APPENDIX 10A. RELATIVE PRIC E 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 Incom e................................................................................................................. .. 10A-1 10A.2.3 Appliance Efficiency and Discount Rates ............................................................ 10A-2 10A.3 VARIABLES DESCRIBING THE MARKET FOR REFRIGERATORS, CLOT HES 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......................................................................................................... 10 A-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 Com bined Appliance Model............................................................... 10A-9 10A.4.5 Additional Regression Specifi cations 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 Re sults, 20 percent di scount rate................... 10A-10 Table 10A.4.6 Disaggregated Regression Re sults, 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

10A-iTable 10A.5.2 Change in Relative Price Elasticity for Home Appliances following a Purchase Price Change............................................................................ 10A-12

LIST OF F IGURES 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

10A-iiAPPENDIX 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 da ta to determine a price elasticity. This appendix begins with a review of th e existing economics literature de scribing the impact of economic variables on the sale of durable goods in section 9A.2. In sec tion 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 a nd 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 impor tance 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 au tomobile market prior to 1970 finds the price elasticity of demand to decline ove r time. The author explains this as the result of buyers delaying purchases after a pric e 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 co nsumer 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 th e 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 el asticity of demand is 0.50 in the appliance study cited in the literature revi ew, much larger in the au tomobile study (Table 9.A.2.1).

10A-110A.2.3 Appliance Efficiency and Discount Rates Many studies estimate the impact of appliance efficiency on consumer appliance choice. Typically, this impact is summari zed by the implicit discount rate, i. e., the rate consumers use to compare future appliance operating cost savings against an appliance pur chase price premium. One early and much cited study c oncludes 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 c onsumer implicit discount rate has a broad range and averages about 37 percent. 7

Table 10A.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
Automobiles 1 -1.07 3.08

- - Linear Regression, stock adjustment - Short run

Automobiles 1 -0.36 1.02

- - Linear Regression, stock adjustment - Long run Clothes Dryers 2 -0.14 0.26

- - Cobb-Douglas, diffusion 1947-1961 Mixed Room Air Conditioners 2 -0.37 8 0.45

- - Cobb-Douglas, diffusion 1946-1962 Mixed
Dishwashers 2 -0.42 0.79

- - Cobb-Douglas, diffusion 1947-1968 Mixed Refrigerators 3 -0.37

- - 39% Logit probability, survey data 1997 Short run
Various 4 - - -1.76 9 - Multiplicative regression

- Mixed Room Air Conditioners 5 - - -1.72

- Non-linear diffusion 1949-1961 Short run Clothes Dryers 5

- - -1.32

- Non-linear diffusion 1963-1970 Short run Room Air Conditioners 6 - - - 20% Qualitative choice, survey data - - Household Appliances 7 - - - 37% 10 Assorted

- - Sources: 1 S. Hymens. 1971; 2 P. Golder and G. Tellis, 1998; 3 D. Revelt and K. Train, 1997; 4 G. Tellis, 1988; 5 D. Jain and R. Rao; 6 J. Hausman; 7 K. Train, 1985. Notes: 8 Logit probability results are not directly comparab le 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 M ARKET 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/app liance variables, and economic variables.

10A-210A.3.4 Physical Household/Appliance Variables
Several variables influence the sale of refr igerators, clothes washers and dishwashers. The most important for explaining appliance sales trends are the annual number of new households formed (housing starts) and the numbe r 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 ne w appliances are typically purchased when old ones wear out. In principle, if households ma intain 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 encourag e 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 ship ments grew 69 percent for clothes washers, 81 percent for refriger ators and 105 percent for dishwash ers (Table 9A.3.1). This rising shipments trend is explained in part by hous ing 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.3.1 Physical Household/Appliance Variables Shipments 1 (millions) Housing Starts 2 (millions) Replacements 3 (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” lin e 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. 10A-3Refrigerator Shipments

0 1 2 3 4 5 6 7 8 9 10

1980 1984 1988 1992 1996 2000Millions New Housing Retirements Shipments Clothes Washer Shipments

0 1 2 3 4 5 6 7 8

1980 1984 1988 1992 1996 2000Millions Dishwasher Shipments

0 1 2 3 4 5 6

1980 1984 1988 1992 1996 2000Millions

Figure 10A.3.1 Trends in Appliance Shipment, Ho using Starts and Replacements Economic variables, including price, cost and income, may explain this increase in appliances per household. Over the period, applian ce prices decreased 40 percent to 50 percent, operating costs fell between 33 percent and 72 pe rcent, and median household income rose 16 percent (Table 9A.3.2).

Table 10A.3.2 Economic Variables Price 1 (1999$) Operating Cost 2 (1999$) Household Income 3 (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 pri ce 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 co st data is incomplete—applian ce 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 anal ysis can at best evalua te broad data trends, utilizing relatively few explanator y variables. This section be gins 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 assumpti ons to minimize the number of explanatory variables. Finally, results are presented of the regression analys is and the estimate of the price 10A-4elasticity of demand for applian ces. In this section (specifi cally section 9A.4.5), DOE also presents the results of regression analysis performed with more co mplex models, and used to test assumptions made to specify the simple mode l. These results support the simple model specification, and estimates of the price elasti city of appliance demand measured with that model.

10A.4.1 Broad Trends
In this section DOE reviews trends in the physical househol d and economic data sets and posit a simple approach for estimating the price el asticity of appliance demand. As noted above, the physical household variables (starts and ap pliance 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 “resid ual shipments”) is explained by economic variables, and present a tabular method for measuring price elasticities described below. To illustrate this tabular approach, DOE de fines two new variables—residual shipments and total price. Residual shipments are defi ned as the difference between shipments and physical household demand (starts plus replacemen ts). Total price, repr esented by the following equation, is defined as applianc e price plus the present value of lifetime appliance operating cost: c

TP = PP + PVOC

where:

TP = Total price, PP = Appliance purchase price, and PVOC = Present value of operating cost. Over the study period, residual sh ipments increase 30 percent for refrigerators, 19 percent for clothes washers, and 23 percent fo r dishwashers in proportion to to tal shipments. At the same time, total prices decline 47 percent, 45 percent a nd 48 percent for refrigerators, clothes washers, and dishwashers, respectively. Assuming that to tal price explains the entire change in per household appliance usage, a rough estimate is calc ulated of the total pr ice elasticity of demand equal to -0.48 for refrigerators, -0.32 for cl othes washers and -0.37 for dishwashers (Table 9A.4.1).

b A log regression of the form: Shipments = a + b • Ho using 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 y ear operating life for refrigerat ors, 14 year operating life for clothes washers, and a 12 year oper ating life for dishwashers. A 37 percen t discount rate is used to sum annual operating costs into a present value operating cost. 10A-5Table 10A.4.1 Simple Estimate of Total Price Elasticity of Demand Residual Shipments (millions) Total Price (199$) Elasticity Appliance 1980 2002 Difference Change 1980 2002 Change 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 betw een total price and residual shipments suggested by these negative price elasticities is illustrated in a gr aph 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 PriceResidual Shipments Clothes Washers

400 600 800 1000 1200

-1.5 -1.0 -0.5 0.0 0.5 Total PriceResidual Shipments Dishwashers

200 400 600 800 1000

-2.0 -1.5 -1.0 -0.5 0.0 0.5 Total PriceResidual Shipments

Yellow points are observed price data; re d 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 in corporated by defining a third variable, termed relative price, calculated as total price divided by household income and represented by the following equation: d

RP = Income TP

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. 10A-6The percent decline in relative price for the three appliances divided by the per cent decline in residual shipments sugge sts a rough estimate of relative price elasticity equal to -0.40 for refrigerators, -0.26 for clothes washers a nd -0.30 for dishwashers (Table 9A.4.2).

Table 10A.4.2 Tabular Estimate of Relative Pric e Elasticity of Appliance Demand Residual Shipments (millions) Relative Price (1999$) Elasticity Appliance 1980 2002 Change 1980 2002 Change 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 expl anatory variables. The following equation chosen for this analysis includes one physical ho usehold variable (starts plus replacements) and
one relative price variable (the sum of purchase pri ce 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 coe fficient b in this model is interpreted as the relative price elasticity of demand fo r the three appliances. The following combined regression equation is used to estimate an average price elasticity of demand across the th ree appliances, using pooled da ta in a single regression. A combined regression specification is justified, gi ven limited data availability and similarity in price and shipment behavior ac ross appliances (see Figure 9A.4.1). Thus, the model represented by the combined regression equation is consider ed 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. 10A-710A.4.3 Model Discussion The most important assumption used to spec ify this model is that changes in economic variables over the study period—income, price, and operating co st—are responsible for all observed growth in residual appliance shipments. In other words, DOE assumes other possible explanations, such as changing consumer pr eferences and increases in the quality of appliances—had no impact. This assumption seems unlikely but without additi onal data, the impact of this assumption on th e 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 rela tively little impact on the total number of appliances purchased in a year. Three additional assumptions used to sp ecify this model deserve comment. The relative price variable is specified in the model, assumi ng 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 di scount rates, DOE calculated “present value operating cost” using a 20 per cent 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, indica te that the elasticity of relative price is relatively insensitive to changes in the discount rate. To investigate the second and third a ssumptions, DOE specified a regression model separating income from total price and replacem ents from starts, thus adding two additional explanatory variables to the basic mode l 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 elas ticity 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

10A-8-0.40 for refrigerators, -0.31 for clothes wash ers and -0.32 for dishwashers (Table 9A.4.3), averaging -0.35. These elasticities are similar to those reported in th e 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 shipme nts increase in direct proportion to an increase in “starts + replacemen ts”, 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.4.3 Individual Appliance Model Results Refrigerator Clothes Washer Dishwasher Variable Coefficient t-stat Coe fficient 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 R 2 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 va riables 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 ta bular approach above.

Table 10A.4.4 Combined 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 R 2 0.983 Observations 69

10A-910A.4.5 Additional Regression Sp ecifications 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 ba sic regression model is specified using a 37 percent imp licit discount rate, to aggregat e appliance price and operating cost. The second states that the implicit price va riable 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 th at 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 di scount rates, DOE calculated “present value operating cost” using a 20 per cent implicit disc ount rate and performed a second regression analysis based on the models described in equati ons 9A.1 and 9A.2. The estimated coefficient associated with the relative price variable in these regressi ons 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 percen t discount rate is -0.33 in the combined regression and averages -0.35 for the th ree 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 V ariable Intercept Total Price / Income Starts + Retirements CW DW Coefficient -1.53 -0.33 1.20 -0.18 -0.32 t-Stat -14.61 -10.69 13.65 -8.69 -6.57

R 2 Observations 0.982 69

V ariable Intercept Total Price / Income Starts + Retirements Refrigerator Coefficient -1.36 -0.38 1.04 t-Stat -6.26 -6.50 5.73 Clothes Washers Coefficient t-Stat -1.41 -7.49 -0.32 -5.29 1.06 5.83 Dishwasher Coefficient -2.04 -0.33 1.34 t-Stat -17.23 -7.30 11.64

R 2 Observations 0.953 23 0.950 23 0.977 23

10A.4.5.2 Disaggregated Variables To investigate the second and third assu mptions, DOE constructed a regression model separating income from total price and replacem ents from starts, thus adding two additional explanatory variables to the basic mo del (as shown earlier as Eq. 9A.3).
10A-10Ship = a + b × TP + c × Incone + d × Start + e × Rplc + f × CW + g × DW

The estim ated 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 an alysis is relatively insensitive to the specification of household income and “starts + replacements” variables in the model.

Table 10A.4.6 Disaggregated Regression Resu lts, 37 percent discount rate Three Appliances V ariable 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

R 2 0.985 Observations 69 Refrigerato r Clothes Washers Dishwasher V ariable 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

R 2 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 re view provides price elasticities over short and long time periods, also referred to as short run and long run price elasticities. As noted in the firs t two rows of Table 9A.2.1, one source (i.e., Hymans) shows that the price elasticity of demand is significantly different over the shor t 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, considerat ion 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 abov e 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 pr ice 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 10A-11elasticity of demand changes in the years follo wing 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.5.1 Change in Price Elasticity of Dema nd 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 1 st 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 de mand 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.5.2 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 1 st 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 lite rature search, tabular analysis and regression analysis of the impact of price and other variab les on appliance shipments. In the literature, DOE finds only a few studies of appliance market s 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 applia nces are a normal good, such that rising incomes increase the demand for appliances. Finally, the l iterature suggests that consumers use relatively high implicit discount rates, when comparing ap pliance prices and appl iance operating costs. There is not enough price and operating cost da ta available to perform complex analysis of dynamic changes in the appliance market. In this analysis, DOE us es data available for refrigerators, clothes washers and dishwashers to evaluate broad market trends and to perform simple regression analysis.

These data indicate that ther e has been a rise in applianc e shipments and a decline in appliance price and operating cost over the period. Household inco me has also risen during this time. To simplify the analysis, DOE combined the available economic information into one 10A-12variable, termed relative price, and used this variable in a ta bular analysis of ma rket trends, and a regression analysis. DOE’s tabular analysis of trends in the num ber of appliances per household suggests that the price elasticity of demand for the three applia nces 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 lit erature. 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 econom ic variables, including price, income and operating costs, explain most of the trend in appliances per hous ehold 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 annu al number of units shipped in millions. These data were collected from th e Association of Home Appliance Manufacturers (AHAM) 8 and Appliance Magazine 9 as annual values for each year, 1980–2002. AHAM was used for the period 1989–2002 while Applia nce 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 ye ars 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 e quipment at the end of its useful life. Since each appliance has a different expected lifespan (19 years for refrigerators 12 , 14 years for clothes washers 13 , 12 years for dishwashers 14 ), 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 wash ers, 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. Elec tricity 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.

10A-13• Operating Cost: Operating Cost is the present value of the electricity consumption of an appliance over its expected lifespan. The lif espans of refrigerators, clothes washers and dishwashers are assumed to be 19, 14, and 12 years respectively. Discount rates of 20 percent 6 and 37 percent 16 were used, producing similar estim ates of price el asticity. 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 dolla rs. This data was collected for each year, 1980–2002, from Table H-6 of the U.S. Census. 17

10A-14REFERENCES

1 S. Hymans. Consumer Durable Sp ending: 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 w ith Repeated Choices: Household's Choice of Appliance E fficiency 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 revi ew of the literature, Energy , 1985.

8 Association of Home Ap pliance Manufacturers. AHAM Fact Books , 2000 and 2003. Washington, DC.

9 Statistical Review. Appliance Magazine , April, 1990.

10 Association of Home Ap pliance 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.

10A-1515 Association of Home Ap pliance 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- a nd 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/in come/histinc/inchhtoc.html >

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