### US. Department of Energy 

### CLOTHES WASHER SHIPMENTS MODEL: Draft
TABLE OF CONTENTS 

### 1.1 OVERVIEW 1.1.1 Definition ofMarket Segments and Ownership Categories 1.1.2 Recent Enhancements ofShipments Model 1.1.3 Review ofOther 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 Logit Equation Description ofDecision 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 ofDecision 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 ofShipments Model 1.4 RESULTS 1.4.1 Sales impacts ofStandards-Induced price changes. 1.4.1.1 New Clothes Washers 1.4.1.2 Used Clothes Washers 1.4.2 Impacts on mean age ofwashers, 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. Inthe Advanced Notice ofProposed Rule making (ANOPR), we examined several different approaches to forecasting newwasher sales. The investigated models include an Auto-Regressive Moving Average Model (ARIMA), a MultiVariate Time Series Fit, a Saturation/Lifetime Model, and an Accounting Model with elasticity. Ofthe different approaches, we selected the Accounting Model because it was the most fullfeatured model which included price and operating cost elasticities. Inthis document, we describe a revised accounting model for projecting annual clothes washer shipments that includes the following factors:


### • 

### • • 

### • • combined effects ofprice, operating cost, and features on annual U.S. shipments mar:ket segments (e.g., newhousing, replacement decisions, non-owner adding a washer) decisions to repair rather than replace purchases ofused washers age categories ofclothes washers This Clothes Washer Shipments Model incorporates information from the DOE Consumer Analysis. Since the ANOPR, DOE has gathered additional information about features ofclothes 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 ofMarket 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 ofclothes washer owners include (1) new housing, (2) existing housing with a regular1washer, (3) housing without a washer, and (4) housing with an extended life washer. We refer to the population ofclothes washers in each ownership category as the stockofclothes washers ofthat category. The different types ofclothes washer owners are faced with different clothes washerpurchase decisions and purchase motivations. The reason for buying a clothes washer determines the lvfarket Segmentthat the purchase represents. The different types ofclothes washer purchases are divided into six separate market segments as follows:

1Regular meaning a washer that has not undergone an "extended repair" 

### 31. New Housing Market: When there is a net increase in the housing stock, the increase inthe number ofhouseholds will force the purchase ofnew clothes washers. 2. Early (Discretionary) Replacement Market: Even before a clothes washer breaks down, about 27% ofclothes washer owners replace the existing clothes washer because they want an updated model, because ofremodeling, orfor other miscellaneous reasons. 3. Regular Replacement Market: Most clothes washer purchases result from the replacement ofan existing washer that has broken down after the completion ofits 

### useful life. 4. Extra Repair Market: Under conditions ofhigh costs for new clothes washers a few consumers will rebuild orrepair 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: Formany clothes washer purchases, the consumer will have the additional decision ofwhether to purchase a new or used machine. There is a significant used clothes washer market (18% oftotal sales) that can interact with the market for new clothes washer purchases. (Source: NFO Research Inc.) Figure 1 shows the structure ofthe model. The boxes represent the different types ofclothes washer owners and households, while the diamonds represent the different decisions that are made by the consumer and howthe results ofthe decisions feed into other elements ofthe model. In the model, the stock ofexisting washers is categorized interms ofownership or household category. Several different types ofowners 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 ofa particular consumer decision. Economic decision variables (such as price, operating cost savings and the foatures available for new clothes washers) influence the magnitude ofthese decision probabilities. The clothes washer shipments model keeps track ofthe population ofeachtype ofclothes 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 1represents the process oftaking an initial stock ofwashers ofthe four different categories, calculating the purchases induced by this initial stocks ofclothes washers, and calculating the new stock levels that result. The rectangles represent the different ownership
4categories, the arrows represent the stock flows ofclothes washer households, and the diamonds represent the decisions that these households are making in the course ofa year. To carry out one year's calculation, one starts in a rectangle with the amount ofclothes washers in that category. Then one flows out in the direction ofthe arrow until one arrives at a diamond that represents a decision. For each decision there is an inflow ofone arrow and an outflow oftwo 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 ofwashers 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 ofwashers that have flowed from one stock to another stock in the course ofone year. To getthe total stock atthe end ofthe year, one adds up the contribution from all possible flow diagram paths. Inthe model this process is repeated each year until the year 2030. Consumer decisions influence howthe stock and supply ofclothes washers flow from one category to another. Decisions which are economically influenced are modeled with econometric equations. Theparameters ofthese econometric equations are calibrated with industry statistics onhistoric 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 ofhouseholds (and their clothes washers) are subjected are described below: Net newhouseholds are those households which represent a net increase in housing stock (new housing construction less housing stockremoved from the market). These households are faced with the decision ofwhether ornot to get a new clothes washer with the house. Forhouseholds with existing regular washers, the first question is whether ornot the current washer is having operational problems (i.e. needs repair). Ifthe washer is without problems then 1he consumer must decide ifhe or she wants to purchase a washer for other discretionary reasons. Ifthe washer has operational problems, then the consumer must decide ifthe washer is to be repaired orreplaced. Ifthe consumer makes an extra repair, one which avoids the purchase ofa new washer, then the model assumes that that repair extends the washer lifetime by 6 years. Forhouseholds without washers a small fraction (at most a few percent) ofconsumers will decide to become clothes washer owners. Those who become owners will do so by purchasing c::ither a new orused clothes washer. Households with extended lifetime washers are those households that have extended the lifetime oftheir washer through an extra repair when the washer last broke down. Ifthe clothes washer breaks down yet again, the consumer will have to have itreplaced 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 ofthe mathematical structure ofthe model, while section 1.3 discusses the modeling ofeconomic consumer decisions, and section 1.4 presents the model results.



### 6

### 1.1.2 Recent Enhancements ofShipments Model Since publication ofthe Technical Support Document (TSD) for the Advanced Notice of Proposed Rule making (U.S. Department ofEnergy, 1998), we have made several improvements to the clothes washer shipments forecast. These improvements include the following: Detailedaccounting of different marketsegments andwasher 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 newwasher when it broke down. The current model now accounts for a variety ofother market dynamics including options to purchase newvs. used washers, changes in repair behavior, and extending the life ofwashers through extra repairs. Price andoperating cost elasticities calibratedto 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-loadingfeature 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 ofinformation to make the model reflect current consumer and market characteristics: • Clothes Washer Consumer Analysis results for both the relative size ofconsumers response to features relative to their response to price and operating expense, and to estimates ofthe rate at which clothes washer owners might drop out ofthe market. • AHAM/NFO survey data onthe proportion ofearly (discretionary) replacements, and on the proportion ofnew vs. used purchases. • AHAM statistics on historical shipments and onthe recent (post 1994 standard) changes in mean clothes washer efficiency. • Consumer Reports data onrepair rates ofwashers. The purpose ofthese model enhancements is to provide the best estimates possible for future clothes washer shipments that are consistent with the recent history ofwasher shipments, and with current clothes washer market structure and consumerpreferences.



### 7

### 1.1.3 Review ofOther Published Research We performed a review ofrecent literature on forecasting purchases ofconsumer 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. Inthis literature, a standard measure ofconsumer sensitivity to features ofthe 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, 

### APIPis 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, consumerprice response and ielasticity varies dramatically depending onthe type oftrade-offs being made, the time scale over which sales variations are being measured, the type ofdurable being examined and the stage of development ofthe 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 consumerhas the. choice ofdifferent brands and makes ofproduct. In this context, which is most relevant to marketing decisions, the choice offrom 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). Inthe long-term sales forecast literature, elasticities are much smaller than those observed in**~:hort** term sales orproduct 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 inthe overall market (Dipak & Rao, 1990; Parker, 1992; and Golder 

### & Tellis, 1998). Research that examines the change in elasticities overtime (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 ofthe 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.

8Since the introduction ofstandards 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 orfeatures 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 ofthree classes ofitems: Stocks, Events, and Decisions. These different classes are defined as follows. 

### 1.2.1.1 Stock A 

### Stock is the number ofhouseholds with a particular washer ofa particular ownership category. The mainproperty ofa stock is that it evolves over the course ofthe year by aging one year and by increasing or decreasing inresponse to inflows and outflows produced by events and decisions. The four permanent stocks inthe model are newhouseholds, 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 ofwashers in need ofrepair, repaired washers, rebuilt washers, washers purchases used, and retired washers. All ofthe temporary stocks are allocated to one ofthe four permanent stocks within the one year computational time step ofthe model. 

### 1.2.1.2 Events Events are things that happen to a stock that can change the status ofa portion ofthat stock, but do not depend on economic conditions. Events do not depend on market conditions, but are dependent on the properties ofthe stock. The main event inthe model is washer problem development orbreakdown. For regular clothes washers, whether ornot a washer develops problems thatrequire 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 consumerreactions to events and market conditions. Decisions are described in terms ofprobabilities that typically depend onthe type ofstock, the age ofthe clothes washer, the incremental cost ofthe decision, and market conditions. The probability oftwo subsequent decisions in the same year is equal to the product ofthe two individual decision probabilities. The dependence ofdecision probabilities onprice 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 ofthe decision, and where the right hand side ofthe equation represents the utility ofthe decision. The coefficients b, c, and d represent sensitivities that the consumerhas for the different aspects ofthe economic decision. The constant term a is an offset for the utility which calibrates the utility to the value ofthe market share in a reference year. These coefficients are determined through a combination ofassumptions about consumer behavior, based upon studies regarding consumer preferences, and model calibration with historic shipments data. The details ofmodel calibration and selection ofparameters for the consumer decision model are presented in Section 1.3 onmodeling economic decisions.


### 1.2.2 Purchases from Net New Housing l.2.2.1 

### Definition Purchases from net newhousing are defmed as those purchases that arise from a net increase 

### inthe 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. 10Datais available for the market saturation ofnewhouseholds with washers up to 1994. This market share is projected into the future using a logit probability ofpurchase 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 = ProbNew Homes· /J.. Housestock CW Used/NewHomes= 0 Eq. 1-3

= =

= New clothes washer purchase for new homes The probability ofpurchase ofwashers for new homes The net increase inhousing Used clothes washerpurchases for new homes (assumed 0).


### CurrentAssumptions 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 offurniture that**1~onsumers** tend to salvage ormove from their old housing. To test this hypothesis, we ranthe model with two assumptions: (1) purchases are proportional to netnewhousing, and (2) purchases are proportional to the previous year's housing starts. We found that ifpurchases 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 ofwashers for net newhousing are new washers.
:l.2.3 

### Existing Housing with RegularWashers :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 nothad an extra repair that extends the life of the clothes washer. Jl.2.3.2 

### Approach The decisions involved with the replacement and repair ofregular washers in existing housing are illustrated in figure 3. The figure shows that several decisions and events affect the replacement ofan existing washer with a new orused 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 ofregularwashers in 

### existing housing.

For a household with an existing washing machine, the first question is whether or not the c:lothes washerhas problems and needs repair. 

### Ifthe washer needs repair, the consumer will then decide whether to repair the machine or replace it. 

### Ifthe machine is replaced, then there is the decision ofwhether to get a new orused machine, or to do without a clothes washer (according to the Clothes Washer Consumer Analysis, about 2% ofcurrent clothes washer owners will consider doing without a washer). 

### Ifthe machine is repaired, then the decision is evaluated to see ifit is an 'extra' repair for a machine that under normal economic conditions would have been replaced. 

### Ifit is an extrarepair, then the washer is assumed to have its life extended by 6 years. 

### Ifthe machine does not have any problems, the consumer still may replace the washer early (before breakdown). According to 

### AHAMINFO survey data about 27% ofclothes 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 ofreplacing, or repairing a machine as a function of age. 3. The probability ofa used/new purchase. 4. The probability ofan early replacement ofa 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 ofa repair in the first five years averages 5% per year. This function is independent oftime. 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 ofSurvival for Regular Clothes Washer

132. 

### The probability ofRepairvs. Replace (replace and retire are used interchangeably) is subject to market variations and changes as described by a probability ofpurchase equation: ProbRepairvs.Retire(

### year,age) 

## =ProbabilityofRepairvs.Retire

## =

(ProbabilityofNeeds- Repair)/[1- (ProbabilityofSurvival)] 

### Eq. 1-5

Ifmore machines are being repaired instead ofretired, we extend the life ofthe repaired machine by 6 years. Inthe model, this clothes washer machine life extension is implemented by moving the machine to the stock ofextended lifetime machines, and using a survival probability function for this stock which is shifted by six years. 3. AHAM/NFO survey data provides 

### the relativeproportion of new vs. usedpurchases. We use this proportion, and project it into the future using a probability ofpurchase model. When a used purchase is made, we assume that the age distribution ofused machines is the same as the age distribution ofthe used machine supply resulting from discretionary replacements. 4. For 

### the probability of early retirement. a simple linear function describes the relative probability ofa 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 ofthis function is chosen so that the relative proportion ofdiscretionary 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 ofresidence are not considered to be 'replacements.' 5. 

### The probability that a machine is not replacedatbreakdown is fixed at 2%, based upon interviewresults from the Clothes Washer ConsumerAnalysis.

14

### 0.8 

## c 

# .... 

# :s 0.6**~** 

### .c 

# e o.4**~** 

### 0.2

## Relative Probability ofDecisions/Events

0 2 4 6 8 10 12 14 16 WasherAge 

### Iii Replace 

### Iii Repair 

### 11Early Replace ONoAction



### Figure 5 Relative Probability ofRegular Replacement, Repair, Early Replacement and No Action as a Function ofClothes WasherAge for 1997 Figure 5 shows the probabilities for the different decisions and events as a function ofclothes washer age for the model calibration year of 1997. Formost ofthe age ofthe washer, the most li.kely disposition ofan existing clothes washer is for itto be kept. There is a significant probability ofrepairs for much ofthe machine's life. Meanwhile as the clothes washerbecomes old the likelihood ofreplacement becomes dominant. Throughout the clothes washers' life, there is some probability ofan early replacement. Though 

### in any given year the probability ofan early replacement may be small, the cumulative effect ofthis small probability is approximately 27% of total clothes washer sales. The equations describing the details ofthe disposition ofthe existing washers are as follows: 

### CWNeedsRepair(year,

### age) 

# =ProbNeedsRepair{year,

### age)* CWstock(year,age) Eq. 

### 1-6 CWRetired(

### year,age) = 

### ProbRetirevs.

### Repair(year,age)* CWNeedsRepair(year,

### age) CWEarly(year,age) 

## =ProbEarly(year,age)* (CWStock(

### 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) (ifProbXraRepairs > 0 

### else CWxtraRepairs = 0) Eq. 1-10



### CW Needs-RepairCyear, age) Prob Needs-RepairCage) 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 ofregular washers ofa given age that need repairs in a given year. The probability that a regular washer ofa given age needs repair (this function is independent ofyear). The number ofregular washers ofa particular age in a given year. The number ofregular washers retired. The relative probability that a regular washer which needs repair will be retired. The number ofwashers 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 ofregular 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 ofa new machine.

165. The probability ofa regular replacement and the probability ofa newvs. used purchase are independent: For example, the probability ofa regular replacement with a used machine is the probability ofreplacement times the probability ofpurchasing a used machine. 6. Ifa greater proportion ofmachines with problems obtain repairs inthe future than they did in 1996, then the additional population ofrepaired machines have an extended lifetime which.is 6 years greater than the regular washer lifetime. 7. Formachines that do not experience problems, the relative probability ofan early replacement is zero for a newmachine 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 ofhouseholds minus the number ofhouseholds 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 ifit is going to purchase a clothes washer, and if so it then decides whether ornotto 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

17We assume an annual probability ofpurchase (relatively small) which varies according to the economic probability ofpurchase model. We also use the ratio ofnew vs. used purchase probability which is calibrated with market conditions in 1997 to be consistent with AHAM/NFO data. The relatively simple dynamics ofthe 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 Washerto Washer (year) Prob No Washerto Washer (year) CW No Washer Stock (year) 

### = The number ofnon-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 ofnon-owner households in a given year. Andthe number ofnon-owner households is calculated from the existing housing stock and the number ofclothes washer owners as described in the following equation: CWNoWasherStock(year) = (HousingStock)(year)-

# LJCWstock

## ](year) Eq. 1-12 

### ll.2.4.3 Current Assumptions The main assumption is that the probability ofpurchase from a non-owner household is very small. Secondly it is assumed that the newvs. used decision probability is the same as it is with the regular washer owners. And finally we assume that the differentprobabilities are independent; i.e., the probability oftwo decisions or events is the product ofthe 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. Itis therefore assumed that the lifetime ofthese clothes washers has been extended by these extra repairs.

18

### 1.2.5.2 Approach The input ofthis particular stock ofwashers comes from regular washer households that have made extrarepairs 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 ofextended-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 ofage). The main event 

### inthis decision tree is whether ornot the machine has problems. This probability function is a shifted version ofthe survival probability function for regular washers; it is illustrated 

### infigure 8. Besides the survival probability function, the decision ofwhether a machine is replaced with a new washer, a used washer, or no washer is the same as that for regular washers. Interms ofequations, the dynaffiics ofthe extended-life clothes washers can be described as follows: First the retirement ofthe clothes washers is calculated simply withthe retirement (replacement) probability function (shown in figure 8).
CW

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

- XRstock(year,age) 

### Eqn. 1-13

Thenthe stock accounting is done suchthat the change in stock is the number ofregular clothes washers that get extrarepairs minus the stock that is returned: 

### 19CW-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) CWXtraRepairs (year, age) =

= The number ofextended-life clothes washers ofa particular age retired in a given year. The probability that an extended-life washer ofa given age will be replaced orretired. The number ofextended-life washers ofa given age in a given year. The number ofregular washers ofa particular age that received extrarepairs 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 CurrentAssumptions There are several assumption ofthe 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 ofthe regular washers. 3. The newvs. 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 oftwo events or 

### 20decisions is the product ofthe individual probabilities. 5. The retirement probability function is independent oftime.


### 1.2.6 Accounting Equations Formaking the shipment forecasts, we specify a series ofequations that define the dynamics and accounting ofthe different types ofclothes washer stocks. For net new housing the equation describing the stock ofnew housing is straight forward. The stock ofnewhousing is the difference betweenthe 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 ofregular washers. Forthe stock ofregular washers we have two equations which describe the accounting ofthe population. The first equation says that the number ofone-year old clothes washers is equal the number ofnew 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 ofthe 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 ofregular clothes washers 

### in existing housing ofa particular age. The number ofnew washer purchases in a particular year. The number ofregular washers from a particular age category that were replaced in a given yearbecause of problems thathad occured The number ofregular washers that are replaced early from a particular age category in a given year for discretionary reasons. The total number ofused purchases 

### in a given year. The total number ofearly replacements (ofall age categories) ofregular washers in a given year.

21CWXtraRepairs (year, age)= The number ofregular washers that have received lifetimeextending repairs. These washing machines get transferred to the extended lifetime stock Equation 16 indicates that the number ofclothes washers in a particular age category is equal to the number ofclothes washers in the younger age category ofthe previous year minus the number ofclothes washers retired orreplaced early and plus the number ofused clothes washers ofthat age category that have beenpurchased inthe previous year. The age distribution ofused clothes washers is assumed to be the same as the age distribution ofclothes washers that are replaced early (since such early replacements are assumed to provide much ofthe 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-XRRetired(year, age) = CWxtra**~epairs** (year, age) = The number ofclothes washers in a given year ofa given age group that belong to the stock ofmachines that have received extra repairs. These extra repairs have extended the life ofthe machine. The number ofmachines ofa particular age that are retired from the extra repair stock in a given year. The number ofregular washers ofa particular age in a given year that receive repairs that extend the machine life in a given year. Equation 17 says that the stock ofextended life clothes washers comes from regular washers whichreceive extrarepairs when they break down. This stock then ages, and is_removed as it is retired due to additional repair problems. Forthe stock ofhouseholds with no washer we have the following equation:

where CWNoWasherStock(year) = (HousingStock)(year)-

# L[ CWstock](year)- 

# L[CW- XRstock

## ](year) Eq. 1-18

CW NoWasherStoclyear) =The stock ofhouseholds who do not own clothes washers 22(Housing Stock) (year) :E[CW stock](year) :E[CW-XR stocJ(year) = The total stock ofhousing in a given year = The total stock ofhouses with regular clothes washers ofany

age category.
= The total stock ofhouses with extended life washers ofany

age category. Equation 18 says that number ofnon-owner households is the number ofhouseholds minus the number ofregular washer owners minus the number ofextended life washer owners. The new andused washerpurchase are related to changes inthe different clothes washer stocks as follows:
CWNew(year} 

## =ProbNewVs.Used(year}*

CWNewNewHomes(

### 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 0.9S* 

### 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 ofnewwasher purchases in a given year. The probability that a purchase is a new washer The number ofwashers purchasedby non-owners in a given year. The number ofused washer purchases in a given year. Inthe rest ofthis report we will describe in more detail howthis 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 orderto estimate the impact ofstandards-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 ofpurchase 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 inthe following process flow diagram:



### Figure 9 Model development Conjoint Analysis LogitProbability ofPurchase Model

24 Initial Model Assessment

-- Does NotMatch

1980

- 19 6 Shi ments
Revised Probability ofPurchase Model

Model Calibration

Purchase Model

### 1.3.1 Logit Probability ofPurchase Model 1.3.1.1 Logit Equation The mathematical building block for the modeling ofconsumer decision probabilities is the logit probability ofpurchase model. In this model, the probability ofpurchase depends onthe utility ofthe clothes washer, U, which depends onthe attributes ofthe appliance. This purchase probability is constrained to be between 0 and 1, and relative changes inthe probability of purchase are proportional to changes inthe utility ofthe appliance. These theoretical requirements for the decision probability function can be satisfied by requiring that the probability ofpurchase function satisfies the following equation: 

### dProb/Prob=dU*(l-Prob) Eq.1-21 where Prob= decisionprobability, and dU is the differential change in utility which is a linear function ofthe clothes washer attribute variables. The factor of(1-Prob) on the right hand side of the equation enforces the condition that the probability ofpurchase never exceeds 1. We can solve the above equation for the probability function assuming a particular :functional form ofthe utility in terms ofthe attribute variables: 

### dU

# =b ·

### d(Price) 

### +c ·

### d(OperatingSavings) 

### +d ·

### d(FeatureIndex) Eq. 1-22 where the differential change inutility is equal to a linear function ofdifferential changes inprice, 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 ofintegration determined by the values ofthe 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 logit probability ofpurchase model.

251.3.1.2 Utility coefficients and elasticity Once the form ofthe purchase probability function is defined, the next task is to estimate the coefficients ofthe model from the available data. Inthis 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 ofclothes washer consumerpreferences, the Clothes Washer ConsumerAnalysis, (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 ofthe model assumptions and setthe approximate relative amplitudes ofthe features and price coefficients. Forthe next step, we adjusted the relative size of the savings coefficient to be consistent with observations onthe approximate market discount rate. Forthe final step, we used historical data to calibrate ofthe utility coefficient amplitudes. 'We used

### AHAMINFO and RECS survey results to set sizes for the initial market segments 

### In discussions ofprice sensitivity ofthe clothes washer market, much ofthe technical literature discusses variations in demand interms ofthe price elasticity. For a logitprobability ofpurchase model, purchase price elasticity for a market segment depends on two mainparameters: (I) the initial probability ofpurchase, or likelihood ofpurchase, ofthat market segment, and (2) the coefficient for price inthe 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 inpurchase 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 interms ofthe probability function ratherthan interms ofa simple elasticity value. We use a probability function model so that the impact oflarge price changes can be properly estimated. Whenprice 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 orderto aid in the description and modeling ofconsumerpreferences 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 ofEnergy, 1999), but we summarize the salient features here. The focus group study was used to determine what features ofclothes washers were of importance to consumers. Forthe 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 ofpriority 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 ofsix different features and their impact onpurchase probabilities. The conjoint study asked respondents which clothes washers would they consider purchasing today given a range ofclothes washer attributes. The prices considered ranged from $400 to $650. Meanwhile 1he amount ofenergy 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 ofpriority, are: (1) price, (2) energy and water savings, (3) water temperature options, and (4) door placement. (Note: loadsize options were ratedmore important than doorplacement, but thisfeature wouldnot be affected by a standard). 

### l.3.3 Stated vs. 

### Revealed Preferences Consumers preferences canbe measured orindicated in several possible ways. Stated consumerpreferences 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 whenthey actually make a clothes washer purchase can be significantly different 

### than the presumed purchase context ofa stated preference study. The difference between stated and revealed consumerpreferences is noted intextbooks that discuss the application ofconjoint 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
27availability. Appropriate adjustments are therefore needed to account for the effect ofthese marketing actions. (Lehmann, Gupta & Steckel, 1997) Therefore the results ofstated 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 oflower-efficiency lower-priced models. Typically a consumer will find himselfor herselfin a more constrained circumstance during an actual clothes washer purchase. For example, over halfofclothes washer purchases are due to the breakdown ofan existing clothes washer. Under constrained purchase circumstances consumers will find themselves with fewer choices, and the influence ofprice, savings, and other dothes washer attributes will diminish. Ifone 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 ofthe 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 ofprice in consumer purchase behavior relative to savings appears to be more than what was stated inthe Clothes Washer Consumer Analysis when one looks at intercept surveys and current market conditions. We therefore decreased the relative size ofthe savings coefficient vis a vis the price coefficient as one adjustment. The second adjustment rescales all coefficients to optimize the back-cast ofhistoric 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 inthe forecast offuture sales, because ifwe can accurately model historical consumer reactions to a 25% price change in the past, then we assume that we can model future consumerreactions to similar price changes. 

### 1.3.4 Determination ofDecision Sensitivities The price and feature sensitivities inthe 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 oflaundry 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 ofclothes washers in newhousing.



### 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 WasherPrice -+- Operating Cost 

### Figure 10 Historical changes in 

### clothes washerprice, operating cost, and non-housing shipments. Figure 10 shows that from 1980 to 1996 there is a 30% decrease inprice and a 30% decrease in operating cost while there is a 63% increase innon-housing shipments. But only a fraction ofthese shipments are due to decreased prices or operating cost, a large fraction ofthis 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 wishto change their current clothes washerbecause it is outdated, because they are remodeling, orbecause they are unhappy withthe features oftheir current washer. The other source ofdemand is from consumers whose present washer breaks down. The AHAM/NFO study estimates that approximately 73% ofnon-housing demand is due to replacement ofbroken machines, and 27% ofnon-housing demand is discretionary. Given the average 14-year lifetime ofclothes washing machines one can estimate the increase from 1980 to 1996 ofreplacement 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 inthe total population ofclothes washers that are subjectto replacement. As the total number ofclothes washers in U.S. households increases, the number ofclothes washers that may bereplaced for discretionary
29reasons will increase proportionally (all other factors being eqUal). We estimate that the total stock ofclothes washers increased from approximately 67 million washers in 1980 to 85 million in 1996, an increase ofabout 27%. With approximately 1.8 million discretionary replacements in 1996, an increase in discretionary sales of0.4 million/year can be attributed to the fact that there is a larger population ofclothes washers in U.S. households to be replaced. Combining the increased number ofwashers that break down and the increase inthe population ofwashers 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 thanprice, or operating cost changes. lbis means that ofthe 2.5 million/year shipments increase from 1980 to 1996, only about 1.1 million washers/year ofshipments increase is probably due to changes in the 1economic decisions ofconsumers caused by price and operating cost changes or other economic :factors. Most ofthe 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 consumerpurchase decisions observed inthe historical shipments data are ofcomparable order ofmagnitude to the type ofchanges we would expect after the imposition of a standard. A standard may cause long-term changes inprices and operating costs for clothes washers relative to other consumer expenses. These changes inrelative 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 inpart, in response to a 30% decrease inpurchase price and 30% decrease in operating costs. The question is howthe consumers economic decisions are influenced by various independent factors: Howmuch ofthe sales increase is due to the fact that washers are cheaperto purchase, howmuch ofthe change is due to the fact that clothes washers are cheaperto operate, and howmuch ofthe 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, butthat other features may be more ofa factor in foture. We examine these questions inmore detail inthe next section. 1.3.4.1 Price Sensitivity For determining the relative importance ofprice and savings (i.e. operating cost) siensitivities, we have three potential sources ofdata including: (1) Results from the Clothes Washer Consumer Analysis (2) The savings/price trade-offimplied 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
30price and savings sensitivities. The relative importance ofsavings and price canbe expressed interms ofa market discount rate. Ifthe 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 paybacktime from more expensive high-efficiency washers, then the market discount rate is relatively low. Ifa consumer will tolerate a price increase ofAP in order to obtain an annual savings of AS, then the ratio ofAP andAS can be expressed interms ofthe 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 andN is the lifetime ofthe clothes washer inyears The above AP/AS ratio represents the ratio ofprice and savings changes which make no change in the consumerutility ofa purchase. Therefore this ratio also is related to the ratio ofthe ,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 ofthe utility coefficients inthe 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. Butthis market discount rate for stated consumerpreferences 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 ofa 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 orderto estimate the market discount rate, we did an analysis ofthe price and savings tradeoffunder current market conditions.

31Qol 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 ofthe 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 ofthe costs ofhigher 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 interviewperformed during the Pacific Energy Associates for the Northwest Energy Efficiency Alliance (Hewitt, et. al., July 1998) indicated a market discount rate ofone to two years for clothes washer shoppers--depending on the details ofhow 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. Whenthe 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 ofthe 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 peryear to 1.3 million shipments peryear with this change
32in discount rate. (The final, calibrated model has an RMS deviation of0.2 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 ifonly 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 ofthe adoption ofnewtechnologies 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 offrontfoading washers (Tomlinson & Rizy, 1998), though the implications ofthe 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 onthe level offamiliarity 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 ofthe entire sample. In the shipments model, we assumed that ifa standard at the 35% level orabove 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 ofthe newtechnology. Therefore the size ofthe top/front loading coefficient in the purchase price model was set at 

### Y2 the size ofthe coefficient for the conjoint sub-sample ofthose familiar with horizontal axis machines. This value presumes that all consumers will be familiar with horizontal axis machines ifthey come to dominate the market, and that there will be some adaptation to the newtechnology, though acceptance will not be complete. 

### 1.3.5 Calibration ofShipments Model The clothes washer shipments model was calibrated with historical shipments data. Figure 12 illustrates the two stages ofmodel 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 ofthe adjustment ofthe market discount rate and the operating cost savings coefficient to reflect observed purchase behavior inthe current market. This frrst adjustment decreases the root mean square (RMS) deviation from historical shipments from 3.6 million peryear to 1.3 million peryear.

33For the final calibration ofthe model, we fixed the relative size ofthe price, savings, and front-loading feature coefficients to values determined from evaluation ofthe Clothes Washer ConsumerAnalysis, and market discount rates. By finding a market discount rate of75%, and by 1estimating the relative size ofthe front loading elasticity.to be about Y2 ofthe sensitivity ofthe**1~onsumers** familiar with front loaders, the ratios ofthe 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 ofhistorical data was obtained as measured by the (RMS) deviation between historical shipments and model shipments between 1981 to 1996 inclusive. Forthe fully calibrated model, the RMS deviation between the model and the industry data on historical shipments is 0.2 million shipments peryear. Figure 12 illustrates the fit ofthe**~:hipments** model withhistorical data and the improvement obtained by adjusting boththe market discount rate and coefficient b.**~** 

# = Q 16
14
12
10 

# = 8 

# -**~** 6
4
2 

# .. Shipments ofClothes Washers

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

- - - - 75% DiscountRate " '' ' ' 

# . ' 

# . '

-- Calibrated Model 

### + Historical

.•



### -.....- 

# . · .. _,



# . 

# . . ..



# . . ' 

# . '

# . _.,"""".... ' 

# ____....

# , 

# ' ' 

# -- .-· 

# ' ' ,-- 

# , __



# .. 

# - -:- 

### .-**O+--.,..---,~~-,-__,~.....---..-~.--.....---.~.----.----.-~.,..-~--r~-..--,-~---,** 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 

### Year Figure 12 Calibration ofshipments model with historical data

34

### 1.4RESULTS Once the model is calibrated with historical data, it provides a rather detailed picture ofthe possible impacts ofstandards on purchases, replacement, and repair ofclothes washers. The results presented in Figure 13 represent our best estimate ofpossible standards impacts. As explained below, actual impacts may differ from our forecast for a number ofreasons. 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. 

### Ifother 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. Itis possible that educational and marketing programs implemented before the standard is implemented canhelp increase revealed consumer preferences to values closer to the stated consumerpreference. • We assume that manufacturers will not add supplementary features to post-standards clothes washers. The addition offeatures to high-efficiency clothes washers can decrease the sales impacts ofhigher prices by further increasing the consumer value ofthe poststandard clothes washers. • We assume that after a standard used clothes washer supply would be unlimited, though more expensive. The model predicts that most ofthe consumers who decide notto purchase more expensive post-standards clothes washer will purchase used clothes washers instead. 

### Ifthere 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 ofstandards:
• We assume that consumers will gradually adapt to front-loading washers. 

### Ifthere is no adaptation to front-loading machines, then sales impacts ofhigh efficiency standards (efficiency levels higher than the 35% level) may be greater than predicted. • We assume that the market discount rate is 75%. 

### Ifin actuality the market discount rate is greater than our assumed rate, then relative size ofthe price elasticity will be greater, and so will standards-induced sales impacts.

35New 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 ofStandards-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 ofthe different proposed standard levels. As shown in the figure, sales and shipment impacts ofthe 5% to 20% standard levels are within 5% ofbase case. Larger sales impacts are forecast for standard levels above the 20% level. For the 25% to 50% standards levels the volume ofnew clothes washers shipments is forecast to decrease, while total dollar volume ofsales is forecast to increase. Both the impacts at the year ofthe standard and the average impacts over the forecast period, 2003 to 2030, are 

### ii1

ustrated.



### 36Estimatro Standards

### Impacts Shipments and SalesofNewWashers

StandardLevel 

### Figure 14 Estimated standards impacts on new clothes washers The biggest factor that influences the size ofthe potential standards-induced changes is the actual retail price increase that is induced by the standard. Ifprice 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 ofthese opposing effects is examined in more detail in the manufacturing impact analysis. Some ofthe measures that consumers mighttake to avoid purchase ofa newhigher-prices clothes washer keep them out ofthe market for only a relatively short period oftime. Therefore there is some recovery from the initial shipments drop that might be seen inthe year ofthe standard. Itis estimated that the long term average shipments drop is about 35% less than the drop which mightbe seen in the first year ofthe standard.

37160% 140% 120%



### .... 

### ... 100% OS c. 

### e

.... " 80%**~** OS

### ~ 60% 40% 20% 0% 5% 10% 

### Estimated Standards Impacts Shipments and Sales ofUsed 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 ofstandards onthe used clothes washer market. The used market will provide one ofthe most attractive options for consumers having broken dothes washers and who wish to avoid the expense ofa 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 inthe used clothes washer market is larger than the initial increase at the year ofthe standard. In estimating the relative impact on used clothes washer sales, we assume that the price of used clothes washers follows the price ofnew clothes washers and increases proportionally.

3810"/o 9"/o 8%

..... 7% y 

# = c. 6% 

## e

.... a.I 5%**~** 

# = 4%

### ~ 3% 2% 1% 00/o 5% 10"/o 

### Estimated StandardsImpacts WasherAge, Lifetime, & Repairs



# • 15% 20"/o 25% 35% StandardLevel 40"/o 45% ,._MeanAge -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 ofwashers, used market, and washer repairs. Figure 16 illustrates the estimated impacts onthe mean age ofclothes washers, the mean clothes washer lifetime, and the total volume ofclothes washer repairs. These are average impacts over the standard period of2003 to 2030. These three different measures ofclothes washer retention measure different types ofconsumerreactions to higherpotential clothes washer pnces. The increase inrepair rate measures the impact ofconsumers who perform an extrarepair on their clothes washer rather thanretire the machine. Suchrepairs are few compared to the total volume ofclothes washer repairs because ofthe large volume ofminor repairs that occur over the lilfetime ofa washer. According to Consumer Reports about 23% ofclothes washers have repairs during the first five years ofownership (Consumer Reports, May 1998). The extended lifetime ofclothes washers reflects repairs that consumers might undertake to extend the lifetime ofclothes washers. Such extended repairs will have a delayed effect on the average lifetime ofa clothes washer, and only a relatively small fraction ofmachines will receive such extended repairs (some machines may not be repairable, and consumer will also have the
39choice ofpurchasing a used washer). An extra repair extends the life ofa 

### 14 year old machine by .at most six years. Atthe 50% standard level lessthan 20% ofmachines receive extra repairs that 1extend the machine life. This implies that the lifetime ofwashers is increased by at most one year by the imposition ofa standard. The increase in mean age ofa clothes washer illustrates both the impacts ofextrarepairs and a more vigorous used clothes washer market. When more machines are cycled through the used market, then the proportion ofolder machines increases slightly, and this results in a slight imcrease in the average age ofmachines. 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 ofthe standard. ll.5 CONCLUSIONS In order to provide a more detailed picture ofpotential 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 newhousing, 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 ofpurchase model for purchase decisions made by consumers that accounts for the impacts ofprice, operating cost, and features on shipments. Model parameters were estimated by using a variety ofdata 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 ofthe predicted impacts are illustrated infigures 13 through 16.



### 40

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