Durable Goods and Residential Demand for Energy and Water:

Evidence from a Field Trial

Lucas W. Davis∗

University of Michigan

July 19, 2007

Abstract

This paper describes a household production model in which energy efficient durable goods

cost less to operate so households may use them more. The model is estimated using householdlevel data from a field trial in which participants received high-efficiency clothes washers free

of charge. The estimation strategy exploits this quasi-random replacement of washers to derive

precise estimates of the household production technology and a demand function for clothes

washing. During the field trial, households increased clothes washing on average by 5.6% after

receiving a high-efficiency washer, implying a price elasticity of -.06. The complete model is

used to evaluate the cost-effectiveness of recent changes in minimum efficiency standards for

clothes washers.

Key Words: Durable Goods; Household Production; Energy Efficiency; Climate Change

JEL: D13, H23, Q25, Q41

∗Department of Economics, University of Michigan, 611 Tappan Street, Ann Arbor, MI 48109;

email:lwdavis@umich.edu. This paper is based on of my Ph.D. dissertation at the University of Wisconsin. I thank

John Kennan, Maurizio Mazzocco, Gary Solon, Matthew White, the Editor, and several anonymous referees as well

as seminar participants at Wisconsin, Harvard, Chicago GSB, Stanford, Columbia and Wharton for helpful comments. Thanks also to D. Tom Rizy at Oak Ridge National Laboratory for providing the records from the Bern

Washer Study. This research was made possible through a NICHD Training Grant (T32 HD07014) and the Center

for Demography Ecology, which receives core support from the National Institute for Child and Human Development

(R24 HD 47873). Generous financial support was also provided by the Christensen Award in Empirical Economics.
1 Introduction

The energy efficiency of household durable goods has improved dramatically since the 1970s.

Between 1972 and 2001, average gasoline consumption per mile for new automobiles decreased 49

percent and average electricity consumption of central air conditioners and refrigerators decreased

by 44 percent and 56 percent, respectively.1 Despite these innovations, energy consumption per

capita in the U.S. decreased only 3 percent during the same period.2 One reason for the small

decrease is that households in 2001 were driving more, keeping their homes cooler in the summer,

and owning larger refrigerators. In part, these changes in utilization were a reaction to the efficiency

improvements. Improvements in energy efficiency decrease the price of using durable goods which

may lead to higher utilization.

It is important to take this behavioral response into account when evaluating the cost-effectiveness

of policies that encourage energy efficiency.3 The argument for these policies is that energy consumption imposes social costs that households do not consider when choosing which durable goods

to purchase. Most important, the combustion of fossil fuels causes emissions of carbon dioxide, the

principal greenhouse gas associated with climate change. However, the effectiveness of these policies in reducing energy consumption depends on the price elasticity of utilization. The larger the

price elasticity, the less effective these policies are at lowering energy consumption. Some critics of

these policies have argued that high-efficiency durable goods actually increase energy consumption,

implicitly claiming that the price elasticity of utilization exceeds one.4

In order to evaluate these claims this paper describes a model of residential energy and water demand that incorporates this behavior. Following Dubin and McFadden (1984), demand for

durable goods and demand for energy and water are determined jointly as the solution to a household production problem. In the model inputs like energy and water are used by durable goods to

produce services that the households cares about. The analysis highlights a simultaneity problem

1U.S. Department of Transportation (2004), Nadel (2002).

2U.S. Department of Energy (2005a), Table 1.5.

3There are many examples of public policies that encourage residential energy efficiency in the United States

including federal minimum efficiency standards, the Credit for Energy Efficient Appliances and the Alternative Motor

Vehicle Credit.

4

“Energy conservation is a waste”, commentary by H. Inhaber, Wall Street Journal. New York: July 28, 1997.

pg. A.18. “Conservation Wastes Energy”, commentary by K. Strassel, Wall Street Journal. New York, N.Y.: May

17, 2001. pg. A.26. “Disappearing Energy Crisis in the US? Paul Georgia on NPR”, interview with Paul J. Georgia

(Policy Analyst, Competitive Enterprise Institute), Talk of the Nation, National Public Radio, July 24, 2001.

1
that makes the price elasticity of utilization difficult to measure in most contexts. Households take

expected utilization into account when deciding which durable goods to purchase. As a result,

households with high demand for utilization are more likely to purchase energy efficient durable

goods and thus have a lower marginal cost of utilization.

The paper addresses this endogeneity by examining household behavior during a field trial

in which participants received a high-efficiency clothes washer free of charge. This quasi-random

replacement of washers during the field trial introduces plausibly exogenous variation in the households’ production technology, making it possible to derive unbiased estimates of the price elasticity

of utilization. As demonstrated in the paper, when this simultaneity is ignored, estimates of the

price elasticity are biased away from zero. The only previous study to exploit a field trial in this

way is Dubin, Miedema, and Chandran (1986) who examine a random sample of homes in Florida

that received free upgraded attic insulation and other free energy efficiency improvements.

The results document large decreases in energy and water consumption per-cycle when the

households receive the high-efficiency clothes washers. The estimates of the production technology

indicate that the high-efficiency washers use an average of 48% less energy and 41% less water

than conventional washers per cycle. The implied estimates of marginal cost are used to estimate a

demand equation for clothes washing. During the field trial, the average household increased clothes

washing by 5.6% after receiving a high-efficiency clothes washer. After controlling for weather and

other covariates the price elasticity of clothes washing is -.06; a magnitude that is smaller than

estimates in the literature for central heating and air conditioning. The estimate is similar across a

variety of alternative specifications. Thus, for clothes washers it appears that only a small portion

of the gains in energy and water efficiency are offset by increased utilization.

The estimated parameters are used to examine the cost-effectiveness of recent changes in minimum efficiency standards for clothes washers. While evidence from the field trial is valuable for

studying utilization behavior, it is less helpful for studying adoption behavior because households

are not observed purchasing washers. In lieu of a formal empirical model of the purchase decision,

reasonable assumptions about production costs, washer lifetimes, and the discount rate are used

to derive preliminary measures of the costs and benefits of the increased standards, as well as

the distribution of the benefits across households. The results suggest that most households are

made better off buying a washer that meets the 2007 standard. When the social benefit of reduced

2
carbon emissions are included in the analysis it appears that the minimum standard does meet a

cost-benefit test.

The format of the paper is as follows. Section 2 describes the household production model and

discusses the endogeneity problem. Section 3 describes the data from the field trial and provides

background for the empirical analysis. Section 4 specifies a functional form for the production technology, solves the cost-minimization problem and presents estimates of the production technology.

Section 5 describes and estimates a demand function for clothes washing. Estimates of the price

elasticity of utilization as well as implied price elasticities for inputs are presented and discussed.

Section 6 presents the cost-benefit analysis and section 7 provides concluding remarks.

2 A Model of Household Production with Durable Goods

This section describes a model of durable good purchase and utilization similar to the model

described by Dubin and McFadden (1984). In the model, demand for energy and water is derived

from demand for household services that are produced in the home according to a household

production technology. The model is general enough to describe a wide variety of household durable

goods or complete durable good portfolios. The analysis clarifies the source of the endogeneity bias

described above and shows how quasi-random variation in household durable good characteristics

during field trials can be used to derive unbiased estimates of the price elasticity of utilization and

other parameters of the model.

Households are assumed to choose the durable good portfolio that yields the highest level of

utility,

max

j∈1,..,J

{V (Θ1), ..., V (ΘJ )} (1)

where V is a conditional indirect utility function and Θj is a vector of observed characteristics for

durable good portfolio j. The decision of which durable goods to purchase is made taking into

account that whichever durable goods are purchased, they will be operated at the optimal level

of utilization. The durable good purchase decision is solved by evaluating the conditional indirect

3
utility function for each alternative,

V (Θj ) = max

{x,t,z2}

U(z1, z2|η) (2)

s.t. z1 = f(x, t|Θj )

px + z2 = tmw − r(Θj )

t + tm = T.

As in the original household production model described by Becker (1965), this model formalizes

the relationship between market inputs and services produced within the home. Household utility

is defined over household services z1 and a composite good z2. The price of the composite good

is normalized to one. Parameter η varies across households reflecting differences in the relative

value a household places on household services z1. The production function for z1 is denoted f

and depends on a vector of inputs, x, and time used in household production, t. The parameters

of the technology depend on the characteristics of the household’s durable goods, Θj . Households

evaluate expenditure on inputs based on the utility derived from z1 and the disutility of foregone

consumption of composite good z2. The budget constraint depends on a vector of input prices p,

the market wage w, and capital cost r that is a function of the characteristics of the durable good

portfolio. Time allocated to household production t and market work tm cannot exceed the total

time endowment T.

Let C(p, w, z1|Θj ) denote the minimum cost of producing z1 given input prices p, wage w, and

durable good characteristics Θj ,

C(p, w, z1|Θj ) = min

{x,t}

px + tw (3)

s.t. z1 = f(x, t|Θj ).

Furthermore, let the marginal cost of producing z1 be denoted π,

π(p, w|Θj ) = ∂C(p, w, z1|Θj )

∂z1

. (4)

Pollak and Wachter (1975) show that if the production technology exhibits constant returns to scale

4
and there is no joint production then marginal cost does not depend on the level of production.5

This is a significant analytical improvement because the household’s problem may be treated as a

classic demand problem,

max

{z1,z2}

U(z1, z2, |η) (5)

s.t. π(p, w|Θj )z1 + z2 = wT − r(Θj ).

In this reformulation of the problem marginal cost plays the traditional role of a price and the

problem can be solved as usual by equating the marginal rate of substitution with the price ratio.6

Under these conditions, the solution to the household’s utility-maximization problem is described by the demand function for z1,

z1 = z1(πj , yj |η). (6)

Demand for household services z1 depends on its marginal cost, πj = π(p, w|Θj ), and net income,

yj = wT − r(Θj ), both of which depend on the characteristics of the household’s durable good

portfolio, Θj .

This description highlights the simultaneity problem that makes the demand function difficult

to estimate empirically. Demand depends on parameter η that varies across households reflecting

differences in the relative value a household places on household services. However, households also

take η into account when deciding which durable goods to purchase. As a result, marginal cost

is endogenous in the demand equation and attempts to estimate the demand for utilization using

cross-sectional variation in marginal cost will be biased. In purchasing durable goods, households

with high demand for utilization tend to purchase high-efficiency durable goods. As a result,

marginal cost will tend to be negatively correlated with demand, causing estimates of the price

elasticity,

∂z1(πj , yj |η)

∂πj

πj

z1(πj , yj |η)

, (7)

5

Joint production occurs when the cost of producing a particular household service depends on the level of

production of another household service. Joint production arises frequently when time is an input in the production

function.

6

In the presence of nonconstant returns to scale, marginal cost depends on the level of production and the feasible

set is no longer a straight line. As a result, even if preferences are strictly convex there may be multiple solutions

and the demand function need not be continuous in p and w.

5
to be biased away from zero. For example, consider the case of vehicles. Households with high

demand for driving will tend to purchase vehicles for which the marginal cost of driving is low.

This causes a negative correlation between the marginal cost of driving and miles traveled. An

econometrician who fails to account for this endogeneity when measuring the effect of marginal

cost on driving will overstate the price elasticity.

The standard approach for addressing this endogeneity is to describe the durable good choice

problem explicitly using a discrete choice model. In the approach originated by Dubin and McFadden (1984), choice probabilities from the purchase decision are used as an instrument for durable

good holdings in estimating the utilization decision. This two-step approach has become the standard in micro-simulation models of energy demand like the U.S. Department of Energy’s National

Energy Modeling System. This paper takes an alternative approach that examines demand for

household services during a field trial. The field trial introduces variation in marginal cost that

is uncorrelated with η and thus can be used to derive unbiased estimates of the price elasticity.

The empirical analysis focuses on the utilization decision (5), rather than the durable good choice

decision (1). Therefore, the results can be used to assess the change in energy and water consumption of households that adopt high-efficiency washers, but they cannot be used to predict adoption

patterns.

3 Description of the Field Trial

The empirical analysis in the paper focuses on the case of clothes washers. Clothes washing is a

particularly lucid example of a household production process where demand for energy and other

inputs is derived from demand for consumption of a household service. In addition, clothes washing

is of significant independent interest because of the high level of energy and water consumption

associated with it. According to the 2001 Residential Energy Consumption Survey, households in

the U.S. use 1 trillion gallons of water and 186 trillion btus of energy annually washing clothes.

Inside the home, clothes washing and drying accounts for 10.1 percent of total energy consumption

and 21.5 percent of total water consumption.

Beginning in the late 1990s, high-efficiency washers were introduced in the United States that

have the potential to reduce this energy and water consumption dramatically. Whereas conventional

6
washers suspend clothes in a tub of water and agitate them along a vertical axis for washing and

rinsing, high-efficiency washers tumble clothes on a horizontal axis through a pool of water at the

bottom of the tub. In large part because they use less hot water, high efficiency washers also use

less energy. Engineering studies demonstrate that high-efficiency washers use up to 40% less water

and up to 60% less energy per cycle than conventional washers.

These large savings led the Department of Energy to conduct a field trial of a high-efficiency

clothes washer in Bern, Kansas (population 200) in 1997. Sponsored by Maytag and conducted by

Oak Ridge National Laboratory, the study provided participants with free high-efficiency clothes

washers in order to evaluate the energy and water consumption characteristics of these washers

under real-world conditions.7 Bern was selected from among a list of potential sites identified

with the cooperation of the National Rural Water Association. The project coordinators wanted a

location small enough that they could replace a high proportion of all washers within a particular

water utility system. This allowed them to assess the municipal impact of the washers as well as the

household-level effect. Bern is a farming community in the northeast corner of Kansas. According

to the 2000 Census, median household income in Bern is 4% below the U.S. median.

All residents of Bern and the surrounding rural water district were invited to participate in the

study. In order to participate, households were required to currently own a clothes washer and

agree to keep records of their clothes washing behavior before and after receiving the new clothes

washer. Ninety-eight out of 171 households in the water district chose to participate. Because

the empirical strategy controls for unobserved household-specific heterogeneity, the estimate of the

price elasticity will not be biased if households with particularly inefficient machines or households

with high demand for clothes washing were more likely to participate than other households. However, the estimate of the price elasticity will be biased if households that chose to participate are

systematically more or less responsive to changes in marginal cost than other households.

Before participating in the study households were made aware of the efficiency characteristics

of the new washers. At a town meeting May 27th in the Bern High School Gym, project managers

met with participants to explain that the goal of the study was to measure the energy and water

consumption characteristics of high-efficiency clothes washers and that in engineering studies these

washers had been shown to decrease energy consumption by up to 60% and water consumption by up

7

See Tomlinson and Rizy (1998) for more information about the Bern Washer Study.

7
to 40%. This is similar to the information typically available to households buying a high-efficiency

washer. Since 1980, the U.S. Federal Trade Commission’s Appliance Labeling Rule has required

manufacturers to attach yellow and black “Energy Guide” labels to most major home appliances

including clothes washers. These labels provide an estimate of annual energy consumption on a

scale showing a range of similar models and estimated annual operating cost based on national

average utilization levels and national average energy rates.

The field trials took place between June and November 1997. Between June 2nd and June

6th, water monitoring instrumentation was installed on the current washers of all participants.

During the next two months households recorded information about each wash cycle including

water readings for hot and cold water usage and load weights before and after washing, as well as

information about detergent usage, machine settings, and self-reported measures of satisfaction with

cleaning performance and dampness. The project managers designed data collection to minimize

misreporting. Water consumption was recorded cumulatively and wash cycle records were collected

and analyzed periodically during the course of the project. This allowed the project managers

to identify and remedy reporting problems. In addition, in order to standardize measurements

households were provided with identical scales, laundry baskets and measuring cups.

Between July 28th and August 1st, all washers were replaced with identical Maytag Neptune

high-efficiency washers. For the next three months households continued to record information

about their wash cycles. Throughout the analysis “phase 1” denotes the period before installation

of the high-efficiency washers and “phase 2” denotes the period after installation. During phase 2

the households received free of charge a low-sudsing laundry detergent designed for high-efficiency

clothes washers. Households paid for their own energy and water throughout the course of the

study.

Table 1 presents descriptive statistics. The dataset includes detailed records of over 18,000 wash

cycles and over 125,000 total pounds of clothes washed. The sample includes all wash cycles recorded

between June 7th and July 27th and between August 2nd and October 31st. The sample excludes

records from washers replaced at the Bern High School, the Bern Meat Plant, the Bern Laundromat,

the Bern Veterinarian Clinic, and three households that reported wash cycles in one phase only.

From the remaining 95 households, 192 out of 18425 total wash cycles were excluded because of

miscoding. Specifically, 57 cycles were excluded because the date was missing, 76 observations were

8
excluded because hot water usage was miscoded and 59 observations were excluded because cold

water usage was miscoded.

Energy and water consumption per cycle decreased substantially between phases. Figure 1

plots histograms of energy and water consumption per cycle. Energy usage for each component

of production is calculated following Tomlinson and Rizy (1998) using hot water usage, water

temperature, hot water heater type, the difference in clothing weight before and after washing

and engineering estimates of per-cycle motor electricity consumption by model. Reported propane

usage for water heating is for the 65 households with propane water heaters. Reported electricity

usage is for the 30 households with electric water heaters. Table 1 also includes prices and weather

characteristics. Water rates are marginal water rates in Bern during the summer of 1997 for the first

10,000 gallons. Electricity and propane rates are average residential prices for Kansas for 1997 from

the U.S. Department of Energy, “State Energy Consumption, Price, and Expenditure Estimates”.

Detergent price in phase 1 is the average price per ounce of 35 common detergents reviewed by

Consumer Reports in February 1995. No distinction is made between liquid ($.083/ounce) and

powder ($.086/ounce) detergents. Maximum daily temperature and daily rainfall are from the

NOAA National Virtual Data System for Centralia, KS, a town that is 27 miles south of Bern.

In addition to energy and water efficiency there are a number of potentially important differences

between high-efficiency washers and conventional washers. First, high-efficiency washers tend to

be more gentle on clothes because they do not have an agitator. Although the difference is subtle,

this could cause households to increase clothes washing because the cost in terms of wear and tear

has decreased or because a wider range of clothes can be washed. Second, high-efficiency washers

tend to have a larger tub capacity than conventional washers. The high-efficiency washers used in

the field trial have a tub volume of 3.3 cubic feet compared to an average tub volume in phase 1

of 2.8 cubic feet. This difference in capacity could cause households to increase clothes washing

because larger items can be washed or because washing requires less time. The empirical analysis

does not model these differences, and thus the results may overstate the responsiveness of demand

to changes in energy and water prices. Between phase 1 and phase 2 the average number of pounds

of clothes washed per day per household increased from 8.95 to 9.46. Thus, on average, households

increased clothes washing by 5.6% after receiving the new washers. This increase occurred almost

entirely in the number of pounds per wash cycle, not in the number of cycles. Had capacity and

9
other characteristics of the washers not changed at the same time, the increase in utilization might

have been even smaller.

4 The Production Technology

This is one of the first studies to estimate a household production technology explicitly. Despite the analytical advantages of this approach, household production models have received little

attention empirically. Instead, most studies focus on household demand for inputs rather than on

the underlying household services from which demand for the inputs is derived. The main reason

household production models have not received more empirical attention is that consumption of

services produced within the home is typically not observed. An attractive feature of many field

trials is that inputs and outputs are recorded. In this particular field trial, measures are recorded

of energy consumption, water consumption, detergent consumption and pounds of clothes washed.

Formally describing the household production technology increases the predictive power of the

model by restricting the pattern of substitution among inputs, making it possible to infer price

elasticities for energy, water, and detergent consumption derived from clothes washing.

This section describes the functional form used for the production technology, solves the costminimization problem, and presents estimates of the input demand functions. Clean clothes, z1,

are produced in the home using a clothes washer, clothes dryer, hot water heater, water, energy,

detergent and time. As described in the model, z1 is assumed to be a source of direct utility for the

household. Production is described using a Leontief production function. This choice of production

function implies that inputs are required proportionally in the production of clothes washing. The

production function, f, describes the number of pounds of clean clothes that are produced for a

given level of water x1, energy for the motor x2, energy for water heating x3, energy for drying x4,

detergent x5, and time t:

z1 = f(x1, x2, x3, x4, x5, t|Θ) = min{

x1

α1

,

x2

α2

,

x3

α3

,

x4

α4

,

x5

α5

,

t

α6

}. (8)

The parameters of the production technology, Θ = {α1, α2, α3, α4, α5, α6} reflect the characteristics

of the durable goods owned by the household. For example, if the clothes washer is water efficient

then α1 is low. Households solve the cost minimization problem for clothes washing by allocating

10
all inputs proportionally,

x1

α1

=

x2

α2

=

x3

α3

=

x4

α4

=

x5

α5

=

t

α6

= z1. (9)

The production technology is estimated using the conditional demand functions:

x1ic = α1iτ z1ic + ε1ic

x2ic = α2iτ z1ic + ε2ic

x3ic = α3iτ z1ic + ε3ic (10)

x4ic = α4iτ z1ic + ε4ic

x5ic = α5iτ z1ic + ε5ic.

Here i indexes households, c indexes wash cycles and τ indexes phase. The input demand function

for time is excluded and discussed below. This system of equations is estimated separately for each

household and each phase using systems least squares. For each household there are five parameters

for phase 1 and five parameters for phase 2. The error term is assumed to be measurement error

orthogonal to the level of output. Substituting the conditional demand functions into the cost

function and dividing by z1 yields marginal cost,

πiτ = p1α1iτ + p2α2iτ + p3α3iτ + p4α4iτ + p5α5iτ . (11)

Table 2 presents estimates of the production technology. The parameters vary across households

and phase. For example, the mean value for α1 in phase one is 5.56 and the standard deviation

across households is 1.90. The parameters demonstrate the improvements in energy and water

efficiency realized with the installation of the high-efficiency washers.

The mean number of gallons of water required to produce one pounds of clean clothes decreased

from 5.56 in phase 1 to 3.27 in phase 2. The parameters for energy usage indicate similar efficiency

improvements. The energy savings are substantial for households with both propane water heaters,

α3a, and electric hot water heaters, α3b. On average, the estimates imply that households used

41% less water and 48% less energy per cycle. Equation (11) implies that during the field trial the

marginal cost of clothes washing decreased from $.11 to $.04 per pound, a change of 65 percent.

Clothes washing is one of the most time-intensive components of household production. In

11
contrast, previous studies of residential energy demand have tended to focus on heating and cooling

equipment, where time is a much smaller component of the production process.8 According to the

EPA Time Use Survey (1994), among household production activities only child care and food

preparation are more time-intensive. Households report spending an average of 7.56 minutes per

household member per day for “clothing care”. For a family of four this implies almost four

hours per week. Using the average number of pounds of clothes washed per day per household

during phase 1 (8.95) and the average number of members per household in Bern (2.58), the timeuse estimates imply a time component of .05 hours per pound. Adopting the mean hourly wage in

Kansas in 1997 ($12.08) from the Bureau of Labor Statistics’ “Occupational Employment Statistics

Survey”, the cost estimates reported in Table 2 demonstrate that time costs increase the cost of

clothes washing considerably. In phases 1 and 2, the cost of time represents 79% and 92% of total

costs. Throughout the analysis that follows, elasticities are reported with respect to the marginal

cost of clothes washing excluding time. For most counterfactuals, this is the elasticity that is most

useful. Also, this facilitates the comparison with previous estimates in the literature for other

durable goods. When elasticities are calculated with respect to total costs, the estimates are larger

because the same variation in demand is now explained by a smaller relative change in prices.

In addition to clothes washing there are many production processes in the home that include a

substantial time component. For these services, the price elasticity with respect to the price of

energy and other non-time inputs will appear small.

5 Demand For Clothes Washing

5.1 Main Results

As described in Section 2, the solution to the household’s utility-maximization problem may

be described by the demand equation. Demand for clean clothes z1it in pounds by household i on

day t is postulated to depend linearly on marginal cost πit, a vector of covariates Xit, unobserved

time-invariant household characteristics ηi and unobserved household-specific time-varying factors

ωit,

z1it = γ0 + γ1πit + γ2Xit + ηi + ωit. (12)

8

See Hausman (1979), Dubin and McFadden (1984), Dubin, Miedema, and Chandran (1986), and Bernard, Bolduc

and Belanger (1996).

12
Dubin and McFadden (1984) show that a demand equation with this functional form can be derived from an internally-consistent utility maximization problem by applying Roy’s identity to a

conditional indirect utility function of the generalized Gorman polar form.

The dependent variable is zero for 45% of all observations and then continuously distributed over

positive values. Accordingly, a Tobit model is used for the main results. With the Tobit model

the household fixed effects are estimated explicitly along with γ0, γ1, and γ2. It has long been

recognized that with a Tobit model estimation of fixed effects introduces an incidental parameters

problem, leading to inconsistent parameter estimates for fixed T and n → ∞. However, in this

case T=142 so the magnitude of the inconsistency is likely to be small. Alternative specifications

are considered in Section 5.2.

Table 3 presents estimates of the demand function. Column (1) reports estimates from a

specification that excludes observations from after the households received high-efficiency washers.

As in a conventional cross-sectional analysis, in this specification the price elasticity is identified

from differences in durable good holdings across households. In this specification the price elasticity

of clothes washing is -.23. This relatively large estimate is consistent with the discussion in Section

2 that argued that endogeneity bias will tend to bias cross-section estimates of the price elasticity

away from zero. Households with high demand tend to purchase high-efficiency durable goods,

causing a spurious negative correlation between marginal cost and the error term.

Column (2) reports estimates from a specification that includes observations from both before

and after households receive high-efficiency washers but again excludes household fixed effects.

This specification represents an improvement over the previous specification because much of the

variation in marginal cost comes from the variation between phases. Because this variation is not

correlated with the unobserved determinants of demand, the estimate of the price elasticity suffers

less from endogeneity bias.

Estimates from the specification with fixed effects are reported in column (3). This specification indicates a price elasticity of -.06. In this specification the coefficient is identified using

within-household variation in the marginal cost of clothes washing. The quasi-random replacement of washers from the field trial mitigates the endogeneity problem that biased the estimates

in columns (1) and (2). This estimate implies that only a small portion of the gains in energy

and water efficiency are offset by increased utilization. According to estimates of the production

13
function, high-efficiency clothes washers cost about 40 percent less per cycle to operate than conventional washers. The estimates of the demand function, therefore, imply that an average household

adopting a high-efficiency clothes washer will increase utilization by less than three percent, only

negligibly offsetting the gains in efficiency.

The fixed effects ηi

from this specification can be compared to marginal cost for a test of

endogeneity. Figure 2 plots the household fixed effects against the marginal cost of clothes washing

for each household in phase 1. The correlation coefficient of the two variables is -.33 (.09), where the

standard error is derived using block bootstrap by households with 500 repetitions. The correlation

coefficient is similar in magnitude, -.36 (.08), when η is estimated using a linear fixed effects model,

suggesting that the negative correlation is not driven by the Tobit normality assumption. This

negative relationship between marginal cost and demand is consistent with the prediction of the

model. Households with high demand tend to own relatively high-efficiency washers in phase 1

so marginal cost is negatively correlated with the household fixed effect. This evidence provides

support for the research design, highlighting the importance of identifying variation in marginal

cost that is uncorrelated with household demand for utilization.

5.2 Alternative Specifications

Table 4 reports price elasticities from alternative specifications. Specification (1) estimates the

price elasticity using a linear fixed effects estimator. The estimate is similar to the estimate from

the fixed effects Tobit, suggesting that the normality assumption is not driving the results. Specification (2) estimates the price elasticity using a fixed effects Poisson estimator with an exponential

conditional mean function. The Poisson provides a convenient alternative treatment of the censoring while avoiding the incidental parameters problem with the fixed effect Tobit. The results

are similar with this specification. Specification (3) instruments marginal cost using a dummy for

phase. In this specification, the coefficient for marginal cost is identified using only variation across

time. The elasticity from this specification is similar to the elasticity from the previous estimates

suggesting that controlling for the unobserved household-specific component effectively purges the

demand equation of endogeneity.

Specification (4) includes dummy variables for the 4th of July, Labor Day, and Columbus day,

as well as for two “Superwash Saturdays” organized by the study coordinators. On “Superwash

14
Saturdays”, June 28th and September 13th, households were encouraged to do as much clothes

washing as possible in order to test the municipal impact of the new washers. Because these

holidays and “Superwash Saturdays” occurred in both phases, it is not clear that they bias the

results in any particular direction. Nevertheless, it is reassuring that the results are similar after

controlling for these days.

Specifications (5) and (6) adopt subsets of the sample that include only particular months.

These specifications address a couple of different concerns. It is important to consider other seasonal

factors that affect demand for clothes washing. If seasonal variation orthogonal to temperature and

precipitation causes households to change their behavior in phase two this could bias the estimates.

Specification (5) assesses this possibility by restricting the sample to include observations from July

1st to August 31st, two relatively homogeneous months. The estimate is similar to the estimate

for the entire sample, suggesting that the results do not appear to be biased by seasonal factors.

Another concern is that there might be a learning process by which households learn about the

new clothes washer and adjust their behavior over a period of time. Accordingly, specification (6)

restricts the sample to exclude wash cycles from August. The estimate from this specification is

similar to the estimate from the entire sample. These specifications are also relevant for assessing

the possibility that the households altered their behavior in some way because they were aware of

the fact that they were being studied. One might expect this effect to be particularly strong at the

beginning of the study or at the beginning of phase 2. The results from these specifications are

reassuring because they suggest that behavior is reasonably consistent over time.

Specification (7) reports a bootstrap standard error. In two-stage estimation procedures, standard errors and test statistics obtained from the second stage are sometimes invalid when sampling

variation in the first-stage estimates is ignored. This concern arises in estimating the demand equation because marginal cost is a function of the estimated parameters of the production technology.

The bootstrap standard errors take this into account by performing both stages of the estimation

for each bootstrap sample. The bootstrap standard errors are similar in magnitude to the standard

errors reported in Table 3.9

Studies of residential demand for heating and cooling provides a point of comparison for these

results. Dubin, Miedema, and Chandran (1986) find a price elasticity of -.13 for air conditioning

9

See Pagan (1984) and Murphy and Topel (1985) for discussion of inference in models with generated regressors.

15
and from -.08 to -.12 for electrical heating. As mentioned in the introduction, their paper is

similar because they exploit evidence from a field trial, examining an energy efficiency program

that provided a random sample of homes with free energy-efficiency improvements. Studies that

have used non-experimental evidence have tended to find larger elasticities. For example, Hausman

(1979) finds a price elasticity of room air conditioning of -.27 using a discrete choice approach.

Dubin and McFadden (1984) find an elasticity of -.31 for space and water heating.

These results may also be compared to evidence from automobiles and demand for driving.

Goldberg (1998) uses a discrete choice model to address the endogeneity of automobile choice in

estimating the demand for miles driven. After finding an elasticity of -.20 using least squares, she

finds the price elasticity of automobile usage to be near zero after correcting for the endogeneity of

automobile choice using instrumental variables. Previous studies of automobile usage that do not

control for endogeneity tend to find larger point estimates; ranging from -.08 to -.32 in a survey by

Greene, Kahn and Gibson (1999).

5.3 Demand for Inputs

The production technology and demand function imply demand functions for water, energy,

and detergent. This section derives the price elasticity for each input. The input price elasticities

are of significant independent interest and relevant to a large literature that examines the price

responsiveness of energy and water in other contexts. Differentiating the conditional demand

functions by input prices and rearranging yields the price elasticity of each input, ζj as a function

of the price elasticity of clothes washing,

ζj =

∂z1

∂π

π

z1

pjαj

π

=

∂z1

∂π

pjαj

z1

(13)

where j indexes water, electricity, propane and detergent. Because the technology is Leontief, the

price elasticity of each input ζj is equal to the price elasticity of z1 multiplied by the proportion of

marginal cost that is represented by that input. The input price elasticities describe the responsiveness of input demand derived from clothes washing to a change in input prices. For example, a

1% increase in the price of input j increases the amount of input j used in clothes washing by ζj .

Table 5 presents the price elasticities for water, electricity, propane, and detergent usage derived

16
from clothes washing. The elasticities are derived using the estimate of the price elasticity from

column (3) in table 3, averaging αj and π across households. The input price elasticities are

very small in magnitude, suggesting that only truly dramatic changes in input prices would have

a meaningful impact on input usage. For example, to decrease water consumption derived from

clothes washing by 10%, water prices would need to increase from $2.50 to over $35.00 per 1000

gallons. The implied input price elasticities are many times larger when biased estimates of the

price elasticities of clothes washing are used. For example, using the estimate from column 1 in

table 3 the implied price elasticity for electricity is -0.08 rather than -0.02. In predicting electricity

demand small differences in price elasticities are economically significant because electricity cannot

be stored easily and increasing capacity requires large capital expenditures.

Previous studies have tended to find larger price elasticities for energy and water. For example,

Reiss and White (2003) find a price elasticity of electricity of -.0910 and Renwick, Green and

McCorkle (1998) find a price elasticity for residential water use of -.16. One explanation for these

larger elasticities is that previous studies typically examine consumption from all end-uses and

many household production processes, such as outdoor water consumption and electric heating

and cooling are likely to be more elastic than clothes washing. Another point of comparison for

the energy price elasticities is the National Energy Modeling System (NEMS) described in U.S.

Department of Energy (2003). NEMS is used to make long-range national forecasts of energy

demand and for simulating the impact of alternative national energy policies. NEMS uses 1, 2,

and 3 year price elasticities for residential energy demand of -.20, -.29, and -.34. These elasticities

are substantially too large for describing energy usage derived from clothes washing. The results

from this paper suggest that the predictive powers of the NEMS could be increased by adopting a

framework in which price elasticities vary across household production process.

This paper is unusual in the residential energy demand literature because it examines energy

consumption derived from a single household production process. There are a number of advantages with this approach. First, this approach is able to distinguish between changes in utilization

and changes in durable goods. In a conventional analysis with household aggregate energy con10Reiss and White (2003) examine electricity consumption in San Diego before, during, and after a large increase

in residential electricity prices during the summer of 2000. After controlling for weather, time trends, and householdspecific heterogeneity they find that electricity demand decreased by 12-13% in response to an average price increase

of 130%.

17
sumption it is difficult to disentangle changes in utilization from changes in the durable good stock.

Second, this approach is able to describe heterogeneity across households. Demand studies have

typically found a large degree of heterogeneity across households in both utilization patterns and

the responsiveness of utilization to price changes.11 The household production model provides a

formal explanation for why price elasticities vary across households with different durable goods.

6 Efficiency Standards: Cost-Benefit Analysis

An appealing feature of the household production model described and estimated in this paper

is that it provides some of the information about demand behavior necessary to evaluate regulatory

policy changes regarding product standards. This is particularly germane in the present application.

The minimum energy efficiency standard for clothes washers sold in the U.S. increased by 27% in

2004, and again by 21% in 2007.12 This section illustrates how the paper’s household production

model can be applied, under simplified assumptions about production costs, to evaluate whether

or not these changes pass a cost-benefit test. This preliminary assessment suggests that most

households are better off buying a high-efficiency washer despite the increased purchase price.

However, there is a substantial minority of households, particularly households who do relatively

few cycles of clothes washing, who are better off buying a washer that does not meet the new

standard. Additional social benefits from the increased standard in the form of reduced carbon

emissions are potentially large.

The parameters of the household production technology (α1, α2, α3, α4, α5) and demand function

(γ0, γ1, γ2) are used to simulate an increase in energy efficiency equal to the total change in the

minimum standard in 2004 and 2007. Demand for clothes washing, energy consumption, and

water consumption are calculated for each household in the Bern sample relative to Phase 1 when

all households had conventional, top-loading washers. In addition, the compensating variation

is measured for each household using a quasi-linear utility function. Compensating variation is

the dollar amount a household would need to be indifferent between the new efficiency level and

11Reiss and White (2005) document large heterogeneity across households in the responsiveness of demand to

changes in price.

12See U.S. Department of Energy, “Energy Conservation Program for Consumer Products: Clothes Washer Energy

Conservation Standards; Final Rule”, Federal Register, 2001, 66(9). The minimum modified energy factor for washers

was .817 prior to 2004, raised to 1.04 on January 1, 2004, and 1.26 beginning January 1, 2007.

18
the old efficiency level. The model implies that the increase in efficiency would save households

an average of 942 kwh of energy per year, implying $61.00 in annual savings at average national

residential prices for electricity and natural gas.13 Because demand is almost perfectly inelastic,

the compensating variation is similar in magnitude, $63.00. Over the 11-year average lifetime of a

clothes washer (U.S. Department of Energy, 2005b), with a 5% annual discount rate this implies

present discounted lifetime savings equal to $524.00 and lifetime compensating variation of $545.00.

These benefits compare favorably with the increase in purchase price. The Association of Home

Appliance Manufacturers predicted that these efficiency improvements would increase retail prices

by $239.00.14 As direct empirical evidence about production costs, changes in quality, and pricing

behavior becomes available it should be incorporated into the analysis to validate this prediction.

Eighty-three percent of households in the Bern sample have a lifetime compensating variation

that exceeds $239.00, suggesting that they would indeed be made better off with a washer that

meets the 2007 standard. The remaining 17% would have been better off with a less expensive

washer. Bern is a single rural community and thus this sample may not be representative of the

U.S. population at large. As a result, caution should be exercised when generalizing these results.

Nevertheless, the analysis highlights the fact that households are not affected equally by minimum

efficiency standards. In particular, households that do relatively few cycles of washing per year and

households facing low energy prices have less to gain from efficiency improvements.

These measures ignore the external benefits of reduced energy consumption. Perhaps most

importantly, energy consumption causes emissions of carbon dioxide, the principal greenhouse gas

associated with climate change. According to the U.S. Department of Energy (2006), .76 pounds

of carbon are emitted per kwh of energy consumption in the United States. Therefore, estimates

from Nordhaus (2006) of the social cost of carbon of $17 per ton imply an additional average social

lifetime benefit of $52.00 per washer. Using larger estimates of the social cost of carbon such as

those from Stern (2007) the social benefits would be much larger. When these external benefits are

included in the analysis it appears that the 2004 and 2007 minimum efficiency requirements indeed

pass a cost-benefit test.

13From U.S. Department of Energy (2006), average national residential prices are $0.083 per kwh for electricity

and $0.047 per kwh for natural gas.

14U.S. Department of Energy. “Final Rule Technical Support Document (TSD): Energy Efficiency Standards for

Consumer Products: Clothes Washers”, 2000, p. 7-3 and 7-4.

19
However, without a formal empirical model of the adoption decision it is difficult to draw definitive conclusions about cost-effectiveness. In particular, had these standards not been implemented,

it is not clear how many households would have purchased efficient washers anyway. By using the

current level of energy efficiency as the baseline, the cost-benefit test may overestimate the benefits

of the efficiency standards. Still, previous studies of residential durable good purchase decisions

such as Hausman (1979) and Dubin and McFadden (1984) have tended to find behavior consistent

with unusually high implied rates of time preference, perhaps indicating information problems or

other market failures that may prevent households from making optimal choices. Moreover, highefficiency front-loading clothes washers have been available in the U.S. for many years even prior to

the Maytag Neptune with minimal sales, suggesting that the comparison with household’s current

washers may be reasonable for this preliminary assessment.

7 Conclusion

This paper describes a model of household production. In the model, high-efficiency durable

goods cost less to operate so households may use them more. The model is estimated using data from

a field trial in which participants received a high-efficiency clothes washer free of charge. Evidence

from the field trial provides measures of both the inputs and output of the household production

process, making it possible to describe the production technology explicitly. The implied estimates

of marginal cost are used to estimate a demand equation for clothes washing. The results indicate

that households are responsive to price, but that the magnitude of the response is small. This

small behavioral response implies that when households adopt high-efficiency washers, only a small

portion of the gains in efficiency are offset by increased usage.

An important feature of the analysis is the quasi-random variation in the household production

technology introduced by the field trial. A typical problem with cross-sectional studies of energy

demand is that the energy efficiency characteristics of durable goods are determined endogenously.

As demonstrated in the paper, ignoring this simultaneity leads to estimates of the price elasticity

that are biased upward. From an econometric perspective, ideally what one would like to do

is randomly assign durable goods to households and then examine their behavior. Field trials

are the closest available approximation to this research design and they represent an important

20
alternative to describing the simultaneous decision explicitly. Field trials are relatively common

in the durable good industry and it would be interesting to use evidence from other field trials to

examine household behavior in other contexts.

Another important feature of the analysis that differentiates it from previous studies of energy

demand is the emphasis on the role of time in household production. The results of the paper

suggest that when production is time-intensive, even large changes in energy efficiency will have

little impact on demand. There is a large and growing number of residential energy-consuming

durable goods that are used in time-intensive production processes including entertainment, food

preparation, cleaning, home office activities and personal care. Examples include dishwashers,

vacuum cleaners, stoves, microwave ovens, televisions, DVD players, computers, printers, power

tools and a large number of smaller appliances. According to the U.S. Department of Energy

(2006), this “all other” category shows the fastest growth of all categories of residential energy

consumption. The percentage of total residential energy consumption for this category is forecast

to increase from 21% in 2004 to 29% in 2030. The results from the paper suggest that when

production processes are time-intensive, improvements in energy efficiency will have only a small

effect on utilization. As a result, concerns about price responsiveness do not make a compelling

argument against public incentives for energy efficiency in these markets.

21
References

[1] Becker, Gary S. “A Theory of the Allocation of Time.” Economic Journal, 1965, 75, 493-517.

[2] Bernard, Jean Thomas, Denis Bolduc and Donald Belanger. “Quebec Residential Electricity Demand:

A Microeconomic Approach.” Canadian Journal of Economics, 1996, 29(1): 92-113.

[3] Dubin, Jeffrey A. and Daniel L. McFadden. “An Econometric Analysis of Residential Electric Durable

Good Holdings and Consumption.” Econometrica, 1984, 52(2), 345-362.

[4] Dubin, Jeffrey A., Allen K. Miedema, and Ram V. Chandran. “Price Effects of Energy-Efficient Technologies: A Study of Residential Demand for Heating and Cooling.” RAND Journal of Economics,

1986, 17(3), 310-325.

[5] Goldberg, Pinelopi Koujianou. “The Effects of the Corporate Average Efficiency Standards in the US.”

Journal of Industrial Economics, 1998, 46, 1-33.

[6] Greene, David L., James Kahn and Robert Gibson. “Fuel Economy Rebound Effect for U.S. Household

Vehicles.” Energy Journal, 1999, 20(3), 1-30.

[7] Hausman, Jerry A. “Individual Discount Rates and the Purchase and Utilization of Energy-Using

Durables.” Bell Journal of Economics, 1979, 10(1), 33-54.

[8] Murphy, Kevin M. and Robert H. Topel. “Estimation and Inference in Two-Step Econometric Models.”

Journal of Business and Economic Statistics, 1985, 3(4), 370-379.

[9] Nadel, Steven. “Appliance and Equipment Efficiency Standards.” Annual Review of Energy and the

Environment, 2002, 27, 159-192.

[10] Nordhaus, William. “The ‘Stern Review’ on the Economics of Climate Change.” NBER Working Paper

No. 12741, 2006.

[11] Pagan, Adrian. “Econometric Issues in the Analysis of Regressions with Generated Regressors.” International Economic Review, 1984, 25(1), 221-232.

[12] Pollak, Robert A. and Michael L. Wachter. “The Relevance of the Household Production Function and

Its Implications for the Allocation of Time.” Journal of Political Economy, 1975, 83(2), 255-277.

22
[13] Reiss, P. and M. White. “Demand and Pricing in Electricity Markets: Evidence from San Diego During

California’s Energy Crisis.” NBER Working Paper No. 9986, 2003.

[14] Reiss, P. and M. White. “Household Electricity Demand, Revisited.” Review of Economic Studies, 2005,

72(3), 853-884.

[15] Renwick, M., R. Green and C. McCorkle. “Measuring the Price Responsiveness of Residential Water

Demand in California’s Urban Areas.” California Department of Water Resources, 1998.

[16] Stern, N. “Stern Review on the Economics of Climate Change.” Cambridge: Cambridge University

Press, 2007.

[17] Tomlinson, J. J. and D. T. Rizy. “Bern Clothes Washer Study Final Report.” Oak Ridge National

Laboratory for the U.S. Department of Energy, Oak Ridge, TN, 1998, ORNL/M-6382.

[18] U.S. Department of Energy. “The National Energy Modeling System: An Overview 2003.” March 2003,

DOE/EIA-0581.

[19] U.S. Department of Energy, Energy Information Administration. “Annual Energy Review 2004.” 2005a,

DOE/EIA-0384.

[20] U.S. Department of Energy. “Revisions to the Energy Star Criteria for Clothes Washers.” 2005b.

[21] U.S. Department of Energy. “Annual Energy Outlook 2006.” 2006, DOE/EIA-0383.

[22] U.S. Department of Transportation, Federal Highway Administration. “Highway Statistics 2002.” April

2004, FHWA-PL-03-010.

23
DAVIS TABLE 1 OF 5

Table 1

Bern Washer Study, Descriptive Statistics

Phase 1 Phase 2

number of households 95 95

number of days 51 91

total number of wash cycles 6559 11674

total number of pounds of clothes washed 43339 81752

percentage of household days with clothes washing .53 .56

mean number of pounds washed per day per household 8.95 9.46

mean number of wash cycles per day per household 1.35 1.35

mean hot water use per cycle (in gallons) 10.4 4.3

mean cold water use per cycle (in gallons) 27.8 19.4

mean electricity use for washer motor per cycle (in kwh) .22 .10

mean propane use for water heating per cycle (in kwh) 3.59 1.41

mean electricity use for water heating per cycle (in kwh) 1.94 0.87

mean electricity use for drying clothes per cycle (in kwh) 2.00 1.85

mean detergent use per cycle (in ounces) 3.97 3.99

water prices in Bern (per 1000 gallons) $2.50 $2.50

electricity rate (per kwh) $.077 $.077

propane rate (per kwh) $.029 $.029

detergent price (per ounce) $.085 $.000

mean maximum daily temperature (fahrenheit) 88.1 77.8

mean daily precipitation (inches) .105 .124

24
DAVIS TABLE 2 OF 5

Table 2

Production Function Estimates – Inputs Required Per Pound

Phase 1 Phase 2

mean sd mean sd

α1 water (gallons) 5.56 1.90 3.27 .901

α2 electricity for motor (kwh) .031 .011 .013 .004

α3a propane for water heating (kwh) .501 .252 .193 .128

α3b electricity for water heating (kwh) .319 .100 .131 .044

α4 electricity for drying (kwh) .294 .055 .258 .042

α5 detergent (ounces) .580 .261 .545 .196

π marginal cost per pound $.11 .03 $.04 .01

cost per cycle $.72 .24 $.26 .09

marginal cost per pound (including time) $.52 .03 $.45 .01

cost per cycle (including time) $3.46 1.34 $3.16 1.38

25
DAVIS TABLE 3 OF 5

Table 3

Demand Function for Clothes Washing

Phase 1 Only Both Phases

(1) (2) (3)

marginal cost (log) -0.23 -0.10 -0.06

(0.18) (0.03) (0.03)

two household members 10.6 9.20 -

(2.37) (1.94)

three household members 19.9 19.3 -

(2.32) (1.88)

four household members 20.3 20.3 -

(2.24) (1.70)

five or more members 25.2 23.6 -

(2.43) (1.87)

daily maximum temperature 0.09 0.00 -0.01

(0.04) (0.01) (0.00)

daily rainfall (inches) 2.96 1.75 1.70

(0.95) (0.39) (0.40)

Saturday Dummy 8.01 7.92 8.04

(1.35) (1.10) (1.13)

Sunday Dummy -4.03 -2.97 -2.86

(1.68) (1.54) (1.55)

Monday Dummy 0.76 0.91 0.90

(1.16) (0.97) (0.99)

Tuesday Dummy -0.86 -1.38 -1.41

(1.25) (0.91) (0.92)

Thursday Dummy -1.58 -1.27 -1.24

(1.31) (1.00) (1.00)

Friday Dummy -0.86 -0.09 -0.05

(1.25) (0.90) (0.92)

Constant -32.9 -19.6 6.84

(7.89) (2.77) (2.00)

Household Fixed Effects No No Yes

n 4,845 13,490 13,490

σˆ 19.3 18.9 18.1

Log-Likelihood Value -12,844 -36,642 -36,096

The dependent variable is daily clothes washing in pounds. The first

row reports the price elasticity of demand implied by the coefficient

on log marginal cost evaluated at the sample mean. The underlying

coefficients are −3.69 (2.94), −1.62 (0.53), and −0.92 (0.51). Standard errors are robust to heteroskedasticity and correlation within

households.

26
DAVIS TABLE 4 OF 5

Table 4

Price Elasticity of Clothes Washing – Robustness Checks

(1) Linear Fixed Effect Model -0.06

(0.03)

(2) Fixed Effect Poisson Model -0.05

(0.03)

(3) Instrumental Variables (Dummy for Phase) -0.07

(0.03)

(4) Holiday Dummies Included -0.07

(0.03)

(5) Observations from July and August Only -0.06

(0.04)

(6) Excluding August -0.06

(0.04)

(7) Bootstrap Standard Errors (Both Steps) -0.06

(0.03)

This table reports the price elasticity of clothes washing from alternative specifications. The dependent variable is clothes washing in pounds. All specifications include maximum daily temperature, daily precipitation, day of the

week dummies and household fixed effects. Standard errors are robust to

heteroskedasticity and correlation within household. With (2) and (7) the

standard errors are derived using block bootstrap by household with 500 repetitions.

27
DAVIS TABLE 5 OF 5

Table 5

Implied Price Elasticities of Inputs

Water -0.01 (0.00)

Electricity -0.02 (0.01)

Propane -0.00 (0.00)

Detergent -0.03 (0.02)

28
Figure 1: Water and Energy Consumption Per Cycle

0 .05 .1 .15

density

10 20 30 40 50 60

Water Consumption Per Cycle in Gallons

Front−Loading Washers

Conventional Washers

0 .1 .2 .3

density

0 5 10 15

Electricity Consumption Per Cycle in KWH

Front−Loading Washers

Conventional Washers

29
Figure 2: Testing for Endogeneity

.05 .1 .15 .2

Price Per Pound in Phase 1

0 5 10 15 20

Household Fixed Effect

30