8C -i APPENDIX 8C. ESTIMATION OF POTENTIAL EQUIPMENT PRICE TRENDS FOR AUTOMATIC COMMERCIAL ICE MAKERS

TABLE OF CONTENTS

8C.1 INTRODUCTION ........................................................................................................ 8C-1 8C.2 DATA EVALUATION AND ANALYSIS .................................................................. 8C-3 REFERENCES ......................................................................................................................... 8C-5

LIST OF FIGURES

Figure 8C.1.1 PPI Data for Automatic Commercial Ice Makers ...............................................8C-2 Figure 8C.2.1 Projected Annual Shipments for Automatic Commercial Ice Makers ...............8C-3 Figure 8C.2.2 Model Fit for Automatic Commercial Ice Makers .............................................8C-48C -1 APPENDIX 8C. ESTIMATION OF POTENTIAL EQUIPMENT PRICE TRENDS FOR AUTOMATIC COMMERCIAL ICE MAKERS

8C.1 INTRODUCTION

In developing the proposed standards, the U.S. Department of Energy ( DOE )

assumes that the manufacturer costs and retail prices of products meeting various efficiency levels remain fixed, in real terms, after 2010 (the year for which the engineering analysis estimated costs) and throughout the period of the analys is. In its

n otice of data a vailability (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 automatic commercial ice makers

. In the following paragraphs, another potential method for forecasting long- term price trends is presented. DOE expects that improvements in the presented methods will be made in future revisions to its analysis.

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. E conomic 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 alterna tively that the price trends for certain sectors of the U.S. 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 website at www1.eere.energy.gov/buildings/appliance_standards/supplemental_info_equipment_pri ce_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. 1 In the experience curve method, the real cost of production is related to the cumulative production or “experience” with a manufactured product. To explain the empirical relationship

, DOE would use the theory of technology learning to substantiate a decline in the cost of producing a given product as firms accumulate experience with the technology . 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 po sitive 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 prod ucing the next unit decreases.8C -2 The percentage reduct ion 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 produ ction and price (or cost). DOE examined h istorical price s through the use of the Bureau of Labor Statistics’ (BLS) Producer Price Index (PPI) and gross domestic product ( GDP ) deflator, available from the Bureau of Economic Analysis (BEA). The PPI data fo r air conditioning , refrigeration, and forced air heating is available for 1978 –2010 and is used to represent aggregate automatic commercial ice maker prices.

Figure 8C.1.1 shows the PPI data series used.

Figure 8C.1 .1 PPI D ata for Automatic Commercial Ice Makers

Inflation -adjusted price indices were calculated by dividing the fitted PPI series by the GDP deflator for the same years . The GDP deflator was used as opposed to the consumer price index because nearly all automatic commercial ice makers are shipped to commercial customers and to be consiste nt with energy price forecast assumptions by Energy Information Administration (EIA). 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3



### 1978 1988 1998 2008 PPI End

- point Interpolation

Deflated, normalized to 2009

Linear Regression to PPI8C -3 8C.2 DATA EVALUATION AND ANALYSIS

Figure 8C.1.1 shows an apparent price trend in automatic commercial ice making equipment that is trending slightly upward from 1978 to 2010, but shows a decrease in the real PPI during two significant periods: 1982

– 1988 and1999

– 2004. Based on these price trends shown above, DOE expects that, in the fut ure, the PPI is likely to resume a downward trend.

In order to perform an experience curve fit, DOE assembled a time

- series of annual shipments for 1975

– 2009 for automatic commercial ice makers (for calculating cumulative production) from the Census B ureau. 2

Projected shipments after 2009 were obtained from the base- case projections made for the NIA (see chapter 10 of this preliminary technical support document ). Projected annual shipments are depicted on Figure 8C.2.1

.

Figure 8C.2 .1 Projected Annual Shipments for Automatic Commercial Ice Makers

To estimate potential product price trends, DOE performed a least

- squares power

law fit on the automatic commercial ice makers price index versus cumulative shipments. The form of the fitting equation is:

P(X) = P o X

-b

where b (the learning rate parameter) and P o (the price or cost o f 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 depend on price, so there is an issue with simultaneity where the independent variable is not truly independent. DOE’s use of 100,000 150,000 200,000 250,000 300,000 350,000 400,000 450,000 500,000

2010 2015 2020 2025 2030 2035 2040 2045 

## Annual ACIM Shipments

Annual ACIM Ref Shipments8C -4 a simple least squares fit is equivalent to an assumption of no significant first price elasticity effects in the cumulative shipments variable.

After modeling the data to the fitting equation

, DOE estimated the learning rate (defined as the fractional r eduction in price expected from each doubling of cumulative production) as 7 percent.
With cumulative shipments through 2045 projected to reach 21.12 million units (compared with 7.77 million units in 2010), the modeled t rend predicts a drop of 4 percent in real price compared to the 2010 prices in the economy as a whole. Figure 8C.2.2 shows the model fit for the projected values for the period after 2009.

Figure 8C.2 .2 Model Fit for Automatic Commercial Ice Makers 2.8 2.9 2.9 3.0 3.0 3.1 3.1 3.2 3.2

0 5 10 15 20 25Fitted PPI



### Cumulative Shipments (Millions)8C -5 REFERENCES

1. 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.

2. U.S. Census Bureau, Current Industrial Reports, 1975 through 2009: NAICS 333415 : Refrigeration, Air Conditioning, and Warm Air Heating Equipment. (Last accessed July 2010.) < www.census.gov/manufacturing/cir/index.html

. >