9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

9.1 INTRODUCTION ........................................................................................................... 9-1

9.2 SHIPMENTS MODEL GENERAL METHODOLOGY ................................................ 9-1

9.2.1 Stock Accounting Approach............................................................................................ 9-2

9.2.2 Market Segments ............................................................................................................. 9-2

9.3 PRODUCT–SPECIFIC MODELS .................................................................................. 9-3

9.3.1 Cooled Cabinets............................................................................................................... 9-4

9.3.1.1 Disaggregation into Market Segments........................................................... 9-4

9.3.1.2 Disaggregation into product categories ......................................................... 9-6

9.3.2 Non-Compressor Refrigerators........................................................................................ 9-6

9.3.2.2 Disaggregation into product categories ......................................................... 9-7

9.3.3 Ice Makers........................................................................................................................ 9-8

9.3.3.1 Disaggregation into Market Segments........................................................... 9-8

9.3.3.2 Disaggregation in Product Classes................................................................. 9-9

9.3.4 Hybrid Products............................................................................................................... 9-9

9.3.4.1 Disaggregation into Market Segments......................................................... 9-10

9.3.4.2 Disaggregation into Product Classes ........................................................... 9-12

9.4 IMPACT OF ENERGY CONSERVATION STANDARDS ON SHIPMENTS.......... 9-12

9.4.2 Application of Relative Price Elasticity......................................................................... 9-14

9.5 AFFECTED STOCK ..................................................................................................... 9-15

9.6 SHIPMENTS FORECASTS IN STANDARDS CASES.............................................. 9-16

`
9-ii

LIST OF TABLES

Table 9.3.1 Product Category Market Shares for Cooled Cabinets........................................ 9-6

Table 9.3.2 Product Category Market Shares for Non-Compressor Refrigerators................. 9-8

Table 9.3.3 Product Class Market Shares for Ice Makers....................................................... 9-9

Table 9.3.4 Product Class Market Shares for Compact Hybrid Refrigerators...................... 9-12

Table 9.4.1 Change in Relative Price Elasticity Following a Purchase Price Change ......... 9-14

LIST OF FIGURES

Figure 9.3.1 Cooled Cabinets: Survival and Retirement Functions......................................... 9-5

Figure 9.3.2 Cooled Cabinets: Historical and Base Case Shipments Forecast by Market 

Segment................................................................................................................ 9-5

Figure 9.3.3 Non-Compressor Refrigerators: Historical and Base Case Shipments 

Forecast by Market Segment ............................................................................... 9-7

Figure 9.3.4 Ice Makers: Base Case Shipments Forecast by Market Segment........................ 9-9

Figure 9.3.5 Standard-sized, Built-In Hybrid All-Refrigerator (H-3A-BI) Base Case 

Shipments Forecast by Market Segment............................................................ 9-11

Figure 9.3.6 Compact Hybrid All-Refrigerator (H-11A and H-13A) Base Case 

Shipments Forecast by Market Segment............................................................ 9-11

Figure 9.3.7 Standard-sized, Built-in Hybrid Freezers (H-9I-BI): Base Case Shipments 

Forecast by Market Segment ............................................................................. 9-12

Figure 9.6.1 All Cooled Cabinets Shipments Forecasts......................................................... 9-17

Figure 9.6.2 CC-1, Vapor Compression Cooled Cabinets Shipment Forecasts..................... 9-18

Figure 9.6.3 CC-2, Thermoelectric Cooled Cabinets Shipment Forecasts ............................ 9-19
9-1

CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

Estimates of future product shipments are a necessary input to calculations of the national 

energy savings (NES) and net present value (NPV), as well as to the manufacturer impact 

analysis (MIA). This chapter describes the data and methods the U.S. Department of Energy 

(DOE) used to forecast annual product shipments and presents results for each of the 

miscellaneous refrigeration products being considered in this analysis. 

As described in chapter 3, DOE defined four types of miscellaneous refrigeration 

products: cooled cabinets (one product class), non-compressor refrigerators (one product class), 

ice makers (three product classes) and hybrid refrigeration products (four product classes). DOE 

developed models that estimate shipments of each product type as a proportion of the total stock. 

The results from these analyses are disaggregated to two market segments: replacements and 

shipments to new housing. DOE then used various data and assumptions to disaggregate total 

shipments into the product classes considered in this rulemaking. 

To estimate the effects of potential standard levels on product shipments, each shipments 

model accounts for the combined effects on consumer purchase decisions of changes in product 

price, annual operating cost, and household income. 

The shipments models were developed as a Microsoft Excel spreadsheet that is accessible 

on the DOE rulemaking website for miscellaneous refrigeration products.

1 Appendix 10A

discusses how to access and utilize the shipments model spreadsheets, which are integrated into 

spreadsheets for the national impact analysis (NIA). The rest of this chapter explains the 

shipments models in more detail. Section 9.2 presents the methodology behind the models; 

section 9.3 describes the data inputs and calibration of each model; section 9.4 discusses the 

impacts on shipments from standards (a more detailed explanation of the methodology DOE 

used to quantify the impacts of these variables on shipments can be found in Appendix 9A); 

section 9.5 discusses the affected stock; and section 9.6 presents the shipments forecast for 

different energy conservation standard levels. 

9.2 SHIPMENTS MODEL GENERAL METHODOLOGY

As explained in chapter 3, the data on shipments of the products under consideration 

were very limited. Therefore, DOE developed a model of the national stock of in-service 

appliances for estimating annual shipments for each of the product types considered for this 

standards rulemaking. This was done using the multi-decadal time series trends for standard 

refrigerators and freezers modelled in the 2011 Final Rule,

2 scaled to stock and lifetime 

estimates obtained from survey data. The shipments models used in this rulemaking take an 

accounting approach, tracking the vintage of units in the existing stock. 
9-2

9.2.1 Stock Accounting Approach

Stock accounting provides an estimate of the age distribution of product stocks for all 

years, using product shipments, a retirement function, and initial product stock as inputs. The age 

distribution of product stocks is a key input to both the NES and NPV calculations, because the 

operating costs for any year depend on the age distribution of the stock. Older, less efficient units 

may have higher operating costs, while younger, more-efficient units have lower operating costs. 

DOE determined the total stock of each product from the results of a study that used 

online surveys.

3 The results of this study were significantly different from estimates based on 

data available from NPD and AHAM (see chapter 3). DOE decided to use the online study in 

favor of these other sources, as the survey results were believed to be more reliable. This is 

because the survey covered a wider sample of the population, compared to NPD and AHAM data

which represented only a portion of the market, and it was difficult to ascertain what fraction of 

the total the data represented.

As units are added to the stock, some of the older ones retire and exit the stock. To 

estimate future shipments, DOE developed a series of equations that define the dynamics and 

accounting of stocks. For new units, the equation is: 

Stock(j, age = 1) = Ship(j − 1)

Where:

Stock(j, age) = number of units of a particular age, 

j = year for which the stock is being estimated, and 

Ship (j) = number of units purchased in year j.

This equation states that the number of one-year-old units is simply equal to the number 

of new units purchased the previous year. The following equation describes how the model 

accounts for the existing stock of units:

Stock(j + 1, age + 1) = Stock(j, age) × [1 − probRtr (age)]

In this equation, as the year is incremented from j to j+1, the age is also incremented 

from age to age+1. Over time, a fraction of the stock is removed; that fraction is determined by a 

retirement probability function, probRtr (age), which is described below. 

9.2.2 Market Segments

The model considers specific market segments in developing a shipments forecast. The 

two primary market segments are replacements and installations in new homes. 

For common appliances that have been used by U.S. consumers for a long time, 

replacements typically constitute the majority of shipments. To estimate shipments of 

replacement units, the models utilize shipments data from previous years and estimates of the 
9-3

lifetime of each product. Estimated shipments of replacement units in a given year are equal to 

the total stock of the appliance minus those units shipped in previous years that remain in the 

stock. DOE determines the useful service life of each product class to estimate the number of 

years products are likely to remain in the stock. The following equation shows how DOE 

estimates shipments of replacement units. 

( ) ( 1) ∑ ∑ ( )

0

1

_ _

_

Rpl j Stock j Ship prob age Rtr

ageMax

age

j

j N

p = p j ×

= =

Where:

StockP(j-1)= total stock of appliances in year j-1, 

probRtr(age)= probability that an appliance of a particular age will be retired, and

N= year in which the model begins its stock accounting.

To forecast annual shipments for the new construction market, the model uses forecasts 

of new housing and the saturation of the product in new housing. The forecast of market shares 

involves knowledge of historical trends, as well as the important drivers of consumer choice and 

their relative impacts. 

For many products, DOE models a third market segment, conversion of an existing unit 

from first to second use. However, the online survey results3 indicated that in the vast majority of 

households that own these products, there is only one such product, so second-use conversion 

was not considered necessary for the products in this rulemaking. 

9.3 PRODUCT–SPECIFIC MODELS

This section describes the models used to forecast shipments of the four types of 

miscellaneous refrigeration products described in section 9.1. For each model, the section 

describes the sources of historical shipments data, the market segments considered, the approach 

for disaggregating total shipments into product classes where appropriate, and the forecast of 

base case shipments. 

Forecasts of new housing are used in the shipments models. New housing includes newly 

constructed single- and multi- family units, termed “new housing completions,” and mobile 

home placements. For new housing completions and mobile home placements, DOE used 

recorded data through 2012 and adopted the projections from DOE’s Energy Information 

Administration (EIA)’s Annual Energy Outlook 2014 (AEO2014) for the period 2013-2040.4 For 

2041-2050, DOE kept completions at the 2040 level. 
9-4

9.3.1 Cooled Cabinets

DOE used data from the online survey3 to gain information on the age distribution of 

existing stocks of cooled cabinets (designated product class CC). The survey addressed wine 

chillers with vapor compression and thermoelectric cooling technologies, CC-1 and CC-2 

respectively. DOE determined the total stock of cooled cabinets in 2012 was 12.3 million, with a 

household saturation of 10.9 percent (1.6 percent for CC-1, 9.0 percent for CC-2). Having no 

satisfactory data on historical shipments of these products, DOE assumed that the household 

saturations of these products would remain the same projecting forward to 2050. DOE used the 

AEO forecasts described earlier to estimate total households. 

As explained in chapter 3, DOE determined the number of new shipments in 2012 as the 

total stock divided by the mean product lifetime. DOE assumed that this ratio would remain the 

same projecting forward to 2050. DOE used the wine chiller survey results to determine a 

survival function based on a product lifetime distribution with an average value of 4.3 years. 

Chapter 8 provides a detailed discussion of product lifetime.

9.3.1.1 Disaggregation into Market Segments

The market for cooled cabinets was assumed to be primarily composed of units for new 

construction and replacement units for products that have been retired. Total shipments are 

represented by the following equation:

ShipCC(j) = RplCC(j) + NHCC(j)

Where:

ShipCC(j) = total shipments of wine chiller cooled cabinets in year j,

RplCC(j) = replacement shipments in year j, and

NHCC(j) = shipments to new homes in year j.

The following sections discuss these market segments in further detail.

New Construction Shipments. To estimate shipments for new residential construction 

DOE multiplied the housing starts forecast for each year by the estimated saturation of cooled 

cabinets in new housing. Due to lack of data, DOE assumed that the saturation in new 

construction would be the same as the saturation in the total stock, which was estimated to be 

10.6 percent as noted above. This was determined for each year going forward by multiplying 

10.6 percent by the total number of projected housing starts taken from AEO2014.

Replacements. DOE assumed that replacements would account for the balance of 

shipments. Over time, some units are retired and removed from the stock, thereby triggering the 

shipment of replacement units. A certain percentage of units will fail each year and need to be 

replaced. 
9-5

Figure 9.3.1 Cooled Cabinets: Survival and Retirement Functions

Shipments forecast by market segment. Figure 9.3.2 shows the forecasted shipments in 

the base case (without new energy conservation standards) and the estimated historical shipments 

(through 2011) for cooled cabinets. The figure presents shipments due to retirements and 

shipments to new housing. 

Figure 9.3.2 Cooled Cabinets: Historical and Base Case Shipments 

Forecast by Market Segment

0%

20%

40%

60%

80%

100%

0 5 10 15 20

Age

% surviving

% retiring

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

2.5E+06

3.0E+06

3.5E+06

4.0E+06

4.5E+06

5.0E+06

2000200420082012201620202024202820322036204020442048

YEAR

New housing projections

Replacement Units

Modelled Total

Shipment
9-6

9.3.1.2 Disaggregation into product categories

To disaggregate the total shipments of cooled cabinets into shipments of each of the 

cooled cabinet product categories (CC-1 and CC-2), DOE used the distribution of products found 

in the results of the online surveys. 

Table 9.3.1 presents the estimated market shares for disaggregating modeled shipments 

of cooled cabinets. Because a reliable method for projecting market share changes was 

unavailable, DOE used these estimated market shares throughout the forecast period. 

Table 9.3.1 Product Category Market Shares for Cooled Cabinets

Vapor compression cooled 

cabinets (CC-1)

Thermoelectric cooled 

cabinets (CC-2)

15% 85%

9.3.2 Non-Compressor Refrigerators

DOE used the results of the online survey3 to gain information on the age distribution of 

non-compressor refrigeration products, covering both thermoelectric (NCR-1) and absorption 

(NCR-2) technologies. DOE also found around 400,000 absorption units mostly located in 

hotels. DOE determined the total stock of non-compressor refrigerators to be 4.9 million units, 

with a household saturation of 4.2 percent (3.8 percent thermoelectric and 0.4 percent

absorption). The majority of these absorption units (75 percent) are believed to be in hotels. 

Having no satisfactory data on historical shipments of these products, DOE assumed that the 

household saturations of these products would remain the same projecting forward to 2050. DOE 

used the AEO forecasts described earlier to estimate total households.

As explained in chapter 3, DOE determined the number of new shipments in 2012 as the 

total stock divided by the mean product lifetime. DOE assumed that this ratio would remain the 

same projecting forward to 2050. DOE found the results of the non-compressor refrigerator 

survey insufficient to determine a survival function; therefore DOE assumed that the survival 

rate would be the same as that determined for cooled cabinets. Chapter 8 provides a detailed 

discussion of product lifetime.

The following sections discuss these market segments in further detail.

New Construction Shipments. To estimate shipments for new residential construction 

DOE multiplied the housing starts forecast for each year by the estimated saturation of noncompressor refrigerators in new housing. Due to lack of data, DOE assumed that the saturation in 

new construction would be the same as the saturation in the total stock, which was estimated to 

be 4.2 percent as noted above. This was determined for each year going forward by multiplying 

4.2 percent by the total number of projected housing starts taken from AEO2014.
9-7

Shipments to Hotels. DOE estimated that about 8 percent of non-compressor 

refrigerators were currently found in hotels. As no other data were available DOE assumed this 

value would be the same throughout the projection period. 

Replacements. DOE assumed that replacements would account for the balance of 

shipments.

Shipments forecast by market segment. Figure 9.3.3 shows the forecasted shipments in 

the base case (without new energy conservation standards) and the estimated historical shipments 

(through 2011) for non-compressor refrigerators. The figure presents shipments due to 

retirements, shipments to new housing, and shipments to hotels. 

Figure 9.3.3 Non-Compressor Refrigerators: Historical and Base 

Case Shipments Forecast by Market Segment 

9.3.2.2 Disaggregation into product categories

To disaggregate the total shipments of non-compressor refrigerators into shipments of 

each of the non-compressor refrigerator product categories (NCR-1 and NCR-2), DOE used the 

distribution of products found in the results of the online survey. 

Table 9.3.2 presents the estimated market shares for disaggregating modeled shipments 

of non-compressor refrigerators. Because a reliable method for projecting market share changes 

was unavailable, DOE used these estimated market shares throughout the forecast period. 

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

2000200420082012201620202024202820322036204020442048

Hotels

Shipments to Housing

Starts

Replacement Units

Modelled Total Shipment
9-8

Table 9.3.2 Product Category Market Shares for Non-Compressor Refrigerators

Thermoelectric refrigerators

(NCR-1)

Absorption refrigerators (NCR-2)

89% 11%

9.3.3 Ice Makers

DOE found no available data on historical shipments of ice makers. DOE used the results 

of the online survey3 to determine the current stock of ice makers and the age distribution of 

these products. DOE found that the current total stock of ice makers in the United States was 

approximately 5.5 million, with a household saturation of 4.7 percent. Similar to cooled cabinets,

DOE assumed that the household saturation would remain the same going forward and projected 

total stock to 2050, using the AEO housing forecasts described previously. 

As explained in chapter 3, DOE determined the proportion of the total stock that 

corresponded to new shipments by dividing the total stock by the mean product lifetime. Due to 

insufficient data DOE assumed the lifetime would the same as that of residential compact 

freezers2

, 7.5 years. 

9.3.3.1 Disaggregation into Market Segments

The market for ice makers is assumed to be primarily comprised of units that replace 

products that have been retired from service and units installed in new construction.

New Housing. To estimate the proportion of total shipments for new construction, DOE 

multiplied the housing starts forecast for each year by the estimated saturation of ice makers in 

new housing. Due to lack of data, DOE assumed that the saturation in new housing would be the 

same proportion as the saturation in the total stock, which was estimated to be 4.7 percent as 

noted above. This was determined for each year going forward by multiplying this proportion by 

the projected number of housing starts taken from AEO2014.

Replacements. DOE assumed shipments to the replacement market would account for the 

balance of shipments.

Shipments Forecast by Market Segment. Figure 9.3.4 shows the forecasted shipments in 

the base case (without new energy conservation standards). Historical shipments are estimated 

by projecting backwards from the current stock of icemakers, as determined by the online 

survey results. The figure presents shipments due to retirements and shipments to new housing. 
9-9

Figure 9.3.4 Ice Makers: Base Case Shipments Forecast by 

Market Segment

9.3.3.2 Disaggregation in Product Classes

To disaggregate the total shipments of ice makers into shipments of each of the ice maker

product classes, DOE used the distribution of products found in the results of the online survey. 

Table 9.3.3 presents the estimated market shares for disaggregating modeled shipments 

of ice makers. Because a reliable method for projecting market share changes was unavailable, 

DOE used these estimated market shares throughout the forecast period. 

Table 9.3.3 Product Class Market Shares for Ice Makers

Portable ice makers (IMP)Non-portable ice makers 

with cooled storage (IM-C)

Non-portable ice makers 

with non-cooled storage 

(RIM-U)

69% 8% 23%

9.3.4 Hybrid Products

DOE found no available data on historical shipments of hybrid standard all-refrigerator, 

standard hybrid freezer, or compact hybrid all-refrigerator products. DOE used the results of the

online survey3 to determine the current stock of hybrid products and their age. DOE found that 

0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

1.2E+06

2000 2007 2014 2021 2028 2035 2042 2049

Year

Shipments to Housing Starts

Replace-ment Units

Modelled Total Shipment
9-10

the current total stock of hybrid products in the United States was approximately 2.2 million 

standard-sized, built-in hybrid all-refrigerators (product class H-3A-BI), 0.3 million compact 

hybrid all-refrigerators with manual defrost (product class H-11A), 1.1 million compact hybrid 

all-refrigerators with automatic defrost (product class H-13A) and 0.9 million standard-sized, 

built-in hybrid freezers (product class H-9I-BI), resulting in household saturations of 1.9 percent, 

0.2 percent, 1.0 percent, and 0.8 percent respectively. Again, DOE assumed that these household 

saturations would remain the same through 2050 and used the AEO housing projections to 

determine the total stocks. 

DOE assumed that the mean lifetime of these products would be the same as those of 

their non-hybrid equivalents, as determined in DOE’s final rule for refrigerators.

2 The mean 

lifetimes are 17.1 years for standard-sized refrigerators, 5.6 years for compact refrigerators, and 

22.8 years for freezers. DOE estimated new shipments as the total stock divided by the mean 

lifetime for all years through 2050. 

9.3.4.1 Disaggregation into Market Segments

The market for hybrid products is assumed to be primarily composed of units that replace 

products that have been retired from service and units installed in new housing. DOE assumed 

that the proportion of new shipments to each market segment would be the same as their nonhybrid equivalents, determined in DOE’s final rule for refrigerators.

2

Shipments Forecast by Market Segment. Figure 9.3.5 to Figure 9.3.7 show the 

forecasted shipments in the base case (without new energy conservation standards) for standard 

hybrid all-refrigerators, compact hybrid all-refrigerators, and hybrid freezers respectively. 

Historical and projected shipments were both calculated assuming that the proportions of 

shipments to total stock were the same as those previously determined by DOE in the 

refrigerators and freezers final rule.

2 The figures present shipments due to retirements and 

shipments to new housing. 
9-11

Figure 9.3.5 Standard-sized, Built-In Hybrid All-Refrigerator (H3A-BI) Base Case Shipments Forecast by Market 

Segment

Figure 9.3.6 Compact Hybrid All-Refrigerator (H-11A and H-13A) 

Base Case Shipments Forecast by Market Segment

0.00

0.05

0.10

0.15

0.20

0.25

2000200420082012201620202024202820322036204020442048

Shipments (millions)

Shipments to new

housing

Replacements

Total new shipments

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2000200420082012201620202024202820322036204020442048

Shipments (millions)

New housing

Replacements

Total Shipments
9-12

Figure 9.3.7 Standard-sized, Built-in Hybrid Freezers (H-9I-BI): 

Base Case Shipments Forecast by Market Segment

9.3.4.2 Disaggregation into Product Classes

As explained in chapter 3, compact hybrid all-refrigerators are divided into two product 

classes (H-11A and H-13A). The relative proportion of each was determined from data on 

available models found on the market; see chapter 7.

Table 9.3.4 Product Class Market Shares for Compact Hybrid Refrigerators

Compact refrigeratorcooled cabinets with 

automatic defrost (H13A)

Compact refrigeratorcooled cabinets with 

manual defrost (H11A)

80% 20%

9.4 IMPACT OF ENERGY CONSERVATION STANDARDS ON SHIPMENTS

DOE projects that appliance standards often result in an increase in the price of the 

product. Economic theory suggests that, all else being equal, an increase in the price of a normal 

product would lead to a decrease in demand for it. DOE conducted a literature review and an 

analysis of appliance price and efficiency data to estimate the effects on product shipments from 

increases in product price. DOE also considered the decreases in operating costs from higher 

energy efficiency and changes over time in household income. Appendix 9A provides a detailed 

explanation of the methodology DOE used to quantify the impacts of these variables on 

shipments. 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

2000200420082012201620202024202820322036204020442048

Shipments (Millions)

Housing starts

Replacements

Total new shipments
9-13

In the literature, DOE found only a few studies of appliance markets that are relevant to 

the issue at hand. DOE identified no studies that use time-series data of product price and 

shipments data after 1980. The information that can be summarized from the literature suggests 

appliances are a normal good, such that rising incomes increase the demand for appliances. 

Finally, the literature suggests that market behavior indicates relatively high “implicit discount 

rates” when comparing appliance prices and appliance operating costs.a

DOE found insufficient data on product purchase price and operating cost to perform a 

thorough analysis of dynamic changes in the appliance market. Instead, it used purchase price 

and efficiency data specific to residential refrigerators, clothes washers, and dishwashers over the 

period 1980-2002 to evaluate broad market trends and conduct simple regression analyses. These 

data indicate that there has been a rise in appliance shipments and a decline in appliance 

purchase price and operating costs over the time period. Household income has also risen during 

this time. 

To simplify the analysis, DOE combined the available economic information into one 

variable, termed the relative price, and used the variable in an analysis of market trends, as well 

as to conduct a regression analysis. The relative price is defined with the following expression: 

RP = TP

Income = PP + PVOC

Income

Where:

RP= relative price, 

TP= total price,

Income= household income

PP= appliance purchase price, and 

PVOC= present value of operating cost. 

DOE used an “implicit discount rate” of 37 percent to determine the present value of 

operating costs. This value is an average from values derived by several studies described in a 

1985 journal article.5

DOE’s regression analysis yields a relative price elasticity of demand, averaged over the 

three appliances, of -0.34. For example, a relative price increase of 10 percent results in a 3.4 

percent decrease in shipments. Note that, because the relative price elasticity incorporates the 

impacts from three effects (i.e., purchase price, operating cost, and household income), the 

impact from any single effect is somewhat mitigated by changes in the other two effects. 

 

a A high implicit discount rate with regard to operating costs means that, based on market behaviour, consumers 

appear to put relatively low economic value on the operating cost savings realized from more-efficient appliances. A 

high value may indicate lack of information, risk aversion, and other factors, as well as the value consumers place 

on savings accrued in the future. 
9-14

The relative price elasticity of -0.34 is consistent with estimates in the literature. 

Nevertheless, DOE stresses that the measure is based on a small data set, using simple statistical 

analysis. More importantly, the measure is based on an assumption that economic variables, 

including purchase price, operating costs, and household income, explain most of the trend in 

appliances per household in the United States since 1980. Changes in appliance quality and 

consumer preferences may have occurred during this period, but DOE did not account for them 

in this analysis. Despite these uncertainties, DOE believes that its estimate of the relative price 

elasticity of demand provides a reasonable assessment of the impact that purchase price, 

operating cost, and household income have on product shipments. 

DOE considers the relative price elasticity provided by the preceding analysis to be a 

short-run value. Because DOE’s forecasts of shipments and national impacts due to standards is 

over a 30-year time period, it needed to consider how the relative price elasticity is affected once 

a new standard takes effect. It was unable to identify sources specific to household durable 

goods, such as appliances, to indicate how short-run and long-run price elasticities differ. To 

estimate how the relative price elasticity changes over time, DOE relied on a study pertaining to 

automobiles.6 This study shows that the automobile price elasticity of demand changes in the 

years following a purchase price change. With increasing years after the purchase price change, 

the price elasticity becomes smaller (more inelastic) until it reaches a terminal value around the 

tenth year after the price change. Table 9.4.1 shows the relative change in the price elasticity of 

demand for automobiles over time. DOE developed a time series of relative price elasticities for 

home appliances based on the relative change in the automobile price elasticity of demand. For 

years not shown in the table, DOE performed a linear interpolation to obtain the relative price

elasticity. 

Table 9.4.1 Change in Relative Price Elasticity Following a Purchase Price Change

Years Following Price Change

1 2 3 5 10 20

Change in 

Elasticity 

Relative to 1st

year

1.00 0.78 0.63 0.46 0.35 0.33

Relative Price 

Elasticity -0.34 -0.26 -0.21 -0.16 -0.12 -0.11

9.4.2 Application of Relative Price Elasticity

DOE estimates shipments in each standards case using the relative price elasticities 

described previously, along with the change in the relative price between a standards case and 
9-15

the base case. Because household income is the same in the standards case and the base case, it 

does not figure into the calculation of the change in the relative price. Note that, in the following 

equation, the relative price and the relative price elasticity are functions of the year because both 

change with time.b

ShipSTD _P (j) = (RplBASE _P (j) + NIBASE _P(j) + MBASE _P(j)) × (1 − eRP (j) × ∆RP(j))

Where:

ShipSTD _P(j)= total shipments under the standards case of product p in year j,

RplBASE _P(j)= units of product p under the base case retired and replaced in year j, 

NIBASE _P(j)= number of new construction installations under the base case of product p in 

year j, 

MBASE _P(j)= units installed in market M under the base case of product p in 

year j (M represents purchases for existing homes), 

eRP(j)= relative price elasticity in year j (equals -0.34 for year 1), and

∆RP(j)= change in relative price due to a standards level in year j. 

9.5 AFFECTED STOCK

In addition to the forecast of product shipments under both the base case and the 

standards case, the affected stock is a key output of DOE’s shipments models. The affected stock 

(stock that is affected by a standards level) consists of those in-service units that are purchased in 

or after the year the standard has taken effect, as described by the following equation: 

Aff Stockp(j) = ShipP(j) + � StockP(age)

j−Std_yr

age=1

Where:

Aff StockP(j)=affected stock of units of product p of all vintages that are in service in year 

j, 

ShipP(j)= shipments of product p in year j,

StockP(j)= stock of units of product p of all vintages that are in service in year j, 

age= age of the units (years), and

Std_yr= effective date of the standards.

 

b The relative price changes slightly over time because the lifetime operating costs are different for each vintage in 

the forecast period. Operating costs change slightly because forecasted energy prices are changing. 
9-16

For its analysis, DOE assumed that amended energy conservation standards will become 

effective in 2021. Thus, all appliances purchased starting in 2021 are affected by the standard 

level. 

9.6 SHIPMENTS FORECASTS IN STANDARDS CASES

This section presents the shipments forecasts for the candidate standard levels (CSLs), 

also known as efficiency levels (ELs), which DOE considered for each of the miscellaneous 

refrigeration product types, as well as for the base case. The ELs are described in chapter 10. 

DOE generally expects that a standard will increase the per unit price of a given product, which 

in turn will lead to a decrease in shipments. In the case of hybrid products, however, DOE does 

not expect the per unit price to increase due to the standards (refer to chapter 5, Engineering 

Analysis, for details). Therefore, it does not expect shipments to be affected. 

DOE determines the percentage decrease in shipments as:

1 − Pricebasecase + Operatingcostsbasecase

Pricestandardscase + Operatingcoststandardscase

∗ elasticity

Pricebasecase= Price per unit in the base case

Operatingcostsbasecase= Operating cost per unit in the base case

Pricestandardscase= Price per unit in the standards case

Operatingcoststandardscase=Operating costs per unit in the standards case

elasticity= relative price elasticity, as described in 9.4

For ice makers, DOE found the increased price per unit in the standards case was 

insignificant compared to the decreased operating costs. This would lead to a negative value in 

the above formula, indicating an increase in shipments. DOE does not expect the standard to lead 

to an increase in shipments and therefore does not expect ice maker shipments to be affected by 

the standards. Similarly DOE does not expect shipments of non-compressor refrigerators to be 

affected by the standards. 

DOE does expect the shipments of cooled cabinets to be affected by the standards for the 

whole 30 year assessment period. Figure 9.6.1 shows the differences between the base case and 

standards case for all cooled cabinets. Figure 9.6.2 and Figure 9.6.3 show the differences 

between the base case and standards case shipments for CC-1 (vapor compression) and CC-2
9-17

(thermoelectric),

c respectively. These forecasts represent the annual shipments reductions 

attributable to the standard levels.

Figure 9.6.1 All Cooled Cabinets Shipments Forecasts

 

c The CC-2 product category is referred to as Thermoelectric Cooled Cabinets in the following figures. The costefficiency curve for CC-2 uses thermoelectric cooling at baseline and vapor compression technology at efficiency 

levels 5 through 11. See chapter 5 for more information. 

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Shipments (millions)

Base Case

EL1

EL2

EL3

EL4

EL5

EL6

EL7

EL8

EL9

EL10

EL11
9-18

Figure 9.6.2 CC-1, Vapor Compression Cooled Cabinets

Shipment Forecasts

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Shipments (millions)

Base Case

EL1

EL2

EL3

EL4

EL5

EL6

EL7

EL8

EL9

EL10

EL11
9-19

Figure 9.6.3 CC-2, Thermoelectric Cooled Cabinets Shipment 

Forecasts

0

0.5

1

1.5

2

2.5

3

3.5

4

Shipments (millions)

Base Case

EL1

EL2

EL3

EL4

EL5

EL6

EL7

EL8

EL9

EL10

EL11
9-20

REFERENCES

1 http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx/ruleid/71. 

Accessed June 26, 2014. This material is available in Docket EERE-2011-BT-STD-0043 at 

regulations.gov.

2 DOE (2011). Energy Conservation Program: Energy Conservation Standards for Residential 

Refrigerators, Refrigerator-Freezers, and Freezers, Final Rule notice (76 FR 57516) U.S. 

Department of Energy. http://www.gpo.gov/fdsys/pkg/FR-2011-09-15/pdf/2011-22329.pdf.

3 Greenblatt, J. B., S. J. Young, H.-C. Yang, T. Long, B. Beraki, S. Price, S. Pratt, H. Willem, L.-

B. Desroches, and S. M. Donovan (2013). U.S. Residential Miscellaneous Refrigeration 

Products: Results from Amazon Mechanical Turk Surveys, Lawrence Berkeley National 

Laboratory, LBNL-6537E, November 2013.

4 U.S. Department of Energy-Energy Information Administration. Annual Energy Outlook 2014

With Projections to 2040. April 2014. Washington, DC. DOE/EIA-0383(2014). 

http://www.eia.gov/forecasts/aeo/pdf/0383%282014%29.pdf

5 Train, K., “Discount Rates in Consumers,” Energy-Related Decisions,” Energy: The 

International Journal, Vol.10, No.12, 1985, pp. 1243-1253.

6 S. Hymans. Consumer Durable Spending: Explanation and Prediction, Brookings Papers on 

Economic Activity, 1971. Vol. 1971, No.1, pp. 234-239.