8

- E

- i APPENDIX 8

- E. ESTIMATION OF EQUIPM ENT PRICE TRENDS FOR

RESIDENTIAL CLOTHES WASHERS

TABLE OF CO NTENTS

8

- E.1 PRICE TREND ESTIMATI ON

................................ ................................ .......... 8

- E

- 1

8

- E.2 DISCUSSION OF ANALYT ICAL 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

- 28

- E

- 1 APPENDIX 8

- E. FORECAST OF PRODUCT PRICES FOR RESIDENTI AL CLOTHES

WASHERS

8

- E.1 PRICE TREND ESTIMATI ON

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

Price Index (PPI) data for household laundry equipment spa nning the time period 19 80

- 2010

from the Bureau of Labor Statistics’ (BLS). DOE used PPI data for household laundry equipment a s representative of residential clothes washers b ecause 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 (s ee Figure 8

- E. 1

. 1)

.

Figure 8

- E.1.1 H istorical Nominal and Real Producer Price Index es for Household Laundry Equipment 0.000 0.500 1.000 1.500 2.000 2.500

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0Deflated 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 exponentia l model with year as the explanatory variable

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

Y = a ∙ e bX

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 a n exponential trend line fit results in an R

- square of 0.99, which indicates a good fit to the data. The final estimated exponential fun t cion is:

Y = 1

. 06 × 10 22

∙ e (

− 0

. 025 ) X

Figure 8

- E. 1 .2 shows t he price factor index to 2045 derived from this exponential model. The value for 2015 used in the LCC and PBP analysis is 0.8 82 . 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 Pri ce Factor Index

for the Default Case 0.000 0.200 0.400 0.600 0.800 1.000 1.200201020122014201620182020202220242026202820302032203420362038204020422044Price Factor Index (2010=1)

Year 

## Price Factor Index for Clothes Washers8

- E

- 3 8

- E.2 DISCUSSION OF ANALYT ICAL ISSUES

To estimate equipment prices in both the standards and the base (no

- standards) case, DOE develops engineering cost estimates that DO E 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 cost s) 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 pri ce 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 cur ves 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 bet ween 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” th e 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

t o 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 tim e, the decreasing share of costs that are declining rapidly can result in a change in the empirically estimated experience curve exponent over time.