CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

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

9.3 DATA INPUTS AND MODEL CALIBRATION .......................................................... 9-3

9.3.1 Historical Shipments........................................................................................................ 9-5

9.3.2 Markets and Model Calibration ....................................................................................... 9-7

9.3.2.1 New Construction .......................................................................................... 9-7

9.3.2.2 Replacements............................................................................................... 9-10

9.3.2.3 Model Calibration—Non-Replacements ..................................................... 9-11

9.3.2.4 Base Case Shipments................................................................................... 9-12

9.3.3 Market Share Forecast ................................................................................................... 9-14

9.4 PURCHASE PRICE AND OPERATING COST IMPACTS ....................................... 9-15

9.5 AFFECTED STOCK ..................................................................................................... 9-17

9.6 RESULTS ...................................................................................................................... 9-18

LIST OF TABLES

Table 9.3.1 Commercial Clothes Washers: Historical Shipments (1972 – 2013) .................... 9-5

Table 9.3.2 Commercial Clothes Washers: Historical New Multi-Family Building................ 9-8

Table 9.3.3 Multi-Family In-Unit Washer Saturations.............................................................. 9-9

Table 9.3.4 Commercial Clothes Washers: Historical New Multi-Family Building.............. 9-12

Table 9.3.4 Commercial Clothes Washers: Historical Market Share of Top-loading 

Units...................................................................................................................... 9-14

Table 9.4.1 Price Elasticity Decrease after CCW Price Change.............................................. 9-16

Table 9.6.1 Top-Loading Commercial Clothes Washers: Cumulative Shipments by 

Standards over the Period 2018–2047 .................................................................. 9-18

Table 9.6.2 Front-Loading Commercial Clothes Washers: Cumulative Shipments............... 9-18

LIST OF FIGURE

Figure 9.3.1 Commercial Clothes Washer Shipments and Trend in Quantity Index ............... 9-6

Figure 9.3.2 Historical and Projected Multi-Family Housing Starts (millions) ....................... 9-8

Figure 9.3.3 Commercial Laundry Saturation in New Multi-Family Housing....................... 9-10

Figure 9.3.4 Commercial Clothes Washers: Survival and Retirement Functions ................. 9-11

Figure 9.3.5 Commercial Clothes Washers: Historical and Base Case Shipments............... 9-13

Figure 9.3.6 Commercial Clothes Washers: Disaggregated Base Case................................. 9-13

Figure 9.3.8 Forecast of Market Share in Base Case and Standards Case TSL 2 for............. 9-15

Figure 9.6.1 Top-Loading Commercial Clothes Washers: Base Case and TSL 

Shipments Projection ......................................................................................... 9-19

Figure 9.6.2 Front-Loading Commercial Clothes Washers: Base Case and TSL 

Shipments Projection ......................................................................................... 9-19

9-i
CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

Product shipments estimates are a necessary input to the national energy savings (NES) 

and net present value (NPV) calculations. Shipments are also a necessary input to the 

manufacturer impact analysis (MIA), which the U.S. Department of Energy (DOE) conducts for 

its notice of proposed rulemaking (NOPR). This chapter describes DOE’s methodology for 

projecting annual shipments and presents results for commercial clothes washers.

DOE estimated shipments for commercial clothes washers with a shipments model. DOE

calibrated the shipments model against historical shipments. For purposes of estimating the 

impacts of prospective trial standard levels (TSLs) on product shipments, the shipments model

accounts for the combined effects of changes in purchase price and annual operating cost on the 

product purchase decision.

The shipments model considers specific market segments to estimate shipments, the 

results of which are then aggregated to estimate total product shipments. In the case of 

commercial clothes washers, DOE accounted for two market segments: (1) shipments due to 

new construction, and (2) replacements of retired units from existing buildings. 

The shipments model is a Microsoft Excel spreadsheet that is accessible on the Internet 

(http://www.eere.energy.gov/buildings/appliance_standards/). Appendix 10-B discusses how to 

access the shipments model contained in the NIA spreadsheet, and provides basic instructions for 

using it. The rest of this chapter explains the shipments model in more detail. Section 9.2 

presents the shipments model methodology; section 9.3 describes the data inputs and the model 

calibration; section 9.4 discusses impacts on shipments from changes in equipment purchase 

price and operating cost; section 9.5 discusses the affected stock; and section 9.6 presents the 

results for different TSL scenarios.

9.2 SHIPMENTS MODEL METHODOLOGY

DOE developed a national stock model for estimating annual shipments for commercial 

clothes washers. The model considers market segmentation as a distinct input to the shipments 

projection. As represented by the following equation, the two primary market segments are new 

installations and replacements. 

Ship ( j) Rpl ( j) NI ( j) p = p + p

Where:

9-1
Shipp(j) = total shipments of product p in year j, 

Rplp(j) = units of product p retired and replaced in year j, and 

NIp(j) = number of new installations of product p in year j.

As section 9.3.2.3 discusses, DOE also considered non-replacements as a factor for most

of the products to calibrate its shipments model to historical shipments data.

In principle, each market segment and each product class responds differently to both the 

base case demographic and economic trends and to the implementation of standards. 

Furthermore, retirements, early replacements, and efficiency trendsa are dynamic and can vary 

among product classes. Rather than simply extrapolating a current shipments trend, the base 

case shipments analysis (i.e., the case without new standards) uses driver input variables, such as 

construction forecasts and product lifetime distributions, to project sales in each market segment. 

Thus, DOE’s shipments model assumes that construction--i.e., new multi-family housing units--

drives new installations. In each year, the product shipments from the new construction market 

segment are equal to the number of new multi-family housing units built times the purchase rate, 

which is determined by the product class market share and the market saturation of the product 

under considerationb. 

DOE’s shipments model takes an accounting approach, tracking market shares of each 

product class, the vintage of units in the existing stock, and expected construction trends. The 

model estimates shipments due to replacements using sales in previous years and assumptions 

about the lifetime of the equipment. Therefore, estimated sales due to replacements in a given 

year are equal to the total stock of the appliance minus the sum of the appliances sold in previous 

years that still remain in the stock. DOE determined the useful service life of each appliance to 

estimate how long the appliance is likely to remain in stock. The following equation represents 

how DOE estimated replacement shipments.

RRRRRRpp (jj) = SSSSSSSSSSpp (jj − 1) − � � SShii jj

jj−1

jj=NN

aaaaaaaaaaaa

aaaaaa=0

× pp ppRRRRRR (aaaaaa)

Where:

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

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

a Efficiency trends affect shipments only in the standards case. A change in the efficiency distribution of the 

stock results in a change in the purchase price and operating cost and, therefore, produces a purchase price and 

operating cost impact on the shipments. This is discussed later in the chapter in section 9.4.

b In this case, market saturation of the product is related to saturation of in-home clothes washer units in multifamily households.

9-2

 
N = start year for when the model begins its stock accounting (start year is 

specific to each product based on available historical shipments data).

Stock accounting takes product shipments, a retirement function, and initial in-service 

product stock as inputs and provides an estimate of the age distribution of in-service product 

stocks for all years. The age distribution of in-service product stocks is a key input to both the 

NES and NPV calculations—the operating costs for any year depend on the age distribution of 

the stock. The dependence of operating cost on the equipment age distribution occurs under a 

TSL that produces increasing efficiency over time, where older, less efficient units may have 

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

DOE calculated total in-service stock of equipment by integrating historical shipments 

data starting from a specific year. The start year depended on the historical data available for 

the product. As units are added to the in-service 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 in-service stocks. For new units, the equation is:

( , 1) ( 1) _ Stock j age = = Ship j

Where: 

Stock(j, age) =the population of in-service units of a particular age,

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

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

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

number of new units purchased the previous year. The slightly more complicated equations 

(e.g., the following equation) are those that describe the accounting of the existing in-service 

stock of units: 

SSSSSSSSSS(jj + 1, aaaaaa + 1) = SSSSSSSSSS(jj, aaaaaa) × [1 − pp ppRRRRRR(aaaaaa)]

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

from age to age+1. With time, a fraction of the in-service stock is removed, and that fraction is 

determined by a retirement probability function, probRtr(age), which is described in section 10.3. 

Because commercial clothes washers are considered to be common appliances that have been 

used by U.S. consumers for a long time, replacements typically constitute the majority of 

shipments. Most replacements are made when equipment wears out and fails. 

9.3 DATA INPUTS AND MODEL CALIBRATION 

As discussed previously, shipments are driven primarily by two market segments: new 

construction and replacements. DOE used historical shipments as the basis for calibrating its 

9-3
shipments model. Because new construction shipments and replacements were not enough to 

account for all product shipments, DOE developed another factor to calibrate its shipments 

model. This factor, retired units not replaced, represents a small share of total shipments. 

Shipments to the different market segments are discussed below.

DOE designed its shipments model for commercial clothes washers by developing a 

single shipments model for all washers destined for the two most predominant product 

applications—multi-family buildings and laundromats—and then disaggregating the shipments 

into its two product classes—top-loading and front-loading washers. DOE developed a crossprice elasticity to estimate the market shares of the considered product classes through the 

forecast period. The Cross-Price elasticity is covered in section 9.3.3.

DOE’s approach for estimating shipments relies on using aggregate historical shipments 

data for all commercial clothes washers. Tracking of product stock and vintage relies on a 

retirement function, which describes the likelihood that equipment installed in a certain year will 

still be in service in any subsequent year. Once a product reaches the end of its useful life it is 

removed from service. In most cases, retirement is followed by replacement, which is a key 

driver of further shipments. The difference between replacements and total shipments for the 

following year provides the shipments going into new construction. The output includes units 

going into both laundromats and multi-family apartment buildings. 

DOE based its shipments model on the following three assumptions: (1) all product 

shipments for new construction are driven by the new multi-family housing market, (2) the 

relative market shares of the two product applications, laundromats and common-area laundry 

facilities in multi-family housing, are constant over time, and (3) the U.S. Census Bureau’s 

quantity index data can be used to validate the shipments trend observed in the historical data. 

DOE’s first assumption is based on the premise that multi-family occupants who do not 

have their own personal washers and dryers must either wash their laundry in the common area 

laundry facility within their building or in a laundromat. Because the vast majority of people 

that use laundromats live in multi-family buildings, the construction of any new laundromats 

would seem to be driven by new multi-family customers. Thus, DOE believes it is reasonable to 

expect that new multi-family construction starts capture all new product shipments, regardless of 

whether the units are destined for multi-family buildings or laundromats.

With regard to the second assumption, i.e., constant market shares, DOE did not have 

sufficient data to project whether the market shares of laundromats and multi-family housing will 

vary over time. Therefore, DOE assumed that market shares will remain constant at current 

levels. DOE relied on a report from the Consortium for Energy Efficiency (CEE) to estimate 

current market shares. Based on the CEE report, multi-family buildings and laundromats 

comprise 85 percent and 15 percent of the commercial clothes washer market, respectively.1

 

Although the CEE report was published more than 10 years ago, it continues to be the most 

reliable data source for developing a market split for commercial clothes washer shipments that 

was available. 

9-4
The third assumption pertains to the use of the U.S Bureau of Economic Analysis’ 

quantity index data to validate historical shipments data.2 The Census Bureau’s quantity index 

for commercial laundry equipment includes shipments of commercial laundry products beyond 

those covered by this rulemaking. Because disaggregated quantity index data were not available, 

DOE assumed that the market share of commercial clothes washers covered under this 

rulemaking relative to all commercial laundry equipment was constant over the period 1977–

2011. Based on this assumption, DOE derived quantity index data specific to the commercial 

clothes washers of interest to this rulemaking and used these data to validate the historical 

shipments.

9.3.1 Historical Shipments

DOE used historical shipments data (i.e., domestic shipments) to calibrate its shipments 

model. It used two sources to establish historical shipments: (1) data the Association of Home 

Appliance Manufacturers (AHAM) provided for the period 2010–20133 and (2) data for the 

period 1972–20054 from the last rulemaking. DOE used a five-year moving average to estimate

shipments for the period 2006–2009. Table 9.3.1 summarizes the historical commercial clothes 

washer shipments data. 

Table 9.3.1 Commercial Clothes Washers: Historical Shipments (1972 – 2013)

Year Shipments 

(thousands) Year Shipments (thousands)

1972 167 1993 190

1973 167 1994 205

1974 166 1995 209

1975 167 1996 232

1976 167 1997 241

1977 167 1998 265

1978 166 1999 239

1979 164 2000 215

1980 170 2001 194

1981 171 2002 175

1982 163 2003 191

1983 163 2004 178

1984 167 2005 177

1985 176 2006 175

1986 186 2007 172

1987 194 2008 169

1988 213 2009 167

9-5
1989 215 2010 164

1990 225 2011 161

1991 193 2012 173

1992 188 2013 206

Sources: 2010–2013: AHAM Data Submittal, 2014; 2006–2009, DOE interpolated values; 1972–2005: DOE 

Standards for Commercial Clothes Washers, Technical Support Document, 2010.

 As indicated in Table 9.3.1, there was a significant drop in commercial clothes washer 

shipments between 1998 and 2011. Therefore, DOE validated the shipments data through a 

review of the U.S. Bureau of Economic Analysis’ quantity index data.2 DOE compared the 

historical shipments data against the quantity index for commercial laundry equipment for the 

period between 1977 and 2011 (represented by North American Industry Classification System 

(NAICS) code 333312)c. As shown in Figure 9.3.1 below, the commercial laundry quantity 

index tracks the shipments trend closely. Thus, DOE concluded that the downward trend 

observed in the historical shipments between 1998 and 2011 was real. 

Figure 9.3.1 Commercial Clothes Washer Shipments and Trend in Quantity Index

c DOE was not able to compare the historical shipments data with the quantity index for commercial laundry 

equipment for the period between 1977 and 2012, as the industry codes were changed in the Bureau of 

Economic Analysis’s 2014 publication. 

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0

20

40

60

80

100

120

140

160

Shipments (millions)

Quantity Index (2000 =100)

Quantity Index Historical Shipments QI-based Shipments

Pre-1988 

shipments

based on QI

Decling 

trend since 

1999

9-6

 
9.3.2 Markets and Model Calibration

The market for commercial clothes washers primarily consists of replacement units for 

equipment that has been retired and units for new housing. Total commercial clothes washers 

shipments are represented by the following equation:

Ship ( j) Rpl ( j) NI ( j) CCW = CCW + CCW

Where:

ShipCCW (j) = total shipments of commercial clothes washers in year j, 

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

NICCW (j) = shipments due to new construction in year j.

The following sections discuss both of these markets in further detail. The model 

calibration is also discussed.

9.3.2.1 New Construction 

To project shipments to the new construction market, DOE assumed shipments are driven 

solely by multi-family construction starts. Implicit in this assumption is the fact that a certain 

percentage of multi-family residents will need to wash their laundry in either a common-area 

laundry facility (within the multi-family building) or a laundromat. 

To estimate shipments to new construction, DOE used projections of multi-family 

housing starts coupled with commercial clothes washer saturation data. In other words, to 

project the shipments for new construction for any given year, DOE multiplied the multi-housing 

projections by the projected saturation of commercial clothes washers for new multi-family 

housing. Because DOE used only multi-family housing starts as a driver for new construction 

shipments, the saturation represents the fulfilled washer demand in both the multi-family housing 

and laundromat markets. 

Figure 9.3.2 presents historical and projected new multi-family housing starts based on 

the DOE Energy Information Administration (EIA)’s Annual Energy Outlook 2014 for the period 

2014–2040.

5

 The AEO typically provides three scenarios of multi-family housing starts: the 

Reference case, the High Economic Growth case, and the Low Economic Growth case. All three 

housing starts projections are presented in Figure 9.3.2. DOE used only the projections from the 

Reference case to estimate its shipments to new construction. For the period 2041−2047, DOE 

froze completions at the level in the year 2040 for all three economic projections.

9-7
Figure 9.3.2 Historical and Projected Multi-Family Housing Starts (millions)

 DOE deduced historical commercial laundry saturations for the new construction market 

based on the remaining portion of historical shipments that did not serve as replacement units. 

(The determination of replacement shipments is discussed in section 9.3.2.2.) Table 9.3.23

shows the historical saturation of commercial clothes washers in new multi-family buildings.

Table 9.3.2 Commercial Clothes Washers: Historical New Multi-Family Building 

 Saturations 

Year Saturation

1990 18.6%

1991 10.8%

1992 9.8%

1993 11.6%

1994 15.6%

1995 11.9%

1996 17.0%

1997 19.0%

1998 23.7%

Average 15.3%

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

Housing Starts (millions)

Year

High

Low

Reference

9-8
DOE assumed that the average saturation over the period 1990−1998 of 15.3 percent 

would likely change during the period 1999 – 2011, due to the increasing saturation of in-unit 

washers in multi-family units as shown by historical data from the Census Bureau’s American 

Housing Survey (AHS).

6 DOE utilized the in-unit washer trends in multi-family buildings to 

estimate the associated trends in the use of commercial clothes washers in multi-family common 

area laundry facilities. 

 Table 9.3.34 shows the saturation of in-unit washers in both the multi-family stock and 

new construction from 1997 to 2011. Between 1997 and 2011, the annual growth rate of 

saturation of in-unit washers in new multi-family construction (i.e., residential washers used in 

newly constructed multi-family units) is 0.68 percent. Therefore, DOE assumed that the annual 

growth rate of saturation of commercial clothes washers is -0.68 percent during the period 2000 

– 2011. DOE also assumed that the average saturation over the period 1999 – 2013 of 14.2 

percent would remain constant over the period 2014–2047.

 

Table 9.3.3 Multi-Family In-Unit Washer Saturations

In-Unit Washer Saturation

Multi-Family Housing 1997 1999 2001 2003 2005 2007 2009 2011

New Construction

70.4% 64.4% 68.7% 68.1% 73.4% 73.5% 78.1% 77.41%

Stock 32.3% 32.7% 35.6% 36.1% 37.3% 37.5% 39.1% 39.56%

Source: AHS, 1997–2011.

 Figure 9.3.3 shows the historical variation in the new construction saturation as well the

projected saturation for the years after 1998.

9-9
 Figure 9.3.3 Commercial Laundry Saturation in New Multi-Family Housing

9.3.2.2 Replacements

DOE determined shipments to the replacement market using an accounting method that 

tracks the total stock of units by vintage. DOE estimated a stock of commercial clothes washers 

by vintage by integrating historical shipments starting from the year 1972. Over time, some 

units will be retired and removed from stock, thereby triggering the shipment of a replacement 

unit. Depending on the vintage, a certain percentage of each type of unit will fail and need to be 

replaced. To determine when a unit fails, DOE used a survival function based on the product 

lifetime distributions of the two product applications considered in the analysis—laundromats 

and multi-family buildings. DOE based the retirement function on a Weibull probability 

distribution for the product lifetime. 

For the commercial clothes washer shipments model, DOE combined the maximum and 

minimum age values for the two product applications based on the market share of each 

application (85 percent for multi-family housing and 15 percent for laundromats). The survival 

function that DOE used had an average lifetime of 10.6 years with minimum and maximum 

values of 6.7 years and 14.6 years, respectively. For a more complete discussion of commercial 

clothes washer lifetimes, refer back to section 8.2.3 of Chapter 8. 

 Figure 9.3.4 shows the survival function that DOE used to estimate replacement 

shipments. 

 

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

Commercial Laundry Saturation in New 

Multi-Family Housing (%)

9-10
 Figure 9.3.4 Commercial Clothes Washers: Survival and Retirement Functions

9.3.2.3 Model Calibration—Non-Replacements

To account for the significant drop in shipments after 1998, and to reconcile the historical 

shipments with the accounting model, DOE assumed every retired unit is not replaced

immediately. The market share of retired units not replaced was relatively large due to the 

significant drop in shipments after 1998 (as discussed in section 9.3.1). Starting in 1999 and 

extending to 2013, DOE estimated the share of retired units that were not replaced. The share of 

retired units not replaced fluctuated between 16 and 41 percent. Table 9.3.45 shows the share of 

retired units not replaced between 1999–2013.

9-11

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

% Surviving by Age
Table 9.3.4 Commercial Clothes Washers: Historical New Multi-Family Building 

 Saturations 

Year % of Retired units not replaced

1999 0.0%

2000 15.9%

2001 27.1%

2002 38.8%

2003 32.3%

2004 38.8%

2005 40.4%

2006 40.9%

2007 40.5%

2008 39.9%

2009 29.2%

2010 29.9%

2011 34.2%

2012 31.0%

2013 16.7%

Average 30.4%

To determine the share of retired units not replaced after the year 2011, DOE reviewed 

data from the American Housing Survey. 

As evident from Table 9.3.34, the saturation of in-unit washers in new construction has 

increased by approximately 10 percent, while the saturation in the multi-family building stock 

has increased by approximately 23 percent. Because the saturation of in-unit washers in new 

construction has increased relatively slowly, there must be another driver for the increase of inunit washers in the building stock. DOE postulates that the growth in in-unit washer saturations 

in the multi-family stock over the last ten years was caused by conversions of rental property to 

condominiums, resulting in the gradual phase out or non-replacement of failed commercial 

clothes washers in common-area laundry facilities. Based on this apparent trend, DOE used the 

average percent of non-replacements over the 1999–2013 timeframe—30.4 percent—and 

maintained it over the entire projection period of 2014–2047. 

9.3.2.4 Base Case Shipments

 Figure 9.3.5 shows the projected commercial clothes washer shipments in the base case 

(i.e., the case without new energy efficiency standards) and the historical shipments DOE used to 

calibrate the projection. To be clear, all commercial clothes washer shipments, including both

top-loading and front-loading units, are represented in the shipments shown in Figure 9.3.5. 

9-12
 Figure 9.3.5 Commercial Clothes Washers: Historical and Base Case Shipments 

 Projection

Figure 9.3.6 presents projected base case commercial clothes washer shipments 

disaggregated into shipments due to retirements and shipments for new construction. The 

unusual jump in shipments going from 2012 to 2013 is driven primarily by the new construction 

starts in multifamily housing. 

 Figure 9.3.6 Commercial Clothes Washers: Disaggregated Base Case 

 Shipments Projection 

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

Shipments (million)

Year

Historical Shipments

Projected Total Shipments

0.00

0.05

0.10

0.15

0.20

0.25

Shipments (millions)

Year

Replacement Modeled Shipments

New Construction Modeled Shipments

9-13
9.3.3 Market Share Forecast

 DOE projected the change in market share between the front-loading and top-loading 

units in the base case on the basis of available market share data. For the base case projection, 

DOE extrapolated compounded annual growth rate (CAGR) of the top-loading market share 

using data submitted by AHAM for the period between 20057 and 20133, as shown in Figure 

9.3.7. DOE assumed the market share of top-loading units would decrease by 1.1 percent 

annually for the period between 2013 and 2047.

Table 9.3.5 Commercial Clothes Washers: Historical Market Share of Top-loading Units

Market Share (%) 2005 2013 CAGR (05-13)

Top-loading 79.7% 73.19% -1.1%

 For the standards case, both available data and cross-price elasticities were used to 

forecast market share changes. Due to insufficient data, DOE was not able to estimate cross-price 

impacts on the market share of top-loading and front-loading commercial clothes washers and instead 

relies on its recent analysis performed for residential clothes washers.

8

 In order to estimate the impact of price changes on market share, DOE applied a logistic 

regression method to regress market share on price variables and other attributes. The basic form of a 

logistic regression is: 

ii = � 1

1 + −�ββ0+ββ1 1,ii+⋯+ββkk kk,ii�

�

 With some simple operations, the model can be transformed to an equivalent log-linear form:

ll � ii

1 − ii

� ββ0 + ββ1xx1,ii + ⋯ + ββkkxxkk,ii

 In this case, is the market share of either top- or front-loading clothes washers, and is the 

ratio of clothes washer market shares, i.e., the relative probability of the market share of top- and

front-loading clothes washers.

 These regression results were used to derive the cross-price impact of a change in the 

front-loading washer price on the top-loading market share (and vice versa). For example, these 

results suggest that a 10% increase in the price of front-loading washers would lead to a 10.7%

decrease in top-loading washers’ market share, holding other variables constant and measured as 

changes from the reference case using average values for each variable. In this case, the frontloading cross-price impact (percent change in top-loading market share over percent change in 

front-loading price) is 1.07.d Similarly, these results indicate that a 20% price increase for topd Price elasticity varies according to the reference price and market share – typically measured as changes from 

mean values for these variables in the data set. In DOE’s data set, the reference top-loading washer price is 

9-14

 
loading washers would yield a 21.49 % increase in front-loading market share, measured as 

changes from the variable means. Thus, in this example, the top-loading washer cross-price 

impact is also 1.07. See the residential clothes washers 2012 Direct Final Rule Technical 

Support Document for additional details.7

 Figure 9.3.8 shows forecasted base and standards case market share of commercial 

clothes washers disaggregated by the two product types. The figures show the standards case for 

top-loading and front-loading clothes washers, TSL 2. Given the direct correlation between price 

and market share, as long as the price changes the market share will also continue to change.

Figure 9.3.7 Forecast of Market Share in Base Case and Standards Case TSL 2 for 

 Front-Loading (EL 2) and for Top-Loading (EL 1)

9.4 PURCHASE PRICE AND OPERATING COST IMPACTS

 DOE conducted a literature review to establish the likely range of values for the price 

elasticity of demand for commercial clothes washers. The price elasticity of demand describes

the responsiveness of the quantity purchased of a product to a change in its price and can be 

generically defined as the ceteris paribus percent change in shipments given a 1% change in 

price, or:

dd = PP0

QQ0

∗

∂∂

∂∂

$403.78, the reference front-loading washer price is $823.83, the corresponding reference top-loading washer 

market share is 71%, and the corresponding reference front washer market share is 29%.

9-15

 
 where P and Q represent price and shipments quantity, respectively.

9

 DOE believes commercial clothes washers to be highly price inelastic and applies a 

default price elasticity of demand of zero for this product, meaning that any cost and price 

increases resulting from efficiency standards are unlikely to substantially affect the quantity of 

washers demanded. As these are somewhat niche products, estimates of commercial clothes 

washer price elasticity were not found in the literature, and DOE does not have the necessary 

data to perform an accurate independent calculation of price elasticity. Instead, the value of zero 

is based on DOE’s understanding of the commercial clothes washer market and distribution 

channels, particularly in relation to the demand for laundry services.

 To validate the use of a price elasticity of zero, DOE estimated an implied commercial 

clothes washer price elasticity based on known variables describing the market for laundry 

services. The implied price elasticity is approximated as follows:

IIII II dd,CCCCCC = dd,LL LLLL LLLLLLLL ∗ � PP CCCCCC

PP LL LLLL LLLLLLLL�

Where:

= the price elasticity of demand for commercial clothes washers,

= the average price elasticity of demand for laundry service,

= the commercial clothes washers wholesale price (or cost), and

= the price (or cost) of providing laundry service.

 DOE estimated an implied price elasticity of demand for commercial clothes washers of 

approximately -0.03 to -0.12 based on laundry equipment distribution channels and the market 

for laundry services. These values are provided as alternatives to the default price elasticity of 

zero.

 Additionally, price elasticity for a given product is not constant over time; numerous 

studies have demonstrated decreases in price elasticity for durable goods as the period of time 

since a price change increases.10, 11,12 Similarly, decreases in price elasticity have been 

demonstrated through the stages of a product’s life cycle.

13 DOE projects that any non-zero 

commercial clothes washer price elasticity will decrease over time, following the proportional

decreases demonstrated for automobiles (Table 9.4.1).

Table 9.4.1 Price Elasticity Decrease after CCW Price Change

Years Following Price Change 

1 2 3 5 10 20

Price Elasticity of Demand -1.20 -0.93 -0.75 -0.55 -0.42 -0.40

Relative Change in Elasticity to 1st 

year 

1.00 0.78 0.63 0.46 0.35 0.33

Implied Price Elasticity (low) -0.031 -0.024 -0.015 -0.007 -0.002 -0.001

Implied Price Elasticity (high) -0.123 -0.096 -0.060 -0.028 -0.010 -0.003

Source: Hymans 1979 and DOE calculations.

9-16
 Based on the following equation, DOE estimated standards case shipments by 

incorporating the impact of the price into the base case shipments projection. Note that in the 

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

with time. 

( ) ( ( ) ( ) ( )) (1 ( ) ( )) _

_ _ _ _ Ship j Rpl j NI j M j e j RP j STD p = BASE p + BASE p + BASE p

× RP × D

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 early replacements for commercial clothes washers),

ed(j)= price elasticity in year j (equals -0.031 or -0.123 for year 1), and 

ΔP(j)= change in price due to a standard level in year j.

9.5 AFFECTED STOCK

The affected stock is the in-service stock of the appliance or product that is affected by a 

TSL. In addition to the projection of product shipments under both the base case and the 

standards case, the affected stock (which represents the difference in the appliance stock for the 

base case and the standards case) is a key output of DOE’s shipments models. The affected 

stock quantifies the impact that new product shipments have on the appliance stock due to a 

TSL. Therefore, the affected stock 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:

∑

_

1

_

( ) ( ) ( )

j Std yr

age

Aff Stock p j Shipp j Stock p age

=

= +

Where:

Aff Stockp(j) = affected stock of units of product p of all vintages that are operational 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 operational in year j,

age = age of the units (years), and

Std_yr = effective date of the standard.

9-17
As noted in this equation, to calculate the affected stock, DOE must define the effective 

date of the standard. For the NES and NPV results presented in Chapter 11, DOE assumed that 

new energy efficiency standards will become effective in the year 2018. Thus, all appliances 

purchased starting on the first day of the year 2018 are affected by the standard level. 

9.6 RESULTS

The following sections show the shipments projections for the various TSLs that DOE 

considered for each of the products. The TSLs are identified and described in chapter 10.

Table 9.6.1 and Table 9.6.2 show the cumulative shipments over the period 2018–2047

caused by each of the TSLs considered for top-loading and front-loading commercial clothes 

washers, respectively. Figure 9.6.1compares the shipments projections for the base case and 

each of the four TSLs for top-loading washers. In Figure 9.6.1, the difference between the base 

case and TSL shipments projections depicts the annual shipments reductions caused by crossprice elasticities. Figure 9.6.2 compares the shipments projections for the base case and each of 

the three TSLs for front-loading washers. 

Table 9.6.1 Top-Loading Commercial Clothes Washers: Cumulative Shipments by 

Standards over the Period 2018–2047

TSL

MEF/IWF (cu.ft/kWh/cycle 

gal/cu.ft)

Cumulative Shipments 

(millions)

1 1.35/8.80 3.74

2 1.35/8.80 3.74

3 1.55/6.90 3.61

4 1.55/6.90 3.68

Table 9.6.2 Front-Loading Commercial Clothes Washers: Cumulative Shipments 

 Caused by Standards over the Period 2018–2047

TSL

MEF/IWF (cu.ft/kWh/cycle 

gal/cu.ft)

Cumulative Shipments 

(millions)

1 1.80/4.50 2.55

2 2.00/4.10 2.55

3 2.00/4.10 2.68

4 2.20/3.90 2.61

9-18
 Figure 9.6.1 Top-Loading Commercial Clothes Washers: Base Case and TSL 

Shipments Projection

 Figure 9.6.2 Front-Loading Commercial Clothes Washers: Base Case and TSL 

Shipments Projection

0.10

0.11

0.12

0.13

0.14

0.15

0.16

Shipments (million)

Year

Top-loading

TSL 3 Base Case

TSL 2 TSL 1

TSL 4

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

Shipments (million)

Year

Front-loading

TSL 3 Base Case

TSL 2 TSL 1

TSL 4

9-19
REFERENCES

1 Consortium for Energy Efficiency. Commercial Family-Sized Washers: An Initiative 

Description of the Consortium for Energy Efficiency, 1998. Boston, MA.

2

 U.S. Department of Commerce-Bureau of Economic Analysis. Industry Economic 

 Accounts, Gross-Domestic-Product-(GDP)-by-Industry-Data, 1998-2011 NAICS Data: 

 GDPbyInd_SHIP_NAICS and SIC Data: GDPbyInd_SHIP_SIC, Commercial Laundry 

 Quantity Index Data, NAICS code 333312. Washington, DC. 

 <http://www.bea.gov/industry/gdpbyind_data.htm>

3 Association of Home Appliance Manufacturers (AHAM). AHAM Data on Commercial 

Clothes Washers for DOE Efficiency Standards Rulemaking, August 11, 2014. Letter to 

Building Technologies Program, U.S. Department of Energy.

4 U.S. Department of Energy, Commercial Clothes Washers Final Rule Technical Support 

Document, Chapter 10. Shipment Analysis, EERE-2006-STD-0127 COMMENT 69.1, 2010-

01-19.

5

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

2014 with Projections to 2040, May 2014. Washington, DC. DOE/EIA-0383(2014). 

 <http://www.eia.gov/forecasts/aeo/pdf/0383(2014).pdf>

6

 U.S. Census Bureau, Housing and Household Economic Statistics Division. The American 

Housing Survey, 1997—2011. Washington, DC. 

<http://www.census.gov/housing/ahs/data/national.html>

7

 AHAM, AHAM Data on Commercial Clothes Washers for DOE Efficiency Standards 

Rulemaking, 2010. Letter to Building Technologies Program, U.S. Department of Energy.

8 U.S. Department of Energy, Technical Support Document: Energy Efficiency Program for 

 Consumer Products and Commercial and Industrial Equipment: Residential Clothes 

 Washers (Direct Final Rule), Building Technologies Program, Editor. 2012: Washinton, D.C. 

9 

 Varian, H. R., Intermediate Microeconomics: A Modern Approach. 1999. Vol. 5th Edition.

 W.W. Norton & Company: New York, London.

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

 Economic Activity, 1971. 1971(1): pp. 234-239. 

11 Fibrich, G., A. Gavious, and O. Lowngart, The Dynamics of Price Elasticity of Demand in 

 the Presence of Reference Price Effects. Journal of the Academy of Marketing Science, 

 2005. 33(1): pp. 66-78. 

12 Gowrisankaran, G. and M. Rysman, Dynamics of Consumer Demand for New Durable 

9-20

 
 Goods. 2009, National Bureau of Economic Research Working Paper: Cambridge, MA. 

13 Lilien, G. L. and E. Yoon, An Exploratory Analysis of the Dynamic Behavior of Price 

 Elasticity over the Product Life Cycle: An Empirical Analysis of Industrial Chemical 

 Products. Issues in Pricing, 1988: pp. 261-408.

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