### Table 7.9 Summary of Payback Period Results-AEO Reference Trial Payback Period in Years Standard MEF Shown by Percentiles of the Distribution of Results' Level 0% 10% 25% 50% 75% 90% 100% Mean

0.860 0.0 0.0 0.0 0.0 0.0 0.2 3.7 0.1 0.908 0.0 0.0 0.0 0.1 0.5 1.8 28.9 0.7 0.961 0.0 0.0 0.1 0.2 0.6 4.2 35.2 1.4 1 1.021 0.0 0.1 0.2 0.6 6.2 12.8 65.0 4.4 2 1.089 0.0 0.9 2.0 4.0 6.7 10.0 55.8 5.0 4 1.257 0.7 2.3 3.3 5.1 8.3 13.7 94.3 7.0 5 1.362 0.9 2.4 3.3 5.1 8.3 13.7 107.4 7.0

1.485 0.9 2.8 4.2 6.8 10.9 16.6 128.9 8.6 6 1.634 1.1 3.1 4.5 7.0 11.0 16.5 83.9 8.7

1.04 MEF 0.1 0.9 1.9 3.5 6.0 9.3 44.5 4.6 3 in 2004

1.26 MEF 0.7 2.3 3.2 5.0 8.1 13.3 93.3 6.8 in 2007 For sample size of 10,000 trials. Energy price trends are from AE099. Operating costs include water prices. 

### Each row in Table 7.9 corresponds to the impacts on a population of households from a possible standard level. For example, for a MEF of 1.26, the sample household with the shortest payback period has a payback period of 0.7 years. This result is in the "0" percentile column. For the same MEF of 1.26, the sample household with the longest payback period of 93.3 years, is represented in the "100" percentile column. In between, 10% of sample households have a payback period of under 2.3 years and 90% of households have a payback period of 13.3 years or less. The mean impact is a payback period of 6.8 years (in column "Mean"). Just prior to the publication of this analysis both RECS97 and AEO2000 data became available. We have updated the analysis for Trial Standard Level 3 using RECS97 and AEO2000 and have included it in Appendix R. As shown in Appendix R, there is no significant change in the results.

7-36

### Table 7.10 Summary of Payback Period Results-AEO High Growth & Water Escalation Rate Trial Payback Period in Years Standard MEF Shown by Percentiles of the Distribution of Results' Level 0% 10% 25% 50% 75% 90% 100% Mean

0.860 0.0 0.0 0.0 0.0 0.0 0.2 3.6 0.1 0.908 0.0 0.0 0.0 0.1 0.5 1.7 21.9 0.6 0.961 0.0 0.0 0.1 0.2 0.6 4.1 32.9 1.4 1 1.021 0.0 0.1 0.2 0.6 5.9 12.5 67.3 4.2 2 1.089 0.0 0.8 1.9 3.7 6.2 9.4 55.0 4.7 4 1.257 0.7 2.2 3.0 4.8 7.8 13.1 82.4 6.6 5 1.362 0.8 2.2 3.0 4.8 7.9 13.1 88.9 6.6

1.485 0.8 2.6 4.0 6.4 10.3 15.7 117.4 8.2 6 1.634 1.0 2.9 4.2 6.5 10.1 15.0 111.2 8.1

1.04 MEF in 0.0 0.9 1.8 3.3 5.6 8.7 55.9 4.3 2004 3 1.26MEFin 0.7 2.0 2.8 4.5 7.4 12.4 81.1 6.2

2007

7-37

### Table 7.11 Summary of Payback Period Results -AEO Low Growth & Water Escalation Rate Trial Payback Period in Years Standard MEF Shown by Percentiles of the Distribution of Results Level 0% 10% 25% 50% 75% 90% 100% Mean

0.860 0.0 0.0 0.0 0.0 0.0 0.2 3.8 0.1 0.908 0.0 0.0 0.0 0.1 0.6 1.9 29.2 0.7 0.961 0.0 0.0 0.1 0.2 0.6 4.4 36.0 1.4 1 1.021 0.0 0.1 0.2 0.7 6.3 13.0 80.2 4.4 2 1.089 0.0 0.9 2.2 4.3 7.3 11.0 66.7 5.4 4 1.257 0.9 2.6 3.5 5.5 8.8 14.4 106.9 7.4 5 1.362 0.8 2.6 3.6 5.6 9.1 15.0 95.6 7.6

1.485 0.9 3.0 4.5 7.3 11.6 17.6 108.3 9.2 6 1.634 1.2 3.3 4.8 7.5 11.7 17.2 96.8 9.2

1.04 MEFin 0.1 1.0 2.0 3.7 6.3 10.1 65.0 4.9 2004 3 1.26 MEFin 0.9 2.6 3.6 5.5 8.9 14.4 106.8 7.5

2007 

### Figure 7-19 below summarizes the payback periods for the reference case and high and low economic growth sensitivities.

7-3814

-.-- Reference 12 -.- AEO-high
-- AEO-Iow 10 1 

# L X

5 10 15 20 1.O4MEF 25 35 1.26MEF 40 45 50 in2004 in2007 Standard Level 

### Figure 7.19 Payback Periods for Reference, High and Low Growth Scenarios
7.4 REBUTTABLE PBP Rebuttable PBPs are presented in order to provide the legally established rebuttable presumption that an energy efficiency standard is economically justified if the additional product costs attributed to the standard are less than three times the value of the first year energy cost savings (42 U.S.C. §6295(o)(2)(B)(iii)).
7.4.1 Metric The basic equation for Rebuttable PBP is the same as that shown in section 7.3. Unlike the analyses in sections 7.2 and section 7.3, the Rebuttable PBP is not based on distributions and does not utilize the crystal Ba11TM option in the spreadsheet model. Rather than using distributions, the Rebuttable PBP is based on discrete values and is based on the DOE clothes washer test procedure assumptions (Appendix Jl).14

7-39

### 7.4.2 Inputs

Rebuttable Presumption Payback Period. Inputs differ from theDistribution PBPin that discrete values are used rather than distributions (where distributions are used in the LCC and Distribution PBP) for inputs. All dollar values are in 1997$. Inputs to the Rebuttable Presumption Payback are outlined below. 

### • For purchase expense: the shipment weighted average (SWA) of most likely price (in the AHAM supplied Engineering data) is used as the input. • The cycles/year are 392, from DOE test procedure • Energy per cycle for each possible standard level is obtained from the AHAM supplied data. Disaggregated values were submitted for each possible standard level for the energy use of machine, hot water and dryer energy. • Marginal electric prices used are weighted average values for the year the standard takes effect, i.e., marginal rates adjusted using AEO projections for the year 2004. • Water use per cycle is the gallons per cycle submitted by AHAM (see Engineering data). • Water plus wastewater rates are the weighted average of a national distribution; $2.48/i 000 gallons. • A discount rate is not required in this calculation • The fuel use is based on the test procedure assumption of an electric water heater and an electric dryer. • Year to start date assumed is 2004. No savings in detergent costs. Payback periods are first calculated between the new standard level and each washer efficiency being sold in the year 2004. We will use a simplified distribution of efficiencies currently being sold - for these calculations we assume a washer is either at the baseline level or at an MEF level of 1.257(35%reduction in energy use level and assumed to be H-axis in the AHAM supplied data). The payback periods are then weighted and averaged according to the percentage of each washer efficiency sold before a new standard is enacted. For the year 2004, we predict that 9% of clothes washer sales will have an energy efficiency equivalent to a 35% reduction in energy use (as compared to the current minimum efficiency requirements). The remaining 91% of sales are assumed to have a baseline energy use as provided by AHAM for the minimum current efficiency level. Rather than distributions, single point values for the inputs are used. These values (including cycles per year, electric fuel source, etc.) correspond to those outlined in the DOE test procedure, discussed in the Code of Federal Regulations, Title 10, Volume 3, Part 430, Subpart B, Appendix Ji. The result is a single payback value and not a distribution of PBPs. The payback is calculated for the expected effective year of the standard (e.g., 2004) and is presented below in Table 7.12.

7-40

### 7.4.3 Results

table 7.12 Rebuttable Market Share Standard Level
5 10 15 20 MEF = 1.04 (in 2004) 25 35 MEF = 1.26 (in 2007) 40 45 50 back in Years 91% 0% (MEF=0.860) to new Standard Level 0.1 0.3 0.7 2.1 2.5 2.9 4.2 4.1 4.3 5.7 5.7 9%

35% (MEF= 1.257) to New Standard Level NA NA NA NA NA NA NA 19.8 19.6 34.6 23.2 Weighted Payback
0.1 0.3 0.7 2.1 2.5 2.9 4.2 5.5 5.7 8.3 7.3 Note: NA = not applicable 

### In Table 7.12, the column labeled "0% to Standard" gives the payback period for each level in the Market Share column when the payback of each higher efficiency level is calculated assuming the cunent washer owned by the consumer is at the minimum efficiency level. The column labeled "35% to Standard" shows the payback period calculated assuming the consumer already has a washer with an efficiency of35% (MEF = 1.257) and incurs a cost and benefits from savings for a washer with an even higher efficiency. The results inTable 7.12 above are based on an increase of high efficiency (e.g., H-axis) sales per year of 0.5%. This percentage is of the market share that has not previously been converted over to H-axis, i.e., each year0.5% of remaining V-axis sales are converted to H-axis sales. The negotiated scenario of a two-tier standard with MEF levels of 1.04 becoming effective in the year 2004 and a MEF level of 1.26 becoming effective in the year 2007 is also represented. The values shown for the second tier were calculated for the year 2007. All other calculations are based on the year 2004. The effective year does not have a great impact on the payback period because only the fuel, water price and assumed stock that are high efficiency washers are different when another year is chosen.

7-41

### The analysis in this TSD is based on inputs from RECS93 and AEO 1999. Just prior to the

publication of this analysis both RECS97 and AEO2000 data became available. We have updated the analysis for Trial Standard Level 3 using RECS97 and AEO2000 and have included it in Appendix R. As shown in Appendix R, there is no significant change in the results.

7.5 USER INSTRUCTIONS FOR SPREADSHEET It is possible to examine and reproduce the detailed results obtained in this part of the analysis using a Microsoft ExcelTM spreadsheet available on the U.S. Department of Energy Office of Codes and Standards website at: www.eren.doe.govlbuildings/codes standards!. To execute the spreadsheets fully you will need both Microsoft Excel and Crystal Ba11TM software. Both applications are commercially available. 7.5.1 What does the Life-Cycle Cost (LCC) Spreadsheet Do? The LCC spreadsheet (currently LccCW_lOf.xls) performs calculations for life-cycle cost and payback periods. The LCC spreadsheet operates in Excel 97 or Excel 7 (Windows 95). The Excel add-on Crystal Ball (version 4.0) allows the user to perform uncertainty analysis on key input variables.

7.5.2 What are the Worksheets in the Workbook? The workbook LccCW_lOf.xls includes the following worksheets: LCC (Sample Calc) contains the input selections and a summary table of energy use, operating costs, LCC and Payback. LCC (Distributions) contains the input selections as in the LCC (Sample Calc) sheet. The energy, cost, LCC and payback data are for the current sample if Crystal Ball is running or the last sample run if not currently running. Water Price Dist contains price and escalation data for water. Household Data contains marginal energy prices for each sample household, washer cycles per year for each household, and fuel use distributions. Engineering contains the manufacturer costs for each efficiency level, as well as the manufacturer and retail markups.

7-42

### Energy Price contains energy prices from the various sources of energy price information; this is used for determining the energy price escalation. dratedist contains data from which an average discount rate and a distribution of discount rates is determined. Lifetime contains the retirement function for clothes washers and the average clothes

washer lifetime in years. Setup this is used as an interface between user inputs and the rest of the worksheets

--

### do not modify this sheet.

7.5.3 How Does the User Operate the Spreadsheet? To execute the spreadsheets fully you will need both Microsoft Excel and Crystal Ball software. Both applications are commercially available. Crystal Ball is available at http://www.decisioneering.com. 1. Once you have downloaded the LCC file from the Web, open the file using Excel. At the bottom, click on the tab for sheet LCC (Sample Caic) or LCC (Distributions). 2. Use Excel's commands at the top View/Zoomto change the size of the display to make it fit your monitor. Note, that the zoom level for each of the worksheets should be set to the same value. Otherwise a bug in Excel will cause a 'Not enough system resources to display completely' error. 3. The user interacts with the spreadsheet by clicking choices or entering data using the graphical interface that comes with the spreadsheet. Choices can be selected from the box labeled ListInputson either of two work sheets: a) LCC (Sample Caic) or, b) LCC (Distributions). A change in either input sheet also changes the other. In the box titled List Inputs select choices from the selection boxes for (1) energy price projection, (2) start year, (3) baseline design, (4) standard case design, (5) water heater (WH) / dryer combination, (6) water escalation rate, (7) manufacturer's cost (percentile or distribution). On the LCC (Distributions) worksheet, discount rate can also be entered if a value other than the default distribution is wanted. After any changes, restore this value to =dratedist if you wish to restore the default distributions. On the LCC (Sample Calc) worksheet, non-default values can be specified for the discount rate, clothes washer lifetime, cycles (wash loads) per year and energy prices. Click on the

7-43

### Restore Defaults command button if you want to restore the default values for these

parameters in this worksheet. 4. To change assumptions onList Inputsclick on the assumption you wish to change, and click on the new assumption from the menu. 5. This spreadsheet gives the user two methods of running the spreadsheet. a) If the LCC (Sample Calc) sheet is chosen, then all calculations are performed for single input values, usually an average. The new results are shown on the same sheet as soon as the new values are entered. b) Alternately, if the LCC (distributions) sheet is used. The spreadsheet generates results that are distributions. Some of the inputs are also distributions. The results on the LCC distribution that are shown as single values only refer to the results from the last Monte Carlo sample and are therefore not meaningful. To run the distribution version of the spreadsheet the Excel add-in software called Crystal Ball must be enabled.
7.5.4 What Is the Lcc (Sample Calculation) Sheet Used For? LCC difference and Payback are in the LCC (Sample Calc) sheet are based on single point values. This page can be used to see the effect of changing a single parameter. It is also used to determine a rebuttable presumption payback (when inputs are based on test procedure values wherever possible).

7.5.5 How Does the User Run the Crystal Ball Simulation? (LCC Distribution Sheet) To produce sensitivity results using Crystal Ball, you need simply select Runfrom theRun menu (on the menu bar). To make basic changes in the run sequence, including altering the number of trials, selectrun preferencesfrom the Run menu. After each simulation run, the user needs to selectReset(also from theRunmenu) beforeRun can be selected again. Once Crystal Ball has completed its run sequence it will produce a series of distributions. Using the menu bars on the distribution results it is possible to obtain further statistical information. The time taken to complete a run sequence can be reduced by minimizing the Crystal Ball window in Excel. A step by step summary of the procedure, for running a distribution analysis, is outlined below: 1) Find the Crystal Ball toolbar 2) Click onRUN 3) SelectPreferenceand choose from the following choices:

7-44a) Monte Carlo'1 b)Latin Hypercube 

### c) Initial seed choices and whether you want it to be constant between runs d) Select number of Monte Carlo Trials (we suggest 10,000 for high accuracy calculations and 500 for quick calculations). 4) To run the simulation, follow the following sequence (on the Crystal Ball toolbar)

RUN RESET RUN 

### 5) Before running Crystal Ball make sure your curser is not on any cell that has content, i.e., put curser on a blank cell). 6) Now wait until the program informs you that the simulation is completed.

7.5.6 What Kind of Output Does Crystal Ball Generate? 3) After the simulation has finished Monte Carlo run, to see the distribution charts generated, click on the Windows tab bar that is labeled Crystal Ball. 4) Currently, the life-cycle cost savings and payback periods are defined as forecast cells. The frequencycharts display the results of the simulations, or trials, performed by Crystal Ball. Click on any chart to bring it into view. The charts show the low and high endpoints of the forecasts. The View selection on the Crystal Ball toolbar can be used to specify whether you want cumulative or frequency plots shown. 5) To calculate the probability of LCC savings being positive, either type 0 in the box by the right arrow, or move the arrow key with the cursor to 0 on the scale. The value in the Certainty box shows the likelihood that the LCC difference between the baseline and standard case will be positive. To calculate the certainty of payback period being below a certain number of years, choose that value as the high endpoint. 6) To generate a printout report, selectCreate Reportfrom theRunmenu. The toolbar choice of Forecast Windows allows you to select the charts and statistics you are interested in. For further information on Crystal Ball outputs, please refer to Understanding the Forecast Chart in the Crystal Ball manual.

aBecause of the nature of the program, there is some variation in results due to random sampling when Monte Carlo or Latin Hypercube sampling is used. We recommend using Latin Hypercube. 7-45

### REFERENCES

1. MTSC Inc./Management Technology Division, Energy Capital in the U.S. Economy, November, 1980. Bethesda, MD. 2. Erikson, J. T., personal communication. The Procter & Gamble Company. Letter to Peter Biermayer. Non-classified information. May 4, 1995. 3. U.S. Department of Energy, Residential Energy Consumption Survey: Household Energy Consumption and Expenditures 1993, October, 1995, Energy Information Administration. Report No. DOE/EIA-0321(93). 

### 4. U.S. Department of Energy-Energy Information Administration, Monthly Energy Review, 1999. <http://www.eia.doe.gov/emeu/mer/prices.html> 5. U.S. Department of Energy-Office of Codes and Standards, Marginal Energy Prices Report, 1999. <http ://www.eren.doe.gov/buildings/codes_standards/applbrf/pdfs/ marginal_energy_price.pdf> 6. U.S. Department of Energy-Energy Information Administration, Annual Energy Outlook1999 with Projections to 2020, December, 1998. Washington, DC. Report No. DOEIEIA0383(99). <http ://www.eia.doe.gov/oiaf/aeo99/homepage.html> 7. Gas Research Institute, 1998 Edition of the GRJ Baseline Projection, 1998. Arlington, VA. 8. Holte, S., Memorandum on extended price methodology used by the Federal Energy Management Program, personal communication. U.S. Department of Energy, Energy Information Administration. 1999. 9. Association of Home Appliance Manufacturers,Docket No. EE-RM-94-403, Comment #83, December 2, 1997. Comments to the Department of Energy. 10. American Water Works Association, WaterWiser, 1998 Water Use Summary, 1998. <www.waterwiser.org> 11. American Water Works Association, 1998 Water and Wastewater Rate Survey Summary

- Data courtesy of Raftelis Financial Consulting PA,1998. <http://www.waterwiser.org/frameset.cfm?b=2> 

### 12. Raftelis Environmental Consulting Group, 1998 Water and Wastewater Rate Survey, 1998. Charlotte, NC.

7-4613. Whirlpool Corporation, Docket No. CE-RM-90-201, p. 1 &2, Attachment #1, December 12, 1990. Comments to the Department of Energy. 14. Title 10, Code of Federal Regulations, Part 430- Energy Conservation Program for Consumer Products, Section 430, Subpt. B, Appendix Ji, January 1, 1999.

7-47

### CHAPTER 8. CONSUMER ANALYSIS

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### TABLE OF CONTENTS
8.1 iNTRODUCTION TO CONSUMER ISSUES 8-1 8.2 FOCUS GROUPS AND CONJOINT ANALYSIS 8-2 8.2.1 Results of Focus Groups and Conjoint Analysis 8-2 8.3 CONSUMER SUB-GROUP ANALYSIS 8-3 8.3.1 Life-Cycle Cost & Payback Results for Subgroups 8-3 8.3.2 Data Used in the Consumer Subgroup Analysis 8-9 LIST OF TABLES Table 8.1 Consumer Subgroup LCC Savings and Percent of Households Benefitting

... 

### 8-4 Table 8.2 Consumer Subgroup Payback Period Comparisons 8-5 Table 8.3 Summary of LCC Results

-

### Low Income 8-7 Table 8.4 Summary of LCC Results - Senior (head of household over65) 8-7 Table8.5 Summary of Payback Period Results - Low Income 8-8 Table 8.6 Summary of Payback Period Results - Senior 8-8 Table 8.7 Profile of RECS Households for Entire Sample and Subgroups 8-10 LIST OF FIGURES Figure 8.1 Summary of Subgroup Life-Cycle Costs 8-5 Figure 8.2 Summary of Subgroup Payback Periods 8-6

8-i

### CHAPTER 8. CONSUMER ANALYSIS

8.1 INTRODUCTION TO CONSUMER ISSUES As part of the process of setting a new energy efficiency standard for clothes washers, legislation requires that "the Secretary consider, among other factors,.. .if any lessening of the utility or the performance of the products is likely to result from the imposition of the standard (42 U.S.C. Sec. 6295 (o) (2) (B) (I) (IV)). In order to better inform the clothes washer standards rulemaking relating to consumer issues, the Department decided to follow the recommendations made by the consumer Subcommittee of the Advisory committee in December of 1997: Adopt a three-step process of obtaining background research, holding focus groups, and conducting interviews/surveys. The Department first conducted an extensive review of secondary sources of information on consumers and clothes washers (see Appendix I). The information was compiled by the Lawrence Berkeley National Laboratory and made available at a March 11, 1998, public workshop attended by manufacturers, trade associations, energy efficiency groups, and other stakeholders. This study was the subject of a review to determine if secondary studies provided adequate information to enable the Department to determine the value consumers placed on different clothes washer attributes. It was the consensus of the workshop participants that the secondary findings were inadequate because the samples contained in the surveys were not representative of the nation, not all the relevant clothes washer attributes were covered, and the methodologies of the different surveys were not comparable. A Clothes Washer Consumer Analysis Working Group (Working Group) was formed representing manufacturers, energy efficiency groups, national laboratories, and other stakeholders. In addition to developing a list of relevant clothes washer attributes, the Working Group reviewed different approaches such as focus groups, surveys, and a conjoint analysis. (A conjoint analysis is research technique that lets the consumer determine the combination of features that the product (or service) must have to appeal to them.) In order for the Department to conduct a consumer survey and/or focus group, the Paper Reduction Act of 1995 requires that the Department seek comments on the proposed information collection in a Federal Register notice, and seek Office of Management and Budget (0MB) approval through submission of the form 0MB 83-1 upon completion of the comment period of the Federal Register notice. DOE received a number of comments concerning the impact of the rule on low-income consumers and the elderly. In response to the concerns raised, the Department added a questionnaire to the conjoint analysis survey phase of the consumer analysis study to better understand how increases in the price of high-efficiency clothes washing machines would impact low-income and elderly consumers. See Appendix J for the full text of the consumer issues report. In addition, separate LCCs were done for the sub-groups of senior and low income consumers to assess if either

8-1

### of these subgroups would be adversely impacted by the expected increased cost of high efficiency

clothes washers. See Appendices K & L for detailed charts on life-cycle cost and payback periods.
8.2 FOCUS GROUPSAND CONJOINT ANALYSIS The clothes washer consumer analysis was completed in two steps. In the first step, ten focus groups were held in five regions of the country to develop a list of clothes washer attributes valued by consumers. In the second step, the six attributes cited most often by the focus groups that were likely to be affected by an efficiency standard were included in a conjoint analysis survey given to 400 respondents in four regions of the country (100 respondents per region). Conjoint analysis is a stated preference technique that requires respondents to trade-off different attributes against each other. By examining how respondents make these tradeoffs, the relative values placed on the clothes washer attributes can be determined. This enables the Department to empirically determine if consumers feel a change in any of the six attributes due to the new energy efficiency standard would lesson the utility of the machines. 8.2.1 Results of Focus Groups and Conjoint Analysis The focus group and conjoint results indicate that price is the most important attribute when consumers are purchasing a new clothes washer, although in each case another attribute is virtually tied with price in terms of importance. In the focus groups, 83 percent of the respondents included price in their top ten list of important clothes washer attributes, while 81 percent included wash tub capacity in that same list. In the conjoint analysis, price had the highest relative importance score (26 percent), followed closely by the availability of a wash load size option on the control panel (25 percent). Of the six attributes included in the conjoint analysis survey, door placement was the fifth most important attribute with a relative importance score of 11 percent. In the likelihood of purchase scenarios, the purchase probabilities were more sensitive to price than any of the other washer attributes.a While the shift from a standard to a high efficiency machine resulted in a drop in the estimated purchase probability, this was due to the change in price rather than to changes in the other attributes. When price was held constant at the standard efficiency level and the other attributes were allowed to change to reflect a high efficiency machine, the likelihood of purchase increased. This is due to the fact that consumers value energy savings more than top load door placement.

apchase probabilities indicate the likelihood a consumer will purchase a particular clothes washer, assuming (s)he has made the decision to buy a new clothes washer. For example, 59%of the full sample would be willing to purchase the standard efficiency clothes washer. 8-2

### The purchase probability findings indicate that low-income consumers and elderly consumers

were slightly more likely to purchase a high efficiency, front-load washing machine than the full sample. When the analysis focused exclusively on the impacts of clothes washer prices increasing, the data indicated that a smaller percentage of low-income consumers would be willing or able to purchase machines in the $650price level, when compared to the full sample. There was no statistical difference between elderly consumers and the full sample at the $650level. While the data from the price impact questions indicate that low-income consumers are more adversely affected by higher clothes washer prices than the sample as a whole, the Department is unable to determine the magnitude of the impact on future clothes washer purchases using the survey data. For instance, the consumer analysis survey found that approximately half of the low-income respondents currently do not own a clothes washer, while more than three-quarters of the respondents making more than $25,000 annually own a washing machine. The Department is unable to determine if this ratio wouldchange with a price increase due to the proposed standards. The fact that the survey found lowincome consumers are more likely to use store financing plans, such as no interest for one year, to purchase a clothes washing machine than the sample as a whole further clouds the magnitude of the new standards' impact on low-income consumers because store financing encourages consumers to purchase high price products by allowing payments to be paid over a number of months. For the entire focus group and conjoint report see Appendix J.
8.3 CONSUMER SUB-GROUP ANALYSIS The consumer analysis evaluated households with low income levels and senior households, who may be disproportionately affected by any national energy efficiency standard level. This was accomplished by analyzing the life-cycle cost and payback periods for those subgroups of households. The spreadsheet model used for the LCC analysis can be used with different data inputs. Among the inputs are the data from the 1993 RECS published by the EIA. The standard LCC analysis (described in Chapter 7) includes all the households having both a washer and a dryer. The subgroups analyzed to see if they were impacted differently then the general population were seniors and the poor. Seniors is defined as head of household over 65. Poor is defined as at 100% of poverty level. These subgroups were modeled by using the LCC spreadsheet model by only sampling the poor and senior head of household subgroups separately. 8.3.1 Life-Cycle Cost & Payback Results for Subgroups Table 8.1 below summarizes the LCC results for senior and low-income subgroups, as well as comparing them to the total sample of RECS households used in the overall analysis.

8-3

### Table 8.1 Consumer Subgroup LCC Savings and Percent of Households Benefitting

Trial Sample Households Benefitting Average LCC Savings Standard Level

_________ MEF

___________ Total



### (%) Senior 

### (%) Low income



### (%) Total



### ($) Senior



### ($) Low income



### ($) 1 1.021 84 79 85 61 41 69 2 1.089 87 80 88 211 137 243 1.04 in 2004 90 84 90 103 68 118 3 1.26in2007 81 72 81 260 147 310 4 1.257 79 71 81 242 132 289 5 1.362 80 70 80 243 130 287 6 1.634 69 55 71 176 61 227 

### The two consumer subgroups show the same trend in average LCC savings and percent of sample households benefitting as the total sample of households. For the low-income subgroup the percentage of households benefitting from standards is either the same or greater than for the general population. This can be explained by looking at the cycles per year (i.e., washer loads) used in determining the LCC. This number is estimated from the number of occupants in a household. Our RECS sample of low income households showed a greater number of people per household and we calculated 410 cycles per year, greater than the 392 used for the general population. The senior household subgroup had less people per household, and therefore had less wash loads per year (on average 299 wash loads per year or 24% less wash loads). Therefore, seniors benefitted somewhat less from standards. Other differences that could explain changes in LCC and the percentage in a subgroup benefitting from standards are other factors that determine the amount spent on fuel. Fuel costs are higher if electric water heaters and dryers are used instead of gas. The geographic location of these populations and the price they pay for fuel also affect the number of households in a subgroup benefitting. These differences were small when compared to the differences in LCC due to the cycles per year between the subgroups and the total sample population. An analysis on the effects on payback period by subgroup are shown in Table 8.2 below. In agreement with the LCC results, the payback periods for the low income subgroup were somewhat shorter than for the overall population, while the payback periods were somewhat longer for the senior subgroup. The primary reason for the differences in payback period is the same as for the LCC analysis; the differences in wash loads per year.

8-4

### Table 8.2 Consumer Subroun Pavback Period Comnarisons

....... 

### Trial Standard Average Payback Period in Years Level MEF Total RECS Sample Senior Low income 1 1.021 4.4 5.4 4.4 2 1.089 5.0 6.4 4.9

1.04in2004 4.6 5.7 4.5 3 1.26 in2007 6.8 8.4 6.5 4 1.257 7.0 8.7 6.8 5 1.362 7.0 8.8 6.9 6 1.634 8.7 10.9 8.4
Figures 8.1 and 8.2 below graphically depict the results shown in Tables 8.1 and 8.2.

C.) 0 -J
C 0 U 0

C > I 4- C 0 C.) I.- w 0 100%

80%

60%

40%

20% •

........

-.- Poor

•••.•••Senior -r- All Consumers

0% I'- 0 co LC) 0 C) o 0 o o cc, V.. cc, q CNJ MEF 

### Figure 8.1 Summary of Subgroup Life-Cycle Costs

8-514
12
10

C.) Cu > cu 0. 4
2
0 -.-- Poor

•-•-.••• Senior -k-- All Consumers

0) N- N- C'.) co tO 0 CD C) C C C C'.) C C) CD

C'.) C'.) CD C C'.) MEF 

### Figure 8.2 Summary of Subgroup Payback Periods

Tables 8.3 and 8.4 show the LCC results for the low income subgroup and for the senior consumer subgroup in greater detail. Percentiles from 0 to 100% including the median (5oth percentile) are shown. For individual distribution charts for each standard level see Appendix K.

8-6Table 8.3 Summary of LCC Results

- Low Income

Trial Standard Change in LCC from Baseline Shown by Percentiles of the Distribution of Results

(values in 1997$) Percent Level with LCC Less than MEF 0 10 25 50 75 90 100 Mean Baseline
1 1.021 (520) (172) (107) (56) (22) 19 141 (69) 84.9 2 1.089 (1,941) (563) (360) (191) (67) 13 143 (243) 87.8 1.04 in (722) (272) (177) (93) (36) 1 123 (118) 89.5 2004 3 1.26 in (2,860) (809) (509) (245) (52) 91 626 (310) 81.4 2007 4 1.257 (2,695) (773) (484) (231) (43) 100 632 (289) 80.7 5 1.362 (2,700) (771) (486) (226) (41) 104 682 (287) 79.9 6 1.634 (2,520) (727) (428) (167) 30 188 661 (227) 70.6

Table 8.4 Summary of LCC Results

- Senior (head of household over 65)

Trial Change in LCC from Baseline Shown by Percentiles of the Distribution of Results

(values in 1997$) Percent with LCC Standard Level MEF Less than 0 10 25 50 75 90 100 Mean Baseline
1 1.021 (455) (112) (68) (38) (10) 31 132 (41) 78.8 2 1.089 (1,831) (352) (213) (106) (20) 41 151 (137) 80.4 1.04 in (733) (168) (103) (53) (16) 17 131 (68) 83.7 2004 3 1.26 in (2,711) (490) (280) (113) 16 155 626 (147) 71.7 2007 4 1.257 (2,541) (462) (263) (104) 22 165 640 (132) 70.6 5 1.362 (2,566) (467) (266) (104) 25 186 683 (130) 70.1 6 1.634 (2,225) (407) (199) (33) 118 260 652 (61) 55.0

8-7

### Detailed results of the payback periods are shown in Tables 8.5and 8.6 below. Individual charts

are provided in Appendix L. Table 8.5 Summary of Payback Period Results

-Low Income Trial Standard Level Payback Period Shown by Percentiles of the Distribution of Results

(values in years) ($) MEF 0 10 25 50 75 90 100 Mean 1 1.021 0.0 0.1 0.2 0.7 5.8 12.6 73.7 4.4 2 1.089 0.0 0,8 1.8 3.6 6.3 10.5 45.6 4.9 1.04 in 0.1 0.8 1.7 3.2 5.8 9.6 59.8 4.5 2004 3 1.26in 0.8 2.0 2.8 4.6 7.8 13.0 116.9 6.5 2007 4 1.257 0.9 2.1 2.9 4.8 8.1 13.5 117.0 6.8 5 1.362 0.8 2.1 2.9 4.8 8.3 13.6 124.8 6.9 6 1.634 1.1 2.8 4.0 6.5 10.4 16.7 82.2 8.4 

### Table 8.6 Summary of Payback Period Results

-Senior Trial Standard Level Payback Period Shown by Percentiles of the Distribution of Results

(values in years) ($) MEF 0 10 25 59 75 90 100 Mean 1 1.021 0.0 0.2 0.3 0.7 7.9 16.3 72,2 5.4 2 1.089 0.0 1.1 2.6 5.3 8.6 12.4 51.9 6.4 1.O4in 0.1 1.2 2.5 4,6 7.5 11,6 63.7 5.7 2004 3 1.26 in 0.8 3.0 4.2 6.3 10.1 16.3 101.8 8.4 2007 4 1.257 0.9 3.1 4.3 6.5 10,4 16.9 102.9 8.7 5 1.362 0.9 3,1 4.3 6.5 10.4 17.7 116.0 8.8 6 1,634 0.9 4.1 5.9 8.9 13.7 20.0 91.7 10.9

8-8

### 8.3.2 Data Used in the Consumer Subgroup Analysis

Table 8.7 shows how the input parameters varied among the senior and low-income households and how these compared to the total RECS sample. Other than the sample size the main the senior and low-income subgroups differ from the overall sample mainly by the number of wash loads or cycles per year. This is a number derived from the number of occupants in a RECS household and is discussed in Chapter 7. Shown here are variables that can vary due to differences in RECS households. Other variables explained in chapter 7 such as lifetime of appliance and discount rate and water price are distributions that are held constant in the subset analysis. The parameters that are variable and dependent on data from a RECS household sample are: cycles per year (derived from occupants per household), fuel type, and fuel cost.

8-9

### Table 8.7 Profile of RECS Households for Entire Sample and Subgroups

Category

__________________________________ Total RIECS Sample Senior

________________ 

### Low income

___________ 

### # of RECS housing Records Un

weighted 

### 4396

______________ 

### 867

________________ 

### 357

___________ 

### sum of weights 59,407,035 13,113,765 4,858,585 Percent of Population Weighted 100.0% 22.1% 8.2% CyclesperYear (derived from occupants per

household) 

### 392

______________ 

### 299

_______________ 

### 410

___________ 

### Marginal Fuel Cost (2007)

______________ ________________ ____________ 

### Electricity (cents/Kwh) $7.67 $7.70 $7.40 Gas ($/MMBtu) $5.85 $5.85 $5.66 Oil ($/MMBtu) $7.87 $7.95 $7.88 LPG ($/MMBtu) $14.44 $9.90 $10.97 Percentage of Households with these WI1/Dryer Fuel Types Elect. /Elect. 40.3 40.1 41.0 Elect./ Gas 0.5 0.5 1.3 Gas / Elect. 33.9 33.0 36.3 Gas/Gas 18.5 19.4 14.8 Oil/Elect. 3.7 3.8 1.6 Oil / Gas 0.2 0.2 0.2 LPG/Elect. 2.9 3.0 4.8

8-10

### CHAPTER 9. CLOTHES WASHER SHIPMENTS MODEL: REVISED MODEL

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### TABLEOF CONTENTS

9.1 OVERVIEW 9-1 9.1.1 Defmition of Market Segments and Ownership Categories in the Shipments Model 9-1 9.1.2 Recent Enhancements of Shipments Model 9-5 9.1.3 Review of Other Published Research 9-6 9.2 METHOD 9-7 9.2.1 Definitions 

### 9-7 9.2.1.1 Stock 9-7 9.2.1.2 Events 9-7 9.2.1.3 Decisions 9-8 9.2.2 Purchases from New Housing and Housing Moves 9-8 9.2.2.1 Definition 9-9 9.2.2.2 Approach 9-9 9.2.2.3 Current Assumptions 9-9 9.2.3 ExistingHousingwithRegularWashers 9-10 9.2.3.1 Definition 9-10 9.2.3.2 Approach 9-10 9.2.3.3 Current Assumptions 

### 9-15 9.2.4 Households without Clothes Washers 9-15 9.2.4.1 Definition 9-15 9.2.4.2 Approach 9-15 9.2.4.3 Current Assumptions 9-17 9.2.5 Households with Extended-Life Washers 9-17 9.2.5.1 Definition 

### 9-17 9.2.5.2 Approach 9-17 9.2.5.3 Current Assumptions 9-19 9.2.6 Accounting Equations 9-19 9.3 MODEL 9-22 9.3.1 Logit Probability of Purchase Model 9-23 9.3.1.1 Logit Equation 9-23 9.3.1.2 Utility Coefficients and Elasticity 9-25 9.3.2 Clothes Washer Consumer Analysis 9-26 9.3.3 Stated vs. Revealed Preferences 9-26 9.3.4 Determination of Decision Sensitivities 9-27 9.3.4.1 Savings/Operating Cost Sensitivity 9-28 9.3.4.2 Features Sensitivity 9-29 9.3.5 Calibration of Shipments Model 9-30
9-i

### 9.3.6 Range of Shipments Model Forecasts . 9-32

9.4 RESULTS

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### 9-33 9.4.1 Sales Impacts of Standards-induced Price Changes

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### 9-35 9.4.1.1 New Clothes Washers

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### 9-35 9.4.1.2 Used Clothes Washers

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### 9-36 9.4.2 Impacts on Mean Age of Washers, Used Market, and Washer Repairs

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### 9-36 9.5 CONCLUSIONS

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### 9-37

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### LIST OF FIGURES Figure 9.1 Flow Diagram for Clothes Washer Shipments Model 9-3 Figure 9.2 Decision Tree for New Housing and Housing Moves 9-8 Figure 9.3 Decision Tree for Replacement and Repair of Regular Washers in Existing Housing9- 10 Figure 9.4 Probability of Survival for Regular Clothes Washer 9-12 Figure9.5 Relative Probability of Regular Replacement, Repair, Early Replacement

and No Action as a Function of Clothes Washer Age for 1997 9-13 Figure 9.6 Decision Tree for Housing Without a Washer 9-16 Figure 9.7 Decision Tree for Housing with Extended-Life Clothes Washers 9-17 Figure 9.8 Survival Probability Function for Extended Lifetime Washers 9-19 Figure 9.9 Model Development 9-23 Figure 9.10 Estimated Price vs. Savings Relation for Current Market Conditions 9-28 Figure 9.11 Inter-comparison of Models with Different Primary Economic

Decision Variables 9-31 Figure 9.12 Clothes Washer Shipments Forecasts 9-33 Figure 9.13 Estimated Standards Impacts on New Clothes Washer

Shipments and Sales 9-34 Figure 9.14 Estimated Standards Impacts on Used Clothes Washer

Shipments and Sales 9-35 Figure 9.15 Estimated Standards Impacts on Washer Age, Lifetime, and

Number of Repairs 9-37



### 9-u

### CHAPTER 9. CLOTHES WASHER SHIPMENTS MODEL: REVISED MODEL

9.1 OVERVIEW Clothes washer shipment estimates are a necessary input for manufacturer impact analysis and national energy savings calculations. In the Advanced Notice of Proposed Rulemaking (ANOPR), we examined several different approaches to forecasting new washer sales. The investigated models include an Auto-Regressive Moving Average Model (ARIIVIA), a Multi-Variate 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 full-featured model which included price and operating cost elasticities. In this chapter, we describe a revised accounting model for projecting annual clothes washer shipments that includes the following factors: • combined effects of price, operating cost, features and other macroeconomic explanatory variables (income, credit, etc.) on annual U.S. shipments • market segments (e.g., new housing and moves, 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. 9.1.1 Definition of Market Segments and Ownership Categories in the Shipments Model This clothes washer shipments model described in this chapter 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 and housing purchases, (2) existing housing with a regulara 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 stockof 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 Market

aRegular meaning a washer that has not undergone an "extended repair." 9-1

### Segmentthat the purchase represents. The different types of clothes washer purchases are divided into

six separate market segments as follows: 1. New Housing and Housing Purchases Market: When there is a net increase in the housing stock, a housing purchase or changes of residence, the increase in the number of households or the changes of residence may force the purchase of a new clothes washer. 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 break down 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.' Figure 9.1 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 ftinction which represents the likelihood of a particular consumer decision. Economic decision variables (such as price, operating cost savings and the features 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 9.1 represents the process of taking an initial stock of washers of the four different categories, calculating the
9-2

### purchases induced by this initial stocks of clothes washers, and calculating the new stock levels that result.

The rectangles represent the different ownership 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.

Houses with

rr0bIem5

Yes Early

Yes 4 Buy New

Repair or Re Replace? New or Used?

aror__ Repair Regular Extra Repsu______r1 Houses No Lifetime with Washers Washers Extended Lifetime 1cjsew or Used}.>' New I Washers I reak Down3.

New Houses h"K..

Housesw/o P chase NUd?


### Figure 9.1 Flow Diagram for Clothes Washer Shipments Model Houses w/o Washers

9-3

### 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 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 survey1 and the Clothes Washer Consumer Analysis.2 

### The decisions to which each category of households (and their clothes washers) are subjected are described below: Net new households and housing moves are those households that must make a clothes washer purchase decision because of a change in residence. These households are faced with the decision of whether or not to get a new clothes washer with the house that they move into. A consumer is faced with this decision when he or she moves into a house without a washer and was not able to take his or her old washer to the new residence. 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 the 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 if the 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 either 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.

9-4

### In Section 1.1.2 we compare the current modeling approach with the models that were examined 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.

9.1.2 Recent Enhancements of Shipments Model Since publication of the Technical Support Document (TSD)3 for the Advanced Notice of Proposed Rulemaking, we have made several improvements to the clothes washer shipments forecast. These improvements include the following: Detailed accounting of dfferent 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 front-loading vs top-loading feature is adapted from the recent Clothes Washer Consumer Analysis. Removal of the 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 survey data on the proportion of early (discretionary) replacements, on the proportion of new vs. used purchases, and the proportion of sales associated with a change in residence.

9-5

### AHAM statistics on historical shipments and on the recent (post 1994 standard) changes in mean

clothes washer efficiency. Consumer Reportsdata 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.

9.1.3 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 saleselasticity. Elasticity is the parameter that relates the relative change in sales relative to a change in a feature (such a price,F). For example: 

# (As/s)/(AP/P) Eq.9-1 where S/Sis the relative change in sales, P/Pis 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 elasticity 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.4'5'6'7 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, 19968). In the long-term sales forecast literature, elasticities are much smaller than those observed in short term sales or product choice applications. These differences in estimated elasticity reflect the difference

9-6

### 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.6'7'9 Research that examines the change in elasticities over lime9 fmds 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.9 These results are based on fitting models with elasticity, to the historical data on shipments and sales of major appliances. 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. 9.2 METHOD 9.2.1 Definitions The model is organized in terms of three classes of items: Stocks, Events, and Decisions. These different classes are defined as follows. 9.2.1.1 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 oufflows 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. 9.2.1.2 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 fmal breakdown is another event.

9-7

### 9.2.1.3 Decisions

Decisionsare 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: ln(Prob/(1

- 

### Prob)) = 

### a+b *

### (Price)+c *

### (operatingCost)+d *

### (Feature Index) Eq. 9-2 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. For the sensitivity cases that we examine, we also include other economic decision parameters like income, interest rate, and the price/income ratio. 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 deterimned 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.



### Purchase New Washer?

Yes No Buy New Join Houses Washer without a Washer

Figure 9.2 Decision Tree for New Housing and Housing Moves 9.2.2 Purchases from New Housing and Housing Moves

9-8

### 9.2.2.1 Definition

Purchases from new housing and housing moves are defmed as those new purchases that arise from changes in residence. 9.2.2.2 Approach The decision tree shown in Figure 9.2 illustrates the approach taken or modeling these purchases. 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. This same market saturation is applied to a market that consists of moves between existing housing. The moves market is assumed to correlate with the new housing market in size and its magnitude is set so that the sum of this market and the new housing market is consistent with AHAM data1 on the fraction of clothes washer purchases obtained due to changes of residence (25%of all purchases). The equations for estimating the purchases from new housing are as follows:

CWNeW/NeW Homes = 

### ProbNew Homes 

### (A House5t0k+ MovesMarket) CWUsed/New Homes = 

### 0 where: CWNewlNewHomes = 

### New clothes washer purchase for new homes Prob New Homes = 

### The probability of purchase of washers for new homes AHouse stock = 

### The net increase in housing MovesMarket = The market of moves between existing housing. CW UsedlNewHomes = 

### Used clothes washer purchases for new homes (assumed 0).
9.2.2.3 Current Assumptions. The model assumes that purchases from new housing and moves arise from two related sources. One source is moves into new housing which is measured by new housing completions, while the second is a related market of moves between existing housing. We assume that the size of the move related market is correlated with new housing construction, and we calibrate the size of this market by enforcing the condition that move-related sales consist of25%of all sales between 1990 and 1996 consistent with

9-9

### AHAM survey data. In this market segment we accounted for only new clothes washer sales, since a used

washer sale is equivalent to just moving an existing washer from one house to another.
9.2.3 Existing Housing with Regular Washers 9.2.3.1 Definition Existing housing with 'regulaf' 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. 9.2.3.2 Approach The decisions involved with the replacement and repair of regular washers in existing housing are illustrated in Figure 9.3. The figure shows that several decisions and events affect the replacement of an existing washer with a new or used machine.

Are there problems
Yes No
ce Washer?

Zacer Yes New, Used, Regular or Buy New Keep Existina or None? Extra' Repair Washer Washer 

# Ii \\ Buy New 

# / Buy Used \Extra \egular Washer 

# / Washer 

## '4 4. Extend Keep Existing Don't Buy Machine Life Washer Any Washer 

### Figure9.3 Decision Tree for Replacement and Repair of Regular Washers in Existing Housing
9-10

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

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 nomial 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 AHAM survey data, about 27% of clothes washers are replaced early. These discretionary purchases are referred to asearly 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: 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 pro babilitv that an existing washer has a problem is a function with a5%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.9-4 

### Where 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 9.4.

9-11Survival Probability Function
1 .-+-.-.-- . .-• ,
0.8

- 0.6 0.4- a 0.2
0- I I 0 5 10 15 20 Washer Age

Figure 9.4 Probability of Survival for Regular Clothes Washer 

### 2. The probability of Repair vs. Replace (replace and retire are used interchangeably) is subject to market variations and changes as described by a probability of purchase equation:

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

### (Probability of Needs- Repair)/[l - (Probability of Survival)] Eq. 9-5

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 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. Forthe probability of ear/v 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

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### 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.

1 -'--- 0.9 0.8- 0.7 0.6 ElReplace 0.5-i DRepair 0.4 - 0 Replace Early 0.3 0 Keep 0.2

- 0.1

0 i p i i p i 0 2 4 6 8 10 12 14 16

Washer Age

Figure 9.5 Relative Probability of Regular Replacement, Repair, Early Replacement and No

Action as a Function of Clothes Washer Age for 1997 

### Figure9.5shows 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 likely 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. 9-6

9-13CWRetired(year,age) = ProbRetirevs. Repair(year,age)* CWNeedsRepair(year,age) Eq. 9-7

CWEar13( year,age) = ProbEarly(year,age)*

(CWstock(year,age) - CWNeedsRepai r(year, age)) Eq. 9-8

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

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

CWxtraRepairs(year,age) = ProbxtraRepairs(year, age)*CWNeedsRepair(year,age) (if ProbxraRepairs > 

### 0 else CWxtraRepaiss =

### 0) Eq. 9-10

where 

### CW NeedsRepaji(yeaI,

### age)
= The number of regular washers of a given age that need repairs in a given year. ProbNeedsRepaii(age) = The probability that a regular washer of a given age needs repair (this function is independent of year). CW SOCk(year, age) = The number of regular washers of a particular age in a given year. CW Retired(year, age)
= The number of regular washers retired. Prob Retire vs Repair(year, age)
= The relative probability that a regular washer which needs repair will be retired. CW Early(year, age)
= The number of washers that are replaced early. Prob Early(year, age)
= The probability that a washer will be replaced early. Prob XtraRepairs(year, age)
= The probability that a regular washer received extra repairs that extended its lifetime. CWXfraRepairs(year, age)
= The number of regular washers that received lifetimeextending repairs.

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### 9.2.3.3 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. 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. 

### 9.2.4 Households without Clothes Washers 9.2.4.1 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. 

### 9.2.4.2 Approach The approach taken to model purchase decisions by households without clothes washers is shown in Figure 9.6. 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.

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