# Base Case Future Shipments: Clothes Washers



# -----------------**~** Jim McMahon JEMcMahon@lbl.gov 

## Ernest Orlando Lawrence Berkeley National Laboratory To USDOE Workshop March 11-12, 1998

# Discussion Topics •Clothes washer shipments

- Percent of homes with clothes washers

- Housing construction 

# • Lifetime of clothes washers

- from wringer to automatic washers 

# • Model of future shipments • Future work: impact of standards 3/11-12/98 Clothes Washer Life Cycle Cost 2..**~i** c_};, • •l 

# 77o/o 

# have a clothes washer (1993) • Single family

- Existing 

## 93°/o New 

## 95°/o

- Existing was 

## 86°/o (1981) • Mobile homes

- Existing 

## 84°/o New 

## 83°/o

- Existing was 

## 66o/o (1981) • Multifamily homes

- Existing 

## 31°/o New 

## 39°/o

- Existing was 

## 28°/o (1981) ---------ClothesWasher Life Cycle Cost" ., (J.;• I) 

## At current saturations, households have 30-35 million more washers

# bl 2030

Households and ClothesWashers



### .. .. .. 

## .. .. 120 +----I------+----!-----+----=--------+---___,


## .... 

# -.. lit 

# -....**40-l----~---+----1----+--------+---- o->----1------+---+---+-----+---~**  1970 1980 1990 2000 2010 2020 2030 YEAR -HH(AHAM) • Iii •HH (EIA) -washers (AHAM) • )( •Washers (77%)

Clothes Washer Life Cycle Cost.• ., fJiy •l 

# Projected shipments • from 

## 1980 to 

## 1996, the annual rate of growth in domestic shipments averaged 

## 2.3°/o • Maintaining current saturations corresponds to:

- annual growth in shipments of 

## 0.9°/o

- domestic shipments over 8.5 million per year by 

## 2030 (compared to 

## 6.2 million in 

## 1996) • Factors that could alter this estimate:

- number of households

- percent of households having washers

- washer lifetimes

- washer prices (and operating expenses)

- consumer decision to repair rather than replace ----------ClothesWasher Life Cycle Cost: '

9

,,_ 8 tl.l 

## = 0 

### .... 

# - - ·9 7 '-' tl.l**~** 

# - = 00. 6 s...**~** .c: tl.l 

## =**~** 5 tl.l**~** .c: 

### .... 0 

# - u 4 3

## Sales may increase to 8.5 million/year to keep up

with population increase

1980 1985 Appliance Magazine:**ProjectedCWs~** Appliance Magazine: 

# ' ProjectedDoIIEstic CWSales (based onfrozensaturations, 14yearlifetiIIE, andAEO 1997 housingstockforecasts) 

# \ ProjectedCWsales (doIIEstic) DoIIEstic CWSales

1990 1995 2000 2005 2010 2015 2020 2025 2030 Year ------------ClothesWasher Life Cycle Cost

## Forecasting Models: Base Case • To check simple saturation model, five different statistical models were studied:

- ARIMA

- Multivariate time series

- Saturation/lifetime model

- Saturation/lifetime model corrected for wringer washers.

- Accounting model 

### • Pros and cons of each model 

## • Each model builds on the previous models -----------ClothesWasher Life Cycle Cost

# Models of clothes washer sales

I 

### FPCR:RifilllNIIDRR

WSHsOO; 

## INllnmrlIB

## ISmraioo 

## IWNHlifuine 

## Ifumn:ic; ARJM.\ D 

### MJltivariatetirre D D Smraim'life 1 D D D D Smraim'life

### 2 D D D D 

### lnmting D D D D (+)

Clothes Washer Life Cycle Cost"' '-..!. Cl-.· -i-.) 

# ARIMA Model Pros



### - Only time-series data is needed to build model • Cons



### - The historical trends may not be a good guide to the future • Wringerwashers

- This model cannot explicitly account for changes in number of households, percent owning washers, price, or operating expense CW sales(t+1) = 0.4196 Z(t) - 0.4372 Z(t-1) + 0.0879 + CWsales(t) where cwsales(t) =cw sales in year t Z(t) = CWsales(t) - CW sales(t-1) Z{t-1) = CWsales(t-1) - CWsales(t-2). -----------ClothesWasher Life Cycle Cost:t ,·,.. "l

-.. fl.) 

# = = = ,.-( '-" fl.)**~** 

# - = rLJ. 

## ARIMA Model -- Sales Forecast 9500 9000 8500 8000 7500 7000 6500 6000 5500 

## • 5000 

## • • 4500 

## • • 4000 

## • 3500 3000 2500 1970 1975 

## •

## ••

## ••

1980 

## • • 

## •••• 

## ••• • 

## • •

## • 

## • •

1985 1990 1995 2000 2005 2010 2015 2020**Clotfli~** Washer Life Cycle Cost 2025 2030•• ••• • ·"'' 

## Multi-Variate Time Series Fit • Pros

- Only 

### two time-series data needed to construct model: 

### • clothes washer shipments in previous year • change in 

### number of households from previous year

- CWsales(t) 

## =CWsales(t-1) +A+ B·[Housestock(t) - Housestock(t-1 )] 

## • Cons: cannot explicitly account for: • replacement sales • changes in saturation



### . • pnce • operating cost ------------ClothesWasher Life Cycle Cost. 

# . ... ' 

## Multi-Variate Times Series Fit -- Sales Forecast 9500 9000 8500 8000 7500 7000 ..-**~** 6500 Q Q 

### e 6000 fl)**~** -; 5500 00 5000 4500 4000 

## • 3500 3000 2500 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 Clntaes Washer Life Cycle Cost

## Saturation/Lifetime Model CWsaies(t) 

## =[Housestock(t) · Satstock(t)] -[Housestock(t-1) · Satstock(t-1)] + CWremova1s 

## • Pros

- Explicitly accounts for 

### washerlifetimes (using retirement function)

- Housingand saturation stocks based only on time-series data, so

- different housing and saturation fits can be used to get "good" fits to historical sales 

## • Cons

- Removals must be based upon assumptions about lifetimes

- Cannot explicitly account for the impact of price or operating cost on housingand saturation stocks ------------ClothesWasher Life Cycle Cost.. 

### •. -- .. 

## Satuation/Lifetime Models -- Sales forecasts 9500 • CWsales 9000 -Sat=5pointcurve fit; Removal= 13.6 avg life 8500 -Sat=auto-regressive fit; Removal = separate auto &wringer 8000 7500 7000 

# - rl.l 6500 

# = = =**~** 6000 

# - rl.l a.> 

# - 5500 

## = 00 5000 4500 4000 3500 3000 2500 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030

----------- Clot-Mit Washer Life Cycle Cost**~\** '-.\. __,, ·•· 

## Accounting Model CWsales= [Satnewhome· Housestartsl 

### + [CWremovals - (Satstockhome· Houseretired)] 

## • Pros

- Simple model

- Explicitly accounts for washers separately in 

### newhouses and 

### replacement

- Price and operating cost dependencies can be incorporated into Saturation terms 

## • Cons

- Saturations of washers in new and stock homes must be forecasted

- Housing starts must be forecasted (e.g., based on AEO forecasts)

- Removals must be based upon assumptions about lifetimes
Clothes Washer Life Cycle Cost

## Accounting Model -- Sales Forecast**9500.--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~--,**



# - 9000 8500 8000 7500 7000 <! 6500 

# = 

# = e, 6000 rl.l**~** 'i 5500 rJJ 5000 4500 4000 3500 3000 

## ••••**2500-+-~~-+-~~-l-~~-1-~~-+-~~-+-~~--+~~~r--~~+--~~-t-~----l** 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030**-----------Cl~** 

### Washer Life Cycle Cost

## Forecasting Models -- Visual Comparisons**9500-.--~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~---.** 9000 8500 8000 7500 7000 

# -**~** 6500 

# = = 0 6000**~** -; 5500 rJJ. 5000 4500 4000 3500 3000 • CWsales

- Accounting -ARIMA -TimeSeries -Sat/Life 1 -Sat/Life2**2500-+-~--1~~-+-~~-1-~~1--~-+-~~--+-~~-+--~--1-~~--+-~~-+-~~r--~---1** 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030

------------ Clot\lali Washer Life Cycle Cost

## Conclusions: Future Shipments • All models forecast increase in shipments

- time trend, increasing saturation and/or

- increasing number of U.S. households 

### • Transition from wringer to automatic washers may have caused a temporary increase in shipments, complicating the time trend • Of five models, only accounting model could be adapted to address economic factors • Next steps: 

## howwill consumers respond to standards? • purchase price • operating expense • decision to repair or replace -----------ClothesWasher Life Cycle Cost I \