APPENDIX 10A. RELATIVE PRICE ELASTICITY OF DEMAND FOR
 

APPLIANCES
 

TABLE OF CONTENTS
 

10A.1 INTRODUCTION ................................................................................................ 10A-1 

10A.2 LITERATURE REVIEW ..................................................................................... 10A-1 

10A.2.1 Price ...................................................................................................................... 10A-1 

10A.2.2 Income................................................................................................................... 10A-1 

10A.2.3 Appliance Efficiency and Discount Rates ............................................................ 10A-2 

10A.3 VARIABLES DESCRIBING THE MARKET FOR REFRIGERATORS, 

CLOTHES WASHERS, AND DISHWASHERS ................................................ 10A-2 

10A.3.4 Physical Household/Appliance Variables............................................................. 10A-3 

10A.3.5 Economic variables............................................................................................... 10A-3 

10A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE 

SHIPMENTS ........................................................................................................ 10A-4 

10A.4.1 Broad Trends......................................................................................................... 10A-5 

10A.4.2 Model Specification .............................................................................................. 10A-7 

10A.4.3 Model Discussion.................................................................................................. 10A-8 

10A.4.4 Analysis Results.................................................................................................... 10A-8 

10A.4.4.1 Individual Appliance Model ............................................................... 10A-8 

10A.4.4.2 Combined Appliance Model............................................................... 10A-9 

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

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

10A.4.5.2 Disaggregated Variables ................................................................... 10A-10 

10A.5 LONG RUN IMPACTS...................................................................................... 10A-11 

10A.6 SUMMARY........................................................................................................ 10A-12 

10A.7 DATA USED IN THE ANALYSIS ................................................................... 10A-13 

LIST OF TABLES 

Table 10A.2.1 Estimates of the Impact of Price, Income and Efficiency on 

Automobile and Appliance Sales.............................................................. 10A-2
 

Table 10A.3.1 Physical Household/Appliance Variables................................................. 10A-3
 

Table 10A.3.2 Economic Variables.................................................................................. 10A-4
 

Table 10A.4.1 Simple Estimate of Total Price Elasticity of Demand .............................. 10A-6
 

Table 10A.4.2 Tabular Estimate of Relative Price Elasticity of Appliance Demand....... 10A-7
 

Table 10A.4.3 Individual Appliance Model Results ........................................................ 10A-9
 

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

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

Table 10A.4.6 Disaggregated Regression Results, 37 percent discount rate.................. 10A-11
 

Table 10A.5.1 Change in Price Elasticity of Demand for Automobiles following a
 

Purchase Price Change............................................................................ 10A-12
 

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Table 10A.5.2 Change in Relative Price Elasticity for Home Appliances following a
 

Purchase Price Change............................................................................ 10A-12
 

LIST OF FIGURES 

Figure 10A.3.1 Trends in Appliance Shipment, Housing Starts and Replacements.......... 10A-4
 

Figure 10A.4.1 Residual Shipments and Appliance Price ................................................. 10A-6
 

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APPENDIX 10A. RELATIVE PRICE ELASTICITY OF DEMAND FOR APPLIANCES 

10A.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. This appendix 

begins with a review of the existing economics literature describing the impact of economic 

variables on the sale of durable goods in section 9A.2. In section 9A.3, the market for home 

appliances and changes in it over the past 20 years is described. In section 9A.4, DOE 

summarizes the results of its regression analysis and presents estimates of the price elasticity of 

demand for the three appliances. In section 9A.5, DOE presents development of an ‘effective’ 

purchase price elasticity. DOE’s interpretation of its results is presented in section 9A.6. 

Finally, section 9A.7 describes the data used in DOE’s analysis. 

10A.2 LITERATURE REVIEW 

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

the sale of household appliances. In this section DOE provides a short review of this literature 

which suggests the likely importance of these variables. 

10A.2.1 Price 

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

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

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

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

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

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

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

10A.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). 

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10A.2.3 Appliance Efficiency and Discount Rates
 

Many studies estimate the impact of appliance efficiency on consumer appliance choice. 

Typically, this impact is summarized by the implicit discount rate, i.e., the rate consumers use to 

compare future appliance operating cost savings against an appliance purchase price premium. 

One early and much cited study concludes that consumers use a 20 percent implicit discount rate 

when purchasing room air conditioners (Table 9A.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 10A.2.1Estimates 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 - -

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

4 5	 6 7 G. Tellis, 1988; D. Jain and R. Rao; J. Hausman; K. Train, 1985. 

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

9 Average brand price elasticity across 41 studies. 

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

10A.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/appliance variables, and 

economic variables. 

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10A.3.4 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. 

10A.3.5 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 the 1980–2002 study period, annual shipments grew 69 percent for clothes 

washers, 81 percent for refrigerators and 105 percent for dishwashers (Table 9A.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 9A.3.1).a For mature markets such as these, replacements 

exceed appliance sales associated with new housing construction. 

Table 10A.3.1Physical Household/Appliance Variables 

Shipments1 (millions) Housing Starts2 (millions) Replacements3 (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% 1

Shipments: Number of units sold. Sources: AHAM Fact Book and Appliance Magazine.
 2

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

Replacements: Average of annual lagged shipments, with lag equal to expected appliance operating life, ± 5 years.
 

Nevertheless, it is apparent that appliance shipments increased somewhat more rapidly 

than housing starts and replacements. This is shown by comparing the beginning and end points 

of lines representing “starts plus replacements” (uppermost solid line in Figure 9A.3.1) and 

“shipments” (diamond linked line in Figure 9A.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 increase in shipments, compared to housing starts plus 

replacements, suggests that the appliance per household ratio increased over the study period. 

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 9A.3. 

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10 

Refrigerator Shipments 

New Housing 

Clothes Washer Shipments 8 6 Dishwasher Shipments 

9 

Retirements 7 

5 8 Shipments 

6 

7 

s 

5 

6 

s 

4 

s 

5

Million

4

Million

3

4 

Million

3 

1 

2 

3 

1 

2 

1 

2 

0 

1980 1984 1988 1992 1996 2000 

0 

1980 1984 1988 1992 1996 2000 

0 

1980 1984 1988 1992 1996 2000 

Figure 10A.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 9A.3.2). 

Table 10A.3.2Economic Variables 

Price1 (1999$) Operating Cost2 (1999$) Household Income3 (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% 1

Price: Shipment weighted retail sales price. Sources: AHAM Fact Book and Appliance Magazine. 2

Operating Cost: Annual electricity price times electricity consumption. Source: AHAM Fact Book. 3

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

10A.4	 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE 

SHIPMENTS 

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

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

for only 12 years of the 1980-2002 study period. Industry price data is 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 

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

variables. Finally, results are presented of the regression analysis and the estimate of the price 

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elasticity of demand for appliances. In this section (specifically section 9A.4.5), DOE also 

presents the results of regression analysis performed with more complex models, and used to test 

assumptions made to specify the simple model. These results support the simple model 

specification, and estimates of the price elasticity of appliance demand measured with that 

model. 

10A.4.1 Broad Trends 

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

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

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

variability in appliance shipments over the period.b DOE assumes the rest of the variability in 

shipments (referred to as “residual shipments”) is explained by economic variables, and present a 

tabular method for measuring price elasticities described below. 

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 c cost: 

TP = PP + PVOC

where: 

TP = Total price,
 

PP = Appliance purchase price, and
 

PVOC = Present value of operating cost.
 

Over the study period, residual shipments increase 30 percent for refrigerators, 19 percent for 

clothes washers, and 23 percent for dishwashers in proportion to total shipments. At the same 

time, total prices decline 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 

9A.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. 

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Table 10A.4.1Simple Estimate of Total Price Elasticity of Demand
 

Residual Shipments (millions) Total Price (199$) 

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 9A.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 10A.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, calculated as total price divided by household income and represented by the 

d 

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

following equation:

RP = 

Income

TP

where: 

RP = 

TP = 

Income = 

Relative price, 

Total price, and 

Household income. 

d 

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. 

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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 9A.4.2). 

Table 10A.4.2Tabular 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 

10A.4.2 Model Specification 

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

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

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

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

Ship = a + b× RP + c ×[Starts + Rplc] Eq. 9A.1 

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. 

The following combined regression equation is used 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 limited data availability and similarity in 

price and shipment behavior across appliances (see Figure 9A.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. 9A.2 

where: 

CW = Quantity of clothes washers sold, and
 

DW = Quantify of dishwashers sold.
 

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10A.4.3 Model Discussion 

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 other possible 

explanations, such as changing consumer preferences and increases in the quality of 

appliances—had no impact. 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 specific 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. 9A.1 and 9A.2. The results of this analysis, 

presented in section 9A.4.5, indicate that the elasticity of relative price is relatively 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, thus 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. 9A.3 

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

10A.4.4 Analysis Results 

10A.4.4.1 Individual Appliance Model 

The individual appliance regression equations are specified as followed (as shown earlier 

as Eq. 9A.1): 

Ship = a + b× RP + c ×[Starts + Rplc] 

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

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

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

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

tabular approach presented above (Table 9A.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 shipments increase in direct 

proportion to an increase in “starts + replacements”, holding economic variables constant. 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 10A.4.3Individual 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 

10A.4.4.2 Combined Appliance Model 

The combined appliance regression equation is specified as follows (as shown earlier as 

Eq. 9A.2): 

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

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 

9A.4.4). The elasticity of relative price estimated with this model 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 above. 

Table 10A.4.4Combined Appliance Model Result 

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 

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10A.4.5 Additional Regression Specifications and Results 

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

appliance models. The first is that the implicit price variable in the basic regression model is 

specified using a 37 percent implicit discount rate, to aggregate appliance price and operating 

cost. 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. 

10A.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 9A.1 and 9A.2. The estimated coefficient 

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

coefficients estimated for same variable reported above using 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 9A.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 relatively insensitive to changes in the discount rate. 

Table 10A.4.5 Combined and Individual Results, 20 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 

10A.4.5.2 Disaggregated Variables 

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

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

explanatory variables to the basic model (as shown earlier as Eq. 9A.3). 

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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 9A.4.6). The elasticity of relative price based on 

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

averages -0.35 across the individual appliances (Table 9A.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 10A.4.6 Disaggregated Regression Results, 37 percent discount rate 

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 

10A.5 LONG RUN IMPACTS 

As noted above in Table 9A.2.1 in section 9A.2, 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 9A.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 as to how the relative price elasticity is 

affected once a new standard takes effect. 

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

run elastcities. 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 9A.5.1 shows how the automobile price 

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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 10A.5.1Change in Price Elasticity of Demand for Automobiles following a Purchase 

Price Change 

Years Following Price Change 

1 2 3 5 10 20 

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

Relative Change in 

Elasticity to 1st year 

1.00 0.78 0.63 0.46 0.35 0.33 

Source: Hymans, 1971. 

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

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

9A.5.2 presents the time series. 

Table 10A.5.2Change 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 

10A.6 SUMMARY 

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

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

DOE finds only a few studies of appliance markets that are relevant to this analysis, and no 

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

summarized from the literature, suggests that the demand for appliances is price inelastic. Other 

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

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

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

There is not enough price and operating cost data available to perform complex analysis 

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

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

simple regression analysis. 

These data indicate that there has been a rise in appliance shipments and a decline in 

appliance price and operating cost over the period. Household income has also risen during this 

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

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variable, termed relative price, and used this 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 important, the 

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

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

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

period, but they are not accounted for in this analysis. 

10A.7 DATA USED IN THE ANALYSIS 

•	 Appliance Shipments: Shipments are defined as the annual number of units shipped in 

millions. These data were collected from the Association of Home Appliance Manufacturers 

(AHAM)8 and Appliance Magazine9 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: 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.10 Price values for other years were interpolated from 

these eight years of data. 

•	 Housing Starts: Housing starts data were collected from U.S. Census construction statistics 

(C25 reports) as annual values for each year, 1980–2002.11 

•	 Replacements: Retirement-driven replacements are estimated with the assumption that some 

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

each appliance has a different expected lifespan (19 years for refrigerators12, 14 years for 

clothes washers13, 12 years for dishwashers14), 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: Electricity Use (UEC) is defined as the energy 

consumption of the unit in kilowatt-hours. Electricity consumption is dependent on appliance 

capacity and efficiency. These data were provided by AHAM for 1980, 1990–1997 and 

1999–2002.15 Data were interpolated in the years for which data were not available. 

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• Operating Cost: 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 

percent 6 and 37 percent16 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. This data was collected for each 

year, 1980–2002, from Table H-6 of the U.S. Census.17 

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REFERENCES
 

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

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

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

Consumer Durables, Journal of Forecasting, 1998. 

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

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

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

Models of Sales, Journal of Marketing Research, 1988. 

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

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

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

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

durables, The Bell Journal of Economics, 1979. 

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

Energy, 1985. 

8	 Association of Home Appliance Manufacturers. AHAM Fact Books, 2000 and 2003. 

Washington, DC. 

9	 Statistical Review. Appliance Magazine, April, 1990. 

10	 Association of Home Appliance Manufacturers. AHAM Fact Books, 1987, 1988, 1993, 1995, 

2000, and 2003. Washington, DC. 

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

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

12	 Duemling, Reubin. Product Life of Refrigerators, 1999. University of California, Berkeley, 

Energy and Resources Group masters thesis. 

13	 U.S. Department of Energy-Office of Building Research and Standards. Final Rule Technical 

Support Document (TSD): Energy Efficiency Standards for Consumer Products: Clothes 

Washers, December, 2000. Washington, DC. Chapter 7. 

14	 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, December, 1990. Washington, DC. DOE/CE-02999P. Chapter 4. 

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15	 Association of Home Appliance Manufacturers. AHAM 2003 Fact Book, 2003. Washington, 

DC. 

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

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

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

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

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