9A

- i APPENDIX 9A. RELATIVE PRICE ELAST ICITY OF DEMAND FOR

APPLIANCE S

TABLE OF CO NTENTS

9A.1 INTRODUCTION

................................ ................................ ................................ .. 9A

- 1

9A.2 LITERATURE REVIEW

................................ ................................ ....................... 9A

- 1

9A.2.1 Price

................................ ................................ ................................ ........................ 9A

- 1

9A.2.2 Income

................................ ................................ ................................ ..................... 9A

- 1

9A.2.3 Appliance Efficiency and Discount Rates

................................ .............................. 9A

- 2

9A.3 VARIABLES DESCRIBING THE MARKET FOR REFRI GERATORS, CLOTHES WASHERS, AND DISHWASHERS

................................ .................. 9A

- 2

9A.3.1 Physical Household/Appliance Variables

................................ ............................... 9A

- 3

9A.3.2 Economic Variables

................................ ................................ ................................ 9A

- 3

9A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTI NG APPLIANCE

SHIPMENTS

................................ ................................ ................................ .......... 9A

- 4

9A.4.1 Broad Trends

................................ ................................ ................................ ........... 9A

- 5

9A.4.2 Specification of Model

................................ ................................ ............................ 9A

- 7

9A.4.3 Discussion of Model

................................ ................................ ............................... 9A

- 8

9A.4.4 Analysis Results

................................ ................................ ................................ ...... 9A

- 8

9A.4.4.1 Individual Appliance Model

................................ ................................ . 9A

- 8

9A .4.4.2 Combined Appliance Model

................................ ................................ . 9A

- 9

9A.4.5 Additional Regression Specifications and Results

................................ ............... 9A

- 10

9A.4.5.1 Lower Consumer Discount Rate

................................ ......................... 9A

- 10

9A.4.5.2 Disaggregated Variables

................................ ................................ ..... 9A

- 11

9A.5 LONG RUN IMPACTS

................................ ................................ ........................ 9A

- 11

9A.6 SUMMARY

................................ ................................ ................................ .......... 9A

- 12

9A.7 DATA USED IN THE ANA LYSIS

................................ ................................ ..... 9A

- 13

LIST OF TAB LES

Table 9A.2.1 Estimates of the Impact of P rice, Income and Efficiency on Automobile and Appliance Sales

................................ ................................ 9A

- 2

Table 9A.3.1 Physical Household/Appliance Variables

................................ ................... 9A

- 3

Table 9A.3.2 Economic Variables

................................ ................................ .................... 9A

- 4

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

................................ ............. 9A

- 6

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

......... 9A

- 7

Table 9A.4.3 Individual Appliance Model Results

................................ .......................... 9A

- 9

Table 9A.4.4 Combined Appliance Model Result

................................ ............................ 9A

- 9

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

..................... 9A

- 10

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

.................... 9A

- 11

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

................................ ................................ .............. 9A

- 129A

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

................................ ................................ .............. 9A

- 12

LIST OF FIGURE S

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

............ 9A

- 4 Figure 9A.4.1 Residual Shipments and Appliance Price

................................ ................... 9A

- 69A

- 1 APPENDIX 9A. RELATIVE PRICE ELAST ICITY OF DEMAND FOR APPLIANCE S

9A.1 INTRODUCTION

This appendix summarizes the U.S. Department of Energy’s ( DOE’s ) study of the price elasticity of demand for home appliances , including refrigerators, clothes washers

, and

dishwashers. DOE chose t his particular set of appliances because of the availability of data to determine a price elasticity. Section 9

- A.2 review s the existing economics literature describing the impact of e conomic variables on the sa le of durable goods. Section 9

- A.3 describes the market for home appliances and the changes that have occurred over the past 20 years . In section

9

- A.4 , DOE summarizes the results of its regression analysis and present s estimates of the price elasticity of demand for the three appliances. In section 9

- A.5, DOE presents development of an ‘effective’ purchase price elasticity. DOE’s interpretation of its re sults is presented in section 9

- A.6

. Finally, section 9

- A.7 describes the dat a used in DOE’s analysis.

9A.2 LITERATURE REVIEW

R elatively few studies measur e the impact of price, income

, and efficiency on the sale of household appliances. T his section briefly review s the literature that describes the likely importance of these variables on the purchase of household appliances

.

9A.2.1 Price

DOE reviewed many studies that sought to measure the impact of price on sales in a dynamic market. One study of the automobile market prior to 1970 finds the price elasticity of

demand to decline over time. The author explains this as the result of buyers delaying purchases after a price increase but eventua lly making the purchase (Table 9

- A.2.1 ). 1 A contrasting study

of househol d 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 n 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 repo rted in these studies is

- 0 .33 in the appliance

market and

- 0 .47 in the combined automobile and appliance markets.

9A.2.2 Income

Higher income households are more li kely to own household appliance s

. 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 and is much larger in the automobile study (Table 9

- A.2.1 ).9A

- 2 9A.2.3 Appliance Efficiency and Discount Rates

Many studies estimate the impact of appliance efficiency on consumer s’ choice of appliance. Typically, this impact is summarized by the implicit discount rate ; that is , the rate consumers use to compare future saving s in appliance operating costs against a higher initial purchase price of a n appliance. One early and much cited study co ncludes that consumers use a
20 percent implicit discount rate when purchasin g room air conditioners (Table 9

- A.2.1 ). 6 A survey of several studies of different appliances suggests that the consumer implicit discount rate has a broad range and averages about 37 percent

. 7

Table 9A.2.1 Estimates of the Impact of P rice, 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% 1 0 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 comparable to other elasticity estimates in this table.

9 Average brand price elasticity a cross 41 studies.

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

9A.3 VARIABLES DESCRIBING THE MARKET FOR REFRI GERATORS,

CLOTHES WASHERS, AND DISHWASHERS

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

washer

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

economic variables.9A

- 3 9A.3.1 Physical Household/Appliance Variables

Several variables influence the sale of refri gerators, clothes washers

, and dishwashers. The most important variables 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 appliance s, shipments should equal housing starts plus appliance replacements.

9A.3.2 Economic V ariables

Appliance price, appliance operating cost

, and household income are important economic variables affecting shipments. Low prices and costs encourage household applia nce purchases

, and a rise in income increases householder ability to purchase appliances. In principle, changes in economic variables should explain changes in the number of appliances per household.

During a 1980

– 2002 study p eriod, annual shipments gre w 69 percent for clothes washers, 81 percent for refrigerators

, a nd 105 percent for dishwashers (Table 9

- A.3.1 ). This rising shipments trend is explained in part by housing starts, which increased 6 percent and by appliance repl acements, which rose between 49 percent and 90 percent, depending on the appliance, over the period (Table 9

- A.3.1 ). a For mature markets such as these, replacements exceed appliance sales associated with new housing construction.

Table 9A.3.1 Physical Household/Appliance Variables

Shipments i ( millions) Housing Starts ii (millions) Replacements iii (millions)
Appliance 1980 2002 Change 1980 2002 Change 1980 2002 Change
Refrigerators 5.124 9.264 81% 1.723 1.822 6% 3.93 5.84 49%

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

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

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

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

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

S hipments increased somewhat more rapidly than housing starts and replacements. This is shown by comparing the beginning and end points of lines that represent “starts pl us replacements” (uppermost solid line in Figure 9

- A.3.1 ) and “shipment s” (diamond linked line in Figure 9

- A.3.1). In 1980 the “shipment” line begins below the “starts plus replacements” line. In 2002, the “shipments” line ends above the “starts plus repla cements” line. This more rapid

a Appliance replacements are determined from the expected operating life of refrigerators (19 years), clothes washers (14 years), and dishwashers (12 years) and from past shipments. Replacements are further discussed in

section 9

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

- 4 increase in shipments, compared to housing starts plus replacements, suggests that the appliance per household ratio increased over the study period.

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

Economic variables, including price, cost

, and income, may explain this increase in appliances per household. Over the period , appliance prices decreased 40 percent to 50 percent

, operating costs fell between 33 percent and 72 percent, and median household income rose 16 percent (Table 9

- A.3.2 ).

Table 9A.3.2 Economic Variables

Price i (1999$) Operating Cost ii (1999$) Household Income iii (1999$)
Appliance 1980 2002 Change 1980 2002 Change 1980 2002 Change
Refrigerators 1208 726

- 40% 333 94

- 72% 37,447 43,381 16%

Clothes Washers 779 392

- 50% 262 175

- 33% 37,447 43,381 16%

Dishwashers 713 369

- 48% 183 95

- 48% 37,447 43,381 16%

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

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

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

9A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTI NG APPLIANCE

SHIPMENTS

Few data are available to estimat e the impact of economic variables on the demand for appliances. Industry operating cost data is incomplete

— appliance energy use data are available for only 12 years of the 1980

- 2002 study period. Industry price data are also incomplete

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

The lack of data suggests that regression analysis can at best evaluate broad data trends, utilizing relatively few explanatory variables. This section begin s by describing broad trends Refrigerator 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 2000Millions9A

- 5 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 of the regression analysis are presented along with an estimate of the price elasticity of demand for appliances. In section 9

- A.4.5

, DOE present s the results of regression analysis performed with more complex models, which are used to test assumptions underlying the simple model. These results support the spe cification of the simple model and the price elasticity of appliance demand estimated with that model.

9A.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 elasticity of appliance demand. As noted previously , the physical household variables ( housing starts and appliance replacements) explain most of the variability in appliance shipments during the study period (19 80

- 2002)

. b DOE

assume s the rest of the variability in shipments ( referred to as “ residual shipments ” ) is explained by economic variables . DOE present s here a tabular method for measuring price elasticities.

To illustrate this tabular approach, DOE define s two new variables

— residual shipments and total price. Residual shipments are defined as the difference between shipments and physical household demand (starts plus replacements). Total price , represented by the following equation, is defined as appliance price plus the present value of lifetime appliance operating cost : c

PVOC PP TP + =

W here:

TP = t otal price,

PP = a ppliance purchase price, and

PVOC = p resent value of operating cost.

Over the study period, residual shipments increased in proportion to total shipments by 30 percent for refrigerators, 19 percent for clothes washers

, a nd 23 percent for dishwashers. At

the sam e time, total prices declined 47 percent, 45 percent

, and 48 percent for refrigerators,

clothes washers

, and dishwa shers, 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

, a nd

- 0.37 for

di shwashers (Table 9

- A.4.1 ).

b A log regression of the form: Shipments = a + b • Housing Starts + c • Retirements, indicates that these two variables explain 89 percent of the variation in refrigerato r 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 clot hes 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.9A

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

Residual Shipments (millions) Total Price (199 9 $)
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 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 to tal price on the x

- axis (Figure 9

- A.4.1 ).

Yellow points are observed price data; red points are interpolated price data. Figure 9A.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 pric e, which is calculated as total price divided by household income and represented by the following equation. d

Income TP RP =

W here:

R P = r elative price,

T

P = t otal price, and

Income = h ousehold income.

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

, and the p rice elasticity of demand cited in the review averages

- 0.35. This suggests that combining the effects of income and price will yield an elasticity less negative than price elasticity alone. Refrigerators

400 800 1200 1600 2000

-2.0 -1.0 0.0 1.0 2.0

Total 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 Shipments9A

- 7 The percent decline in relative price fo r 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

, a nd

- 0.30 for dishwashers (Table 9

- A.4.2 ).

Table 9A.4.2 Tabular Estimate of Relative Price 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

9A.4.2 Specification of Model

The limited price data suggest it is appropriate to us e a simple regression model to estimate the impact of economic variables on shipments, using few explanatory variables. The following equation

, chosen for this analysis

, includes one physical household variable ( housing starts plus replacements) and one rel ative price variable (the sum of purchase price plus

ope rating cost, divided by income).


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

- A.1

W here:

Ship = q uantity of appliance sold,

R P = r elative price,

Starts = n umber of new homes, and Rplc = n umber 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 v ariable. Thus, the coefficient b in this model is interpreted as the relative price elasticity of demand for the three appliances.

DOE used the following combined regression equation to estimate an average price elasticity of demand across the three app liances, using pool ed data in a single regression. A combined regression specification is justified, given the limited data availab le and the similarity in price and shipment behavior across appliances ( see Figure 9

- A.4.1 ). Thus, the model represented by t he 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 × + × + + × + × + = Eq. 9

- A.2

W here:

CW = q uantity of clothes washers sold, and9A

- 8 DW = q uantify of dishwashers sold.

9A.4.3 Discussion of Model

The most important assumption used to specify this model is that changes in economic variables over the study period

— income, price

, and operating cost

— are responsible for all observed growth in residual appliance shipments. In other words, DOE assu me s no impact from other possible factors , such as changing consumer preferences or increases in the quality of appliances. This assumption seems unlikely

, but without additional data, the impact of this assumption on the price elasticity of demand cannot be measured. DOE effectively assume s that changes in consumer preferences and appliance characteristics, while affecting which models are purchased, have relatively little impact on the total number of appliances purchased in a year.

Three additional ass umptions 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

i mpact 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 v alue operating cost” using a 20 percent implicit discount rate and performed a second regression analysis based on the models described in equations 9

- A.1 and 9

- A.2. The results of this analysis, presented in section 9

- A.4.5 , indicate that the elasticity of relative price is fairly insensitive to changes in the discount rate.

To investigate the second and third assumptions, DOE specified a regression model separating income from total price and replacements from starts, th ereby adding two additional

exp lanatory variables to the basic mo del as shown in the following equation:



### DW g CW f Rplc e Start d Incone c TP b a Ship × + × + × + × + × + × + = Eq. 9

- A.3

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

- A.4.5

. These results suggest that the elasticity of total price (coefficient b ) is relatively insensitive to changes i n the treatment of income and “starts + r eplacements ” in the model.

9A.4.4 Analysis Results

The following sections describe results of analyses using both the individual and combined models for appliances and the effects of a lower consumer discount rate and disaggregated variables.

9A.4.4.1 Individual Appliance Model

The individual appliance regression eq uations are specified in the following equation.9A

- 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 .4 0 for refrigerators,

- 0 .31 for clothes washers

, and

- 0 .32 for dishwashers (T able 9

- A.4.3 ), averaging

- 0 .35. These elasticities are similar to those reported in the literatur e survey for appliances (Table 9

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

tabular a pproach (Table 9

- A.4.2 ).

The estimated coefficient associated with the “s tarts + r epl acements ” 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 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 9A.4.3 Individual Appliance Model Results

Refrigerator Clothes Washer Dishwasher

Variable Coefficient t

- stat Coefficient t

- stat Coefficient t

- stat
Intercept

- 1.51

- 7.26

- 1.47

- 8.23

- 2.08

- 16.78

Relative Price

- 0.40

- 6.60

- 0.31

- 5.69

- 0.32

- 7.03
Starts + Replacements 1.05 5.90 1.08 6.41 1.35 11.46

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 in the following equation.


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

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 st atistically significant (Table

9

- A.4.4 ). Estimated with this model, t he elasticity of relative price is

- 0 .34, close to the average value estimated in the individual appliance models (

- 0 .35). It is also similar to elasticity estimates reported in the literature survey and calculated using the tabular approach in Table 9

- A.4.2

.

Table 9A.4.4 Combined Appliance Model Result

Variable Coefficient t

- statistic
Intercept

- 1.60

- 15.54

Relative Price

- 0.34

- 10.74
Starts + Replacements 1.21 13.95

CW

- 0.20

- 9.04

DW

- 0.32

- 6.58

R 2 0.983

Observations 699A

- 10 9A.4.5 Additional Regression Specifications and Results

As described in section 9

- A.4.3, DOE used three assumptions to specify its appliance models. The first, made to aggregate appliance price and operating cost , is that the implicit price variable in the basic regressio n model is specified using a 37 percent implicit discount rate. The

second states that the implicit price variable is defined assuming that rising income has the same impact on shipments as fallin g total price. The third states that the “s tarts + r eplacements ” variable is defined assuming that housing starts have a similar impact on shipments as appliance replacements.

9A.4.5.1 Lower Consumer Discount Rate

To investigate the first assumption about discoun t rates, DOE calculated “present value operating cost” using a 20 percent implicit discount rate and performed a second regression analysis based on the models described in equations 9

- A.1 and 9

- A.2

. The estimated coefficient

associated with the relative p rice 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 ). 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. DOE conclude s from this ana lysis that the elasticity of relative price is fairly insensitive to changes in the discount rate.

Table 9A.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

R 2 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

R 2 0.953 0.950 0.977

Observations 23 23 239A

- 11 9A.4.5.2 Disaggregated Variables

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

that separat es income from total price and replacements from starts, thus adding two additional explanatory variables to the basic model ( as shown earlier as Eq. 9

- A.3 and shown below ).



### DW g CW f Rplc e Start d Income 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 previously

. The elasticity of total price in th is equation is

- 0 .36 in the combined appliance regression and

averages

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

- A.4.6 ). The elasticity of relative price based on the model described in equation 9

- A.2 is

- 0 .34 in the combined regression (Table 9

- A.4.4) and

averages

- 0 .35 across t he ind ividual 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 household

income and “s tarts + r eplacements ” variables in the model.

Table 9A.4.6 Disaggregated Regression Result s, 37 percent discount rate

9A.5 LONG RUN IMPACTS

As noted in Table 9

- A.2.1, the literature review provides price elasticities over short and long time periods, also referred to as short run and long run price elasticities. As noted in the first

two rows of Table 9

- A.2.1, one source (i.e., Hymans) shows that the price elasticity of demand is significantly different over the short run and long run for automobiles. 1 Because DOE’s forecasts of shipments and national impacts due to standards is over a 30

- year tim e period, consideration must be given to how the relative price elasticity is affected once a new standard takes effect. 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

R 2 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

R 2 0.984 0.958 0.979

Observations 23 23 239A

- 12 DOE considers the relative price elasticities determined in section 9

- A.4 to be short run

elasticities . DOE was unable to identify sources specific to household durable goods, such as appliances, to indicate how short run and long run price elasticities differ. Therefore, to estimate

how the relative price elasticity changes over time, DOE relied on the Hy mans study pertaining to automobiles. Based on the Hymans study, Table 9

- A.5.1 shows how the automobile price elasticity of demand changes in the years following a purchase price change. With increasing years after the price change, the price elasticity be comes more inelastic until it reaches a terminal value around the tenth year after the price change.

Table 9A.5.1 Change in Price Elasticity of Demand for Automobiles following a Purchase Price Change
Years Following Price Change

1 2 3 5 10 20
Price Elasticity of Demand

- 1.20

- 0.93

- 0.75

- 0.55

- 0.42

- 0.40
Relative Change in Elasticity to 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.

Table 9A.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

9A.6 SUMMARY

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

, and regression analys e s of the impact of price and other variables on appliance shipments. In the literature, DOE

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

after 1980 using time series price and shipments data. The informatio n 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, t he literature suggests that consumers use relatively high implicit discount rates, when comparing appliance prices and appliance operating costs.

There are too few price and operating cost data available to perform a complex analysis of dynamic changes in the appliance market. In this analysis, DOE use d data available for9A

- 13 refrigerators, clothes washers

, and dishwashers to evaluate broad market trends and perform a simple regression analysis.

These data indicate an increase in appliance shipments and a decline in appliance price and operating cost over the study period 1980

- 2002

. Household income has also risen during this time. To simplify the analysis, DOE combined the available economic information into one variable, termed relative price, and used t h at 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 a nalysis 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 stress es 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.

9A.7 DATA USED IN THE ANA LYSIS

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

data were collected from the Association of Home Appliance Manufacturers ( AHAM ) 8

, 9 and Appliance Magazine 10 as annual values for each year, 1980

– 2002

. AHAM was used for the period 1989

– 2002

, while Appliance Magazine was used for the period 1980

– 1988.

• Appliance Price is defined as the shipments

- weighted retail sales pri ce of the unit in 1999 dollars. Price values for 1980, 1985, 1986, 1991, 1993, 1994, 1998 , and 2002 were collected

from AHAM Fact B ook s. 11 Price values for other years were interpolated from these eight years of data.

• Housing Starts data were collected from the U.S. Census construction statistics (C25 reports) as annual values for each year, 1980

– 2002. 12

• Replacements , driven by equipment retirements, are estimated with the assumption that some fraction of sales arise from consumers replacing equipment at the end of its useful life.

As each appliance has a different expected lifespan (19 years for refrigerators, 13 14 years for

clothes wa shers, 14 12 years for dishwashers 15 ), replacements are calculated differently for each appliance type. Replacement s are estimated as the average of shipments 14

– 24 years previous for refrigerators, 9

– 19 years prev ious for clothes washers, and 7

– 17 years previous

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

.9A

- 14 • Annual Electri city Consumption (UEC) is defined as the energy consumption of the unit in

kilowatt

- hours. Electricity consumption depend s on appliance capacity and efficiency. These data were provided by AHAM for 1980, 1990

– 1997

, and 1999

– 2002. 9 Data were interpolated in the years for which data were no t available.

• Operating Cost is the present value of the electricity consumption of an appliance over its expected lifespan. The lifespans of refrigerators, clothes washers

, and dishwashers are assumed to be 19, 14, and 12 years resp ectively. Discount rate s of 20 percent 6 and 37

percent 16 were used, producing similar estimates of price elasticity. A study by Hausman

recommend ed a discount rate of “about 20 percent ” in its introduction and pres ented 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 impli cit discount rates averaging 35 percent f or appliances.

• Income : Median annual household income in 2003 dollars. Th ese data w ere collected for each year, 1980

– 2002, from Table H

- 6 of the U.S. Census

. 179A

- 15 REFERENCES

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

. Brookings Papers on Economic Activity , 1971. 1971(1): pp. 234

- 239

.

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

of New Consumer Durables

. Journal of Forecasting , 1998. 17

.

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

. Review of Economics and Statistics , 1997

.

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

- Analysis of Econometric

Models of Sales

. Journal of Mark eting 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.go v/emeu/recs/appliances/appliances.html >

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

durables

. The Bell Journal of Economics , 1979

.

7. Train, K., Discount Rates in Consumers' Energy

- Related Decisions

. Energy: The

International Journal , 1985. 10(12)

.

8. Association of Home Appliance Manufacturers, AHAM 2000 Fact Book . 2000. Washington, DC.

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

10. Statistical Review

. Appli ance Magazine , April, 1990

.

11. Association of Home Appliance Manufacturers, AHAM Fact Books , 1987, 1988, 1993, 1995, 2000, and 2003. Washington, DC.

12. U.S. Census Bureau, Current Construction Reports, C25

– New One

- Family Houses

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

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

14. 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 , 2000. U.S. Department of Energy. Washington, DC. Report

No. LBNL

- 47462.

< http://www.eren.doe.gov/buildings/codes_standards/reports/cwtsd/index.html >9A

- 16 15. U.S. Department of Energy

- Office of Codes and Standards, Technical Support

Document: Energy Conservation Standards for Consumer Products: Dishwashers, Clothes Washers, and Clothes Dryers including: Environmental Impacts, Regulatory Impact Analysis, December, 1990. Washington, DC. Report No. DOE/CE

- 0299P.

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

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

- and revealed

- preference data

. The Energy Journal , 1995

.

17. U.S. Census Bureau, Income, Historical Incom e Tables

– Households, Table H

- 6

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