8-J-i

APPENDIX 8-J. FORECAST OF EQUIPMENT PRICE TRENDS FOR CENTRAL AIR 

CONDITIONERS, HEAT PUMPS AND FURNACES

TABLE OF CONTENTS

8-J.1 INTRODUCTION .................................................................................................. 8-J-2

8-J.2 PRICE, COST AND MARKET STRUCTURE..................................................... 8-J-3

8-J.3 DERIVATION OF LEARNING RATES............................................................... 8-J-4

8-J.4 EQUIPMENT PRICE TRENDS FORECAST....................................................... 8-J-8

LIST OF TABLES

Table 8-J.3.1 Learning Parameter as a Function of Time Period ..................................... 8-J-8

LIST OF FIGURES

Figure 8-J.3.1 Historical Normalized Prices of Warm Air Furnaces................................. 8-J-4

Figure 8-J.3.2 Historical Normalized Prices of Unitary Air Conditioners and Heat 

Pumps.......................................................................................................... 8-J-5

Figure 8-J.3.3 Historical and Projected Total Shipments of Warm Air Furnaces ............. 8-J-6

Figure 8-J.3.4 Historical and Projected Total Shipments of Unitary Air Conditioners..... 8-J-6

Figure 8-J.3.5 Relative Price versus Cumulative Shipments of Warm Air Furnaces, 

with Power Law Fit..................................................................................... 8-J-6

Figure 8-J.3.6 Relative Price versus Cumulative Shipments of Unitary Air 

Conditioners, with Power Law Fit.............................................................. 8-J-7
8-J-2

APPENDIX 8-J. FORECAST OF EQUIPMENT PRICE TRENDS FOR CENTRAL AIR 

CONDITIONERS, HEAT PUMPS AND FURNACES

8-J.1 INTRODUCTION

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 air 

conditioning equipment and furnaces. For this equipment, DOE found consistent negative real 

price trends. Therefore, DOE concluded that the real prices of air conditioning equipment and 

furnaces have a different long term trend than prices in the economy as a whole. In the analysis 

for the direct final rule, DOE concluded that the manufacturer selling prices of products meeting 

various efficiency levels may not remain fixed, in real terms, after 2010 (the year for which the 

engineering analysis estimated costs). DOE maintained the constant real price trend as a 

sensitivity analysis to evaluate how the impact of potential standards might change under this 

scenario. 

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. 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 US 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 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 and equipment. 

The extensive literature on the “learning” 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 production 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 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. The 

 

a In addition to the draft paper mentioned above, see 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. 
8-J-3

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). 

8-J.2 PRICE, COST AND MARKET STRUCTURE

DOE uses a cost-based analysis in estimating equipment prices. To estimate equipment 

prices in both the standards and the baseline or 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 costs) 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 price 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 curves 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 between 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 presents 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 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 if market concentration accelerated 
8-J-4

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. 

8-J.3 DERIVATION OF LEARNING RATES

To derive learning rate parameters for HVAC products, DOE obtained historical 

Producer Price Index (PPI) data for warm air furnaces and unitary air conditioners from the 

Bureau of Labor Statistics’ (BLS). Because PPI data specific to air-source heat pumps were not 

available prior to 2008, DOE used PPI data for unitary air conditioners as representative of both 

unitary air conditioner and heat pump prices. For warm air furnaces, DOE used PPI data 

spanning the time period 1990-2010, while for unitary air conditioners and heat pumps, DOE use 

data from 1978-2010. Inflation-adjusted price indices for warm air furnaces and unitary air 

conditioners and heat pumps were calculated by dividing the PPI series by the Consumer Price 

Index (CPI) “all items” index for the same years. These inflation-adjusted price indices (shown 

in Figures 8-J.3.1 and 8-J.3.2) were used in subsequent analysis steps.

Figure 8-J.3.1 Historical Normalized Prices of Warm Air Furnaces
8-J-5

Figure 8-J.3.2 Historical Normalized Prices of Unitary Air Conditioners and 

Heat Pumps

DOE assembled a time-series of annual shipments for 1953-2009 for unitary air 

conditioners and furnaces using data from AHRI and the Gas Appliance Manufacturers 

Association. (Chapter 9 in the final rule TSD describes the data sources for 1972-2009. For 

shipments before 1972, DOE used earlier data from the same sources.) Heat pump shipments 

data were also available but were not utilized in this analysis due to the unavailability of PPI 

data. (Projected heat pump prices were based on the learning rate derived from the PPI and 

shipments data for unitary air conditioners.) For furnaces, shipments prior to 1953 were 

extrapolated backward based on a linear trend to the historical shipments. The annual shipments 

data were used to estimate cumulative shipments (production). Projected shipments after 2009 

were obtained from the base case projections made for the NIA (see chapter 9 of this TSD). 

Figures 8-J.3.3 and 8-J.3.4 show the shipments time series used in the analysis.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1920 1940 1960 1980 2000 2020 2040 2060

Annual Total Shipments (millions)

Year

Historical

Projected

Extrapolated
8-J-6

Figure 8-J.3.3 Historical and Projected Total Shipments of Warm Air

Furnaces

Figure 8-J.3.4 Historical and Projected Total Shipments of Unitary Air 

Conditioners

To estimate a learning rate parameter, a least-squares power-law fit was performed on the 

unified price index versus cumulative shipments. See Figures 8-J.3.5 and 8-J.3.6.

Figure 8-J.3.5 Relative Price versus Cumulative Shipments of Warm Air 

Furnaces, with Power Law Fit

0

1

2

3

4

5

6

7

1940 1960 1980 2000 2020 2040 2060

Ammual Total Shipments (millions)

Year

Historical

Projected

y = 13.184x-0.527

R2 = 0.954

0.8

0.9

1.0

1.1

1.2

1.3

1.4

60 80 100 120 140 160

Relative Price (2010=1)

Cumulative Shipments (millions)

Historical

Learning Fit
8-J-7

Figure 8-J.3.6 Relative Price versus Cumulative Shipments of Unitary Air 

Conditioners, with Power Law Fit

The form of the fitting equation is:

P(X) = PoX-b

,

where the two parameters, 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 have a dependence 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.

The parameter values obtained are:

Po = 13.18−3.02

+3.92 (95% confidence) for furnaces and 3.77−0.31+0.34 (95% confidence) for 

unitary air conditioners, and 

b = 0.527±0.056 (95% confidence) for furnaces and 0.288±0.021 (95% confidence) for 

unitary air conditioners.

For warm air furnaces, the estimated learning rate (defined as the fractional reduction in 

price expected from each doubling of cumulative production) is 30.6−2.7

+2.6% (95% confidence). 

For unitary air conditioners, the estimated learning rate is 18.1−1.2

+1.2% (95% confidence).

Projected heat pump prices were based on the learning rate derived for unitary air conditioners.

y = 3.775x-0.288

R2 = 0.960

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100 120 140

Relative Price (2010=1)

Cumulative Shipments (millions)

Historical

Learning Fit
8-J-8

DOE recognizes that there is uncertainty in its estimates of equipment price trends. 

Uncertainty arises from potentially systematic long term changes in the trend. To provide a 

potential indication of long term changes in the trend, DOE performed price trend fits to two 

component periods in the historical data. DOE analyzed years in which the historical efficiency 

standards for the product changed that were approximately in the middle of the time series of the 

available data. For warm air furnaces, the selected year was 2000, and for central air 

conditioners, the selected year was 1992.

Table 8-J.3.1 Learning Parameter as a Function of Time Period

Product Period Learning Parameter (%)

Furnaces 1990-2010 30.6 (medium)

Furnaces 1990-1999 33.3 (high)

Furnaces 2000-2010 19.2 (low)

Central Air Conditioners 1978-2010 18.1 (medium)

Central Air Conditioners 1978-1991 20.5 (high)

Central Air Conditioners 1992-2010 11.5 (low)

8-J.4 EQUIPMENT PRICE TRENDS FORECAST

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 LR and the 

cumulative production forecast through that year. DOE applied the same value to forecast prices 

for each furnace and air conditioner product class at each considered efficiency level.

For the LCC and PBP analysis, DOE used the medium learning rates to forecast product 

prices in 2016. These rates were also used as default values to forecast prices through 2045 for 

the national impact analysis (NIA).

For the NIA, DOE also examined the impacts of potential standards using high and low 

values of the learning rate parameter. The “high learning” rates are 20.5 percent for central air 

conditioners and heat pumps and 33.3 percent for furnaces. The “low learning” rates are 11.5 

percent for central air conditioners and heat pumps and 19.2 percent for furnaces. In addition, 

DOE examined a constant real price scenario as a sensitivity calculation.