Many empirical estimates of the direct rebound effect are based upon Definitions 2, 3 or 4 

rather than Definition 1 and rely either primarily (Definition 2) or entirely (Definitions 3 & 4) 

upon historical or cross-sectional variations in energy prices. This section has argued that 

such studies could potentially overestimate the magnitude of the effect. Three important 

factors that may contribute to this are: 

• the anticipated positive correlation between energy efficiency and other categories of 

input costs, notably capital costs (Extension 1); 

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23 

• the role of price induced energy efficiency improvements (Extension 2); and 

• the anticipated negative correlation between energy efficiency and time efficiency 

and the corresponding implication that direct rebound effects may decline with 

income (Extension 3). 

Consideration of these factors led to the derivation of three extensions to Definition 2 which 

are summarised in Table 2.2. 

Table 2.3 Extensions of Definition 2 

= −[ − ( )]−1)()()()( ηε E η PS η PK ηε PSS K

Extension 1 

(capital costs) 

1

)(1

)()( )( −

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−

+ −= εη

εηη

ηε

E

E E

P

P E P E Extension 2 

(endogneity) 

η −= [η + (η η η θ )]−1)()()()()( ε E P P θ PSS T ε S T

Extension 3 

(time costs) 

Notes: 

 Symbols in parentheses stand for elasticity numerators while subscripts represent elasticity denominators 

 S: Useful work; E: Energy; PS: Energy cost of useful work; PE: Energy price; ε: energy efficiency; θ: time 

efficiency 

Combining all these extensions leads to the following expression: 

 (2.15) ( )( )()()()( ) 1 )()( ) ⎥ −

⎦

⎤ ⎢

⎣

⎡ ⎟ +

⎠

⎞

⎜

⎜

⎝

⎛ +

ηηηη

εηη P ε K P θ T

P

P P PS PS

E

E K T

E

E )( )(1 (

⎢ ⎥

− − ⎟ −= θη

εη

ηε ε

E

Consideration of time costs also points to the potential importance of the substitution of 

energy for time in the provision of energy services, together with possibility of a parallel 

‘rebound effect with respect to time’. Both of these subjects deserve further research. 

Two additional factors were identified that could potentially lead to upwardly biased 

estimates of the direct rebound effect. First, it was noted that energy price elasticities tend 

to be higher for periods with rising energy prices than for those with falling energy prices. 

Since the appropriate proxy for energy efficiency improvements is reductions in energy 

prices, empirical estimates using time-series data that include periods of rising energy prices 

could potentially overestimate the effect. Second, it was argued that energy efficiency 

cannot always be treated as exogenous since it may be influenced by other variables in 

ways that could bias the results of empirical studies. For example, if consumers expect to 

have a high demand for useful work, they may be more likely to choose an energy-efficient 

conversion device in order to minimise the energy cost of useful work. This may create a 

positive correlation between S and ε that is in addition to the positive correlation created by 

the direct rebound effect. If such endogneity is not corrected for in empirical studies, the 

magnitude of the direct rebound effect will again be overestimated. 

Different studies address these factors in different ways and to a greater or lesser extent, 

with some of the best examples being recent US studies of personal automotive transport 

(Greene, et al., 1999b; Small and Van Dender, 2005). The relative merits of different 

empirical approaches to estimating the direct rebound effect are discussed further in Section 

3. 

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3 Econometric approaches to estimating the direct 

rebound effect 

3.1 Introduction 

Subsequent sections review a selection of empirical estimates of the direct rebound effect. 

The selected studies form a subset of a much larger literature that uses econometric 

techniques to estimates the own price elasticity of energy demand in different 

circumstances. All of this literature has some relevance to the direct rebound effect, but a 

comprehensive review would be wholly impractical. Instead, we confine attention to a 

relatively small number of studies that are considered to provide robust estimates of the 

direct rebound effect for particular energy services. This section sets out the criteria by 

which these studies were selected. 

In an early survey of econometric studies of energy demand, Bohi and Zimmerman (1984) 

noted that: “.... the information is sometimes bewildering...because of the variety of 

techniques employed and the disparities among the results.” In the 20 years since this 

comment was made, the literature has become even more confusing owing to the number of 

studies published, their increasing diversity and the introduction of new and highly 

sophisticated techniques such as cointegration (Madlener, 1996). This makes it difficult to 

provide a meaningful overview of the literature, or to compare the results of different 

studies. 

While Bohi and Zimmerman’s review covered the full range of econometric studies of energy 

demand in OECD countries, attention is confined here to a relatively small subset of this 

literature. Nevertheless, many of the same difficulties of interpretation arise. In particular, 

individual studies are found to vary widely in terms of: 

 the definition and measurement of useful work and other relevant variables; 

 the types of data employed (e.g. cross-section; time-series; panel; etc.); 

 the model structure chosen (e.g. structural; reduced form; household production; 

etc.); 

 the functional forms used (e.g. linear; double log; translog; etc.); and 

 the estimation techniques used (e.g. Ordinary Least Squares; Generalised Least 

Squares etc.) 

This section therefore reviews of the different choices available under each of the above 

headings. The aim is to provide a basis for understanding, categorising and comparing the 

empirical studies discussed in subsequent sections. 

3.2 Identifying the econometric evidence base 

Econometric estimates of the direct rebound effect use one of the three definitions derived 

in Section 2. This means that the relevant evidence base consists of econometric studies 

that estimate one or more of the elasticities listed in Table 3.1. 

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Table 3.1 Elasticities used in estimating the direct rebound effect 

Symbol Name 

Definition 1

E)( ηε Elasticity of the demand for energy with respect to energy efficiency 

Elasticity of the demand for useful work with respect to energy 

efficiency 

S)( ηε

Definition 2

Elasticity of the demand for useful work with respect to the energy cost 

of useful work 

S)( PS η

Definition 3

Elasticity of the demand for useful work with respect to the price of 

energy 

S)( PE η

Definition 4

E)( PE η Elasticity of the demand for energy with respect to the price of energy 

In practice, econometric estimates of energy efficiency elasticities ( E)( ηε and S)( ηε ) are 

relatively uncommon, largely as a result of lack of data or insufficient variation in the 

independent variable. Instead, most empirical studies estimate one or more of the price 

elasticities ( S)( PS η , S)( PE η or E)( PE η ), for the reasons given in Section 2. 

There are an enormous number of empirical studies that use econometric methods to 

estimate the own-price elasticity of energy demand ( E)( PE η ) for different energy services, 

or groups of services, in different sectors and at different levels of aggregation.14 However, 

as argued in Section 2, this elasticity is likely to provide a relatively poor approximation to 

the direct rebound effect since it effectively assumes that energy efficiency is unaffected by 

changes in energy prices (η ε = 0)( PE ). Hence, given both the size of this literature and its 

limitations as a measure of the direct rebound effect, we do not attempt a comprehensive 

literature review in Sections 4 and 5. Instead, we simply provide some indicative figures 

that are taken from meta-analyses of the own price elasticity of energy demand for a 

number of sectors and energy services. The reason for including these is that, as shown in 

Section 2.5, the own price elasticity of energy demand may under certain assumptions be 

considered as an upper bound for the direct rebound effect.15 This finding is of some 

importance, since it means that this voluminous literature may be used to place some upper 

bounds on the likely magnitude of direct rebound effects for different energy services. This 

was precisely the approach taken by Khazzoom (1980), who pointed to evidence that the 

long-run own-price elasticity of energy demand for water heating, space heating and 

cooking exceeded (minus) unity, implying that energy efficiency improvements for these 

services could lead to backfire. However, literature reviews and meta-analyses generally 

suggest that energy demand is price inelastic, with values typically less than unity (Dahl, 

1994; Atkinson, 1995; Espey, 1998; Graham, 2002; Hanly, 2002). Important exceptions 

include low income groups and consumers in developing countries, who are found to be 

more responsive to energy prices. 

Own price elasticities for energy demand are most useful when the demand relates to a 

single energy service, such as refrigeration. They are less useful when (as is more common) 

 

14 For a good review, see Barker, et al., (1995). 

ES )()( PS PE≤ ηη 15 Since from Equation 2.11: ). 

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26 

the measured demand derives from a collection of energy services, such as total household 

energy consumption. In this case, a high (low) own price for energy demand may suggest 

that improvements in the ‘overall’ efficiency of energy use by households will lead to large 

(small) direct rebound effects.16 It may also suggest that the direct rebound effect for the 

energy services that dominate overall household energy consumption (such as heating) may 

be large (small). But such aggregate data disguises the own price elasticity of energy 

demand for individual energy services. For example, it is possible that the energy demand 

for refrigeration is elastic – suggesting the possibility of large rebound effects - but if overall 

household energy demand is inelastic and if refrigeration forms only a small portion of that 

demand, then such a possibility is disguised. 

A small number of econometric studies estimate either the energy price elasticity of the 

demand for useful work or the own-price elasticity of the demand for energy, but include 

some measure of energy efficiency in their specifications (i.e. ε η S)( PE or ε η E)( PE ). The 

behaviour being measured here is the short run response to a change in energy prices, 

conditional upon a particular level of energy efficiency, which results primarily from changes 

in equipment utilisation. A number of these studies are included in the review of literature in 

Sections 4 to 6, since they are considered to provide a reasonable approximation to the 

short run direct rebound effect. However, they do not provide estimates of long-run effects. 

Given both the paucity of estimates of energy efficiency elasticities and the limitations of 

energy demand elasticities as a proxy for the direct rebound effect, the literature review in 

Sections 4 and 5 is largely confined to studies that estimate either: 

 the elasticity of the demand for useful work with respect to the energy cost of useful 

work ( S)( PS η ); or 

 the elasticity of demand for useful work with respect to the price of energy ( S)( PE η ) 

(with or without controlling for energy efficiency). 

The direct rebound effect may be estimated from either of these this using Definitions 2 and 

3. However, estimates of S)( PS η are preferred to estimates of S)( PE η , since the latter may 

underestimate the direct rebound effect.17. Moreover, while a number of studies estimate 

either S)( PS η or S)( PE η for a particular energy service, only a portion of these refer 

explicitly to the direct rebound effect. 

The primary focus on elasticities of demand for useful work constrains the scope of the 

review, since such estimates are only possible if data is available on a relevant measure of 

useful work, such as vehicle kilometres. This is only the case for a subset of (mostly 

household) energy services. As a consequence, the evidence base for the direct rebound 

effect is heavily biased towards personal transportation and household heating, where proxy 

measures of useful work are most readily available. These energy services form a significant 

component of final demand in OECD countries and may be expected to be relatively price 

elastic: first, because energy costs (PS) form a relatively large proportion of the generalised 

cost of these services (PG); and second, because energy costs are relatively visible to the 

 

16 Although in this case the relevant measure of useful work is a composite of several different services. 

SS )()( PE PS≤ ηη 17 Since from Equation 2.11: ). 

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18 consumer through regular utility bills and visits to the petrol station. To the extent that 

energy forms a smaller proportion of total costs for other energy services (e.g. clothes 

washing), and/or those costs are less visible to the user, standard theoretical arguments 

suggest that energy price elasticities – and hence rebound effects – should be lower for 

those services.19 However, this hypothesis needs to be tested empirically. 

Two other features of the econometric evidence base may be noted. First, there are 

practically no estimates of the own-price elasticity of the demand for useful work (e.g. 

lighting, heating, motive power) by producers. As a consequence, almost all of the 

discussion in Sections 4 and 5 focuses on household energy services. While there is an 

extensive literature on the own-price elasticity of energy demand for producers in different 

sectors, this is not reviewed in the current report. Rebound effects for producers are, 

however, the main focus of Technical Reports 3, 4 and 5, where alternative approaches to 

estimating such effects are investigated (see also the Supplementary Report). 

Second, the evidence base is overwhelmingly biased towards OECD countries in general and 

the US in particular, reflecting in part the high quality data available in the latter. However, 

estimates from the US may not necessarily be generalised to other OECD countries. For 

example, higher residential densities and the greater availability of public transport 

alternatives may make the own-price elasticity of demand for personal automotive travel 

higher in European countries than in the US. Similarly, results from OECD countries cannot 

be generalised to the developing world, since both theoretical arguments and empirical 

evidence suggests that direct rebound effects may be greater for low-income groups, 

including ‘marginal’ consumers that did not previously have access to particular energy 

services (Zein-Elabdin, 1997; Roy, 2000). 

3.3 Measurement issues 

To estimate the elasticity of demand for useful work with respect to the energy cost of 

useful work ( S)( PS η ), empirical studies must have data on useful work (S), energy prices 

(PE), energy efficiency ε )( and/or energy consumption (E). In principle, since = εES , data 

on two of these variables should allow the third to be calculated. If data is additionally 

available on the number (NO), capacity (CAP), utilisation (UTIL) and/or average load factor 

(LF) of the relevant conversion devices, the demand for useful work may be further 

decomposed (e.g. S=NO*CAP*UTIL*LF). However, this approach is only valid if the relevant 

variables have been independently and accurately determined. As shown by Schipper et al

(1993), this is not always the case, even in well studied areas such as passenger transport. 

For many energy services, the relevant data is simply unavailable, while for others the data 

must either be estimated or is subject to considerable measurement error. In the case of 

passenger transport, for example, several studies have misleadingly equated the total 

 

18 Information on household energy consumption and costs is nevertheless much less than could be desired. For 

example, Kempton and Montgomery (1982) have compared the information value of the average household energy 

bill to that of receiving a single monthly bill from the supermarket for ‘food’. Recent developments in smart 

metering and electronic display technologies offer the opportunity to improve the information available to 

consumers, and this could potentially make the demand for energy services more price elastic. 

19 The second Hicks-Marshall rule of derived demand states that: “ the demand for anything is likely to be less 

elastic, the less important is the part played by the cost of that thing in the total cost of some other thing, in the 

production of which it is employed” 

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consumption of gasoline with the consumption of gasoline by passenger cars (Schipper, et 

al., 1993). This is incorrect when vehicles other than passenger cars use gasoline, (e.g. light 

trucks, motorcycles, mopeds, boats) and when many passenger cars use diesel.20 However, 

estimating the relative proportion of each fuel going to each category of vehicle can be a 

source of error. 

Compared to most energy services, passenger transport is relatively straightforward. In 

comparison, data on the energy consumption for individual household energy services is 

rarely available, except when those services are sub-metered as part of an evaluation 

exercise. Even when available, sub-metered data usually applies only to a subset of 

households and for a limited period of time and hence may need to be scaled up. Data on 

total household energy consumption is relatively accurate, but may need to be ‘unbundled’ 

to estimate the proportion going to lighting, water heating, cooking, refrigeration and so on. 

Techniques such as ‘conditional demand analysis’ estimate appliance-specific energy 

consumption by combining engineering models of individual end uses with data on energy 

consumption, appliance ownership and other variables (Parti, 1980). However, these 

approaches have only been used in a handful of studies of the direct rebound effect (Dubin, 

et al., 1986; Dubin and Henson, 1988). 

Measurement of useful work is extremely problematic, which partly explains the limited 

scope of the available studies. Aggregate measures are only available for a subset of 

services such as transport, while disaggregate measures may require expensive monitoring. 

In the case of household heating, a number of studies have monitored thermostat settings 

and internal temperatures for individual households (Greening and Greene, 1998). But as 

argued in Technical Report 1, only a portion of the internal temperature change in a building 

following certain types of energy efficiency improvement may be due to changes in 

thermostat settings. For example, daily average household temperatures will generally 

increase following improvements in thermal insulation, even if the heating controls remain 

unchanged. This is because insulation contributes to a more even distribution of warmth 

around the house, reduces the rate at which a house cools down when the heating is off and 

delays the time at which it needs to be switched back on (Milne and Boardman, 2000). 

This example points to a generic issue regarding the appropriate definition and 

measurement of direct rebound effects, namely should this be based upon the total change 

in demand for useful work that follows an energy efficiency improvement, or only on the 

portion of this change that result from behavioural change by the relevant individuals. In the 

case of household heating, the former would correspond to changes in heat output as a 

result of the change in internal temperature while the latter would correspond to changes in 

heat output as a result of the change in thermostat settings. The preceding discussion has 

implicitly assumed that these two measures are identical, but the heating example 

illustrates that this may not always be the case. Moreover, to assess the full benefits of an 

improvement in household heating systems, the temperature change in each room of the 

building would need to be measured, while controlling for outside temperature, changes in 

occupancy and other factors. In addition, internal temperature is only one of the 

determinants of thermal comfort, with others including activity levels, air velocity and 

humidity (Frey and Labay, 1988). If, for example, an energy efficiency improvement 

reduces internal airflow as well as thermal loss, measured changes in internal temperature 

 

20 The latter is especially problematic in Europe, where diesel forms a large and increasing proportion of the fuel 

mix for passenger cars. 

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may not fully reflect changes in comfort. Measurement issues are therefore closely linked to 

the appropriate definition of the direct rebound effect. 

If data on both energy consumption and useful work is available, energy efficiency can be 

estimated. Alternatively, the demand for useful work could be estimated from data on 

energy consumption and energy efficiency. Again, however, such data is difficult to obtain 

and subject to inaccuracy. In practice, the relevant measures of energy efficiency may 

depend upon a number of variables beyond the thermodynamic efficiency of particular 

conversion devices. This is evident, for instance, in most household heating studies where 

various energy audit data have to be included to accurately estimate the demand for space 

heating. Moreover, the thermodynamic efficiency of conversion devices is frequently absent 

from datasets and may have to be estimated using techniques such as ‘frontier analysis’ 

(Guertin, 2003). Some studies use relatively crude techniques: Douthitt (1986), for 

example, uses a dummy variable to indicate whether a furnace has been replaced or 

serviced in the current year and can therefore be assumed to be more energy efficient. This 

again shows the attraction of S)( PE η or E)( PE η as proxies for the direct rebound effect, 

since these can be estimated in the absence of data on energy efficiency. 

Measurement difficulties are not limited to the above variables, but also apply to exogenous 

variables that affect the demand for energy, useful work or energy efficiency. These may 

include demographic or geographical factors, for example. Omission of such variables could 

lead to bias if they are correlated with the dependent or independent variables, while 

inclusion of such variables could lead to error if they are measured or estimated 

inaccurately. As a consequence, empirical estimates of elasticities may be expected to 

include some sort of bias (e.g. sampling, measurement or missing variables bias), which 

may be either positive or negative. If a sufficiently large number of estimates are available, 

this problem may be overcome by post-regression techniques such as meta-analysis, but in 

the case of the direct rebound effect the evidence base is too small and too diverse for this 

to be possible. 

3.4 Types of Data 

Four broad categories of data can be distinguished: 

 Cross-section: a sample of households, states, countries or other units, ideally taken 

at random from a population at a given point in time. An example would be data on 

total gasoline fuel consumption and related variables for OECD countries in the year 

2000. 

 Time-series: a series of observations on several variables at regular intervals (e.g. 

monthly, annually) over a period of time. An example would be annual data on total 

gasoline fuel consumption and related variables for the UK over the period 1970 to 

2000. 

 Pooled cross-section (or cross-sectional time-series): a cross-sectional sample from 

the same population taken at two or more intervals in time. An example would be 

data on gasoline fuel consumption and related variables from a survey of households 

in 1995 and 2000. With a pooled cross-section, the units (households in this case) 

need not be the same in each sample period. 

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30 

 Panel: similar to a pooled cross-section, but with data from the same units in each 

sample period. An example would be data on gasoline fuel consumption and related 

variables from each US state over a period 1972 to 2000. 

For each category, a further broad distinction may be made between aggregate and 

disaggregate data sets. For energy studies, the level of aggregation ranges from household 

survey data to country level data collected by the national authorities. Panel and pooled 

cross-section data frequently apply to the household level, while cross-section and timeseries data more commonly apply to the sectoral, regional or country level. Time-series data 

also varies in periodicity (e.g. monthly, quarterly, annual), the length of time covered and 

the particular time periods analysed. 

All four types of data have been used to estimate the direct rebound effect although studies 

using cross-sectional and time-series data are more common than those using pooled crosssectional and panel data. Annual time-series are particularly common in transportation 

studies and form the basis of a number of studies of the direct rebound effect for passenger 

transport (Greene, 1992; Jones, 1993; Schimek, 1996). Cross-section data from household 

surveys are more common in studies of household heating and other residential end-uses 

(e.g. Houthakker (1980)) although there are fewer applications to the direct rebound effect. 

Pooled cross-sections are also common, given the large number of repeated household 

surveys that have been collected, particularly in the US. A small number of studies use 

panel data for households, derived from repeated surveys of the same participants 

(Goldberg, 1996; Puller and Greening, 1999; Frondel, et al., 2007). The US is particularly 

fortunate in that state-level data can be used to form an aggregate panel, providing 

variations in the relevant variables both across time and between different states. Compared 

to conventional aggregate time-series data this approach provides substantially more 

observations, while compared to disaggregate panel data this approach provides more 

information on the effects that are of interest to policymakers without having to conduct 

household surveys and scale up the results. This data therefore forms the basis of some of 

the most robust studies of direct rebound effects in transport, including Haughton and 

Sarkar(1996) and Small and Van Dender (2005). 

Generally speaking, the analysis of time-series data is more challenging than the analysis of 

cross-sectional data, since the assumptions of the ‘classical linear model’ are more likely to 

be violated (Wooldridge, 2003). Of particular importance is serial correlation in the error 

terms - where the error in one period depends in part upon the errors in previous periods. 

However, time-series econometrics has improved significantly over the last two decades, 

with substantial improvements in the goodness-of-fit and explanatory power of testing 

routines. 

Pooled cross-sectional data may have advantages over individual time-series estimates, 

notably because of the increased number of observations and hence degrees of freedom 

(Baltagi and Griffin, 1983). Panel data sets are more difficult to obtain than pooled crosssection data, but are more valuable still since the multiple observations on the same units 

allow the unobserved characteristics of those units to be controlled for. Models using pooled 

cross-section or panel data appear particularly well suited to estimating the impact of 

energy efficiency improvements. 

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31 

3.5 Model structures 

Four broad types of econometric model can be identified in the literature, namely: single 

equation models, structural models, discrete/continuous models, and household production 

models. Each is outlined below. 

3.5.1 Single equation models 

Many empirical studies employ a single equation for estimating the demand for either useful 

work or energy. The very simplest approach uses the price of energy (PE) and income (Y) as 

independent variables, together with other exogenous variables such as weather conditions 

(Xi): 

 (3.1) 

The price and income elasticities estimated from such models include both short-run 

changes in equipment utilisation and long-run changes in equipment stock. However, the 

model does not allow these individual effects to be distinguished. The approach may also 

lead to biased results since relevant variables are excluded. 

If data is available, an alternative approach is to also include measures of the number (NO), 

capacity (CAP) and/or the energy efficiency (ε ) of the relevant stock of equipment as 

independent variables: 

 (3.2) 

This approach can capture very short-run income and price elasticities, since it effectively 

measures changes in utilisation while holding equipment stock and energy efficiency 

constant. But the long-run effects are embedded in the variables for equipment stock (NO

and/or CAP) and energy efficiency ( ε ) and hence cannot be identified without estimating 

separate equations for these variables (Dahl and Sterner, 1991). This requires a structural

model, which is described further below. Moreover, as described in Section 2.5, estimation 

of Equation 3.2 by Ordinary Least Squares (OLS) can lead to bias because equipment stock 

and energy efficiency are likely to be endogenous and therefore correlated with the error 

term. For example, unobserved factors that cause the demand for useful work to be high 

may also cause energy efficiency to be high. This creates a negative correlation between the 

demand for useful work (S) and the energy cost of useful work ( / ε = PP ES ) which is 

additional to that implied by the relationship in Equation 3.2 (Small and Van Dender, 2005). 

Equation 3.1 is a static model that is suitable for use with cross-sectional data. If it is 

assumed that demand is in equilibrium at the point of observation,21 the resulting parameter 

estimates can be assumed to reflect long-run price and income elasticities. But a static 

model is only suitable for time-series data if demand can be assumed to adjust completely 

to changes in prices or income within the unit time period (e.g. one year). This is unlikely to 

be the case for most energy services, since adjustments to equipment capacity take place 

over periods of several years. To address this, a dynamic version of Equation 3.1 needs to 

be employed. 

 

(

),,(

E E

SE

YP

= XYPfS

ZYCAPPS E

= , XgE ),

= f /( ε ),,,

21 Or at least that the relationship between the explanatory variables has been approximately constant in the recent 

past. 

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32 

The partial adjustment model is perhaps the most common dynamic model and is based on 

the assumption that consumers adjust their demand towards a desired level (S*

) over the 

long term. Since this adjustment process takes time, the actual change in the demand for 

useful work in a given time period is assumed to be proportional to the discrepancy between 

the desired value and the previous value: 

 (3.3) SS σ −+= S )( 1

*

−1 −

Where σ ≤≤ 10 . The desired value of demand (S*

) is not observed, but may be eliminated 

by substituting Equation 3.3 into Equation 3.1 to yield an expression in terms of the 

observable variable St.

 (3.4) 

tt tt S

t tttE −1 = fS ,,,( SZYP t )

The result is an equation that includes a ‘one period lag’ of the dependent variable as an 

independent variable. When expressed in algebraic form, the coefficients of PE and Y provide 

estimates of the short-run price and income effects, while the coefficient of the lagged 

dependent variable gives an estimate of the adjustment factor (σ ). These may then be 

combined to give estimates of the long-run price and income elasticities (which should 

always be at least as large as the short-run elasticities). 

The partial adjustment model implicitly assumes that each independent variable has a 

gradually and identically decreasing effect on the dependent variable over time.22 In some 

circumstances this assumption may be inappropriate, so an alternative is to use a 

distributed lag model incorporating explict lags of one or more of the independent variables: 

 (3.5) ( ),

,1 ,1 ,1

∑ ∑ ∑=

−

=

−

=

− = i i i k

it

k

it

k

t E it ZYPfS

Both of these approaches can lead to inefficient parameter estimates when there is 

colliniearity between the lagged variables and the current values of the other variables. Also, 

a major drawback of the distributed lag model is that the larger number of terms reduces 

the degrees of freedom and hence increases the standard error of the parameter estimates. 

In practice, the ‘lag distribution’ may take a number of standard forms and there is some 

debate in the literature as to which form is most appropriate in different circumstances 

(Puller and Greening, 1999).23

Single equation models in both static and dynamic forms provide the basis of a great many 

empirical estimates of the direct rebound effect. Examples include Greene (1992) and 

Orasch and Wirl (1997) for personal transport and Schwarz and Taylor (1995) and Haas, et 

al. (1998b) for household heating. Their popularity results from the fact that compared to 

other models, they require the least amount of information and are relatively easy to 

estimate. However, they do not distinguish explicitly between changes in equipment stock 

and changes in equipment utilisation and the distinction between short and long-run 

 i

ni

∑ ar

= ,1

22 Taking the form of a declining geometric series where r ≤ 1

23 Recent years have seen significant developments in dynamic modelling techniques, notably the introduction of 

cointegration models as a means to solve the problem of ‘spurious regression’ with time-series data (Madlener, 

1996). Spurious regression may arise because both dependent and independent variables move in the same 

direction over time because of some common trend (Granger and Newbold, 1974). Standard models may indicate a 

high goodness of fit, not because of a true association between the variables but because of this common trend. 

The traditional way to deal with this is to include a time trend in the model, but this only acceptable if the common 

trend is deterministic rather than stochastic. Cointegration techniques can deal with this problem and estimate both 

short and long-run demand characteristics (Engle and Granger, 1987). However, to our knowledge, no studies have 

used such techniques to estimate direct rebound effects.

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33 

adjustments is based upon an arbitrary specification of the adjustment process (Bohi and 

Zimmerman, 1984). The final specification depends upon the trade-offs between the 

explanatory power of included or excluded variables, the number of degrees of freedom and 

the problem of multicollinearity. For instance, demographic variables might be expected to 

influence the demand for useful work, but the overall fit of the model can deteriorate when 

these variables are included in the final specification because of the loss of degrees of 

freedom and the possible correlation with other independent variables. Hence, researchers 

might prefer to slightly “bias” their results by omitting demographic variables in order to 

obtain a better overall fit of the model to the rest of the data. 

3.5.2 Structural/simultaneous equation models 

Structural models can provide a more illuminating approach to estimating direct rebound 

effects, but are less common owing to their greater data requirements. 

As discussed in Section 2.1, the demand for useful work may be decomposed in a variety of 

ways to reveal the relative importance of different contributory variables. For example, the 

useful work (S) from household lamps could in theory be measured in lumen hours per year 

and decomposed into the product of the total capacity (CAP) of the lamp stock in lumens 

and the average utilisation of that stock (UTIL) in hours/year: = *UTILCAPS m ε 24 . If is a 

measure of the mean energy efficiency of the lamp stock in lumens/kW, the annual energy 

consumption (E) for household lighting (in kWh) is then given by: = UTILCAPE ε m )/1(** . 

Households can be assumed to make separate, but interrelated decisions on how many 

lamps to purchase, the energy efficiency of those lamps and how frequently to use them. 

For example, lamp utilisation may be expected to depend in part upon the energy efficiency 

of the lamps since this affects running costs, but at the same time the demand for energy 

efficiency may be expected to depend in part upon the expected utilisation. Unlike a single 

equation model, a structural model reproduces this decision-making structure explicitly, 

through the use of separate equations for capacity, utilisation and energy efficiency: 

 (3.8) 

Where ε )( PK represents the capital cost of lamps, which is assumed to depend upon their 

energy efficiency ε )( , and XC, XU and Xε represent vectors of exogenous variables that 

influence the demand for lamp capacity, utilisation and energy efficiency respectively 

(several of which may be common to each). 

In a structural model such as this, the dependent variables are endogenous in that they also 

appear on the right-hand side of the equation. The solution of a structural model therefore 

requires appropriate econometric techniques, such as two-stage least squares (2SLS). For 

cross-sectional data the static model represented by Equation 3.3 is appropriate, while for 

time-series or panel data the model may be specified in a dynamic form in a similar manner 

to that described above (most commonly by including a one period lag of each independent 

variable) 

 

[

],),/[(

],),/(),([

ε

ε

ε ε

= h εε ),( ,, YUTILPP X ],

XYPgUTIL

XYPPfCAP

m K E

mE U

K mE C

=

=

24 A distinction could also be made between the number of lamps (NO) and their average capacity (ACAP) – so 

S=NO*ACAP*UTIL.

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34 

A key advantage of a structural model is that it allows the individual components of price 

and income elasticities, including the direct rebound effect, to be isolated. For example, it 

enables one to estimate how changes in utilisation and changes in capacity individually 

contribute to long-term changes in the demand for useful work or energy - something which 

is hidden by a single equation approach. The improved understanding of how the direct 

rebound effect operates may be useful, for example, when assessing the implications of 

energy efficiency standards for new equipment, since stock-wide energy efficiency is 

determined endogenously. However, the estimation of a set of structural equations such as 

this requires data on, amongst other things, the capacity, utilisation and energy efficiency of 

the equipment stock. For many energy services, this type of data is not available. 

As argued by Small and van Dender (2005), the development of a structural model can 

highlight the potential limitations of many a single equation models. Since the structural 

model (Equation 3.8) is formed of three equations in three unknowns, it may be solved to 

express each endogenous variable solely as a function of the exogenous variables. This 

gives the so-called reduced form equations as follows: 

 (3.9) ,),( ] ε = ε XXXPgUTIL

],,,),([

[ ,,

],,,),([

~

~

~

ε

ε

εε

ε

XXXYPPh

YP

XXXYPPfCAP

m K E UC

K E UC

K E UC

=

=

Equation 3.9 shows that if any one of these variables is to be estimated using a single 

equation approach then (at least in principle) all of the relevant exogenous variables need to 

be included. For example, the capital cost of equipment should be included in an equation 

for equipment utilisation since it affects utilisation indirectly. The same applies to the 

estimation of useful work (S) or energy consumption (E) within a single equation. But in 

practice, many single equation models exclude these variables due to lack of data. At the 

same time, many of them include endogenous variables such as CAP or m ε to give what 

Small and van Dender (2005) term a ‘partially reduced form’ model. In principle, such a 

model needs to be estimated using an instrumental variable technique (see below) to 

account for the endogeneity of these variables, but in practice this is rarely done. Hence, 

many single equation models could potentially lead to biased estimates. 

Structural equation models have been most commonly applied to passenger transport, and a 

number of studies have estimated such models using aggregate data from the US (Archibald 

and Gillingham, 1981; Wheaton, 1982; Mayo and Mathis, 1988; Puller and Greening, 1999). 

The particular specification varies from one study to another, but typically separate 

equations are estimated for the number of vehicles and the annual distance driven (which 

may be specified in total or on a per-capita or per-driver basis) and the average stock-wide 

fuel efficiency. One of the best approaches of this type is Small and Van Dender (2005), who 

estimate such a model using aggregate cross-section time-series data from each US state. 

Other studies have used disaggregate data from household surveys and estimated models 

for the usage of individual cars within multi vehicle households – endogneity occurs here 

because the usage of one car depends upon the usage of others (Mannering, 1983; Golob, 

et al., 1996). A particularly good example is Greene, et al (1998) who estimate separate 

equations for annual distance driven, fuel efficiency and fuel prices for households owning 

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35 

25 one, two, three and four vehicles respectively. However, while this model estimates the 

demand for travel by households with different numbers of cars, it does not explain the 

decision of how many cars to own. This requires a discrete/continuous model, described 

next. 

3.5.3 Discrete/continuous models 

In many structural models, the number or capacity of the equipment stock is treated as a 

continuous variable. While this is appropriate for aggregate data, it may be inappropriate for 

modelling decision-making by individual households. For example, while the aggregate 

vehicle stock may vary continuously over time and between regions, the demand for cars by 

an individual household can only take a discrete number of values (e.g. from zero to a 

maximum of four per household). ‘Discrete choice models’ (or ‘qualitative choice models’) 

calculate the probability that a decision-maker will choose a particular alternative from a 

finite set of alternatives, given data observed by the researcher (Train, 1993). These models 

have been widely employed to predict the demand for various types of energy-using capital 

stock: for example, to predict whether a household will purchase air conditioning equipment, 

given data on income, fuel prices, demographic characteristics, external temperatures and 

other variables (Dubin and McFadden, 1984). The choice set can reflect both the number 

and capacity of the relevant equipment as well as other characteristics such as low or high 

energy efficiency (Hausman, 1979). 

Once the equipment is purchased, the user will make a second decision on the utilisation of 

this equipment - for example, how many hours to run the air conditioning system each year. 

Unlike the first decision, the second may be represented by a continuous variable (UTIL). 

This second choice is conditional on the first (e.g. utilisation must be zero if no equipment is 

purchased) and in general may be expected to depend, at least in part, on the same 

exogenous variables as the first decision. For example, higher incomes may be positively 

correlated with both the ownership of air conditioning systems and the higher utilisation of 

those systems. Endogneity issues also arise, in a similar manner to those described above. 

For example, households whose dwellings for some unobserved reasons tend to become 

unusually hot are both more likely to purchase air conditioning systems and more likely to 

use them during hot weather. 

Sophisticated methods have been developed for specifying and estimating models that 

describe such discrete/continuous situations and these have been applied to the estimation 

of direct rebound effects using household survey data (Dubin and McFadden, 1984; 

Mannering, 1985; Kayser, 2000). The general approach is to estimate an equation for the 

discrete choice of equipment, and then to estimate a second equation describing either the 

utilisation of this equipment or the demand for energy/useful work conditional upon the 

relevant equipment choice.26 Since the values taken by the discrete variable cannot be 

taken as exogenous when estimating the equation for the continuous variable, appropriate 

estimation techniques such as 2SLS are again required. Typically, the choice probabilities 

 

25 Fuel efficiency is endogenous for the reasons given in Section 2.5, while Greene et al argue (rather 

unconvincingly) that fuel prices are also endogenous because the consumer can choose between different gasoline 

stations. 

26 The discrete choice model relies upon ‘conditional indirect utility functions’ for each alternative which specify the 

maximum utility obtainable from a particular discrete alternative given prices and incomes (Train, 1993). 

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27 estimated from the discrete choice equation are used as an instrumental variable (see 

below) for equipment ownership and equipment characteristics when estimating the 

utilisation equation. The endogeneity problem may be avoided, however, if the equipment is 

allocated to individual households as part of a controlled experiment (Davis, 2004). 

As with structural models, the separation of the demand for energy into capital stock and 

utilisation components can help to clarify the differences between short and long-run direct 

rebound effects as well as the relative contribution of each factor. It may also allow the 

impact of specific policy measures such as equipment subsidies to be assessed. 

3.5.4 Household production models 

As illustrated in Section 2.1, the household production model provides an illuminating 

framework for exploring household energy demand, since it treats energy and capital as a 

means to provide energy services, with utility being derived from these services rather than 

from energy itself. Several researchers have estimated such models for household energy 

use (Archibald and Gillingham, 1981; Quigley and Rubinfield, 1989) although the key 

innovation introduced by Becker (1965) – namely the importance of time costs - has 

generally been overlooked. Moreover, even when time costs are ignored, the onerous data 

requirements of the household production approach have restricted its range of application. 

A good illustration of this approach is provided by Klein (1987; 1988), who estimates a 

household production model for a household demand for space heat (useful work). Klein 

specifies the total cost of space heat as a function of the demand for space heat, the capital 

cost of energy efficiency (e.g. insulation), energy prices, the internal area of the house and 

heating degree days. Klein also specifies a second equation for the share of energy in the 

total cost of space heat, and a third equation for the demand for space heat as a function of 

household income, the price of space heat and other variables. These simultaneous 

equations are estimated using appropriate methods to give estimates for the elasticity of 

substitution between energy and capital in the production of space heat as well as price and 

income elasticities for the demand for space heat. On the basis of these, Klein estimates 

short and long-run elasticities for the demand for energy. 

It is possible to incorporate dynamic adjustment into a household production framework in a 

similar manner to that indicated above. However, since these models require more detailed 

data on equipment costs than is generally available, their further application is dependent 

upon the availability of high quality micro data sets. 

3.6 Functional Forms 

The functional form refers to the manner in which the dependent variable is related to the 

independent variables (e.g. whether the relationship is linear or nonlinear). The options 

include the following: 

Linear: β β21 E ++= β3

YPS ( P E SPS E /)( η = β 2 ) 

Log-linear: ln S = β + β21 E + β3YP ( ))( η PE = β 2PS E

Double-log: S β1 β2 E ++= lnlnlnln β3

YP ( ))( η S = β 2 PE

 

27 The final choice may be the outcome of a decision tree, with the probability of the final decision calculated from 

the product of the probability in each stage. 

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The linear functional form in real numbers is rarely used nowadays because of the 

advantages that are associated with the transformation of the data in natural logs. Hence, 

the most popular forms are log-linear or double-log.28 Both are easy to specify and estimate 

and the resulting coefficients may be easily interpreted as short-run demand elasticities - 

with the standard errors providing measures of the variability of these estimates. An 

important drawback of the double-log specification is that it assumes that elasticities are 

constant and do not vary with the level of the independent variables or over the estimated 

sample period. It also imposes a multiplicative relationship between the variables,29 which is 

not always justifiable on theoretical grounds (Plourde and Ruyan, 1985; Madlener, 1996). A 

‘Box-Cox test’ may be used to test the relative appropriateness of different specifications, 

while a ‘Box-Cox transformation’ may be used to make such models more appropriate to the 

data - however, the resulting model must then be estimated using non-linear techniques 

such as ‘maximum likelihood’. 

While double-log specifications are more popular for the estimation of single equation and 

structural models, the translog specification is more popular for the estimation of cost 

functions and associated share equations within household production models (Christensen, 

et al., 1973).30 This form – which has become standard in empirical tests of production 

theory – has a strong basis in economic theory and imposes a minimum of restrictions on 

demand behaviour (Madlener, 1996). However, it is more difficult to estimate and interpret 

and frequently leads to a greater loss of degrees of freedom, because of the many 

parameters involved in estimation.31 

3.7 Estimation Techniques 

The wide variety of methodologies and datasets encourages the use of many different 

estimation techniques – with several studies using more than one technique and comparing 

the results. The main techniques found in the literature include: 

 Ordinary Least Squares (OLS): This is the standard approach, but the conditions 

required for these estimators to be unbiased and efficient are frequently violated. 

OLS results are sometimes provided solely for comparison. 

 Feasible Generalised Least Squares (FGLS): This approach can deal with 

heteroskedasticity32 in studies using cross-sectional data and is frequently used in 

time-series studies to correct for serial correlation in the error terms. 

 Instrumental variables (IV): This provides a means to estimate model parameters 

when one or more explanatory variables are endogenous. The instrumental variable 

substitutes for the endogenous variable and must be partially correlated with the 

latter as well as uncorrelated with the error term. 

 

28 Terminology here is inconsistent, since the double-log formulation is also referred to as log-linear. 

29 The double log formula implies that 2 3

1

β β = β E YPS

30 The cost function is the dual of the production function. A brief discussion of the translog functional form is 

contained in Annex 1 of Technical Report 3 and Annex 2 of Technical Report 5. 

31 This drawback is particularly important for dynamic specifications, since the introduction of lags further reduces 

the degrees of freedom. 

32 This means that the variance of the error terms depends upon the magnitude of the independent variables. As an 

example, the variability of food consumption increases with income. Heteroskedasticity makes estimation by OLS 

inefficient. 

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 Two-stage least squares (2SLS): This is an IV technique for structural equation 

models. The first stage is to estimate the ‘reduced form’ equations for each of the 

endogenous variables, in which each endogenous variable is expressed solely as a 

function of the exogenous variables. The second stage is to use the predicted values 

of the endogenous variables from the first stage as instrumental variables in the 

structural equations. The latter may then be estimated by OLS. 

 Three stage least squared (3SLS): This is a related and more sophisticated approach 

that also takes into account the covariance between the error terms. 

 Fixed effects (FE), between effects (BE)) and random effects (RE): These techniques 

are all suitable for panel data and make different assumptions about whether and 

how the relevant parameters vary between units and over time.33 

 Logit/Probit/Tobit: The Logit and Probit techniques are used when the dependent 

variable is binary, while the Tobit is used when the dependent variable is zero for a 

non-trivial portion of the population and takes continuous values for the remainder. 

 Maximum likelihood (ML): This is suitable for the estimation of non-linear models as 

well as discrete models such as Tobit. Variations of the technique (like FullInformation ML or Limited Information ML) are also used. 

3.8 Summary 

Based upon the analysis in Section 2, the relevant evidence base for the direct rebound 

effect has been identified as econometric studies that estimate one or more of the 

elasticities listed in Table 3.1. In practice, however, estimates of energy efficiency 

elasticities are relatively rare, while estimates of the own price elasticity of the demand for 

energy (while numerous) provide a relatively poor approximation to the direct rebound 

effect. As a result, the literature survey in Sections 4 to 6 is largely confined to econometric 

estimates of the elasticity of the demand for useful work with respect to the energy cost of 

useful work and/or the price of energy. However, some estimates of the own-price demand 

for energy are also included, since in theory these provide an upper bound to the direct 

rebound effect. 

The definition and measurement of key variables should be taken into account before any 

comparisons of empirical estimates are made. Given the above criteria, the econometric 

evidence base for direct rebound effects is largely confined to those energy services where 

useful work can be easily defined and measured. Even for these services, the particular 

measure of useful work vary from one study to another and may hide technical and 

behavioural factors that are relevant to direct rebound effects, such as changes in vehicle 

load factors. Measurement difficulties typically lead to many relevant variables being 

excluded and the measurement or estimation of the key variables of energy consumption, 

useful work and energy efficiency is usually far from straightforward. 

Individual empirical studies also vary widely in terms of the type of data employed, the 

model structure chosen, the functional forms used and the estimation techniques employed. 

Table 3.1 summarises the different choices available. Note that the appropriate choice for 

 

33 Fixed effects controls for omitted variables that differ between cases but are constant over time; between effects

controls for omitted variables that change over time but are constant between cases; and random effects allows for 

omitted variables that vary both over time and between cases. 

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functional form and estimation techniques depends upon the type of data and model 

structure. 

It is difficult to make general statements regarding the relative methodological quality of 

different choices under each of these categories. Single equation models using aggregate 

cross-sectional or time-series data are the most popular and easiest to estimate, but they 

typically neglect the endogneity problem and do not separate the relative effect of changes 

in equipment capacity and changes in utilisation. Structural models perform better in this 

regard but have correspondingly greater data requirements, while discrete/continuous and 

household production models are more demanding still and are largely confined to 

disaggregate studies using comprehensive household survey data. Some model structures 

may be used to estimate both short-term and long-term direct rebound effects, while others 

may only estimate one or the other. Since the direct rebound effect can vary over time and 

have multiple repercussions within sectors, studies using pooled cross-section or panel data 

may be more likely to provide robust estimates. However, such data sets are less widely 

available. Examples of all these categories are included in the subsequent sections. 

Table 3.2 Summary of econometric approaches to estimating the direct rebound effect 

Category Choices available 

Aggregate versus Disaggregate 

Cross-section; 

Type of data Time-series; 

Pooled cross-section; 

Panel 

Static versus dynamic

Single equation; 

Model structure Structural; 

Discrete/continuous; 

Household production 

Linear 

Log-linear Functional form Double log 

Translog 

Ordinary Least Squares (OLS); 

Feasible Generalised Least Squares 

(FGLS); 

Instrumental Variables (IV); 

Two-stage least squares (2SLS); 

Estimation technique Three-stage least squares (3SLS); 

Fixed Effects (FE) and Random Effects 

(RE); 

Error Correction (ECM); 

Logit/Probit/Tobit; 

Maximum Likelihood (ML) 

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4 Evidence for direct rebound effects for personal 

automotive transportation 

4.1 Introduction 

The demand for motor fuels by passenger vehicles is one of the best studied areas in energy 

(and transport) economics. It is also the best studied areas for the direct rebound effect, 

partly because relatively good data is available on distance travelled as a measure of useful 

work. There is therefore greater consensus on the size of direct rebound effects for this 

energy service than for any other energy service. This is not to say that the empirical 

literature is without weaknesses, bias or controversies. For example, the methodological 

approaches are diverse, problems of measurement error are common there are far more 

studies of direct rebound effects in the US than in other OECD countries, and there is 

inconsistency between the results of studies using aggregate data and those using 

household survey data. Nevertheless, personal automotive transportation provides one of 

the few areas where the evidence base for the direct rebound effect is strong and where the 

size of the effect can be estimated with some confidence. 

This section reviews this literature in some detail, using it to illustrate the broader 

methodological issues associated with obtaining econometric estimates of the direct rebound 

effect. It begins by reviewing the large empirical literature containing estimates of the fuel 

price elasticity of gasoline demand and the demand for travel In principle, these should 

provide upper and lower bounds on the size of the direct rebound effect. It then reviews a 

selection of studies that estimate either the elasticity of distance travelled with respect to 

fuel efficiency ( S)( ηε ), or he elasticity of distance travelled with respect to the fuel cost per 

kilometre ( S)( PS η ). In principle, both of these should provide more accurate estimates of 

the direct rebound effect. These studies are organised according to the type of data they 

use, distinguishing between: a) aggregate time-series data or cross-sectional data; b) 

aggregate panel data; and c) disaggregate (household survey) data. The literature review is 

not entirely comprehensive, but includes the most prominent studies in this area and pays 

particular attention to those that are considered to be methodologically robust. 

4.2 Setting bounds on the direct rebound effect for personal automotive 

transportation 

A large number of studies estimate own-price elasticities of the demand for motor fuels (E) 

by passenger cars ( E)( PE η ), while a much smaller number of studies estimate price 

elasticities of the demand for distance travelled (S). Of the latter, the majority estimate the 

elasticity of demand for distance travelled with respect to the price of fuel ( S)( PE η ), while 

relatively few estimate either the elasticity of distance travelled with respect to fuel 

efficiency ( S)( ηε ), or the elasticity of distance travelled with respect to the fuel cost per 

kilometre ( S)( PS η ). 

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The elasticity of distance travelled with respect to fuel efficiency ( S)( ηε ) provides a direct 

measure of the rebound effect, while the elasticity of distance travelled with respect to the 

fuel cost per kilometre ( S)( PS η ) relies upon the assumption that the response to a change in 

fuel prices is equal and opposite to the response to a change in fuel efficiency. Whether this 

‘symmetry’ assumption is valid is a key issue for the studies reviewed below. But the reason 

for making this assumption is both to increase the degrees of freedom and provide for 

greater variation in the independent variable. Many studies have insufficient variation in fuel 

efficiency (and/or excessive measurement error) to base estimates of the direct rebound 

effect on S)( ηε so they rely instead upon S)( PS η . 

In principle, estimates of S)( ηε and/or S)( PS η should provide the most accurate estimates 

of the direct rebound effect for personal automotive transportation. The studies are 

therefore discussed in detail in the following sections. However, for the reasons discussed in 

Section 2.5, estimates of the own-price elasticity of fuel demand ( E)( PE η ) should, in 

principle, provide an upper bound for the direct rebound effect, while estimates of the fuel 

price elasticity of distance travelled ( S)( PE η ) should provide a lower bound. Hence, it is 

useful to summarise these estimates in the case of personal automotive transportation. 

Since personal automotive transportation is one of the best studied energy services, there 

are number of comprehensive reviews and meta-analyses of published elasticity estimates 

(Goodwin, 1992; Espey, 1998; Hanley, et al., 2002; Graham and Glaister, 2004). These 

reviews cover a wide range of different countries and time periods, which may contribute to 

the large variance in results. For example, Hanley et al (2002) reviewed 69 studies 

containing 491 different elasticity estimates from more than 20 countries and regions spread 

over the period 1929 to 1991. 

Table 4.1 summarises the mean values of the estimates of E)( PE η from each of these 

reviews, while Tables 4.2 and 4.3 summarise the mean values of the estimates of S)( PE η . 

While Table 4.2 refers to studies of the 34 total distance travelled by all automobiles , Table 

4.3 refers to studies of the distance travelled per vehicle. In principle, the former should be 

greater than the latter since changes in fuel prices should also lead to changes in the 

number of vehicles. Table 4.4 summarises estimates of the elasticity of vehicle numbers 

with respect to the price of fuel ( NO)( PE η ), while Table 4.5 summarises estimates of the 

elasticity of fuel efficiency (per vehicle) with respect to the price of fuel (η ε )( PE ). The tables 

distinguish between static models that provide only a single elasticity estimates and 

dynamic models which allow short and long-run elasticities to be identified (see Section 

3.5.1). In each case, the tables show the mean of the estimates and the number of 

estimates on which this figure is based. In addition, the results from Hanley et al (2002) 

also show the range and standard deviation. 

 

34 The terms automobile, vehicle and car are used interchangeably in this section to refer to the privately-owned 

vehicles used for passenger travel. However, identifying measures for vehicle numbers, distance driven and fuel 

consumption for these vehicles is far from straightforward. For example, an increasing volume of passenger travel 

takes place in light trucks and vans that may also be used for the transport of light goods. 

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Table 4.1 Elasticity of automobile fuel consumption with respect to fuel prices ( E)( PE η ) - 

summary of empirical literature 

Dynamic Static 

Short-run Long-run 

Hanley et al 

(2002) 

Mean -0.25 -0.64 -0.43 

Standard deviation 0.15 0.44 0.23 

Range -0.01 to -0.57 0 to -1.81 -0.11 to -1.12 

No. of estimates 46 51 24 

Goodwin (1992)

Mean -0.27 -0.73 

No. of estimates 57 53 

Espey (1998) 

Mean -0.26 -0.58 

No. of estimates 277 363 

Graham and 

Glaister (2002) 

Mean -0.2 to - 0.3 -0.6 to -0.8 

Table 4.2 Elasticity of total distance travelled by automobiles with respect to fuel prices 

( S)( PE η ) - summary of empirical literature 

Dynamic Static 

Short-run Long-run 

Hanley et al 

(2002)

Mean -0.10 -0.29 -0.31 

Standard deviation 0.06 0.29 0.14 

Range -0.17 to -0.05 -0.63 to -0.10 -0.54 to -0.13 

No. of estimates 3 3 7 

Goodwin (1992)

Mean -0.16 -0.32 

No. of estimates 4 6 

Graham and 

Glaister (2002)

Mean -0.15 -0.3 

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Table 4.3 Elasticity of distance travelled per automobile with respect to fuel prices ( S)( PE η ) 

- summary of empirical literature 

Dynamic Static 

Short-run Long-run 

Hanley et al 

(2002)

Mean -0.10 -0.30 -0.51 

Standard deviation 0.06 0.23 -0.25 

Range -0.14 to -0.06 -0.55 to -0.11 -0.69 to -0.33 

No. of estimates 2 3 2 

Table 4.4 Elasticity of vehicle stock (automobile numbers) with respect to fuel prices 

( NO)( η P ) - summary of empirical literature E

Dynamic Static 

Short-run Long-run 

Hanley et al 

(2002)

Mean -0.08 -0.25 -0.06 

Standard deviation 0.06 0.17 0.08 

Range -0.21 to -0.02 -0.63 to -0.10 -0.13 to -0.03 

No. of estimates 8 8 3 

Table 4.5 Elasticity of vehicle fuel efficiency with respect to fuel prices (η ε )( PE ) - summary 

of empirical literature 

Dynamic Static 

Short-run Long-run 

Hanley et al 

(2002)

Mean 0.08 1.1 0.30 

Standard deviation n/a n/a 0.22 

Range n/a n/a 0.89 to 0.04 

No. of estimates 1 1 22 

Some key points to emerge from these summaries are as follows: 

 As Equation 2.11 predicts, the elasticities for fuel consumption are generally higher 

than the elasticities for distance travelled - by a factor of 1.5 to 2.0. This 

demonstrates that fuel prices have a considerable influence on fleet average fuel 

efficiency, both through short-term changes in driving styles and the pattern of 

journeys and long-term changes in the mean fuel-efficiency of new vehicles. Only a 

small number of (mostly static) studies estimates this effect directly, with the results 

being summarised in Table 4.5. This suggests that a 10% increase in fuel prices will 

lead to a 3% improvement in fleet average fuel efficiency. 

 For both fuel consumption and distance travelled, the estimated long-run fuel price 

elasticities are found to be at least twice the size of the short-run elasticities, with 

the result from static models falling somewhere between the two. Given the 

limitations of static models, the results from dynamic models should perhaps be 

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given greater weight. However, the estimates of long-run price elasticities exhibit 

considerable variance. 

 The range of estimates for the elasticity of total distance travelled with respect to 

fuel prices is comparable to that for the estimates of distance travelled per vehicle. 

However, in both cases, the number of relevant studies is relatively small. 

 The results do not provide any strong evidence that price elasticities decline over 

time with increasing incomes – as would be expected from the theoretical 

considerations reviewed in Section 2.6. However, there is some evidence that price 

elasticities are related to price levels and were generally higher in the period 

immediately following the oil price shocks in the 1970s (Hanley, et al., 2002). 

Using the mean values of E)( PE η suggests an upper bound for the short-term direct 

rebound effect of 20-25% and an upper bound for the long-term effect of 80%. Similarly, 

using the mean values of S)( PE η suggest a lower bound for the short-term direct rebound 

effect of 10-15% and an lower bound for the long-term effect of 30%. In principle, the 

actual rebound effect should lie somewhere within this range. However, the mean values 

disguise a large variance in the results. For example, using the full range of estimates 

suggests that the upper bound for the long-run direct rebound effect lies somewhere 

between zero and 181%, while the lower bound lies somewhere between 10% and 61%. 

The breadth of this range is not very helpful. Also, the upper bound is likely to be a 

significant overestimate of the direct rebound effect since it neglects the effect of fuel prices 

on fuel efficiency – which appears to be substantial (Table 4.5). 

Using Extension 2, the mean estimates of E)( PE η (Table 4.1) and η ε )( PE (Table 4.5) may be 

combined to give an estimate of the elasticity of distance travelled with respect to the fuel 

cost per kilometre ( S)( PS η ). This leads to an estimate of the long-run direct rebound effect 

in the range 18% (static estimates) to 49% (dynamic estimates). The upper value is higher 

than obtained from most studies that directly estimate S)( PS η - reviewed in detail below. 

Also, these studies generally produce estimates of the long-run direct rebound effect that lie 

below the mean value of the lower bound (30%) implied by Table 4.2. Hence, direct 

estimates of S)( PS η are not wholly consistent with the ‘bounds’ on the direct rebound effect 

calculated above. 

A notable weakness of most of the studies included in these reviews is that they assume 

that the effect of a price reduction on demand is equal and opposite to the effect of a price 

increase. This is at odds with the literature on the price asymmetry of energy demand 

(Dargay, 1992; Gately, 1993), which includes studies of the road transport sector (Gately, 

1992b; Walker and Wirl, 1993). For example, Dargay and Gately (1994) estimate the ownprice elasticity of gasoline demand in the US transport sector to be -0.21 during periods of 

rising prices, but only -0.04 during periods of falling prices. For studies using time-series 

data, the extent to which neglect of this price asymmetry can lead to biased estimates of 

elasticities in general and the direct rebound effect in particular will depend upon the price 

trends (in real terms) over the period in question. Since an improvement in fuel efficiency 

corresponds to a reduction in fuel prices, it is possible that the direct rebound effect is 

significantly smaller than suggested by elasticities estimated during periods of rising fuel 

prices. The incorporation of asymmetric price responses should therefore be a priority for 

future research. 

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The following three sections review a selection of studies that estimate the price elasticity of 

distance travelled with respect to the fuel cost per kilometre ( S)( PS η ). Provided the studies 

are methodologically robust, they should provide a more accurate estimate of the direct 

rebound effect than the figures quoted in the above tables. The studies are grouped as 

follow: 

 studies using either aggregate time-series data or aggregate cross-sectional data; 

 studies using aggregate panel data; and 

 studies using disaggregate (household survey) data. 

4.3 Evidence from studies using aggregate time-series or cross-sectional data 

This group of studies uses aggregate data on road fuel consumption; fuel prices, distance 

travelled and/or fleet average fuel efficiency taken from a either a single region or country 

over an interval of time (time-series), or a number of regions or countries at a single point 

in time (cross-section). Each study estimates the elasticity of the demand for travel with 

respect to the fuel cost per kilometre (PS) – which is in turn estimated from the ratio of fuel 

prices to fleet average fuel efficiency ( /ε PE ). The direct rebound effect may be estimated 

from this elasticity, but not all the studies mention the rebound effect explicitly. Although 

the studies vary greatly in terms of model structure and other factors, the estimated values 

for short and long-run direct rebound effects appear broadly comparable. Table 4.6 provides 

a summary of the studies reviewed. 

One of the first studies to derive an estimate for the direct rebound effect from S)( PS η was 

Blair et al. (1984b). This used monthly time-series data from Florida covering the period 

1948 to 1976. As with many studies from the 1970s and early 1980s, the available historical 

data provided relatively little variation in fuel prices in real terms. More recent studies that 

incorporate the effect of the second oil price shock of 1979-1982, together with the 

subsequent oil price collapse of 1986, benefit from greater variation in the independent 

variable. 

Blair et al estimated a static equation for total distance travelled by the vehicle fleet as a 

function of fuel cost per kilometre, income and population, together with a second equation 

for fleet average fuel efficiency as a function of fuel prices and income. A third equation for 

the number of vehicles would have been useful, but was not feasible due to lack of data. 

Blair et al employ a linear functional form, which means that the estimates of S)( PS η

depend upon the particular values of fuel cost per kilometre and distance traveled. Using 

data from 1970, Greene (1992) puts their estimate of the direct rebound effect to be 

between 25% and 40% depending upon the method of estimation used (OLS and GLS 

respectively). 

Mayo and Mathis (1988) use US national data covering the period 1958 to 1984, which 

includes the large increase in gasoline prices that followed the two oil shocks. Following Blair

et al, they estimate equations for total distance travelled and fleet average fuel efficiency, 

but are able to distinguish short and long-run elasticities by using a dynamic specification 

incorporating a one period lag of the dependent variable. They justify omitting an equation 

for vehicle stock on the grounds that only income is significant in predicting vehicle 

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numbers, although the more recent meta-analysis by Hanly et al (2002) suggests that this 

assumption is incorrect (Table 4.4).35 

Mayo and Mathis find the short-run direct rebound effect to be 22% and the long-run effect 

to be 26%. However, the coefficient on the lagged dependent variable in their distance 

equation is not statistically significant (t=0.73), making the long-run estimate questionable 

(Greene, 1992). The distance equation is estimated using 3SLS, owing to the presence of 

‘serial correlation’ in the error terms. Serial correlation means that the error in one time 

period is correlated with the error from one or more previous time periods, perhaps as a 

result of the influence of unobserved variables that persist over time. Identifying and 

correcting for serial correlation is a major issue in time-series econometrics and is relevant 

to many of the studies reviewed here. 

A notable result from the Mayo and Mathis study is that US regulatory standards on 

‘corporate average vehicle fuel efficiency’ (CAFE) were not found to have a statistically 

significant effect on either fleet average fuel efficiency or the demand for gasoline. But since 

the standards were imposed about the same time as a major increase in fuel prices occured, 

and also became more stringent as fuel prices increased in the early 1980s, it may be 

difficult to separate the two effects (Small and Van Dender, 2005). To the extent that 

comparable problems arise in other US studies, this could influence estimates of the direct 

rebound effect. In contrast, Greene (1996) argues that the CAFE standards were successful 

in improving on-road fuel economy in the US by 50% over the period 1975 to 1995. 

Gately (1990) uses US national data over the period 1966-88 to estimate an equation for 

the total distance travelled by cars and light trucks. He employs a static, double-log 

equation to give an estimated direct rebound effect of 9%, for both the short and long term. 

An interesting feature of this study is the inclusion of a measure of the number of licensed 

drivers, rather than population. The ratio of the two varies significantly over time and the 

first should be more relevant to vehicle ownership and use. Gateley argues that omission of 

this variable in previous studies may have led the income elasticities of gasoline and travel 

demand to be overestimated. 

One of the most rigorous studies of the direct rebound effect using aggregate data is that by 

Greene (1992), who uses US national data covering the period 1957-1989. Following 

Gately (1990), Greene estimates an equation for total distance traveled by cars and light 

trucks as a function of fuel cost per kilometre, income and the number of licensed drivers. 

Fleet average fuel efficiency is estimated from total car and light truck vehicle kilometres 

divided by the total fuel consumption of these vehicles. A notable feature of this study is the 

use of different model specifications to address two linked problems: namely the appropriate 

lag structure for dependent and/or independent variables and first order serial correlation in 

the error terms. The presence of the latter, which is confirmed, suggests that the 

appropriate model structure is one that contains one period lags of each independent 

variable as well as the dependent variable, although this reduces the degrees of freedom. 

Greene finds that once serial correlation is accounted for, the coefficient on the lagged 

dependent variable is no longer significant. The surprising implication of this is that long-run 

direct rebound effects are no greater than the short-run effects, which Greene estimates to 

be between 5% and 15%. He argues that the reason other studies found significant long-run 

 

35 Table 4.4 suggests that fuel prices have a significant influence on vehicle numbers. However, these results derive 

from a small number of studies and hence should be treated with caution. 

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47 

effects was that they failed account properly for serial correlation. Greene explains the 

absence of a long-run effect by noting that fuel costs account for less than 10% of long-run 

travel costs. If correct, similar conclusions should apply to an even greater extent to other 

household energy services where energy forms an even smaller proportion of (long-run) 

total costs. 

Greene also finds that estimates of the direct rebound effect are relatively insensitive to the 

functional form of the equation used, as well as to the lag length and the particular lag 

structure. He also finds that the number of vehicles and the number of licensed drivers are 

so closely correlated that their respective effects on distance driven are indistinguishable – 

suggesting that a measure of one or the other should be sufficient. One particularly 

interesting result is that the direct rebound effect over the period 1978-89 is estimated to 

be only 5.9%, compared to 27.4% over the period 1966-77. This suggests that the direct 

rebound effect declines with income as theory predicts, but little confidence can be placed in 

this result as it is only statistically significant at the 10% level. 

The value of Greene’s study is further enhanced by Jones (1993) re-examination of 

Greene’s data. While Jones confirms that the statistical model selected by Greene is valid, 

other models including those with the lagged dependent variables also appear consistent 

with the data. These give a long-run direct rebound effect of around 30%, which (in contrast 

to Greene’s results) is approximately twice the short-run effect. One drawback with the 

dynamic models, however, is that they estimate the income elasticity of the demand for 

travel to be approximately zero, which seems implausible. In summarising his results, Jones 

notes that: “.....we are not completely sure about the long-run rebound effect, but if it does 

exist, it is probably not very large.” 

In a more recent study, Schimek (1996) uses US aggregate data for a longer time period 

than Greene and estimates a system of three equations for the number of vehicles, fleet 

average fuel efficiency and total distance travelled. Applying formal tests, Schimek is able to 

reject the possibility that endogeneity is biasing the results, which means he can avoid the 

use of simultaneous equation models and estimate each equation using OLS. This 

specification provides estimates for the direct rebound effect from both and , 

which are found to be approximately equal in magnitude and opposite in sign. This gives a 

short-run direct rebound effect of 5-7% and a much larger long-run effect of 21-29%. 

S)( PE ηε S)( η

All the above studies use aggregate data from the US, so the results may be specific to the 

US context. European countries for example have greater population density than the US, 

higher fuel prices, higher levels of fuel efficiency and greater scope for substitution to other 

transport modes, all of which may influence short-run price elasticities. Unfortunately, 

estimates of from aggregate time-series data for other countries appear to be rare. 

However, an alternative approach is to use data from multiple regions or countries at a 

single instant of time. This may give wider variation in the relevant independent variables 

(e.g. fuel prices), although results may be influenced by inter-country differences which may 

not be measurable. 

S)( PS η

An early but relatively robust example of this approach is Wheaton (1982), who uses 

cross-section data from 25 countries for the year 1972 (i.e. prior to the first oil crisis). 

Wheaton develops separate equations for the number of vehicles per capita, the average 

distance travelled per vehicle and the average fuel efficiency of the vehicle fleet. The latter 

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S)( ηε

NO)( ε

is estimated from sales weighted data on new car fuel efficiencies in each country, which 

provide a poor approximation to on-road fuel efficiency (Schipper, et al., 1993) 

Although Wheaton specifies a structural model, he estimates the three equations using OLS 

since tests show the relative absence of endogneity bias. This gives an elasticity of distance 

travelled with respect to fuel efficiency ( ) of +0.06, suggesting a rebound effect of 

only 6%.36 However, since the dependent variable is distance travelled per vehicle, the 

direct rebound effect may be expected to be smaller than in the other studies reviewed here 

(since η is not accounted for). Also, the reliability of the result depends upon the 

accuracy of the fuel efficiency estimates, which are questionable. In contrast to Schimek 

(1996), Wheaton finds that the elasticity of distance travelled with respect to fuel prices 

( ) is significantly larger than the elasticity of the demand for travel with respect to 

fuel efficiency (( ). The estimated magnitude of is -0.5, suggesting a much 

larger direct rebound effect of 50%. The disparity between these two figures could result 

from measurement error or may suggest that the standard assumption regarding the equal 

and opposite effect of changes in fuel prices and changes in fuel efficiency is incorrect. This 

assumption is only tested in the small number of studies that have sufficient variability in 

both fuel prices and fuel efficiency to obtain statistically significant estimates of both 

elasticities. As will be seen below, Wheaton’s study is not the only one to question the 

symmetry assumption. 

S)( PE η

S)( ηε S)( PE η

One drawback with all the above studies is that they pay insufficient attention to the quality 

of data sources. Problems include the inappropriate use of total gasoline consumption as a 

proxy for the fuel consumed by automobiles, the uncertainties in estimates of distance 

driven obtained from roadside counts or surveys of vehicle users, and the uncertainties over 

the number of cars in use in each year (Sorrell, 1992; Schipper, et al., 1993). For example, 

many countries measure automobile fuel consumption (E) as the residual after the 

estimated fuel consumption of trucks, buses and other vehicles is removed. This estimate is 

then calibrated against estimates of automobile fuel efficiency (ε ) and total distance driven 

(S), thereby creating a circularity between the estimates of these three variables. Hence, 

using any two of these variables to estimate the third (as Wheaton does) may be 

inappropriate. These measurement difficulties may have been compounded by the 

increasing use of light trucks for personal transport in the US and the increasing penetration 

of diesel vehicles in Europe. While the difficulties can be resolved to some extent, the size of 

the measurement error may in some circumstances be comparable to the size of the 

variation in key variables. 

In summary, studies using aggregate time-series and cross-sectional data estimate the 

long-run direct rebound effect for personal automotive transport to be somewhere between 

5% and 30%. While there is disagreement over the appropriate specification, particularly 

in relation to the appropriate treatment of serial correlation and lagged dependent variables, 

the limited number of data points available makes it difficult to settle the issue from this 

type of data alone. Also, since the available studies refer solely to the US and use relatively 

old data, it is not possible to establish whether any confidence whether price elasticities 

have declined over time or whether they are substantially different in other countries. 

 36 From Table 2, using the 25 countries sample with undeflated prices (Wheaton, 1982).

48 
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Table 4.6 Estimates of the direct rebound effect for personal automotive transport using aggregate time-s

Author/year 

Shortrun 

rebound 

effect 

Longrun 

rebound 

effect 

Country Data Model structure Functional form Es

te

Blair (1984a) 25-40% 25 – 40% US Monthly TS for Florida 1967-76 Recursive (S and ε ) Static Linear OMayo and Mathis(1988) 22% 26% US TS 1958-84 National Recursive (S and ε ) Dynamic Linear and Double log Gateley (1992b) 9% 9% US TS 1966-88, National Recursive (S and ε ) Static Double log, incorporating asymmetric effects Greene (1992) 

5-19% 

(linear) 

13% 

(loglinear) 

5-19% 

(linear) 

13% 

(loglinear) 

US TS 1957-89, 

National 

Single 

equation 

(S) 

Static and 

dynamic 

Linear and 

log-linear 

Jones (1992) 13% 30% US TS 1957-89, National 

Single 

equation 

(S) 

Static and 

dynamic 

Linear and 

log-linear 

Schmiek (1996) 5-7% 21-29% US TS National 

Recursive 

(S, ε &

NO) 

Dynamic 

Double log 

Double Log 

Recursive 

(S, NO &

ε )

Dynamic 

XS 1972 25 OECD countries Wheaton (1982) 6% 6% 
50 

4.4 Evidence from studies using aggregate panel data 

Some of the limitations of the above studies may be addressed through the use of 

aggregate panel data. This gives a much larger number of data points that includes both 

cross-sectional and temporal variations in the relevant variables. Both theory and empirical 

evidence suggests that panel data should provide more efficient parameter estimates (i.e. 

lower variance) (Baltagi and Griffin, 1983). The US is particularly fortunate in this respect 

since high quality time-series data is available from 50 different states as well as the District 

of Columbia, which may be combined to form a very large panel dataset. This section 

summarises two studies that estimate the rebound effect from cross-country panel data and 

two that use aggregate panel data from the US. The results are summarised in Table 4.7. 

Orasch & Wirl (1997) use aggregate panel data from France, Italy and the UK covering 

the period 1971 to 1993. They estimate an equation for distance travelled as a function of 

fuel cost per kilometre, income and a one-period lag of the dependent variable. Their 

estimates of the short-run direct rebound effect are 10% for the UK and almost 20% for 

France and Italy, while the long-run equivalents are 27% for the UK and almost 30% for 

France and Italy. 

Johansson and Schipper (1997) use cross-country panel data to study the determinants 

of automobile fuel demand in 12 OECD countries. They estimate a recursive system of 

equations for the number of vehicles, the mean fuel efficiency of the vehicle fleet and the 

mean annual driving distance per vehicle. They rule out the possibility of the simultaneous 

determination of fuel efficiency and driving distance on theoretical grounds, thereby 

avoiding the need for simultaneous equation techniques. However, since the possibility of 

bias is not investigated empirically, this assumption may be flawed. Also, they assume (but 

do not test) that changes in fuel prices have an equal and opposite effect on distance driven 

to changes in fuel efficiency - justifying this on the grounds of maximising the degrees of 

freedom. 

Johansson and Schipper’s study is notable for two reasons. First, very careful attention is 

paid to the quality of the data sources from each country, with fuel use being disaggregated 

between gasoline, diesel, LPG and CNG. This makes the study less vulnerable to 

measurement error than, for example, Orasch & Wirl (1997). Second, they use several 

different estimation methods, including OLS, GLS and 2SLS, and take some care in pointing 

out the possible drawbacks of each. In the case of the distance equation, the independent 

variables are strongly correlated, leading to a high variance on the parameter estimates and 

reduced confidence in the elasticity estimates. 

The use of a structural system of equations allows the change in total distance driven to be 

decomposed into changes in distance driven per vehicle and changes in the vehicle stock. 

The former is found to be more important than the latter, with ‘best value’ elasticity 

estimates of -0.2 and -0.1 respectively. If the long-run direct rebound effect is measured on 

the basis of total distance driven by the vehicle fleet, this leads to a best guess estimate of 

30% (with a range from 5% and 55%). In contrast, if the rebound effect is measured on the 

basis of distance driven per vehicle, this leads to a ‘best guess’ estimates of 20% (with a 

range from 5% to 35%.). Both estimates are at the upper end of the range in the literature 

and highlight the importance of the appropriate choice of dependent variable. The estimate 

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51 

of the long-run own-price elasticity of fuel demand (-0.7) is also at the upper end of the 

range. 

Haughton and Sakar (1996) use US state-level data covering the period 1972 to 1991. 

They estimate seperate equations for fleet average fuel efficiency and kilometres driven per 

driver, with fuel consumption being calculated from the product of these two variables and 

the number of drivers. A 2SLS method is used to allow for simultaneous determination of 

these two variables, but this is not found to greatly influence the results. Although the 

authors refer to Greene’s (1992) estimate of the direct rebound effect, they fail to note the 

difference between their dependent variable (kilometres per driver) and the one used by 

Greene (total vehicle kilometres). These two variables are not equivalent, since the same 

vehicle kilometres can be driven by two or more drivers. However, in contrast to the use of 

kilometres per vehicle for the dependent variable, this is unlikely to have a major influence 

on the estimated rebound effect. 

Haughton and Sakar estimate a dynamic equation for fleet average fuel efficiency that 

includes a variable representing the highest real fuel price reached in the years preceding 

the current year. This implies that high fuel prices induce improvements in fuel efficiency 

that remain in place when fuel prices subsequently fall (‘hysteresis’). They find that the 

current price of gasoline does not affect fuel efficiency unless it rises above its previous peak 

– demonstrating again the price asymmetry of energy demand.37 They also include a 

variable representing the difference between the CAFE standard in the current year and the 

average fuel efficiency in 1975. However, the strong correlation between this variable and 

gasoline prices makes it difficult to separate the two effects, suggesting that alternative 

specifications of the CAFE standard need to be found (Small and Van Dender, 2005). 

Distance driven per driver is estimated as a function of income, the fuel cost per kilometre, 

population density, the proportion of drivers in the total adult population38 and a one period 

lag of the dependent variable. This leads to an estimated short run direct rebound effect of 

between 9% and 16%, and a long-run effect of 22%, with relatively little variation between 

different model specifications. Haughton and Sakar find serial correlation in the error terms, 

but unlike Greene (1992) they find that the coefficient on the lagged dependent variable is 

still significant when serial correlation is accounted for - implying that the long-run direct 

rebound effect is at least a third larger than the short-run effect. The advantages of 

Haughton and Sakar’s panel dataset compared to Greene’s time-series data gives some 

confidence in this conclusion. 

Small and van Dender (2005) provide one of the most methodologically rigorous 

estimates of the direct rebound effect for passenger travel, incorporating a number of 

important innovations. As with Haughton and Sakar, they employ aggregate panel data from 

all 50 US states, but since this data covers a longer time period (1961-2001) their 

parameter estimates may be expected to be more precise. By estimating simultaneous 

equations for fleet average fuel efficiency, vehicle numbers and vehicle kilometres travelled 

(both of which are normalised to population rather than number of drivers), they provide 

one of the few studies to explicitly address the endogneity problem discussed in Section 2.5. 

 

37 While fuel prices are found to be significant, Haughton and Sakar observe that the link between US fuel prices 

and new car fuel efficiency may be weakening, as the US car market is becoming increasingly influenced by the 

demands of the European and Japanese markets. 

38 As a greater proportion of adults become drivers, the amount driven per driver is likely to fall. Secondary drivers 

tend to drive less as the total amount of driving is distributed more widely. 

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52 

In this case, endogneity appears to be very important since, compared to the use of 2SLS 

and 3SLS, estimation of the individual equations by OLS leads to the short and long-run 

rebound effects being overestimated by 88% and 53% respectively (although it is possible 

that factors other than endogneity contribute to this). 

In contrast to Haughton and Sakar, Small and van Dender represent the CAFE standards by 

a variable indicating the gap between the mandated fuel efficiency and an estimate of the 

fuel efficiency that would have been chosen in the absence of the standards. The latter is 

obtained from a partial adjustment model that incorporates pre-1977 data and estimates 

the demand for fuel efficiency as a function of fuel prices, taking into account the difference 

between the test performance of vehicles and their on-road fuel efficiency.39 Small and van 

Dender are able to develop both short and long-run elasticity estimates through the use of a 

lagged dependent variable, but at the same time employ an estimation procedure that 

addresses the problem of serial correlation without introducing bias. Most importantly, by 

interacting the fuel cost per kilometre and income variables, they are able to allow for the 

fact that the response to changes in fuel costs may vary with income (since, as incomes 

increase, fuel costs account for a declining proportion of the generalised cost of car travel 

while time costs account for an increasing portion). This elasticity is also allowed to vary 

with spatial density and the level of fuel costs itself. 

Small and Van Dender estimate the short-run direct rebound effect for the US as a whole to 

be 4.5% and the long-run effect to be 22%. The former is lower than most of the estimates 

in the literature, while the latter is close to the consensus.40 However, they estimate that a 

10% increase in income reduces the short-run direct rebound effect by 0.58% – as the 

theoretical considerations reviewed in Section 2.6 predict. Using US average values of 

income, urbanisation and fuel prices over the period 1997-2001, they find a direct rebound 

effect of only 2.2% in the short-term and 10.7% in the long-term - approximately half the 

values estimated from the full data set. If this result is robust, it has some very important 

implications. However, two-fifths of the estimated reduction in the rebound effect derives 

from the assumption that the magnitude of this effect depends upon the absolute level of 

fuel costs per kilometre. But since the relevant coefficient (on ) is not statistically 

significant, the claim that direct rebound effects have fallen is called into question. 

2 PS

Despite its methodological sophistication, Small and Van Dender’s study is not without its 

problems. First, despite covering 50 states over a period of 36 years, the data provides 

relatively little variation in vehicle fuel efficiency making it difficult to determine its effect 

separately from that of fuel prices. This is illustrated by an alternative specification that 

allows for separate estimates of S)( PE η and S)( ηε . While S)( PE η is found to be 

approximately equal to the original estimate of S)( PS η , S)( ηε is found to be small and 

statistically insignificant. Since S)( ηε is a more direct estimate of the direct rebound effect 

than S)( PS η , this could be interpreted as implying that the direct rebound effect is 

approximately zero. However, the new specification performs rather poorly overall, with 

 

39 Small and van Dender estimate that, in the absence of the standards, increases in fuel prices in real terms would 

have led to a gradually increasing demand for more fuel-efficient vehicles. As a result, while the CAFE standard is 

estimated to have been binding since 1997, its tightness has gradually diminished and was largely ineffective in 

2001. 

40 They estimate the long-run, own-price elasticity of gasoline demand to be -0.43, which is also in the mid-range 

of recent studies (Table 4.1). 

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S)( PS

several of the coefficients becoming unstable with respect to the inclusion or exclusion of 

other variables. This leads Small and Van Dender to prefer the original specification and (as 

with most studies) to base their estimates of the direct rebound effect on η . 

Second, the difference between the estimated direct rebound effect in individual states and 

the national average depends upon the difference between the state’s income and the 

national mean (i.e. states with higher incomes have rebound effects that are below the 

national mean). But as shown by Harrison et al (2005), this leads to the implausible result 

that the direct rebound effect in some states (including Connecticut and the District of 

Columbia) is negative. This raises questions about the validity of the results and particularly 

about the use of the model for projecting declining rebound effects in the future (since 

increasing incomes could make rebound effects negative in many states). 

In summary, both cross-country and regional panel data provide substantially more 

observations than time-series or cross-sectional data and thereby provide a more robust 

basis for estimates of the direct rebound effect. Three of the studies reviewed above are 

very carefully done, incorporate important methodological innovations and should be given 

some weight in forming a judgement about the magnitude of the direct rebound effect for 

personal automotive transport. Johansson and Schipper’s (1997) cross-country study gives 

results at the high end of the range in the literature (i.e. a best guess for the long-run direct 

rebound effect of 30%), while both Haughton and Sakar and Small and van Dender 

converge on a long-run value of 22% for the US. 

53 

Small and van Dender’s results provide a strong indication that the direct rebound effect 

declines with increasing income - as theory predicts. If so, this result has considerable 

importance for future policy in this area. However, their model has a number of weaknesses 

and their result is not supported by Hanley et al’s (2002) meta-analysis of other studies in 

this area. Hence, this issue should be a priority for further research. 
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Table 4.7 Estimates of the direct rebound effect for personal automotive transport using aggregate panel Author/year 

Shortrun 

rebound 

effect 

Longrun 

rebound 

effect 

Country Data Model structure Functional form E

t

Orasch & Wirl, 1997 10-20% 27 – 30% UK, France, Italy Aggregate Panel (X- country) KOKO Single equation (

S) 

Dynamic 

Double Log 

Johansson and Schipper (1997) 

5 – 55% 

Best 

guess: 

30% 

12 OECD 

Aggregate 

Panel (Xcountry)1973-

1992 

Recursive 

(S, ε , NO) Double Log 

Haughton and Sakar (1996) 9 – 16% 22% US 

Aggregate 

Panel (US 

states) 

1973-1992 

Simultaneous 

(S, ε ) Double Log 

Double Log 

Simultaneous 

(S, ε , NO) 

1961-2001 

Aggregate 

Panel (US 

states) 4.5% 22% US Small and van Dender (2005) 
55 

4.5 Evidence from studies using disaggregate data 

A number of studies have used household survey data to estimate elasticities of fuel and 

travel demand for passenger cars. While less common, this approach avoids some of the 

measurement difficulties associated with aggregate data (Schipper, et al., 1993) and has 

the potential to provide very accurate data on distance travelled and fuel consumption. It 

also allows variations in demand patterns between different types of households and/or 

vehicles to be investigated, including in particular how the ownership of two or more 

vehicles can affect price responses (Mannering, 1983). The disadvantage is that the relevant 

datasets are generally larger and more difficult to handle, while the results may be less easy 

to generalise to the national level. Studies using disaggregate data also show greater 

variability in their estimates of the direct rebound effect; with several studies estimating 

rebound effects of 50% or more. 

Disaggregate studies include those that use survey data from a single year (cross-section), 

those that use multi-year data from the same households (panel) and those that use multiyear data from a different sample of households in each sample year (pooled). This section 

contains examples of each and focuses upon a five studies that are considered to be 

methodologically robust. The results are summarised in Table 4.8. 

Goldberg (1996) provides an impressively detailed study of the effect of the CAFE 

standards, drawing upon data from the US Consumer Expenditure Survey covering the 

period 1984-1990, together with additional information on new car fuel efficiency. The CES 

provides comprehensive information on household and vehicle characteristics including 

vehicle ownership, size, age, type, capital costs, operating costs and usage patterns, based 

upon odometer data from each car during each quarter. Following Durbin and McFadden 

(1984), Goldberg estimates a discrete/continuous model for the ownership and use of 

different types of vehicle. In the first stage, Goldberg estimates a four-stage nested logit 

model to give the probability of a household: buying a car; choosing between new and 

second-hand cars; choosing between one of nine categories of new car; and choosing 

between foreign and domestic models. The independent variables vary with each level but 

include capital cost, operating cost per kilometre, size, income and various demographic 

factors. In the second stage, Goldberg estimates an equation for the distance travelled by 

new cars, using the choice probabilities from the discrete choice equations as an 

instrumental variable for vehicle ownership and characteristics (second-hand cars are 

excluded, owing to lack of data on production year and hence fuel efficiency). The direct 

rebound effect can be estimated from this second equation using the estimated value of 

S)( PS η . This elasticity relates to new cars only and since it is conditional on the choice of a 

particular vehicle, Goldberg interprets it as a short-term direct rebound effect. 

Using instrumental variables to estimate the second equation avoids potential endogneity 

bias. To examine the importance of this, Goldberg estimates a reduced form equation using 

OLS and compares the results with the instrumental variable estimation. The results suggest 

that the endogneity bias is significant. Without correcting for this bias, the direct rebound 

effect (using S)( PS η ) averaged across all (new) vehicles is estimated to be 22%. However, 

once the instrumental variable approach is employed, the direct rebound effect becomes 

negative implying that higher fuel efficiency leads to less driving. But since the coefficient in 

this case is highly insignificant, Goldberg’s results essentially imply that the direct rebound 

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56 

effect for new cars is zero. Goldberg’s results also show that S)( PS η for individual vehicles 

within multi vehicle households is larger than for single vehicle households, presumably 

because households can shift to more fuel-efficient vehicles. 

There are a number of qualifications to this result. First, the results are short run, since they 

do not reflect the effect of fuel price/fuel efficiency changes on new vehicle purchases.41

Second, the results apply to new cars alone, although it is not clear why direct rebound 

effects for used cars should be significantly different. Third, the data provides relatively little 

variation in fuel costs and hence may not reflect the hysteresis effects noted by Haughton 

and Sakar (1996). 

Puller and Greening (1999) also use 9 years of data from the US Consumer Expenditure 

Survey (CES), but combine this with data on car fuel efficiency that is taken from a different 

source. Unlike Goldberg, this study includes all vehicles, estimates the distance travelled by 

each household rather than each vehicle, and uses a simultaneous equation model, rather 

than a discrete/continuous model. Since the CES is a ‘rotating panel’ data set (each 

household participates for one year), this means that the study only provides information on 

how households adjust to changes in fuel efficiency or fuel prices within one year. Puller and 

Greening justify this with reference to the meta-analysis by Espey (1996), which indicates 

that 70% of the response to changes in fuel prices occurs within one year. But this 

nevertheless limits the ability of the study to capture long-run changes in vehicle stock (as 

with the Goldberg study, although for different reasons). 

Puller and Greening estimate simultaneous equations for the average fuel efficiency of each 

household (i.e. averaged across all vehicles) and the total distance travelled by each 

household, excluding business mileage (note that Goldberg included business mileage). The 

specification includes the current gasoline price and gasoline prices in the previous four 

quarters, together with income, demographic characteristics the price of new vehicles and 

the endogenous variables. Vehicle age is not included, although it is known to be strongly 

correlated with both fuel efficiency and vehicle utilisation. This is potentially important, since 

it could induce a spurious correlation between fuel cost per kilometre and distance travelled, 

by their mutual correlation with vehicle age (Greene, et al., 1999a). The fact that attention 

is confined to non-business travel could also be important, since this may be expected to be 

more responsive to changes in the fuel cost per kilometre. 

Based upon the estimated elasticity of distance travelled by the household with respect to 

fuel costs per kilometre ( S)( PS η ), Puller and Greening estimate the direct rebound effect to 

be 49%. This is significantly larger than the estimates from studies using aggregate data, 

despite the fact that it relates solely to the short to medium-term and despite the fact that it 

is based upon the same data as Goldberg’s study, which estimates the direct rebound effect 

to be zero. Puller and Greening also estimate that a 1% increase in fuel prices would result 

in 0.22% decrease on-road in fuel efficiency (i.e. η ε < 0)( PE ). The explanation given is that 

households respond to fuel price increases by cutting back on long journeys, such as 

vacations, which generally have higher fuel efficiency than short trips. Hence, higher fuel 

prices encourage households to reduce fuel consumption and fuel costs, but in doing so they 

 

41 From the discrete choice equation, Goldberg estimates that 1% increase in fuel efficiency increases the 

probability of buying a particular vehicle type by 10%. But she does not indicate the effect on the probability of 

buying any vehicle. 

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57 

worsen average fuel efficiency. The same response is unlikely in the long term, since higher 

fuel prices should encourage the purchase of more fuel-efficient vehicles (Table 4.5). 

The two equation model gives an own-price elasticity of gasoline consumption of -0.47, 

which is within the range of other studies.42 However, the finding that the fuel price 

elasticity for fuel efficiency is negative means that Puller and Greening’s estimates for 

S)( PS η and S)( PE η are not consistent with Equation 2.11. This provides a partial 

explanation for why the estimated direct rebound effect is so high, while the omission of a 

variable for vehicle age and the exclusion of business travel may provide additional 

explanations. Puller and Greening also estimate a single equation model for gasoline 

consumption, which gives a lower elasticity of -0.32. But many of the parameters of this 

equation are not significant, the model shows very poor goodness of fit and an alternative 

pooled model (including data points from all nine years) gives fuel price elasticities greater 

than unity which are considered implausible. 

Greene et al. (1999a) is a very comprehensive and methodologically rigorous study, 

based upon US household survey data of vehicle ownership and use that covers six different 

years over the period 1979 to 1994 (i.e. pooled data with ~3000 households and ~6000 

vehicles in each survey). The particular advantage of this study – at least in the US context 

- is the detailed treatment of multi-vehicle households. 

Greene et al. estimate different sets of simultaneous equations for households with one, 

two, three, four and five (!) vehicles. For single vehicle households there are three 

equations for distance driven, fuel efficiency and fuel prices,43 while for two vehicle 

households there are two sets of three equations - and so on. These equations reflect two 

sources of endogenity. First, the fuel efficiency of a vehicle will depend upon its (expected) 

usage, while its usage will depend upon its fuel efficiency (Section 2.5). Second, the 

utilisation of one car will depend upon the utilisation of another (e.g. if you use one car to 

drive to the shops, you won't be using the other) (Mannering, 1983). Higher fuel prices may 

be expected to encourage greater use of the more fuel-efficient car in the household. Also, 

while the usage of one vehicle will directly affect the usage of a second vehicle, it will also 

indirectly affect the on-road fuel efficiency of that vehicle via its effect on usage. 

Distance driven is estimated as a function of the on-road fuel efficiency of the vehicle, 

together with current gasoline prices and other household, vehicle and location variables 

including vehicle age. In turn, on-road fuel efficiency is estimated as a function of distance 

driven, current gasoline prices and other variables, including the average fuel efficiency of 

all cars produced in the model year of the relevant vehicle.44 Current fuel prices affect onroad fuel efficiency through changes in how the vehicle is used. However, the model does 

not explain the decision of how many vehicles to own, or the choice of new-car fuel 

efficiency. As a result, it cannot be used to estimate the long-run own-price elasticity of 

gasoline consumption because it does not represent the effect of fuel prices on the fuel 

 

42 Since E=S/ε, taking logs and differentiating with respect to the fuel price gives: εηηη )()()( . pE pE pE SE −=

43 Fuel prices are claimed to be endogenous because drivers can react higher fuel prices by searching harder for 

cheaper fuel and because if you travel further you pass more petrol stations with a greater range of prices. Neither 

argument is convincing and the empirical evidence for this endogneity is weak. 

44 Unlike Puller and Greening, distance driven includes business use, although this is included as a right hand side 

variable. 

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58 

efficiency of new vehicle purchases. Echoing Puller and Greening’s results, Greene et al find 

that current fuel prices have a negative effect the on on-road fuel efficiency of vehicles, 

presumably because drivers cut back on long distance travel. 

Greene et al test the hypothesis that consumers respond symmetrically to changes in fuel 

prices and changes in fuel efficiency. This is done by imposing the restriction that the 

coefficients of fuel prices and on-road fuel efficiency in the distance travelled equation sum 

to zero. This hypothesis is not rejected, lending support to the symmetry argument - and 

thereby supporting the findings of Schimek (1996) but not those of Wheaton (1982) or 

Small and van Dender (2005)). However, the R2

 for the distance traveled equation for one 

vehicle households is only 0.29 and the fact that the adjusted autocorrelation coefficients 

are consistently high for the fuel cost equation but not for the utilisation equation suggests 

potential misspecification. 

By manipulation, Greene et al estimate the total system elasticity of household travel 

demand with respect to fuel efficiency ( S)( ηε ) for each level of vehicle ownership. This is 

taken as a measure of the long-run direct rebound effect, since the data consists of different 

households in different circumstances spanning a 15 year time interval. This may be an 

underestimate, since the model does not represent the influence of fuel prices and fuel 

efficiency on the number of vehicles owned (including the purchase of a vehicle for the first 

time). Greene et al argue that this effect should be small because fuel costs form less than 

10% of vehicle ownership costs (an argument that can be used for other energy services), 

but this is not supported by the results summarized in Table 4.4. Greene et al estimate the 

long-run direct rebound effect to range from 17% for three-vehicle households to 28% for 

one-vehicle households. Weighting by the distance driven by each type of household gives 

an average long-run direct rebound effect of 23%, which compares well with the estimates 

from aggregate data (including Haughton and Sakar (1996) and Small and van Dender 

(2005)). Since income growth leads to more households owning multiple vehicles, the 

results also suggest another reason why the direct rebound effect may decline with income, 

West (2004) is the third study to use the US Consumer Expenditure Survey, this time for a 

detailed investigation of the distributional effects of vehicle pollution control policies. Unlike 

Goldberg (1996) and Puller and Greening (1999), this study uses cross-sectional data from 

a single year of the survey (1997), which is supplemented by additional information on 

vehicle fuel efficiency. The latter uses data from a survey of 667 vehicles in California as the 

basis of a regression equation on vehicle age and engine size.45 

Following Goldberg, West estimates a discrete/continuous model for the ownership and use 

of different types of vehicle. In the first stage, West estimates a nested logit model that 

gives the probability of choosing one of 18 combinations of the number (between one and 

two), age and engine size of vehicle. Independent variables here include capital cost, 

operating cost per kilometre, income and various demographic factors. In the second stage, 

West estimates an equation for the total distance travelled by the household, using the 

choice probabilities from the discrete choice equation as an instrumental variable for vehicle 

ownership and characteristics. 

 

45 It is notable that each of the 3 studies which rely upon the US CES estimates the fuel efficiency of vehicles from 

a different data source. 

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59 

As with Puller and Greening, the use of distance travelled by the household as the 

dependent variable means that study overlooks any response to fuel prices by shifting to the 

more fuel-efficient vehicle (in two-car households)46 – although the study by Greene et al

suggested that this is of some importance. Using the correction for endogeneity, West 

calculates the elasticity of demand for distance travelled with respect to the operating cost 

per kilometre of vehicles, conditional upon vehicle choice. Using the sample means of 

distance travelled, operating cost per kilometre and total expenditures, this gives an 

elasticity of -0.87. Operating cost is defined as the sum of fuel costs, maintenance costs and 

tyre costs per kilometre and is therefore greater than fuel costs alone.47 The estimated 

magnitude of direct rebound effects therefore depends upon the share of fuel costs in total 

operating costs - which in turn will vary with the age and fuel efficiency of the vehicle. Since 

West does not provide a breakdown of operating costs at the sample mean, the best that 

can be said is that the study suggests an upper bound for the direct rebound effect of 87%. 

In practice, it appears likely that fuel costs will form at least half of the operating costs as 

defined here, suggesting a direct rebound effect of 40% or more. West’s estimate of the 

direct rebound effect is therefore much larger than obtained from studies in using aggregate 

data. 

Finally, Frondel, et al (2007) provide a rare example of a European study using household 

survey data. Their data source is the German Mobility Panel, comprising a group of 

households surveyed for a period of six weeks in spring in three consecutive years. Frondel 

et al’s sample of 293 single-car households is significantly smaller than in the studies 

reviewed above, but includes data on monthly distance driven, monthly fuel consumption, 

vehicle age and other demographic variables A notable feature of this study is the 

estimation of direct rebound effects from three different elasticities derived from three 

different models, namely: a) S)( ηε with fuel prices as a control variable; b) S)( PS η

imposing the restriction that the response to a change in fuel efficiency is equal and 

opposite to the response to a change in fuel prices ( SS )()( PE ηε = −η ); and c) E)( PE η from a 

regression of fuel consumption on fuel prices and other variables. In the case of the second 

model, the null hypothesis of equal and opposite coefficients is not rejected, thereby lending 

support to the symmetry argument. 

Frondel, et al (2007) also estimate each model in three different ways, namely fixed effects, 

between effects and random effects (see Section 3.7). Fixed-effects controls for timeinvariant factors that vary across households while between-effects controls for household 

invariant factors that vary over time. Random effects allow for factors that vary both 

between households and over time. 

What is notable about this study is that the estimates of the rebound effect appear 

remarkably insensitive to either the choice of elasticity measure or the choice of estimation 

method – thereby suggesting that they are robust. In all cases, the direct rebound effect is 

estimated to lie between 56% and 66%, which is significantly higher than the consensus 

 

46 The fuel efficiency of vehicles used by a two-car households is taken as a simple average, thereby implicitly 

assuming equal use of each vehicle. 

47 Insurance costs are not mentioned. West notes that time costs and expected accident costs are omitted from the 

definition of operating costs. Since the former is determined largely by income, regressions that include total 

operating costs give positive coefficients – implying that higher operating costs increase the demand for distance 

travelled. A better approach, therefore, is to exclude time costs from operating costs and include income as a 

separate variable. The dependence of rebound effects on income could then be investigated through the use of 

interaction terms (i.e. income*fuel costs). 

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values results from US studies. However, given the small sample size, it is not possible to 

judge whether this reflects any systematic difference between Germany and the US. 

In summary, studies using disaggregate data sources provide much less consistent 

estimates of the direct rebound effect than those using aggregate data sources. Moreover, 

several of the estimates are significantly higher than those from aggregate data sources. 

While disaggregate data should avoid some of the measurement difficulties reported by 

Schipper et al (1993), the greater complexity of the models can create some difficulties of 

interpretation - especially when discrete/continuous models are used. It is notable that 

three of the studies use data from the US Consumer Expenditure Survey taken from 

overlapping periods, but nevertheless produce estimates of the direct rebound effect that 

range from 0% to 87%. This diversity suggests that the results from disaggregate studies 

should be interpreted with a much greater caution. 

60 

Of the studies reviewed, Greene et al (1999) provides the most careful investigation of the 

direct rebound effect, albeit neglecting long-term changes in the vehicle stock. This study 

also produces an estimate of the long-run direct rebound effect (23%) which is consistent 

with the results of aggregate studies. As with the aggregate studies, there is again a strong 

bias towards studies from the US. While Frondel et al’s study is suggestive of large rebound 

effects in Germany, the small sample size, the lack of comparable studies from Europe and 

the inconsistency between these results and those of aggregate estimates of fuel price 

elasticities provide an insufficient basis to conclude that direct rebound effects are larger in 

Europe. Indeed, a number of theoretical considerations suggest that rebound effects should 

be smaller. 
UK Energy Research Centre UKERC/WP/TPA/

Table 4.8 Estimates of the direct rebound effect for personal automotive transport using disaggregate datAuthor/year 

Shortrun 

rebound 

effect 

Longrun 

rebound 

effect 

Country Data Model structure Functional form Es

te

Goldberg, (1996) 0% US 

Rotating 

panel 

1984-1990 

(CES) 

Discrete/ 

continuous 

Double Log 

(utilisation 

equation) 

N

(d

In

v

(u

Puller and Greening (1999) 49% US 

Rotating 

panel 

1980-1990 

(CES) 

Simultaneous 

equation 

(dynamic – 

single year) 

Double log 

Greene (1999) 23% US 

Pooled cross 

section 

(travel 

survey) 

Simultaneous 

equation Double log 

West (2004) 87% US 

Crosssection 

(CES - 

1997) 

Discrete/ 

continuous 

Double Log 

(utilisation 

equation) 

N

(d

In

v

(u

Fix

Double log Single equation Frondel (2007) 56-66% Germany Panel 
62 

4.6 Summary 

Personal automotive transportation is one of the few areas where the evidence base is 

sufficiently strong to allow the magnitude of the direct rebound effect to be quantified with 

some confidence. This section summarises the main findings. 

First, estimates of the own price elasticity of gasoline demand suggest a mean value of the 

upper bound for the long-term direct rebound effect of 80%. However, this mean value 

disguises a large variance in the results and using the full range of estimates suggests an 

upper bound of between 0 and 181%. The breadth of this range reflects the wide range of 

countries and time periods on which the estimates are based and hence is rather unhelpful. 

Moreover, the majority of these studies assume that the effect of a price reduction on 

demand is equal and opposite to the effect of a price increase. Studies that take price 

asymmetry into account typically find elasticities during periods of falling prices to be 

significantly smaller than those during periods of rising prices. The implication is that price 

elasticities - and hence direct rebound effects - may be smaller than suggested by many 

time-series studies. 

In principle, estimates of the elasticity of distance travelled with respect to either fuel 

efficiency ( S)( ηε ) or the fuel cost per mile S)( PS η should provide an accurate estimate of 

the direct rebound effect. Estimates of the latter are more common in practice, owing to the 

greater variation in the independent variable (PS) and the additional degrees of freedom this 

provides. However, these estimates rely upon the assumption that that the response to a 

change in fuel prices is equal and opposite to the response to a change in fuel efficiency. 

Few studies test this assumption explicitly and those that do are either unable to reject the 

null hypothesis that the two elasticities are equal, or find that the fuel efficiency elasticity is 

less than the fuel cost per mile elasticity. Again, the implication is that the direct rebound 

effect may be smaller than suggested by the results of many of the studies reviewed here. 

The studies reviewed vary considerably in terms of the data used and the specifications 

employed. Most studies use aggregate data that can in principle capture long-term effects 

on demand like fuel efficiency standards or price-induced technical change. Disaggregated 

studies better describe household behaviour at the micro level. However, aggregate studies 

face numerous measurement difficulties, while disaggregate studies are more difficult to 

implement and produce results that are more difficult to generalise. Also, the relevant 

dependent variable varies between total distance travelled, distance travelled per capita, 

distance travelled per licensed driver and distance travelled per vehicle. 

Studies using aggregate time-series and cross-sectional data estimate the long-run direct 

rebound effect for personal automotive transport to be somewhere between 5% and 30%. 

While there is disagreement over the appropriate specification, the limited number of data 

points available makes it difficult to settle the issue from this type of data alone. 

Aggregate panel data should provide a more robust basis for estimates of the direct rebound 

effect, owing to the greater number of observations. Johansson and Schipper’s (1997) 

cross-country study gives a best guess for the long-run direct rebound effect of 30%, while 

both Haughton and Sakar (1996) and Small and van Dender (2005) converge on a long-run 

value of 22% for the US. Small and van Dender’s study incorporates some important 

methodological innovations and suggests that the direct rebound effect declines with 

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63 

increasing income. However, their model has a number of weaknesses and the results are 

not supported by Hanley et al’s (2002) meta-analysis of estimates of E)( PE η for personal 

automotive transport. 

Studies using disaggregate data sources provide much less consistent estimates of the 

direct rebound effect and several of these estimates are significantly higher than those from 

aggregate data sources. Three US studies using comparable data sources produce estimates 

of the direct rebound effect that range from 0% to 87%. This diversity suggests that the 

results from disaggregate studies should be interpreted with a much greater caution. Greene 

et al (1999) appears the most rigorous of the studies reviewed and estimates the long-run 

direct rebound effect to be 23%, which is consistent with the results of aggregate studies. 

Taken together, the review suggests that the long-run direct rebound effect for personal 

automotive transport lies somewhere between 10% and 30%. The relative consensus on 

estimates, despite wide differences in data and methodologies suggests that the findings are 

robust. Also, the asymmetry of demand responses and the limitations of the ‘symmetry’ 

assumption both suggest that the long-run direct rebound effect may be towards the lower 

end of this range. 

The extent to which the direct rebound effect for this energy service declines with income 

remains unclear, although the methodologically rigorous studies by Small and van Dender 

(2005) and Greene et al (1999a) both suggest that it does. Measurement problems remain 

an issue for aggregate studies, as does the geographical bias towards the United States. The 

evidence reviewed here is insufficient to determine whether direct rebound effects are larger 

or smaller in Europe, but it is notable that the meta-analysis by Espey (1998) found no 

significant difference in long-run gasoline demand elasticities. Overall, it must be concluded 

that direct rebound effects in this sector have not obviated the benefits of technical 

improvements in vehicle fuel efficiency. Between 70 to 100% of the potential benefits of 

such improvements should be realised in reduced on-road fuel consumption. 

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5 Evidence for direct rebound effects for household 

heating 

5.1 Introduction 

After road transport, energy use by households is perhaps the best studied area in the 

economics of energy demand (Madlener, 1996). Since household energy demand is 

dominated by the use of fuel and/or electricity for space heating, the evidence on the 

economics of household heating is relatively good. As a result, the evidence for direct 

rebound effects for this energy service is also relatively good, although weaker than that for 

personal automotive transport. 

As with all energy services, there are two broad approaches to estimating direct rebound 

effects for space heating. The first is to use a quasi-experimental research design that 

includes measurements of the change in demand for either useful work or energy 

consumption following an improvement in energy efficiency. A number of studies that use 

this approach for household heating are reviewed in Technical Report 1, which concludes 

that the methodological quality of most of these studies is relatively poor. Nevertheless, 

they suggest a direct rebound effect for household heating of around 30%, with higher 

values for low income groups 

The second approach relies upon secondary data sources, frequently collected for other 

purposes, that include information on the demand for energy, useful work and/or energy 

efficiency and which use econometric techniques to estimate one or more of the elasticities 

listed in Table 3.1. Most of these studies do not mention the rebound effect explicitly. This 

section reviews a number of studies that follow this second approach, focusing upon those 

that are considered to be methodologically rigorous. While the studies have been selected 

through an extensive literature search, the coverage is not comprehensive. Compared to the 

evidence for personal automotive transport, these studies exhibit a greater range of 

methodological approaches and a greater diversity in empirical results. 

Section 5.2 reviews the empirical literature estimating the own-price elasticity of the total

demand for fuel and electricity by households ( )( η E EtotalP ). In principle, this should provide 

an indication of the upper bound for direct rebound effects for household energy services. 

However, unlike the corresponding estimates for personal automotive transport discussed in 

Section 4.2, these estimates apply to all household energy services and hence are less 

useful in setting bounds on the direct rebound effect for space heating. 

Section 5.3 reviews some of the methodological challenges associated with estimating direct 

rebound effects for space heating, focusing upon the choice of elasticity measures and the 

factors contributing to variations in these measures between different types of household. 

Sections 5.4 and 5.5 then review a selection of studies that provide estimates of the 

elasticity of demand for energy use or useful work for space heating. In principle, each of 

these studies should provide a more accurate estimate of direct rebound effects for space 

heating than reliance upon estimates of )( η E EtotalP . However, the diversity of elasticity 

measures used reflects the rather patchy nature of the evidence base and makes it difficult 

to compare the results of different studies. Section 5.6 concludes. 

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5.2 Setting bounds on the direct rebound effect for household heating 

5.2.1 The importance of heating in household energy consumption 

Measured on the basis of thermal content, household heating dominates household energy 

demand in most OECD countries. In the UK in 2005, for example, space heating accounted 

for 60% of (delivered) household energy use, 72% of household fuel demand and 18% of 

electricity demand.48 Natural gas was the dominant fuel for space heating, with electricity 

accounting for only 6.4%. However, the fuel mix for space heating varies widely from one 

OECD country to another, with electricity playing a significantly more important role in the 

US and Scandinavia and with district heating playing an important role in several northern 

European countries. Changes in energy prices may encourage consumers to switch fuels for 

space heating, while many households use two or more fuels for heating. Also, in countries 

and regions with warmer climates, energy use for space heating may be less important than 

that for space cooling. These factors contribute to a wide variation in energy price 

elasticities between different countries, regions and households. 

Table 5.1 Household fuel use by end use in the UK (tonnes of oil equivalent - 2005) 

Space 

heating 

Lighting and 

Water Cooking Appliances Total 

Solid fuel 468.7 201.7 26.7 - 697.1 

Gas 23,536.0 8,791.4 691.4 - 33,018.8 

Electricity 1,811.4 1,002.1 621.6 6,608.9 10,043.9 

Oil 2,394.4 634.0 64.6 - 3,093.1 

Total 28,210.5 10,629.2 1,404.3 6,608.9 46,853.0 

Source: DTI (2007) 

Table 5.2 Household fuel use by end use in the UK in 2005 (% of total - 2005) 

Space 

heating 

Lighting and 

Water Cooking Appliances Total 

Solid fuel 67.2 28.9 3.8 - 100.0 

Gas 71.3 26.6 2.1 - 100.0 

Electricity 18.0 10.0 6.2 65.8 100.0 

Oil 77.4 20.5 2.1 - 100.0 

Total 60.2 22.7 3.0 14.1 100.0 

Source: DTI (2007) 

5.2.2 Heating elasticities and overall elasticities 

As Table 5.2 suggests, space heating typically accounts for more than two thirds of 

household fuel use in the UK, with most of the remainder being used for water heating. In 

these circumstances, estimates of the own-price elasticity of total household fuel 

consumption using aggregate data should provide a rough indication of the own-price 

elasticity of fuel use for space heating (i.e. )()( η E EheatP ≈η E EtotalP ). This may not be the case 

in other countries if electricity forms a greater share of energy use for space heating or if 

fuel use for non-heating purposes is proportionately more important. Similarly, if electricity 

 

48 Space and water heating combined accounted for 83% of UK household fuel demand. Since 1970, energy use for 

space heating in the UK has increased by 24%, for water heating by 15% and for lighting and appliances by 157%. 

Energy used for cooking has fallen by 16% (DTI, 2007). 

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provides the main energy source for space heating, the own-price elasticity of electricity use 

for heating may be roughly approximated by the own-price elasticity of total household 

electricity demand. Whether such approximations are appropriate for studies using 

disaggregate data sources will depend upon the particular households being studied. 

Whether estimated for electricity or fuel, )( η E EtotalP may not provide an upper bound for 

)( η E EheatP since it is possible (indeed likely) that the own-price elasticity of other energy 

services (e.g., cooking and water heating) is less than )( η E EheatP . In these circumstances, 

)( η E EheatP could exceed )( η E EtotalP , although in the case of fuel use the difference is unlikely 

to be large. Also, many households use more than one energy carrier for space heating and 

there may be scope for long-term substitution between different heating technologies. This 

suggests that )( η E EheatP should be estimated for all heating fuels combined, excluding the 

fuel used for other energy services. But measurement difficulties preclude this option in 

most cases49 and the demand response will depend upon the particular composition of price 

changes. If instead, price elasticities are estimated for each individual fuel, it is possible that 

)( η E EheatP for all fuels combined could be less than )( η E EtotalP for an individual fuel since an 

increase in the price of one fuel relative to another could induce substitution away from the 

fuel whose relative price has increased. These two considerations may therefore partially 

offset each other and their relative importance will depend in part upon the actual scope for 

fuel substitution and the extent to which the prices of different fuels are correlated. 

Fuel use for heating is rarely sub-metered, but it may be estimated by subtracting the mean 

fuel demand during the summer months or by statistical analysis incorporating information 

on heating degree days, appliance ownership and other factors. Hence, in many cases it is 

possible to estimate )( η E EheatP for individual fuels. In cases where a single fuel is used, 

)( η E EheatP should provide an upper bound for the own-price elasticity of ‘useful work’ for 

space heating ( )( η S SheatP ), where a suitable measures for Sheat is kilowatt hours of heat 

output from the heating system. The latter measure, in turn, is a better proxy for the direct 

rebound effect. 

It is difficult to make general statements on the short or long-run price elasticity of total 

household energy demand, since this depends upon the energy carrier, the type of 

household, the particular country or region and the level of household income. Also, price 

elasticities tend to change over time, to vary with the price level (with higher prices 

generally encouraging higher elasticities) and to be asymmetric (with a response to 

increasing energy prices generally being greater than the response to falling energy prices) 

(Kouris, 1982; Berkhout, et al., 2000). To the extent that many studies rely upon double log 

specifications that implicitly assume that elasticities are constant, the latter effect may 

frequently be overlooked. Nevertheless, the estimates summarised below suggest that 

household fuel and electricity demand in OECD countries is price-inelastic (i.e. 

< )1)( η E EtotalP . This suggests that improvements in the energy efficiency of household 

energy services are unlikely to lead to backfire. 

 

49 Nesbakken (2001) is a notable exception. 

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5.2.3 The price elasticity of total household electricity demand 

Generally speaking, there have been rather more studies of household electricity demand 

than household fuel demand. The majority of these apply to the US, where electricity forms 

a greater proportion of household heating demand than in Europe and where in many 

regions there is a large demand for electricity for space cooling. Studies of US electricity 

demand over the period 1945 to 1970 appeared to find very high price elasticities, although 

this may be partly a consequence of the rapid growth in electrical appliance ownership 

during this period.50 For example, Wilson (1971) used a simple cross-sectional analysis of 

77 US cities to estimate an own-price elasticity of electricity demand of -1.33. But with 

ownership of many durable goods reaching saturation levels, such estimates may no longer 

be valid. 

More recent studies have generally provided lower estimates of price elasticities. For 

example, in their review of 18 studies, Bohi and Zinnerman (1984) estimated the short and 

long-run own-price elasticities of residential electricity demand to be -0.2 and -0.7 

respectively. This review was recently updated by Espey and Espey (2004), who conducted 

a meta-analysis of 123 estimates of short-run price elasticities and 125 estimates of longrun price elasticities taken from 36 studies (again, mostly from the US). 

Taken together, the mean values of these estimates suggests an upper bound for the shortterm direct rebound effect for all household electricity services combined of 20-35% and an 

upper bound for the long-term effect of 80-85%.51 However, these values disguise a large 

variance in the results between different countries, regions and households as well as 

between different methodological approaches. For example, using the full range of estimates 

suggests that the upper bound for the long-run direct rebound effect lies somewhere 

between between 4% and 225%, which is an even wider range than found for passenger 

transport. This upper bound is likely to be an overestimate of the direct rebound effect, both 

because the use of )( η E EtotalP neglects the effect of electricity prices on energy efficiency 

(Equation 2.11) and because most of the studies neglect the price asymmetry of energy 

demand behaviour (discussed further below), However, it could also be an underestimate of 

the direct rebound effect for some electricity services since it represents a weighted average 

of all services, implying that some services will be more price elastic and some less. 

5.2.4 The price elasticity of total household fuel demand 

Evidence on the own price elasticity of household fuel demand is more variable and less 

robust than that for household electricity demand, although several studies suggest a lower 

price elasticity than for electricity. For example, in a study of UK households, Baker and 

Blundell (1991) estimate the mean weighted own-price elasticity for natural gas to be -0.41, 

-0.62 and -0.47 for winter, spring/ autumn and summer respectively, while the 

 

50 With lower levels of appliance ownership, electricity is less of a necessity. This could lead to higher price 

elasticities than in the current period. Alternatively, the smaller range of options in terms of the energy efficiency of 

appliances compared to the current period could lead to lower price elasticities (Espey and Espey, 2004). 

51 The short-run elasticities ranged from -0.004 to -2.01, with a mean of -0.35 and a median of -0.28. The long-run 

elasticities ranged from -0.04 to -2.25, with a mean of -0.85 and a median of -0.81. The distribution of the results 

was skewed towards the lower end. The meta-analysis also allowed Espey and Espey to identify how factors such 

as data type and estimation methods influenced the results. For example: studies using non-US data estimated 

electricity demand to be less elastic in the short-run but more elastic in the long-run; short-run electricity demand 

was more inelastic during the energy crisis of the 1970, but not significantly different in the long-run compared 

with either before or after that time; and omission of the price of substitute fuels appeared to bias the results and 

lead to significantly lower estimates of long-run price elasticities. 

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68 

corresponding figures for electricity were -0.67, -0.98 and -1.03. Similarly, following a 

review of four studies, Bohi and Zinnerman (1984) estimate the short and long-run ownprice elasticities of US household gas demand to be -0.2 and -0.3 respectively, compared to 

-0.2 and -0.7 for electricity demand. This review points to an upper bound for the long run 

rebound effect for household fuel consumption in the range 20-70%, while corresponding 

figures from a cross-country analysis by the IEA suggest a figure in the range 25-40% 

(Vouyoukas, 1995). 

Not all results follow this pattern, however. For example, in a review of US estimates of the 

own price elasticity of residential natural gas demand, Dahl (1993) finds short-run estimates 

in the range +0.02 to -0.88 and long-run estimates in the range +1.86 to -3.44. The 

corresponding estimates for heating oil suggested a short-run value of <-0.3, but a long-run 

value of a least -0.6 and possibly a more elastic demand than that for electricity. How much 

more is unclear, because simple dynamic models suggested an elastic price response with 

aggregate data but not with disaggregate data, whereas static models suggest the opposite. 

This area would clearly benefit from a meta-analysis of estimates comparable to that 

conducted by Espey and Espey for electricity. 

5.3 Estimating the direct rebound effect for household heating 

The estimated direct rebound effect for household heating will depend upon the type of 

household being studied and the choice of elasticity measure. Both these issues are 

discussed below. 

5.3.1 Choice of households 

The behavioural response to energy efficiency improvements or changes in fuel prices may 

be expected to vary widely between different demographic groups. In particular, low income 

households may be expected to be more sensitive to price changes, since energy forms a 

greater portion of their total expenditure. There is evidence for this from a number of 

sources, including Baker et al (1989), who find the own-price elasticity of gas (electricity) 

consumption by UK households to be two and a half times (two times) larger for the top 

income decile than for the lowest income decile. However, not all studies find this to be the 

case. For example, Nesbakken (1999) finds that the price elasticity of Norwegian household 

energy demand increases with income.52

In a similar manner, direct rebound effects may be expected to be larger for low income 

groups, since they may be expected to take back more of the energy efficiency 

improvements as improved comfort (Dumagan and Mount, 1993). Hence, a greater 

responsiveness to price changes among low income groups may result both from energy 

forming a greater proportion of total expenditure and the lower baseline level of thermal 

comfort (two factors which are related). Direct rebound effects following heating 

improvements are a key policy issue for the UK, where several million households live in 

‘fuel poverty’ – defined as spending more than 10% of their income on energy. Technical 

Report 1 reviews several UK-based evaluation studies that investigate this issue. 

 

52 The explanation offered is that the marginal utility of energy consumption is low for high income households. 

Thus, a reduction in energy consumption due to energy price increases only gives a small reduction in utility (e.g. 

no longer using the swimming pool). In contrast, the marginal utility of energy consumption is greater for low 

income households, since any curtailment would necessitate considerable reductions in comfort. Since plausible 

explanations can be found for both findings, it is essential to examine the data and methodology of each study. 

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69 

Low income groups are also more likely to live in rental accommodation and may therefore 

have less control over the characteristics of energy using appliances - which are frequently 

chosen by the landlord instead. The response of such households to changes in energy 

prices may therefore be expected to be different from that of owner-occupiers. On the one 

hand, short-run elasticities (determined largely by decisions on equipment utilisation) may 

be expected to be higher than those for owner-occupiers since households in rental 

accommodation are typically on lower incomes. On the other hand, long-run elasticities 

(determined in part by decisions on new and replacement equipment) may be lower due to 

the occupants lack of control over investment decisions (Poyer and Williams, 1992). Baker 

and Blundell (1991) present some estimates of long-run energy price elasticities for the UK, 

disaggregated by type of tenure, which shows this pattern in the case of gas but not for 

electricity (Table 5.3). 

Table 5.3 Estimates of the long-run own-price elasticity of UK household energy demand, 

broken down by type of tenure 

Tenure Gas Electricity 

Mortgaged -0.640 -1.044 

Owner-occupier -0.481 -0.871 

Council tenant -0.330 -0.659 

Rented accommodation -0.333 -0.937 

Source: Baker and Blundell (1991) 

For high income households, saturation effects may be expected to reduce the direct 

rebound effect from improvements in the energy efficiency of household heating systems. 

These include an upper limit to temperature levels, heated space and the duration of use of 

heating equipment. This is analogous to the declining direct rebound effects for personal 

automotive transport, noted in Section 4, although in this case the primary cause is likely to 

be declining marginal utility rather than the declining importance of energy costs relative to 

time costs. However, saturation effects may be disguised in estimates of the (energy 

efficiency or price) elasticity of total household energy consumption, since there may be a 

corresponding increase in fuel/electricity consumption for other uses, such as patio heating. 

5.3.2 Choice of elasticity measure 

The dependent variable for an accurate estimate of the direct rebound effect should either 

be useful work (Sheat) or energy use (Eheat) for space heating. Energy use may be measured 

in kWh energy input to the heating system while useful work may be measured in kWh 

energy output. The relationship between the two may be expressed as , where 

 is the energy efficiency of the heating system. 

ES heatcheat = ε

c ε

However, the energy service provided by the heating system is thermal comfort. To a first 

approximation, this may be measured by the mean internal temperature (Ti) of the occupied 

areas of during the hours of occupation. It may be possible to directly monitor either the 

mean internal temperature of the occupied areas or the thermostat setting, but these two 

measures will not be equivalent. For example, daily average household temperatures will 

generally increase following improvements in the thermal insulation of buildings, even if the 

thermostat setting remains unchanged. This is because insulation contributes to a more 

even distribution of warmth around the house, reduces the rate at which a house cools down 

when the heating is off and delays the time at which it needs to be switched back on (Milne 

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70 

and Boardman, 2000). Also, thermal comfort is determined not just by internal temperature, 

but also by air velocity, humidity and other factors (Frey and Labay, 1988; Dewees and 

Wilson, 1990). Hence, if only internal temperatures or thermostat settings are monitored, 

the contribution of these other factors to improved thermal comfort will be overlooked. 

The amount of useful work (Sheat) required to maintain a particular internal temperature will 

depend upon the heated area or volume (A), the difference between internal and external 

temperatures (Ti-To), occupancy levels (H), solar gain (G), the thermal resistance of the 

house ( ) and other factors (X): i.e. ),,),(,( heat oi GHTTAfS h = − ε h ε . Hence, the energy use 

for space heating will depend upon both the energy efficiency of the heating system ( ) 

and the thermal resistance of the house ( ): i.e. 

c ε

XGHTTAgE ),,),(,,,( heat = − oicc ε ε h ε . 

Thermal resistance, in turn, will depend upon a number of factors such as building 

materials, thickness of insulation, windows, air infiltration, humidity and so on. Hence, an 

appropriate independent variable for an estimate of the direct rebound effect could be , 

, a combination of the two, or one of the elements that comprise such as the level of 

roof insulation. Improvements in (e.g. better insulation) may affect any or all of the 

factors that determine thermal comfort while improvements in will generally only affect 

the amount of fuel required to provide a particular level of heat output. As a result, a 

change in 

c ε

h ε h ε

h ε

c ε

c ε h may have a different effect on the demand for Sheat than a change in ε . Also, 

a change in one of the factors determining h ε (e.g. cavity wall insulation) may have a 

different effect on the demand for Sheat than a change in another factor (e.g. window 

glazing). The estimated magnitude of the direct rebound effect may therefore be expected 

to depend upon the choice of independent variable. 

Energy efficiency elasticities may not provide a suitable basis for estimating the direct 

rebound effect owing to lack of data, measurement error or insufficient variation in the 

relevant measure of energy efficiency. But as described in Section 2, the direct rebound 

effect may also be estimated from the energy cost elasticity of the demand for useful work 

for space heating ( )( η S SheatP ) provided it is reasonable to assume that the change in 

demand for useful work following a change in energy efficiency is equivalent to that 

following a change in energy prices, but opposite in sign. This assumption appears more 

likely to hold for changes in c ε h rather than changes in ε , since the latter may change 

thermal comfort in a variety of ways independently of conscious behavioural change, while 

the former may not. More generally, the use of price elasticities is likely to lead to different 

estimates of the direct rebound effect than the use of energy efficiency elasticities. 

The direct rebound effect may also be estimated from the own-price elasticity of the 

demand for energy for space heating ( )( η E EheatP ), but this measure is likely to overestimate 

the effect owing to the neglect of price-induced improvements in energy efficiency (Box 

5.1). However, more accurate estimates of the short-run direct rebound effect may be 

obtained if energy efficiency can be controlled for within the specification - ε η )( E EheatP - 

where ε h ε c refers to , ε or (preferably) both. This elasticity effectively captures short-run 

changes in equipment utilisation in response to changes in energy prices. Under certain 

assumptions, this may be comparable to the change in equipment utilisation in response to 

changes in energy efficiency. 

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71 

Box 5.1 The importance of price-induced improvements in energy efficiency 

A study by Haas and Schipper (1998) shows how the neglect of price-induced energy efficiency 

improvements can lead to the rebound effect being overestimated. Haas and Schipper estimate ownprice elasticities of total household energy demand ( )( η E EtotalP ) in ten OECD countries over the period 

1970-1993. Elasticities are estimated over the whole period, the period of rising energy prices from 

1970 to 1982 and the period of falling energy prices from 1982 onwards. 

The estimates are rather lower than the consensus in the literature, but the interesting point is the 

dependence of the results upon the time period chosen. For example, in the case of the US the 

estimates are -0.09 (1972-92), -0.32 (1970-82) and zero (1982-92) respectively. Generally, the 

estimated price elasticities are much higher for the period of rising prices (1970-82) than for the 

period as a whole. Moreover, for the period of falling energy prices (1982-92) most estimates are not 

significantly different from zero. Haas and Schipper interpret this result as evidence of irreversible 

improvements in energy efficiency induced during the period of rising energy prices, such as fitting loft 

insulation and tightening building regulations. Haas and Schipper also estimate another set of 

equations which incorporate measures of the energy efficiency of different household consumption 

activities. These provide a better statistical fit to the data and indicate much smaller price elasticities 

(i.e. EE )()( PE PE ηη ε

< ). 

The implication of Haas and Schipper’s results is that the price elasticity of household energy 

consumption is significantly smaller during periods of declining prices than during periods of rising 

prices. Since energy efficiency improvements are analogous to periods of declining energy prices, the 

long-run direct rebound effect may be overestimated if it is based upon energy price elasticities 

estimated from time series data that includes periods of rising energy prices. 

Estimates of long-run energy efficiency elasticities may differ from estimates of short-run 

elasticities owing to long-run adjustment in the number, capacity and utilisation of the 

relevant conversion devices (e.g. boilers) and/or behavioural adaptation to higher 

temperature internal environments. While structural models can identify the relative 

contribution of these different factors, single equation models cannot. However, with the 

exception of low income groups, most households own heating systems of sufficient capacity 

to heat the occupied areas to an acceptable temperature. In these circumstances, the longterm adjustments in the number and capacity of conversion equipment in response to 

improvements in energy efficiency may be relatively small. Hence, estimates of long-run 

energy efficiency elasticities may be comparable to short-run estimates, since both derive 

primarily from changes in equipment utilisation. In turn, estimates of ε η )( E EheatP may 

provide a suitable proxy for both the short and long-run direct rebound effect. 

Hence, this summary suggests that, depending upon the availability and variability of data, 

a range of elasticity estimates could potentially be used as a proxy for the direct rebound 

effect for space heating, including: 

)(Sheat c ηε  : the elasticity of demand for useful work with respect to the energy 

efficiency of the heating system. 

)(Sheat h ηε  : the elasticity of demand for useful work with respect to the energy 

efficiency of the building. 

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72 

)(Eheat c ηε  : the elasticity of demand for energy for space heating with respect to the 

energy efficiency of the heating system. 

)(Eheat h ηε  : the elasticity of demand for energy for space heating with respect to the 

energy efficiency of the building. 

)( η S SheatP  : the elasticity of demand for useful work with respect to the energy cost of 

useful work ( PP cES= /ε ) 

η ε )( E EheatP  : the own-price elasticity of demand for energy for space heating 

controlling for the energy efficiency of the building and/or the heating system. 

The following two sections summarise a number of studies that estimate one or more of 

these elasticities. Each of these studies may be used to derive an estimate of the direct 

rebound effect, although most of the studies do not mention the rebound effect explicitly. 

Several of these estimates were previously cited in the literature review by Greene and 

Greening (1998), but they did not clarify the differences between them. 

All of the studies rely upon disaggregate (i.e. household survey) data corresponding to a 

wide range of geographical areas and time periods which contributes to the diversity of 

results. The discussion seeks to highlight the methodological issues associated with 

estimating direct rebound effects for household heating, as well as summarising the 

empirical results. The studies are grouped under two headings, namely single equation 

models and multiple equation models. 

5.4 Evidence from single equation models 

These studies estimate the demand for either energy or useful work as a function of various 

engineering, economic and demographic variables, compiled from household surveys and 

related data sources. Studies using cross-sectional data are the most common, although 

studies using pooled cross-section or panel data are also available. The number and type of 

independent variables varies widely from one study to another, as does the accuracy of 

measurement of these variables and the methodological approach. If such studies are to be 

used to accurately estimate the direct rebound effect they must including variables 

representing the energy efficiency of the building ( h ε ) and/or the energy efficiency of the 

relevant heating equipment ( c ε ). Importantly, only three of the studies mention the 

rebound effect explicitly. 

Douthitt’s (1986) rigorous study of the demand for heating fuel in Canada is notable for 

both allowing the price elasticity to vary with the level of prices and for paying explicit 

attention to potential selection bias. The data source is a cross-sectional sample of 370 

households from across Canada conducted in 1981-82. The households are classified 

according to the main fuel use for space heating (oil, gas or electricity) and the proportion of 

fuel use attributable to space heating (Eheat) is estimated. This estimate then forms the 

dependent variable for a dynamic single equation model, with the independent variables 

including current and lagged fuel prices, variables relating to the energy efficiency of the 

house ( h ε ) such as the thermal resistance of the walls, the average daytime internal 

temperature and demographic factors such as the number of occupants. The model provides 

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73 

a reasonable fit to the data for each fuel group (adjusted R2 between 0.37 and 0.76) with 

most variables being significant. Douthitt’s sample is biased towards those utilities with 

complete billing records and Greene and Greening (1998) discount the results for that 

reason. But problems of selection bias are likely to be found in many studies using survey 

data and Douthitt (1986) is one of the few studies to both explicitly test for this and to use a 

procedure proposed by Heckman (1979) to correct for it. 

Although in principle, the model could provide an estimate of E)( h ηε , this is not quoted 

(largely because the rebound effect is not Douthitt’s primary interest). Instead, Douthitt 

quotes short and long-run53 estimates of h E EheatP ε η )( for each fuel. Taking this as a proxy 

for the direct rebound effect suggests a short-run effect of between 10% (gas) and 17% 

(electricity). The long-run effect is estimated by setting the lagged fuel price equal to the 

current fuel price (Donnelly and Diesendorf, 1985) and leads to an estimate of between 

25% (gas) and 60% (electricity). A notable result is that the estimated elasticities vary 

widely with the price level faced by each household, being higher for those consumers facing 

higher than average prices. For the latter, the results suggest a long-run direct rebound 

effect of between 24% (oil heating) and 93% (electrical heating) – which suggests that 

improvements in the efficiency of electrical heating systems for these consumers may 

achieve few energy savings. 

In a rare study of the direct rebound effect for space heating, Hseuh and Gerner (1993)

estimate an equation for the household demand for fuel incorporating variables determining 

the cost of warmth. This specification allows the short-run direct rebound effect to be 

estimated from ε η E)( PE , although the presentation of the model makes the results difficult 

to interpret. The study uses cross-sectional data from the 1980-81 US Residential Energy 

Consumption Survey (RECS) which includes information on the demographic characteristics 

of the participating households, the thermal characteristics of their houses, appliance 

ownership and other variables. Attention is confined to owner-occupied, single-family 

detached houses using a single fuel for heating, leading to sample sizes of 1028 (gas 

heating) and 253 (electrical heating) respectively. 

Hseuh and Gerner specify an equation for the demand for the main heating fuel (Etotal) as a 

function of heating and cooling degree days, income, fuel prices, the number of occupants, 

various parameters determining the size and energy efficiency of the building ( h ε ), binary 

variables for the ownership of seven types of appliances (air-conditioners, ovens, water 

heaters, refrigerators and freezers), data on the size of those appliances and cooling degree 

days (interacted with the binary variable for ownership of air-conditioners. The model 

provides a reasonable fit the data with adjusted R2

 of 0.51 (electricity) and 0.59 (gas). 

In principle, the model should allow )(Etotal h ηε to be estimated, but Hseuh and Gerner only 

quote the estimated change in energy consumption following a particular physical change in 

one of the elements determining h ε - such as increasing the thickness of roof insulation by 

one inch. Comparing these estimates with those of engineering model suggests direct 

rebound effect of between 30% and 100% depending upon the type of measure and the 

 

53 Based on Donnelly and Diesendorf (1985), the long-run effect is estimated by setting the lagged fuel price equal 

to the current fuel price. 

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74 

geographical region. However, this may be an overestimate of the direct rebound effect 

since the engineering estimates may be incorrect. 

The model also allows the own-price elasticity of total fuel demand to be estimated, 

conditional on h ε and a particular pattern of appliance ownership - h E EtotalP ε η )( . However, 

this estimate does not control for the energy efficiency of either the heating system ( c ε ) or 

the appliances. Hseuh and Gerner interpret this as a short-run elasticity, corresponding 

primarily to changes in the utilisation of heating equipment following changes in energy 

prices. Greening and Greene (1998) use the estimate of h E EtotalP ε η )( for electrically-heated 

homes as a proxy for the direct rebound effect for space heating, suggesting a short-run 

effect of 35%. However, they ignore the corresponding estimate of 58% for gas heated 

homes, despite the gas equation performing better as a result of the smaller sample size. 

Also, the appropriate proxy for the direct rebound effects for space heating is h E EheatP ε η )(

which will be larger than h E EtotalP ε η )( . The range of 35-58% could therefore be taken as a 

lower bound for the direct rebound effect for space heating implied by this study. 

Schwarz and Taylor (1995) provide a rare example of a study that includes 

measurements of thermostat settings as a dependent variable - although the source and 

accuracy of these measurements is not made clear. As with Hseuh and Gerner, they use 

data from the US RECS, in this case applying to 1984-85 and confined to single family 

households that have a thermostat on their main heating equipment - leading to a sample 

size of 1188. Low income households are excluded, which may mean that the study 

underestimates direct rebound effects for households overall. 

Schwarz and Taylor estimate an equation for thermostat setting (Ti) as a function of energy 

prices, external temperatures (To), heated area (A), household income and an estimate of 

the overall thermal resistance of the house ( h ε ) obtained by combining RECS data with an 

engineering model. The energy output from the heating system (Sheat) is estimated from the 

product of heated area and the difference between internal and external temperature, 

divided by the thermal resistance of the house ( heat TTAS hoi = − /)( ε ). Since Schwarz and 

Taylor are able to derive a proxy estimate of using data on building energy efficiency 

(

Sheat

h ε ), they do not use any data on actual energy consumption for space heating. 

Their equation allows the (building) energy efficiency elasticity of the thermostat setting 

( )(Ti h ηε ) and the corresponding energy efficiency elasticity of the demand for useful work 

( )(Sheat h ηε ) to be estimated. The former represents a behavioural response to lower heating 

costs (as a result of better insulation) while the latter represents the corresponding change 

in demand for useful work - which may not result solely from behavioural change by the 

occupants. Other factors which may affect heating costs, such as the thermal energy 

efficiency of the boiler ( c ε ), were not included in the specification, but these would only lead 

to biased estimates if they were correlated with the included variables. 

The average value of )(Ti h ηε ranged from 0.6% to 2.0% depending upon house size and 

climate – with larger responses in big houses in cold climates. The resulting rebound (or 

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75 

takeback) effect, based upon )(Sheat h ηε varied between 1.36% and 3.41%, which is smaller 

than most other studies in the literature. The behavioural response ( )(Ti h ηε ) is considerably 

smaller than the ‘physical’ response ( )(Sheat h ηε ), which is consistent with theory (Milne and 

Boardman, 2000) provided that a linear relationship between S and Ti can be assumed. 

Since this is a cross-sectional study, the results may be interpreted as a long-run effect. 

Haas et al. (1998a) present some estimates of the direct rebound effect for household 

heating from a cross-sectional survey of ~400 Austrian households. Haas and Biermayr

(2000) provide some additional analysis of this data, together with estimates of the direct 

rebound effect taken from a number of other sources – their main argument being that the 

different sources are broadly consistent in their results. Both studies are marred by 

unconventional terminology (e.g. service factor), unhelpful notation and insufficient 

attention to the content and quality of data sources. For example, the sample size is quoted 

as ~400 households in Haas et al. (1998a) and ~500 in Haas and Biermayr (2000) and the 

source of data on both the energy efficiency of the heating system ( c ε ) and the overall 

thermal integrity of the building ( h ε ) is unclear. Also, the estimates of internal temperature 

are based upon self-reports by the occupants and hence must be considered of questionable 

accuracy. 

The portion of total fuel use that is used for space heating (Eheat) is estimated from a simple 

regression incorporating heating degree days. This is then used as the dependent variable in 

a regression incorporating h ε c , ε , PE, heating degree days (again), number of occupants, 

internal area, income, internal temperature and type of heating system (central or noncentral heating). This leads to three estimates of the direct rebound effect, namely 20% 

from )( η E EheatP , 48% from )(Eheat c ηε and 22% from )(Eheat h ηε . Haas and Biermayr also 

estimate the energy use for space heating as a polynomial function of h ε and find a concave 

relationship that departs from the simple linear relationship that would be expected in the 

absence of a direct rebound effect. The magnitude of the direct rebound effect can be 

estimated from difference between the polynomial and linear curves and suggests an effect 

in the range 15-30% - which is broadly consistent with the elasticity estimates. These 

results suggest that the magnitude of the direct rebound effect varies with the initial level of 

energy efficiency, the amount of improvement in energy efficiency and the type of energy 

efficiency improvement. Importantly, they also find that changes in energy prices (and by 

implication, changes in the price of useful work) only have an impact on the demand for 

useful work when energy prices exceed a certain threshold. 

Guertin et al. (2003) provides some valuable estimates of the direct rebound effect for 

three aggregate categories of energy service in Canadian households – namely household 

heating, hot water and appliances/lighting. They use cross-sectional data from 440 low-rise 

single-family dwellings (188 gas heated and 252 electricity heated) located in seven 

provinces and dating from 1993. This includes comprehensive data on demographics and 

appliance ownership. By examining seasonal demand patterns and other factors, they are 

able to estimate the energy consumption for space heating, hot water and 

appliances/lighting as well as the average internal temperature during the heating season. 

Also, by the use of ‘frontier analysis’ they are able to estimate the energy efficiency of gas 

boilers and other conversion technologies ( c ε ). This enables them to construct separate 

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UK Energy Research Centre UKERC/WP/TPA/2007/010

ES heatcheat

equations for the energy demand for space heating (Eheat) and the demand for useful work 

( = ε

)( S S heatP

). 

On the basis of research by Douthitt (1989) and others, Guertin et al. restrict the own-price 

elasticity for heating and other energy services to be linear function of income. Using 

η suggests a direct rebound effect for household heating in the range 29% (highincome groups) to 47% (low income groups), with a sample average of 39%.54 Since this is 

a cross-sectional study, the results may be interpreted as a long-run effect. The comparable 

estimates for )( η E EheatP are 34% (high-income groups) to 51% (low income groups) and 

43% (sample average) showing again how the use of this measure could lead the direct 

rebound effect to be overestimated. The higher price elasticities for low income groups 

appear to result from a combination of the higher share of energy expenditure in total 

expenditure, the higher share of heating in total energy expenditure and the higher price of 

useful work owing to slightly lower energy efficiencies. Oddly, the results suggest that low 

income households have higher than average internal temperatures, while high income 

households have lower temperatures. 

In summary, the selected studies provide estimates of the short-run direct rebound effect 

for space heating in the range 10-58% and estimates of the long-run direct rebound effect 

in the range 1.4%-60% (Table 5.4). The coincidence of these ranges is arguably consistent 

with the argument that the primary source of direct rebound effects for household heating is 

changes in the utilisation of heating equipment. The diversity of results partly reflects the 

diversity of countries, regions and household types being studied, but is also strongly 

influenced by the different variables used in each study, the measurement errors associated 

with these variables and the different methodological approaches to estimation. Most 

importantly, only three of the studies directly address the rebound effect and the measures 

used to estimate this effect (selected either by the authors or ourselves) varies widely from 

one study to another. Indeed, the number of measures used exceeds the number of studies! 

This diversity demonstrates that the econometric literature has yet to develop a consistent 

approach to this issue. 

 54 The variation in )( heatP S S

η between income groups was much greater for space heating than for other energy 

services. 

76 
UK Energy Research Centre UKERC/WP/TPA/2

Table 5.4 Estimates of the direct rebound effect for household heating using single equation models Author/year 

Shortrun 

rebound 

effect 

Longrun 

rebound 

effect 

Country Data Functional form Estimation technique 

Douthitt (1986) 10-17% 35-60% Canada 

Cross 

section 

1980-1981 

SS: 370 

Double log OLS 

RE e

Elas

Hseuh and Gerner (1993) 

35% 

(electric) 

58% 

(gas) 

- US 

Crosssection 

1980-1981 

SS: 1028 

Gas, 

253 

Electricity 

Double log OLS 

Equ

de

es

Schwarz and Taylor (1995) - 

1.4 - 

3.4% US 

Crosssection 

1984-1985 

SS: 1188 

Double log OLS 

Me

ins

Haas et al. (1998) - 15-48% Austria 

Crosssection 

SS: ~400 

Double log OLS 

RE 

so

Guertin et al.(2003) - 29-47% Canada 

Cross 

section 1993

SS: 440 

(188 gas; 

252 elec.) 

Double log OLS 

U

esti

η 
78 

5.5 Evidence from multiple equation models 

The determinants of the direct rebound effects for space heating may be better understood 

with the use of multiple equation models, including the structural, discrete-continuous and 

household production approaches described in Section 3. However, while there are an 

increasing number of applications of these approaches to space heating, they generally do 

not include data on either c ε h or ε . Hence, while the studies provide good estimates of 

)( η E EtotalP , they are less useful for estimating the direct rebound effect. 

A number of authors have applied the discrete-continuous model to space heating 

(Nesbakken, 1999; Halvorsen and Larsen, 2001; Liao and Chang, 2002). The pioneering 

studies in this area is by Dubin and McFadden (1984), who develop a discrete-continuous 

model of the demand for heating systems and the derived demand for energy. While 

methodologically rigorous and widely cited, the complexity of this model and the associated 

notation system make interpretation difficult. Dubin and McFadden (1984) use crosssectional data from a sample of 313 households undertaken in 1975. They first estimate an 

equation for the probability of choosing a gas or electric heating system, based upon relative 

fuel prices, capital costs, income, average annual demand and other variables. Gas heating 

systems have higher capital costs but lower operating costs and tend to be chosen by higher 

income households. The estimated probability from this discrete choice model is then used 

as an instrumental variable in an equation for the demand for electricity, conditional upon 

the choice of heating system. Dubin and McFadden show how the failure to use instrumental 

variables in this second equation can lead to biased estimates of the price and income 

elasticities of energy demand. 

Using the estimates of )( η E EtotalP for electrically heated households, the short-term direct 

rebound effect can be estimated to lie between 25% and 31%. The long-term estimates of 

E)( PE η are smaller, as they allow for switching from electricity to gas. However, since the 

study contains no information on c ε h or ε ., these figures must be considered as an upper 

bound for the direct rebound effect. 

Nesbakken (2001) provides a more recent example of this approach, using cross-sectional 

data from a sample of 551 Norwegian households in 1990. This differs from the Dubin and 

McFadden study number of ways including: focusing solely upon the energy consumption for 

space heating; allowing choice between four heating technologies (namely electricity only; 

electricity and oil; electricity and wood; and electricity, oil and wood); estimating the choice 

of space heating equipment at one point in time jointly with the utilisation that equipment at 

a later point in time; and estimating these equations simultaneously rather than 

sequentially. The estimates of )( η E EheatP are based upon changes in the average energy 

price and are conditional on the choice of heating system. They vary between -0.15 for 

electricity+oil+wood and -0.55 for electricity only, suggesting that elasticities are lower 

when there is greater flexibility to switch fuels. Using the average value for )( η E EheatP across 

all households suggests a short-term direct rebound effect of 21%. But again, this figure 

must be considered as an upper bound since the study contains no information on c ε h or ε . 

UK Energy Research Centre UKERC/WP/TPA/2007/010
79 

There are fewer examples of household production models since the data requirements are 

onerous. The only example we have found relevant to rebound effects in household heating 

is Klein (1987; 1988). However, Klein uses the same household survey data as, for 

example, Hseuh and Guerner (1993) and Schwarz and Taylor (1995), which in turn is 

comparable in detail to the household survey data used by Douthitt (1986) and others. Klein 

has to supplement this with engineering models of the thermal performance of buildings, 

together with data on the capital cost of energy efficiency improvements, both of which may 

be subject to error. Nevertheless, this suggests that there may be scope for the wider 

application of this approach. 

Klein uses US national household survey data from 1973 and 1981. The former is from a 

survey conducted on behalf of the US Federal Energy Administration while the latter is the 

1981 RECS. Both surveys provide detailed information on energy consumption, energy 

expenditure, demographic characteristics, appliance ownership and the thermal 

characteristics of the buildings. The availability of data on thermostat settings allows the 

demand for space heat (Sheat) to be estimated from the difference between external 

temperature and desired internal temperature. The energy use for space heating (Eheat) is 

estimated from billing data after subtracting the ‘baseload’ demand in the summer months. 

The thermal performance of the household ( h ε ) is estimated from data on thermal 

insulation and secondary glazing, and the annualised capital cost of these measures (PK) is 

estimated from data on installation costs. Similarly, the energy cost of useful work (PS ) is 

estimated by allocating fuel costs among the (estimated) baseload, space heating and space 

cooling demands and adjusting for differences in the c average combustion efficiency (ε ) 

between different fuels (i.e. household specific measures are not available). The sum of PK

and PS provides an estimate of the ‘generalised’ unit cost of space heat (PG) for each 

household (i.e. combining energy and annualised capital costs). 

Klein then specifies an equation for the total cost of space heat (C) as a function of PE, PK, 

S 55

heat, the size of the housing unit and heating degree days. Differentiating this equation 

with respect to energy prices leads to a second equation for the share of energy costs in the 

generalised cost of space heat. A third equation expresses the demand for space heat as a 

function of generalised costs (PG), income, number of household members and heating 

degree days. Since the demand for space heat appears as an explanatory variable in the 

cost equations, and the cost of space heat appears as an explanatory variable in the 

demand equation, the model needs to be estimated using simultaneous equation techniques 

(Klein uses 3SLS). 

The results indicate that the elasticity of demand for space heat with respect to the 

generalised cost of space heat ( )( η G SheatP ) is -0.43 in 1973 and -0.44 in 1981. Klein argues 

that this represents the short-run behaviour of households, since it is conditional on the 

existing capital stock. While Greening et al (1998) quote these figures as estimates of the 

direct rebound effect for space heating, this appears to be incorrect. The rebound effect 

should instead be estimated from the elasticity of demand for space heat with respect to the 

energy cost of space heat ( S)( PS η ). Using mean values of the energy cost of useful work, 

this can be calculated as -0.287 in 1973 and -0.251 in 1981. Hence, Klein’s model suggests 

short-run direct rebound effects for household heating in the range 25% to 29%. 

 

55 This equation uses the ‘translog’ functional form that is widely used within neoclassical production theory (see 

Technical Report 3). 

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UK Energy 

80 

In summary, the multiple equation studies reviewed here give estimates of the short run 

direct rebound effect in the range 15% to 55%, with Klein’s estimates of an effect in the 

range 25% to 29% being the most reliable (Table 5.5). These results are consistent with 

those from the single equation studies reviewed in the previous section. 

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Table 5.5 Estimates of the direct rebound effect for household heating using multi-equation models Author/year 

Shortrun 

rebound 

effect 

Longrun 

rebound 

effect 

Country Data Functional form Estimation technique 

Dubin and McFadden (1986) 25-31% US 

Cross 

section 

1975 

SS: 313 

Discretecontinuous 

Logit 

(discrete) & 

Instrumental 

variables 

(utilisation)

Ele

RE 

c

Nesbakken (2001) 

15-55% 

(average 

21%) 

Norway 

Cross 

section 

1990 

SS: 551 

Discretecontinuous 

Logit 

(discrete) & 

Instrumental 

variables 

(utilisation)

RE 

c

Klein (1987; 1988) 25-29% US 

Pooled cross 

section: 

1973-81 

SS: 2157 

Household 

production 3SLS 

S

co

fu

fo

R

wh
82 

5.6 Summary 

In contrast to personal automotive transport, the available evidence from econometric 

studies does not permit the direct rebound effect for space heating to be quantified with 

much confidence. While this is partly because space heating is inherently more complex 

than personal automotive transport it is also because the topic has received insufficient 

attention in the econometric literature. However, there is no evidence to suggest that 

energy efficiency improvements for space heating will lead to backfire for the majority of 

households. 

The results from the studies reviewed here suggest direct rebound effects in the range 1.4 

to 60%. The diversity of results suggests that quoting a single number for the rebound 

effect for space heating could be misleading, since the effect appears to vary greatly with 

the type of household, fuels used and type of energy efficiency improvement. Many of the 

estimates quoted here are based upon price elasticities, but these may provide a less 

accurate estimate of the direct rebound effect than in the case of personal automotive 

transport. Also, the strong evidence for the price asymmetry of energy demand responses 

for space heating suggests that the true effect may be towards lower rate end of the above 

range. Nevertheless, for the purpose of policy evaluation, a figure of 30% for the direct 

rebound effect for household heating would appear a reasonable assumption, which is 

consistent with the results of the evaluation studies reported in Technical Report 1. 

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6 Evidence for direct rebound effects for other 

household energy services 

6.1 Introduction 

A number of theoretical considerations suggest that direct rebound effects for most other 

household energy services should be less than those for household heating. For example, 

compared to household heating: 

 energy typically forms a smaller proportion of the total costs of useful work; 

 the total cost (excluding time costs) of useful work typically forms a small proportion 

of total household expenditure; and 

 the energy cost of useful work is typically relatively invisible to the consumer. 

In principle, all these factors should contribute to low own-price elasticities E)( PE η for these 

energy services, in both the short and long-run. Price elasticities may also be low if the 

service is to some extent essential for everyday life (a ‘necessity good’). Cooking, water 

heating and clothes washing arguably fall into this category, although in each case there is 

scope for some variation in utilisation patterns in response to changes in energy prices. 

Other services, such as consumer electronics, are not necessity goods, but may 

nevertheless have low own price elasticities for the reasons given above. 

In the UK, other household energy services are commonly grouped under three headings, 

namely water heating, cooking, and lighting/appliances. In 2007, water heating accounted 

for 26.6% of UK household fuel use and 10% of electricity use, while cooking accounted for 

only 2.1% of fuel use and 6.2% of electricity use (DTI, 2007). The generic category of 

lighting/appliances accounted for 60.6% of electricity consumption, broken down as follows: 

lighting (14.2%), fridges/freezers (13.4%); consumer electronics (13.3%); ICT (7.9%); and 

washing equipment (11.4%) (DTI, 2007). A similar breakdown may be anticipated in other 

countries or regions with a comparable climate to the UK. However, in warmer countries 

space cooling may form a substantial component of household electricity demand. 

It is difficult to directly measure either useful work or energy consumption for these energy 

services, while the estimation of energy consumption from billing data is prone to error. As a 

result, the econometric evidence for direct rebound effects for other household energy 

services is extremely poor. This section summarises just four relevant studies, each of which 

is considered to be methodologically robust. Two of these studies are for space cooling and 

two for other energy services. 

6.2 Direct rebound effects for space cooling 

Space cooling forms a large and increasing proportion of household electricity consumption 

in warmer regions and the demand for space cooling has much in common with that for 

space heating. In 2001, 78% of US households owned space cooling equipment of some 

kind, up from 58% in 1981. The trend was towards central space cooling and away from 

room units. In the US as a whole, space cooling accounted for more than 11% of electricity 

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consumption. While per capita ownership of space cooling equipment is lower in most other 

OECD countries, it appears to be growing rapidly. 

The estimation of rebound effects of space cooling raises comparable measurement issues to 

that for space heating. For example, internal temperatures may only be one of the 

determinants of thermal comfort, with factors such as relative humidity also playing an 

important role. Rebound effects may also be expected to differ between room and central 

space cooling units, and may vary with electricity price levels and external temperatures. In 

particular, rebound effects may lower when systems are required to run at full capacity to 

maintain an acceptable internal temperature. 

Despite the importance of space cooling in many regions, we have only been able to find 

two econometric studies of direct rebound effects, namely Hausman (1979) and Dubin et al. 

(1986). 

Hausman (1979) develops a sophisticated discrete-continuous model of the demand for 

room air-conditioners and the associated use of the equipment. The data source is a 1978 

survey of 1985 households across the US, which includes comprehensive details of appliance 

ownership and characteristics, together with socio-economic data and electricity 

consumption. A subsample of 51 households had the energy consumption of their room airconditioners individually metered (Ecool), of which 46 provided usable data. Hausman also 

conducts a separate analysis of the market for room air-conditioners, which yields an 

estimate of the capital cost of room air-conditioners as a function of capacity and energy 

efficiency ( c ε ). 

The data permits the electricity consumption of the equipment to be estimated as both 

quadratic and double log functions of capacity, cooling degree days, electricity prices and 

energy efficiency. However, using the measured value of energy efficiency to estimate the 

direct rebound effect could lead to endogeneity bias, since households that anticipate a high 

level of utilisation may be expected to purchase a more efficient model (thereby creating a 

correlation between the consumption of useful work and c ε that is in addition to that 

created by the direct rebound effect). To avoid this, Hausman uses other variables to form 

an instrumental variable for c ε h . While the energy efficiency of the dwelling (ε ) may also be 

expected to influence equipment utilisation patterns, this is not measured or controlled for. 

However, while h ε c may be correlated with ε , it is less likely to be correlated with the 

instrumental variables that substitute for c ε . 

On the basis of estimates of )( η E EcoolP for the mean of the sample, both the quadratic and 

double-log specifications suggest a short-run direct rebound effect of ~4% (ie conditional 

upon the choice of air conditioning equipment). However, the quadratic specification also 

gives an estimate of )( ηε Ecool which suggests a much larger direct rebound effect of 26.5%. 

Since this is a cross-sectional study, the latter may be taken as an estimate of the long-run 

effect. While long-run effects may be expected to be larger than short run effects, this 

appears insufficient to explain the magnitude of the difference between the two estimates - 

thereby raising questions about the appropriateness of )( η E EcoolP as a proxy. 

Dubin et al. (1986) provide a rigorous examination of the direct rebound effect for space 

cooling, based upon a quasi-experimental study conducted by the Florida Power and Light 

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company in 1981. The study involved a random sample of 504 single-family households, 

each with central electric heating and air-conditioning. These were assigned to one of four 

experimental groups, namely: upgraded insulation; upgraded insulation and a highefficiency central air-conditioner; upgraded insulation and a high-efficiency heat pump; and 

a control group. The upgrades were provided free of charge. 

The experimental design did not include before and after measurements of energy 

consumption in each household, but instead used econometric techniques to explore the 

cross-sectional variation in consumption across the sample in the year following equipment 

installation. Total electricity consumption in each household was monitored, together with 

the monthly consumption of the heat pump or air-conditioner. The study also included 

comprehensive surveys of the structural features of each dwelling, together with 

demographic data and the level of appliance ownership. 

c This design ensured that the energy efficiency of the air conditioning equipment (ε ) was an 

exogenous variable, thereby circumventing the endogeneity problem highlighted in Section 

2.6. An additional advantage was to create a much larger variation this variable than would 

have been obtainable through a cross-sectional study of existing households - very few of 

whom owned high-efficiency central air-conditioners in 1981. Combined with the variation in 

unit electricity prices ( ) within the sample this led to considerable variation in the energy 

cost of useful work ( ). In addition, the data on the structural features of each 

dwelling permitted relatively accurate estimates of 

PE

PP cES = /ε

h ε to be made with the help of an 

engineering model. For space conditioning, this was expressed as the change in kWh of 

useful work from the air conditioner (Scool) per degree change of the thermostat setting for 

cooling ( )(/ h cool −ΔΔ= TTS oi ε ). 

With the help of an engineering model, Dubin et al. are able to estimate the electricity use 

for space cooling in each household (Ecool). Combining this with data on the energy efficiency 

of the relevant cooling equipment ( c ε ) gives the monthly consumption of useful work for 

cooling (Scool) This was then used as the dependent variable in econometric equation, whose 

independent variables included income, the number of occupants and the cost associated 

with a 1° change of the internal thermostat setting ( )/ P hcE ε ε . Hence, unlike the household 

heating studies reviewed in Section 5, the independent variable in this study was a 

combination of . h ε c ε and 

Dubin et al. estimate this equation separately for each season, with sample sizes varying 

from 214 to 396 (owing to missing data). Overall, the equations show a large amount of 

unexplained variation (e.g. adjusted R2

=0.07) On the basis of , Dubin et al. 

estimate the direct rebound effect to be 1-2% during summer months and up to 13% during 

the remainder of the year. This seasonal variation is revealing, since it suggests that both 

energy price elasticities and direct rebound effects are greater when average daily 

temperatures are lower and air-conditioning units are not running at full capacity. Similar 

results are reported for both heating and cooling by Poyer and Williams (1992), which 

suggests that the number of heating and cooling degree days is an important but frequently 

neglected source of variation in demand behaviour. Hence, the extent to which Hausman’s 

results provide an indication of anticipated behaviour in other regions will depend in part 

upon relative climatic conditions. 

)( ηε Ecool

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In summary, the two studies reviewed here suggest a direct rebound effect for space cooling 

in the range 1%-26%. While the first study focuses upon variations in c ε , the second 

incorporates variations in both c ε h and ε . While both of these studies are methodologically 

rigorous, they are also dated, use relatively small sample sizes and were conducted during 

periods of rising electricity prices. Moreover, both studies focus solely upon changes in 

equipment utilisation. To the extent that ownership of this technology is rapidly increasing in 

many countries (owing to income growth, technical improvements, falling capital costs, 

changes in climatic conditions and other factors) demand from ‘marginal consumers’ may be 

an important consideration, together with increases in the capacity of space cooling systems 

among existing users. Hence, unlike household heating (where most households have a 

system of sufficient capacity), this may make the long-term direct rebound effect for space 

cooling significantly higher than suggested by these two studies. 

6.3 Direct rebound effects for other energy services 

Only two methodologically rigorous studies of direct rebound effects for other household 

energy services have been identified, namely Guertin et al. (2003) and Davis (2007). 

Guertin et al. (2003) estimates rebound effects for both water heating and other energy 

services combined, while Davis (2007) estimates rebound effects for clothes washing. 

The study of 440 single-family Canadian households by Guertin et al. (2003) was 

described earlier in Section 5. In addition to the results for household heating reported 

earlier, Guertin et al. also estimate the own price elasticity of energy demand for hot water 

and for all other energy services combined (i.e. appliances and lighting). By combining 

seasonal demand patterns with comprehensive cross-sectional data on building type and 

appliance ownership, Guertin et al. are able to estimate the energy consumption for hot 

water and appliances/lighting. A potential source of error is the assumption that the ratio of 

energy consumption for hot water to that for appliances/lighting is the same in all 

households. Guertin et al. use ‘frontier analysis’ to estimate the energy efficiency of 

electricity and gas water heaters ( c ε ), but assume that the energy efficiency of appliances 

and lighting is 100%. These assumptions allow them to construct separate equations for the 

demand for energy and useful work for water heating and other services. A notable feature 

of the model is that price elasticities are restricted to be a linear function of income. 

The models account for 40-50% of the variation in the dependent variable. High-income 

households were found to have higher than average energy demands for appliances and 

lighting, while low-income households have lower than average. The demand for energy for 

water heating was insensitive to income. 

For water heating, the estimates of S)( PS η suggest a direct rebound effect in the range 34% 

(high-income groups) to 38% (low income groups), with a sample average of 36%. Since 

this is a cross-sectional study, the results may be interpreted as a long-run effect. The 

comparable estimates for E)( PE η are 33% (high-income groups) to 39% (low income 

groups), with a sample average of 36%. Hence, for water heating (unlike space heating), 

this studies suggests that η ε )( PE is relatively small and E)( PE η provides a good proxy for 

the rebound effect. 

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For other energy services combined, the estimates of S)( PS η suggest a direct rebound effect 

in the range 32% (high-income groups) to 49% (low income groups), with a sample average 

of 41%. Since appliance efficiency was assumed to be 100%, the estimates of S)( PE η are 

identical. 

These results are surprising, since they suggest that the own price elasticity of other energy 

services exceeds that for water and space heating56 - despite the strong theoretical 

arguments in favour of lower price elasticities given above. While this may partly be a 

consequence of the assumption that the energy efficiency of the relevant conversion devices 

is 100% (and hence, implicitly that η ε = 0)( PE ), this seems insufficient to account for all the 

difference. It is also notable that the price elasticities for both water heating and other 

energy services show much smaller variation with income than those for space heating. 

Davis (2007) provides a unique example of an estimate of direct rebound effects for 

household clothes washing - which together with clothes drying accounts for around one 

tenth of household energy consumption in the US. The estimate is based upon a US 

government-sponsored field trial of high-efficiency washing machines involving 98 

participants. 

Participants in the trial received a high-efficiency clothes washer free of charge. As with 

Dubin et al. (1986), the quasi-random replacement of capital equipment effectively made 

the energy efficiency of the clothes washer an exogenous variable, thereby circumventing 

the endogeneity problem highlighted in Section 2.6. Also, while participation in the trial was 

voluntary, both the utilisation of existing washers and the associated consumption of energy 

and water was monitored for a period of two months prior to the installation of the new 

washer, thereby allowing any household-specific variations in utilisation patterns to be 

controlled for. Taken together, these features of the study meant that unbiased estimates of 

the own-price elasticity of clothes washing - S)( PG η - could be obtained. 

The monitoring allowed household-specific estimates to be made of the consumption of 

detergent, water, electricity for the motor, energy for water heating and energy for drying 

for each kg of clothes washed, both before and after the installation of the new machine. 

These estimates showed a mean saving of 41% in water consumption and 48% in energy 

consumption per kg of washed clothes. By including data on the unit cost of water, energy 

and detergent the marginal cost of clothes washing for each household could be estimated 

(PG). This was then used as the primary independent variable in an equation for the demand 

for clean clothes in kg/day (S), thereby allowing S)( PG η to be estimated. Davis found that 

the demand for clean clothes increased by an average of 5.6% after receiving the new 

washers, largely as a result of increases in the weight of clothes washed per cycle rather 

than the number of cycles. This relatively small direct rebound effect suggests that only a 

small portion of the gains from energy efficient washing machines will be offset by increased 

utilisation. 

This estimate of the direct rebound effect takes into account all the cost savings from the 

new washer, including savings in water and detergent costs. It highlights the fact that many 

energy efficiency improvements will be associated with reductions in other input costs (see 

 

56 The corresponding figures for space heating were 29% (high-income groups), 47% (low income groups) and 

39% (sample average). 

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S)( PG Technical Report 5). However, while η could be the most relevant variable for policy 

purposes, only a portion of this effect results from the saving in energy costs alone. If, 

instead, the estimate of the direct rebound effect was based upon S)( PS η , the estimated 

effect would be smaller. Indeed, Davis estimates E)( PE η for electricity and propane use to 

be -0.02 and ~0.0 respectively, which suggests a direct rebound effect close to zero. 

The above elasticity estimates do not include the time costs associated with washing 

clothes, which is approximately the same for both efficient and inefficient washers. Based 

upon time-use survey data, Davis estimates that time costs form 79-92% of the total cost of 

washing clothes. The results therefore support the theoretical prediction that, for time 

intensive activities, even relatively large changes in energy efficiency should have little 

impact on demand, since they lead to relatively small changes in the total cost of useful 

work (PG

88 

In summary, the two studies reviewed above produce rather contrasting results. Guertin et 

al. estimate long-term direct rebound effects for both water heating and appliances/lighting 

in the range 32-49%, while Davis estimates short-term direct rebound effects for clothes 

washing of less than 5%. While rebound effects may be expected to be larger in the longterm, this explanation seems insufficient to account for the difference between the two 

results. The study by Davis is the more rigorous of the two, involving a quasi-experimental 

design in which energy efficiency is exogenous and household-specific effects are controlled 

for. Since these results are also more consistent with theoretical predictions, they may be 

given greater weight. However, this study is confined to clothes washing, while Guertin et 

al. examines a composite of household energy services. 

). Similar conclusions should therefore apply to other time-intensive energy 

services that are both produced and consumed by households, including those provided by 

dishwashers, vacuum cleaners, televisions, power tools, computers and printers. 
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Table 6.1 Estimates of the direct rebound effect for space cooling Author/year 

Shortrun 

rebound 

effect 

Longrun 

rebound 

effect 

Country Data Functional form Estimation technique 

Hausman (1979) 4% 26.5% US 

Cross 

section 

1978 

SS: 46 

Discretecontinuous 

Nested logit 

(discrete) & 

Instrumental 

variables 

(utilisation) 

R

Dubin et al. (1986) 1 – 26% US (Florida) 

Cross 

section 

1981 

SS: 214-396

Discretecontinuous 

Nested logit 

(discrete) & 

Instrumental 

variables 

(utilisation) 

En

Table 6.2 Estimates of the direct rebound effect for other household energy services Author/year 

Shortrun 

rebound 

effect 

Long-run 

rebound 

effect 

Country Data Functional form Estimation technique 

Guertin et al.(2003) 

34-38% 

(water) 

32-49% 

(appliances/

lighting) 

Canada 

Cross 

section 

1993 

SS: 440 

Double log OLS 

RE 

Davis (2007) 

<5.6 

clothes 

washing 

US 

Panel 

1997 

SS: 98 

Double log Fixed effects 

Q
90 

6.4 Summary 

In theory, direct rebound effects for most other household energy services should be smaller 

than those for household heating. The reasons include: energy forming a smaller proportion 

of the total costs of useful work; the total cost of useful work forming a smaller proportion 

of total household expenditure; and the energy cost of useful work being relatively invisible 

to the consumer. However, it is difficult to directly measure either useful work or energy 

consumption for these energy services, while the estimation of energy consumption from 

billing data is prone to error. As a result, the econometric evidence for direct rebound effects 

for other household energy services is very poor. 

Two rather dated studies of space cooling both suggest a direct rebound effect in the range 

1%-26%. However, both focus solely upon changes in equipment utilisation and therefore 

neglect both demand from ‘marginal consumers’ and increases in the capacity of space 

cooling systems among existing users. A study by Guertin et al. (2003) suggests a direct 

rebound effect of 34-38% for water heating and 32-39% for appliances/lighting, but both 

of these estimates appear suspiciously high. A more rigorous study by Davis (2007) 

estimates a direct rebound effect for clothes washing of <5%. As well as being more 

reliable, this estimate may be more representative of direct rebound effects from timeintensive energy services, such as those provided by dishwashers, vacuum cleaners and 

electronic appliances. 

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7 Summary and conclusions 

This report has examined the evidence for direct rebound effects that is available from 

studies that use econometric techniques to analyse secondary data. The focus throughout 

has been on consumer energy services, since this is where the bulk of the evidence lies. 

The econometric literature was found to be hard to interpret, partly as a result of lack of 

clarity over basic definitions. Different studies use different definitions of the direct rebound 

effect, estimate the effect through a number of different measures, express these measures 

in a variety of ways and frequently fail to clarify the relationship between them. The 

situation is compounded by the fact that many of the relevant studies do not mention the 

rebound effect at all, since their primary focus lies elsewhere. These studies nevertheless 

provide elasticity estimates that may, under certain assumptions, be used as proxy 

measures of the direct rebound effect. A key objective of this report, therefore, has been to 

clarify these different definitions and to develop a common terminology that aids 

interpretation of the relevant literature. 

The direct rebound effect may be estimated from the elasticity of demand for either energy 

or useful work with respect to either energy efficiency, the energy cost of useful work or 

energy prices. However, the assumption that consumers respond in the same way to 

decreases in energy prices as they do to improvements in energy efficiency (and vice versa) 

is likely to be flawed and could lead to biased estimates of the effect. Reasons for this 

include: 

 Input costs: Changes in energy efficiency may be correlated with changes in other 

input costs, while changes in energy prices may not. 

 Asymmetry: Energy price elasticities tend to be lower for periods with falling prices 

than for those with rising prices and it is the former that is the more appropriate 

proxy for improvements in energy efficiency. 

 Endogeneity: Energy efficiency and the demand for useful work are in part 

determined by each other. Unless this is controlled for, estimates of the effect could 

be biased. 

 Time costs: For many energy services, direct rebound effects may decline in 

importance in the future, owing to time costs increasing in importance relative to 

energy costs. 

Evidence for the direct rebound effect for automotive transport and household heating 

within developed countries is relatively robust. Evidence for direct rebound effects for other 

consumer energy services is much weaker, as is that for energy efficiency improvements by 

producers. Evidence is particularly weak for energy efficiency improvements in developing 

countries although theoretical considerations suggest that direct rebound effects in this 

context will be larger than those in developed countries. 

Under certain assumptions, estimates of the own-price elasticity of energy demand for an 

individual energy service should provide an upper bound for the direct rebound effect for 

that service. If the measured energy demand relates to a group of energy services (e.g. 

household fuel demand), the own price elasticity should provide an approximate upper 

bound for the weighted average of direct rebound effects for those services. Since the 

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92 

demand for energy is generally found to be inelastic in OECD countries, the long-run direct 

rebound effect for most energy services should be less than 100%. 

Table 7.1 summarises the results of our literature review. 

Table 7.1 Estimates of the long-run direct rebound effect for consumer energy services in 

OECD countries 

Range of 

Values in 

Evidence 

Base 

‘Best 

guess’ 

No. of 

Studies 

Degree of 

Confidence End-Use 

Personal 

automotive 

transport 

3-87% 10-30% 17 High 

Space heating 1.4-60%% 10-30% 9 Medium 

Space cooling 1-26% 1-26% 2 Low 

Other consumer 

energy services 0-39% <20% 3 Low 

Personal automotive transportation is the only area where the evidence is sufficiently strong 

to allow the magnitude of the direct rebound effect to be quantified with some confidence. 

Overall, the review suggests that the long-run direct rebound effect for personal automotive 

transport lies somewhere between 10% and 30%. The relative consensus on estimates, 

despite wide differences in data and methodologies suggests that the findings are robust. 

Also, the asymmetry of demand responses suggests that a value towards the lower end of 

this range is more likely. There is some evidence to suggest that the direct rebound effect 

for this energy service declines with income, but there is insufficient evidence to determine 

how it varies between different countries. 

In contrast, the available evidence does not permit the direct rebound effect for space 

heating to be quantified with much confidence. While this is partly because space heating is 

inherently more complex, it is also because the topic has received insufficient attention. The 

studies reviewed here suggest direct rebound effects in the range 1.4 to 60%, with 

considerable variation between different countries, households, fuels and types of energy 

efficiency improvement. The strong evidence for the price asymmetry of energy demand 

responses for space heating suggests that the mean effect may be towards lower rate end 

of the above range, but direct rebound effects appear to be higher for low-income groups. 

For the purpose of policy evaluation, a figure of 30% would appear a reasonable 

assumption, which is consistent with the results of the evaluation studies reported in 

Technical Report 1. 

There are a number of reasons why direct rebound effects for most other household energy 

services should be smaller than those for household heating. However, the econometric 

evidence is very poor, owing largely to measurement difficulties. Two rather dated studies of 

space cooling both suggest a direct rebound effect in the range 1%-26%, but these neglect 

the demand from ‘marginal consumers’ acquiring space cooling equipment for the first time, 

as well as any increases in the capacity of space cooling systems among existing users. A 

rigorous study estimates the direct rebound effect for energy efficient washing machines to 

be less than 5% and this figure is likely to be representative of many other time-intensive 

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energy services, such as those provided by dishwashers, vacuum cleaners and electronic 

appliances. 

All econometric estimates should be treated with caution. As Dahl (1993) has noted: “.... 

despite our attempts, it appears that demand elasticities are like snowflakes, no two are 

alike.” Aside from the difficulties of estimation, behavioural responses are known to be 

contingent upon technical, institutional, policy and demographic factors that vary widely 

between different groups and over time. Demand responses are known to vary with the 

level of energy prices, the origin of price changes (e.g. exogenous versus policy induced), 

expectations of future prices, saturation effects and other factors. The past is not 

necessarily a good guide to the future in this area, and it is possible that the very long-run 

responses may exceed those found in empirical studies that rely upon data from relatively 

short time periods. 

Nevertheless, the evidence suggests that direct rebound effects for consumer energy 

services are likely to be low to moderate in developed economies and may decline further in 

the future. Therefore, direct rebound effects should not undermine the objectives of energy 

efficiency programmes aimed at reducing the energy required to deliver particular energy 

services. However, these conclusions are subject to a number of qualifications, including the 

relatively limited time periods over which the effects have been studied, the frequent 

neglect of marginal consumers and the restrictive definitions of ‘useful work’ that are 

commonly employed. 

The current state of knowledge on direct rebound effects must be considered insufficient for 

policy purposes. Hence, research on direct rebound effects needs to improve in rigour and 

expand in scope. This requires both good data sets and more robust methodologies that 

address the potential sources of bias indicated above. There is scope for studies of a greater 

range of consumer energy services, provided that individual appliances can be monitored. 

Estimates of the direct rebound effect for personal automotive transport would benefit from 

more appropriate definitions of useful work. A study employing tonne-kilometres as the 

dependent variable appears feasible and could potentially capture the effect of increasing 

car sizes. Analysis is also needed of other modes of transport, including freight. There is also 

scope for more empirical work on the ‘rebound effect with respect to time’, especially in the 

area of transportation, and on the dependence of direct rebound effects on income. The 

geographical bias of the evidence base also needs to be addressed, including in particular 

studies of consumer energy services in developing countries. 

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Annex A – Mathematical deriviations 

Derivation of Definition 1 

Given = εES 

1 11 )()(

2

2 − ∂

∂ =⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞ ⎜

⎝

⎛

∂

∂

+−=⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

= S

S

S

S S S

S

E ε

ε

ε

εεε

ε

ε

ε

ε ηε

−= SE −1)()( Or: ηε ηε

Decomposing Definition 1 

Given = εES and = ** UTILCAPNOS

⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛

∂

∂

+

∂

∂

+

∂

∂ −= +

ε ε ε ε ε

ε

ηε

NO UTILCAP CAP UTILNO UTIL CAPNO UTILCAPNO

E

E )*()*()*( 1)**( )( 2

Substituting = UTILCAPNOE /)**( ε and cancelling terms: 

⎟

⎠

⎞ ⎜

⎝

⎛

∂

∂

+

∂

∂

+

∂

∂

+−=

ε

ε

ε

ε

ε

ε

ηε

NO

NO

CAP

CAP

UTIL

UTIL

E 1)(

E NO += CAP + UTIL −1)]()()([)( Or: ηε ηε ηε ηε

Derivation of Definition 2 

/)( ε = PSE S /ε Given = PP ES and and assuming that PE is exogenous, we have: 

⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂

∂

∂

+−=

∂

∂

εε

εε

ε

S

S

P

P

SS

EE

E

2 ⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂ −−=

S

E

P

SPS

E 2 2

1

εεε

ε E)( ηε =

S

E

P

S

E

P

E

S

∂

∂ −−= 2 εε S

S

P

S

S

P

∂

∂ 1−−= 

E S −−= 1)()( PS Or: ηε η

Derivation of Definition 4 

/)( ε = PSE S /ε Given = PP ES and we have: 

E

P

P

E

S

P

P

S S E

E

S

S

PS ε

ε

ε

ε

η

/

)/(

)( )( ∂

∂ −= ∂

∂ =

UK Energy Research Centre UKERC/WP/TPA/2007/010
95 

But if energy efficiency is held constant the above relationship becomes: 

E

P

P

E E

∂ E

∂ S)( PS η = = E)( PE η

Or: E E −−= 1)()( PE ηε η

Derivation of the relative magnitude of price elasticities 

)(

)](/[

E

EE

P

PPS E

ε

ε

Starting with the identity = , the energy cost elasticity of the demand for 

useful work may be expressed as: 

S

S

S

S

S S

S

S

S

P P

P

P

E

E

P

P

E

P

S

S

P

P

S

S

P S S ∂

∂

+

∂

∂ ⎥ =

⎦

⎤ ⎢

⎣

⎡

∂

∂

+

∂

∂ = ∂

∂ = ε

ε

ε

η )( ε

Or: 

η η η ε )()()( PS PS PS SE −=

We expect that η ε ≥ 0)( PS (higher costs for useful work encourages higher energy 

efficiency). In contrast, we expect that S ≤ 0)( PS η (higher prices reduce demand). Hence we 

expect that: 

SE )()( PS PS ≥ ηη

By a very similar process we can show: 

η η η ε )()()( PE PE PE SE −=

And hence we can argue that: 

SE )()( PE PE ≥ ηη

From Extension 2 we have: 

)(1

)()( )(

εη

εηη

η

E

E E

S

P

P P

P

E

S −

+ = . Rearranging we obtain: 

[ ] εηεηηη )()(1)()( PE PS PE PE SE −−=

S ≥≥ −1)(0 PS η ε ≥≥ 0)(1 η PE In most cases we would expect and . This implies that: 

ES )()( PS PE ≤ ηη

UK Energy Research Centre UKERC/WP/TPA/2007/010
96 

Combining the above three relationships, we obtain: 

EESS )()()()( PE PS PE PS ≤≤≤ ηηηη

Derivation of Extension 1 

Including the capital costs of new equipment (PK), the basic identity becomes: 

ε ε /)](),([ ε = S PPsE K

Taking derivatives with respect to energy efficiency, we have: 

⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂

∂

∂

+

∂

∂

∂

∂

+−=

∂

∂

+−=

∂

∂

ε ε ε εε εεε

K

K

S

S

P

P

P S

P

1 1 SSSSE

2 2 ∂εεεε

∂

∂

∂

+

∂

∂ −− K

S K

E P

P

S

P

S P S 1 = 32

Multiply through by ε / E to obtain E)( ηε : 

ε ε

ε

∂

∂

∂

∂

+

∂

∂ −− K

S K

E P

P

S

EP

S

E

P / 1 1

εε ε

ε

ε ∂

∂

∂

∂

+

∂

∂ −−= ∂∂ K

S K

E P

P

S

EP

S

E

P

E

S

E

E 1

2 = 

ε

ε ε

ε ∂

∂

∂

∂

+

∂

∂ −−= ∂

∂ K

S K

S P

P

S

SP

S

S

P

E

E 1

Multiplying numerator and denominator of the last term with PK, we have: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+

∂

∂ −−= ∂

∂

ε

ε ε

ε

K

KK

K

S

S P

PP

S

S

P

P

S

S

P

E

E 1

)]()([)(1)( Or: ηε E η PS +−−= η PK ηε PSS K

Derivation of Extension 2 

If energy efficiency depends upon energy prices, the basic identity can be written as follows: 

)(

)](/[

)(

)(

E

EE

E

S

P

PPs

P

PSS E

ε

ε

εε ===

Use the product and chain rules to differentiate this with respect to energy commodity 

prices: 

⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂

∂

∂

∂

∂

+

∂

∂

∂

∂

+

∂

∂ −= ∂

∂

E

S

SE

S

E E S P

P

P

S

P

P

P

S

P

S

P

E ε

ε ε

ε

ε

1

2

⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂

∂

∂ − ∂

∂

+

∂

∂ −= ∂

∂

E

E

E E S S P

P

P

S

P

S

P

S

P

E ε

εεε

ε

ε2 2

11

ES

E

E S PP

P S

P

S

P

S

∂

∂

∂

∂ − ∂∂

+

∂

∂ − ε

εε

ε

ε2 2 3

1 = 

UK Energy Research Centre UKERC/WP/TPA/2007/010
97 

Multiplying both sides by PE/E to switch into elasticity forms: 

ES

EE

S

E

E

E E

E PP

S

E

PP

P

P S

P

S P

E

P

P

E

∂

∂

∂

∂ − ∂

∂

+

∂

∂ −= ∂

∂ ε

εεε

ε

εε2 2 3

1

= εES / ε Noting that = PP ES and , we can simplify: 

E

E

S

S

S

S

E

E E

E P

P

P

S

S

P

P

S

S

P

P

P

E

P

P

E

∂

∂

∂

∂ − ∂

∂

+

∂

∂ −= ∂

∂ ε

ε

ε

ε

Expressing each term as an elasticity, we obtain: 

SE [ S)(1)()()( ] PE PS PE PS +−= ηεηηη

Or alternatively: )(1

)()( )(

εη

εηη

η

E

E E

S

P

P P

P

E

S −

+ =

Substituting into Definition 2 gives: 

1

)(1

)()( )( −

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−

+ −= εη

εηη

ηε

E

E E

P

P E P E

Derivation of Extension 3 

Including time costs and assuming time efficiency θ )( is a function of energy efficiency (ε ) 

we have: 

ε θ ε /))]((),([ ε = PPsE TS

Taking derivatives with respect to energy efficiency, we have: 

⎥

⎦

⎤ ⎢

⎣

⎡

∂

∂

∂

∂

∂

∂

+

∂

∂

∂

∂

+−=

∂

∂

ε

θ

ε ε θεε

T

T

S

S

P

P

P S

P

1 SSE

2 ε

θ

θεεε ∂

∂

∂

∂

∂

∂

+

∂

∂ −− T

S T

E P

P

S

P

S P S 1 = 32

Multiply through by ε / E to obtain E)( ηε : 

ε

θ

εε θ

ε

ε ∂

∂

∂

∂

∂

∂

+

∂

∂ −−= ∂

∂ T

S T

E P

P

S

EP

S

E

P

E

S

E

E 1

2

Multiply the third term by (θ θPP TT / ) and rearrange: 

⎟

⎠

⎞ ⎜

⎝

⎛

∂

∂

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+

∂

∂ −−= ∂

∂

ε

θ

θ

ε

θ

ε θ

ε

T

TT

T

S

S P

PP

S

S

P

P

S

S

P

E

E 1

Or: η η η η η θ )]()()([)(1)( ε E P P θ PSS T ε S T +−−=

UK Energy Research Centre UKERC/WP/TPA/2007/010
98 

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