APPENDIX 9A. RELATIVE PRICE ELASTICITY OF DEMAND FOR

APPLIANCES

TABLE OF CONTENTS

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 CENTRAL AIR CONDITIONERS

AND HEAT PUMPS .................................................................................................... 9A-3

9A.3.1 Physical Household/Appliance Variables............................................. 9A-3

9A.3.2 Economic variables ............................................................................... 9A-3

9A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE

SHIPMENTS ................................................................................................................ 9A-5

9A.4.1 Variable Definition ............................................................................... 9A-5

9A.4.2 Model Specification.............................................................................. 9A-6

9A.4.3 Model Discussion.................................................................................. 9A-6

9A.4.4 Analysis Results.................................................................................... 9A-7

9A.4.5 Analysis Critique .................................................................................. 9A-7

9A.5 LONG RUN IMPACTS ................................................................................................ 9A-9

9A.6 SUMMARY ................................................................................................................ 9A-10

LIST OF TABLES

Table 9A.2.1 Estimates of the Impact of Price, Income and Efficiency on Automobile and App liance Sales................................................................ 9A-2

Table 9A.3.1 Physical Household/Appliance Variables................................................... 9A-3

Table 9A.3.2 Economic Vari ables .................................................................................... 9A-4

Table 9A.4.1 Individual Appliance Model Results .......................................................... 9A-7

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

Table 9A.5.2 Change in Relative Price Elasticity for Home Appliances following a Purchase Price Change.............................................................................. 9A-10

LIST OF FIGURES

Figure 9A.3.1 Trends in CAC Shipments, Housin g Starts and Replacements .................. 9A-4 Figure 9A.4.1 Trends in CAC Resi dual Shipments and Re lative Price ............................. 9A-8 Figure 9A.4.2 CAC Shipments vs Re lative Price .............................................................. 9A-8

9A-iAPPENDIX 9A. RELATIVE PRICE ELASTICITY OF DEMAND FOR

APPLIANCES

9A.1 INTRODUCTION

This appendix summarizes DOE’s study of th e price elasticity of demand for central air conditioners and heat pumps (CAC). This appe ndix begins with a review of the existing economics literature describing the impact of econo mic variables on the sale of durable goods in section 9-A.2. In section 9-A.3, the market for CAC and changes in it over the past 20 years is described. In section 9-A.4, DOE summarizes the re sults of its analysis and presents estimates of the price elasticity of demand. In section 9-A .5, DOE developes an ‘effective’ purchase price elasticity. DOE’s interpretation of these results is presented in section 9-A.6.

9A.2 LITERATURE REVIEW

There are relatively few studies measuring the impact of price, income and efficiency on the sale of appliances like central air conditioners and heat pumps. In this section DOE provides a short review of this literature which suggests the likely importance of these variables.

9A.2.1 Price

The goal of many of the studies covered in th is review is to measure the impact of price on sales in a dynamic market. One study of the automobile market prior to 1970 finds the price elasticity of demand to decline over time. The author explains this as the result of buyers delaying purchases after a price increase but eventually making the purchase (Table 9-A.2.1). 1 A contrasting study of household white goods also prior to 1970, finds the elasticity of demand to increase over time as more price-conscious buyers enter the market. 2 A recent analysis of refrigerator market survey data finds that consumer purchase probability decreases with an increase in survey asking price. 3 Estimates of the price elasticity of demand for different brands of the same product tend to be relatively high. A review of 41 studies of the impact of price on market share found the average price elasticity to be -1.75. 4 Estimates of the price elasticity of demand for appliances and other consumer durables are much lower. The price elasticity of demand reported in several studies averaged -0.33 in studies of the appliance market and -0.47 in studies of the automobile and appliance markets.

9A.2.2 Income

Higher income households are more likely to own household appliances. 5 The impact of income on appliance shipments is explored in two econometric studies of the automobile and appliance markets. 1,2 The average income elasticity of demand in our literature review is 0.50 for appliances and over 1.0. for automobiles (Table 9.A.2.1).

9A-19A.2.3 Appliance Efficiency and Discount Rates

Many studies estimate the impact of appliance efficiency on consumer appliance purchases. Typically, this impact is summarize d by the implicit discount rate, i.e., the rate consumers use to compare future appliance operating cost savings against an appliance purchase price premium. One early and much cited st udy concludes that consumers use a 20 percent implicit discount rate when purchasing r oom air conditioners (Table 9-A.2.1). 6 A survey of several studies of different appliances suggests that the consumer imp licit discount rate has a broad range and averages about 37 percent. 7
Additionally, a previous study by DOE on the price elasticity of demand for refrigerators, dishwashers, and clothes washers estimates that the relative price elasticity of demand for home appliances is -0.34. 8

Table 9A.2.1 Estimates of the Impact of Price, In come and Efficiency on Automobile and Appliance Sales

Durable Good Price Elasticity Income Elasticity Brand

Price Elasticity Implicit

Discount

Rate Model Data

Years Time

Period

Automobiles 1 -1.07 3.08

- - Linear Regression, stock adjustment - Short run

Automobiles 1 -0.36 1.02

- - Linear Regression, stock adjustment - Long run

Clothes Dryers 2 -0.14 0.26

- - Cobb-Douglas, diffusion 1947-1961 Mixed

Room Air

Conditioners 2 -0.37 8 0.45

- - Cobb-Douglas, diffusion 1946-1962 Mixed

Dishwashers 2 -0.42 0.79

- - Cobb-Douglas, diffusion 1947-1968 Mixed

Refrigerators 3 -0.37

- - 39% Logit probability, survey

data 1997 Short run

Various 4

- - -1.76 9

- Multiplicative regression

- Mixed

Room Air

Conditioners 5 - - -1.72

- Non-linear diffusion 1949-1961 Short run

Clothes Dryers 5

- - -1.32

- Non-linear diffusion 1963-1970 Short run

Room Air

Conditioners 6 - - - 20% Qualitative choice, survey

data - -

Household Appliances 7 - - - 37% 10 Assorted

- -

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

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

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

9 Average brand price elasticity across 41 studies.

10 Averaged across several household applia nce studies referenced in this work.

9A-29A.3 VARIABLES DESCRIBING THE MARKET FOR CENTRAL AIR

CONDITIONERS AND HEAT PUMPS

In this section DOE evaluates variables th at are expected to account for central air conditioner and heat pump shipments, including physical household/appliance variables, and

economic variables.

9A.3.1 Physical Household/ Appliance Variables

Several variables influence the sale of cent ral air conditioners and heat pumps. The most important for explaining these sales trends ar e the annual number of ne w houses constructed (housing starts) and the number of applian ces reaching the end of their operating life (replacements). Housing starts influence sales because new homes increasingly include central air conditioners or heat pumps, with a new hous ing saturation of 90% na tionally, and nearly 100% in some regions. Replacements are correlated with sales because new appliances are typically purchased when old ones wear out.

9A.3.2 Economic variables

Appliance price, appliance operating cost and household income may also influence appliance shipments. Low prices and costs encourage purchases and a rise in income increases householder ability to pay for appliances. In prin ciple, changes in these economic variables can help explain changes in the number of shipments.

During the 1983-2005 study period, annual shipments of central air conditioners grew by 238 percent (Table 9-A.3.1). This rising shipment s trend is explained in part by housing starts, which increased 21 percent and by replacemen ts, which rose by 212 percent over the period (Table 9-A.3.1).

Table 9A.3.1 Physical Household/Ap pliance Variables

1983 2005 Change
Shipments 1 (millions) 1.75 5.92 238%
Housing Starts 2 (millions) 1.70 2.07 21%
Replacements 3 (millions) 0.90 2.79 212%

1 Shipments: Number of units sold. Sources: AHRI.

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

3 Replacements: Estimated from past shipments with Weibull distribution, Weibull scale: 20.288, Weibull shape: 1.885, Weibull delay: 1 year, resulting in mean lifetime: 19.01 years and median lifetime: 17.70 years.

It is apparent that housing starts and re placements do not account for all shipments of central air conditioners. This is shown by comparing the trend in total shipments against the trend in shipments to housing st arts, and replacements between 1983 and 2005 (Figure 9-A.3.1). This residual shipments trend, illu strated by the un-shaded portion of the Figure, rises over time and exhibits significant volatility.

9A-31 9 8 3 1 9 8 4 1 9 8 5 1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 6,000,000

Year

Figure 9A.3.1 Trends in CAC Shipments, Housing Starts and Replacements

Economic variables, including price, cost and income, may explain part of the trend in residual CAC shipments. Over th e period, appliance prices decreased 40 percent to 50 percent, operating costs fell between 33 and 72 percent, and median household income rose 16 percent (Table 9-A.3.2). However, a lack of data make s it difficult to determine how much of the trend is explained by these economic variables and how much by other variables including changes in consumer preferences and regional saturation levels.

Table 9A.3.2 Economic Variables 0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000Total Central Air Conditioner Shipments Total Shipments

Replacements

Ship to Housing Starts

1983 2005 Change

Price 1 (1999$) 3319 2567 -23%
Operating Cost 2 (1999$) 1031 607 -41%

Household Income 3 (1999$) 33623 40110 19%

1 Price: Estimated from average price in 1999, weighted by inflation adjusted Producer Price Index. Source:

Burearu of Labor Statistics.

2 Operating Cost: Annual electricity price times electri city consumption., 37% implicit discount rate Source:

AHAM Fact Book.

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

9A-49A.4 REGRESSION ANALYSIS OF VARIABLES AFFECTING APPLIANCE

SHIPMENTS

Limited data is available for estimating the impact of economic variables on the demand for appliances. Shipments da ta is available only between 1983-2005 and there is no industry price data, The producer price index is used as a proxy for the trend in the average price of

central air conditioners.

The limited data suggests that regression analysis can at best evaluate broad data trends. This section begins by describi ng broad trends apparent in the economic and physical household data sets and then specifies a simple regr ession model to measure these trends, making assumptions to minimize the number of explanatory variables. Finally, results are presented of the regression analysis.

9A.4.1 Variable Definition

As noted above, housing starts and appliance replacements (physical household demand), explain much of the increase in CAC shipme nts over the 1983-2005 period. Before specifying a regression model, DOE defines two new variab les—residual shipments and relative price. Residual shipments are defined as the di fference between shipments and physical household demand, and estimated by the following equation:

Residual Shipments = Total Shipments – Shipments to Starts – Replacements

where: Shipments to Starts = New Housing Starts x New Housing CAC Saturation.

Much of the CAC market is unlikely to be price sensitive. For example, CAC in new housing is likely to be very price insensitive. In recent years, CAC has become a standard feature of new houses—most (90%) new homes in the U.S. have CAC and in rapidly growing regions in the South and Midwest, virtually all new homes have CAC. The cost of CAC represents a small fraction of the typical house pr ice, and most analysts believe that house buyer purchase behavior is independent of CAC cost. CAC replacement sales may be somewhat more price sensitive, but only slightly so. The industry literature suggests that appliance owners grow accustomed to CAC over time and come to regard it as a necessity. In other words, appliance owners may at most delay replacing old air conditione rs after a rise in price, but in the long run old units are almost always replaced.

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 relative price, represented by the following equation:

PP + PVOC RP = I ncome

9A-5where:

RP = Relative price,

PP = Appliance purchase price, and

PVOC = Present value of operating cost a

Income = Median household income.

9A.4.2 Model Specification

The limited price data suggests using a simple regression model to estimate the impact of economic variables on shipments, using few explanatory variables. The following equation chosen for this analysis includes one physical household variable (starts plus replacements) and

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

Shipments = a + b × RP + c × 

## [ Starts + Re placements 

## ]

where:

Shipments = Total CAC shipments,

RP = Relative price,

Starts = Shipments to housing starts, and Replacements = Number of CAC at the end of their operating life.

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

9A.4.3 Model Discussion

DOE specified a regression model similar to the model used to estimate relative price elasticity of demand for the home appliances rulemaking. 9 One assumption used to specify this model is that changes in econom ic variables over the study peri od—income, price, and operating cost—are responsible for observed growth in re sidual shipments and that other variables, including changing consumer preferences and changes in the qua lity of CAC—have no additional or independent impact on shipments. b This assumption seems unlikely but without more data, the impact of this assumption on th e price elasticity of demand cannot be measured. An additional, perhaps even more important assumption is that the explanatory variables are

a Estimated using a 37% implicit discount rate.

b DOE considered additional variables including the impact of GDP and stock market indices as measures of wealth (instead of income), annual cooling degree days, and electri city prices as additional variables, but none of these variables was found to be significantly correlated with the trend in residual shipments.
9A-6accurately measured. This assumption is also incorrect. Recall for example, that the CAC producer price index is used in the regression as a proxy for CAC prices c

9A.4.4 Analysis Results

In regression analysis of this model, the elasticity of relative price (coefficient b) is estimated to be -1.26 for the residual shipments market for CAC.

Table 9A.4.1 Individual Appliance Model Results

Variable Coefficient t-stat
Intercept 4.77 2.07

Relative Price -1.26 -3.3
Starts + Replacements 0.49 2.29

R 2 0.93

Observations 24

9A.4.5 Analysis Critique

As reported above, the regression m odel analysis suggests that the relative price elasticity of demand for residual shipments of CAC will be -1.26. For several reasons, DOE rejects this estimate of relative price elasticity. There is a high degree of multicolinearity between relative price and the “starts + replacements” variable in the regression. Thus, it is difficult to determine the statistical significance of the relative price coefficient. The coefficient associated with other explanatory variable in the regression (starts + replacements), appears to be biased downward.

The coefficient for this variable is estimated to be 0.49 but is expected to be close to 1. That is because each CAC installed in new housing or pu rchased as a replacemen t requires an additional unit to be shipped. Since this coefficient is si gnificantly less than 1, it suggests that the relative price coefficient is picking up some of the infl uence on shipments that should be attributed to housing starts and replacements. DOE concludes that the regression model is overestimating the magnitude of the relative price elasticity of demand for CAC.

This conclusion is supported by a graphical comparison of residual shipments and relative price. During the time period of 1983-2005, residual shipme nts of CAC varied significantly, with a small peak around 1990, a much larger peak around 1999, and a spike in 2004 (Figure 9-A.4.1). Over the same time period , the relative price of CAC decreased steadily (Figure 9-A.4.2). This suggests that the re lationship between relativ e price and residual shipments within our data set is tenuous at best. For example, at the end of the study period, the same relative price (roughly 0.08) is associated with residual shipments ranging from about .4

million to almost 2.0 million.

Three additional assumptions used to specify this model deserve comment. The relative price variable is specified in the model, assuming that (1) the correct implic it discount rate is used to combine appliance price and operating cost and that (2) rising income has the same impact on shipments as falling total price. The “starts + replacements” variable is specified, assuming (3) that starts and replacements have similar impacts on shipments.

9A-7 c0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 1,400,000 1,600,000 1,800,000 2,000,000Residual Shipments

0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140Relative Price ($CAC Cost / $Income)

Residual Shipments

Relative Price

1983 1988 1993 1998 2003

Year

Figure 9A.4.1 Trends in CAC Residual Shipments and Relative Price

0.14

0.12

0.1

0 250000 500000 750000 1000000 1250000 1500000 1750000 2000000

Residual ShipmentsRelative Price

0.08

0.06

0.04

0.02

0

Figure 9A.4.2 CAC Shipments vs Relative Price

9A-8For reasons described above, DOE relies on the results of previous analysis of other appliances to estimate the relative price elasticity of CAC demand. In previous analysis of those appliances, DOE was able to obtain a better set of data, including more ac curate appliance price data. In that previous analysis, DOE estimated the relative price elasticity of demand of refrigerators, dishwashers and clothes washers to be -0.34. 9 DOE acknowledges that there may

be differences between the market for central ai r conditioners and heat pumps, and the market of other household appliances, but given the problems associated with the above CAC regression analysis, and the lack of other CAC price elasticity studies, DOE believes that the relative price elasticity of demand for refrigerators, dish washers, and clothes washers is an acceptable proxy

for the relative price elasticity of demand for CAC.

9A.5 LONG RUN IMPACTS

As noted above 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 sour ce (Hymans) shows that the price elasticity of demand is significantly different over th e short run and long run for automobiles. 1 Because DOE’s forecasts of shipments and national imp acts due to standards is over a 30-year time period, consideration must be given as to how the relative price elasticity is affected once a new

standard takes effect.

DOE considers the relative price elasticity of -0.34 determ ined above in section 9-A.4 to be a short run elasticity. DOE was unable to identify sources specific to household durable goods, such as appliances, to indicate how short run and long run price elasticities differ. Therefore, to estimate how the relative price elasticity changes over time, DOE relied on the Hymans study pertaining to automobiles. Based on the Hymans study, Table 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 becomes more inelastic until it reaches a terminal value around the tenth year after the price change.

Table 9A.5.1 Change in Price Elastici ty 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 adopted the time series of relative price elasticities developed for home appliances and applies them to CAC. Table 9-A.5.2 presents the time series.

9A-9Table 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 review and regression analysis of the impact of price and other variables on CAC shipments. In the literature, DOE finds only a few studies of appliance markets that are relevant to this analysis, and no studies using time series price and shipments data after 1980. The information that can be summarized from the literature suggests that the demand for appliances is price inelastic. Other information in the literature suggests that appliances are a normal good, su ch that rising incomes increase the demand for appliances. Finally, the literature suggests that consumers use relatively high implicit discount rates, when comparing appliance prices and appliance operating costs.

The available price and operating cost data are too limited to perform a complex analysis of dynamic changes in the CAC market. In this analysis, DOE uses data available for CAC to

evaluate broad market trends and to perform simple regression analysis. These data indicate that there has been an unsteady rise in CAC shipments and a constant decline in CAC price and operating cost over the period. Household income has also risen during this time. To simplify the analysis, DOE combined the available econom ic information into one variable, termed

relative price, and used this variable in a regression analysis.

Due to a lack of CAC price and other data, DOE doubts the accuracy of relative price elasticity estimates obtained using that data. Instead DOE relies on a previous regression analysis of the relative price elasticity of demand for other appliances, including refrigerators, dish washers, and clothes washers. That analysis suggests that the relative price elasticity of appliances is -0.34. Although this elasticity is consistent with other estimates in the literature, DOE stresses that the measure is based on a small data set, using very simple statistical analysis. More important, the measure is ba sed 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.

9A-10REFERENCES

1 S. Hymans. Consumer Durable Spending: Explanation and Prediction, Brookings Papers on Economic Activity , 1971. Vol. 1971, No. 1, pp. 234-239.

2 P. Golder and G. Tellis. Beyond Diffusion: An Affordability Model of the Growth of New Consumer Durables, Journal of Forecasting , 1998.

3 D. Revelt and K. Train. Mixed Logit w ith Repeated Choices: Household's Choice of Appliance Efficiency Level, Review of Economics and Statistics , 1997.

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

5 U.S. Department of Energy-Energy Information Agency. The Effect of Income on Appliances in U.S. Households, 2002. Washington, DC.

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

6 J. Hausman. Individual discount rates and the purchase and utilization of energy using durables, The Bell Journal of Economics , 1979.

7 K. Train. Discount rates in consumer' energy related decisions: a review of the literature, Energy , 1985.

8 Larry Dale and K. Sydny Fujita. An Analysis of the Price Elasticity of Demand for Household Appliances , February 2008. Lawrence Berkeley National Laboratory: Berkeley,

CA. LBNL-326E.

9 U.S. DOE. Technical Support Document: Energy Efficiency Program for Consumer Products and Commercial and Industrial Equipment: Residential Dishwashers, Dehumidifiers, and Cooking Products, and Commercial Clothes Washers. March 2009. http://www1.eere.energy.gov/buildings/appliance_standards/residential/cooking_products_fi
nal_rule_tsd.html

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