US. Department of Energy 

CLOTHES WASHER SHIPMENTS MODEL: Draft 

TABLE OF CONTENTS 

1.1 OVERVIEW 

1.1.1 Definition of Market Segments and Ownership Categories 

1.1.2 Recent Enhancements of Shipments Model 

1.1.3 Review of Other Published Research 

1.2 METHOD 

1.2.1 Definitions 

1.2.1.1 Stock 

1.2.1.2 Events 

1.2.1.3 Decisions 

1.2.2 New Housing 

1.2.2.1 Definition 

1.2.2.2 Approach 

1.2.2.3 Current Assumptions 

1.2.3 Existing Housing with a Regular Washer 

1.2.3. I Definition 

I .2.3 .2 Approach 

I .2.3.3 Current Assumptions 

I .2.4 Housing without a Washer 

1.2.4.1 Definition 

1.2.4.2 Approach 

1.2.4.3 Current Assumptions 

1.2.5 Housing with an Extended-Life Washer 

1.2.5.1 Definition 

1.2.5.2 Approach 

I .2.5.3 Current Assumptions 

1.2.6 Accounting Equations 

I.3 MODEL 

1.3 .1 Lo git Equation Description of Decision Probabilities 

I .3. I . I Logit Equation 

I .3 .12 Utility coefficients and elasticity 

1.3.2 Clothes Washer Consumer Analysis 

I .3 .3 Stated vs. Revealed Preferences. 

1.3 .4 Determination of Decision Sensitivities 

1.3.4.l Price Sensitivity 

1 

June 1999 
1.3 .4.2 Savings/Operating Cost Sensitivity 

1.3.4.3 Features Sensitivity 

1.3.5 Calibration of Shipments Model 

1.4 RESULTS 

1.4.1 Sales impacts of Standards-Induced price changes. 

1.4.1.1 New Clothes Washers 

1.4.1.2 Used Clothes Washers 

1.4.2 Impacts on mean age of washers, used market, and washer repairs. 

1.4.3 Model Sensitivities. 

1.4.3.1 Price Sensitivity 

1.4.3.2 Operating Cost Sensitivity 

1.4.3.3 Features Sensitivity 

l.5 CONCLUSIONS 

1 .6 REFERENCES 

2 
1.1 OVERVIEW 

Clothes washer shipment estimates are a necessary input for manufacturer impact analysis and 

national energy savings calculations. In the Advanced Notice of Proposed Rule making 

(ANOPR), we examined several different approaches to forecasting new washer sales. The 

investigated models include an Auto-Regressive Moving Average Model (ARIMA), a MultiV ariate Time Series Fit, a Saturation/Lifetime Model, and an Accounting Model with elasticity. 

Of the different approaches, we selected the Accounting Model because it was the most fullfeatured model which included price and operating cost elasticities. 

In this document, we describe a revised accounting model for projecting annual clothes 

washer shipments that includes the following factors: 

• 

• 

• 

• 

• 

combined effects of price, operating cost, and features on annual U.S. shipments 

mar:ket segments (e.g., new housing, replacement decisions, non-owner adding a 

washer) 

decisions to repair rather than replace 

purchases of used washers 

age categories of clothes washers 

This Clothes Washer Shipments Model incorporates information from the DOE Consumer 

Analysis. Since the ANOPR, DOE has gathered additional information about features of clothes 

washers that influence consumers' purchase decisions, and analyzed consumer's stated 

preferences. This new information also has been calibrated with updated information about 

historical purchases. .. ·· 

1.1.1 Definition of Market Segments and Ownership Categories in the Shipments 

Model 

This clothes washer shipments model described in this document segments both clothes 

washer owners (i.e. households) and clothes washer purchases into different categories. The 

different types of clothes washer owners include (1) new housing, (2) existing housing with a 

regular1 washer, (3) housing without a washer, and (4) housing with an extended life washer. We 

refer to the population of clothes washers in each ownership category as the stock of clothes 

washers of that category. 

The different types of clothes washer owners are faced with different clothes washer purchase 

decisions and purchase motivations. The reason for buying a clothes washer determines the 

lvfarket Segment that the purchase represents. The different types of clothes washer purchases are 

divided into six separate market segments as follows: 

1

Regular meaning a washer that has not undergone an "extended repair" 

3 
1. New Housing Market: When there is a net increase in the housing stock, the increase 

in the number of households will force the purchase of new clothes washers. 

2. Early (Discretionary) Replacement Market: Even before a clothes washer breaks 

down, about 27% of clothes washer owners replace the existing clothes washer 

because they want an updated model, because of remodeling, or for other 

miscellaneous reasons. 

3. Regular Replacement Market: Most clothes washer purchases result from the 

replacement of an existing washer that has broken down after the completion of its 

useful life. 

4. Extra Repair Market: Under conditions of high costs for new clothes washers a few 

consumers will rebuild or repair a broken down washer (thus extending its lifetime) 

rather than purchasing a new clothes washer. Eventually, even extended life washers 

breakdown and are replaced 

5. Non-owner to owner conversion market: A few households without a clothes washer 

will purchase a clothes washer and become new clothes washer owners. 

6. Used clothes washer purchases market: For many clothes washer purchases, the 

consumer will have the additional decision of whether to purchase a new or used 

machine. There is a significant used clothes washer market (18% of total sales) that 

can interact with the market for new clothes washer purchases. (Source: NFO 

Research Inc.) 

Figure 1 shows the structure of the model. The boxes represent the different types of clothes 

washer owners and households, while the diamonds represent the different decisions that are 

made by the consumer and how the results of the decisions feed into other elements of the model. 

In the model, the stock of existing washers is categorized in terms of ownership or household 

category. Several different types of owners may participate in a particular market segment, and 

each ownership category may participate in one to several market segments. Each market 

segment is modeled by a probability function which represents the likelihood of a particular 

consumer decision. Economic decision variables (such as price, operating cost savings and the 

foatures available for new clothes washers) influence the magnitude of these decision probabilities. 

The clothes washer shipments model keeps track of the population of each type of clothes 

washer and clothes washer purchase. The model is run with an annual time step. Thus, annual 

purchases represent the incremental changes in clothes washer stocks for each time period. The 

flow diagram in Figure 1 represents the process of taking an initial stock of washers of the four 

different categories, calculating the purchases induced by this initial stocks of clothes washers, 

and calculating the new stock levels that result. The rectangles represent the different ownership 

4 
categories, the arrows represent the stock flows of clothes washer households, and the diamonds 

represent the decisions that these households are making in the course of a year. 

To carry out one year's calculation, one starts in a rectangle with the amount of clothes 

washers in that category. Then one flows out in the direction of the arrow until one arrives at a 

diamond that represents a decision. For each decision there is an inflow of one arrow and an 

outflow of two arrows. One apportions the stock according to the probability function that 

Houses with 

Washers 

Houses with 

Extended Lifetime 

Washers 

New Houses 

Housesw/o 

Washers 

No 

Yes 

Replace 

~--Repair---< 

Yes 

t 

No 

Buy New Washer 

New 

Used 

Regular 

ra Repair __.. Houses 

,----------No-----

Yes 

>-----------~Yes 

~------~No-----­

.--------~No------

Yes 

New 

Used 

~ New 

Used 

with 

Extended 

Lifetime 

Washers 

Housesw/o 

Washers 

Figure 1 Flow Diagram for Clothes Washer Shipments Model 

5 

-

-

-

-

Houses 

with 

Washers 

; 

I 

; 

:::-
describes the proportion of washers that are subjected to each outcome. One keeps flowing 

through the diagram until one arrives back at a shaded rectangle that represents a stock category. 

The result is the number of washers that have flowed from one stock to another stock in the 

course of one year. To get the total stock at the end of the year, one adds up the contribution 

from all possible flow diagram paths. In the model this process is repeated each year until the 

year 2030. 

Consumer decisions influence how the stock and supply of clothes washers flow from one 

category to another. Decisions which are economically influenced are modeled with econometric 

equations. The parameters of these econometric equations are calibrated with industry statistics 

on historic shipments and are also calibrated with market information from both the AHAM/NFO 

survey and the Clothes Washer Consumer Analysis. 

The decisions to which each category of households (and their clothes washers) are subjected 

are described below: 

Net new households are those households which represent a net increase in housing stock 

(new housing construction less housing stock removed from the market). These households are 

faced with the decision of whether or not to get a new clothes washer with the house. 

For households with existing regular washers, the first question is whether or not the current 

washer is having operational problems (i.e. needs repair). If the washer is without problems then 

1he consumer must decide if he or she wants to purchase a washer for other discretionary reasons. 

If the washer has operational problems, then the consumer must decide ifthe washer is to be 

repaired or replaced. If the consumer makes an extra repair, one which avoids the purchase of a 

new washer, then the model assumes that that repair extends the washer lifetime by 6 years. 

For households without washers a small fraction (at most a few percent) of consumers will 

decide to become clothes washer owners. Those who become owners will do so by purchasing 

c::ither a new or used clothes washer. 

Households with extended lifetime washers are those households that have extended the 

lifetime of their washer through an extra repair when the washer last broke down. If the clothes 

washer breaks down yet again, the consumer will have to have it replaced with either a new or 

used machine. 

In section 1.1.2 we compare the current modeling approach with the models that were 

e:xamined in the ANOPR analysis. In section 1.1.3 we review the economics durables sales 

forecasting literature; section 1.2 describes the details of the mathematical structure of the model, 

while section 1.3 discusses the modeling of economic consumer decisions, and section 1.4 

presents the model results. 

6 
1.1.2 Recent Enhancements of Shipments Model 

Since publication of the Technical Support Document (TSD) for the Advanced Notice of 

Proposed Rule making (U.S. Department of Energy, 1998), we have made several improvements 

to the clothes washer shipments forecast. These improvements include the following: 

Detailed accounting of different market segments and washer ownership categories: Previous 

shipments models accounted for only the new clothes washer market and the replacement 

market. The previous model assumed that a washer was replaced by a new washer when it 

broke down. The current model now accounts for a variety of other market dynamics 

including options to purchase new vs. used washers, changes in repair behavior, and extending 

the life of washers through extra repairs. 

Price and operating cost elasticities calibrated to historical data: The model now includes 

consumer responsiveness to price and operating costs calibrated to historical clothes washer 

shipments. The operating cost response relative to the price sensitivity is calibrated to 1997 

purchase decisions and the current engineering analysis. 

Consumer response to the front-loading feature is included: The model includes a consumer 

response to whether top-loading machines are available. Elasticity with regards to the frontloading vs top-loading feature is adapted from the recent Clothes Washer Consumer Analysis. 

Removal ofthe income elasticity: We assumed no income elasticity, for consistency with the 

Clothes Washer Consumer Analysis. 

Utilization of a wide variety of data sources: The current shipments model utilizes a wide 

range of information to make the model reflect current consumer and market characteristics: 

• Clothes Washer Consumer Analysis results for both the relative size of consumers 

response to features relative to their response to price and operating expense, and to 

estimates of the rate at which clothes washer owners might drop out of the market. 

• AHAM/NFO survey data on the proportion of early (discretionary) replacements, and on 

the proportion of new vs. used purchases. 

• AHAM statistics on historical shipments and on the recent (post 1994 standard) changes 

in mean clothes washer efficiency. 

• Consumer Reports data on repair rates of washers. 

The purpose of these model enhancements is to provide the best estimates possible for future 

clothes washer shipments that are consistent with the recent history of washer shipments, and with 

current clothes washer market structure and consumer preferences. 

7 
1.1.3 Review of Other Published Research 

We performed a review of recent literature on forecasting purchases of consumer durables in 

order to evaluate studies regarding price and features sensitivities and their application to long 

term sales forecast models. We report on eight relevant studies published from 1990 to the 

present. 

In this literature, a standard measure of consumer sensitivity to features of the products and 

the market is sales elasticity. Elasticity is the parameter that relates the relative change in sales 

relative to a change in a feature (such a price, P). For example: 

s = (~SI s)/( ~P/ P) Eq. 1-1 

where MIS is the relative change in sales, APIP is the relative change in price, and & is the 

elasticity. Elasticities are generally negative numbers ranging from 0 to -3. A product which has 

an elasticity -2 will experience a 2% drop in sales for a 1 % increase in price. 

According to the marketing and sales forecasting literature, consumer price response and 

ielasticity varies dramatically depending on the type of trade-offs being made, the time scale over 

which sales variations are being measured, the type of durable being examined and the stage of 

development of the particular durables market in question. 

The greatest price sensitivity is observed when consumers are being asked to make trade-offs 

between price, brand, and features in an unconstrained market where the consumer has the. choice 

of different brands and makes of product. In this context, which is most relevant to marketing 

decisions, the choice of from whom to buy a product is highly sensitive to the price being charged 

by a particular manufacturer. Price/features trade-offs are typically applied to set prices for 

different product classes according to the overall value that consumers place on other features 

relative to price (e.g. Dolan, 1996). 

In the long-term sales forecast literature, elasticities are much smaller than those observed in 

~:hort term sales or product choice applications. These differences in estimated elasticity reflect 

the difference between a long-term perspective (whether to own a washer) and a short-term one 

(which washer to purchase and when to buy). Furthermore, durables undergo a time dependent 

price sensitivity as they go from introduction to acceptance in the overall market (Dipak & Rao, 

1990; Parker, 1992; and Golder & Tellis, 1998). Research that examines the change in elasticities 

over time (Parker, 1992) finds that for clothes dryers and appliances that are deemed 'necessities' 

(i.e. have a high market penetration) that 'elasticities are either constant, not statistically different 

from zero, or decline toward the later stages of the adoption life cycle (Parker, 1992). These 

results are based on fitting models with elasticity, to the historic~ data on shipments and sales of 

major appliances. 

8 
Since the introduction of standards could potentially cause long-term structural changes in 

prices and features, we consider the results from the long-term sales forecast literature most 

relevant to the present clothes washer shipments modeling effort. It is expected that elasticities 

will be smaller than what is found when consumers are evaluating brand or features choices. 

Calibrating elasticities to fit historical sales data is present practice in the long-term sales forecast 

modeling literature. 

1.2 METHOD 

1.2.1 Definitions 

The model is organized in terms of three classes of items: Stocks, Events, and Decisions. 

These different classes are defined as follows. 

1.2.1.1 Stock 

A Stock is the number of households with a particular washer of a particular ownership 

category. The main property of a stock is that it evolves over the course of the year by aging one 

year and by increasing or decreasing in response to inflows and outflows produced by events and 

decisions. The four permanent stocks in the model are new households, households with washers, 

the households without washers, and households with rebuilt or extended-life washers. In 

addition to the permanent stocks, there are temporary stocks of washers in need of repair, 

repaired washers, rebuilt washers, washers purchases used, and retired washers. All of the 

temporary stocks are allocated to one of the four permanent stocks within the one year 

computational time step of the model. 

1.2.1.2 Events 

Events are things that happen to a stock that can change the status of a portion of that stock, 

but do not depend on economic conditions. Events do not depend on market conditions, but are 

dependent on the properties of the stock. The main event in the model is washer problem 

development or breakdown. For regular clothes washers, whether or not a washer develops 

problems that require a repair is an event. For extended-life washers, whether the washer suffers 

from a final breakdown is another event. 

l..2.1.3 Decisions 

Decisions are consumer reactions to events and market conditions. Decisions are described in 

terms of probabilities that typically depend on the type of stock, the age of the clothes washer, the 

incremental cost of the decision, and market conditions. The probability of two subsequent 

decisions in the same year is equal to the product of the two individual decision probabilities. The 

dependence of decision probabilities on price and market conditions is given by a standard 

econometric logit equation: 

9 
In( Prob/ ( 1 - Prob)) = a +b * (Price )+c * (Operating Cost )+d * {Feature Index) Eq. 1-2 

where Prob is the probability of the decision, and where the right hand side of the equation 

represents the utility of the decision. The coefficients b, c, and d represent sensitivities that the 

consumer has for the different aspects of the economic decision. The constant term a is an offset 

for the utility which calibrates the utility to the value of the market share in a reference year. 

These coefficients are determined through a combination of assumptions about consumer 

behavior, based upon studies regarding consumer preferences, and model calibration with historic 

shipments data. 

The details of model calibration and selection of parameters for the consumer decision model 

are presented in Section 1.3 on modeling economic decisions. 

1.2.2 Purchases from Net New Housing 

l.2.2.1 Definition 

Purchases from net new housing are defmed as those purchases that arise from a net increase 

in the total housing stock. 

Jl.2.2.2 Approach 

The decision tree shown in Figure 2 illustrates the approach taken for modeling these 

purchases. 

Buy New 

Washer 

Join Houses 

without a Washer 

Figure 2 Decision Tree for New Housing Purchases. 

10 
Data is available for the market saturation of new households with washers up to 1994. This 

market share is projected into the future using a logit probability of purchase equation as 

described in section 1.3. 

The equations for estimating the purchases from new housing are as follows: 

where: 

1.2.2.3 

CW New/NewHomes 

Prob New Homes 

.6.House stock 

CW Used/NewHomes 

CW New/New Homes = Prob New Homes· /J.. Housestock 

CW Used/NewHomes= 0 Eq. 1-3 

= 

= 

= 

New clothes washer purchase for new homes 

The probability of purchase of washers for new homes 

The net increase in housing 

Used clothes washer purchases for new homes (assumed 0). 

Current Assumptions 

The model assumes that purchases from new housing arise from the NET increase in new 

housing. This assumption is equivalent to saying that washers are mobile pieces of furniture that 

1~onsumers tend to salvage or move from their old housing. To test this hypothesis, we ran the 

model with two assumptions: (1) purchases are proportional to net new housing, and (2) 

purchases are proportional to the previous year's housing starts. We found that if purchases were 

assumed to be proportional to housing starts, then the model systematically over-estimated 

historical shipments. We therefore chose the first assumption. We also assumed that all 

purchases of washers for net new housing are new washers. 

:l.2.3 Existing Housing with Regular Washers 

:l.2.3.1 Definition 

Existing housing with "regular" clothes washers are those existing households that have a 

washing machine, and whose washing machine has not had an extra repair that extends the life of 

the clothes washer. 

Jl.2.3.2 Approach 

The decisions involved with the replacement and repair of regular washers in existing housing 

are illustrated in figure 3. The figure shows that several decisions and events affect the 

replacement of an existing washer with a new or used machine. 

11 
!~~~:rw/ ~!~:red Don't Buy 

Any Washer 

Houses with a Washer 

Extend 

Machine Life 

Buy New 

Washer 

Keep Existing 

Washer 

Keep Existina 

Washer 

Figure 3 Decision tree for replacement and repair of regular washers in existing 

housing. 

For a household with an existing washing machine, the first question is whether or not the 

c:lothes washer has problems and needs repair. If the washer needs repair, the consumer will then 

decide whether to repair the machine or replace it. If the machine is replaced, then there is the 

decision of whether to get a new or used machine, or to do without a clothes washer (according 

to the Clothes Washer Consumer Analysis, about 2% of current clothes washer owners will 

consider doing without a washer). If the machine is repaired, then the decision is evaluated to see 

if it is an 'extra' repair for a machine that under normal economic conditions would have been 

replaced. If it is an extra repair, then the washer is assumed to have its life extended by 6 years. 

If the machine does not have any problems, the consumer still may replace the washer early 

(before breakdown). According to AHAMINFO survey data about 27% of clothes washers are 

replaced early. These discretionary purchases are referred to as early replacements. 

The decisions and events in the decision tree are modeled with probability functions. We 

therefore need five relative probability functions to model this purchase decision process: 

12 
1. The probability that an existing washer has a problem 

2. The probability of replacing, or repairing a machine as a function of age. 

3. The probability of a used/new purchase. 

4. The probability of an early replacement of a machine without problems. 

5. The probability that a washer is not replaced. 

1. The probability that an existing washer has a problem is a function with a 5% annual repair 

:rate for the first five years, increasing linearly with age, and a 100% needs-repair rate at 17 years. 

To do this we assume that the relative probability that a surviving machine required repairs is 5%. 

So we have: 

Probability of Needs-Repair= C *age *Probability of Survival Eqn. 1-4 

~Nhere C is chosen so that the probability of a repair in the first five years averages 5% per year. 

This function is independent of time. The survival function for a clothes washer is derived from 

the replacement function used in the ANOPR analysis, and is illustrated in Figure 4. 

Survival Probability Function 

1 

;t:• 0.8 

:s 

.c = 0.6 e 

=-- -; 0.4 .=:: 

c: 

= VJ 0.2 

0 

0 s 10 15 20 

Washer Age 

Figure 4 Probability of Survival for Regular Clothes Washer 

13 
2. The probability ofRepair vs. Replace (replace and retire are used interchangeably) is subject 

to market variations and changes as described by a probability of purchase equation: 

ProbRepair vs. Retire( year, age) = Probability of Repair vs.Retire = 

(Probability of Needs- Repair)/[ 1-(Probability of Survival)] Eq. 1-5 

If more machines are being repaired instead of retired, we extend the life of the repaired 

machine by 6 years. In the model, this clothes washer machine life extension is implemented by 

moving the machine to the stock of extended lifetime machines, and using a survival probability 

function for this stock which is shifted by six years. 

3. AHAM/NFO survey data provides the relative proportion of new vs. used purchases. We use 

this proportion, and project it into the future using a probability of purchase model. When a used 

purchase is made, we assume that the age distribution of used machines is the same as the age 

distribution of the used machine supply resulting from discretionary replacements. 

4. For the probability of early retirement. a simple linear function describes the relative 

probability of a discretionary clothes washer replacement over time. This function is assumed to 

be 0 at age 0 and to increase linearly with clothes washer age. The slope of this function is chosen 

so that the relative proportion of discretionary replacements vs. all replacements in the model 

output is consistent with AHAM data (i.e. 27% in 1996). Clothes washer purchases that result 

from a change of residence are not considered to be 'replacements.' 

5. The probability that a machine is not replaced at breakdown is fixed at 2%, based upon 

interview results from the Clothes Washer Consumer Analysis. 

14 
0.8 

c .... :s 0.6 ~ 

.c 

e o.4 ~ 

0.2 

Relative Probability of Decisions/Events 

0 2 4 6 8 10 12 14 16 

Washer Age 

Iii Replace 

Iii Repair 

11 Early Replace 

ONoAction 

Figure 5 Relative Probability of Regular Replacement, Repair, Early 

Replacement and No Action as a Function of Clothes Washer Age for 

1997 

Figure 5 shows the probabilities for the different decisions and events as a function of clothes 

washer age for the model calibration year of 1997. For most of the age of the washer, the most 

li.kely disposition of an existing clothes washer is for it to be kept. There is a significant 

probability of repairs for much of the machine's life. Meanwhile as the clothes washer becomes 

old the likelihood of replacement becomes dominant. Throughout the clothes washers' life, there 

is some probability of an early replacement. Though in any given year the probability of an early 

replacement may be small, the cumulative effect of this small probability is approximately 27% of 

total clothes washer sales. 

The equations describing the details of the disposition of the existing washers are as follows: 

CWNeedsRepair(year, age) = ProbNeedsRepair{year, age)* CWstock(year, age) Eq. 1-6 

CW Retired( year, age) = ProbRetirevs. Repair(year, age)* 

CWNeedsRepair(year, age) 

CWEarly(year,age) = ProbEarly(year,age)* 

(CW Stock( year, age) - CWNeedsRepair(year, age)) 

15 

Eq. 1-7 

Eq. 1-8 
where 

ProbxtraRepairs(year, age) = ProbRetirevs. Repair( year, age) -

ProbRetirevs. Repair( 1996, age) Eq. 1-9 

CWxtraRepairs(year, age) = ProbxtraRepairs(year, age)* CWNeedsRepair(year, age) 

(if ProbXraRepairs > 0 else CWxtraRepairs = 0) Eq. 1-10 

CW Needs-RepairCyear, age) 

Prob Needs-RepairC age) 

CW s1oclyear, age) 

CW Retired (year, age) 

Prob RetirevsRepair (year, age) 

CW Early (year, age) 

Prob Early (year, age) 

Prob xtra Repairs (year, age) 

CW Xtra Repairs (year' age) 

= 

= 

= 

= 

= 

= 

= 

= 

= 

The number of regular washers of a given age that 

need repairs in a given year. 

The probability that a regular washer of a given age 

needs repair (this function is independent of year). 

The number of regular washers of a particular age in 

a given year. 

The number of regular washers retired. 

The relative probability that a regular washer which 

needs repair will be retired. 

The number of washers that are replaced early. 

The probability that a washer will be replaced early. 

The probability that a regular washer received extra 

repairs that extended its lifetime. 

The number of regular washers that received 

lifetime-extending repairs. 

1.2.3.3 Current Assumptions 

There are several important assumptions made in modeling the replacement and repair of 

existing clothes washers. These include: 

1. The needs-repair (or problems) probability function is independent in time. 

2. For a clothes washer which is not retired in 1997, the probability that a clothes washer 

needs repair is zero when the machine is new, and increases linearly with clothes washer 

age. The mean annual probability that a washer needs repair in the first five years is 5%. 

3. The probability that a broken down machine is not replaced is fixed at 2%. 

4. All early replacements result in the purchase of a new machine. 

16 
5. The probability of a regular replacement and the probability of a new vs. used purchase are 

independent: For example, the probability of a regular replacement with a used machine is 

the probability of replacement times the probability of purchasing a used machine. 

6. If a greater proportion of machines with problems obtain repairs in the future than they did 

in 1996, then the additional population of repaired machines have an extended lifetime 

which. is 6 years greater than the regular washer lifetime. 

7. For machines that do not experience problems, the relative probability of an early 

replacement is zero for a new machine and increases linearly with washer age. 

1.2.4 Households without Clothes Washers 

1.2.4.1 Definition 

Households without clothes washers are those households that do not have a clothes washer 

within the residence. This is equal to the number of households minus the number of households 

with clothes washers. 

:L.2.4.2 Approach 

The approach taken to model purchase decisions by households without clothes.washers is 

shown in figure 6. First the household decides if it is going to purchase a clothes washer, and if 

so it then decides whether or not to purchase new or used. 

Houses without a Washer 

Remain without 

a Washer 

Buy Used 

Buy New Washer 

Washer 

Figure 6 Decision Tree for Housing without a Washer 

17 
We assume an annual probability of purchase (relatively small) which varies according to the 

economic probability of purchase model. We also use the ratio of new vs. used purchase 

probability which is calibrated with market conditions in 1997 to be consistent with AHAM/NFO 

data. 

The relatively simple dynamics of the decision by a non-owner household deciding to buy a 

washer is described by one equation: 

CWNoWasherToWasher(year) = 

Eq. 1-11 

ProbNoWasherToWasher(year) · CWNoWasherStock(year) 

where: 

CW No Washer to Washer (year) 

Prob No Washer to Washer (year) 

CW No Washer Stock (year) = 

The number of non-owner households that purchase clothes 

washers in a given year. 

The probability that a non-owner household will purchase a 

clothes washer in a given year. 

The number of non-owner households in a given year. 

And the number of non-owner households is calculated from the existing housing stock and the 

number of clothes washer owners as described in the following equation: 

CWNoWasherStock(year) = (HousingStock)(year )-LJ CW stock ](year) Eq. 1-12 

ll.2.4.3 Current Assumptions 

The main assumption is that the probability of purchase from a non-owner household is very 

small. Secondly it is assumed that the new vs. used decision probability is the same as it is with 

the regular washer owners. And finally we assume that the different probabilities are independent; 

i.e., the probability of two decisions or events is the product of the individual event /decision 

probabilities. 

l.2.5 Households with Extended-Life Washers 

1.2.5.1 Definition 

These households have clothes washers that received more repairs than was normal in the 

r1~ference year of 1996. It is therefore assumed that the lifetime of these clothes washers has been 

extended by these extra repairs. 

18 
1.2.5.2 Approach 

The input of this particular stock of washers comes from regular washer households that have 

made extra repairs on their washing machines. Once an extra repair has been made, it is assumed 

that no more repairs will be made after the next machine breakdown. 

Buy New 

Washer 

Figure 7 

Houses with Extended Life Washer 

Don't Buy 

Any Washer 

Keep Existing 

Washer 

Buy Used 

Washer 

Decision Tree for Housing with Extended-Life 

Clothes Washers 

Figure 7 illustrates the decision tree for the stock of extended-life clothes washers. Note that 

1hese washers are already quite old because they are regular washers that have received extra 

repairs near breakdown (between 11 and 17 years of age). The main event in this decision tree is 

whether or not the machine has problems. This probability function is a shifted version of the 

survival probability function for regular washers; it is illustrated in figure 8. 

Besides the survival probability function, the decision of whether a machine is replaced with a 

new washer, a used washer, or no washer is the same as that for regular washers. 

In terms of equations, the dynaffiics of the extended-life clothes washers can be described as 

follows: First the retirement of the clothes washers is calculated simply with the retirement 

(replacement) probability function (shown in figure 8). 

CW - XRRetirect(year,age) = ProbXRi..tu.(age)*CW 

- XRstock( year, age) 

Eqn. 1-13 

Then the stock accounting is done such that the change in stock is the number of regular 

clothes washers that get extra repairs minus the stock that is returned: 

19 
CW-XRstock(year,age) = CW-XRstock(year-1,age-1)-CW-XRRetired(year-1,age-1) + E 1

_

14 CWxtraRepairs(year -1,age- I) q. 

where: 

CW-XRRetired(year, age) 

Prob XR-Retire( age) 

CW-XRstock(year, age) 

CW XtraRepairs (year, age) 

= 

= 

The number of extended-life clothes washers of a particular 

age retired in a given year. 

The probability that an extended-life washer of a given age 

will be replaced or retired. 

The number of extended-life washers of a given age in a 

given year. 

The number of regular washers of a particular age that 

received extra repairs in a given year. 

Survival Probability Function 

= 

0.8 

:s 

.. .I:>. 

= 0.6 .. 

~ 

;; 0.4 .ii: 

i: 

= "' 0.2 

0 

0 s 1 0 1 s 20 25 

Washer Age 

Figure 8 Survival probability function for extended lifetime washers 

l.2.5.3 Current Assumptions 

There are several assumption of the extended-life clothes washer modeling. These 

assumptions include: 

1. Extended life washers are never repaired again. 

2. The extended-life washers have a lifetime that is 6 years greater than that of the regular 

washers. 

3. The new vs. used vs. no replacement decision has the same relative probabilities as in 

the regular washer case. 

4. The different probabilities are independent, that is the probability of two events or 

20 
decisions is the product of the individual probabilities. 

5. The retirement probability function is independent of time. 

1.2.6 Accounting Equations 

For making the shipment forecasts, we specify a series of equations that define the dynamics 

and accounting of the different types of clothes washer stocks. For net new housing the equation 

describing the stock of new housing is straight forward. The stock of new housing is the 

difference between the current year housing stock and the previous year's housing stock. 

Meanwhile the most complicated accounting equation is that which describes the accounting of 

the existing stock of regular washers. 

For the stock of regular washers we have two equations which describe the accounting of the 

population. The first equation says that the number of one-year old clothes washers is equal the 

number of new clothes washers purchased the previous year: 

CWstock(year,age = 1) = CWNew(year-1) Eq. 1-15 

Meanwhile the next equation describes the accounting for washers of the different, older age 

eategories: 

CW Stock(year, age) = CW Stock(year - 1, age - 1) - CW Retired( year -1, age - 1) -

CWEarty(year - l,age-1)-CWxtraReparrs{year-1,age-1) + Eq. 1-16 

( CWusect(year-1)/L [ CWEarlyl)*CWEarty(year-1,age- l) 

where 

year 

CW Stock (year, age) 

CW New (year) 

CW Retired(year, age) 

CW Early (year, age) 

CW usec1(year) 

:E[CW Early](year) 

= 

= 

= 

= 

= 

The year that the stock is being estimated 

The population of regular clothes washers in existing 

housing of a particular age. 

The number of new washer purchases in a particular year. 

The number of regular washers from a particular age 

category that were replaced in a given year because of 

problems that had occured 

The number of regular washers that are replaced early from 

a particular age category in a given year for discretionary 

reasons. 

The total number of used purchases in a given year. 

The total number of early replacements (of all age 

categories) of regular washers in a given year. 

21 
CW XtraRepairs (year, age)= The number of regular washers that have received lifetimeextending repairs. These washing machines get transferred 

to the extended lifetime stock 

Equation 16 indicates that the number of clothes washers in a particular age category is equal 

to the number of clothes washers in the younger age category of the previous year minus the 

number of clothes washers retired or replaced early and plus the number of used clothes washers 

of that age category that have been purchased in the previous year. The age distribution of used 

clothes washers is assumed to be the same as the age distribution of clothes washers that are 

replaced early (since such early replacements are assumed to provide much of the used clothes 

washer supply). 

Then for the stock accounting for the extended life machines (those that have received extra 

:repairs), we have the following: 

CW- XRstock(year, age) = CW- XRstock(year - I, age - 1) - CW- XRRetired(year - 1, age - 1) + E 1_17 CWXtraRepairs(year - 1, age -1) q. 

where 

CW-XR stock (year, age) = 

CW-XR Retired(year, age) = 

CW xtra ~epairs (year, age) = 

The number of clothes washers in a given year of a given age 

group that belong to the stock of machines that have received 

extra repairs. These extra repairs have extended the life of the 

machine. 

The number of machines of a particular age that are retired 

from the extra repair stock in a given year. 

The number of regular washers of a particular age in a given 

year that receive repairs that extend the machine life in a given 

year. 

Equation 17 says that the stock of extended life clothes washers comes from regular washers 

which receive extra repairs when they break down. This stock then ages, and is_removed as it is 

retired due to additional repair problems. 

For the stock of households with no washer we have the following equation: 

where 

CWNoWasherStock(year) = (HousingStock)(year)-L [ CWstock](year)-

L [CW- XRstock ](year) Eq. 1-18 

CW No WasherStoclyear) =The stock of households who do not own clothes washers 

22 
(Housing Stock) (year) 

:E[CW stock](year) 

:E[CW-XR stocJ(year) 

= The total stock of housing in a given year 

= The total stock of houses with regular clothes washers of any 

age category. 

= The total stock of houses with extended life washers of any 

age category. 

Equation 18 says that number of non-owner households is the number of households minus the 

number of regular washer owners minus the number of extended life washer owners. 

The new and used washer purchase are related to changes in the different clothes washer 

stocks as follows: 

CWNew(year} = ProbNewVs.Used(year}* 

CWNew New Homes( year} 

[

0.

98* (CWRetired(year, age} + J +] L CW-XRRetired(year,age) + 

CWEarly(year, age} 

CWNoWasherToWasher(year} 

+ 

Eq. 1-19 

CWused(year} = (1-ProbNew(year} )* L 0.

9

S* CW-XRR.etired(year,age} + l [ (

CWRetired(year, age} + J] ) 

Eq. 1-20 

where: 

CW New (year) = 

Prob New (year) = 

CW No Washer to Washer (year) = 

CW Used (year) = 

CWNoWasherToWasher(year} 

The number of new washer purchases in a given 

year. 

The probability that a purchase is a new washer 

The number of washers purchased by non-owners in 

a given year. 

The number of used washer purchases in a given 

year. 

In the rest of this report we will describe in more detail how this accounting approach is 

implemented to forecast clothes washer shipments. 2 

2

Note that in equations 19 and 20, the 98% replacement rate for retired machines was 

obtained from the Clothes Washer Consumer Analysis. 

23 
1.3 MODEL 

In order to estimate the impact of standards-induced price and features changes it is 

necessary to have a model which describes consumer decisions and is consistent with historical 

experience. 

In this forecasting effort we took the following approach: First we used the clothes 

washer consumer analysis to provide the framework for the modeling approach and the 

probability of purchase model. We then used market discount rates to adjust the relative size of 

the price and operating savings coefficients for the logit purchase probability model. Finally, we 

used industry statistics on historical clothes washer shipments to perform the final calibration of 

the model parameters. 

This procedure for developing the economic decision model is illustrated in the following 

process flow diagram: 

Figure 9 Model development 

Conjoint Analysis 

Logit Probability of Purchase Model 

24 

Initial Model Assessment 

-- Does Not Match 

1980 - 19 6 Shi ments 

Revised Probability 

of Purchase Model 

Model Calibration 

Purchase Model 
1.3.1 Logit Probability of Purchase Model 

1.3.1.1 Logit Equation 

The mathematical building block for the modeling of consumer decision probabilities is the 

logit probability of purchase model. In this model, the probability of purchase depends on the 

utility of the clothes washer, U, which depends on the attributes of the appliance. This purchase 

probability is constrained to be between 0 and 1, and relative changes in the probability of 

purchase are proportional to changes in the utility of the appliance. These theoretical 

requirements for the decision probability function can be satisfied by requiring that the probability 

of purchase function satisfies the following equation: 

dProb/Prob=dU*(l-Prob) Eq.1-21 

where Prob= decision probability, and dU is the differential change in utility which is a linear 

function of the clothes washer attribute variables. The factor of ( 1-Prob) on the right hand side of 

the equation enforces the condition that the probability of purchase never exceeds 1. 

We can solve the above equation for the probability function assuming a particular 

:functional form of the utility in terms of the attribute variables: 

dU = b · d( Pr ice) + c · d( Operating Savings) + d · d( Feature Index) Eq. 1-22 

where the differential change in utility is equal to a linear function of differential changes in price, 

operating savings and features changes. Then we obtain: 

ln(Prob/(1-Prob)) =a+ b ·(Price)+ c· (Operating Savings)+ d·(Feature Index) 

or Eq. 1-23 

Prob= 1/( 1 +exp(-( a+ b · (Price)+ c· (Operating Savings)+ d·(Feature Index)))) 

where a is a constant of integration determined by the values of the probability at initial market 

conditions. This can also be written as: 

Prob= exp(u)/(1 + exp(u)) Eq. 1-24 

where U =a+ b·(Price)+c·(Operating Savings)+d·(Feature Index) is the utility. The above 

equations thus define the lo git probability of purchase model. 

25 
1.3.1.2 Utility coefficients and elasticity 

Once the form of the purchase probability function is defined, the next task is to estimate the 

coefficients of the model from the available data. In this regard there are four main sources of 

purchase behavior and ownership data that we utilized: (I )Industry statistics on historical clothes 

washer shipments, (2) Results from a marketihg study of clothes washer consumer preferences, 

the Clothes Washer Consumer Analysis, (3) AHAM/NFO survey results, and (4) EIAIRECS 

survey results. 

For model calibration, we used the conjoint analysis from the Clothes Washer Consumer 

Analysis was used to verify elements of the model assumptions and set the approximate relative 

amplitudes of the features and price coefficients. For the next step, we adjusted the relative size of 

the savings coefficient to be consistent with observations on the approximate market discount 

rate. For the final step, we used historical data to calibrate of the utility coefficient amplitudes. 

'We used AHAMINFO and RECS survey results to set sizes for the initial market segments 

In discussions of price sensitivity of the clothes washer market, much of the technical 

literature discusses variations in demand in terms of the price elasticity. 

For a logit probability of purchase model, purchase price elasticity for a market segment 

depends on two main parameters: (I) the initial probability of purchase, or likelihood of purchase, 

of that market segment, and (2) the coefficient for price in the utility function. Specifically: 

elasticity = ( dProb/ dPrice) / (Prob/Price) = d( In( Prob))/ d( In( Price)) 

= h* ( 1 - Prob)* Price Eq. 1-25 

The elasticity therefore decreases with increasing purchase probability, and is proportional to the 

Uttility coefficient. Note that elasticity describes changes in purchase behavior for small changes 

about existing market conditions. For large changes in prices and market conditions, elasticity 

will not be constant. 

The fact that elasticity decreases with increasing purchase probability also helps explain the 

observation in the long-term sales forecasting literature that elasticities for necessities decrease 

towards zero as the durable reaches acceptance and market saturation. 

In the shipments model, we model price impacts on consumer behavior in terms of the 

probability function rather than in terms of a simple elasticity value. We use a probability function 

model so that the impact of large price changes can be properly estimated. When price changes, 

the purchase probability changes, and so does the elasticity. A full non-linear description of 

purchase probability variations is a more accurate approach for modeling economic decisions. 

26 
1.3.2 Clothes Washer Consumer Analysis 

DOE initiated a clothes washer consumer study in order to aid in the description and modeling 

of consumer preferences and purchase behavior. This study used two approaches to identifying 

and characterizing consumer preferences: (1) Focus Groups and (2) Conjoint Analysis. 

This study is described in detail elsewhere (Department of Energy, 1999), but we summarize 

the salient features here. 

The focus group study was used to determine what features of clothes washers were of 

importance to consumers. For the focus group study, the participants indicated which clothes 

washer feature are important to them. The study showed that the ten most important clothes 

washer features in order of priority are: (1) price, (2) capacity, (3) energy and water costs, (4) 

load size options, ( 5) durability, ( 6) water temperature options, (7) door placement, (8) quiet 

operation, (9) wash time, and (10) warranty. 

In addition to the focus groups, a conjoint analysis was performed to quantify the relative 

importance of six different features and their impact on purchase probabilities. The conjoint 

study asked respondents which clothes washers would they consider purchasing today given a 

range of clothes washer attributes. The prices considered ranged from $400 to $650. Meanwhile 

1he amount of energy and water savings considered ranged from $0 to $50. In addition, features 

such as door placement, capacity , water temperature options, and load size adjustment were 

considered in the analysis as binary variables which could be either 0 or 1. 

For the shipments model spreadsheet, we included the top four features that may be affected 

by clothes washer standards. These features, include in order of priority, are: (1) price, (2) energy 

and water savings, (3) water temperature options, and (4) door placement. (Note: load size 

options were rated more important than door placement, but this feature would not be affected 

by a standard). 

l.3.3 Stated vs. Revealed Preferences 

Consumers preferences can be measured or indicated in several possible ways. Stated 

consumer preferences are those which are obtained through surveys such as the conjoint analysis 

Ulsed in the DOE study. Revealed preferences are those which are demonstrated through actual 

purchase behavior. The situation in which consumers find themselves when they actually make a 

clothes washer purchase can be significantly different than the presumed purchase context of a 

stated preference study. The difference between stated and revealed consumer preferences is 

noted in textbooks that discuss the application of conjoint analysis: 

Market share estimates obtained from conjoint analysis differ from actual shares due to 

marketing activities such as advertising and distribution, which affect awareness and 

27 
availability. Appropriate adjustments are therefore needed to account for the effect of these 

marketing actions. (Lehmann, Gupta & Steckel, 1997) 

Therefore the results of stated preference studies and revealed preference studies can often 

be significantly different. Especially when considering application to a post-standards situation 

where the standard affects the availability of lower-efficiency lower-priced models. 

Typically a consumer will find himself or herself in a more constrained circumstance 

during an actual clothes washer purchase. For example, over half of clothes washer purchases are 

due to the breakdown of an existing clothes washer. Under constrained purchase circumstances 

consumers will find themselves with fewer choices, and the influence of price, savings, and other 

dothes washer attributes will diminish. 

If one tries to construct a shipments forecast model using stated consumer preferences, it 

does not fit the historical data (as shown later in Figure 12). This is due to differences between 

what consumers say they will buy (stated preferences) and their actual purchase behavior 

(revealed preferences). This means that the parameters describing stated preference consumer 

purchase probabilities need to be recalibrated to fit actual historical behavior. In the purchase 

probability model for the clothes washer shipment forecast, we make two parameter calibration 

adjustments. The first adjustment changes the relative size of the savings coefficient. This 

adjustment is made because consumers seem to react sensitively to purchase price differences 

relative to potential differences in operating costs. The importance of price in consumer purchase 

behavior relative to savings appears to be more than what was stated in the Clothes Washer 

Consumer Analysis when one looks at intercept surveys and current market conditions. We 

therefore decreased the relative size of the savings coefficient vis a vis the price coefficient as one 

adjustment. The second adjustment rescales all coefficients to optimize the back-cast of historic 

clothes washer sales. This second adjustment allows us to utilize the historical data to translate the 

stated price sensitivites to revealed consumer preferences as indicated by historic clothes washer 

sales. Our ability to match historic sales data increases confidence in the forecast of future sales, 

because if we can accurately model historical consumer reactions to a 25% price change in the 

past, then we assume that we can model future consumer reactions to similar price changes. 

1.3.4 Determination of Decision Sensitivities 

The price and feature sensitivities in the economic consumer decision model were 

calibrated using historical shipments, price, and efficiency data. 

Figure 10 shows the relative changes in price, operating cost, and non-housing shipments 

from 1980 to 1996. We plot the price of laundry equipment in constant dollars ([CPI-Laundry 

Equipment]/ [CPI-All Items]) relative to 1985. We also plot the relative change in non-housing 

c:tothes washer shipments. Non-housing shipments are total shipments minus the net increase in 

housing times the estimated saturation of clothes washers in new housing. 

28 
-

Clothes Washer Shipments, Price, and 

Operating Cost · 

~ .._, 40 ~--------------------~ 

~ 30 -+----------------A::-__,..."""'llt---~ 

~ 20 -+-------------<---~,,,,.::=.------~ 

~ 10 -+---___,.:--------:.=..-----IL---------~ 

~ 0 +-----=~.-=i~~~:------------~ 

: -10 -+----~---1----""......,:"!"'"-r---------~ ~ 

-= -20 -r----7-=--------=-~""'*~~~:--I u -30 +------=::;__ ________ __,,,----=-----1 .~ - -40 +---------------::::Jlllo.....--.------i 

.! 

~ -50 

1975 1980 1985 1990 1995 2000 

Year 

~shipments 

--1r- Average Washer Price 

-+- Operating Cost 

Figure 10 Historical changes in clothes washer price, operating cost, and 

non-housing shipments. 

Figure 10 shows that from 1980 to 1996 there is a 30% decrease in price and a 30% 

decrease in operating cost while there is a 63% increase in non-housing shipments. But only a 

fraction of these shipments are due to decreased prices or operating cost, a large fraction of this 

increase is due to increases in clothes washer demand. 

There are two main sources for increased clothes washer demand. One source is 

discretionary demand from consumers who wish to change their current clothes washer because it 

is outdated, because they are remodeling, or because they are unhappy with the features of their 

current washer. The other source of demand is from consumers whose present washer breaks 

down. The AHAM/NFO study estimates that approximately 73% of non-housing demand is due 

to replacement of broken machines, and 27% of non-housing demand is discretionary. 

Given the average 14-year lifetime of clothes washing machines one can estimate the 

increase from 1980 to 1996 of replacement demand by examining the increase in shipments from 

1966 to 1982. This increase is from 3.9 million to 4.9 million washers/year, or a 26% increase. 

Increases in discretionary purchases depend on increases in the total population of clothes 

washers that are subject to replacement. As the total number of clothes washers in U.S. 

households increases, the number of clothes washers that may be replaced for discretionary 

29 
reasons will increase proportionally (all other factors being eqUal). We estimate that the total 

stock of clothes washers increased from approximately 67 million washers in 1980 to 85 million in 

1996, an increase of about 27%. With approximately 1.8 million discretionary replacements in 

1996, an increase in discretionary sales of 0.4 million/year can be attributed to the fact that there 

is a larger population of clothes washers in U.S. households to be replaced. Combining the 

increased number of washers that break down and the increase in the population of washers that 

undergo discretionary replacements, we calculate that at a minimum, a 1.4 million/year sales 

increase from 1980 to 1996 can be attributed to increased demand for reasons other than price, or 

operating cost changes. lbis means that of the 2.5 million/year shipments increase from 1980 to 

1996, only about 1.1 million washers/year of shipments increase is probably due to changes in the 

1economic decisions of consumers caused by price and operating cost changes or other economic 

:factors. Most of the increase was simply due to the fact that there were more clothes washers in 

U.S. households in 1996 compared to 1980. 

The changes in consumer purchase decisions observed in the historical shipments data are 

of comparable order of magnitude to the type of changes we would expect after the imposition of 

a standard. A standard may cause long-term changes in prices and operating costs for clothes 

washers relative to other consumer expenses. These changes in relative price and costs will 

potentially have long-term impacts on clothes washer sales. The long term sales changes for the 

l. 980 to 1996 period were, at least in part, in response to a 30% decrease in purchase price and 

30% decrease in operating costs. 

The question is how the consumers economic decisions are influenced by various 

independent factors: How much of the sales increase is due to the fact that washers are cheaper to 

purchase, how much of the change is due to the fact that clothes washers are cheaper to operate, 

and how much of the effect is due to other correlated economic factors not accounted for in the 

economic decision model, such as income changes? (Incomes also varied during this period.) We 

are taking a modeling approach which assumes that the elastic increase in sales from 1980 to 1996 

is due solely to price and operating cost effects, but that other features may be more of a factor in 

foture. We examine these questions in more detail in the next section. 

1.3.4.1 Price Sensitivity 

For determining the relative importance of price and savings (i.e. operating cost) 

siensitivities, we have three potential sources of data including: 

(1) Results from the Clothes Washer Consumer Analysis 

(2) The savings/price trade-off implied by current market equilibrium 

(3) Historical shipments data 

A necessary requirement for the model parameters is to at least be consistent with 

historical shipments data, but it was not found to be a sufficient condition for estimating the 

operating cost savings elasticity. We therefore used the other sources to aid in assessing relative 

30 
price and savings sensitivities. 

The relative importance of savings and price can be expressed in terms of a market 

discount rate. If the market actors expect a very fast payback time from efficiency savings, then 

the market discount rate is high. If, on the other hand, market actors expect a several year 

payback time from more expensive high-efficiency washers, then the market discount rate is 

relatively low. 

If a consumer will tolerate a price increase of AP in order to obtain an annual savings of 

AS, then the ratio of AP and AS can be expressed in terms of the market discount rate as follows: 

M' I AS = (I/ d) ( 1-( 1/ ( 1 + d) N)) Eq. 1-26 

where d is the annual discount rate and N is the lifetime of the clothes washer in years 

The above AP/AS ratio represents the ratio of price and savings changes which make no 

change in the consumer utility of a purchase. Therefore this ratio also is related to the ratio of the 

,coefficients in the logit purchase decision model. Specifically we have 

L\ U = 0 = b · L\ P+ c · L\ S 

M/L\S = -c/b Eq. 1-27 

and the market discount rate is directly related to the relative size of the utility coefficients in the 

economic consumer decision model. 

In the Clothes Washer Consumer Analysis study, the ratio -c/b = 4.75 implies a consumer 

discount rate of 19% with regards to their stated preferences. 

But this market discount rate for stated consumer preferences seems to overstate consumer 

preferences for operating cost savings. When the shipments model is run with the unadjusted 

coefficients from the Clothes Washer Consumer Analysis, there is a prediction of a large spike in 

sales arising from the efficiency standard implemented in 1994 which resulted in an 18% increase 

in washer efficiency. A large sales response to the 1994 standard was not observed, and therefore 

iit is likely that the market discount is larger than 19% and should be adjusted. 

In order to estimate the market discount rate, we did an analysis of the price and savings 

tradeoff under current market conditions. 

31 
Qol 

u 

·c: 

i:i.. 

$700.00 

$600.00 

$500.00 

$400.00 

$300.00 

$200 .00 

$100.00 

$0.00 

$0.00 

-

Price vs. Savings 

y = 0.0772x2 + l.2361x + 419.31 ~ 

-- -

$10.00 $20.00 

~ 

$30.00 

Savings 

$40.00 $50.00 $60.00 

• Price 

-Poly. (Price) 

llfigure 11 Estimated price vs. savings relation for current market conditions 

l.3.4.2 Savings/Operating Cost Sensitivity 

We estimated the current relative size of the savings/operating cost sensitivity by assuming 

that the current market is in equilibrium, and by estimating Af>/~S for the current market. Figure 

il 1 illustrates the approximate relationship between price and operating cost savings that is implied 

by the engineering analysis of the costs of higher efficiency washing machines. Since most 

purchases are near the baseline model, this data implies a typical market payback time between 

one and two years, though the precise value in this range cannot be specified with statistical 

certainty. Similarly, the intercept interview performed during the Pacific Energy Associates for 

the Northwest Energy Efficiency Alliance (Hewitt, et. al., July 1998) indicated a market discount 

rate of one to two years for clothes washer shoppers--depending on the details of how the 

responses are quantitatively interpreted. Given these two indicators, we selected 75% as a market 

discount rate halfway between a one-year (100% discount) and two-year (50%) payback. The 

75% market discount rate corresponds to a price-to-savings ratio of 1.33 for the current market 

behavior. 

When the 75% market discount rate is incorporated into the clothes washer shipments model, 

sales response to the 1994 standard is considerably more moderate. As shown in figure 12, 

adjustment of the operating cost sensitivity moves the model closer to a fit with historical 

shipments. The root mean squared (RMS) deviation between the model and the historical data 

decreases from 3.6 million shipments per year to 1.3 million shipments per year with this change 

32 
in discount rate. (The final, calibrated model has an RMS deviation of 0.2 million shipments per 

year from historical data). 

1.3.4.3 Features Sensitivity 

An issue with the higher standards levels is whether the higher efficiency standards will force 

manufacturers to produce only horizontal axis machines. And if only horizontal axis clothes 

washers are available, this change in available clothes washer features may impact sales. Among 

stakeholders, there is no consensus with regards to which standard level might require horizontal 

axis machines. 

Another issue is that the market dynamics of the adoption of new technologies can be 

extremely complex. Initially, there may be some resistance to a new technology, but as new 

technologies become more familiar, this market resistance often diminishes. The Bern study of 

high efficiency clothes washers indicated that consumers can adapt to the technology of frontfoading washers (Tomlinson & Rizy, 1998), though the implications of the Bern study results for 

predicting shipments impacts is uncertain. 

The conjoint study indicated that there was a rather dramatic change in consumer sensitivity to 

door placement depending on the level of familiarity with front-loading washing machines, and 

geographic location. Those consumers who were familiar with front-loading machines have a 

sensitivity to front loaders that is 30% less than the sensitivity of the entire sample. 

In the shipments model, we assumed that if a standard at the 35% level or above is 

implemented, the dominant machines will be front-loaders. But we also assumed that all 

c:onsumers would become familiar with front-loading washers and that there would be further 

acceptance of the new technology. Therefore the size of the top/front loading coefficient in the 

purchase price model was set at Y2 the size of the coefficient for the conjoint sub-sample of those 

familiar with horizontal axis machines. This value presumes that all consumers will be familiar 

with horizontal axis machines if they come to dominate the market, and that there will be some 

adaptation to the new technology, though acceptance will not be complete. 

1.3.5 Calibration of Shipments Model 

The clothes washer shipments model was calibrated with historical shipments data. 

Figure 12 illustrates the two stages of model calibration. The line with short dashes shows the 

model results when unadjusted coefficients from the conjoint analysis are used. The line with long 

dashes shows the result of the adjustment of the market discount rate and the operating cost 

savings coefficient to reflect observed purchase behavior in the current market. This frrst 

adjustment decreases the root mean square (RMS) deviation from historical shipments from 3.6 

million per year to 1.3 million per year. 

33 
For the final calibration of the model, we fixed the relative size of the price, savings, and 

front-loading feature coefficients to values determined from evaluation of the Clothes Washer 

Consumer Analysis, and market discount rates. By finding a market discount rate of 75%, and by 

1estimating the relative size of the front loading elasticity.to be about Y2 of the sensitivity of the 

1~onsumers familiar with front loaders, the ratios of the coefficients are fixed as follows: 

c/b = -1.33 Eq. 1-28 

d/b=-39.7 

The coefficient b was then adjusted until a best fit of historical data was obtained as measured by 

the (RMS) deviation between historical shipments and model shipments between 1981 to 1996 

inclusive. For the fully calibrated model, the RMS deviation between the model and the industry 

data on historical shipments is 0.2 million shipments per year. Figure 12 illustrates the fit of the 

~:hipments model with historical data and the improvement obtained by adjusting both the market 

discount rate and coefficient b. 

~ 

= Q 

16 

14 

12 

10 

= 8 -

~ 

6 

4 

2 .. 

Shipments of Clothes Washers 

· -· -· · · Conjoint Analysis (19% Discount Rate) 

- - - - 75% Discount Rate 

" '' 

. ' ' ' . ' 

--Calibrated Model 

+ Historical 

.• -..... -

. ·.. 

_, 

. 

. 

. . 

. 

. . 

' 

. ' 

. 

____ _.,"""".... ' .... , ' ' 

-- .-· ' ' ,-- , __ 

.. 

-:- .- -

O+--.,..---,~~-,-__,~.....---..-~.--.....---.~.----.----.-~.,..-~--r~-..--,-~---, 

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 

Year 

Figure 12 Calibration of shipments model with historical data 

34 
1.4RESULTS 

Once the model is calibrated with historical data, it provides a rather detailed picture of the 

possible impacts of standards on purchases, replacement, and repair of clothes washers. The 

results presented in Figure 13 represent our best estimate of possible standards impacts. As 

explained below, actual impacts may differ from our forecast for a number of reasons. 

The standards-induced impacts may be over-estimated in the shipments model for several 

reasons including: 

• Model calibration assumes that the net increase in shipments from 1980 to 1996 is due to 

price and operating cost savings effects. If other correlated effects (such as income) are 

also responsible for the 1980 to 1996 shipments increase, then the price and savings 

sensitivities are over-estimated. 

• We assume that the operating cost savings coefficient from the Clothes Washer Consumer 

Analysis was over-estimated. It is possible that educational and marketing programs 

implemented before the standard is implemented can help increase revealed consumer 

preferences to values closer to the stated consumer preference. 

• We assume that manufacturers will not add supplementary features to post-standards 

clothes washers. The addition of features to high-efficiency clothes washers can decrease 

the sales impacts of higher prices by further increasing the consumer value of the poststandard clothes washers. 

• We assume that after a standard used clothes washer supply would be unlimited, though 

more expensive. The model predicts that most of the consumers who decide not to 

purchase more expensive post-standards clothes washer will purchase used clothes 

washers instead. If there are limitations in used clothes washer supply, this may induce 

more consumers to purchase new washers. 

Similarly, there are several reasons why the shipments model may underestimate the sales 

impacts of standards: 

• We assume that consumers will gradually adapt to front-loading washers. If there is no 

adaptation to front-loading machines, then sales impacts of high efficiency standards 

(efficiency levels higher than the 35% level) may be greater than predicted. 

• We assume that the market discount rate is 75%. If in actuality the market discount rate is 

greater than our assumed rate, then relative size of the price elasticity will be greater, and 

so will standards-induced sales impacts. 

35 
New Clothes Washer Shipments 

o;--~----r-~~.,..-~----r-~~-r-~~~~~~~~~~~~~--1 

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 

Year 

l~igure 13 Clothes Washer Sales Forecasts. 

1.4.1 Sales impacts of Standards-Induced price changes 

1.4.1.1 New Clothes Washers 

+ Historical 

-easeline 

__.,_ 20% Level 

-+-25% Level 

----35%/40% Level 

--45% Level 

-llE-50% Level 

Figure 14 shows the forecasted clothes washer sales impact of the different proposed standard 

levels. As shown in the figure, sales and shipment impacts of the 5% to 20% standard levels are 

within 5% of base case. Larger sales impacts are forecast for standard levels above the 20% 

level. For the 25% to 50% standards levels the volume of new clothes washers shipments is 

forecast to decrease, while total dollar volume of sales is forecast to increase. Both the impacts 

at the year of the standard and the average impacts over the forecast period, 2003 to 2030, are 

ii 1 ustrated. 

36 
Estimatro Standards Impacts 

Shipments and Sales ofNew Washers 

Standard Level 

Figure 14 Estimated standards impacts on new clothes washers 

The biggest factor that influences the size of the potential standards-induced changes is the 

actual retail price increase that is induced by the standard. If price increases are large, the 

shipments volume decreases almost proportional to the price increase, but because the price 

elasticity is less than one, price increases result in increased gross sales dollar volume. The net 

financial impact of these opposing effects is examined in more detail in the manufacturing impact 

analysis. 

Some of the measures that consumers might take to avoid purchase of a new higher-prices 

clothes washer keep them out of the market for only a relatively short period of time. Therefore 

there is some recovery from the initial shipments drop that might be seen in the year of the 

standard. It is estimated that the long term average shipments drop is about 35% less than the 

drop which might be seen in the first year of the standard. 

37 
160% 

140% 

120% 

.... 

... 

OS 100% c. 

e 

.... 

" 80% 

~ OS 

~ 60% 

40% 

20% 

0% 

5% 10% 

Estimated Standards Impacts 

Shipments and Sales of Used Washers 

15% 20% 25% 35% 40% 

Standard Level 

45% 50% 

_._Used Shipments (03-30) 

-X-used Shipments (@2003) 

_._Used Sales($, 03-30) 

-+-Used Sales $ 2003 

llfigure 15 Estimated standards impacts on used clothes washer shipments and sales 

Jl.4.1.2 Used Clothes Washers 

Figure 15 illustrates the potential impacts of standards on the used clothes washer market. 

The used market will provide one of the most attractive options for consumers having broken 

dothes washers and who wish to avoid the expense of a new clothes washer. The model 

e:stimates that initially~ consumers will keep their clothes washers longer, but eventually they will 

Illeed to be replaced when they breakdown. This means that the long-term increase in the used 

clothes washer market is larger than the initial increase at the year of the standard. 

In estimating the relative impact on used clothes washer sales, we assume that the price of 

used clothes washers follows the price of new clothes washers and increases proportionally. 

38 
10"/o 

9"/o 

8% 

..... 7% y 

c. = 6% e 

.... 

a.I 5% 

~ 

= 4% 

~ 3% 

2% 

1% 

00/o 

5% 10"/o 

Estimated Standards Impacts 

Washer Age, Lifetime, & Repairs 

• 

15% 20"/o 25% 35% 

Standard Level 

40"/o 45% 

,._Mean Age 

-X-Lifetime 

-+-Re iJ's 

Figure 16 Estimated standards impacts on average washer age, lifetime, and total 

repairs. 

l.4.2 Impacts on mean age of washers, used market, and washer repairs. 

Figure 16 illustrates the estimated impacts on the mean age of clothes washers, the mean 

clothes washer lifetime, and the total volume of clothes washer repairs. These are average 

impacts over the standard period of 2003 to 2030. These three different measures of clothes 

washer retention measure different types of consumer reactions to higher potential clothes washer 

pnces. 

The increase in repair rate measures the impact of consumers who perform an extra repair on 

their clothes washer rather than retire the machine. Such repairs are few compared to the total 

volume of clothes washer repairs because of the large volume of minor repairs that occur over the 

lilfetime of a washer. According to Consumer Reports about 23% of clothes washers have repairs 

during the first five years of ownership (Consumer Reports, May 1998). 

The extended lifetime of clothes washers reflects repairs that consumers might undertake to 

extend the lifetime of clothes washers. Such extended repairs will have a delayed effect on the 

average lifetime of a clothes washer, and only a relatively small fraction of machines will receive 

such extended repairs (some machines may not be repairable, and consumer will also have the 

39 
choice of purchasing a used washer). An extra repair extends the life of a 14 year old machine by 

.at most six years. At the 50% standard level less than 20% of machines receive extra repairs that 

1extend the machine life. This implies that the lifetime of washers is increased by at most one year 

by the imposition of a standard. 

The increase in mean age of a clothes washer illustrates both the impacts of extra repairs and a 

more vigorous used clothes washer market. When more machines are cycled through the used 

market, then the proportion of older machines increases slightly, and this results in a slight 

imcrease in the average age of machines. Again, it takes several years for used shipments to have 

a significant impact on the clothes washer age distribution, so the averaged impact over the period 

is significantly smaller than the peak age increase which occurs several years after implementation 

of the standard. 

ll.5 CONCLUSIONS 

In order to provide a more detailed picture of potential standards-induced impacts on the 

c:lothes washer market, we have formulated an accounting model for clothes washer purchases. 

The model keeps separate accounts for the new housing, early replacement, breakdown 

replacement/repair, and non-owner markets. The method also apportions washer purchases to the 

new and used clothes washer market segments. The method uses a logit probability of purchase 

model for purchase decisions made by consumers that accounts for the impacts of price, operating 

cost, and features on shipments. 

Model parameters were estimated by using a variety of data sources. The data sources 

included AHAM/NFO data on current market shares for different clothes washer markets, AHAM 

historical shipments and efficiency data, AHAM engineering data and results from a Clothes 

''-'asher Consumer Analysis. 

The shipments model estimates potential standards-induced impacts on new and used clothes 

washer shipments, gross sales revenue, mean clothes washer ages, lifetimes, and repair rates. 

Details of the predicted impacts are illustrated in figures 13 through 16. 

40 
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41 
\ 

Parker, Philip M. 

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42