9

- i CHAPTER 9

. SHIPMENTS ANALYSIS

TABLE OF CO NTENTS

9.1 INTRODUCTION

................................ ................................ ................................ ....... 9

- 1

9.2 METHODOLOGY

................................ ................................ ................................ ...... 9

- 1

9.3 DATA INPUTS AND MODEL CALIBRATIO N

................................ ........................ 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 EF FECTS OF PURCHASE PR ICE, 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

Ta ble 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 FIGURE S

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

- 129-1 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 calculati ng national energy savings (NES) and net present v alue (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 rulemaking s

. This chapter

describes DOE’s method and results of projecting annual shipments for front

- loading and top

loading 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 co st s , and household income on the consumer purchase decision.

In estimating shipments, the m odel 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 accessib le 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 cost s , and household income on shipments; and section 9. 5 discusses the affected stock of products

. S ection 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 ( T SLs ) 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 segment s as distinct input s to the shipments foreca st. As represented by the following equation, the two primary market segments are new installations and replacements.9-2 ) ( ) ( ) ( j NI j Rpl j Ship

cw cw cw **+ =** 

Where:

Ship

cw (j) = t otal shipments of clothes washers in year j

, Rpl

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

, and

NI

cw (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, retirement s , and efficiency trends a are dynamic and can differ among product

classes. Rather than simply extrapolating a current shipm ents 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 utilize s 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

_ _ _
age prob Ship j Stock j Rpl
Rtr ageMax

age j

N j j cw cw **× =** 

**= =**  Where:

Stock

cw (j

- 1) = total stock of clothes washers in year j

- 1

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

N = year in which the mod el 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 NP V 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, les s efficient units may have higher operating costs, while younger, more

- efficient units will have lower operating costs. As units are added to the in

service 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 shipme nts, DOE developed a series of equations that define the dynamics and accounting of stocks. For new units, the equation is:

) j ( Ship ) age , j ( Stock 1 = 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 follow ing equation, describe how the model accounts for the existing stock of units.



# [ ] ) age ( prob ) age , j ( Stock ) age , j ( Stock 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, p rob Rtr (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 MODE L 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

200 7, and adopted the projections from the DOE Energy Information Administ ration (EIA)’s9-4 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 usin g 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 t hen disaggregating the shipments into its two product classes

— front

loading and top

- loading clothes washers. DOE developed a cross

- price elasticity to estimate the

market share s of the considered product classes through the forecast period. The Cross

- Price elasticity is covered in Section 9. 4

.

9.3.1 H istorical 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

– 2005 2 a nd (2) data from Appliance Magazine 3

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 million s Shipments Year million s Shipments

1972 million s

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 6.161 200 6 9.500

1982 3.826 1995 6.080 200 7 8.825

1983 4.431 1996 6.225 2008 8.292

1984 4.945

Source s: 1972

- 2005: AHAM; 2006

- 08: AHAM data submittal, 2009.9-5 9.3.2 Markets and Model Calibration

As described in section 9.2, t he 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 represente d below:

) ( ) ( ) ( j NI j Rpl j Ship 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 forecast ed shipments to the new construction market based on forecasts of housing starts coupled with data on the market saturation of clothes washer s . DOE

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

. DOE used historical and forecasted new housing star ts to calibrate its model.

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

AEO200 9 for 1990

– 203 5

. 1 AEO20 10 provid es three scenarios for housing starts: a r eference case plus cases for h igh and l ow e conomic g rowth. Table 9.3.2 shows q uantities based on a ll three

forecasts

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

construction , however

. For 203 6 −204 5 , DOE froze completions at the level in 203 5

.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, 20 10

.

DOE us ed 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 2045Saturation9-8 vintage, a certain percentage of unit s will fail and need to be replaced. To estimat e how long a unit will function before fail ing , 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, e stimated 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

matc h the observed clothes wa s her stock in new housing reported in the American Housing Surveys. The early replacement rate is distributed among products that rang e from 9 to 30 years old

. DOE weighted tho se ages by their respective popu lation s in the surviving stock. The following equati on illustrates the calculations.



## ∑ ∑ 1

4 _

_ _ _ ) 1 ( )

, 1 ( )

, 1 ( ) ( AgeMax

age

age CW j Stock ERRate

age j Stock age j Stock j ER

**= ×**  **× =**  0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0 5 10 15 20 25 30 35 40 45 50

Years % Surviving

% Retiring9-9 W here:

ER C W (j) = n umber 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 = e arly replacement rate, and AgeMax = m aximum age of unit s before they are retire d

.

9.3.3 Base

- Case Shipments

Figure 9.3.3 shows the forecaste d 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 th at forecast. A ll shipments of residenti al clothes washers are represented in Figure

9.3.3 3

.

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 dat a for additional years. DOE fit an S

- curve to the six NPD data points to adequately capture the change in market share, with the front

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

1985 1995 2005 2015 2025 2035Millions 

### Shipments

- Historical and Projected

Historical Shipments

Modelled Shipments9-10 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

- c urve 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

- load ing

and front

- load ing clothes wash ers

. 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 regress ion model equation estimated in our clothes washer analysis:

ln � Market S h are Front
1

− Marke t S h are Front �

=
− 2

. 985386 + 0

. 0035452 × Price Top − 0

. 0049114 × Price Front + 4

. 24347

× Size Front
Size Top

where:

Market S h are Front

1

− Market S h are Front = the relative probability of the market share of top

- and front

load ing clothes washers,

Price Top = monthly sales

- weighted average price of top

- loaders,

Price Front = monthly sales

- weighted average price of front

- loaders, and 0% 10% 20% 30% 40% 50% 60%

1995 1997 1999 2001 2003 2005 2007 2009FL Mkt Share NPD

AHAM

S-Curve

Extrap for Backcast9-11 Size Fonrt

Size Top = ratio of the monthl y 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 was hers in the data resulted in a 10.7 % increase in the top

- loading market share. Thus, the cross

- price e lasticity on top

- loading market share (percent change in top

- loading

market share o ver 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.

** **  ** **  ** ** 

**− ×** 

**− **  ** **  ** **  ****

**− ×**  **+ =** 

FL BC FL BC FL S

qTL pFL TL BC

TL BC TL BC TL S

qFL pTL FL BC FL S EP EP EP E MS EP EP EP E MS MS

_ _ _

_ _

_ _ _

_ _ _ 1

Where:

MS S_FL = market share in the s tandards case for front

- loaders,

MS BC _FL = market share in the base case for front

- loaders,

E

pTL_qFL = cross

- price elasticity of top

- loader price on front

- loader market share, which is
estimated to be 1.07,

EP S_T L = market share in the standards case for top

- loaders,

EP BC

_ T

L = market share in the base case for top

- loaders,

MS BC

_ T

L = market share in the base case for top

- loaders,

E

p F

L_q T L = cross

- price elasticity of front

- loader price on top

- loader market share, which is estimated to be 1.07,

EP S_FL = ma rket share in the standards case for front loaders,

EP BC _FL = market share in the base case for front loaders,

Figure 9.3.5 show s 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, T SL 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 TSL 3

for Front

- Loading (CSL5) and for Top

- Loading (CSL6)

9.4 E FFECTS OF PURCHASE PRICE, OPER ATING COST S , 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 purch ase price,

decreases in product operating costs, and changes to household income. Appendix 10 A 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 d ata after 1980. The

information that can be derived from the literat ure 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, s o that rising incomes incre ase the demand for them. Finally, the literature suggests that consumers us e relatively high implicit discount rates b 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 co st s to perform a thorough analysis of dynamic changes in the appliance market. Rather, it use d purchase price and efficiency data specific to residential refrigerators, clothes washers, and dishwashers during

1980

– 2002 to evalua te broad market trends and c onduct simple regression analyse s. Th o se data

indicate that during that period shipments of appliance s increased while purchase price and operating cost s declined

. In addition, h ousehold 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 analy ze market trends, as well as to conduct a regression analysis. DOE used t he following expression to define relative price

.

Income PVOC PP

Income TP RP **+**

**= =** 

Where :

RP = relative price,

TP = total price,

Income = household income,

PP = appliance purchase price, and

PVOC = present value of operating cost s

.

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

, ha s an elasticity less than 1.0). DOE’s regression analysis suggests that the relative price elast icity of demand is

- 0.34. Thus, f or 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 cost s
, 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 important ly , 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 househo ld 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

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

cost s , 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 a9-14 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 Th at 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 10 th 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 F ollowing a Change in Purchase Price

Years Following Price Change Change in Relative Price Elasticity

1 2 3 5 10 20
Change Relative to First

Y ear 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

t wo product classes of clothes washers . The equation incorporat es the effect of the relative price

into the forecast of base

- case shipments. I n the equation, the relative price and the relative price elasticity are functions of the year

, because both change with time.


# ( **)** 

# ( **)** ) ( ) ( 1 ) ( ) ( ) ( ) (

_

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

W here:

Ship STD_p (j) = t otal shipments of product p in year j under a given standards case ; Rpl BASE_p (j) = units of product p retired and replaced in year j under the base case ;
NI BASE_p (j) = number of new construction installations of product p in year j under the base

case ;
M BASE_p (j) = units of product p installed in market M in year j ( M represents early replacements) under the base case ;

e RP (j)= relative price elasticity in year j ( equals

- 0.34 for year 1 ); and

Δ RP(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 ( T SL)

, a key output of DOE’s shipments model is the affected9-15 stock

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

. DOE

calculates t he 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 pu rchased in or after the year a standard take s effect, as described by the following equation

.



# ∑ _

1 _ ) ( ) ( ) ( yr Std j

age p p p age Stock j Ship j Stock Aff

**= +**  **=**

Where :

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

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

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

, age = age of the aff ected 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 201 5 . 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

combination s for fro nt

- 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 TSL s 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 level s 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 consis ts 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 front

loading 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 t op

- 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 show s the cumulative impacts on shipments during 2015

– 204 4 from the selective set of TSL combination s for front

loading and top

- loading standard clothes washers . For all TSL combinations , shi pments are
forecasted to decrease ; that is, the effects of an increase d pu rchase price offset s 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 ( I MEF), 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 ( I WF), which stand s for the gallons per cubic foot of washer capacity

associated with ea ch standard level.

Table 9.6.1 Front

- and Top

- loading Clothes Washers: T SL 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

– 204 4

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 3 29

. 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 32 8

. 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 3 2 5

. 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 3 2 3

. 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 Spendi ng: Explanation and Prediction. Brookings Papers on

Economic Activity

. 1971. ( 1 ): pp. 234

– 239.