9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

9.2 METHODOLOGY...................................................................................................... 9-1

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

9.3.1 Historical Shipments.................................................................................................... 9-4

9.3.2 Markets and Model Calibration.................................................................................... 9-5

9.3.2.1 New Housing ............................................................................................. 9-5

9.3.2.2 Replacements............................................................................................. 9-7

9.3.2.3 Early Replacements.................................................................................... 9-8

9.3.3 Base-Case Shipments .................................................................................................. 9-9

9.4 EFFECTS OF PURCHASE PRICE, OPERATING COSTS, AND HOUSEHOLD 

INCOME....................................................................................................................9-12

9.5 AFFECTED STOCK..................................................................................................9-14

9.6 RESULTS ..................................................................................................................9-15

LIST OF TABLES

Table 9.3.1 Historical Shipments: Domestic plus Imports................................................... 9-4

Table 9.3.2 Historical and Forecasted Housing Starts millions............................................ 9-6

Table 9.3.3 Historical Saturation of Clothes Washers in New Housing Units...................... 9-7

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

Table 9.6.1 Front- and Top-loading Clothes Washers: TSL Combinations for Analysis.....9-16

Table 9.6.2 Front- and Top-loading Clothes Washers: Cumulative Effects of Standards 

on Shipments, 2015–2044 ...............................................................................9-16

LIST OF FIGURES

Figure 9.3.1 Saturation of Clothes Washers in New Housing Units...................................... 9-7

Figure 9.3.2 Survival Function............................................................................................. 9-8

Figure 9.3.3 Historical and Forecasted Shipments for Base Case.......................................... 9-9

Figure 9.3.4 Market Share Estimation.................................................................................9-10

Figure 9.3.5 Forecast of Market Share in Base Case and Standards Case TSL3 for 

Front-Loading (CSL5) and for Top-Loading (CSL6).......................................9-12
9-1

CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

The U.S. Department of Energy (DOE) analyzes shipments of affected products as part of 

every rulemaking regarding new or amended energy efficiency standards for appliances. 

Estimates of product shipments are a necessary input for calculating national energy savings 

(NES) and net present value (NPV) of the investment, which are required to justify potential new 

energy efficiency standards. Shipments also are a necessary input to the manufacturer impact 

analysis, which DOE conducts to prepare its notices of proposed rulemakings. This chapter

describes DOE’s method and results of projecting annual shipments for front-loading and toploading standard clothes washers under base- and standards-case efficiency levels.

DOE used a computer model to predict shipments of clothes washers. It calibrated the 

model against historical records of shipments. In estimating the effects of potential new standard 

levels on product shipments, the model accounts for the combined effects of increases in 

purchase price, decreases in annual operating costs, and household income on the consumer 

purchase decision.

In estimating shipments, the model considers specific market segments, the results for 

which are then aggregated to estimate total product shipments. DOE accounted for two market 

segments: (1) shipments to new construction; and (2) replacement shipments going into existing 

building. .

The shipments models are prepared as Microsoft Excel spreadsheets that are accessible 

on the Internet (www.eere.energy.gov/buildings/appliance_standards/). Appendix 9A discusses

how to access the shipments model and other related spreadsheets and provides basic instructions 

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

describes the methodology that underlies development of the model; section 9.3 describes the 

data inputs and model calibration; section 9.4 discusses the effects of changes in purchase price, 

operating costs, and household income on shipments; and section 9.5 discusses the affected stock

of products. Section 9.6 presents the model results for the five efficiency levels for top-loading

and front-loading residential clothes washers that have been identified as trial standard levels 

(TSLs) for this rulemaking.

9.2 METHODOLOGY

DOE developed a model of the national stock of in-service appliances for estimating 

annual shipments for this standards rulemaking. The model considers market segments as 

distinct inputs to the shipments forecast. As represented by the following equation, the two 

primary market segments are new installations and replacements. 
9-2

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

Where:

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

Rplcw(j) = clothes washer units retired and replaced in year j, and 

NIcw(j) = number of new installations of clothes washers in year j.

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. In 

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

economic trends in the base case (without new standards) than in any of the standards cases. 

Furthermore, retirements, and efficiency trendsa are dynamic and can differ among product 

classes. Rather than simply extrapolating a current shipments trend, the analysis of the base case 

for each product class (i.e., the case without new standards) uses input variables as drivers, 

including construction forecasts and product lifetime distributions, to forecast sales in each 

market segment. 

To estimate shipments of replacement units, the model utilizes shipments data from 

previous years and assumptions about the 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 determined the useful service life of 

each product class to estimate how many years it is likely to remain in stock. The following 

equation shows how DOE estimated shipments of replacement units.

( ) ( 1) ∑ ∑ ( )

0

1

_ _

_

Rpl j Stock j Ship prob age Rtr

ageMax

age

j

j N

cw = cw j ×

= =

Where:

Stock cw(j-1) = total stock of clothes washers 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.

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. Operating cost is 

dependent on the product age distribution under a standards case scenario that produces 

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

produces a change in purchase price and operating costs, which affects shipments. This effect is discussed further 

in section 9.4.
9-3

increasing efficiency over time, where older, less efficient units may have higher operating costs, 

while younger, more-efficient units will have lower operating costs. As units are added to the inservice stock, some older ones are retired and exit the stock.

DOE calculated total stock of each product by integrating historical shipments data 

beginning with a specific year. The start year depended on the historical data available for the 

product. 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.

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

number of new units purchased the previous year. Slightly more complicated equations, such as 

the following equation, describe how the model accounts for the existing stock of units. 

Stock( j ,age ) Stock( j,age ) [ prob ( age )] Rtr

_ +1 +1 = ? 1

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 in section 8.3. Because the 

products considered in this rulemaking are common appliances that have been used by U.S. 

consumers for a long time, replacements typically constitute the majority of shipments. Most of 

those replacements occur when a unit wears out and fails.

9.3 DATA INPUTS AND MODEL CALIBRATION

As noted above, shipments are driven primarily by the two market segments of new 

construction and replacements.

DOE used two inputs to estimate shipments driven by new construction: new housing 

forecasts and saturation of the product in new housing. 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 

2007, and adopted the projections from the DOE Energy Information Administration (EIA)’s 
9-4

Annual Energy Outlook 2009 (AEO2009) for 2008–2030.1 To determine new construction 

shipments for clothes washer shipments, DOE used forecasts of market saturations combined 

with forecasts of housing starts.

DOE estimated replacements using product retirement functions that it developed based 

on product lifetimes. The retirement function is described in detail in chapter 8. 

DOE designed its shipments model for residential clothes washers by developing a single 

model for all washers and then disaggregating the shipments into its two product classes—frontloading and top-loading clothes washers. DOE developed a cross-price elasticity to estimate the 

market shares of the considered product classes through the forecast period. The Cross-Price

elasticity is covered in Section 9.4.

9.3.1 Historical Shipments

DOE used data on historical shipments (domestic and imports) to calibrate its shipments 

model. It relied on two sources to establish historical shipments: (1) data AHAM provided for 

2002–20052

and (2) data from Appliance Magazine3

Table 9.3.1

for 1988–1998. For 1999–2001, DOE 

interpolated between the shipments for 1998 and 2002. summarizes the historical 

data regarding clothes washer shipments.

Table 9.3.1 Historical Shipments: Domestic plus Imports

Year Shipments Year millions

Shipments Year millionsShipments 

1972

millions

4.754 1985 5.182 1997 6.326

1973 5.158 1986 5.619 1998 6.835

1974 4.631 1987 5.750 1999 7.313

1975 3.944 1988 5.787 2000 7.495

1976 4.194 1989 5.610 2001 7.362

1977 4.639 1990 5.591 2002 7.745

1978 4.732 1991 5.415 2003 8.146

1979 4.667 1992 5.632 2004 8.832

1980 4.308 1993 5.923 2005 9.225

1981 4.136 1994 6.161 2006 9.500

1982 3.826 1995 6.080 2007 8.825

1983 4.431 1996 6.225 2008 8.292

1984 4.945

Sources: 1972-2005: AHAM; 2006-08: AHAM data submittal, 2009.
9-5

9.3.2 Markets and Model Calibration

As described in section 9.2, the market for clothes washers comprises primarily replacement 

units for products that have been retired and units for new housing. Total clothes washers 

shipments are represented by the equation 9.2.1 as represented below:

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

The following sections discuss both the new housing and replacement markets in further 

detail. 

9.3.2.1 New Housing

As described above, DOE forecasted shipments to the new construction market based on

forecasts of housing starts coupled with data on the market saturation of clothes washers. DOE 

then multiplied the housing forecasts by the forecasted saturation of clothes washers for new 

housing units. DOE used historical and forecasted new housing starts to calibrate its model.

Table 9.3.2 presents historical and forecasted new housing starts based on EIA’s 

AEO2009 for 1990–2035.

1 AEO2010 provides three scenarios for housing starts: a reference case

plus cases for high and low economic growth. Table 9.3.2 shows quantities based on all three 

forecasts. DOE used only the forecasts from the reference case to estimate its shipments to new 

construction, however. For 2036−2045, DOE froze completions at the level in 2035.
9-6

Table 9.3.2 Historical and Forecasted Housing Starts 

Year

millions

Reference High Low Year Reference High Low

1990 1.38 1.38 1.38 2018 2.00 2.41 1.59

1991 1.18 1.18 1.18 2019 2.03 2.35 1.55

1992 1.41 1.41 1.41 2020 2.03 2.20 1.42

1993 1.54 1.54 1.54 2021 1.97 2.15 1.36

1994 1.76 1.76 1.76 2022 1.92 2.14 1.31

1995 1.69 1.69 1.69 2023 1.89 2.14 1.29

1996 1.82 1.82 1.82 2024 1.88 2.16 1.28

1997 1.49 1.49 1.49 2025 1.89 2.21 1.28

1998 1.54 1.54 1.54 2026 1.89 2.28 1.26

1999 1.64 1.64 1.64 2027 1.85 2.30 1.24

2000 1.70 1.70 1.70 2028 1.81 2.30 1.20

2001 1.72 1.72 1.72 2029 1.78 2.30 1.17

2002 1.75 1.75 1.75 2030 1.78 2.32 1.18

2003 1.79 1.79 1.79 2031 1.75 2.29 1.17

2004 1.80 1.80 1.80 2032 1.71 2.24 1.14

2005 2.22 2.22 2.22 2033 1.70 2.22 1.13

2006 1.15 1.92 1.92 2034 1.70 2.22 1.13

2007 1.26 1.26 1.26 2035 1.70 2.22 1.13

2008 1.36 1.33 1.33 2036 1.70 2.22 1.13

2009 1.22 1.40 1.40 2037 1.70 2.22 1.13

2010 1.75 2.21 1.62 2038 1.70 2.22 1.13

2011 1.49 1.78 1.28 2039 1.70 2.22 1.13

2012 1.72 2.06 1.47 2040 1.70 2.22 1.13

2013 1.79 2.15 1.51 2041 1.70 2.22 1.13

2014 1.81 2.20 1.53 2042 1.70 2.22 1.13

2015 1.88 2.33 1.56 2043 1.70 2.22 1.13

2016 1.95 2.38 1.59 2044 1.70 2.22 1.13

2017 1.97 2.38 1.60 2045 1.70 2.22 1.13

Source: Energy Information Administration. Annual Energy Outlook, 2010.

DOE used the RECS data on clothes washer ownership in new housing to determine the 

historical saturations. Table 9.3.3 shows the historical saturation of clothes washers in new 

housing units.
9-7

Table 9.3.3 Historical Saturation of Clothes Washers in New Housing Units 

Year Saturation % Year Saturation %

1990 75.1% 1998 88.7%

1991 75.1% 1999 87.5%

1992 75.1% 2000 86.2%

1993 87.0% 2001 85.0%

1994 87.7% 2002 86.5%

1995 88.5% 2003 87.9%

1996 89.2% 2004 89.5%

1997 90.0% 2005 91.0%

Figure 9.3.1 shows the historical variation in saturation in new housing units as well as 

the forecasted saturation after 2005. 

Figure 9.3.1 Saturation of Clothes Washers in New Housing Units

9.3.2.2 Replacements

To determine shipments to the replacement market, DOE used an accounting method that 

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

integrating historical shipments starting from 1972. Over time, some units are retired and 

removed from the stock, triggering the shipment of a replacement unit. Depending on the 

50.0%

55.0%

60.0%

65.0%

70.0%

75.0%

80.0%

85.0%

90.0%

95.0%

1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045

Saturation
9-8

vintage, a certain percentage of units will fail and need to be replaced. To estimate how long a 

unit will function before failing, DOE used a survival function based on the distributions of 

product lifetime. The survival function that DOE used had an average lifetime of 14.2 years. For 

a more complete discussion of clothes washer lifetimes, refer to section 8.2.3 of chapter 8. Figure 

9.3.2 shows the survival function DOE used to estimate replacement shipments.

Figure 9.3.2 Survival Function

9.3.2.3 Early Replacements

DOE also calibrated its shipments model through early replacements. In the historical 

backcast of the model, estimated shipments were more than those indicated by data for new 

housing and replacements through retirements. To calibrate estimated shipments with the 

historical data, DOE introduced into the model a function for the early replacement market. DOE 

assumed that early replacements occur at the rate of 2 and 4 percent of the surviving stock per 

year during 1989-2003 and 2004–2045, respectively. The differential early replacement rates 

match the observed clothes washer stock in new housing reported in the American Housing 

Surveys. The early replacement rate is distributed among products that range from 9 to 30 years

old. DOE weighted those ages by their respective populations in the surviving stock. The 

following equation illustrates the calculations.

∑ ∑

1

4

_

_

_ _

( 1) ( 1, )

( 1, ) ( )

AgeMax

age

age

CW ERRate Stock j Stock j age

Stock j age ER j

=

= × ×

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 5 10 15 20 25 30 35 40 45 50

Years

% Surviving

% Retiring
9-9

Where:

ERCW (j) = number of clothes washers replaced early in year j,

Stock (j-1, age) = number of in-service units of a particular age in year j-1,

ERRate = early replacement rate, and

AgeMax = maximum age of units before they are retired.

9.3.3 Base-Case Shipments

Figure 9.3.3 shows the forecasted shipments of clothes washer in the base case (i.e., the 

case without new energy efficiency standards) and the historical shipments DOE used to 

calibrate that forecast. All shipments of residential clothes washers are represented in Figure 

9.3.33. 

Figure 9.3.3 Historical and Forecasted Shipments for Base Case

9.3.4. Market Share Forecast

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

units in the base case based on available data. For the standards case, both available data and 

cross-price elasticities were used to forecast market share changes. For the base case market 

share forecast, DOE fit a curve to estimate the front-loading market share on the basis of the data 

from NPD and the data submitted by AHAM. Although there are only three data points from 

AHAM on market share, the NPD dataset provides data for additional years. DOE fit an S-curve 

to the six NPD data points to adequately capture the change in market share, with the front0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

1985 1995 2005 2015 2025 2035

Millions

Shipments - Historical and Projected

Historical Shipments

Modelled Shipments
9-10

loading share stabilizing over time, as shown in Figure 9.3.4. Two of the three AHAM points 

show a close fit with the S-curve based on the NPD data.

Figure 9.3.4 Market Share Estimation

DOE performed an analysis of the cross-price impacts on the market share of top-loading

and front-loading clothes washers. Cross-price impacts measure the change in the market share 

of one washer configuration (e.g., top loaders) caused by a change in the price of the other 

washer configuration (e.g., front loaders). 

The logistic regression model equation estimated in our clothes washer analysis:

ln � Market ShareFront

1 − Market ShareFront

�

= −2.985386 + 0.0035452 × PriceTop − 0.0049114 × PriceFront + 4.24347

×

SizeFront

SizeTop

where: 

Market ShareFront

1−Market ShareFront

= the relative probability of the market share of top- and frontloading clothes washers,

PriceTop= monthly sales-weighted average price of top-loaders, 

PriceFront= monthly sales-weighted average price of front-loaders, and

0%

10%

20%

30%

40%

50%

60%

1995

1997

1999

2001

2003

2005

2007

2009

FL Mkt Share

NPD

AHAM

S-Curve

Extrap for Backcast
9-11

SizeFonrt

SizeTop

= ratio of the monthly sales-weighted average of front-loaders tub volume to the 

monthly sales-weighted average of top-loaders tub volume.

The equation indicates that front loader market share is positively correlated with top 

loader price and size and negatively correlated with front loader price. 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, a 10% increase in the mean price of 

front loader washers in the data resulted in a 10.7 % increase in the top-loading market share. 

Thus, the cross-price elasticity on top-loading market share (percent change in top-loading

market share over percent change in front-loading price) is 1.07.

The equation below shows how the shipments model implements the relationship 

between price and market share, the cross-price elasticity. See Appendix 9A for the development 

of the cross-price elasticities.





 



 −  − ×



 



 − = + ×

BC FL

S FL BC FL

pFL qTL BC TL

BC TL

S TL BC TL

pTL qFL S FL BC FL

EP

EP EP MS E

EP

EP EP MS MS E _

_ _

_ _

_

_ _

_ _ _ 1

Where:

MSS_FL = market share in the standards case for front-loaders,

MSBC_FL = market share in the base case for front-loaders,

EpTL_qFL = cross-price elasticity of top-loader price on front-loader market share, which is 

estimated to be 1.07,

EPS_TL = market share in the standards case for top-loaders,

EPBC_TL = market share in the base case for top-loaders,

MSBC_TL = market share in the base case for top-loaders,

EpFL_qTL = cross-price elasticity of front-loader price on top-loader market share, which is 

estimated to be 1.07,

EPS_FL = market share in the standards case for front loaders,

EPBC_FL = market share in the base case for front loaders,

Figure 9.3.5 shows forecasted base and standards case market share of clothes washers 

disaggregated by the two product types. The figures show the standards case for top-loading and 

front-loading clothes washers, TSL 3. Given the direct correlation between price and market 

share, as long as the price changes the market share will also continue to change.
9-12

Figure 9.3.5 Forecast of Market Share in Base Case and Standards Case TSL3

for Front-Loading (CSL5) and for Top-Loading (CSL6)

9.4 EFFECTS OF PURCHASE PRICE, OPERATING COSTS, AND 

HOUSEHOLD INCOME

DOE conducted a literature review and an analysis of appliance price and efficiency data 

to estimate the combined effects on product shipments from increases in product purchase price, 

decreases in product operating costs, and changes to household income. Appendix 10A explains 

in detail the method DOE used to quantify the effects of the above variables.

DOE found only a few studies of appliance markets that are relevant to this analysis and 

identified no studies that use time-series data of product price and shipments data after 1980. The 

information that can be derived from the literature suggests that the demand for appliances is 

price-inelastic (i.e., price does not affect demand). Other information in the literature suggests 

that appliances are a normal good, so that rising incomes increase the demand for them. Finally, 

the literature suggests that consumers use relatively high implicit discount ratesb when 

comparing the price of an appliance to its operating costs. For this analysis, DOE did not 

consider the impacts of consumer rebate programs.

 b A high implicit discount rate with regard to operating costs means that consumers place little economic value on 

the savings in operating costs realized from more efficient appliances. In other words, consumers are much more 

concerned with higher purchase prices than with lower operating costs.
9-13

DOE found too few data on product purchase price and operating costs to perform a 

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

efficiency data specific to residential refrigerators, clothes washers, and dishwashers during

1980–2002 to evaluate broad market trends and conduct simple regression analyses. Those data 

indicate that during that period shipments of appliances increased while purchase price and 

operating costs declined. In addition, household income rose during that period. To simplify the 

analysis, DOE combined the available economic information into one variable, termed the 

relative price. DOE used that variable to analyze market trends, as well as to conduct a

regression analysis. DOE used the following expression to define relative price.

Income

PP PVOC

Income

TP RP + = =

Where:

RP = relative price,

TP = total price,

Income = household income,

PP = appliance purchase price, and

PVOC = present value of operating costs.

In the above equation, DOE used an implicit discount rate of 37 percent to determine the 

present value of operating costs.

DOE’s analysis of market trends suggests that the demand for clothes washers is 

relatively price inelastic (that is, has an elasticity less than 1.0). DOE’s regression analysis 

suggests that the relative price elasticity of demand is -0.34. Thus, 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 effects of three factors (purchase price, operating costs, 

and household income), the impact from any single effect is mitigated by changes in the other 

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

DOE nevertheless stresses that the measure is based on applying simple statistical analysis to a 

small data set. More importantly, the measure is based on the 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’s analysis did not 

account for them. Despite the uncertainties, DOE believes that its estimate of the relative price 

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

costs, and household income have on shipments of clothes washers.

Because DOE’s forecasts of shipments and national impacts attributable to standards 

pertain to a 30-year period, it needed to consider how the relative price elasticity is affected after 

a new standard takes effect. DOE considered the relative price elasticity described above to be a 
9-14

short-term value. It was unable to identify sources specific to household durable goods, such as 

appliances, to indicate how short- and long-term price elasticities differ. Therefore, to estimate 

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

automobiles.4

Table 9.4.1

That study showed that the price elasticity of demand for automobiles changes in 

the years following a change in purchase price. As the number of years increases, the price 

elasticity decreases until it reaches a terminal value at about the 10th year after the price change. 

shows the relative change in the price elasticity of demand for automobiles over 

time. DOE developed a time-series of relative price elasticities of demand for residential clothes 

washers based on the relative change in the automobile price elasticity. For years not shown in 

Table 9.4.1, DOE performed a linear interpolation to obtain a relative price elasticity.

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

Years Following Price 

Change

Change in Relative Price Elasticity 

1 2 3 5 10 20

Change Relative to First 

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

DOE used the following equation to estimate shipments under each standards case for the

two product classes of clothes washers. The equation incorporates the effect of the relative price 

into the forecast of base-case shipments. In the equation, the relative price and the relative 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 × ∆

Where:

ShipSTD_p(j) = total shipments of product p in year j under a given standards case;

RplBASE_p(j) = units of product p retired and replaced in year j under the base case;

NIBASE_p(j) = number of new construction installations of product p in year j under the base 

case;

MBASE_p(j) = units of product p installed in market M in year j (M represents early 

replacements) under the base case;

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

ΔRP(j)= change in relative price due to the given standard in year j.

9.5 AFFECTED STOCK

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

energy efficiency standard. In addition to the forecast of product shipments under both the base 

case and each trial standard level (TSL), a key output of DOE’s shipments model is the affected 
9-15

stock, which represents the difference in the stock under the base case and each TSL. DOE 

calculates the affected stock to quantify the effect attributable to a TSL that new product 

shipments have on the appliance stock. The affected stock therefore consists of those in-service 

units that are purchased in or after the year a standard takes effect, as described by the following 

equation.

∑

_

1

_

( ) ( ) ( )

j Std yr

age

p p p Aff Stock j Ship j Stock age

=

= +

Where:

Aff Stockp(j) = affected 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 affected units (years), and

Std_yr = effective date of the standard.

As the above equation shows, to calculate the affected stock DOE must define the 

effective date of the standard. For the NES and NPV results presented in chapter 10, DOE 

assumed that new energy efficiency standards would become effective in 2015. Thus, all 

appliances purchased beginning on the first day of 2015 would be affected by the standard level. 

9.6 RESULTS

The following sections show the shipments forecasts for a selective set of TSL

combinations for front- and top-loading washers of all the levels that DOE considered for each 

product class of clothes washers.

This section presents the shipments forecasts for the TSLs that DOE considered for each 

of the product classes of clothes washers. Table 9.6.1 shows a selective set of TSL combinations

for both front-loading (FL) and top-loading (TL) clothes machines in both standard and compact 

sizes. For standard sizes, TSL 1 consists of the efficiency level at two levels from the base level. 

TSL 2 represents an intermediary point between the efficiency levels chosen for TSL 1 and the 

efficiency levels recommended in the Joint Petition. TSL 3 consists of the efficiency levels 

recommended in the Joint Petition. In the case of TSL 3, for top-loading standard clothes 

washers, one set of values would apply starting in 2015, and another set would apply starting in 

2018. TSL 4 consists of the efficiency levels that are one level below the max-tech efficiency 

levels. TSL 5 consists of the max-tech efficiency levels. For top-loading compact size clothes 

washers, TSL 1 through TSL 3 consist of the efficiency level at one level from the base level, 

and TSL 4 and TSL 5 consist of the efficiency level at two levels form the base level. For frontloading compact size clothes washers, TSL 1 through TSL 5 consist of the efficiency level at one 

level from the base level.
9-16

TSL 3 represents the consensus agreement level and is a tiered efficiency level. Until 

2018, the efficiency level for top-loading standard size clothes washers would have an IMEF of 

1.29; from 2018 forward, the IMEF level would become 1.57. Table 9.6.2 shows the cumulative 

impacts on shipments during 2015–2044 from the selective set of TSL combinations for frontloading and top-loading standard clothes washers. For all TSL combinations, shipments are 

forecasted to decrease; that is, the effects of an increased purchase price offsets the effects of 

decreased operating costs, resulting in a net decrease in shipments. The table provides the

modified energy factor (MEF), the integrated modified energy factor (IMEF), which both are the 

cubic feet of washer capacity per kilowatt-hour per cycle, associated with each TSL. It also lists 

the integrated water factor (IWF), which stands for the gallons per cubic foot of washer capacity 

associated with each standard level.

Table 9.6.1 Front- and Top-loading Clothes Washers: TSL Combinations for Analysis

Trial Standard Level

Standard Size Compact Size

TSL

Top-Loading Clothes 

Washer

Front-Loading Clothes 

Washer

Top-Loading Compact 

Clothes Washer

Front-Loading Compact 

Clothes Washer

1 2 2 1 1

2 4 5 1 1

3 5 2 until 2018 and then 6 1 until 2018 then 2 1

4 7 7 2 1

5 8 8 2 1

Table 9.6.2 Front- and Top-loading Clothes Washers: Cumulative Effects of Standards 

on Shipments, 2015–2044

Standard Size Compact Size

Cumulative 

Shipments 

million

MEF/IMEF/IWF (cu.ft/kWh/cycle gal/cu.ft)

TSL Top-Loading Front-Loading

Top-Loading 

Compact

Front-Loading 

Compact

Base 330.3

1 1.72/1.29/8.44 1.72/1.41/8.31 1.26/0.86/14.40 1.72/1.13/8.30 330.1 (-0.1%)

2 1.80/1.37/7.95 2.00/1.66/6.26 1.26/0.86/14.40 1.72/1.13/8.30 329.6 (-0.2%)

3 2.00/1.57/6.47 2.20/1.84/4.73 1.26/0.86/14.40 1.72/1.13/8.30 328.8 (-0.5%)

4 2.26/1.83/4.96 2.60/2.20/4.01 1.81/1.15/12.00 1.72/1.13/8.30 325.0 (-1.6%)

5 2.47/2.04/4.10 2.89/2.46/3.39 1.81/1.15/12.00 1.72/1.13/8.30 323.6 (-2.0%)

Note: Figures in parenthesis indicate % change in cumulative shipments from the base case.
9-17

REFERENCES

 1 U.S. Department of Energy-Energy Information Administration. An Updated Annual Energy 

Outlook 2009 Reference Case Reflecting Provisions of the American Recovery and 

Reinvestment Act and Recent Changes in the Economic Outlook, April, 2009. Washington, 

DC. SR/OIAF/2009-03.

<http://www.eia.doe.gov/oiaf/servicerpt/stimulus/pdf/sroiaf(2009)03.pdf>

2 Association of Home Appliance Manufacturers. AHAM Data on Commercial Clothes 

Washers for DOE Efficiency Standards Rulemaking. October 12, 2006. Letter to Building 

Technologies Program, U.S. Department of Energy.

3 Statistical Review. Appliance Magazine. April 1998 and 1999.

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

Economic Activity. 1971. (1): pp. 234–239.