< <

- i APPENDIX 9

- A RELATIVE PRICE ELASTICITY OF DEMAND FOR CLOTH E S 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 DESCR IBE THE MARKET FOR C LOTHES WASHERS

................................ ................................ ................................ ........ 9

- A

- 3 9

- A.3.4 Household/Appliance Var iables

................................ ................................ ......... 9

- A

- 3 9

- A.3.5 Economic Variables

................................ ................................ ........................... 9

- A

- 3 9

- A.4 REGRESSION ANALYS IS OF VARIABLES AFFE CTING 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 Resu lts

................................ ............. 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 FRON T AND TOP LOADER CLOTHES WASHE RS

................................ ................................ .... 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 Re sults 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 F ollowing 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

- 169

- A

- 1 Appendix 9

- A. RELATIVE PRICE ELAST ICITY OF DEMAND FOR CLOTH E S 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 review s the literature regard ing the impact of economic variables on the sa le 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 est imates 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 re sults in section 9

- A.7

. Finally, section 9

- A.8 describes the data DOE used in its analysis.

9

- A.2 LITERATURE REVIEW

R elatively few studies measur e the effe ct of price, income

, and efficiency on the sale of household appliances. T his section briefly review s th e literature that describe s the likely importance of th o se variables to the purchase of residential clothes washers

.

9

- A.2.1 Price

DOE review ed m any studies that sought to measure the impact of price o n 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 pur chase (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 deman d reported in those studies was

- 0.3 4 in the appliance market and

- 0.47 in the combined automobile and appliance markets.9

- A

- 2 Table 9

- A.2.1 Effe ct 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

Automobiles 1

- 1.07 3.08

- - Linear r egression, stock adjustment - Short term

Automobiles 1

- 0.36 1.02

- - Linear r egression, stock adjustment - Long term Clothes Dryers 2

- 0.14 0.26

- - Cobb

- Douglas, diffusion 1947

– 1961 Mixed Room Air Conditioners 2

- 0.37 * 0.45

- - Cobb

- Douglas, diffusion 1946

– 1962 Mixed

Dishwashers 2

- 0.42 0.79

- - Cobb

- Douglas, diffusion 1947

– 1968 Mixed
Refrigerators 3

- 0.37

- - 3 9 Logit probability, survey data * 1997 Short term

Various 4

- - - 1.76 †

- Multiplicative regression

- Mixed
Room Air Conditioners 5 - - - 1.72

- Non

- linear diffusion 1949

– 1961 Short term Clothes Dryers 5

- - - 1.32

- Non

- linear diffusion 1963

– 1970 Short term Room Air Conditioners 6 - - - 20 Qualitative choice, survey data - -
Household Appliances 7 - - - 37 ‡ 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: * 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 appliance s

.

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 effe ct of income on appliance shipments is explored in two econometric studies of the au tomobile and appliance markets. 1

, 2 The average income elasticity of demand is 0.50 in the appliance study cite d in the literature review, much larger in the automobile study (Table 9.A.2.1 ).

Many studies estimate the effe ct of appliance efficiency on consumers’ choice of appliance. T his effe ct 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 co ncluded that consumers use a 20

- percent implicit discount rate when purchasin g room air conditioners (Table 9

- A.2.1 ). 5 A survey of several studies of various appliances suggest ed that the consumer implicit discount rate has a broad range , averag ing about 37 percent

. 69

- A

- 3 9

- A.3 VARIABLES THAT DESCRIB E THE MARKET FOR CLOTH ES
WASHERS

In this sec tion DOE discuss e s variables that appear to affect shipments of clothes washers, including those pertaining to the consumer household, the appliance itself , and economic factor s.

9

- A.3.1 Household/Appliance Variables

Several variables influence the sale of cloth es 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 affe ct 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 pur chased when old ones wear out. In principle, if house holds maintain a fixed number of appliances, shipments should equal housing starts plus appliance replacements.

9

- A.3.2 Economic V ariables
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 a n increase in income improves a consumer’s a bility to purchase appliances. In principle, changes in economic variables should explain changes in the number of appliances per ho usehold.

During a 1980

– 2002 study p eriod, 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 percent 11 and by repl acements, 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 a s the one for clothes washers , replacements exceed sales to new housing construction.

S hipments increased somewhat more rapidly than housing starts plus replacements (69 percent versus 56 percent). This situation is shown by comparing the beginning and e n d points of lines that represent starts plus replaceme nts (uppermost solid line in Figure 9

- A.3.1) and shipment s (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 l ine lie s above the line for starts plus replacements. Th e more rapid increase in shipments, compared to housing starts plus replacements, suggests that the ratio of appliance s per household increased during the study period

.9

- A

- 4 Figure 9

- A.3.1 Trends in Clothes Washer Shipment s , Housing Starts , and Replacements

Economic variables, including price, cost

, and income, may explain th e increase in clothes washers per household. During the study period, clothes wa sher 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 AFFECTI NG APPLIANCE
SHIPMENTS

Few data are available for estimating the effe ct of economic variables on the demand for appliances. Industry data regarding operating cost s 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 f or each type of appliance

. The lack of data suggests that regression analysis can at best evaluate broad trends, utilizing relativ ely few explanatory variables. This section begin s by describing broad trends apparent in the economic and household data s ets and then specifies a simple regression model to measure th o se trends, making assumptions to minimize the nu mber of explanatory variables. Finally, results of the regression analysis are presented, along with an estimate of the price elasti city of deman d for appliances. In section 9

- A.4.5, DOE present s the results of regression analys e s 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 estimate d with that model.

9

- A.4.1 Broad Trends

In this section DOE review s trends in the physical household and economic data sets and posit s a simple approach for estimating the price el asticity of appliance demand. As noted above, household variables ( housing sta rts 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 indi cates 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 assume s the rest of the variability in shipmen ts ( referred to as “ residual shipments ” ) can be explained by economic variables. Below DOE present s a tabular method for measu ring price elasticities

.

To illustrate th e tabular approach, DOE define d two new variables

— resid ual 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 operat ing cost s. a

PVOC PP TP + =

Where:

TP = total price, PP = appliance purchase price, and PVOC = present value of operating costs.

During the stud y 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 explai ns 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$ Elasticity Appliance 1980 2002 Difference Change % 1980 2002 Change % 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 sug gested by the negative price elasticities is illustrated in a graph of residual shipments on the y

- axis and to tal 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 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; 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 hous eholds to purchase appliances. Assuming that a rise in income has a similar effe ct on shipments as a decline in price, the effe ct of income is incorporated by defining a third variable, termed relative price, which is calculated as total price divided by household income . The variable i s represented by the following equation. b

Income TP RP =

Where:

R P = relative price, T

P = 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 pr ice 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 residua l 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$ Elasticity Appliance 1980 2002 Change % 1980 2002 Change % Refrigerator

- 0.532 1.597 30 0.041 0.019

- 74

- 0.40 Clothes Washer

- 0.953 0.174 1 9 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 us e a simple regression model to estimate the effe ct of economic variables on shipments, using fe w explanatory variables. T he 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
ope rating costs, divided by income). 

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

Where:

Ship = quantity of appliance sold, R P = 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 chang e in shipments associated with the p ercent change in the variable. Thus, the coefficient b in th e model is interpreted as t he relative price elasticity of demand for the three appliances.

DOE used the following combined regression equation to estimate a n 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 applianc es ( 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. 

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

Where:

CW = quantity of clothes washers sold, and9

- 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 cost s

— are responsible for the total observed increase in residual appliance shipments during t he study period

. In other words, DOE assume d no impact from other possible factor s, such as changing consumer preferences or increases in the qualit y of appliances. Th e assumption seems unlikely

, but without additional data, the effe ct of other variables o n the price elasticity of demand cannot be measured. DOE effectively assume d that changes in consumer preferences and appliance characteristics, while affecting which models are purchased, ha d relatively little effe ct on the total number of appliances purc hased in a year.

Three additional assumptions used to speci fy the model deserve comment. The relative price variable is specified, assuming that (1) the correct implicit discount rate wa s used to combine appliance price and operating cost s and that (2) rising income has the same effe ct on shi pments as does falling total price. In addition, t he “ starts + replacements ” variable i s specified assuming (3) that starts and replacements have similar effe cts on shipments.

To investigate the firs t 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, pre sented 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 separat es income from total price and rep lacements from starts, th ereby adding two explanatory variables to the basic mo del. The following equation shows the separations.



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

The results of the regression analysis using this model are presented in section 9

- A.4.5. The result s suggest that the elasticity of total price (coefficient b ) is relatively insensitive to changes i n the treatment of income and “starts + r eplacements ” 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 eq uations are specified as shown by the following

e quation.9

- A

- 9 

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

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 elasticiti es are similar to the ones reported in the literatur e survey for appliances (Table 9

- A.2.1). They are remarkably simila r to the price elasticities calculated using a tabular a pproach (Table 9

- A.4.2).

The estimated coefficient associated with the “s tarts + r eplacements ” 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 “s tarts + r eplacements .” 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 th e analysis, despite the small data set.

Table 9

- A.4.4 Results of Individual Appliance Model s 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 R 2 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. 

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

This regression analysis indicates that the model fits the shipm ents data well (high R

squared), and that the variables included in the model are st atistically significant (Table 9

- A.4.4). Based on this model t he 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 Result s 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 R 2 0.983 Observations 699

- 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 appli ance 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 assump tion 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 r elative 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 c ombined regression and averages

- 0 .35 f or the three appliances (Table 9

- A.4.5 and Table 9

- A.4.6 ). The elasticity o f price calculated using a 37

- percent discount rate is

- 0 .34 in the combined regression and averages

- 0 .35 for the three appliances. DO E conclude s from this analysis that the elasticity of relative price is fairly insensitive to changes in the discount rate.

Table 9

- A.4.6 Comb ined Results, 20

- Percent D iscount R ate

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 R 2 0.982 Observations 69

Table 9

- A.4.7 Individual Results, 20

- Percent D iscount R ate 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 R 2 0.953 0.950 0.977 Observations 23 23 239

- 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 separat es income from total price and replacements from starts, thus adding two additional explanatory variables to the basic model (id entified in section 9

- A.4.2)

.



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

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 f or 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 t he individual appliances (Table 9

- A.4.3). DOE conclude s that the price elasticity calculated in this analysis is relatively insensitive to the specifi cation of the variables for hous ehold income and “s tarts + r eplacements ” in the model.

Table 9

- A.4.8 Disag gregated Results: Combined Appliances, 37

- Percent D iscount R ate

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 R 2 0.985 Observations 699

- A

- 12 Table 9

- A.4.9 Disag gregated Results: Individual Appliances, 37

- Percent D iscount R ate 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 R 2 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 elast icities 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 pri ce 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 pri ce. With increasing years after the price change, the price elasticity becomes more inelastic until it reaches a terminal value about the 10 th year following the price change.

Table 9

- A.5.10 Change in Price Elasticity of Demand for Automobiles Following a Change in Purc hase 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 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 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 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

9

- A.6 PRICE IMPACTS ON THE MARKET SHARE OF FRONT AND TOP
LOADER CLOTHES WASHE RS
This section provides pre liminary estimates of cross

- price impacts on the market share of top

- load ing and front

- load ing clothes wash ers

. 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 was her 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

. F or 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 1000Jan-04Apr-04Jul-04Oct-04Jan-05Apr-05Jul-05Oct-05Jan-06Apr-06Jul-06Oct-06Jan-07Apr-07Jul-07Oct-07Jan-08Apr-08Jul-08Oct-08Jan-09Apr-09Jul-09Oct-09

YearRCW 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. T he 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. Th e 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

- L oad ing Clothes Washers

The price trend sh own 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 pr ice 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

- load ing 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 f uture.

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 a nd Electric Controls of Front

- and Top

- L oad ing 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 was her 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 top

loaders. To calculate a ratio trend, we take the weighted average of front

- loader washer tub siz es 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 th at 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 cha rt 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 to tal number of front

loading 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 relat ively 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 appl ied a logistic regression method to regress market share on price variables and other attrib utes. The basic form of a logistic regression is:

p i = 1
1 + e − ( β 0 + β 1 x 1 , i + ⋯ + β k x k

, i )

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

- linear form :

ln � p i 1

− p i �

= β 0 + β 1 x 1
, i + ⋯ + β k x k
, i

In this case, p i is the market share of either top

- or front

- load ing clothes washers, and
p i 1

− p i is the ratio of clothes washer market shares, i. e. , the relative probability of the market share of top and front

- load ing clothes washers. T he explanatory variables inclu de price

- related variables , washer size and other washer attributes.

9

- A.6.2 Regression Results

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

ln � Market S h are Front 1

− Market S h are Front �

= − 2

. 985386 + 0

. 0035452 × Price Top − 0

. 0049114 × Price Front + 4

. 24347

× Size Front Size Top

W here:

= the relative probability of the market share of front and top

load ing 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 regressi on 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 analys e s of the impact of price and other var iables on appliance shipments. In the liter ature, DOE find s only a few studies that are relevant to th e analysis and no studies after 1980 that use time

series price and shipments data. The information that can be summarized from the literature suggests that the demand for appliances is price

- inela stic. Other information in the literature suggests that appliances are a normal good, s o that rising incomes incr ease the demand for appliances. Finally, the literature suggests that consumers use relatively high implicit discount rates when comparing appl iance prices and operating costs.

There are too few data available on price s and operating cost s to perform a complex analysis of dynamic ch anges in the appliance market. Instead, DOE use d available data to evaluate broad market trends and to perform si mple regression analyse s. The data indicate a n increase in appliance shipments and a decline in appliance price s and operating cost s for1980

– 2002. Household income also r ose during th at period . To simplify the analysis, DOE combined

d All variables in this regression were statistically significant; the R 2 in the regression was 0.88.

e P rice elasticity var ies 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 refer ence front washer market share is 29%

.9

- A

- 19 the available economic information into one variable, termed relative price, and used th at variable in a ta bular analysis of market trends and in a regression analysis.

DOE’s tabular analysis of trends in the number of appliances per household indicate s a price in elasticity 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 wit h estimates in the literature. Nevertheless, DOE stress es that the measu re is based on a small data set and employs simple statistical analysis. More important ly , the measure is based on an assumption that economic variables, including price, income

, and operating costs, explain most of the trend in appliances p er household in the United States since 1980. Changes in appliance quality and consumer preferences may have occurred during th at period, but they are not accounted for in this analysis.

The estimates of cross

- pr ice 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 front

and top

- load ing clothes washers supports the assumption that the two types of washers are substitute goods. Although more information coul d be captured by incorporating more washer attributes in the regression for estimating cross

- price impacts , th o se 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 program s 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 Econome tric Models of Sales. Journal of Marketin g Research

. November 1988.

4 U.S. Department of Energy

– Energy Information A gency. 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 D iscount R ates and the P urchase and U tiliza tion 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.