9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

9.1 INTRODUCTION ........................................................................................................... 9-1

9.2 SHIPMENTS MODEL METHODOLOGY.................................................................... 9-1

9.3 DATA INPUTS AND MODEL CALIBRATION .......................................................... 9-3

9.3.1 Historical Shipments........................................................................................................ 9-3

9.3.2 Markets and Model Calibration ....................................................................................... 9-4

9.3.3 Base Case Shipments....................................................................................................... 9-7

9.4 IMPACT OF PURCHASE PRICE INCREASE ON SHIPMENTS ............................... 9-8

9.5 AFFECTED STOCK ..................................................................................................... 9-11

9.6 SHIPMENTS FORECAST BY TRIAL STANDARD LEVEL.................................... 9-11

LIST OF TABLES

Table 9.3.1 Microwave Ovens: Historical Shipments, Domestic plus Imports...................... 9-4

Table 9.3.2 Microwave Ovens: Historical Market Saturations............................................... 9-6

Table 9.4.1 Change in Relative Price Elasticity following a Purchase Price Change .......... 9-10

LIST OF FIGURE

Figure 9.3.1 Microwave Ovens: Survival and Retirement Functions...................................... 9-7

Figure 9.3.2 Microwave Ovens: Historical and Base Case Shipments Forecast ..................... 9-7

Figure 9.3.3 Microwave Ovens: Disaggregated Base Case Shipments Forecast..................... 9-8

Figure 9.6.1 Base Case and TSL 4 Shipments Forecasts....................................................... 9-12
9-1

CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

Estimates of future product shipments are a necessary input to calculations of the 

national energy savings (NES) and net present value (NPV), as well as to the manufacturer 

impact analysis (MIA). This chapter describes the data and methods the U.S. Department of 

Energy (DOE) used to forecast annual product shipments and presents results for each set of 

products being considered for this standards rulemaking. 

DOE estimated shipments for each product with a shipments model, which is calibrated 

with historical shipments data. The shipments model considers specific market segments to 

estimate shipments, the results for which are then aggregated to estimate total product shipments. 

To estimate the impacts of potential standard levels on product shipments, the shipments model 

accounts for the combined effects of changes in purchase price, annual operating cost, and 

household income on the consumer purchase decision.

The shipments model was developed as a part of the NIA spreadsheet that is accessible 

on the internet (http://www.eere.energy.gov/buildings/appliance_standards/). Appendix 10-A 

discusses how to access the NIA spreadsheet and provides basic instructions for use. 

The rest of this chapter explains the shipments models in more detail. Section 9.2 

presents the shipments model methodology for each product; section 9.3 describes the data 

inputs and the model calibration; section 9.4 discusses impacts on shipments from changes in 

equipment purchase price, operating cost, and household income; section 9.5 discusses the 

affected stock; and section 9.6 presents results.

9.2 SHIPMENTS MODEL METHODOLOGY

DOE developed a national stock model for estimating annual shipments for this standards 

rulemaking. The model considers market segmentation as a distinct input to the shipments 

forecast. As represented by the following equation, the two primary market segments are new 

installations and replacements. 

Ship ( j) Rpl ( j) NI ( j) p = p + p

Where:

Shipp(j) = Total shipments of product p in year j, 

Rplp(j) = Units of product p retired and replaced in year j, and 

NIp(j) = Number of new installations of product p in year j.
9-2

DOE’s shipments models take an accounting approach, tracking market shares of each 

product class, the vintage of units in the existing stock, and expected construction trends. The 

models estimate shipments due to replacements using sales in previous years and assumptions 

about the lifetime of the equipment. Therefore, estimated sales due to replacements in a given 

year are equal to the total stock of the appliance minus the sum of the appliances sold in previous 

years that still remain in the stock. DOE determined the useful service life of each appliance to 

estimate how long the appliance is likely to remain in stock. The following equation represents 

how DOE estimated replacement shipments.

( ) ( 1) ∑ ∑ ( )

0

1

_ _

_

Rpl j Stock j Ship prob age Rtr

ageMax

age

j

j N

p = p j ×

= =

Where:

Stockp (j-1) = Total stock of in-service appliances in year j-1,

probRtr (age) = Probability that an appliance of a particular age will be retired, and

N = Start year for when the model begins its stock accounting (start year is 

specific to each product based on available historical shipments data).

Stock accounting takes product shipments, a retirement function, and initial in-service 

product stock as inputs and provides an estimate of the age distribution of in-service product 

stocks for all years. The age distribution of in-service product stocks is a key input to both the 

NES and NPV calculations—the operating costs for any year depend on the age distribution of 

the stock. The dependence of operating cost on the equipment age distribution occurs under a 

standards case scenario that produces increasing efficiency over time, where older, less efficient 

units may have higher operating costs, while younger, more-efficient units will have lower 

operating costs. Furthermore, in the case of an early replacement scenario, retirements due to 

early replacement will depend on the age of the units that are subject to early replacement.

DOE estimated replacements using product retirement functions that it developed from 

product lifetimes. For all products, DOE based the retirement function on a Weibull distribution 

for the product lifetime. The shipments model assumes that no units are retired below a 

minimum product lifetime and all units are retired before exceeding a maximum product 

lifetime. The models determine the probability of retirement at a certain age for all products 

using a Weibull equation:

e x

P x

β

α

θ 



 



 − −

( ) = for x > θ and

P(x) = 1 for x ≤ θ

Where:

P(x) = probability that the appliance is still in use at age x;

x = appliance age;

α = scale parameter, which would be the decay length in an exponential 

distribution;
9-3

β = shape parameter, which determines the way in which the failure rate 

changes through time; and

θ = delay parameter, which allows for a delay before any failures occur.

The retirement probability is the difference in the survival function from one year to 

another.

DOE calculated total in-service stock of equipment by integrating historical shipments 

data starting from a specific year. The start year depended on the historical data available for the 

product. As units are added to the in-service stock, some of the older ones retire and exit the 

stock. To estimate future shipments, DOE developed a series of equations that define the 

dynamics and accounting of in-service stocks. For new units, the equation is:

Stock( j,age = 1) = Ship( j 1) _

Where: 

Stock(j, age) =The population of in-service units of a particular age,

j = Year for which the in-service stock is being estimated, and

Ship (j) = Number of units purchased in year j.

The above equation states that the number of one-year-old units is simply equal to the 

number of new units purchased the previous year. The following equation describes the 

accounting of the existing in-service stock of units: 

( 1, 1) ( , ) [1 ( )] _ Stock j age Stock j age prob age + + = × Rtr

In the above equation, as the year is incremented from j to j+1, the age is also 

incremented from age to age+1. With time, a fraction of the in-service stock is removed, and 

that fraction is determined by a retirement probability function, probRtr(age), which is described 

in section 9.3. Most replacements are made when equipment wears out and fails. Over time, 

some of the units will be retired and removed from the stock, thus triggering the shipment of a 

new unit. Because the products considered in this rulemaking are common appliances that have 

been used by U.S. consumers for a long time, replacements constitute the majority of shipments.

9.3 DATA INPUTS AND MODEL CALIBRATION 

The sections below describe the data inputs and market segments considered for each 

product.

9.3.1 Historical Shipments

DOE used data on historical shipments (i.e., domestic shipments and imports) to calibrate 

its shipments model for microwave ovens. DOE’s sources for historical shipments data were: (1) 
9-4

AHAM Factbooks for the years 20001, 20032, 20053, 20094 covering the period 1989−2009 and 

(2) Appliance Magazine5 for the period 1981−1988.a Table 9.3.1 summarizes the historical 

microwave oven shipments data.

Table 9.3.1 Microwave Ovens: Historical Shipments, Domestic plus Imports

Year Shipments (millions) Year Shipments (millions)

1980 3.41 1995 8.16

1981 4.18 1996 8.77

1982 3.85 1997 9.14

1983 5.60 1998 10.37

1984 8.63 1999 11.42

1985 10.28 2000 12.64

1986 11.76 2001 13.45

1987 11.91 2002 13.31

1988 10.38 2003 14.27

1989 9.78 2004 15.53

1990 7.69 2005 13.86

1991 6.62 2006 13.69

1992 7.19 2007 11.85

1993 7.24 2008 11.34

1994 8.57 2009 9.63

Source: 1989–2009: AHAM Fact Books, 2000, 2003, 2005, 2009; 1981–1988: Appliance Magazine, “Statistical 

Review,” 2009.

9.3.2 Markets and Model Calibration

The market for microwave ovens is primarily comprised of replacement units for 

equipment that has been retired from service, and units for new housing. Total microwave oven 

shipments are represented by the following equation:

Ship ( j) Rpl ( j) NI ( j) MWO = MWO + MWO

Where:

ShipMWO (j) = Total shipments of microwave ovens in year j, 

RplMWO (j) = Replacement shipments in year j, 

NIMWO (j) = Shipments to new households in year j, and 

The sections below discuss these markets in further detail. 

 a Shipments estimates from Appliance Magazine included exports. Thus, DOE reduced total shipments by 12.3 

percent (the average percentage of exports for the years 1989–1993 based on the five-year average difference 

between the AHAM Fact Book 2000 and Appliance Magazine) to estimate total domestic shipments plus imports.
9-5

New Construction. DOE estimated new construction shipments using two inputs: new 

housing forecasts and market saturation data. New housing includes newly constructed singleand multi-family units, referred to as “new housing completions,” and mobile home placements. 

For new housing completions and mobile home placements, DOE used actual data through 2005, 

and adopted the projections from the DOE Energy Information Administration (EIA)’s Annual 

Energy Outlook 2010 (AEO2010) for the period 2006–2035.6

Table 9.3.2 presents historical market saturations of microwave ovens based on various 

sources, including AHAM’s 2009 Fact Book,

4 Appliance Magazine,5 NFO World Group,7 and 

EIA’s RECS for the years 1993,8 1997,9 2001,10 2005.11 The table presents market saturations 

for the overall housing stock, new households only, and households with two or more microwave 

ovens. 

Because the forecast of shipments for the new housing market depends on the saturation 

of microwave ovens in new housing, DOE focused its attention on the market saturations for new 

housing as well as the saturations of housing with multiple microwave ovens. According to 

RECS, microwave oven saturation in new housing for 1993, 1997, 2001, and 2005 was 92 

percent, 87.5 percent, 93.3 percent, and 90.3 percent, respectively. According to NFO, 

households with more than one microwave oven represented 3.7 percent, 4.9 percent, and 4.1 

percent of the housing market for the years 1990, 1996, and 2001, respectively. RECS did not 

provide data about number of microwave ovens in its 2005 survey.b Therefore, DOE 

incremented the saturation levels for new housing estimated by RECS by the amounts provided 

by NFO to estimate the new housing saturations. As a result, DOE determined the effective 

saturation of microwave ovens in new housing to be 95.7 percent, 92.4 percent, 97.4 percent, and 

94.6 percent for 1993, 1997, 2001, and 2005, respectively. Because 2005 is the most recent year 

for which data are available, DOE decided to freeze the saturation at 94.6 percent to estimate the 

shipments to new construction for future years. 

 b RECS did not provide data about numbers of microwave ovens per household in its 2005 survey.
9-6

Table 9.3.2 Microwave Ovens: Historical Market Saturations

Year

Overall Household New 

Households

Households 

with ≥ 2 ovens

AHAM* Appl** NFO*** RECS† RECS† NFO***

1978 7.2%

1982 25.6%

1983 33.3%

1987 65.9%

1990 82.7% 81.1% 3.9%

1991 85.2%

1992 84.5%

1993 85.5% 84.1% 92.0%

1994 88.8%

1995 88.9%

1996 90.6% 88.7% 4.9%

1997 91.0% 83.0% 87.5%

1998 91.3%

1999 93.1%

2000 95.6%

2001 90.7% 95.7% 91.8% 86.1% 93.3% 4.1%

2002 95.0%

2003 95.0%

2004 95.5%

2005 89.3% 87.9% 90.3%

* Source: AHAM, Fact Book, 2005; ** Source: Appliance Magazine, “The Saturation Picture,” September issues; 

*** Source: NFO World Group, 2001; † Source: DOE-EIA, RECS, 1993, 1997, 2001, and 2005.

Replacements. DOE determined shipments to the replacement market using an 

accounting method that tracks the total stock of units by vintage. DOE estimated a stock of 

microwave ovens by vintage by integrating historical shipments starting from the year 1980.

Over time, some units will be retired and removed from the stock, thereby triggering the 

shipment of a replacement unit. Depending on the vintage, a certain percentage of each type of 

unit will fail and need to be replaced. To determine when a microwave oven fails, DOE used a 

product survival function based on a lifetime distribution with an average value of nine years, 

and minimum and maximum values of seven years and 10 years, respectively. For a more 

complete discussion of microwave lifetimes, refer to section 8.2.2.5 of Chapter 8. Figure 9.3.1

shows the survival and retirement function that DOE used to estimate replacement shipments.
9-7

Figure 9.3.1 Microwave Ovens: Survival and Retirement Functions

9.3.3 Base Case Shipments

Figure 9.3.2 shows the forecasted shipments in the base case (i.e., the case without new 

energy efficiency standards) and the historical shipments DOE used to calibrate the forecast. 

Figure 9.3.2 Microwave Ovens: Historical and Base Case Shipments 

Forecast

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

% Surviving

% Retiring

0

2

4

6

8

10

12

14

16

18

20

1972 1982 1992 2002 2012 2022 2032 2042

Shipments (million)

Year

Historical Shipments

Modeled Shipments
9-8

Figure 9.3.3 presents forecasted base case microwave oven shipments disaggregated into 

shipments due to retirements and shipments to new housing. Note that replacement shipments 

comprised 85–92 percent of total microwave oven shipments over the period 2006–2035. The 

percentage of total shipments represented by replacements is high because the microwave oven 

market is fairly mature. 

Figure 9.3.3 Microwave Ovens: Disaggregated Base Case Shipments Forecast 

9.4 IMPACT OF PURCHASE PRICE INCREASE ON SHIPMENTS

Economic theory suggests that, all else being equal, an increase in the price of a good 

would lead to a decrease in demand for it. Because DOE projects that appliance standards often 

result in an increase in the price of the product, DOE conducted a literature review and an 

analysis of appliance price and efficiency data to estimate the effects on product shipments from 

increases in product price. DOE also considered the decreases in operating costs from higher 

energy efficiency and changes over time in household income.

In the literature, DOE found only a few studies of appliance markets that are relevant to 

this rulemaking analysis and identified no studies that use time-series data of equipment price 

and shipments data after 1980. The information that can be summarized from the literature

suggests that the demand for appliances is price inelastic. Other information in the literature 

suggests that appliances are a normal good, such that rising incomes increase the demand for 

0

2

4

6

8

10

12

14

16

18

20

2010 2015 2020 2025 2030 2035 2040

Shipments (million)

Year

New Units

Replacement Units
9-9

appliances. Finally, the literature suggests that consumers use relatively high implicit discount 

ratesc when comparing appliance prices and appliance operating costs. 

DOE found insufficient data on product purchase price and operating cost to perform a 

thorough analysis of dynamic changes in the appliance market. Rather, it used purchase price and 

efficiency data specific to residential refrigerators, clothes washers, and room air conditioners 

over the period 1980–2002 to evaluate broad market trends and conduct simple regression 

analyses. These data indicate that there has been a rise in appliance shipments and a decline in 

appliance purchase price and operating costs over the time period. Household income has also 

risen during this time. To simplify the analysis, DOE combined the available economic 

information into one variable, termed the relative price, and used this variable in an analysis of 

market trends, as well as to conduct a regression analysis. The relative price is defined with the 

following expression:

Income

PP PVOC

Income

TP

RP

+ = =

Where:

RP = Relative price,

TP = Total price,

Income = Household income,

PP = Appliance purchase price, and

PVOC = Present value of operating cost.

In the above equation, DOE used an implicit discount rate of 37 percent to determine the 

present value of operating costs. 

DOE’s analysis of market trendssuggests that the relative price elasticity of demand for 

the three appliances is relatively inelastic (i.e., under 1.0). DOE’s regression analysis suggests 

that the relative price elasticity of demand, averaged over the three appliances, is -0.34. For 

example, a relative price increase of 10 percent results in a shipments decrease of 3.4 percent. 

Note that, because the relative price elasticity incorporates the impacts from three effects (i.e., 

purchase price, operating cost, and household income), the impact from any single effect is 

mitigated by changes from the other two effects. 

The relative price elasticity of -0.34 is consistent with estimates in the literature.

Nevertheless, DOE stresses that the measure is based on a small data set, using simple statistical 

analysis. More important, the measure is based on an assumption that economic variables, 

including purchase price, operating costs, and household income, explain most of the trend in 

appliances per household in the United States since 1980. Changes in appliance quality and 

 c A high implicit discount rate with regard to operating costs means that consumers do not put much economic value 

on the operating cost savings realized from more-efficient appliances. In other words, consumers are much more 

concerned with higher purchase prices.
9-10

consumer preferences may have occurred during this period, but DOE did not account for them 

in this analysis. Despite these uncertainties, DOE believes that its estimate of the relative price 

elasticity of demand provides a reasonable assessment of the impact that purchase price, 

operating cost, and household income have on product shipments.

Because DOE’s forecasts of shipments and national impacts due to standards are over a 

30-year time period, it needed to consider how the relative price elasticity is affected once a new 

standard takes effect. DOE considered the relative price elasticity provided above to be a shortrun value. It was unable to identify sources specific to household durable goods, such as 

appliances, to indicate how short-run and long-run price elasticities differ. Therefore, to estimate 

how the relative price elasticity changes over time, DOE relied on a study pertaining to 

automobiles.12, 13 This study shows that the automobile price elasticity of demand changes in the 

years following a purchase price change. With increasing years after the purchase price change, 

the price elasticity becomes more inelastic until it reaches a terminal value around the tenth year 

after the price change. Table 9.4.1 shows the relative change in the price elasticity of demand for 

automobiles over time. As shown in the table, DOE developed a time series of relative price

elasticities for home appliances based on the relative change in the automobile price elasticity of 

demand. For years not shown in the table below, DOE performed a linear interpolation to obtain 

the relative price elasticity.

Table 9.4.1 Change in Relative Price Elasticity following a Purchase Price Change

Years Following Price Change

1 2 3 5 10 20

Relative Change in 

Elasticity to 1st year

1.00 0.78 0.63 0.46 0.35 0.33

Relative Price Elasticity -0.34 -0.26 -0.21 -0.16 -0.12 -0.11

Based on the following equation, DOE estimated standards case shipments by 

incorporating the impact of the relative price into the base case shipments forecast. Note that in 

the equation below, the relative price and the relative price elasticity are functions of the year 

because both change with time. 

( ) ( ( ) ( ) ( )) (1 ( ) ( )) _

_ _ _ _ Ship j Rpl j NI j M j e j RP j STD p = BASE p + BASE p + BASE p

× RP ×∆

Where:

ShipSTD_p(j) = Total shipments under the standards case of product p in year j, 

RplBASE_p(j) = Units of product p under the base case retired and replaced in year j,

NIBASE_p(j) = Number of new home installations under the base case of product p in year 

j,

MBASE_p(j) = First time owners market M of product p in year j under the base case 

eRP(j)= Relative price elasticity in year j (equals -0.34 for year 1), and 

ΔRP(j)= Change in relative price due to a standard level in year j.
9-11

9.5 AFFECTED STOCK

The affected stock is the in-service stock of the appliance or product that is affected by a 

standard level. In addition to the forecast of product shipments under both the base case and the 

standards case, the affected stock (which represents the difference in the appliance stock for the 

base case and the standards case) is a key output of DOE’s shipments models. The affected stock 

quantifies the impact that new product shipments have on the appliance stock due to a standard 

level. Therefore, the affected stock consists of those in-service units that are purchased in or after 

the year the standard has taken effect, as described by the following equation:

∑

_

1

_

( ) ( ) ( )

j Std yr

age

Aff Stock p j Shipp j Stock p age

=

= +

Where:

Aff Stockp(j) = Affected stock of units of product p of all vintages that are operational in 

year j,

Shipp(j) = Shipments of product p in year j, 

Stockp(j) = Stock of units of product p of all vintages that are operational in year j,

age = Age of the units (years), and

Std_yr = Effective date of the standard.

As noted in the above equation, to calculate the affected stock, DOE must define the 

effective date of the standard. For the NES and NPV results presented in chapter 10, DOE 

assumed that new energy efficiency standards will become effective in 2014. Thus, all 

appliances purchased starting in 2014 are affected by the standard level. 

9.6 SHIPMENTS FORECAST BY TRIAL STANDARD LEVEL

This section compares the base case shipments forecast with the forecast for the 

maximum trial standard level (TSL) that DOE considered for microwave oven standby power. 

As will be described in Chapter 10, the TSLs are comprised of specific candidate standard levels 

(CSL).

Figure 9.6.1 shows the shipments impacts over the period 2014–2043 caused by the 

maximum TSL considered for microwave oven standby power for both product classes (TSL 4). 

For all TSLs, shipments are forecasted to decrease—the effects from the increase in product 

purchase prices offset the effects from decreased operating costs, resulting in a net decrease in 

shipments. In Figure 9.6.1, the difference between the base case and the TSL shipments forecast 

depicts the annual shipments reduction caused by the TSL. The other TSLs have a smaller effect 

on shipments than does TSL 4.
9-12

Figure 9.6.1 Base Case and TSL 4 Shipments Forecasts

12.0

13.0

14.0

15.0

16.0

17.0

18.0

2010 2015 2020 2025 2030 2035 2040 2045

Millions

Year

Projected Shipments

Base Case

TSL 4
9-13

REFERENCES

1. Association of Home Appliance Manufacturers, AHAM 2000 Fact Book. 2000. 

Washington, DC.

2. Association of Home Appliance Manufacturers, AHAM 2003 Fact Book. 2003. 

Washington, DC.

3. Association of Home Appliance Manufacturers, AHAM 2005 Fact Book. 2005. 

Washington, DC.

4. Association of Home Appliance Manufacturers, AHAM 2009 Fact Book. 2009. 

Washington, DC.

5. The Life Expectancy/Replacement Picture. Appliance Magazine,, 2009. 64(9): pp. 65-66. 

6. Energy Information Administration, Annual Energy Outlook 2010 with Projections to 

2035, 2010. Washington, DC. Report No. DOE/EIA-0383(2010). 

<http://www.eia.doe.gov/oiaf/aeo/>

7. Association of Home Appliance Manufacturers, Average Useful Life of Major Home 

Appliances, September, 1996. Washington, D.C. Prepared by NFO Research, Inc. 

<www.aham.org>

8. U.S. Department of Energy - Energy Information Administration, Residential Energy 

Consumption Survey: 1993 Public Use Data Files 1993.

<http://www.eia.doe.gov/emeu/recs/93publicuse.html>

9. U.S. Department of Energy - Energy Information Administration, Residential Energy 

Consumption Survey: 1997 Public Use Data Files, 1997.

<http://www.eia.doe.gov/emeu/recs/public.html>

10. U.S. Department of Energy - Energy Information Administration, Residential Energy 

Consumption Survey: 2001 Public Use Data Files, 2001.

<http://www.eia.doe.gov/emeu/recs/recs2001/publicuse2001.html>

11. U.S. Department of Energy: Energy Information Administration, Residential Energy 

Consumption Survey: 2005 Public Use Data Files. 2008: Washington, DC. 

http://www.eia.doe.gov/emeu/recs/recspubuse05/pubuse05.html

12. Hymans, S., Consumer Durable Spending: Explanation and Prediction. Brookings Papers 

on Economic Activity, 1971. 1971(1): pp. 234-239 

13. Dale, L. and K. Fujita, An Analysis of the Price Elasticity of Demand of Household 

Appliances. LBNL 326E, 2008<http://www.osti.gov/bridge/servlets/purl/929429-

Vm1S9X/929429.pdf>