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APPENDIX 8-J. ESTIMATION OF EQUIPMENT PRICE TRENDS FOR RESIDENTIAL 

CLOTHES DRYERS AND ROOM AIR CONDITIONERS

TABLE OF CONTENTS

8-J.1 INTRODUCTION .................................................................................................. 8-J-1

8-J.2 PRICE, COST AND MARKET STRUCTURE ..................................................... 8-J-2

8-J.3 DATA EVALUATION AND ANALYSIS ............................................................ 8-J-3

8-J.4 PRICE TRENDS FOR SENSITIVITY ANALYSES ............................................ 8-J-8

LIST OF TABLES

Table 8-J.4.1 Learning parameter as a function of time period ........................................ 8-J-8

LIST OF FIGURES

Figure 8-J.3.1 Historical Normalized Prices of Household Laundry Equipment .............. 8-J-3

Figure 8-J.3.2 Historical Normalized Prices of Room Air Conditioners ........................... 8-J-4

Figure 8-J.3.3 Historical and Projected Total Shipments of Household Laundry 

Equipment ................................................................................................... 8-J-5

Figure 8-J.3.4 Historical and Projected Total Shipments of Room Air Conditioners ....... 8-J-5

Figure 8-J.3.5 Relative Price versus Cumulative Shipments of Household Laundry 

Equipment, with Power Law Fit ................................................................. 8-J-6

Figure 8-J.3.6 Relative Price versus Cumulative Shipments of Room Air 

Conditioners, with Power Law Fit .............................................................. 8-J-7
8-J-1

APPENDIX 8-J. ESTIMATION OF EQUIPMENT PRICE TRENDS FOR RESIDENTIAL 

CLOTHES DRYERS AND ROOM AIR CONDITIONERS

8-J.1 INTRODUCTION

In the standards established in today’s direct final rule, DOE assumes that the 

manufacturer costs and retail prices of products meeting various efficiency levels may not 

remain fixed, in real terms, after 2010 (the year for which the engineering analysis estimated 

costs) and throughout the period of the analysis. In its Notice of Data Availability (NODA) 

published on February 22, 2011 (76 FR 9696), DOE stated that it may consider improving 

regulatory analysis by addressing equipment price trends. Consistent with the NODA, DOE 

examined historical producer price indices (PPI) for household laundry equipment and room air 

conditioners. For this equipment, DOE found consistent negative real price trends. Therefore, 

DOE concluded that the real prices of residential clothes dryers and room air conditioners have a 

different long term trend than prices in the economy as a whole. DOE maintained the constant 

real price trend as a sensitivity analysis to evaluate how the impact of potential standards might 

change under this scenario. 

DOE stated in the NODA that examination of historical price data for certain appliances 

and equipment that have been subject to energy conservation standards indicates that the 

assumption of constant real prices and costs may, in many cases, over-estimate long-term 

appliance and equipment price trends. Economic literature and historical data suggest that the 

real costs of these products may in fact trend downward over time according to “learning” or 

“experience” curves, or alternatively that the price trends for certain sectors of the US economy 

may be different than the price trends for the economy as a whole. A draft paper, “Using the 

Experience Curve Approach for Appliance Price Forecasting,” posted on the DOE web site at 

http://www1.eere.energy.gov/buildings/appliance_standards/supplemental_info_equipment_pric

e_forecasting.html, provides a summary of the data and literature currently available to DOE that 

is relevant to price forecasts for selected appliances and equipment. 

The extensive literature on the “learning” or “experience” curve phenomenon is typically 

based on observations in the manufacturing sector.a In the experience curve method, the real cost 

of production is related to the cumulative production or “experience” with a manufactured 

product. This experience is usually measured in terms of cumulative production. A common 

functional relationship used to model the evolution of production costs in this case is: 

Y = aX-b

 

a In addition to the draft paper mentioned above, see Weiss, M., Junginger, H.M., Patel, M.K., Blok, K., (2010a). A 

Review of Experience Curve Analyses for Energy Demand Technologies. Technological Forecasting & Social 

Change. 77:411-428. 
8-J-2

where a is an initial price (or cost), b is a positive constant known as the learning rate parameter, 

X is cumulative production, and Y is the price as a function of cumulative production. Thus, as 

experience (production) accumulates, the cost of producing the next unit decreases. The 

percentage reduction in cost that occurs with each doubling of cumulative production is known 

as the learning rate (LR), given by:

LR = 1 – 2-b 

In typical learning curve formulations, the learning rate parameter is derived using two 

historical data series: cumulative production and price (or cost). 

8-J.2 PRICE, COST AND MARKET STRUCTURE

DOE uses a cost-based analysis in estimating equipment prices. To estimate equipment 

prices in both the standards and the baseline or no-standards case, DOE develops engineering 

cost estimates that DOE then uses to estimate manufacturer selling price. The manufacturer 

selling price includes direct manufacturing production costs (labor, material, and overhead 

estimated in DOE’s manufacturer production costs) and all non-production costs (SG&A, R&D, 

and interest), along with profit. The process of the cost-based method for developing the 

manufacturer selling prices is described in the engineering analysis described in Chapter 5 of this 

TSD. To convert the manufacturer selling price to an equipment price for the consumer, DOE 

performs an analysis of distribution chain markups and estimates markups on both the baseline 

and incremental manufacture selling prices to determine equipment prices after distribution to 

the consumer. 

In analyzing experience curves to estimate price trends, DOE uses producer price indices 

as a key data input and analyzes this data to estimate the experience curve exponent. This 

approach has only one model parameter to describe the price trend and assumes a simple 

relationship between producer price and retail equipment price. Specifically, the approach 

assumes that producer prices, distribution chain markups and equipment prices all scale 

proportionally over time for the same product.

DOE could have developed a more complex price trend forecasting model with more 

parameters that could explain different trends in different equipment price and cost components 

over time. But the relatively few available data points presents a risk that a fit with multiple 

parameters would “overfit” the data. Overfitting occurs when there are too many degrees of 

freedom in a statistical model compared to the data and the fits are sensitive to random noise 

unrelated to long term trends. Due to the risk of overfitting the available data, DOE has decided 

to not develop a more complex multi-parameter price trend estimation model at this time. 

Due to the simple nature of the price trend estimation model, there are several well 

known economic and market phenomenon that will not be captured in detail by the price trend 

forecast. Some effects might lead to an overestimate of the long term price trend and other 

effects may lead to an underestimate. 
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For example, if there has been increasing market concentration historically on the part of 

manufacturers, this may have resulted in increasing manufacturer and wholesale markups over 

time. This would result in an observed historical producer price trend that did not decrease as 

fast as the underlying industrial learning rate. Depending on if market concentration accelerated 

or decelerated into the future this could lead to an over- or under-estimation of future price 

trends. 

Similarly, if there are cost components that have relatively slow long term price trends 

that have an increasing impact on price over time, the decreasing share of costs that are declining 

rapidly can result in a change in the empirically estimated experience curve exponent over time. 

8-J.3 DATA EVALUATION AND ANALYSIS

 To derive a learning rate parameter for residential clothes dryers and room air 

conditioners, DOE obtained historical Producer Price Index (PPI) data for household laundry 

equipment and room air conditioners from the Bureau of Labor Statistics’ (BLS). Because PPI 

data specific to residential clothes dryers were not available, DOE used PPI data for household 

laundry equipment as representative of residential clothes dryers. For household laundry 

equipment, DOE used PPI data spanning the time period 1980-2010, while for room air 

conditioners, DOE use data from 1990-2009. Inflation-adjusted price indices for household 

laundry equipment and room air conditioners were calculated by dividing the PPI series by the 

Consumer Price Index (CPI) “all items” index for the same years. These inflation-adjusted price 

indices (shown in Figure 8-J.3.1 and Figure 8-J.3.2) were used in subsequent analysis steps.

Figure 8-J.3.1 Historical Normalized Prices of Household Laundry 

Equipment
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Figure 8-J.3.2 Historical Normalized Prices of Room Air 

Conditioners

DOE assembled a time-series of annual shipments for 1946-2009 for clothes dryers, 

1972-2008 for clothes washers, and for 1946-2009 for room air conditioners from data submittals 

from AHAM, AHAM Fact Books, and Appliance Magazine. Decadal shipments up to 1979 for 

clothes washers were obtained from the 2005 AHAM Fact Book. Household laundry equipment 

is assumed to consist of only residential clothes washers and dryers. The annual and decadal 

shipments data were used to estimate cumulative shipments (production). Projected shipments 

after 2008/2009 were obtained from the base case projections made for the NIA (see chapter 9 of 

this TSD). Figure 8-J.3.3 and Figure 8-J.3.4 show the shipments time series used in the analysis. 
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Figure 8-J.3.3 Historical and Projected Total Shipments of 

Household Laundry Equipment

Figure 8-J.3.4 Historical and Projected Total Shipments of Room 

Air Conditioners
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To estimate a learning rate parameter, a least-squares power-law fit was performed on the unified 

price index versus cumulative shipments. 

See Figure 8-J.3.5 and Figure 8-J.3.6. 

Figure 8-J.3.5 Relative Price versus Cumulative Shipments of 

Household Laundry Equipment, with Power Law 

Fit
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Figure 8-J.3.6 Relative Price versus Cumulative Shipments of 

Room Air Conditioners, with Power Law Fit

The form of the fitting equation is:

P(X) = PoX-b, 

where the two parameters, b (the learning rate parameter) and Po (the price or cost of the first 

unit of production), are obtained by fitting the model to the data. DOE notes that the cumulative 

shipments on the right hand side of the equation can have a dependence on price, so there is an 

issue with simultaneity where the independent variable is not truly independent. DOE’s use of a 

simple least squares fit is equivalent to an assumption of no significant first price elasticity 

effects in the cumulative shipments variable.

The parameter values obtained are:

Po = 128.0−22.5

+27.4 (95% confidence) for household laundry equipment and 43.7−11.7

+15.9 (95% 

confidence) for room air conditioners, and 

b = 0.775±0.034 (95% confidence) for household laundry equipment and 0.710±0.062 

(95% confidence) for room air conditioners. 

For household laundry equipment, the estimated learning rate (defined as the fractional 

reduction in price expected from each doubling of cumulative production) is 41.6−1.4

+1.3% (95% 

confidence). For room air conditioners, the estimated learning rate is 38.9−2.7

+2.6% (95% 

confidence). 
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DOE then derived a price factor index, with 2010 equal to 1, to forecast prices in each 

future year in the analysis period. The index value in a given year is a function of the LR and the 

cumulative production forecast through that year. Table 1 shows the price factors used in the 

analysis. DOE applied the same value to forecast prices for each residential clothes dryer and 

room air conditioner product class at each considered efficiency level.

8-J.4 PRICE TRENDS FOR SENSITIVITY ANALYSES

DOE recognizes that there is uncertainty in its estimates of equipment price trends. 

Uncertainty arises from potentially systematic long term changes in the trend. To provide a 

potential indication of long term changes in the trend, DOE performed price trend fits to two 

component periods in the historical data. DOE analyzed years in which the historical efficiency 

standards for the product changed that were approximately in the middle of the time series of the 

available data. For household laundry equipment, the selected year was 1994, and for room air 

conditioners, the selected year was 2000. 

Table 8-J.4.1 Learning parameter as a function of time period

Product Period Learning Parameter (%)

Household Laundry Equipment 1980-2010 41.6

Household Laundry Equipment 1980-1993 33.9

Household Laundry Equipment 1994-2010 42.0

Room Air Conditioners 1990-2009 38.9

Room Air Conditioners 1990-1999 34.7

Room Air Conditioners 2000-2009 31.0

DOE examined the impacts of a range of learning parameters on the range of net benefit 

impacts from potential standards using high, medium and low values of the learning rate 

parameter. DOE examined the range of estimates as sensitivities to the national impact analysis. 

The low learning rate is from the time period with the lowest value, or the low end of the 95% 

confidence range of the full period learning estimate. The medium value is the estimate for the 

full time period. The high value is the higher of the high time period estimate or upper range of 

the 95% confidence interval for the full time period estimate. In addition, DOE examined a 

constant real price scenario as a sensitivity calculation for its national impact analysis. 

 DOE considered another sensitivity calculation for residential clothes dryers. An 

effective PPI series for clothes dryers only was determined from the household laundry 

equipment PPI series, by factoring out the contribution from clothes washers. DOE used average 

selling prices from two sources: NPD (2004-2009 for clothes washers, 2007-2008 for clothes 

dryers), and Consumer Reports (1992, 1993, 1995, 1997, 1999 for clothes washers). Clothes 

washer prices were separated into top-loading and front-loading models. Market shares for toploading clothes washers, front-loading clothes washers, and clothes dryers were available for all 

years. Using the 2007-2008 washer and dryer price data to normalize the relative household 

laundry PPI index to nominal dollars, DOE created an effective PPI series for clothes washers 

only for years 1992, 1993, 1995, 1997, 1999, and 2004-2009. Assuming the household laundry 

PPI series is dominated by clothes washers and clothes dryers only, and using the known market 
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shares between clothes washers and dryers, DOE derived an effective clothes dryer PPI series 

from the household laundry PPI and the effective clothes washer PPI series. Learning parameters 

were calculated from the effective clothes dryer PPI series (using clothes dryer cumulative 

production) and used as another sensitivity estimate.