9-A-i

APPENDIX 9-A. RELATIVE PRICE ELASTICITY OF DEMAND FOR 

APPLIANCES

TABLE OF CONTENTS

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

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

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

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

9-A.2.3 Appliance Efficiency and Discount Rates ............................................................ 9-A-2

9-A.3 VARIABLES DESCRIBING THE MARKET FOR REFRIGERATORS, 

CLOTHES WASHERS, AND DISHWASHERS ................................................ 9-A-2

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

9-A.3.2 Economic Variables.............................................................................................. 9-A-3

9-A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE 

SHIPMENTS ........................................................................................................ 9-A-4

9-A.4.1 Broad Trends......................................................................................................... 9-A-5

9-A.4.2 Specification of Model.......................................................................................... 9-A-7

9-A.4.3 Discussion of Model ............................................................................................. 9-A-8

9-A.4.4 Analysis Results.................................................................................................... 9-A-8

9-A.4.4.1 Individual Appliance Model ............................................................... 9-A-9

9-A.4.4.2 Combined Appliance Model............................................................... 9-A-9

9-A.4.5 Additional Regression Specifications and Results ............................................. 9-A-10

9-A.4.5.1 Lower Consumer Discount Rate....................................................... 9-A-10

9-A.4.5.2 Disaggregated Variables................................................................... 9-A-11

9-A.5 LONG RUN IMPACTS...................................................................................... 9-A-12

9-A.6 SUMMARY........................................................................................................ 9-A-13

9-A.7 DATA USED IN THE ANALYSIS ................................................................... 9-A-14

LIST OF TABLES

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

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

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

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

Table 9-A.4.1 Estimate of Total Price Elasticity of Demand............................................9-A-6

Table 9-A.4.2 Tabular Estimate of Relative Price Elasticity of Appliance Demand........9-A-7

Table 9-A.4.3 Individual Appliance Model Results .........................................................9-A-9

Table 9-A.4.4 Combined Appliance Model Result...........................................................9-A-9

Table 9-A.4.5 Combined and Individual Results, 20 percent discount rate....................9-A-10

Table 9-A.4.6 Disaggregated Regression Results, 37 percent discount rate...................9-A-11

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

Purchase Price Change.............................................................................9-A-12

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

Purchase Price Change.............................................................................9-A-13
9-A-ii

LIST OF FIGURE

Figure 9-A.3.1 Trends in Appliance Shipment, Housing Starts and Replacements...........9-A-4

Figure 9-A.4.1 Residual Shipments and Appliance Price ..................................................9-A-6
9-A-1

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

9-A.1 INTRODUCTION

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

appliances, including refrigerators, clothes washers and dishwashers. DOE chose this particular 

set of appliances because of the availability of data to determine a price elasticity. Section 9-A.2 

reviews the existing economics literature describing the impact of economic variables on the sale 

of durable goods. Section 9-A.3 describes the market for home appliances and the changes that 

have occurred over the past 20 years. In section 9-A.4, DOE summarizes the results of its

regression analysis and presents estimates of the price elasticity of demand for the three 

appliances. In section 9-A.5, DOE presents its development of an ‘effective’ purchase price 

elasticity. DOE’s interpretation of its results is presented in section 9-A.6. Finally, section 9-A.7 

describes the data used in DOE’s analysis.

9-A.2 LITERATURE REVIEW

Relatively few studies measure the impact of price, income and efficiency on the sale of 

household appliances. This section briefly reviews the literature that describes the likely 

importance of these variables on the purchase of household appliances.

9-A.2.1 Price

DOE reviewed many studies that sought to measure the impact of price on sales in a 

dynamic market. One study of the automobile market prior to 1970 finds the price elasticity of 

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

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

of household white goods, also prior to 1970, finds the elasticity of demand to increase over time 

as more price-conscious buyers enter the market.2 An analysis of refrigerator market survey data 

finds that consumer purchase probability decreases with survey asking price.3 Estimates of the 

price elasticity of demand for different brands of the same product tend to vary. A review of 41 

studies of the impact of price on market share found the average price elasticity to be -1.75.4 The 

average estimate of price elasticity of demand reported in these studies is -0.33 in the appliance 

market and -0.47 in the combined automobile and appliance markets.

9-A.2.2 Income

Higher income households are more likely to own household appliances.

5 The impact of 

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

appliance markets.1, 2

 The average income elasticity of demand is 0.50 in the appliance study 

cited in the literature review, much larger in the automobile study (Table 9-A.2.1).
9-A-2

9-A.2.3 Appliance Efficiency and Discount Rates

Many studies estimate the impact of appliance efficiency on consumers’ choice of

appliance. Typically, this impact is summarized by the implicit discount rate; that is, the rate 

consumers use to compare future savings in appliance operating costs against a higher initial 

purchase price of an appliance. One early and much cited study concludes that consumers use a 

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

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

has a broad range and averages about 37 percent.

7

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

Automobile and Appliance Sales

Durable Good Price 

Elasticity

Income 

Elasticity

Brand 

Price 

Elasticity

Implicit 

Discount 

Rate

Model Data 

Years

Time 

Period

Automobiles1 -1.07 3.08 - - Linear Regression, stock 

adjustment - Short run

Automobiles1 -0.36 1.02 - - Linear Regression, stock 

adjustment - Long run

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

Room Air 

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

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

Refrigerators3 -0.37 - - 39% Logit probability, survey 

data 1997 Short run

Various4 - - -1.769 - Multiplicative regression - Mixed

Room Air 

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

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

Room Air 

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

Household 

Appliances7 - - - 37%10 Assorted - -

Sources: 1S. Hymens. 1971;2 P. Golder and G. Tellis, 1998;3 D. Revelt and K. Train, 1997;3

4

G. Tellis, 1988;5 D. Jain and R. Rao, 1979;

6 J. Hausman, 1985;7 K. Train, 1985.8

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

9 Average brand price elasticity across 41 studies.

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

9-A.3 VARIABLES DESCRIBING THE MARKET FOR REFRIGERATORS, 

CLOTHES WASHERS, AND DISHWASHERS

In this section DOE evaluates variables that appear to account for refrigerator, clothes 

washer and dishwasher shipments, including physical household and appliance variables and 

economic variables.
9-A-3

9-A.3.1 Physical Household/Appliance Variables

Several variables influence the sale of refrigerators, clothes washers and dishwashers.

The most important for explaining appliance sales trends are the annual number of new 

households formed (housing starts) and the number of appliances reaching the end of their 

operating life (replacements). Housing starts influence sales because new homes are often 

provided with, or soon receive, new appliances, including dishwashers and refrigerators.

Replacements are correlated with sales because new appliances are typically purchased when old 

ones wear out. In principle, if households maintain a fixed number of appliances, shipments 

should equal housing starts plus appliance replacements. 

9-A.3.2 Economic Variables

Appliance price, appliance operating cost and household income are important economic 

variables affecting shipments. Low prices and costs encourage household appliance purchases 

and a rise in income increases householder ability to purchase appliances. In principle, changes 

in economic variables should explain changes in the number of appliances per household.

During a 1980–2002 study period, annual shipments grew 69 percent for clothes washers, 

81 percent for refrigerators and 105 percent for dishwashers (Table 9-A.3.1). This rising 

shipments trend is explained in part by housing starts, which increased 6 percent and by 

appliance replacements, which rose between 49 percent and 90 percent, depending on the 

appliance, over the period (Table 9-A.3.1).a For mature markets such as these, replacements 

exceed appliance sales associated with new housing construction.

Table 9-A.3.1 Physical Household/Appliance Variables 

Shipmentsi(millions) Housing Startsii (millions) Replacementsiii (millions)

Appliance 1980 2002 Change 1980 2002 Change 1980 2002 Change

Refrigerators 5.124 9.264 81% 1.723 1.822 6% 3.93 5.84 49%

Clothes Washers 4.426 7.492 69% 1.723 1.822 6% 3.66 5.50 50%

Dishwashers 2.738 5.605 105% 1.723 1.822 6% 1.99 3.79 90% i

Shipments: Number of units sold. Sources: AHAM Fact Book and Appliance Magazine. iiHousing Starts: Annual number of new homes constructed. Source: U.S. Census. iiiReplacements: Average of annual lagged shipments, with lag equal to expected appliance operating life, ± 5 years.

Shipments increased somewhat more rapidly than housing starts and replacements. This 

is shown by comparing the beginning and end points of lines that represent “starts plus 

replacements” (uppermost solid line in Figure 9-A.3.1) and “shipments” (diamond linked line in 

Figure 9-A.3.1). In 1980 the “shipment” line begins below the “starts plus replacements” line. In 

2002, the “shipments” line ends above the “starts plus replacements” line. This more rapid 

 

a Appliance replacements are determined from the expected operating life of refrigerators (19 years), clothes 

washers (14 years), and dishwashers (12 years) and from past shipments. Replacements are further discussed in 

section 9-A.3. The dishwasher lifetime used in this analysis does not match the dishwasher used in the primary 

analysis. 
9-A-4

increase in shipments, compared to housing starts plus replacements, suggests that the appliance 

per household ratio increased over the study period. 

Figure 9-A.3.1 Trends in Appliance Shipment, Housing Starts and Replacements

Economic variables, including price, cost and income, may explain this increase in 

appliances per household. Over the period, appliance prices decreased 40 percent to 50 percent, 

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

percent (Table 9-A.3.2).

Table 9-A.3.2 Economic Variables

Pricei(1999$) Operating Costii (1999$) Household Incomeiii (1999$)

Appliance 1980 2002 Change 1980 2002 Change 1980 2002 Change

Refrigerators 1208 726 -40% 333 94 -72% 37,447 43,381 16%

Clothes Washers 779 392 -50% 262 175 -33% 37,447 43,381 16%

Dishwashers 713 369 -48% 183 95 -48% 37,447 43,381 16% i

Price: Shipment weighted retail sales price. Sources: AHAM Fact Book and Appliance Magazine. iiOperating Cost: Annual electricity price times electricity consumption. Source: AHAM Fact Book. iiiIncome: Mean Household income. Source: U.S. Census.

9-A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE

SHIPMENTS

Few data are available to estimate the impact of economic variables on the demand for 

appliances. Industry operating cost data is incomplete—appliance energy use data are available 

for only 12 years of the 1980-2002 study period. Industry price data are also incomplete—

available for only 8 years of the study period for each of the appliances.

The lack of data suggests that regression analysis can at best evaluate broad data trends, 

utilizing relatively few explanatory variables. This section begins by describing broad trends 

apparent in the economic and physical household data sets and then specifies a simple regression 

Refrigerator Shipments

0

1

2

3

4

5

6

7

8

9

10

1980 1984 1988 1992 1996 2000

Millions 

New Housing

Retirements

Shipments

Clothes Washer Shipments

0

1

2

3

4

5

6

7

8

1980 1984 1988 1992 1996 2000

Millions 

Dishwasher Shipments

0

1

2

3

4

5

6

1980 1984 1988 1992 1996 2000

Millions 
9-A-5

model to measure these trends, making assumptions to minimize the number of explanatory 

variables. Finally, results of the regression analysis are presented along with an estimate of the 

price elasticity of demand for appliances. In section 9-A.4.5, DOE presents the results of 

regression analysis performed with more complex models, which are used to test assumptions 

underlying the simple model. These results support the specification of the simple model and the 

price elasticity of appliance demand estimated with that model.

9-A.4.1 Broad Trends

In this section DOE reviews trends in the physical household and economic data sets and 

posits a simple approach for estimating the price elasticity of appliance demand. As noted above, 

the physical household variables (housing starts and appliance replacements) explain most of the 

variability in appliance shipments during the study period (1980-2002).

b DOE assumes the rest 

of the variability in shipments (referred to as “residual shipments”) is explained by economic 

variables. Below, DOE presents a tabular method for measuring price elasticities.

To illustrate this tabular approach, DOE defines two new variables—residual shipments 

and total price. Residual shipments are defined as the difference between shipments and physical 

household demand (starts plus replacements). Total price, represented by the following equation,

is defined as appliance price plus the present value of lifetime appliance operating cost:

c

TP = PP + PVOC

Eq. 9-A.1

Where:

TP = Total price,

PP = Appliance purchase price, and

PVOC = Present value of operating cost.

Over the study period, residual shipments increased in proportion to total shipments by 

30 percent for refrigerators, 19 percent for clothes washers, and 23 percent for dishwashers. At 

the same time, total prices declined 47 percent, 45 percent and 48 percent for refrigerators, 

clothes washers, and dishwashers, respectively. Assuming that total price explains the entire 

change in per household appliance usage, a rough estimate is calculated of the total price 

elasticity of demand equal to -0.48 for refrigerators, -0.32 for clothes washers and -0.37 for 

dishwashers (Table 9-A.4.1).

 

b A log regression of the form: Shipments = a + b • Housing Starts + c • Retirements, indicates that these two 

variables explain 89 percent of the variation in refrigerator shipments, 97 percent of the variation in clothes washer 

shipments, and 97 percent of the variation in dishwasher shipments.

c Present value operating cost is calculated assuming a 19-year operating life for refrigerators, 14-year operating life 

for clothes washers, and a 12-year operating life for dishwashers. A 37 percent discount rate is used to sum annual 

operating costs into a present value operating cost.
9-A-6

Table 9-A.4.1 Estimate of Total Price Elasticity of Demand

Residual Shipments (millions) Total Price (1999$)

Appliance 1980 2002 Difference Change 1980 2002 Change Elasticity

Refrigerators -0.5 1.6 2.1 30% 1541 820 -61% -0.48

Clothes Washers -1.0 0.2 1.1 19% 1042 567 -59% -0.32

Dishwashers -1.0 -0.01 1.0 23% 896 464 -64% -0.37

The negative correlation between total price and residual shipments suggested by these 

negative price elasticities is illustrated in a graph of residual shipments on the y-axis and total 

price on the x-axis (Figure 9-A.3.1).

Yellow points are observed price data; red points are interpolated price data.

Figure 9-A.4.1 Residual Shipments and Appliance Price

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

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

decline in price, the impact of income is incorporated by defining a third variable, termed 

relative price, which is calculated as total price divided by household income and represented by 

the following equation.d

Income

TP

RP =

Eq. 9-A.2

Where:

RP = Relative price,

TP = Total price, and

Income = Household income.

 

d Recall that the income elasticity of demand cited in the literature review is 0.50 and the price elasticity of demand 

cited in the review averages -0.35. This suggests that combining the effects of income and price will yield an 

elasticity less negative than price elasticity alone.

Refrigerators

400

800

1200

1600

2000

-2.0 -1.0 0.0 1.0 2.0

Total Price

Residual Shipments 

Clothes Washers

400

600

800

1000

1200

-1.5 -1.0 -0.5 0.0 0.5

Total Price

Residual Shipments 

Dishwashers

200

400

600

800

1000

-2.0 -1.5 -1.0 -0.5 0.0 0.5

Total Price

Residual Shipments 
9-A-7

The percent decline in relative price for the three appliances divided by the percent 

decline in residual shipments suggests a rough estimate of relative price elasticity equal to -0.40 

for refrigerators, -0.26 for clothes washers and -0.30 for dishwashers (Table 9-A.4.2).

Table 9-A.4.2 Tabular Estimate of Relative Price Elasticity of Appliance Demand

Residual Shipments (millions) Relative Price (1999$)

Appliance 1980 2002 Change 1980 2002 Change Elasticity

Refrigerators -0.532 1.597 30% 0.041 0.019 -74% -0.40

Clothes Washers -0.953 0.174 19% 0.028 0.013 -72% -0.26

Dishwashers -0.974 -0.005 23% 0.024 0.011 -76% -0.30

9-A.4.2 Specification of Model

The limited price data suggest it is appropriate to use a simple regression model to 

estimate the impact of economic variables on shipments, using few explanatory variables. The 

following equation, chosen for this analysis, includes one physical household variable (housing 

starts plus replacements) and one relative price variable (the sum of purchase price plus 

operating cost, divided by income). 

Ship = a + b× RP + c ×[Starts + Rplc]

Eq. 9-A.3

Where:

Ship = Quantity of appliance sold,

RP = Relative price,

Starts = Number of new homes, and

Rplc = Number of appliances at the end of their operating life.

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

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

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

price elasticity of demand for the three appliances.

DOE used the following combined regression equation to estimate an average price 

elasticity of demand across the three appliances, using pooled data in a single regression. A 

combined regression specification is justified, given the limited data available and the similarity 

in price and shipment behavior across appliances (see Figure 9-A.4.1). Thus, the model 

represented by the combined regression equation is considered the basic model in DOE’s

analysis of appliance shipments.

Ship = a + b× RP + c ×[Starts + Rplc]+ d ×CW + e × DW

Eq. 9-A.4

Where:
9-A-8

CW = Quantity of clothes washers sold, and

DW = Quantify of dishwashers sold.

9-A.4.3 Discussion of Model

The most important assumption used to specify this model is that changes in economic 

variables over the study period—income, price, and operating cost—are responsible for all 

observed growth in residual appliance shipments. In other words, DOE assumes no impact from

other possible factors, such as changing consumer preferences or increases in the quality of 

appliances. This assumption seems unlikely, but without additional data, the impact of this 

assumption on the price elasticity of demand cannot be measured. DOE effectively assumes that 

changes in consumer preferences and appliance characteristics, while affecting which models are 

purchased, have relatively little impact on the total number of appliances purchased in a year.

Three additional assumptions used to specify this model deserve comment. The relative

price variable is specified in the model, assuming that (1) the correct implicit discount rate is 

used to combine appliance price and operating cost and that (2) rising income has the same 

impact on shipments as falling total price. The “starts + replacements” variable is specified, 

assuming (3) that starts and replacements have similar impacts on shipments.

To investigate the first assumption about discount rates, DOE calculated “present value 

operating cost” using a 20 percent implicit discount rate and performed a second regression 

analysis based on the models described in Equations 9-A.1 and 9-A.2. The results of this 

analysis, presented in section 9-A.4.5, indicate that the elasticity of relative price is fairly

insensitive to changes in the discount rate.

To investigate the second and third assumptions, DOE specified a regression model 

separating income from total price and replacements from starts, thereby adding two additional 

explanatory variables to the basic model as shown in the following equation:

Ship = a + b ×TP + c × Incone + d × Start + e× Rplc + f ×CW + g × DW

Eq. 9-A.5

The results of the regression analysis of this model are presented in section 9-A.4.5.

These results suggest that the elasticity of total price (coefficient b) is relatively insensitive to 

changes in the treatment of income and “starts + replacements” in the model.

9-A.4.4 Analysis Results

The following sections describe results of analyses using both the individual and 

combined models for appliances and the effects of a lower consumer discount rate and 

disaggregated variables.
9-A-9

9-A.4.4.1 Individual Appliance Model

The individual appliance regression equations are specified in the following equation.

Ship = a + b× RP + c ×[Starts + Rplc]

Eq. 9-A.6

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

be -0.40 for refrigerators, -0.31 for clothes washers and -0.32 for dishwashers (Table 9-A.4.3), 

averaging -0.35. These elasticities are similar to those reported in the literature survey for 

appliances (Table 9-A.2.1). They are remarkably similar to the price elasticity calculated using a 

tabular approach (Table 9-A.4.2).

The estimated coefficient associated with the “starts + replacements” variable is close to 

one. A coefficient equal to one for this variable would imply that, holding economic variables 

constant, shipments increase in direct proportion to an increase in “starts + replacements.” The 

high R-squared values (above 95) and t-statistics (above 5) in the results provide a measure of 

confidence in this analysis, despite the very small data set.

Table 9-A.4.3 Individual Appliance Model Results

Refrigerator Clothes Washer Dishwasher

Variable Coefficient t-stat Coefficient t-stat Coefficient t-stat

Intercept -1.51 -7.26 -1.47 -8.23 -2.08 -16.78

Relative Price -0.40 -6.60 -0.31 -5.69 -0.32 -7.03

Starts + Replacements 1.05 5.90 1.08 6.41 1.35 11.46

R2 0.954 0.954 0.975

Observations 23 23 23

9-A.4.4.2 Combined Appliance Model

The combined appliance regression equation is specified in the following equation. 

Ship = a + b× RP + c ×[Starts + Rplc]+ d ×CW + e × DW

Eq. 9-A.7

This regression analysis indicates that the model fits the existing shipments data well 

(high R-squared) and that the variables included in the model are statistically significant (Table 

9-A.4.4). Estimated with this model, the elasticity of relative price is -0.34, close to the average 

value estimated in the individual appliance models (-0.35). It is also similar to elasticity 

estimates reported in the literature survey and calculated using the tabular approach in Table 9-

A.4.2. 

Table 9-A.4.4 Combined Appliance Model Result
9-A-10

Variable Coefficient t-statistic

Intercept -1.60 -15.54

Relative Price -0.34 -10.74

Starts + Replacements 1.21 13.95

CW -0.20 -9.04

DW -0.32 -6.58

R2 0.983

Observations 69

9-A.4.5 Additional Regression Specifications and Results

As described in section 9-A.4.3, DOE used three assumptions to specify its appliance 

models. The first, made to aggregate appliance price and operating cost, is that the implicit price 

variable in the basic regression model is specified using a 37 percent implicit discount rate. The 

second states that the implicit price variable is defined assuming that rising income has the same 

impact on shipments as falling total price. The third states that the “starts + replacements”

variable is defined assuming that housing starts have a similar impact on shipments as appliance 

replacements. 

9-A.4.5.1 Lower Consumer Discount Rate

To investigate the first assumption about discount rates, DOE calculated “present value

operating cost” using a 20 percent implicit discount rate and performed a second regression 

analysis based on the models described in equations 9-A.1 and 9-A.2. The estimated coefficient 

associated with the relative price variable in these regressions is almost identical to the 

coefficients estimated for the same variable based on a 37 percent implicit discount rate. The 

elasticity of relative price calculated using a 20 percent discount rate is -0.33 in the combined

regression and averages -0.35 for the three appliances (Table 9-A.4.5). The elasticity of price 

calculated using a 37 percent discount rate is -0.34 in the combined regression and averages -

0.35 for the three appliances. DOE concludes from this analysis that the elasticity of relative

price is fairly insensitive to changes in the discount rate.

Table 9-A.4.5 Combined and Individual Results, 20 percent discount rate
9-A-11

9-A.4.5.2 Disaggregated Variables

To investigate the second and third assumptions, DOE constructed a regression model 

that separates income from total price and replacements from starts, thus adding two additional 

explanatory variables to the basic model (as shown earlier as Eq. 9-A.4 and shown below).

Ship = a + b ×TP + c × Income + d × Start + e× Rplc + f ×CW + g × DW

The estimated coefficient associated with the total price variable in these regressions is 

almost identical to the coefficients estimated for the relative price variable reported above. The 

elasticity of total price in the above equation is -0.36 in the combined appliance regression and 

averages -0.35 for the three appliances (Table 9-A.4.6). The elasticity of relative price based on 

the model described in equation 9-A.2 is -0.34 in the combined regression (Table 9-A.4.4) and 

averages -0.35 across the individual appliances (Table 9-A.4.3). DOE concludes that the price 

elasticity calculated in this analysis is relatively insensitive to the specification of household 

income and “starts + replacements” variables in the model.

Table 9-A.4.6 Disaggregated Regression Results, 37 percent discount rate

Three Appliances

Variable Coefficient t-Stat

Intercept -1.53 -14.61

Total Price / Income -0.33 -10.69

Starts + Retirements 1.20 13.65

CW -0.18 -8.69

DW -0.32 -6.57

R2 0.982

Observations 69

Refrigerator Clothes Washers Dishwasher

Variable Coefficient t-Stat Coefficient t-Stat Coefficient t-Stat

Intercept -1.36 -6.26 -1.41 -7.49 -2.04 -17.23

Total Price / Income -0.38 -6.50 -0.32 -5.29 -0.33 -7.30

Starts + Retirements 1.04 5.73 1.06 5.83 1.34 11.64

R2 0.953 0.950 0.977

Observations 23 23 23
9-A-12

9-A.5 LONG RUN IMPACTS

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

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

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

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

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

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

standard takes effect. 

DOE considers the relative price elasticities determined above in section 9-A.4 to be 

short run elasticities. DOE was unable to identify sources specific to household durable goods, 

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

estimate how the relative price elasticity changes over time, DOE relied on the Hymans study 

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

price elasticity of demand changes in the years following a purchase price change. With 

increasing years after the price change, the price elasticity becomes more inelastic until it reaches 

a terminal value around the tenth year after the price change.

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

Purchase Price Change

Years Following Price Change

1 2 3 5 10 20

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

Relative Change in 

Elasticity to 1st year

1.00 0.78 0.63 0.46 0.35 0.33

Source: Hymans, 1971.

Three Appliances

Variable Coefficient t-Stat

Intercept -2.92 -1.26

Income 0.58 2.92

Total Price -0.36 -7.06

Housing Starts 0.44 10.02

Retirements 0.62 8.12

CW -0.24 -9.25

DW -0.46 -7.68

R2 0.985

Observations 69

Refrigerator Clothes Washers Dishwasher

Variable Coefficient t-Stat Coefficient t-Stat Coefficient t-Stat

Intercept -6.19 -2.24 -6.64 -1.63 1.00 0.23

Income 0.89 3.80 0.87 2.31 0.20 0.52

Total Price -0.35 -5.48 -0.27 -2.51 -0.43 -5.18

Housing Starts 0.41 7.38 0.25 3.29 0.62 8.24

Retirements 0.56 6.06 0.56 2.09 0.65 5.86

R2 0.984 0.958 0.979

Observations 23 23 23
9-A-13

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

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

A.5.2 presents the time series. 

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

Purchase Price Change

Years Following Price Change

1 2 3 5 10 20

Relative Change in 

Elasticity to 1st year

1.00 0.78 0.63 0.46 0.35 0.33

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

9-A.6 SUMMARY

This appendix describes the results of a literature search, tabular analysis, and regression 

analyses of the impact of price and other variables on appliance shipments. In the literature, DOE

found only a few studies of appliance markets that are relevant to this analysis and no studies

after 1980 using time series price and shipments data. The information that can be summarized 

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

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

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

discount rates, when comparing appliance prices and appliance operating costs. 

There are too few price and operating cost data available to perform complex analysis of 

dynamic changes in the appliance market. In this analysis, DOE used data available for 

refrigerators, clothes washers, and dishwashers to evaluate broad market trends and perform 

simple regression analysis.

These data indicate an increase in appliance shipments and a decline in appliance price 

and operating cost over the study period 1980-2002. Household income has also risen during this 

time. To simplify the analysis, DOE combined the available economic information into one 

variable, termed relative price, and used that variable in a tabular analysis of market trends and a 

regression analysis.

DOE’s tabular analysis of trends in the number of appliances per household suggests that 

the price elasticity of demand for the three appliances is inelastic. Our regression analysis of 

these same variables suggests that the relative price elasticity of demand is -0.34. The price 

elasticity is consistent with estimates in the literature. Nevertheless, DOE stresses that the 

measure is based on a small data set, using very simple statistical analysis. More importantly, the 

measure is based on an assumption that economic variables, including price, income and 

operating costs, explain most of the trend in appliances per household in the United States since 

1980. Changes in appliance quality and consumer preferences may have occurred during this 

period, but they are not accounted for in this analysis.
9-A-14

9-A.7 DATA USED IN THE ANALYSIS

• Appliance Shipments are defined as the annual number of units shipped in millions. These 

data were collected from the Association of Home Appliance Manufacturers (AHAM)

9,10 and 

Appliance Magazine11 as annual values for each year, 1980–2002. AHAM was used for the 

period 1989–2002 while Appliance Magazine was used for the period 1980–1988.

• Appliance Price is defined as the shipments weighted retail sales price of the unit in 1999 

dollars. Price values for 1980, 1985, 1986, 1991, 1993, 1994, 1998, and 2002 were collected 

from AHAM Fact Books.

12 Price values for other years were interpolated from these eight 

years of data.

• Housing Starts data were collected from the U.S. Census construction statistics (C25 

reports) as annual values for each year, 1980–2002.13

• Replacements, driven by product retirements, are estimated with the assumption that some 

fraction of sales arise from consumers replacing a product at the end of its useful life. Since 

each appliance has a different expected lifespan (19 years for refrigerators,14 14 years for 

clothes washers,15 12 years for dishwashers16), replacements are calculated differently for 

each appliance type. Replacements are estimated as the average of shipments 14–24 years 

previous for refrigerators, 9–19 years previous for clothes washers, and 7–17 years previous 

for dishwashers. Historical shipments data were collected from AHAM and Appliance 

Magazine.

• Annual Electricity Consumption (UEC) is defined as the energy consumption of the unit in 

kilowatt-hours. Electricity consumption depends on appliance capacity and efficiency. These 

data were provided by AHAM for 1980, 1990–1997 and 1999–2002.10 Data were 

interpolated in the years for which data were not available.

• Operating Cost is the present value of the electricity consumption of an appliance over its 

expected lifespan. The lifespans of refrigerators, clothes washers and dishwashers are 

assumed to be 19, 14, and 12 years respectively. Discount rates of 20 percent6 and 37

percent17 were used, producing similar estimates of price elasticity. A study by Hausman 

recommended a discount rate of “about 20 percent” in its introduction and presented results 

ranging from 24.1 percent to 29 percent based on his calculations for room air conditioners.

A study by Train suggests a range of implicit discount rates averaging 35 percent for 

appliances.

• Income: Median annual household income in 2003 dollars. These data were collected for 

each year, 1980–2002, from Table H-6 of the U.S. Census.

18
9-A-15

REFERENCES

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

on Economic Activity, 1971. 1971(1): pp. 234-239 

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

of New Consumer Durables. Journal of Forecasting, 1998. 17

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

Appliance Efficiency Level. Review of Economics and Statistics, 1997

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

Models of Sales. Journal of Marketing Research, 1988

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

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

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

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

durables. The Bell Journal of Economics, 1979

7. Train, K., Discount Rates in Consumers' Energy-Related Decisions. Energy: The 

International Journal, 1985. 10(12)

8. Train, K., Discount Rates in Consumers' Energy-Related Decisions. Energy: The 

International Journal, 1985. 10(12): pp. 1243-1253 

9. Association of Home Appliance Manufacturers, AHAM 2000 Fact Book. 2000. 

Washington, DC.

10. Association of Home Appliance Manufacturers, AHAM 2003 Fact Book. 2003. 

Washington, DC.

11. Statistical Review. Appliance Magazine, April, 1990

12. Association of Home Appliance Manufacturers, AHAM Fact Books, 1987, 1988, 1993, 

1995, 2000, and 2003. Washington, DC. 

13. U.S. Census Bureau, Current Construction Reports, C25 – New One-Family Houses 

Sold. Washington, DC. <http://www.census.gov/prod/www/abs/c25.html>

14. Duemling, R., Energy and Resources Group, University of California. Berkeley, 1999. 

15. U.S. Department of Energy-Office of Building Research and Standards, Final Rule 

Technical Support Document (TSD): Energy Efficiency Standards for Consumer 
9-A-16

Products: Clothes Washers, 2000. U.S. Department of Energy. Washington, DC. Report 

No. LBNL-47462. 

<http://www.eren.doe.gov/buildings/codes_standards/reports/cwtsd/index.html>

16. U.S. Department of Energy-Office of Codes and Standards, Technical Support 

Document: Energy Conservation Standards for Consumer Products: Dishwashers, 

Clothes Washers, and Clothes Dryers including: Environmental Impacts, Regulatory 

Impact Analysis, December, 1990. Washington, DC. Report No. DOE/CE-0299P. 

<http://papyrus.lbl.gov/>

17. K.E. Train and T. Atherton, Rebates, loans, and customers’ choice of appliance efficiency 

level: combining stated- and revealed-preference data. The Energy Journal, 1995

18. U.S. Census Bureau, Income, Historical Income Tables – Households, Table H-6. 

Washington, DC. <http://www.census.gov/hhes/www/income/histinc/inchhtoc.html>