9-A-i

APPENDIX 9-A. RELATIVE PRICE ELASTICITY OF DEMAND FOR 

APPLIANCES

TABLE OF CONTENTS

9-A.1 INTRODUCTION .................................................................................................9-A-1

9-A.2 LITERATURE REVIEW ......................................................................................9-A-1

9-A.2.1 Price .......................................................................................................................9-A-1

9-A.2.2 Income....................................................................................................................9-A-1

9-A.2.3 Appliance Efficiency and Discount Rates .............................................................9-A-1

9-A.3 VARIABLES DESCRIBING THE MARKET FOR CENTRAL AIR 

CONDITIONERS AND HEAT PUMPS ..............................................................9-A-2

9-A.3.4 Physical Household/Appliance Variables..............................................................9-A-2

9-A.3.5 Economic variables................................................................................................9-A-3

9-A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE 

SHIPMENTS .........................................................................................................9-A-5

9-A.4.1 Variable Definition ................................................................................................9-A-5

9-A.4.2 Model Specification...............................................................................................9-A-6

9-A.4.3 Model Discussion...................................................................................................9-A-6

9-A.4.4 Analysis Results.....................................................................................................9-A-7

9-A.4.5 Analysis Critique ...................................................................................................9-A-7

9-A.5 LONG RUN IMPACTS.........................................................................................9-A-9

9-A.6 SUMMARY.........................................................................................................9-A-10

LIST OF TABLES

Table 9-A.2.1 Estimates of the Impact of Price, Income and Efficiency on 

Automobile and Appliance Sales...............................................................9-A-2

Table 9-A.3.1 Physical Household/Appliance Variables..................................................9-A-3

Table 9-A.3.2 Economic Variables...................................................................................9-A-4

Table 9-A.4.1 Individual Appliance Model Results .........................................................9-A-7

Table 9-A.5.1 Change in Price Elasticity of Demand for Automobiles following a 

Purchase Price Change.............................................................................9-A-10

Table 9-A.5.2 Change in Relative Price Elasticity for Home Appliances following a 

Purchase Price Change.............................................................................9-A-10

LIST OF FIGURES

Figure 9-A.3.1 Trends in CAC Shipments, Housing Starts and Replacements .................9-A-4

Figure 9-A.4.1 Trends in CAC Residual Shipments and Relative Price............................9-A-8

Figure 9-A.4.2 CAC Shipments vs. Relative Price ............................................................9-A-9
9-A-1

APPENDIX 9-A. RELATIVE PRICE ELASTICITY OF DEMAND FOR APPLIANCES

9-A.1 INTRODUCTION

This appendix summarizes DOE’s study of the price elasticity of demand for central air 

conditioners and heat pumps (CAC). This appendix begins with a review of the existing 

economics literature describing the impact of economic variables on the sale of durable goods in 

section 9-A.2. In section 9-A.3, the market for CAC and changes in it over the past 20 years is 

described. In section 9-A.4, DOE summarizes the results of its analysis and presents estimates of 

the price elasticity of demand. In section 9-A.5, DOE developes an ‘effective’ purchase price 

elasticity. DOE’s interpretation of these results is presented in section 9-A.6. 

9-A.2 LITERATURE REVIEW

There are relatively few studies measuring the impact of price, income and efficiency on 

the sale of appliances like central air conditioners and heat pumps. In this section DOE provides 

a short review of this literature which suggests the likely importance of these variables.

9-A.2.1 Price

The goal of many of the studies covered in this review is to measure the impact of price 

on sales in a dynamic market. One study of the automobile market prior to 1970 finds the price 

elasticity of demand to decline over time. The author explains this as the result of buyers 

delaying purchases after a price increase but eventually making the purchase (Table 9-A.2.1).1

 A 

contrasting study of household white goods also prior to 1970, finds the elasticity of demand to 

increase over time as more price-conscious buyers enter the market.2 A recent analysis of 

refrigerator market survey data finds that consumer purchase probability decreases with an 

increase in survey asking price.3

 Estimates of the price elasticity of demand for different brands 

of the same product tend to be relatively high. A review of 41 studies of the impact of price on 

market share found the average price elasticity to be -1.75.4

9-A.2.2 Income

 Estimates of the price elasticity of 

demand for appliances and other consumer durables are much lower. The price elasticity of 

demand reported in several studies averaged -0.33 in studies of the appliance market and -0.47 

in studies of the automobile and appliance markets. 

Higher income households are more likely to own household appliances.5

9-A.2.3 Appliance Efficiency and Discount Rates

 The impact of 

income on appliance shipments is explored in two econometric studies of the automobile and 

appliance markets.1,2 The average income elasticity of demand in our literature review is 0.50 for 

appliances and over 1.0. for automobiles (Table 9.A.2.1).

Many studies estimate the impact of appliance efficiency on consumer appliance

purchases. Typically, this impact is summarized by the implicit discount rate, i.e., the rate 

consumers use to compare future appliance operating cost savings against an appliance purchase 

price premium. One early and much cited study concludes that consumers use a 20 percent 
9-A-2

implicit discount rate when purchasing room air conditioners (Table 9-A.2.1).6

 A survey of 

several studies of different appliances suggests that the consumer implicit discount rate has a 

broad range and averages about 37 percent.7

Additionally, a previous study by DOE on the price elasticity of demand for refrigerators, 

dishwashers, and clothes washers estimates that the relative price elasticity of demand for home 

appliances is -0.34.8

Table 9-A.2.1 Estimates of the Impact of Price, Income and Efficiency on Automobile 

and Appliance Sales

Durable Good

Price 

Elasticity

Income 

Elasticity

Brand 

Price 

Elasticity

Implicit 

Discount 

Rate Model

Data 

Years

Time 

Period

Automobiles1 -1.07 3.08 - - Linear Regression, stock 

adjustment - Short run

Automobiles1 -0.36 1.02 - - Linear Regression, stock 

adjustment - Long run

Clothes Dryers2 -0.14 0.26 - - Cobb-Douglas, diffusion 1947-1961 Mixed

Room Air 

Conditioners2 -0.378 0.45 - - Cobb-Douglas, diffusion 1946-1962 Mixed

Dishwashers2 -0.42 0.79 - - Cobb-Douglas, diffusion 1947-1968 Mixed

Refrigerators3 -0.37 - - 39% Logit probability, survey 

data 1997 Short run

Various4 - - -1.769 - Multiplicative regression - Mixed

Room Air 

Conditioners5 - - -1.72 - Non-linear diffusion 1949-1961 Short run

Clothes Dryers5 - - -1.32 - Non-linear diffusion 1963-1970 Short run

Room Air 

Conditioners6 - - - 20% Qualitative choice, survey data - -

Household 

Appliances7 - - - 37%10 Assorted - -

Sources: 1 S. Hymens. 1971; 2 P. Golder and G. Tellis, 1998; 3 D. Revelt and K. Train, 1997; 4 G. Tellis, 1988; 5 D. Jain and R. Rao; 6 J. Hausman; 7 K. Train, 1985.

Notes: 8 Logit probability results are not directly comparable to other elasticity estimates in this table.

9 Average brand price elasticity across 41 studies.

10 Averaged across several household appliance studies referenced in this work.

9-A.3 VARIABLES DESCRIBING THE MARKET FOR CENTRAL AIR 

CONDITIONERS AND HEAT PUMPS

In this section DOE evaluates variables that are expected to account for central air 

conditioner and heat pump shipments, including physical household/appliance variables, and 

economic variables.

9-A.3.4 Physical Household/Appliance Variables

Several variables influence the sale of central air conditioners and heat pumps. The most 

important for explaining these sales trends are the annual number of new houses constructed

(housing starts) and the number of appliances reaching the end of their operating life 
9-A-3

(replacements). Housing starts influence sales because new homes increasingly include central 

air conditioners or heat pumps, with a new housing saturation of 90% nationally, and nearly 

100% in some regions. Replacements are correlated with sales because new appliances are 

typically purchased when old ones wear out. 

9-A.3.5 Economic variables

Appliance price, appliance operating cost and household income may also influence 

appliance shipments. Low prices and costs encourage purchases and a rise in income increases 

householder ability to pay for appliances. In principle, changes in these economic variables can 

help explain changes in the number of shipments. 

During the 1983-2005 study period, annual shipments of central air conditioners grew by 

238 percent (Table 9-A.3.1). This rising shipments trend is explained in part by housing starts, 

which increased 21 percent and by replacements, which rose by 212 percent over the period 

(Table 9-A.3.1). 

Table 9-A.3.1 Physical Household/Appliance Variables 

1983 2005 Change

Shipments1 (millions) 1.75 5.92 238%

Housing Starts2 (millions) 1.70 2.07 21%

Replacements3 (millions) 0.90 2.79 212% 1

Shipments: Number of units sold. Sources: AHRI. 2

Housing Starts: Annual number of new homes constructed. Source: U.S. Census. 3

Replacements: Estimated from past shipments with Weibull distribution, Weibull scale: 20.288, Weibull shape: 

1.885, Weibull delay: 1 year, resulting in mean lifetime: 19.01 years and median lifetime: 17.70 years.

It is apparent that housing starts and replacements do not account for all shipments of 

central air conditioners. This is shown by comparing the trend in total shipments against the 

trend in shipments to housing starts, and replacements between 1983 and 2005 (Figure 9-A.3.1). 

This residual shipments trend, illustrated by the un-shaded portion of the Figure, rises over time 

and exhibits significant volatility. 
9-A-4

Figure 9-A.3.1 Trends in CAC Shipments, Housing Starts and Replacements

Economic variables, including price, cost and income, may explain part of the trend in 

residual CAC shipments. Over the period, appliance prices decreased 40 percent to 50 percent, 

operating costs fell between 33 and 72 percent, and median household income rose 16 percent 

(Table 9-A.3.2). However, a lack of data makes it difficult to determine how much of the trend 

is explained by these economic variables and how much by other variables including changes in 

consumer preferences and regional saturation levels. 

Table 9-A.3.2 Economic Variables

1983 2005 Change

Price1 (1999$) 3319 2567 -23%

Operating Cost2 (1999$) 1031 607 -41%

Household Income3 (1999$) 33623 40110 19% 1

Price: Estimated from average price in 1999, weighted by inflation adjusted Producer Price Index. Source:

Burearu of Labor Statistics.

2

Operating Cost: Annual electricity price times electricity consumption., 37% implicit discount rate Source:

AHAM Fact Book.

3

Income: Mean Household income. Source: U.S. Census.

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006

Year

Total Central Air Conditioner Shipments 

Total Shipments

Replacements

Ship to Housing Starts
9-A-5

9-A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE 

SHIPMENTS

Limited data is available for estimating the impact of economic variables on the demand 

for appliances. Shipments data is available only between 1983-2005 and there is no industry 

price data, The producer price index is used as a proxy for the trend in the average price of 

central air conditioners. 

The limited data suggests that regression analysis can at best evaluate broad data trends. 

This section begins by describing broad trends apparent in the economic and physical household 

data sets and then specifies a simple regression model to measure these trends, making 

assumptions to minimize the number of explanatory variables. Finally, results are presented of 

the regression analysis.

9-A.4.1 Variable Definition

As noted above, housing starts and appliance replacements (physical household demand), 

explain much of the increase in CAC shipments over the 1983-2005 period. Before specifying a 

regression model, DOE defines two new variables—residual shipments and relative price.

Residual shipments are defined as the difference between shipments and physical 

household demand, and estimated by the following equation:

Residual Shipments = Total Shipments – Shipments to Starts – Replacements

where: 

Shipments to Starts = New Housing Starts x New Housing CAC Saturation.

Much of the CAC market is unlikely to be price sensitive. For example, CAC in new 

housing is likely to be very price insensitive. In recent years, CAC has become a standard 

feature of new houses—most (90%) new homes in the U.S. have CAC and in rapidly growing 

regions in the South and Midwest, virtually all new homes have CAC. The cost of CAC 

represents a small fraction of the typical house price, and most analysts believe that house buyer

purchase behavior is independent of CAC cost. CAC replacement sales may be somewhat more 

price sensitive, but only slightly so. The industry literature suggests that appliance owners grow 

accustomed to CAC over time and come to regard it as a necessity. In other words, appliance 

owners may at most delay replacing old air conditioners after a rise in price, but in the long run 

old units are almost always replaced. 

Household income rose during the study period, making it easier for households to 

purchase appliances. Assuming that a rise in income has a similar impact on shipments as a 

decline in price, the impact of income is incorporated by defining relative price, represented by 

the following equation: 

Income

PP PVOC RP + =

where:
9-A-6

RP = Relative price,

PP = Appliance purchase price, and

PVOC = Present value of operating costa

Income = Median household income.

9-A.4.2 Model Specification

The limited price data suggests using a simple regression model to estimate the impact of 

economic variables on shipments, using few explanatory variables. The following equation 

chosen for this analysis includes one physical household variable (starts plus replacements) and 

one relative price variable (the sum of purchase price plus operating cost, divided by income). 

Shipments = a + b × RP + c ×[Starts + Re placements] 

where:

Shipments = Total CAC shipments,

RP = Relative price,

Starts = Shipments to housing starts, and

Replacements = Number of CAC at the end of their operating life.

The natural logs are taken of all variables so that the estimated coefficients for each 

variable in the model may be interpreted as the percent change in shipments associated with the 

percent change in the variable. Thus, the coefficient b in this model is interpreted as the relative

price elasticity of demand for the three appliances. 

9-A.4.3 Model Discussion

DOE specified a regression model similar to the model used to estimate relative price 

elasticity of demand for the home appliances rulemaking.9

 One assumption used to specify this 

model is that changes in economic variables over the study period—income, price, and operating 

cost—are responsible for observed growth in residual shipments and that other variables, 

including changing consumer preferences and changes in the quality of CAC—have no 

additional or independent impact on shipments.

b

 

a Estimated using a 37% implicit discount rate.

 This assumption seems unlikely but without 

more data, the impact of this assumption on the price elasticity of demand cannot be measured.

An additional, perhaps even more important assumption is that the explanatory variables are 

b DOE considered additional variables including the impact of GDP and stock market indices as measures of wealth 

(instead of income), annual cooling degree days, and electricity prices as additional variables, but none of these 

variables was found to be significantly correlated with the trend in residual shipments.
9-A-7

accurately measured. This assumption is also incorrect. Recall for example, that the CAC 

producer price index is used in the regression as a proxy for CAC pricesc

9-A.4.4 Analysis Results

 

In regression analysis of this model, the elasticity of relative price (coefficient b) is 

estimated to be -1.26 for the residual shipments market for CAC. 

Table 9-A.4.1 Individual Appliance Model Results

Variable Coefficient t-stat

Intercept 4.77 2.07

Relative Price -1.26 -3.3

Starts + Replacements 0.49 2.29

R2 0.93

Observations 24

9-A.4.5 Analysis Critique

As reported above, the regression model analysis suggests that the relative price elasticity 

of demand for residual shipments of CAC will be -1.26. For several reasons, DOE rejects this 

estimate of relative price elasticity. There is a high degree of multicolinearity between relative 

price and the “starts + replacements” variable in the regression. Thus, it is difficult to determine 

the statistical significance of the relative price coefficient. The coefficient associated with other 

explanatory variable in the regression (starts + replacements), appears to be biased downward. 

The coefficient for this variable is estimated to be 0.49 but is expected to be close to 1. That is 

because each CAC installed in new housing or purchased as a replacement requires an additional 

unit to be shipped. Since this coefficient is significantly less than 1, it suggests that the relative 

price coefficient is picking up some of the influence on shipments that should be attributed to 

housing starts and replacements. DOE concludes that the regression model is overestimating the 

magnitude of the relative price elasticity of demand for CAC.

This conclusion is supported by a graphical comparison of residual shipments and 

relative price. During the time period of 1983-2005, residual shipments of CAC varied 

significantly, with a small peak around 1990, a much larger peak around 1999, and a spike in 

2004 (Figure 9-A.4.1). Over the same time period, the relative price of CAC decreased steadily 

(Figure 9-A.4.2). This suggests that the relationship between relative price and residual 

shipments within our data set is tenuous at best. For example, at the end of the study period, the 

same relative price (roughly 0.08) is associated with residual shipments ranging from about .4 

million to almost 2.0 million. 

 

c Three additional assumptions used to specify this model deserve comment. The relative price variable is 

specified in the model, assuming that (1) the correct implicit discount rate is used to combine appliance price and 

operating cost and that (2) rising income has the same impact on shipments as falling total price. The “starts + 

replacements” variable is specified, assuming (3) that starts and replacements have similar impacts on shipments. 
9-A-8

Figure 9-A.4.1 Trends in CAC Residual Shipments and Relative Price

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

1983 1988 1993 1998 2003

Year

Residual Shipments 

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

Relative Price ($CAC Cost / $Income) 

Residual

Shipments

Relative Price
9-A-9

Figure 9-A.4.2 CAC Shipments vs. Relative Price

For reasons described above, DOE relies on the results of previous analysis of other 

appliances to estimate the relative price elasticity of CAC demand. In previous analysis of those 

appliances, DOE was able to obtain a better set of data, including more accurate appliance price 

data. In that previous analysis, DOE estimated the relative price elasticity of demand of 

refrigerators, dishwashers and clothes washers to be -0.34.9 DOE acknowledges that there may 

be differences between the market for central air conditioners and heat pumps, and the market of 

other household appliances, but given the problems associated with the above CAC regression 

analysis, and the lack of other CAC price elasticity studies, DOE believes that the relative price 

elasticity of demand for refrigerators, dish washers, and clothes washers is an acceptable proxy 

for the relative price elasticity of demand for CAC.

9-A.5 LONG RUN IMPACTS

As noted above in Table 9-A.2.1, the literature review provides price elasticities over 

short and long time periods, also referred to as short run and long run price elasticities. As noted 

in the first two rows of Table 9-A.2.1, one source (Hymans) shows that the price elasticity of 

demand is significantly different over the short run and long run for automobiles.1

 Because 

DOE’s forecasts of shipments and national impacts due to standards is over a 30-year time 

period, consideration must be given as to how the relative price elasticity is affected once a new 

standard takes effect. 

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 250000 500000 750000 1000000 1250000 1500000 1750000 2000000

Residual Shipments

Relative Price
9-A-10

DOE considers the relative price elasticity of -0.34 determined above in section 9-A.4 to 

be a short run elasticity. DOE was unable to identify sources specific to household durable 

goods, such as appliances, to indicate how short run and long run price elasticities differ. 

Therefore, to estimate how the relative price elasticity changes over time, DOE relied on the 

Hymans study pertaining to automobiles. Based on the Hymans study, Table 9-A.5.1 shows how 

the automobile price elasticity of demand changes in the years following a purchase price 

change. With increasing years after the price change, the price elasticity becomes more inelastic 

until it reaches a terminal value around the tenth year after the price change.

Table 9-A.5.1 Change in Price Elasticity of Demand for Automobiles following a Purchase 

Price Change

Years Following Price Change

1 2 3 5 10 20

Price Elasticity of Demand -1.20 -0.93 -0.75 -0.55 -0.42 -0.40

Relative Change in 

Elasticity to 1st year

1.00 0.78 0.63 0.46 0.35 0.33

Source: Hymans, 1971.

Based on the relative change in the automobile price elasticity of demand shown in Table 

9-A.5.1, DOE adopted the time series of relative price elasticities developed for home appliances

and applies them to CAC. Table 9-A.5.2 presents the time series. 

Table 9-A.5.2 Change in Relative Price Elasticity for Home Appliances following a 

Purchase Price Change

Years Following Price Change

1 2 3 5 10 20

Relative Change in 

Elasticity to 1st year

1.00 0.78 0.63 0.46 0.35 0.33

Relative Price Elasticity -0.34 -0.26 -0.21 -0.16 -0.12 -0.11

9-A.6 SUMMARY

This appendix describes the results of a literature review and regression analysis of the 

impact of price and other variables on CAC shipments. In the literature, DOE finds only a few 

studies of appliance markets that are relevant to this analysis, and no studies using time series 

price and shipments data after 1980. The information that can be summarized from the literature 

suggests that the demand for appliances is price inelastic. Other information in the literature 

suggests that appliances are a normal good, such that rising incomes increase the demand for 

appliances. Finally, the literature suggests that consumers use relatively high implicit discount 

rates, when comparing appliance prices and appliance operating costs. 

The available price and operating cost data are too limited to perform a complex analysis 

of dynamic changes in the CAC market. In this analysis, DOE uses data available for CAC to 

evaluate broad market trends and to perform simple regression analysis. These data indicate that 

there has been an unsteady rise in CAC shipments and a constant decline in CAC price and 
9-A-11

operating cost over the period. Household income has also risen during this time. To simplify 

the analysis, DOE combined the available economic information into one variable, termed 

relative price, and used this variable in a regression analysis.

Due to a lack of CAC price and other data, DOE doubts the accuracy of relative price 

elasticity estimates obtained using that data. Instead DOE relies on a previous regression 

analysis of the relative price elasticity of demand for other appliances, including refrigerators, 

dish washers, and clothes washers. That analysis suggests that the relative price elasticity of 

appliances is -0.34. Although this elasticity is consistent with other estimates in the literature, 

DOE stresses that the measure is based on a small data set, using very simple statistical analysis. 

More important, the measure is based on an assumption that economic variables, including price, 

income and operating costs, explain most of the trend in appliances per household in the United 

States since 1980. 
9-A-12

REFERENCES

 1 S. Hymans. Consumer Durable Spending: Explanation and Prediction, Brookings Papers on 

Economic Activity, 1971. Vol. 1971, No. 1, pp. 234-239.

2 P. Golder and G. Tellis. Beyond Diffusion: An Affordability Model of the Growth of New 

Consumer Durables, Journal of Forecasting, 1998.

3 D. Revelt and K. Train. Mixed Logit with Repeated Choices: Household's Choice of 

Appliance Efficiency Level, Review of Economics and Statistics, 1997.

4 G. Tellis. The Price Elasticity of Selective Demand: A Meta-Analysis of Econometric 

Models of Sales, Journal of Marketing Research, 1988.

5 U.S. Department of Energy-Energy Information Agency. The Effect of Income on 

Appliances in U.S. Households, 2002. Washington, DC. 

<http://www.eia.doe.gov/emeu/recs/appliances/appliances.html> 

6 J. Hausman. Individual discount rates and the purchase and utilization of energy using 

durables, The Bell Journal of Economics, 1979.

7 K. Train. Discount rates in consumer' energy related decisions: a review of the literature, 

Energy, 1985.

8 Larry Dale and K. Sydny Fujita. An Analysis of the Price Elasticity of Demand for 

Household Appliances, February 2008. Lawrence Berkeley National Laboratory: Berkeley, 

CA. LBNL-326E.

9 U.S. DOE. Technical Support Document: Energy Efficiency Program for Consumer 

Products and Commercial and Industrial Equipment: Residential Dishwashers, 

Dehumidifiers, and Cooking Products, and Commercial Clothes Washers. March 2009. 

http://www1.eere.energy.gov/buildings/appliance_standards/residential/cooking_products_fi

nal_rule_tsd.html