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-4
8C-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 analysis. 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. 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, overestimate 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 “learning” or “experience” curves, or alternatively 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 positive 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 producing the next 

unit decreases. 
8C-2 

The percentage reduction 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 production and price (or cost). 

DOE examined historical prices 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 for 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 Data 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 consistent 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 PPI
8C-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 future, 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 Bureau.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 powerlaw fit on the automatic commercial ice makers price index versus cumulative shipments. 

The form of the fitting equation is: 

P(X) = PoX-b

where b (the learning 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 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 Shipments
8C-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 reduction 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 trend 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 25

Fitted 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.>