8C

- i APPENDIX 8C. ESTIMATION OF EQUIPM ENT PRICE TRENDS FOR

RESIDENTIAL DISH WASHERS

TABLE OF CO NTENTS

8C.1 INTRODUCTION

................................ ................................ ................................ ... 8C

- 1

8C.2 EXPERIENCE RATE ESTI MATION

................................ ................................ .... 8C

- 2

8C.3 DISCUSSION OF ANALYT ICAL ISSUES

................................ ........................... 8C

- 5

LIST OF FIGURE S

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

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- 48C

- 1 APPENDIX 8C. ESTIMATION OF EQUIPM ENT 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 improv ing 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 co nstant real prices and costs may, in many cases, over

- estimate long

- term appliance and equipment price trends. E conomic literature and historical data suggest that the

real costs of these products may in fact trend downward over time according to “ experien ce ” 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 an d 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 productio n 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 prod ucing the next unit decreases. The percentage reduction in cost that occurs with each doubling of cumulat ive production is known as the experience rate (E R), given by:

E R = 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., Pat el, M.K., Blok, K., (2010a). A Review of Experience C urve Analyses for Energy Demand T echnologies. Technological Forecasting & Social Change . 77:411

- 428

.8C

- 2 Consistent with the NODA, DOE us ed 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 l ife

- c ycle c ost (LCC) analysis

.

8C.2 EXPERIENCE RATE ESTI MATION

To derive experience rate parameter s for dishwashers , DOE obtained historical Producer

Price Index (PPI) data for miscellaneous household appliances spanning the time period 19 88

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

. b

Figure 8

- C.2

. 1 DOE used PPI data for miscellaneous household appliances a s representative of residential dishwashers b ec ause 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 seri es by the Gross Domestic Product Chained Price Index (see )

.

Figure 8C.2

. 1 H istorical 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 95.0 100.0 105.0 110.0 115.019881989199019911992199319941995199619971998199920002001200220032004200520062007200820092010Deflated PPI (2010=1)Nominal PPI (1982=100)

Year

Nominal Misc. Household Appliance PPI Deflated Misc. Household Appliance PPI8C

- 3 DOE assembled a time

- series of historical annual shipments for 1972

- 2010 for

dish washers from the 2005 AHAM Fact Book. The historical annual shipments data were used to estimate cumulative shipments (production). Figure 8

- C.2

. 2 show s the shipments time series used in the analy sis.

Figure 8C.2

. 2 H istorical Total Shipments of Dishwashers

To estimate experience rate parameter s , 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) = P

o X

- b

,

where the two parameters, b (the experience rate parameter) and P

o (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 th ere 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 2020Shipments (millions)

Year

Historical Dishwashers Shipment8C

- 4 Figure 8C.2

. 3 R elative Price versus Cumulative Shipments of

Miscellaneous Household Appliance Equipment

, with Power Law Fit

The parameter values obtained are:

P

o = 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

.

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

each doubli ng 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

parame ter 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 t he price factor index to 2047 derived from this experience curve model. The average annual price deline rate is 1.27%. The

value for 201 8 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 efficie ncy 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

- 50.000 100.000 150.000 200.000Price 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 ANALYT ICAL 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 cost s) and all non

- production costs (SG&A, R&D, and interest), along with profit . The process of the cost

- based method fo r 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 marku ps 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 da ta 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 approac h 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 1.2002010201220142016201820202022202420262028203020322034203620382040204220442046Price Factor Index (2010=1)

Year8C

- 6 DOE could have developed a more complex price trend forecasting model with more parameters that could explain differen t 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 l ong 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.