<<-i

APPENDIX 9-A RELATIVE PRICE ELASTICITY OF DEMAND FOR CLOTHES 

WASHERS

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-2

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

9-A.3 VARIABLES THAT DESCRIBE THE MARKET FOR CLOTHES 

WASHERS........................................................................................................ 9-A-3

9-A.3.4 Household/Appliance Variables......................................................................... 9-A-3

9-A.3.5 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-4

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

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

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

9A.4.4.1 Individual Appliance Model ............................................................. 9-A-8

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

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

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

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

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

9-A.6 PRICE IMPACTS ON THE MARKET SHARE OF FRONT AND TOP 

LOADER CLOTHES WASHERS....................................................................9-A-13

9-A.6.1 Data and Method Used to Perform Analysis......................................................9-A-13

9-A.6.2 Regression Results............................................................................................9-A-17

9-A.7 SUMMARY .....................................................................................................9-A-18

LIST OF TABLES

Table 9-A.2.1 Effect of Price, Income, and Efficiency on Automobile and Appliance 

Sales ...................................................................................................... 9-A-2

Table 9-A.4.2 Tabular Estimate of Total Price Elasticity of Demand ............................ 9-A-6

Table 9-A.4.3 Estimate of Relative Price Elasticity of Appliance Demand .................... 9-A-7

Table 9-A.4.4 Results of Individual Appliance Models................................................. 9-A-9

Table 9-A.4.5 Results of Combined Appliance Model .................................................. 9-A-9

Table 9-A.4.6 Combined Results, 20-Percent Discount Rate........................................9-A-10

Table 9-A.4.7 Individual Results, 20-Percent Discount Rate ........................................9-A-10
<<-ii

Table 9-A.4.8 Disaggregated Results: Combined Appliances, 37-Percent Discount 

Rate.......................................................................................................9-A-11

Table 9-A.4.9 Disaggregated Results: Individual Appliances, 37-Percent Discount 

Rate.......................................................................................................9-A-12

Table 9-A.5.10 Change in Price Elasticity of Demand for Automobiles Following a 

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

Table 9-A.5.11 Change in Relative Price Elasticity for Home Appliances Following a 

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

LIST OF FIGURES

Figure 9-A.3.1 Trends in Clothes Washer Shipments, Housing Starts, and 

Replacements......................................................................................... 9-A-4

Figure 9-A.4.2 Residual Shipments and Appliance Price................................................ 9-A-6

Figure 9-A.6.1 Front- and Top-Loading Clothes Washer Price Trends (monthly 

average prices) ......................................................................................9-A-14

Figure 9-A.6.2 Trends in Relative Sales and Prices of Front- and Top-Loading Clothes 

Washers ................................................................................................9-A-15

Figure 9-A.6.3 Trends in Relative Volume, Number of Cycles and Electric Controls 

of Front- and Top-Loading Clothes Washers.........................................9-A-16
9-A-1

Appendix 9-A. RELATIVE PRICE ELASTICITY OF DEMAND FOR CLOTHES 

WASHERS

9-A.1 INTRODUCTION

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

clothes washers. Section 9-A.2 reviews the literature regarding 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 during the past 20 years. In section 9-A.4, DOE summarizes the 

results of its regression analysis and presents estimates of the relative price elasticity of demand 

for clothes washers. In section 9A.5, DOE presents development of an “effective” purchase price 

elasticity. Cross-price elasticity of demand for front- and top-loading washers is discussed in 

section 9-A.6. DOE presents its interpretation of results in section 9-A.7. Finally, section 9-A.8 

describes the data DOE used in its analysis.

9-A.2 LITERATURE REVIEW

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

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

importance of those variables to the purchase of residential clothes washers.

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 found that the price elasticity 

of demand declined over time. The author attributed this effect to buyers delaying a purchase 

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, found the elasticity of demand to increase over 

time as more price-conscious buyers enter the market.2 Estimates of the price elasticity of 

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

effect of price on market share found an average price elasticity of -1.75.3 The average estimate 

of price elasticity of demand reported in those studies was -0.34 in the appliance market and -

0.47 in the combined automobile and appliance markets.
9-A-2

Table 9-A.2.1 Effect 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 Duration

Automobiles1 -1.07 3.08 - - Linear regression, stock 

adjustment - Short term

Automobiles1 -0.36 1.02 - - Linear regression, stock 

adjustment - Long term

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

Room Air 

Conditioners2 -0.37* 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 term

Various4 - - -1.76† - Multiplicative regression - Mixed

Room Air 

Conditioners5 - - -1.72 - Non-linear diffusion 1949–1961 Short term

Clothes Dryers5 - - -1.32 - Non-linear diffusion 1963–1970 Short term

Room Air 

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

Household 

Appliances7 - - - 37‡ Assorted - -

Sources: 1S. Hymens, 1971; 2P. Golder and G. Tellis, 1998; 3D. Revelt and K. Train, 1997; 4G. Tellis, 1988; 5D. 

Jain and R. Rao; 6J. Hausman; 7K. Train, 1985.

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

† Average brand price elasticity across 41 studies.

‡ Averaged across several studies referenced herein regarding household appliances.

9-A.2.2 Income

Higher-income households are more likely to own appliances.4

9-A.2.3 Appliance Efficiency and Discount Rate

The effect 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).

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

appliance. This effect typically is summarized by the implicit discount rate; that is, the rate 

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

price. One early and much-cited study concluded that consumers use a 20-percent implicit

discount rate when purchasing room air conditioners (Table 9-A.2.1).5 A survey of several 

studies of various appliances suggested that the consumer implicit discount rate has a broad 

range, averaging about 37 percent.

6
9-A-3

9-A.3 VARIABLES THAT DESCRIBE THE MARKET FOR CLOTHES 

WASHERS

In this section DOE discusses variables that appear to affect shipments of clothes 

washers, including those pertaining to the consumer household, the appliance itself, and 

economic factors.

9-A.3.1 Household/Appliance Variables

Several variables influence the sale of clothes washers. The most important for 

explaining trends in appliance sales are the annual number of new housing units constructed

(housing starts) and the number of appliances that reach the end of their operating life 

(replacement units). Housing starts affect appliance sales, because new homes often are provided 

with, or soon receive, new appliances, including clothes washers. Replacements are correlated 

with sales, because new appliances typically are 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 economic variables 

that affect shipments. Low prices and costs encourage consumers to purchase household 

appliances, and an increase in income improves a consumer’s 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 of clothes washers grew 69 

percent.8, 9 This rising trend in shipments is explained in part by housing starts, which increased 

6 percent11 and by replacements, which rose 50 percent during the period. Replacements are 

determined based on the expected operating life of 14.2 years for clothes washers and on past 

shipments (average of annual lagged shipments, with lag equal to expected appliance operating 

life ± 5 years). For a mature market such as the one for clothes washers, replacements exceed 

sales to new housing construction.

Shipments increased somewhat more rapidly than housing starts plus replacements (69 

percent versus 56 percent). This situation 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 shipments line lies below the line 

for starts plus replacements. In 2002, the shipments line lies above the line for starts plus 

replacements. The more rapid increase in shipments, compared to housing starts plus 

replacements, suggests that the ratio of appliances per household increased during the study 

period.
9-A-4

Figure 9-A.3.1 Trends in Clothes Washer Shipments, Housing Starts, and 

Replacements

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

clothes washers per household. During the study period, clothes washer prices decreased 50 

percent,

8, 9 operating costs fell 33 percent,8 and median household income rose 16 percent.13

9-A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE 

SHIPMENTS

Few data are available for estimating the effect of economic variables on the demand for 

appliances. Industry data regarding operating costs are incomplete—appliance energy use data 

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

available for only 8 years of the study period for each type of appliance.

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

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

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

measure those 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 

analyses performed using more complex models, which are used to test the assumptions 

underlying the simple model. The 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, 

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

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

in appliance shipments during the study period (1980–2002). A log regression of the form: 

shipments = a + b × housing starts + c × retirements indicates that the 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. DOE assumes the rest of the 

variability in shipments (referred to as “residual shipments”) can be explained by economic 

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

To illustrate the tabular approach, DOE defined two new variables—residual shipments 

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

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

equation, is defined as appliance price plus the present value of lifetime operating costs.a

TP = PP + PVOC

Where:

TP = total price,

PP = appliance purchase price, and

PVOC = present value of operating costs.

During the study period, residual shipments in proportion to total shipments increased 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).

 a 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.4.2 Tabular Estimate of Total Price Elasticity of Demand

Residual Shipments million Total Price 2002$

Appliance 1980 2002 Difference Change % 1980 2002 Change % Elasticity

Refrigerator -0.5 1.6 2.1 30 1,541 820 -61 -0.48

Clothes Washer -1.0 0.2 1.1 19 1,042 567 -59 -0.32

Dishwasher -1.0 -0.01 1.0 23 896 464 -64 -0.37

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

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.4.1).

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 

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

Figure 9-A.4.2 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 effect on shipments as a 

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

price, which is calculated as total price divided by household income. The variable is represented 

by the following equation.b

Income

TP

RP =

Where:

RP = relative price,

TP = total price, and

Income = household income.

 b Recall that the income elasticity of demand cited in the literature review was 0.50, and the price elasticity of 

demand cited in the review averaged -0.35. Those results suggest that combining the effects of income and price 

will yield an elasticity less negative than price elasticity alone.
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.4.3 Estimate of Relative Price Elasticity of Appliance Demand

Residual Shipments millions Relative Price 1999$

Appliance 1980 2002 Change % 1980 2002 Change % Elasticity

Refrigerator -0.532 1.597 30 0.041 0.019 -74 -0.40

Clothes Washer -0.953 0.174 19 0.028 0.013 -72 -0.26

Dishwasher -0.974 -0.005 23 0.024 0.011 -76 -0.30

9-A.4.2 Model Specification

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

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

following equation, which DOE chose for this analysis, includes one physical household variable 

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

operating costs, divided by income). 

Ship = a + b× RP + c ×[Starts + Rplc]

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 coefficient 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 the 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

Where:

CW = quantity of clothes washers sold, and
9-A-8

DW = quantify of dishwashers sold.

9-A.4.3 Discussion of Model

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

variables—income, price, and operating costs—are responsible for the total observed increase in

residual appliance shipments during the study period. In other words, DOE assumed no impact 

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

appliances. The assumption seems unlikely, but without additional data, the effect of other 

variables on the price elasticity of demand cannot be measured. DOE effectively assumed that 

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

purchased, had relatively little effect on the total number of appliances purchased in a year.

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

price variable is specified, assuming that (1) the correct implicit discount rate was used to 

combine appliance price and operating costs and that (2) rising income has the same effect on 

shipments as does falling total price. In addition, the “starts + replacements” variable is specified

assuming (3) that starts and replacements have similar effects 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 the previous equations. The results of this analysis, 

presented in section 9-A.4.4, indicate that the elasticity of relative price is fairly insensitive to 

changes in discount rate.

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

separates income from total price and replacements from starts, thereby adding two explanatory 

variables to the basic model. The following equation shows the separations.

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

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

The 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. Also described are the effects of a lower consumer discount 

rate and disaggregated variables.

9A.4.4.1 Individual Appliance Model

The individual appliance regression equations are specified as shown by the following 

equation.
9-A-9

Ship = a + b× RP + c ×[Starts + Rplc]

In 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. Those elasticities are similar to the ones reported in the literature survey for 

appliances (Table 9-A.2.1). They are remarkably similar to the price elasticities 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 values for R-squared (greater than 0.95) and t-statistics (t-stat in the table; greater than 5) in 

the results provide a measure of confidence in the analysis, despite the small data set.

Table 9-A.4.4 Results of Individual Appliance Models

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

9A.4.4.2 Combined Appliance Model

The combined appliance regression equation is specified as shown in the next equation.

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

This regression analysis indicates that the model fits the shipments data well (high Rsquared), and that the variables included in the model are statistically significant (Table 9-A.4.4). 

Based on this model the elasticity of relative price estimated is -0.34, close to the average value 

estimated by the individual appliance models (-0.35). The elasticity also is close to estimates 

reported in the literature survey and calculated using the tabular approach described in section 9-

A.4.1. 

Table 9-A.4.5 Results of Combined Appliance Model 

Variable Coefficient t-stat

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-10

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 price variable 

in the basic regression model is a 37-percent implicit discount rate. The second states that the 

implicit price variable is defined assuming that rising income has the same effect on shipments 

as does falling total price. The third states that the “starts + replacements” variable is defined 

assuming that housing starts have a similar effect on shipments as do appliance replacements. 

9A.4.5.1 Lower Consumer Discount Rate

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

operating costs using a 20-percent implicit discount rate and performed a second regression 

analysis based on the models described in earlier equations. 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 and Table 9-A.4.6). 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.4.6 Combined Results, 20-Percent Discount Rate

Variable Coefficient t-stat

Intercept -1.53 -14.61

Total price/income -0.33 -10.69

Starts + Replacements 1.20 13.65

Clothes Washers -0.18 -8.69

Dishwashers -0.32 -6.57

R2 0.982

Observations 69

Table 9-A.4.7 Individual Results, 20-Percent Discount Rate

Refrigerators Clothes Washers Dishwashers

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 + Replacements 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-11

9A.4.5.2 Disaggregated Variables

To investigate its second and third assumptions (identified in section 9-A.4.3), 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 (identified in section 

9-A.4.2).

Ship = a + b×TP + c × Incone + 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.4.7 and Table 9-A.4.8). The elasticity of 

relative price based on the model described in section 9-A.4.2 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 the variables for household income and “starts + replacements” in the model.

Table 9-A.4.8 Disaggregated Results: Combined Appliances, 37-Percent Discount Rate

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

Replacements 0.62 8.12

Clothes Washers -0.24 -9.25

Dishwashers -0.46 -7.68

R2 0.985

Observations 69
9-A-12

Table 9-A.4.9 Disaggregated Results: Individual Appliances, 37-Percent Discount Rate

Refrigerators Clothes Washers Dishwashers

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

Replacements 0.56 6.06 0.56 2.09 0.65 5.86

R2 0.984 0.985 0.979

Observations 23 23 23

9-A.5 LONG-RUN IMPACTS

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

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

the first two rows of Table 9-A.2.1, one source (Hymans) indicates that for automobiles the price 

elasticity of demand differs significantly over the short run and long run.1 Because DOE’s 

forecasts of shipments and national impacts due to standards comprises a 30-year 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 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. To estimate how the 

relative price elasticity changes over time, therefore, DOE relied on the Hymans study pertaining 

to automobiles. Table 9-A.5.1 shows how, based on the Hymans study, the price elasticity of 

demand for automobiles changes in the years following a change in purchase price. With 

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

a terminal value about the 10th year following the price change.

Table 9-A.5.10 Change in Price Elasticity of Demand for Automobiles Following a 

Change in Purchase Price 

Years Following Price Change

1 2 3 5 10 20

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

Relative Change in 

Elasticity to 1st year

1.00 0.78 0.63 0.46 0.35 0.33

Source: Hymans, 1971.

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

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

A.5.2 presents the time-series. 
9-A-13

Table 9-A.5.11 Change in Relative Price Elasticity for Home Appliances Following a 

Change in Purchase Price 

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 PRICE IMPACTS ON THE MARKET SHARE OF FRONT AND TOP 

LOADER CLOTHES WASHERS

This section provides preliminary estimates of cross-price impacts on the market share of 

top-loading and front-loading clothes washers. Cross-price impacts measure the change in the 

market share of one washer configuration (e.g., top loaders) caused by a change in the price of 

the other washer configuration (e.g., front loaders). 

9-A.6.1 Data and Method Used to Perform Analysis 

The data DOE used to conduct this analysis derive from washer sales data collected by 

the NPD Group between 2004 and 2009.

c

Figure 9-A.6.1

The NPD data includes comprehensive product 

information, including number of programmed wash cycles available, loading type, type of 

sensor, capacity, ENERGY STAR certification, unit price, unit sales, and so on. For this 

analysis, cross-price impacts are estimated using a subset of the NPD data including loading 

type, washer capacity, number of programmed cycles, control type, monthly market share, and 

monthly average price. , Figure 9-A.6.2 and Figure 9-A.6.3 summarize the data

used in this analysis. 

 

c The subset of data points DOE used in this analysis accounts for around 84% of the total NPD data from 2004 

through2009. The other 16% of the data points were deleted due to missing values of some washer attributes. 
9-A-14

Weighted Average Price

300

400

500

600

700

800

900

1000

Jan-04

Apr-04

Jul-04

Oct-04Jan-05

Apr-05

Jul-05

Oct-05Jan-06

Apr-06

Jul-06

Oct-06Jan-07

Apr-07

Jul-07

Oct-07Jan-08

Apr-08

Jul-08

Oct-08Jan-09

Apr-09

Jul-09

Oct-09

Year

RCW Price ($)

Front-Loader

Top-Loader

Figure 9-A.6.1 Front- and Top-Loading Clothes Washer Price 

Trends (monthly average prices)

Weighted average price for each class of clothes washer was calculated by dividing the 

total dollar value of all sales in a given month by the number of units sold in that month. These 

data show two trends: First that the absolute price of front-loading clothes washers is decreasing, 

and second, that the absolute price of top-loading clothes washers is increasing. The decreasing 

price trend of front-loading clothes washers may be explained by their increasing market share 

and increasing number of absolute unit sales, which allow manufacturers to take advantage of 

economies of scale to lower prices.

The relationship between historical trends of front- and top-loading clothes washers may 

be better viewed as ratios, as in the following two figures. In each figure, individual trends are 

ratios of front-loading (numerator) to top-loading (denominator) clothes washers. The points 

above 1.00 represent a higher proportion going to front-loaders, and the points below 1.00 

represents a higher proportion going to top-loaders. 
9-A-15

Ratios of front- to top-loading clothes washers

0.00

0.50

1.00

1.50

2.00

2.50

3.00

2004 2005 2006 2007 2008 2009

Price

Unit Sales

Figure 9-A.6.2 Trends in Relative Sales and Prices of Front- and Top-Loading 

Clothes Washers

The price trend shown in Figure 9-A.6.2, based on sales-weighted price data, shows that 

in 2004, the average price of front-loaders was on average 2.5 times more than the average price 

of top-loaders. However, the trend decreases continuously over the six-year period, showing that 

in late 2009 this ratio has dropped to about 1.5; at this point front-loaders cost about 1.5 times as 

much as top-loaders. This trend results both from the decreasing average price of front-loaders 

and the increasing average price of top-loaders, as illustrated in Figure 9-A.6.1 above.

The unit sales ratio complements the price ratio and demonstrates the decreasing market 

dominance of top-loaders. In January 2004 (the left-most point on the chart), a ratio of 0.15 

indicates that total front-loading washing machine sales were only 15% of total top-loading 

washing machine sales. However, this ratio has moved steadily toward unity, even crossing the 

1.00 line at one point in late 2009. The unit sales trend indicates that total sales of front-loaders 

will equal or surpass sales of top-loaders in the near future.

Together, these two trends illustrate an important point: that the prices of top-loaders and 

front-loaders are growing closer, and that the market share breakdown is becoming increasingly 

balanced. 
9-A-16

Ratios of front- to top-loading clothes washers

0.00

1.00

2.00

3.00

4.00

5.00

6.00

2004 2005 2006 2007 2008 2009

Washer Tub Volume

Available Wash Cycles

Available Models with Electronic

Controls

Figure 9-A.6.3 Trends in Relative Volume, Number of Cycles and Electric 

Controls of Front- and Top-Loading Clothes Washers

Figure 9-A.6.3 illustrates three trends: 1) The relative size of washer tub volume, 2) the 

relative number of available wash cycles, and 3) the relative number of washer models with 

electronic controls. We explain each of these in turn.

Washer tub volume has been increasing in absolute terms for both front-loaders and toploaders. To calculate a ratio trend, we take the weighted average of front-loader washer tub sizes 

for a given month and divide by the weighted average of top-loader washer tub volume for the 

same month. While both of these averages have increased steadily, they do so in parallel, 

producing a nearly flat trend line. We note only that the trend hovers at slightly above one, 

showing that front-loaders tend to have a slightly larger capacity on average.

Available wash cycles refers to the number of pre-programmed wash cycles in a given 

model. For example, a simple clothes washer might have a cold water permanent press cycle, a 

hot water permanent press cycle, and warm water delicate cycle, for a total of three available 

wash cycles. Here, we calculate the ratio between the average number of wash cycles available 

on front-loaders in a given month (weighted by sales) and the average number of wash cycles 

available on top-loaders in the same month (also weighted by sales). Data shows that the average 

number of cycles for both classes of clothes washer has remained at about 10 between 2004 and 

2008. Then in 2009 we see an increase to about 13 cycles for top-loaders, which pulls the ratio 

down to about 0.7 for that year, as seen in the chart above.

Electronic controls differentiate a particular model of clothes washer from one with 

mechanical controls. Today, consumers can find both top- and front-loaders with either 

mechanical or electronic controls. Here we calculate the ratio of the total number of frontloading models available with electronic controls to the total number of top-loading models 

available with electronic controls. These numbers are not sales-weighted, but simply reflect the 

total number of models that consumers purchased. In January 2004, manufacturers offered 22 

front-loading models with electronic controls and 33 top-loading models with electronic controls. 
9-A-17

By January 2009 this number had increased to 207 and 50, respectively. The trend line above 

illustrates this relatively sharp increase in the number of available front-loaders with electronic 

controls.

In order to estimate the impact of price changes on market share, DOE applied a logistic 

regression method to regress market share on price variables and other attributes. The basic form 

of a logistic regression is: 

pi = 1

1 + e−(β0+β1x1,i+⋯+βkxk,i)

With some simple operations, the model can be transformed to an equivalent log-linear 

form:

ln � pi

1 − pi

� = β0 + β1x1,i + ⋯ + βkxk,i

In this case, pi is the market share of either top- or front-loading clothes washers, and 

pi

1−pi

is the ratio of clothes washer market shares, i.e., the relative probability of the market share 

of top and front-loading clothes washers. The explanatory variables include price-related 

variables, washer size and other washer attributes.

9-A.6.2 Regression Results

The logistic regression model equation estimated in our clothes washer analysis is shown below.

ln � Market ShareFront

1 − Market ShareFront

�

= −2.985386 + 0.0035452 × PriceTop − 0.0049114 × PriceFront + 4.24347

×

SizeFront

SizeTop

Where: 

= the relative probability of the market share of front and toploading clothes washers

= weighted monthly average price of top-loaders (as described in Figure 9-

A.6.1)

= weighted monthly average price of front-loaders (as described in Figure 9-

A.6.1)
9-A-18

= ratio between the monthly weighted average of front-loaders tub volume and 

the monthly weighted average of top-loaders tub volume

The equation indicates that front loader market share is positively correlated with top loader 

price and size and negatively correlated with front loader price.d The price coefficients suggest 

that top- and front-loading washers are substitutes for each other. The positive coefficient 

associated with the size variable indicates that capacity is a desirable clothes washer feature for 

most consumers.

These regression results were used to derive the cross price impact of a change in the front 

loading washer price on the top loading market share (and vice versa). For example, these results 

suggest that a 10% increase in the price of front loader washers would lead to a 10.7 % decrease 

in top-loader market share, holding other variables constant and measured as changes from the 

reference case using average values for each variable. In this case, the front-loading cross-price 

impact (percent change in top-loading market share over percent change in front-loading price) is 

1.07.e

9-A.7 SUMMARY

Similarly, these results indicate that a 20% price increase for top-loading washers would 

yield a 21.49 % increase in front-loading market share, measured as changes from the variable 

means. Thus, in this example the top-loader cross-price impact is also 1.07.

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

finds only a few studies that are relevant to the analysis and no studies after 1980 that use timeseries 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, so 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 operating costs. 

There are too few data available on prices and operating costs to perform a complex 

analysis of dynamic changes in the appliance market. Instead, DOE used available data to 

evaluate broad market trends and to perform simple regression analyses. The data indicate an 

increase in appliance shipments and a decline in appliance prices and operating costs for1980–

2002. Household income also rose during that period. To simplify the analysis, DOE combined 

 

d All variables in this regression were statistically significant; the R2 in the regression was 0.88. e Price elasticity varies according to the reference price and market share – typically measured as changes from 

mean values for these variables in the data set. In our data, the reference top-loading washer price is $403.78, the 

reference front-loading washer price is $823.83, the corresponding reference top-loading washer market share is 

71% and the corresponding reference front washer market share is 29%.
9-A-19

the available economic information into one variable, termed relative price, and used that

variable in a tabular analysis of market trends and in a regression analysis.

DOE’s tabular analysis of trends in the number of appliances per household indicates a

price inelasticity of demand for residential clothes washers. DOE’s regression analysis of the

same variables suggests that the relative price elasticity of demand is -0.34, a figure consistent 

with estimates in the literature. Nevertheless, DOE stresses that the measure is based on a small 

data set and employs 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 that period, but they are not 

accounted for in this analysis.

The estimates of cross-price impacts on the market share provided in section 9-A.6 are 

intuitive, but preliminary. The positive cross-price impacts on the market share for both frontand top-loading clothes washers supports the assumption that the two types of washers are 

substitute goods. Although more information could be captured by incorporating more washer 

attributes in the regression for estimating cross-price impacts, those attributes may be highly 

correlated with each other and with the price variables. Further analysis needs to be done to 

determine the value of adding more variables in estimating cross elasticity or the value of using 

an alternative methodology to evaluate this problem. In general, we should expect to see a 

reduced price impact on the market share when more variables are included in the analysis. 

That is because many of the variables missing from this analysis, including changes in rebate 

programs and energy efficiency awareness, have impacted clothes market share. 
9-A-20

REFERENCES

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

Economic Activity. 1971. 1971(1): pp. 234–239.

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

Consumer Durables. Journal of Forecasting. 1998. 17(3): pp. 259–280.

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

Models of Sales. Journal of Marketing Research. November 1988.

4 U.S. Department of Energy–Energy Information Agency. The Effect of Income on Appliances 

in U.S. Households. 2002. Washington, D.C. (Last accessed March 23, 2010.) 

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

5 Hausman, J. Individual Discount Rates and the Purchase and Utilization of Energy-Using 

Durables. The Bell Journal of Economics. 1979. 10(1): pp. 33–54.

6 Train, K. Discount Rates in Consumers' Energy Related Decisions: a Review of the 

Literature. Energy. 1985. 10(12): pp. 1243–53.