8C-i

APPENDIX 8C. ESTIMATION OF EQUIPMENT PRICE TRENDS FOR

RESIDENTIAL DISHWASHERS

TABLE OF CONTENTS

8C.1 INTRODUCTION ...................................................................................................8C-1

8C.2 EXPERIENCE RATE ESTIMATION ....................................................................8C-2

8C.3 DISCUSSION OF ANALYTICAL ISSUES...........................................................8C-5

LIST OF FIGURES

Figure 8C.2.1 Historical Nominal and Defalted Producer Price Indexes for 

Miscellaneous Household Appliance Equipment ........................................8C-2

Figure 8C.2.3 Relative Price versus Cumulative Shipments of Miscellaneous 

Household Appliance Equipment, with Power Law Fit ..............................8C-4
8C-1

APPENDIX 8C. ESTIMATION OF EQUIPMENT PRICE TRENDS FOR RESIDENTIAL 

DISHWASHERS

8C.1 INTRODUCTION 

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. 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 “experience” or 

“experience” curves. 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 “experience” 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

where a is an initial price (or cost), b is a positive constant known as the experience 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 experience rate (ER), given by:

ER = 1 – 2-b

In typical experience curve formulations, the experience rate parameter is derived using 

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

 

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. 
8C-2

Consistent with the NODA, DOE used the experience curve method to derive experience

rates to forecast future prices of clothes washers at each considered efficiency level. This

appendix describes the method used to derive experience rate and to project future product prices

used in the life-cycle cost (LCC) analysis.

8C.2 EXPERIENCE RATE ESTIMATION

To derive experience rate parameters for dishwashers, DOE obtained historical Producer 

Price Index (PPI) data for miscellaneous household appliances spanning the time period 1988-

2010 from the Bureau of Labor Statistics’ (BLS).

b

Figure 8-C.2.1

DOE used PPI data for miscellaneous

household appliances as representative of residential dishwashers because PPI data specific to 

residential dishwashers are not available. The PPI data reflect nominal prices, adjusted for 

product quality changes. An inflation-adjusted price index for miscellaneous household 

appliances was calculated by dividing the PPI series by the Gross Domestic Product Chained 

Price Index (see ).

Figure 8C.2.1 Historical Nominal and Defalted Producer Price

Indexes for Miscellaneous Household Appliance 

Equipment

 b Series ID PCU3352283352285; http://www.bls.gov/ppi/

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1.400

1.600

1.800

90.0

95.0

100.0

105.0

110.0

115.0

19881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010

Deflated PPI (2010=1)

Nominal PPI (1982=100)

Year

Nominal Misc. Household Appliance PPI Deflated Misc. Household Appliance PPI
8C-3

DOE assembled a time-series of historical annual shipments for 1972-2010 for 

dishwashers from the 2005 AHAM Fact Book. The historical annual shipments data were used to 

estimate cumulative shipments (production). Figure 8-C.2.2 shows the shipments time series

used in the analysis.

Figure 8C.2.2 Historical Total Shipments of Dishwashers

To estimate experience rate parameters, a least-squares power-law fit was performed on 

the unified price index versus cumulative shipments. See Figure 8-C.2.3. The form of the fitting 

equation is:

P(X) = PoX-b

,

where the two parameters, b (the experience 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.

0.0000

1.0000

2.0000

3.0000

4.0000

5.0000

6.0000

7.0000

8.0000

1970 1980 1990 2000 2010 2020

Shipments (millions)

Year

Historical Dishwashers Shipment
8C-4

Figure 8C.2.3 Relative Price versus Cumulative Shipments of 

Miscellaneous Household Appliance Equipment,

with Power Law Fit

The parameter values obtained are:

Po = 9.308−1.411

+1.664 (95% confidence) for miscellaneous household appliance equipment, and 

b = 0.436±0.036 (95% confidence) for miscellaneous household appliance equipment.

The estimated experience rate (defined as the fractional reduction in price expected from 

each doubling of cumulative production) is 26.1−1.9

+1.8% (95% confidence). 

DOE 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 experience

parameter and the cumulative production forecast through that year, which is based on the 

shipments forecast described in chapter 9. Figure 8-C.2.4 shows the price factor index to 2047 

derived from this experience curve model. The average annual price deline rate is 1.27%. The 

value for 2018 and 2013 used in the LCC and PBP analysis is 0.876 and 0.948 respectively. 

Thus, prices forecast for the LCC and PBP analysis in 2018 are equal to 0.876 times the 2010 

values for each efficiency level in each product class; prices forecast for the LCC and PBP 

analysis in 2013 are equal to 0.948 times the 2010 values for each efficiency level in each 

product class

y = 9.3084x-0.436

R2 = 0.9685

0.500

0.700

0.900

1.100

1.300

1.500

1.700

1.900

- 50.000 100.000 150.000 200.000 

Price Index (2010=1)

Cumulative Shipments (millions)

Dishwashers 

Learning (Default)

Power (Dishwashers 

Learning (Default))
8C-5

Figure 8C.2.4 Miscellaneous Household Appliance Equipment 

Price Factor Index for the Default Case

8C.3 DISCUSSION OF ANALYTICAL ISSUES

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

prices in both the standards and the base (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.

0.000

0.200

0.400

0.600

0.800

1.000

1.200

2010201220142016201820202022202420262028203020322034203620382040204220442046

Price Factor Index (2010=1)

Year
8C-6

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 present 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. 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 experience rate. 

Depending on whether 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.