8-E-i

APPENDIX 8-E. ESTIMATION OF EQUIPMENT PRICE TRENDS FOR

RESIDENTIAL CLOTHES WASHERS

TABLE OF CONTENTS

8-E.1 PRICE TREND ESTIMATION..........................................................................8-E-1

8-E.2 DISCUSSION OF ANALYTICAL ISSUES .......................................................8-E-3

LIST OF FIGURE

Figure 8-E.1.1 Historical Real Producer Price Index for Household Laundry 

Equipment...............................................................................................8-E-1

Figure 8-E.1.2 Household Laundry Equipment Price Factor Index for the Default 

Case ........................................................................................................8-E-2
8-E-1

APPENDIX 8-E. FORECAST OF PRODUCT PRICES FOR RESIDENTIAL CLOTHES 

WASHERS

8-E.1 PRICE TREND ESTIMATION

To derive a price trend for residential clothes washers, DOE obtained historical Producer 

Price Index (PPI) data for household laundry equipment spanning the time period 1980-2010

from the Bureau of Labor Statistics’ (BLS). DOE used PPI data for household laundry 

equipment as representative of residential clothes washers because PPI data specific to 

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

product quality changes. An inflation-adjusted price index for household laundry equipment was

calculated by dividing the PPI series by the Gross Domestic Product Chained Price Index (see

Figure 8-E.1.1).

Figure 8-E.1.1 Historical Nominal and Real Producer Price Indexes

for Household Laundry Equipment

0.000

0.500

1.000

1.500

2.000

2.500

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

Deflated PPI (2010 normalized)

Nominal PPI (1979$)

Year

Household Laundry Nominal PPI Household Laundry Deflated Annual PPI (2010 normalized)
8-E-2

To project the price trend for clothes washers, DOE used the inflation-adjusted household 

laundry equipment PPI in the past 20 years (1991 to 2010) to fit an exponential model with year

as the explanatory variable. In this case, the exponential function takes the form of:

Y = a ∙ ebX 

where Y is the clothes washer price index, X is the time variable, a is the constant and b is the 

slope parameter of the time variable. 

The regression performed as an exponential trend line fit results in an R-square of 0.99, 

which indicates a good fit to the data. The final estimated exponential funtcion is:

Y = 1.06 × 1022 ∙ e(−0.025)X 

Figure 8-E.1.2 shows the price factor index to 2045 derived from this exponential model. 

The value for 2015 used in the LCC and PBP analysis is 0.882. Thus, prices forecast for the LCC 

and PBP analysis are equal to 0.882 times the 2010 values for each efficiency level in each 

product class.

Figure 8-E.1.2 Household Laundry Equipment Price Factor Index 

for the Default Case

0.000

0.200

0.400

0.600

0.800

1.000

1.200

201020122014201620182020202220242026202820302032203420362038204020422044

Price Factor Index (2010=1)

Year

Price Factor Index for Clothes Washers
8-E-3

8-E.2 DISCUSSION OF ANALYTICAL ISSUES

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 the 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 nonproduction 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 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 learning 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.