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-8

LIST OF TABLES

Table 8C.1.1 Producer Price Index for Air Conditioning, Refrigeration, and Forced Air 

Heating...............................................................................................................8C-3

Table 8C.2.1 Historical Automatic Commercial Ice Maker Shipments....................................8C-5

Table 8C.2.2 Experience (Price) Learning Scenarios................................................................8C-7

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-4

Figure 8C.2.2 Model Fit for Automatic Commercial Ice Makers .............................................8C-6
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. Table 8C.1.1 provides the PPI data.

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

Table 8C.1.1 Producer Price Index for Air Conditioning, Refrigeration, and Forced 

Air Heating

Year Annual Producer Price 

Index

PPI, Inflation Adjusted 

(2010=1.000)

Linear Regression to 

PPI*

PPI, End-point 

Interpolation**

1978 75.700 0.966 1.125 0.966

1979 81.900 1.013 1.118 0.967

1980 87.200 1.082 1.112 0.968

1981 95.400 1.154 1.106 0.969

1982 98.800 1.219 1.100 0.970

1983 100.800 1.190 1.094 0.971

1984 100.300 1.104 1.087 0.972

1985 103.600 1.095 1.081 0.973

1986 104.500 1.068 1.075 0.974

1987 105.900 1.049 1.069 0.975

1988 110.100 1.047 1.063 0.976

1989 116.700 1.072 1.056 0.977

1990 120.300 1.084 1.050 0.978

1991 122.300 1.105 1.044 0.980

1992 125.800 1.099 1.038 0.981

1993 125.600 1.067 1.032 0.982

1994 130.600 1.066 1.025 0.983

1995 133.300 1.062 1.019 0.984

1996 135.900 1.043 1.013 0.985

1997 140.200 1.030 1.007 0.986

1998 142.100 1.001 1.001 0.987

1999 144.000 0.967 0.995 0.988

2000 142.800 0.921 0.988 0.989

2001 143.600 0.916 0.982 0.990

2002 144.100 0.903 0.976 0.991

2003 145.400 0.889 0.970 0.992

2004 146.600 0.866 0.964 0.994

2005 151.500 0.868 0.957 0.995

2006 155.900 0.870 0.951 0.996

2007 177.500 0.972 0.945 0.997

2008 185.300 1.014 0.939 0.998

2009 184.600 1.038 0.933 0.999

2010 182.900 1.000 0.926 1.000

* PPI data smoothed using regression techniques.

** PPI data smoothed by simply interpolating between the 1978 and 2010 values.

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

 Historical shipments are shown on 

Table 8C.2.1.
8C-4

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

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-5

Table 8C.2.1 Historical Automatic Commercial Ice Maker Shipments

Year Shipments

(units)

1975 113,525

1976 166,312

1977 156,496

1978 162,969

1979 187,406

1980 156,699

1981 152,511

1982 136,131

1983 153,271

1984 204,622

1985 187,644

1986 190,174

1987 231,739

1988 236,776

1989 188,012

1990 164,192

1991 158,104

1992 148,826

1993 172,396

1994 186,665

1995 192,929

1996 187,028

1997 192,796

1998 260,267

1999 328,237

2000 352,495

2001 246,062

2002 296,332

2003 292,577

2004 274,348

2005 288,108

2006 306,999

2007 305,042

2008 276,546

2009 213,426

* Source: U.S. Census Bureau, Current Industrial 

Reports, 1975 - 2009.

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 

a simple least squares fit is equivalent to an assumption of no significant first price 

elasticity effects in the cumulative shipments variable. 
8C-6

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

Table 8C.2.2 shows the price change values estimated through this analysis. 

The average annual rate of price decline in the default case for the 2016–2045 analysis 

period is 0.2 percent and is based on historical PPI data for refrigeration equipment

between 1978–2010. Although not used in the preliminary analysis, DOE analyzed two 

additional sensitivity cases that also use a price trend based on an exponential-in-time 

extrapolation of refrigeration equipment PPI data. DOE developed a high price decline 

case and a low price decline case in this analysis. The high price decline case is based on 

the upper end of the 95 percent confidence interval for an exponential fit to the inflationadjusted PPI series of 1978 to 2010. The low price decline case is based on the lower end 

of the 95 percent confidence interval for an exponential fit to the nominal PPI series of 

1978 to 2010. The high and low cases are presented on Table 8C.2.2 along with the 

reference price change values used in the preliminary analysis.

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-7

Table 8C.2.2 Experience (Price) Learning Scenarios

Year Historically Derived Changes

High Change Reference Change Low Change

2010 100.00% 100.00% 100.00%

2011 99.55% 99.70% 99.85%

2012 99.12% 99.41% 99.71%

2013 98.70% 99.13% 99.56%

2014 98.29% 98.85% 99.42%

2015 97.89% 98.58% 99.29%

2016 97.49% 98.32% 99.15%

2017 97.11% 98.06% 99.02%

2018 96.74% 97.81% 98.90%

2019 96.37% 97.56% 98.77%

2020 96.01% 97.32% 98.65%

2021 95.66% 97.09% 98.53%

2022 95.32% 96.85% 98.41%

2023 94.99% 96.63% 98.29%

2024 94.66% 96.40% 98.18%

2025 94.33% 96.18% 98.07%

2026 94.02% 95.97% 97.96%

2027 93.71% 95.76% 97.85%

2028 93.40% 95.55% 97.74%

2029 93.11% 95.35% 97.64%

2030 92.81% 95.15% 97.54%

2031 92.53% 94.95% 97.44%

2032 92.24% 94.75% 97.34%

2033 91.96% 94.56% 97.24%

2034 91.69% 94.38% 97.14%

2035 91.42% 94.19% 97.05%

2036 91.16% 94.01% 96.95%

2037 90.90% 93.83% 96.86%

2038 90.64% 93.66% 96.77%

2039 90.39% 93.48% 96.68%

2040 90.14% 93.31% 96.59%

2041 89.90% 93.14% 96.50%

2042 89.66% 92.98% 96.42%

2043 89.42% 92.81% 96.33%

2044 89.19% 92.65% 96.25%

2045 88.96% 92.49% 96.16%
8C-8

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.>