## 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 e nergy efficient durable goods cost less to operate so households may use them more. The mode l 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-ran dom 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 elastic ity 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 Effic iency; 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 Univer sity 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 NICH D Training Grant (T32 HD07014) and the Center for Demography Ecology, which receives core support from th e 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 pe riod. 2 One reason for the small decrease is that households in 2001 were driving more, keepi ng 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 th e 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 consid er 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. H owever, 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 good s actually increase energy consumption, implicitly claiming that the price elasticity of utilizati on exceeds one. 4 In order to evaluate these claims this paper describes a mode l of residential energy and water demand that incorporates this behavior. Following Dubi n 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 analy sis highlights a simultaneity problem

1 U.S. Department of Transportation (2004), Nadel (2002). 2 U.S. Department of Energy (2005a), Table 1.5. 3 There are many examples of public policies that encourage re sidential 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. St rassel, 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.

1that makes the price elasticity of utilization difficult to me asure 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 househol d behavior during a field trial in which participants received a high-efficiency clothes was her 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 simu ltaneity is ignored, estimates of the price elasticity are biased away from zero. The only previou s study to exploit a field trial in this way is Dubin, Miedema, and Chandran (1986) who examine a rand om 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 con sumption 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 co ntrolling 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 cond itioning. 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 increas ed utilization. The estimated parameters are used to examine the cost-effect iveness of recent changes in minimum efficiency standards for clothes washers. While evidenc e 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 empi rical model of the purchase decision, reasonable assumptions about production costs, washer lif etimes, and the discount rate are used to derive preliminary measures of the costs and benefits of th e increased standards, as well as the distribution of the benefits across households. The resu lts suggest that most households are made better off buying a washer that meets the 2007 standard. When the social benefit of reduced

2carbon 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 clot hes 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 pr ovides 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 h ome according to a household production technology. The model is general enough to descr ibe 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 hou sehold durable good characteristics during field trials can be used to derive unbiased estimates o f 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 (Θ 1 ) , ..., V (Θ J ) } (1)
where V is a conditional indirect utility function and Θ j is a vector of observed characteristics for durable good portfolio j . The decision of which durable goods to purchase is made taki ng into account that whichever durable goods are purchased, they wi ll be operated at the optimal level of utilization. The durable good purchase decision is solve d by evaluating the conditional indirect

3utility function for each alternative,

V (Θ j ) = max

{ x,t,z 2 } U ( z 1 , z2 | η ) (2)

s.t. z 1 = f ( x, t | Θ j )
px + z2 = t m w
− r (Θ j )
t + t m = T.
As in the original household production model described by B ecker (1965), this model formalizes the relationship between market inputs and services produc ed within the home. Household utility is defined over household services z 1 and a composite good z2 . The price of the composite good is normalized to one. Parameter η varies across households reflecting differences in the relat ive value a household places on household services z 1 . The production function for z 1 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 house hold’s durable goods, Θ j . Households evaluate expenditure on inputs based on the utility derived from z 1 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 t m cannot exceed the total time endowment T

. Let C (p, w, z 1 | Θ j ) denote the minimum cost of producing z 1 given input prices p , wage w , and durable good characteristics Θ j ,
C (p, w, z 1 | Θ j ) = min { x,t } px + tw (3)
s.t. z 1 = f ( x, t | Θ j )

. Furthermore, let the marginal cost of producing z 1 be denoted π ,

π (p, w | Θ j ) = ∂C (p, w, z 1 | Θ j )

∂z 1 . (4) Pollak and Wachter (1975) show that if the production techno logy exhibits constant returns to scale

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

This is a significant analytical improvement because the hou sehold’s problem may be treated as a classic demand problem,

max { z 1 ,z 2 } U ( z 1 , z2 , | η ) (5)

s.t. π (p, w | Θ j ) z 1 + z2 = wT

− r (Θ j )

. 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 o f substitution with the price ratio. 6 Under these conditions, the solution to the household’s uti lity-maximization problem is described by the demand function for z 1 ,

z 1 = z 1 ( π j , y j | η )

. (6)

Demand for household services z 1 depends on its marginal cost, π j = π (p, w | Θ j ), and net income, y j = wT

− r (Θ j ), both of which depend on the characteristics of the househo ld’s durable good portfolio, Θ j . 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 house hold 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 estimat e 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-effici ency durable goods. As a result, marginal cost will tend to be negatively correlated with dem and, causing estimates of the price elasticity, ∂z 1 ( π j , y j | η ) ∂π j π

j z 1 ( π j , y j | η ) , (7)

5 Joint production occurs when the cost of producing a particu lar 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 co st depends on the level of production and the feasible set is no longer a straight line. As a result, even if preferen ces are strictly convex there may be multiple solutions and the demand function need not be continuous in p and w . 5to 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 t he marginal cost of driving is low. This causes a negative correlation between the marginal cos t of driving and miles traveled. An econometrician who fails to account for this endogeneity wh en 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 app roach originated by Dubin and McFadden (1984), choice probabilities from the purchase decisio n 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 app roach that examines demand for household services during a field trial. The field trial intro duces 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 th e change in energy and water consumption of households that adopt high-efficiency washers, but th ey 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 proce ss 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 int roduced in the United States that have the potential to reduce this energy and water consumpti on dramatically. Whereas conventional

6washers suspend clothes in a tub of water and agitate them alo ng 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 wate r, high efficiency washers also use less energy. Engineering studies demonstrate that high-effi ciency 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. Spo nsored by Maytag and conducted by Oak Ridge National Laboratory, the study provided particip ants with free high-efficiency clothes washers in order to evaluate the energy and water consumptio n characteristics of these washers under real-world conditions. 7 Bern was selected from among a list of potential sites identi fied with the cooperation of the National Rural Water Associatio n. The project coordinators wanted a location small enough that they could replace a high proport ion of all washers within a particular water utility system. This allowed them to assess the munici pal impact of the washers as well as the household-level effect. Bern is a farming community in the no rtheast 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 distri ct 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 befo re and after receiving the new clothes washer. Ninety-eight out of 171 households in the water dist rict 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 parti cularly inefficient machines or households with high demand for clothes washing were more likely to part icipate than other households. However, the estimate of the price elasticity will be biased if h ouseholds that chose to participate are systematically more or less responsive to changes in margin al cost than other households. Before participating in the study households were made awar e of the efficiency characteristics of the new washers. At a town meeting May 27th in the Bern High S chool 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 was hers and that in engineering studies these washers had been shown to decrease energy consumption by up t o 60% and water consumption by up

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

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

washer. Since 1980, the U.S. Federal Trade Commission’s App liance Labeling Rule has required manufacturers to attach yellow and black “Energy Guide” lab els to most major home appliances including clothes washers. These labels provide an estimat e 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 rat es. 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 b efore and after washing, as well as information about detergent usage, machine settings, and s elf-reported measures of satisfaction with cleaning performance and dampness. The project managers de signed 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 w ith identical Maytag Neptune high-efficiency washers. For the next three months household s continued to record information about their wash cycles. Throughout the analysis “phase 1” d enotes the period before installation of the high-efficiency washers and “phase 2” denotes the perio d after installation. During phase 2 the households received free of charge a low-sudsing laundr y 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 inclu des detailed records of over 18,000 wash cycles and over 125,000 total pounds of clothes washed. The s ample 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 Be rn Meat Plant, the Bern Laundromat, the Bern Veterinarian Clinic, and three households that rep orted 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 th e date was missing, 76 observations were

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

water usage was miscoded. Energy and water consumption per cycle decreased substanti ally 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 (1 998) using hot water usage, water temperature, hot water heater type, the difference in clothi ng weight before and after washing and engineering estimates of per-cycle motor electricity c onsumption 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. T able 1 also includes prices and weather characteristics. Water rates are marginal water rates in Be rn during the summer of 1997 for the first 10,000 gallons. Electricity and propane rates are average r esidential prices for Kansas for 1997 from the U.S. Department of Energy, “State Energy Consumption, P rice, 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 temperatu re and daily rainfall are from the NOAA National Virtual Data System for Centralia, KS, a town t hat 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. F irst, 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 bec ause the cost in terms of wear and tear has decreased or because a wider range of clothes can be washe d. 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 househo lds to increase clothes washing because larger items can be washed or because washing requir es less time. The empirical analysis does not model these differences, and thus the results may ove rstate 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

9other 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, househol d production models have received little attention empirically. Instead, most studies focus on hous ehold 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 empiric al 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 parti cular field trial, measures are recorded of energy consumption, water consumption, detergent consu mption and pounds of clothes washed. Formally describing the household production technology i ncreases 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 prod uction technology, solves the costminimization problem, and presents estimates of the input d emand functions. Clean clothes, z 1 , are produced in the home using a clothes washer, clothes drye r, hot water heater, water, energy, detergent and time. As described in the model, z 1 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 i n the production of clothes washing. The production function, f , describes the number of pounds of clean clothes that are pro duced for a given level of water x 1 , energy for the motor x 2 , energy for water heating x 3 , energy for drying x 4 , detergent x 5 , and time t :

z 1 = f ( x 1 , x 2 , x 3 , x 4 , x 5 , t | Θ) = min { x 1 α 1 , x 2 α 2 , x 3 α 3 , x 4 α 4 , x 5 α 5 , t α 6 }

. (8)
The parameters of the production technology, Θ = { α 1 , α 2 , α 3 , α 4 , α 5 , α 6 } reflect the characteristics of the durable goods owned by the household. For example, if t he clothes washer is water efficient then α 1 is low. Households solve the cost minimization problem for c lothes washing by allocating

10all inputs proportionally, x 1 α 1 = x 2 α 2 = x 3 α 3 = x 4 α 4 = x 5 α 5 = t α 6 = z 1 . (9) The production technology is estimated using the condition al demand functions:

x 1 ic = α 1 iτ z 1 ic + ε 1 ic

x 2 ic = α 2 iτ z 1 ic + ε 2 ic

x 3 ic = α 3 iτ z 1 ic + ε 3 ic (10)

x 4 ic = α 4 iτ z 1 ic + ε 4 ic

x 5 ic = α 5 iτ z 1 ic + ε 5 ic .
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 as sumed to be measurement error orthogonal to the level of output. Substituting the conditi onal demand functions into the cost function and dividing by z 1 yields marginal cost,

πiτ = p 1 α 1 iτ + p 2 α 2 iτ + p 3 α 3 iτ + p 4 α 4 iτ + p 5 α 5 iτ . (11)
Table 2 presents estimates of the production technology. Th e parameters vary across households and phase. For example, the mean value for α 1 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-efficien cy washers. The mean number of gallons of water required to produce one po unds of clean clothes decreased from 5

. 56 in phase 1 to 3

. 27 in phase 2. The parameters for energy usage indicate simil ar efficiency improvements. The energy savings are substantial for house holds with both propane water heaters,

α 3 a , and electric hot water heaters, α 3 b . On average, the estimates imply that households used 41% less water and 48% less energy per cycle. Equation (11) im plies 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 component s of household production. In
11contrast, previous studies of residential energy demand ha ve tended to focus on heating and cooling equipment, where time is a much smaller component of the prod uction 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 sp ending 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 t ime 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 previou s estimates in the literature for other durable goods. When elasticities are calculated with respe ct 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 pro cesses in the home that include a substantial time component. For these services, the price e lasticity 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 ut ility-maximization problem may be described by the demand equation. Demand for clean clothe s z 1 it in pounds by household i on day t is postulated to depend linearly on marginal cost πit , a vector of covariates X it , unobserved time-invariant household characteristics ηi and unobserved household-specific time-varying factors

ω it ,
z 1 it = γ0 + γ 1 πit + γ2 X it + ηi + ω it . (12)

8 See Hausman (1979), Dubin and McFadden (1984), Dubin, Miede ma, and Chandran (1986), and Bernard, Bolduc and Belanger (1996).
12Dubin and McFadden (1984) show that a demand equation with th is 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 G orman polar form. The dependent variable is zero for 45% of all observations an d then continuously distributed over positive values. Accordingly, a Tobit model is used for the m ain results. With the Tobit model the household fixed effects are estimated explicitly along with γ0 , γ 1 , 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 hou seholds received high-efficiency washers. As in a conventional cross-sectional analysis, in this spec ification 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 di scussion in Section 2 that argued that endogeneity bias will tend to bias cross-s ection 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 c ost and the error term. Column (2) reports estimates from a specification that inclu des observations from both before and after households receive high-efficiency washers but again excludes household fixed effects. This specification represents an improvement over the previ ous 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 report ed 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 smal l portion of the gains in energy and water efficiency are offset by increased utilization. Acco rding to estimates of the production

13function, high-efficiency clothes washers cost about 40 perc ent less per cycle to operate than conventional washers. The estimates of the demand function, there fore, imply that an average household adopting a high-efficiency clothes washer will increase util ization 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 again st the marginal cost of clothes washing for each household in phase 1. The correlation coefficient of t he 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 th e Tobit normality assumption. This negative relationship between marginal cost and demand is c onsistent with the prediction of the model. Households with high demand tend to own relatively hi gh-efficiency washers in phase 1 so marginal cost is negatively correlated with the househol d fixed effect. This evidence provides support for the research design, highlighting the importan ce 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 specifi cations. Specification (1) estimates the price elasticity using a linear fixed effects estimator. The e stimate is similar to the estimate from the fixed effects Tobit, suggesting that the normality assump tion is not driving the results. Specification (2) estimates the price elasticity using a fixed effect s Poisson estimator with an exponential conditional mean function. The Poisson provides a convenie nt 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) instr uments marginal cost using a dummy for phase. In this specification, the coefficient for marginal cos t is identified using only variation across time. The elasticity from this specification is similar to th e 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 stu dy coordinators. On “Superwash

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

washing as possible in order to test the municipal impact of t he 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 re assuring that the results are similar after controlling for these days. Specifications (5) and (6) adopt subsets of the sample that in clude 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 i n 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 e stimate is similar to the estimate for the entire sample, suggesting that the results do not app ear to be biased by seasonal factors. Another concern is that there might be a learning process by w hich 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 specifi cations 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 e ffect to be particularly strong at the beginning of the study or at the beginning of phase 2. The resu lts 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 conc ern arises in estimating the demand equation because marginal cost is a function of the estimated par ameters of the production technology. The bootstrap standard errors take this into account by perf orming both stages of the estimation for each bootstrap sample. The bootstrap standard errors ar e similar in magnitude to the standard errors reported in Table 3. 9 Studies of residential demand for heating and cooling provi des 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 o f inference in models with generated regressors.

15and 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-effici ency 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 automobi les and demand for driving. Goldberg (1998) uses a discrete choice model to address the e ndogeneity of automobile choice in estimating the demand for miles driven. After finding an elas ticity 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 fo r each input. The input price elasticities are of significant independent interest and relevant to a lar ge literature that examines the price responsiveness of energy and water in other contexts. Differ entiating the conditional demand functions by input prices and rearranging yields the price e lasticity of each input, ζ j as a function of the price elasticity of clothes washing,
ζ j = ∂z 1 ∂π π z 1 pj αj π = ∂z 1 ∂π pj αj z 1 (13)

where j indexes water, electricity, propane and detergent. Becaus e the technology is Leontief, the price elasticity of each input ζ j is equal to the price elasticity of z 1 multiplied by the proportion of marginal cost that is represented by that input. The input pr ice elasticities describe the responsiveness of input demand derived from clothes washing to a ch ange 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 ζ j . Table 5 presents the price elasticities for water, electric ity, propane, and detergent usage derived

16from clothes washing. The elasticities are derived using th e 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 dramati c 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 f rom $2

. 50 to over $35

. 00 per 1000 gallons. The implied input price elasticities are many time s 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 economic ally significant because electricity cannot be stored easily and increasing capacity requires large cap ital expenditures. Previous studies have tended to find larger price elasticiti es for energy and water. For example, Reiss and White (2003) find a price elasticity of electricity of -

. 09 10 and Renwick, Green and McCorkle (1998) find a price elasticity for residential wate r 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 washin g. Another point of comparison for the energy price elasticities is the National Energy Modeli ng 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 der ived from clothes washing. The results from this paper suggest that the predictive powers of the NEM S could be increased by adopting a framework in which price elasticities vary across househol d production process. This paper is unusual in the residential energy demand liter ature because it examines energy consumption derived from a single household production pro cess. There are a number of advantages with this approach. First, this approach is able to dis tinguish between changes in utilization and changes in durable goods. In a conventional analysis wit h household aggregate energy con10 Reiss and White (2003) examine electricity consumption in S an Diego before, during, and after a large increase in residential electricity prices during the summer of 2000 . After controlling for weather, time trends, and household

specific heterogeneity they find that electricity demand dec reased by 12-13% in response to an average price increase of 130%.

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

Second, this approach is able to describe heterogeneity acr oss households. Demand studies have typically found a large degree of heterogeneity across hous eholds 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 h ouseholds 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 beha vior necessary to evaluate regulatory policy changes regarding product standards. This is partic ularly germane in the present application. The minimum energy efficiency standard for clothes washers so ld in the U.S. increased by 27% in 2004, and again by 21% in 2007. 12 This section illustrates how the paper’s household product ion model can be applied, under simplified assumptions about pro duction 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 desp ite 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 wash er 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 ( α 1 , α 2 , α 3 , α 4 , α 5 ) and demand function ( γ0 , γ 1 , 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 washin g, energy consumption, and water consumption are calculated for each household in the B ern 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

11 Reiss and White (2005) document large heterogeneity across households in the responsiveness of demand to changes in price. 12 See 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.

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

an average of 942 kwh of energy per year, implying $61.00 in an nual 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 li fetime 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 imp rovements 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 t he 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 m ade 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 exer cised when generalizing these results. Nevertheless, the analysis highlights the fact that househ olds 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 effi ciency improvements. These measures ignore the external benefits of reduced energy consumption. Perhaps most importantly, energy consumption causes emissions of carbo n dioxide, the principal greenhouse gas associated with climate change. According to the U.S. Depar tment 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 to n imply an additional average social lifetime benefit of $52.00 per washer. Using larger estimate s 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 min imum efficiency requirements indeed pass a cost-benefit test.

13 From U.S. Department of Energy (2006), average national res idential prices are $0

. 083 per kwh for electricity and $0

. 047 per kwh for natural gas. 14 U.S. Department of Energy. “Final Rule Technical Support Do cument (TSD): Energy Efficiency Standards for Consumer Products: Clothes Washers”, 2000, p. 7-3 and 7-4.

19However, without a formal empirical model of the adoption de cision 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 effici ent washers anyway. By using the current level of energy efficiency as the baseline, the cost-b enefit test may overestimate the benefits of the efficiency standards. Still, previous studies of resid ential durable good purchase decisions such as Hausman (1979) and Dubin and McFadden (1984) have ten ded 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 maki ng 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 c omparison 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. Th e 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 o utput of the household production process, making it possible to describe the production tech nology 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 magnit ude of the response is small. This small behavioral response implies that when households ado pt 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 var iation in the household production technology introduced by the field trial. A typical problem w ith cross-sectional studies of energy demand is that the energy efficiency characteristics of durab le goods are determined endogenously. As demonstrated in the paper, ignoring this simultaneity le ads to estimates of the price elasticity that are biased upward. From an econometric perspective, id eally what one would like to do is randomly assign durable goods to households and then exam ine their behavior. Field trials are the closest available approximation to this research de sign and they represent an important

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

in the durable good industry and it would be interesting to us e evidence from other field trials to examine household behavior in other contexts. Another important feature of the analysis that differentiat es 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 o f residential energy-consuming durable goods that are used in time-intensive production pr ocesses including entertainment, food preparation, cleaning, home office activities and personal c are. Examples include dishwashers, vacuum cleaners, stoves, microwave ovens, televisions, DV D 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 o f all categories of residential energy consumption. The percentage of total residential energy co nsumption for this category is forecast to increase from 21% in 2004 to 29% in 2030. The results from th e 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 resp onsiveness do not make a compelling argument against public incentives for energy efficiency in t hese 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 Cool ing.” RAND Journal of Economics , 1986, 17(3), 310-325. [5] Goldberg, Pinelopi Koujianou. “The Effects of the Corpor ate Average Efficiency Standards in the US.” Journal of Industrial Economics , 1998, 46, 1-33. [6] Greene, David L., James Kahn and Robert Gibson. “Fuel Eco nomy Rebound Effect for U.S. Household Vehicles.” Energy Journal, 1999, 20(3), 1-30. [7] Hausman, Jerry A. “Individual Discount Rates and the Pur chase 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 Inf erence in Two-Step Econometric Models.” Journal of Business and Economic Statistics , 1985, 3(4), 370-379. [9] Nadel, Steven. “Appliance and Equipment Efficiency Stand ards.” Annual Review of Energy and the Environment , 2002, 27, 159-192. [10] Nordhaus, William. “The ‘Stern Review’ on the Economic s 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 Relevanc e 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, 2 003. [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 Pr ice 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 Stu dy 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 Modeli ng System: An Overview 2003.” March 2003, DOE/EIA-0581. [19] U.S. Department of Energy, Energy Information Adminis tration. “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 Ad ministration. “Highway Statistics 2002.” April 2004, FHWA-PL-03-010.

23DAVIS 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 1.4 1 mean electricity use for water heating per cycle (in kwh) 1.9 4 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

24DAVIS TABLE 2 OF 5 Table 2 Production Function Estimates – Inputs Required Per Pound Phase 1 Phase 2 mean sd mean sd

α 1 water (gallons) 5.56 1.90 3.27 .901 α 2 electricity for motor (kwh) .031 .011 .013 .004 α 3 a propane for water heating (kwh) .501 .252 .193 .128 α 3 b electricity for water heating (kwh) .319 .100 .131 .044 α 4 electricity for drying (kwh) .294 .055 .258 .042 α 5 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

25DAVIS 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

ˆ σ 19.3 18.9 18.1 Log-Likelihood Value -12,844 -36,642 -36,096 The dependent variable is daily clothes washing in pounds. T he first row reports the price elasticity of demand implied by the coe fficient 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 correlati on within households.

26DAVIS 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 pou nds. All specifications include maximum daily temperature, daily precipit ation, day of the week dummies and household fixed effects. Standard errors are robust to heteroskedasticity and correlation within household. Wit h (2) and (7) the standard errors are derived using block bootstrap by househ old with 500 repetitions.

27DAVIS 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)

28Figure 1: Water and Energy Consumption Per Cycle0.05.1.15density

10 20 30 40 50 60 Water Consumption Per Cycle in Gallons

Front−Loading Washers Conventional Washers0.1.2.3density

0 5 10 15 Electricity Consumption Per Cycle in KWH

Front−Loading Washers Conventional Washers

29Figure 2: Testing for Endogeneity.05.1.15.2Price Per Pound in Phase 1

0 5 10 15 20 Household Fixed Effect

30