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) 

---------Clothes Washer Life Cycle Cost 
" ., (J.;• I) 

At current saturations, households have 

30-35 million more washers bl 2030 

Households and Clothes Washers 

.. .. .. .. .. 

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 

----------Clothes Washer Life Cycle Cost 
: ' 

9 

,,_ 8 

tl.l 

= 0 

.... 

-·9 - 7 

'-' 

tl.l 

~ 

-

00. = 

s... 6 ~ 

.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: 

' Projected DoIIEstic CW Sales (based 

on frozen saturations, 14 year lifetiIIE, 

andAEO 1997 housing stock forecasts) 

\ Projected CW sales (doIIEstic) 

DoIIEstic CW Sales 

1990 1995 2000 2005 2010 2015 2020 2025 2030 

Year 

------------Clothes Washer 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 

-----------Clothes Washer Life Cycle Cost 
Models of clothes washer sales 

I FPCR:RifilllNIIDRR 

WSHsOO; I NllnmrlIB I Smraioo I WNHlifuine I fumn:ic; 

ARJM.\ D 

MJltivariate tirre 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 

• Wringer washers 

- 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 + CW sales(t) 

where cwsales(t) =cw sales in year t 

Z(t) = CW sales(t) - CW sales(t-1) 

Z{t-1) = CW sales(t-1) - CW sales(t-2). 

-----------Clothes Washer 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 

------------Clothes Washer 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 

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

• Pros 

- Explicitly accounts for washer lifetimes (using retirement function) 

- Housing and 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 housing and 

saturation stocks 

------------Clothes Washer Life Cycle Cost 
.. •. -- .. 

Satuation/Lifetime Models -- Sales forecasts 

9500 

• CWsales 

9000 

-Sat= 5 point curve 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 

CW sales= [Satnew home· Housestartsl + [CW removals - (Satstock home· Houseretired)] 

• Pros 

- Simple model 

- Explicitly accounts for washers separately in new houses 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 

-Time Series 

-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: how will consumers respond to standards? 

• purchase price 

• operating expense 

• decision to repair or replace 

-----------Clothes Washer Life Cycle Cost 

I 

\