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Lawrence Berkeley National Laboratory

Title: An Analysis of the Price Elasticity of Demand for Household Appliances

Author: Dale, Larry

Publication Date:

06-10-2008

Publication Info: Lawrence Berkeley National Laboratory

Permalink: http://escholarship.org/uc/item/5qr2f2nz

Keywords: price elasticity of demand

Abstract: This report summarizes our study of the price elasticity of demand for home appliances, including refrigerators, clothes washers, and dishwashers. In the context of increasingly stringent appliance standards, we are interested in what kind of impact the increased manufacturing costs caused by higher efficiency requirements will have on appliance sales. We begin with a review of existing economics literature describing the impact of economic variables on the sale of durable goods. We then describe the market for home appliances and changes in this market over the past 20 years, performing regression analysis on the shipments of home appliances and relevant economic variables including changes to operating cost and household income. Based on our analysis, we conclude that the demand for home appliances is price inelastic.

## An Analysis of the Price Elasticity of Demand for Household Appliances

Larry Dale and K. Sydny Fujita

February 2008

Energy Analysis Department Environmental Energy Technologies Division Lawrence Berkeley National Laboratory University of California Berkeley, CA 94720DISCLAIMER

This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor The Regents of the Universit y of California, nor any of their employees, makes any warranty, express or i mplied, or assumes any legal responsibility for the accuracy, completeness, or usef ulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific comme rcial product, process, or service by its trade name, trademark, manufacturer, or otherwise , does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or The Regents of the Univer sity of California. The views and opinions of authors expressed herein do not necessarily stat e or reflect those of the United States Government or any agency thereof or The Regent s of the University of California.

This work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy of the U.S. Department of Energy under Contract No. DE-AC0 2-05CH11231.i 

## TABLE OF CONTENTS

1.0 INTRODUCTION..................................................................... ..1

1.1 Literature Review...............................................................1

1.1.1 Price.......................................................................1

1.1.2 Income....................................................................2 1.1.3 Appliance Efficiency and Discount Rates..................... ...2 2.0 VARIABLES DESCRIBING THE MARKET FOR REFRIGERATORS, CLOTHES WASHERS, AND DISHWASHERS........................... ......3 2.1 Physical Household and Appliance Variables..................... ........3

2.2 Economic Variables................................. ...........................3

3.0 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE

SHIPMENTS.......................................

............ ........................ ..5

3.1 Broad Trends............................................................ ........5 3.2 Model Specification...................................................

...... ...7

3.3 Model Discussion......................................................

...... ...7

4.0 ANALYSIS RESULTS......................................................

...... .....8 4.1 Individual Appliance Model..................................................8 4.2 Combined Appliance Model..................................................9

5.0 CONCLUSION...........................................................................9

APPENDIX A. ADDITIONAL REGRESSION SPECIFICATIONS AND

RESULTS.............................................

...... .11

A.1 Lower Consumer Discount Rate....................................................11 A.2 Disaggregated Variables................................................ ..............11

APPENDIX B. DATA USED IN THIS ANALYSIS......................... .....13

REFERENCES.............................................................................. ....15ii 

## LIST OF CHARTS

Chart 2.1 Trends in Appliance Shipments, Housing Starts and Replaceme nts....4 Chart 3.1 Residual Shipments and Appliance Price.................................... 6



## LIST OF TABLES

Table 1.1 Estimates of the Impact of Price, Income and Efficiency on Automobile and Appliance Sales...............................................2

Table 1.2 Discount Rates.....................................................................3 Table 2.1 Physical Household and Appliance Variables...............................4

Table 2.2 Economic Variables...............................................................4 Table 3.1 Simple Estimate of Total Price Elasticity of Demand......................6 Table 3.2 Tabular Estimation of Relative Price Elasticity of Demand..............6 Table 4.1 Individual Appliance Model Results.......................................... 9 Table 4.2 Combined Appliance Model Results.......................................... 9 Table A.1 Combined and Individual Results, 20% Discount Rate..................11 Table A.2 Disaggregated Regression Results, 37% Discount Rate..................12iii

1.0 INTRODUCTION

This article summarizes our study of the price elasticity of demand 1 for home appliances, including refrigerators, clothes washers and dishwashers. In the context of in creasingly stringent appliance standards, we are interested in what kind of impact the inc reased manufacturing costs caused by higher efficiency requirements will have on appliance sales. We chose to study this particular set of appliances because data for the elasticity calculation was more readily available for refrigerators, clothes wash ers, and dishwashers than for other appliances.

We begin with a review of the existing economics literature describing the i mpact of economic variables on the sale of durable goods. We then describe the market for home appliances and changes in it over the past 20 years. We conclude with summary and interpretation of the results of our regression analysis and present estimate s of the price elasticity of demand for the three appliances.

1.1 Literature Review

There are relatively few studies measuring the impact of price, income a nd efficiency on the sale of household appliances. In this section we provide a short review of this literature which suggests the likely importance of these variables.

1.1.1 Price

The goal of many of the studies covered in this review is to measure the impact of price on sales in a dynamic market. One study of the automobile market prior to 1970 finds the price elasticity of demand to decline over time. The author explains this as the r esult of buyers delaying purchases after a price increase but eventually making t he purchase out of necessity (Table 1.1). 2 A contrasting study of household white goods also prior to 1970, finds the elasticity of demand to increase over time as more price-consci ous buyers

enter the market. 3 A recent analysis of refrigerator market survey data finds that consumer purchase probability decreases with survey asking price. 4 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 brand pri ce elasticity 5 to be -1.75. 6 The average estimate of price elasticity of demand reported in

1 Price elasticity is the percent change in shipments given a percent change in price

. 2 S. Hymens "Consumer Durable Spending: Explanation and Prediction” Brookings Papers on Economic Activ ity. 1971

3 P. Golder and G. Tellis, "Beyond Diffusion: An Aff ordability Model of the Growth of New Consumer Dura bles" Journal of Forecasting. 1998.

4 D. Revelt and K. Train, "Mixed Logit with Repeated Choices: Household's Choice of Appliance Efficienc y Level." Review of

Economics and Statistics. 1997

5 Brand price elasticity is the percent change in shi pments given a percent change in price for a partic ular brand of appliance. Sales of a particular brand of appliance will be more sensit ive to price changes than sales of appliances in ge neral.

6 G. Tellis. "The Price Elasticity of Selective Deman d: A Meta-Analysis of Econometric Models of Sales" . Journal of Marketing

Research. 1988.2

these studies is -0.33 in the appliance market and -0.47 in the combined automobile and appliance markets.

1.1.2 Income

Higher income households are more likely to own household appliances. 7 The impact of income on appliance shipments is explored in two econometric studies of the automobile and appliance markets. 8 9 The average income elasticity of demand is 0.50 in the appliance study cited in the literature review; the average income elas ticity is much larger in the automobile study.

Table 1.1 Estimates of the Impact of Price, Income and Efficiency on Automobile and Appliance Sales

Product Price

Elasticity Income

Elasticity Brand Price

Elasticity Implicit Discount

Rate Model Data

years Time

Period

1 Automobiles 1 -1.07 3.08 - - Linear Regression, stock adjustment Short run

2 Automobiles 1 -0.36 1.02 - - Linear Regression, stock adjustment Long run
3 Cloths Dryers

2 -0.14 0.26 - - Cobb-Douglas, diffusion 1947-1961 Mixed

4 Room Air Conditioner 2 -.37

6 0.45 - - Cobb-Douglas, diffusion 1946-1962 Mixed

5 Dishwasher

2 -0.42 0.79 - - Cobb-Douglas, diffusion 1947-1968 Mixed

6 Refrigerators

3 -0.37 - - 39% Logit probability, using survey data. 1997 Short run

7 Various

4

- - -1.76 7 - Multiplicative regregression Mixed

8 Room Air Conditioner 5 - - -1.72 - Non-linear diffusion 1949-1961 Short run

9 Cloths Dryers

5 - - -1.32 - Non-linear diffusion 1963-1970 Short run
Sources:

1 S. Hymens. "Consumer Durable Spending: Explanation and Prediction" Brookings Papers on Economic Acti vity. 1971

2 P. Golder and G. Tellis, "Beyond Diffusion: An Aff ordability Model of the Growth of New Consumer Dura bles" Journal of Forecasting. 1998.

3 D. Revelt; K.Train,"Mixed Logit with Repeated Choic es: Households Choice of Appliance Efficiency Level " Review of Economics and Statistics. 1997

4 G. Tellis. "The Price Elasticity of Selective Deman d: A Meta-Analysis of Econometric Models of Sales" . Journal of Marketing Research. 1988.

5 D.Jain; R.Rao. "Effect of Price on the Demand for Durables: Modeling, Estimation and Findings" Journ al of Business and Economic Statistics. 1990.

Notes:

6 Logit probability results are not directly comparab le to other elasticity estimates in this table.

7 Average brand price elasticity across 41 studies.

1.1.3 Appliance Efficiency and Discount Rates

Many studies estimate the impact of appliance efficiency on consumer applia nce choice. Typically, this impact is summarized by the implicit discount rate, i.e., the rate consumers use to compare future appliance operating cost savings against an appliance pur chase price premium. One early and much cited study concludes that consumers use a 20% implicit discount rate when purchasing room air conditioners (Table 1.2). 10 A survey of several studies of different appliances suggests that the average consumer implicit

discount rate is about 37%. 11 In Section 3, we use a discount rate of 37% to estimate

7 Energy Information Agency. “The Effect of Income o n Appliances in U.S. Households.” U.S. Department of Energy: http://www.eia.doe.gov/emeu/recs/appliances/applian ces.html . 2002. Accessed February 1, 2007

8 S. Hymens "Consumer Durable Spending: Explanation and Prediction." Brookings Papers on Economic Acti vity. 1971

9 P. Golder and G. Tellis, "Beyond Diffusion: An Aff ordability Model of the Growth of New Consumer Dura bles" Journal of Forecasting. 1998.

10 J. Hausman. "Individual discount rates and the purc hase and utilization of energy using durables." The Bell Journal of Economics.

1979.

11 K. Train. "Discount rates in consumer' energy relat ed decisions: a review of the literature." Energy. 19853

discounted operating costs, based on appliance efficiency. The implications of a 20% discount rate are considered in Appendix A.

Table 1.2 Discount Rates

Product Implicit

Discount Rate Model

Room Air Conditioners 1 20% Qualitative choice, survey data
Household Appliances 2 37% 3 Assorted

1 J. Hausman. "Individual discount rates and the pur chase and utilization of energy using durables."

The Bell Journal of Economics. 1979.

2 K. Train. "Discount rates in consumer' energy relat ed decisions: a review of the literature." Energy. 1985

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

2.0 VARIABLES DESCRIBING THE MARKET FOR REFRIGERATORS, CLOTHES WASHERS, AND DISHWASHERS

In this section we evaluate variables that appear to account for refriger ator, clothes washer and dishwasher shipments, including physical variables and economic vari ables.

2.1 Physical Household and Appliance Variables

Several variables influence the sale of refrigerators, clothes washers and dishwashers. The most important for explaining appliance sales trends are the annual number of new households formed (housing starts) and the number of appliances reaching the end of their operating life (replacements). Housing starts influence sales be cause new homes are often provided with – or soon receive – new appliances, including dishwashers and refrigerators. Replacements are correlated with sales because new appl iances are typically purchased when old ones wear out. In principle, if households maintain a fixed number of appliances, shipments should equal housing starts plus appliance replacements.

2.2 Economic variables

Appliance price, appliance operating cost and household income are important economic variables affecting shipments. Low prices and operating costs encourage household appliance purchases and a rise in income increases householder ability to purchase appliances. In principle, changes in economic variables should explain changes in the number of appliances per household.

During the 1980 – 2002 study period, annual shipments grew 69% for clothes washers, 81% for refrigerators and 105% for dishwashers (Table 2.1). This rising shipments t rend is explained in part by housing starts, which increased 6% and by appliance replacements, which rose between 49% and 90% over the period (Table 2.1). 12 For

12 Appliance replacements are determined from the expe cted operating life of refrigerators (19 years), cl oths washers (14 years) and dishwashers (12 years) and from past shipments. Re placements are further described in Appendix II.4

mature markets such as these, replacements exceed appliance sales associ ated with new housing construction.

Table 2.1 Physical Household and Appliance Variables

Appliance Change Change Change 1980 2002 (%) 1980 2002 (%) 1980 2002 (%) 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%

Shipments: Number of units sold, in millions. AHA M Factbook and Appliance Magazine. Housing starts: Annual number of new homes constru cted. U. S. Census. Replacements: Average of annual lagged shipments, with lag equal to expected appliance operating life

, plus or minus 5 years. Shipments Housing Starts Replacements

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) a nd “shipments” (diamond linked line) (Chart 2.1). In 1980 the “shipment” line begins below the “starts plus replacements” line. In 2002, the “shipments” line ends above the “sta rts plus replacements” line. This more rapid increase in shipments, compared to housing starts plus replacements, suggests that the appliance per household ratio increa sed over the study period.

Chart 2.1 Trends in Appliance Shipment, Housing Starts and Replacemen ts

Economic variables, including price, cost and income, may explain this increase in appliances per household. Over the period, appliance prices increased 40% to 50%, operating c osts fell between 33% and 72% and median household income rose 16% (Table 2.2).

Table 2.2 Economic Variables

Appliance Change Change Change 1980 2002 (%) 1980 2002 (%) 1980 2002 (%) Refrigerators 1208 726 -40% 333 94 -72% 37,447 43,381 16%

Clothes Washers 779 392 -50% 262 175 -33% 37447 43381 16%

Dishwashers 713 368 -48% 183 95 -48% 37447 43381 16%

Price. Shipment weighted retail sales price, in 19 99 dollars for selected years. AHAM Fact Book, TSDs

. Operating cost. Annual electricity price times ele ctricity consumption (UEC), for selected years. 199 9 dollars. AHAM fact book.

Income. Mean household income. U.S. Census. Household Income Operating Cost Price 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 2000Millions .5

3.0 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE

SHIPMENTS

Little data is available for estimating the impact of economic variable s on the demand for appliances. Industry operating cost data is incomplete – appliance energy use data is available for only 12 years of the 1980-2002 study period. Industry price data is als o incomplete – available for only 8 years of the study period for each of the applianc es.

The lack of data suggests that regression analysis can at best evaluate broad data trends, utilizing relatively few explanatory variables. In this section we begin b y describing broad trends apparent in the economic and physical household data sets. We then specify a simple regression model to measure these trends, making assumptions to minimiz e the number of explanatory variables. Finally, we present results of the regress ion analysis and our estimate of the price elasticity of demand for appliances. In an appendi x, we also present the results of regression analysis performed with more complex model s, and used to test assumptions made to specify the simple model. These results support the simpl e model specification, and estimates of the price elasticity of appliance de mand measured

with that model.

3.1 Broad Trends

In this section we review trends in the physical household and economic data sets and posit a simple approach for estimating the price elasticity of appliance dem and. As noted above, the physical household variables (starts and appliance replacements) expl ain most of the variability in appliance shipments over the period. 13 We assume the rest of the variability in shipments (residual shipments) is explained by economic vari ables, and present a tabular method for measuring price elasticities described bel ow.

To illustrate this tabular approach, we define two new variables – residual shi pments and total price. Residual shipments are defined as the difference between shipm ents and physical household demand (starts plus replacements). Total price is defined as a ppliance price plus the present value of lifetime appliance operating cost. 14 Over the study period, residual shipments increase 30% for refrigerators, 19% for clothes washers a nd 23% for dishwashers in proportion to total shipments. At the same time, total prices decline 47%, 45% and 48% for refrigerators, clothes washers and dishwashers, respectively. A ssuming that total price explains the entire change in per household appliance purchases , we calculate a rough estimate of the total price elasticity of demand equal t o -.48 for refrigerators, -.32 for clothes washers and -.37 for dishwashers (Table 3.1).

13 A log linear regression of the form: Shipments = a + b (Housing starts) + c (Retirements), indicates that these two variables explain 89% of t he variation in refrigerator shipments, 97% of the variation in cloths washer shipments and 97% of the variation in dishwasher shipments.

14 Present value operating cost is calculated assumin g a 19 year operating life for refrigerators, 14 ye ar operating life for washing machines and a 12 year o perating life for dishwashers. A 37% discount rate is used to sum annual operating costs into a total pre sent value operating cost.6

Table 3.1 Simple Estimate of Total Price Elasticity of Demand

Appliance Residual Shipments, millions Change Change Elasticity

1980 2002 2002 (%) 1980 2002 (%) 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 Residual Shipments,

millions Total Price

The negative correlation between total price and residual shipments suggested b y these negative price elasticities is illustrated in a graph of residual shipment s and total price (Chart 3.1).

Chart 3.1 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 s hipments as a decline in price, we incorporate the impact of income by defining a third var iable, termed relative total price, calculated as total price divided by household income. 15 The percent decline in relative price for the three appliances divided by the perc ent change in residual shipments suggests a rough estimate of relative price elasticit y equal to -.40 for refrigerators, -.26 for clothes washers and -.30 for dishwashers (Table 3.2).

Table 3.2 Tabular Estimation of Relative Price Elasticity of Demand

Appliance Change Change Elasticity 1980 2002 (%) 1980 2002 (%) 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 Residual Shipments Relative Total Price

15 Recall that the income elasticity of demand cited in the literature review is .50 and the price elast icity of demand cited in the review averages -.35. This sug gests that combining the effects of income and pric e will yield an elasticity less negative than price e lasticity alone.

Refrigerators

400 800 1200 1600 2000

-2.0 -1.0 0.0 1.0 2.0

Total PriceResidual Shipments . Interpolation

Observation 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 .7

3.2 Model Specification

The limited price data suggests using a simple regression model to estimate the impact of economic variables on shipments, using few explanatory variables. The equation c hosen for this analysis includes one physical household variable (starts plus replace ments) and one relative price variable (the sum of price plus operating cost, divided by income ) (Equation 3.1). These variables in this model, termed the individual appliance model, are defined in foot notes below and in Appendix B. 16 17

Equation 3.1 Shipments = a + b (Relative Price) + c (Starts+Replacements)

The natural logs are taken of all variables so that the estimated coefficie nts for each variable in the model may be interpreted as the percent change in shipments assoc iated with the percent change in the variable. Thus, the coefficient b in this model is interpreted as the relative price elasticity of demand for the three appli ances.

A combined regression equation is used to estimate an average price elasticity of demand across the three appliances, using pooled data in a single regression (Equation 3. 2). A combined regression specification is justified, given limited data availabil ity and similarity in price and shipment behavior across appliances (Chart 3.1). Thus, the model represented by the combined regression equation is considered the basic model in our analysis of appliance shipments.

Equation 3.2 Shipments = a + b (Relative Price) + c (Starts+Replacements) + d (CW) + e (DW) 18

3.3 Model Discussion

The most important assumption used to specify this model is that changes in economic variables over the study period – income, price and operating cost – are responsible f or all observed growth in residual appliance shipments. In other words, we assume other possible explanations, such as changing consumer preferences and increases in t he quality of appliances, had no impact. This assumption seems unlikely but without additional data, the impact of this assumption on the price elasticity of demand ca nnot be measured. We effectively assume that changes in consumer preferences and a ppliance characteristics, while affecting which specific models are purchased, ha ve relatively little impact on the total number of appliances purchased in a year.

Three additional assumptions used to specify this model deserve comment. The rela tive price variable is specified in the model, assuming that (1) the correct implicit di scount

16 Shipments is the quantity of appliances sold, hous ing starts is the number of new homes, replacements is the number at the end of their operating life and a bility to pay is defined in footnote (15) below ( natural logs taken of all variables).

17

Income Cost) Operating Value (Present Price) (First

Income Price Total Price Relative +

= = .

18 CW and DW are dummy variables for clothes washers and dishwashers.8

rate is used to combine appliance price and operating cost and that (2) rising income h as the same impact on shipments as falling total price. The starts + replacem ents variable is specified, assuming (3) that starts and replacements have similar impact s on shipments.

To investigate the first assumption about discount rates, we calculated “pres ent value operating cost” using a 20% implicit discount rate and performed a second regre ssion analysis of equation 1. The results of this analysis, presented in Appendix A, indicat e that the elasticity of relative price is relatively insensitive to change s in the discount rate.

To investigate the second and third assumptions, we specified a regression model separating income from total price and replacements from starts, thus adding two additional explanatory variables to the basic model (Equation 3.3).

Equation 3.3 Shipments = a + b (Total Price) + c (Income) + d (Starts) + e (Replacements) + f (CW) + g (DW).

The results of the regression analysis of this model are also presented in Appendi x A. These results suggest that the elasticity of total price (coefficient b) is relatively insensitive to changes in the treatment of income and starts + replacements in the model.

4.0 ANALYSIS RESULTS

4.1 Individual Appliance Model

The individual appliance regression equations are specified as described in e quation 3.1. In regression analysis of this model, the elasticity of relative price (b) is estimated to be - 0.4 for refrigerators, -0.31 for clothes washers and -0.32 for dishwashers (Table 6)

, averaging -0.35. These elasticities are similar to those reported in the li terature survey for appliances (Table 1.1). They are remarkably similar to the price elasti city calculated using a tabular approach presented above (Table 3.2).

The estimated coefficient associated with the starts + replacements va riable is close to one. A coefficient equal to one for this variable would imply that shipments increas e in direct proportion to an increase in starts + replacements, holding economic variable s constant. The high R-squared values (above 95) and t-statistics (above 5) in the resul ts provide a measure of confidence in this analysis, despite the very small data s et.

Table 4.1 Individual Appliance Model Results

Coefficient tStat Coefficient tStat Coefficient tStat Intercept -1.51 -7.26 -1.47 -8.23 -2.08 -16.78

Relative Full 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 23.00 Refrigerator Clothes Washer Dishwasher Variable9

4.2 Combined Appliance Model

The combined appliance regression equation is specified as described in eq uation 3.2. Our regression analysis indicates that the model fits the existing shipments data well (high R-squared) and that the variables included in the model are statistically s ignificant (Table 4.2). 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 si milar to elasticity estimates reported in the literature survey and calcula ted using the tabular approach above.

Table 4.2 Combined Appliance Model Result

Variable Coefficient tStat Intercept -1.60 -15.54

Relative Full 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

5.0 CONCLUSION

At the beginning of this report, we describe the results of a literature search, tabular analysis and regression analysis of the impact of price and other variables on appl iance shipments. In the literature, we find only a few studies of appliance markets tha t are relevant to this analysis, and no studies using time series price and shipments dat a after 1980. The information that can be summarized from the literature, suggests that the demand for appliances is price inelastic. Other information in the literatur e suggests that appliances are a normal good, such that rising incomes increase the demand for appliances. Finally, the literature suggests that consumers use relati vely high implicit discount rates, when comparing appliance prices and appliance operating costs.

There is not enough price and operating cost data available to perform complex ana lysis of dynamic changes in the appliance market. In this analysis, we use data avai lable for refrigerators, clothes washers and dishwashers to evaluate broad market tre nds and to perform simple regression analysis.

These data indicate that there has been a rise in appliance shipments and a decl ine in appliance price and operating cost over the period. Household income has also risen during this time. To simplify the analysis, we combined the available economic information into one variable, termed relative price, and used this variable in a tabula r analysis of market trends, and a regression analysis.10

Our 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 regr ession analysis of these same variables suggests that the price elasticity of demand is -.35, a veraged over the three appliances. The price elasticity is similar to estimates in the literature. Nevertheless, we stress that the measure is based on a small data set, using ver y 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 thi s period, but they are not accounted for in this analysis. The capacity of most applianc es has increased since 1980, and it is likely that there have been increases in qualit y and durability as well. If these factors have impacted the sales of appliances , our estimate of the price elasticity of demand is an over-estimate, since some of the increas es in sales over the 1980-2002 time period would have been driven by changing preferences rather than decreasing prices.11

APPENDIX A. ADDITIONAL REGRESSION SPECIFICATIONS AND RE SULTS

As mentioned above, the implicit price variable in the basic regression m odel is specified using a 37% implicit discount rate, to aggregate appliance price and operati ng cost. In addition, the implicit price variable is defined assuming that rising income has the sa me impact on shipments as falling total price. Similarly, the Starts+Replacements vari able is defined assuming that housing starts have a similar impact on shipments as appliance replace ments.

A.1 Lower Consumer Discount Rate

To investigate the first assumption about discount rates, we calcula ted “present value operating cost” using a 20% implicit discount rate and performed a second regression ana lysis of equations 3.1 and 3.2. The estimated coefficient associated with the relative pr ice variable in these regressions is almost identical to the coefficients estimated f or same variable reported above using a 37% implicit discount rate. The elasticity of relative price c alculated using a 20% discount rate is -.33 in the combined regression and averages -.35 for the t hree appliances (Table A.1). The elasticity of price calculated using a 37% discount rate is -.34 in the combined regression and averages -.35 for the three appliances. We conclude fr om this analysis that the elasticity of relative price is relatively insensitive to chang es in the discount rate.

Table A.1 Combined and Individual Results, 20% discount rate

Variable Coefficient tStat Intercept -1.53 -14.61

Relative Full Price -0.33 -10.69 Starts+Replacements 1.20 13.65

CW -0.18 -8.69

DW -0.32 -6.57

R 2 0.982

Observations 69

Coefficient tStat Coefficient tStat Coefficient tStat Intercept -1.36 -6.26 -1.41 -7.49 -2.04 -17.23

Relative Full Price -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 23.00

Variable Refrigerator Clothes Washer Dishwasher

A.2 Disaggregated Variables

To investigate the second and third assumptions, we constructed a regres sion model separating income from total price and replacements from starts, thus adding two addit ional explanatory variables to the basic model (Equation A.1).

Equation A.1 Shipments = a + b (Total Price) + c (Income) + d (Starts) + e (Repla cements) + f (CW) + g (DW).

The estimated coefficient associated with the total price variabl e in these regressions is almost identical to the coefficients estimated for the relative pric e variable reported above. The elasticity12

of total price in Equation A.1 is -.36 in the combined appliance regression and aver ages -.35 for the three appliances (Table A.2). The elasticity of relative pr ice in Equation 3.2 is -.34 in the combined regression and averages -.35 across the individual appliances (T ables 4.1 and 4.2). We conclude that the price elasticity calculated in this analysis is re latively insensitive to the specification of household income and starts + replacements variables in the model.

Table A.2 Disaggregated Regression Results, 37% Discount Rate

Variable Coefficient tStat
Intercept -2.92 -1.26

Income 0.58 2.92

Full Price -0.36 -7.06 Houseing Starts 0.44 10.02 Replacements 0.62 8.12

CW -0.24 -9.25

DW -0.46 -7.68

R2 0.985

Observations 69

Coefficient tStat Coefficient tStat Coefficient tStat 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

Full Price -0.35 -5.48 -0.27 -2.51 -0.43 -5.18 Houseing Starts 0.41 7.38 0.25 3.29 0.62 8.24 Replacements 0.56 6.06 0.56 2.09 0.65 5.86

R2 0.984 0.958 0.979

Observations 23 23 23

Variable Refrigerator Clothes Washer Dishwasher13

APPENDIX B. DATA USED IN THIS ANALYSIS

1. Appliance Shipments: Shipments are defined as the annual number of units shipped in millions. These data were collected from the Association of Home Appliance Manufacturers ( AHAM) and Appliance Magazine as annual values for each year, 1980-2002.

2. Appliance Price: Price is defined as the shipments weighted retail sales price of the unit in 19 99 dollars. Price values for 1980, 1985, 1986, 1991, 1993, 1994, 1998, and 2002 were collected from The AHAM. Fact Book and Department of Energy Technical Support Documents. P rice values for other years were interpolated from these eight years of data.

3. Housing Starts: Housing starts data were collected from U.S. Census construction statistic s (C25 reports) as annual values for each year, 1980-2002.

4. Replacements: Retirement-driven replacements are estimated with the assumption that som e fraction of sales arise from consumers replacing equipment at the end of its useful life. Since each appliance has a different expected lifespan (19 years for refrigerators 19 , 14 years for

clothes washers 20 , 12 years for dishwashers 21 ), replacements are calculated differently for each appliance type. Replacements are estimated as the average of shipme nts 14-24 years previous for refrigerators, 9-19 years previous for clothes washers, and 7 t o 17 years previous for dishwashers. Historical shipments data were collected from AHAM and Appliance Magazine.

5. Annual Electricity Consumption: Electricity Use (UEC) is defined as the energy consumption of the unit in kil owatt-hours. Electricity consumption is dependent on appliance capacity and efficiency. The se data were provided by AHAM for 1980, 1990-1997 and 1999-2002. Data were interpolated in the years for which data were not available.

6. Operating Cost: Operating Cost is the present value of the electricity consumption of an applia nce over its expected lifespan. The life spans of refrigerators, clothes washers and dishw ashers are assumed to be 19, 14, and 12 years respectively. Discount rates of 20% 22 and 37% 23
were used, producing similar estimates of price elasticity. A study by H ausman

19 Duemling, Reubin. 1999 “Product Life of Refrigerat ors.” University of California, Berkeley, Energy an d Resources Group masters thesis.

20 U.S. Department of Energy. 2000. “Technical Suppor t Document (TSD): Energy Efficiency Standards

for Consumer Products: Clothes Washers.”

21 U.S. Department of Energy. “Technical Support Docum ent: Home Appliances.”

22 Hausman, Jerry A. 1979 “Individual discount rates and the purchase and utilization of energy-using

durables.”

23 Train, Kenneth E. and Terry Atherton. 1995 The Energy Journal , “Rebates, loans, and customers’ choice of appliance efficiency level: combining sta ted- and revealed-preference data.”14

recommended a discount rate of “about 20%” in its introduction, and presented results ranging from 24.1% to 29% based on his calculations for room air conditioners. A study by Train suggests a range of implicit discount rates averaging 35% for appl iances.

7. Income: Median annual household income in 2003 dollars. This data was collected for each year, 1980-2002, from Table H-6 of the U.S. Census, http://www.census.gov/hhes/income/histinc/h06ar.html (accessed February 1, 2007).15 REFERENCES

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