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 MARKET SEGMENTS .............................................................. 9-1

9.3.1 Clothes Dryers ................................................................................................................. 9-1

9.3.1.1 Historical Shipments ...................................................................................... 9-1

9.3.1.2 Markets and Model Calibration ..................................................................... 9-2

9.3.1.3 Base Case Shipments ..................................................................................... 9-4

9.3.2 Room Air Conditioners .................................................................................................... 9-5

9.3.2.1 Historical Shipments ...................................................................................... 9-5

9.3.2.2 Markets and Model Calibration ..................................................................... 9-5

9.3.2.3 Base Case Shipments ..................................................................................... 9-8

9.3.2.4 Disaggregation into Product Classes ............................................................. 9-8

9.4 IMPACT OF PURCHASE PRICE INCREASE ON SHIPMENTS ............................. 9-10

9.5 AFFECTED STOCK ..................................................................................................... 9-13

9.6 CANDIDATE STANDARD LEVELS.......................................................................... 9-13

9.7 SHIPMENTS FORECASTS .......................................................................................... 9-14

9.7.1 Clothes Dryers ............................................................................................................... 9-14

9.7.2 Room Air Conditioners .................................................................................................. 9-16

LIST OF TABLES

Table 9.3.1 Clothes Dryer Product Class Market Shares ........................................................ 9-2

Table 9.3.2 Room Air Conditioner Product Class Market Shares .......................................... 9-9

Table 9.4.1 Change in Relative Price Elasticity following a Purchase Price Change .......... 9-12

Table 9.6.1 Combined Energy Factor (CEF) Levels Corresponding to Candidate 

Standard Levels for Clothes Dryers ................................................................... 9-14

Table 9.6.2 Combined Energy Efficiency Rating (CEER) Levels Corresponding to 

Candidate Standard Levels for Room Air Conditioners .................................... 9-14

LIST OF FIGURES

Figure 9.3.1 Historical Shipments of Electric and Gas Clothes Dryers ................................... 9-1

Figure 9.3.2 Clothes Dryers: Retirement Function .................................................................. 9-3

Figure 9.3.3 Clothes Dryers: Base Case Shipments Forecast by Market Segment .................. 9-4

Figure 9.3.4 Clothes Dryers: Base Case Shipments Forecast by Product Class ...................... 9-5

Figure 9.3.5 Room Air Conditioners: Retirement Function ..................................................... 9-7

Figure 9.3.6 Room Air Conditioners: Base Case Shipments Forecast by Market 

Segment................................................................................................................ 9-8

Figure 9.3.7 Room Air Conditioners: Base Case Shipments Forecast by Product Class....... 9-10

Figure 9.7.1 Clothes Dryers, Electric Standard: Base Case and Standards Case 

Shipments Forecasts........................................................................................... 9-15
9-ii

Figure 9.7.2 Room Air Conditioners, < 6,000 Btu/h Without Reverse Cycle and With 

Louvered Sides: Base Case and Trial Standards Level Shipments 

Forecasts ............................................................................................................ 9-16
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 separate shipments model, which is 

calibrated with historical shipments data. Each 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, 

each 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 models were developed as Microsoft Excel spreadsheets that are 

accessible on the Internet (http://www.eere.energy.gov/buildings/appliance_standards/).

Appendix 10-A discusses how to access the shipments model spreadsheet and other related 

spreadsheets, and provides basic instructions for using them. 

 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; section 9.6 shows the candidate standard levels considered for each product class, 

and section 9.7 presents the results for different energy-efficiency standard-level scenarios.

9.2 SHIPMENTS MODEL METHODOLOGY

DOE developed national stock models for estimating annual shipments for the products 

considered for this standards rulemaking. The models consider market segments appropriate for 

the considered products. Typically, the primary market segments are new home installations, 

replacements, and first-time owners: 

jNIjRpljShip FTO j)()()()( p 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, 
9-2

NIp(j) = Number of new home installations of product p in year j, and 

NIp(j) = Number of product p going to first-time owners in year j. 

 For room air conditioners, DOE did not consider the new construction market since this 

product, unlike some major household appliances, is not a standard product for new homes (as 

opposed to central air conditioners). However, DOE did include a market segment for new 

purchases of room air conditioners. 

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

__

_

jStockjRpl Ship Rtr ageprob

ageMax

age

j

Nj

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: 
9-3

e x

xP

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; 

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

 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( ] _ agejStock =++ agejStock × Rtr ageprob

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. 
9-1

9.3 DATA INPUTS AND MARKET SEGMENTS 

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

product. 

9.3.1 Clothes Dryers

9.3.1.1 Historical Shipments

DOE used historical shipments data (domestic shipments and imports) to calibrate its 

shipments model. It used three sources to establish historical shipments of electric and gas 

clothes dryers: (1) data provided by AHAM for the period 1999–20091, (2) data from the 20002

and 20033 AHAM Factbooks for the period 1989–1998, and (3) data from Appliance Magazine4, 

5, 6 for the period 1972–1988. Figure 9.3.1 shows the historical shipments of electric and gas 

clothes dryers.

Figure 9.3.1 Historical Shipments of Electric and Gas Clothes 

Dryers

DOE then disaggregated the shipments of electric clothes dryers based on the market 

shares for 2007 according to data provided by AHAM (see Table 9.3.1). 

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1980 1985 1990 1995 2000 2005 2010

Shipments (millions)

Electric

Gas
9-2

Table 9.3.1 Clothes Dryer Product Class Market Shares

Product Class Market Share (%)

Vented Electric Standard 77.7

Vented Electric Compact (120V) 0.2

Vented Electric Compact (240V) 0.8

Vented Gas 20.9

Vent-less Electric Compact (240V) 0.5

Vent-less Combination Washer/Dryer 0.5

9.3.1.2 Markets and Model Calibration

 The shipments market for clothes dryers consists of three main segments: (1) replacement 

units for equipment that has been retired, (2) units purchased by households in new homes, and 

(3) households without clothes dryers who purchase the equipment (referred to as first-time 

owners, or FTOs). Total clothes dryer shipments are represented by the following equation: 

jNHjRpljShip FTO j)()()()( cd cd += cd + cd

 Where: 

Shipcd (j) = Total shipments of clothes dryers in year j, 

Rplcd (j) = Replacement shipments in year j, 

NHcd (j) = New home shipments in year j, and 

FTOcd (j)= Shipments to households without clothes dryers in year j. 

 

Replacements. DOE determined shipments for the replacement clothes dryer market 

segment using an accounting method that tracks the stock of units. Depending on vintage, a 

certain percentage of clothes dryers will fail and be replaced. To determine when a unit fails, 

DOE used a survival function based on a product lifetime distribution with an average value of 

16 years, and minimum and maximum values of 5 years and 30 years, respectively. For a more 

complete discussion of clothes dryer lifetimes, refer back to chapter 8. Figure 9.3.2 shows the 

survival and retirement functions that DOE used to estimate replacement shipments. 
9-3

Figure 9.3.2 Clothes Dryers: Retirement Function

 

New Home Shipments. For clothes dryers, DOE estimated new home shipments using 

new housing forecasts and product saturation. 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 2008, 

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

Energy Outlook 2010 (AEO2010) for 2009–2035.7 DOE estimated the fraction of new homes for 

which the owner or builder purchased an electric or gas clothes dryer based on RECS 2005 data. 

The saturation over the forecast period is 90 percent. DOE then disaggregated the projected new 

home shipments of clothes dryers using the market shares in Table 9.3.1. 

First-Time Owners. To estimate the number of households without clothes dryers who 

purchase the equipment, DOE considered the historical percentage of households which 

purchased a clothes dryer as a first-time owner. DOE derived this rate by dividing historical 

shipments from 1989-2009 that were not accounted for by replacement or new construction 

installations by the number of existing households without a clothes dryer. DOE determined that 

the average first-time owner rate over the past 20 years was 3.3 percent. Taking into account the 

current economic climate, DOE estimated that this average would be reached by 2013, and 

would then decrease at a rate of 5 percent annually, as the market becomes saturated with clothes 

dryers. 

0%

1%

2%

3%

4%

5%

6%

7%

Retirement Probability

Years
9-4

9.3.1.3 Base Case Shipments

Figure 9.3.3 shows the forecasted total clothes dryer shipments in the base case (i.e., the 

case without amended standards), disaggregated into the three market segments, and the 

historical shipments DOE used to calibrate the forecast. Figure 9.3.4 shows the forecasted 

clothes dryer shipments in the base case, disaggregated into the considered product classes, and 

the historical shipments.

Figure 9.3.3 Clothes Dryers: Base Case Shipments Forecast by 

Market Segment

0

2

4

6

8

10

12

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040

Shipments (Millions)

First Time Owners

New Homes

CD Replacements

Historical Shipments
9-5

Figure 9.3.4 Clothes Dryers: Base Case Shipments Forecast by 

Product Class

9.3.2 Room Air Conditioners

9.3.2.1 Historical Shipments

DOE used historical shipments data (domestic shipments and imports) to populate and 

calibrate its shipments model for room air conditioners. It used three sources to establish 

historical shipments: (1) data provided by the Association of Home Appliance Manufacturers 

(AHAM) for the period 1995–2009,1

 (2) data from the 2000 AHAM Factbook for the period 

1989–1994,3

 and (3) data from Appliance Magazine4,5,6 for the period 1972–1988.a

9.3.2.2 Markets and Model Calibration

The 

shipments data aggregates all product classes and include units for the residential and 

commercial sectors. 

The market for room air conditioners primarily consists of replacement units for 

equipment that has been retired. DOE’s shipments model also assumes that some existing 

 

a Shipments estimates from Appliance Magazine included exports. Thus, DOE reduced total shipments by 4.1 

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 data) to estimate total domestic shipments plus 

imports.

0

2

4

6

8

10

12

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040

Shipments (Millions)

Elec Combination Washer/Dryer

Electric Compact 240v -Ventless

Electric Compact (240v)

Elec Compact (120v)

Gas Shipments

Electric Standard Shipments

Historical Shipments
9-6

households without room air conditioners as well as households who already own units will 

purchase the equipment. Total room air conditioner shipments are represented by the following 

equation: 

jNPjRpljShip )()()( rac = rac + rac

 Where: 

Shiprac (j) = Total shipments of room air conditioners in year j, 

Rplrac (j) = Replacement shipments in year j, and

NPrac (j)= Shipments to existing households adding a new room air conditioners in 

year j. 

 The sections below discuss these markets in further detail. 

Replacements. DOE determined shipments to the replacement market using an 

accounting method that tracks the total stock of units by vintage. Over time, some units will be 

retired and removed from 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 unit fails, DOE used a survival function based on a product 

lifetime distribution with an average value of 10.5 years, and minimum and maximum values of 

3 years and 20 years, respectively. For a more complete discussion of room air conditioner 

lifetimes, refer back to chapter 8. Figure 9.3.5 shows the retirement function that DOE used to 

estimate replacement shipments. 
9-7

Figure 9.3.5 Room Air Conditioners: Retirement Function

New Purchases. To calibrate the modeled shipments with the historical data, DOE 

introduced a market segment for new purchases of room air conditioners. These include purchase 

of additional units by households that already own a room air conditioner, as well as purchases 

by households without room air conditioners, also referred to as first-time owners (FTOs). 

Through 2009, DOE derived new purchases as the difference between the historic total 

shipments and the calculated replacement shipments. 

For 2010 and onward, DOE estimated new purchases in the following way. On average, 

households with room air conditioners own 1.7 units per household, according to the American 

Housing Survey (AHS) 2007. The AHS indicates that 21 million households did not own a room 

air conditioner in 2007. Assuming that the households without a room air conditioner would 

potentially purchase 1.7 units on average, DOE estimated that the total potential for room air 

conditioner sales in the FTO segment in 2007 was around 36 million. Over time, this pool 

decreases as some of the households purchase room air conditioners. In 2009, after subtracting 

the replacement market sales, DOE estimated that the remaining sales imply that less than 1 

percent of the FTO potential sales were realized, as opposed to 10 percent over the period 2007-

2009. DOE assumed that this would be the case in the next two years until the economy recovers 

from the economic downturn. In the following years, DOE estimated that 10 percent of the 

remaining segment in each year in 2012–2044 purchases a unit. DOE based these fractions on 

the estimated purchases by FTOs in 2009 and in the period 2007–2009 compared to the potential 

market.

 

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

02468

101214161820

22

242628

30

Annual Retirement Rate
9-8

Commercial Sector Shipments. As described in chapter 8, DOE estimated that 12 percent 

of total room air conditioner shipments go to the commercial sector. DOE used this fraction to 

estimate shipments to the commercial sector for all years in the forecast period.

9.3.2.3 Base Case Shipments 

Figure 9.3.6 presents forecasted room air conditioner shipments in the base case, 

disaggregated into the considered market segments. The leveling off in shipments forecast by the 

shipments model reflects the saturation of the potential market for this product.

Figure 9.3.6 Room Air Conditioners: Base Case Shipments Forecast 

by Market Segment

9.3.2.4 Disaggregation into Product Classes

 DOE’s shipments model for room air conditioners forecasted aggregate shipments. DOE 

considered 16 product classes for room air conditioners. DOE estimated the market shares for 

each of the 16 product classes using market share data AHAM provided for 2005–2007.3 Where

AHAM did not disaggregate shipments into all of the product classes, DOE assumed that the 

distribution of models for the product classes is representative of the distribution of shipments. 

Table 9.3.2 shows the market shares used for the forecast period, and Figure 9.3.7 shows the 

shipments forecast by product class. 
9-9

Table 9.3.2 Room Air Conditioner Product Class Market Shares

Product 

Class 2005 2006 2007 

Share of 

Models* 

Share Used 

After 2007

1 37.0% 23.0% 32.0% 11.6% 30.7%

2 19.0% 19.0% 16.0% 9.9% 18.0%

3 30.0% 34.0% 36.0% 31.1% 33.4%

4 3.0% 5.5% 6.0% 12.1% 4.8%

5 2.0% 3.9% 2.6% 9.0% 2.8%

6

7.0% 12.0% 7.0% 

0.1% 0.1%

7 0.9% 0.4%

8 19.1% 8.0%

9 0.7% 0.3%

10 0.0% 0.0%

11 0.7% 1.0% NA 0.6% 0.8%

12 0.1% 0.5% 0.1%

13 0.4% 0.6% NA 0.7% 0.3%

14 0.0% 0.0%

15 0.4% 0.6% 0.4% 1.1% 0.1%

16 2.6% 0.3% 

* Based on 2007 CEC directory and AHAM email communication for disaggregation between the product classes 

5a and 5b, and 8a and 8b. 
9-10

Figure 9.3.7 Room Air Conditioners: Base Case Shipments Forecast 

by Product Class 

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 
9-11

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

ratesb

 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 

 

b 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.
9-12

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

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.8, 9 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 jejMj RP j pSTD = 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. 
9-13

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 p p jShipjStock p ageStock

=

= +

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 CANDIDATE STANDARD LEVELS

Table 9.6.1 and Table 9.6.2 show the efficiency levels corresponding to each candidate 

standard level (CSL) for each product class.
9-14

Table 9.6.1 Combined Energy Factor (CEF) Levels Corresponding to Candidate 

Standard Levels for Clothes Dryers

Product Class Candidate Standard Level

1 2 3 4 5 6

Vented Electric Standard 3.56 3.61 3.73 3.81 4.08 5.42

Vented Electric Compact 120V 3.48 3.61 3.72 3.80 4.08 5.41

Vented Electric Compact 240V 3.16 3.27 3.36 3.48 3.60 4.89

Vented Gas 3.16 3.20 3.30 3.41 3.61

Vent-less Electric 240V 2.59 2.69 2.71 2.80 4.03

Vent-less Combination 

Washer/Dryer 2.35 2.38 2.46 2.56 3.69

Table 9.6.2 Combined Energy Efficiency Rating (CEER) Levels Corresponding to 

Candidate Standard Levels for Room Air Conditioners 

Product Class

Base 

Case

Candidate Standard Level

1 2 3 4 5

Less than 6,000 Btu/h, with Louvers 9.5 10.1 10.6 11.1 11.4 11.7

8,000-13,999 Btu/h, with Louvers 

9.7 10.2 10.7 10.9 11.5 12.0

20,000-24,999 Btu/h, with Louvers 8.5 9.0 9.4 9.8 10.2

25,000 Btu/h or more, with Louvers 

8.5 9.0 9.4 9.8

8,000-10,999 Btu/h, without Louvers 8.4 9.3 9.6 10.0 10.4

11,000-13,999 Btu/h, without Louvers 8.4 9.3 9.5 9.8 10.0

9.7 SHIPMENTS FORECASTS 

 The following sections show the shipments forecasts for the various standard levels that 

DOE considered for clothes dryers and room air conditioners, as well as for the base case.

9.7.1 Clothes Dryers

Figure 9.7.1 compares the shipments forecasts for the base case and TSLs 1 through 6 for 

electric standard clothes dryers. In Figure 9.7.1, the difference between the base case and 

standard level shipments forecasts depicts the annual shipments reductions caused by the 

standard levels. For all standard levels, shipments are forecasted to decrease compared to the 

base case —the effects from the increase in product purchase prices offset the effects from 

decreased operating costs, resulting in a net decrease in shipments. Similar effects are seen for 

the other clothes dryer product classes. 
9-15

Figure 9.7.1 Clothes Dryers, Electric Standard: Base Case and Standards Case 

Shipments Forecasts

4.00

4.50

5.00

5.50

6.00

6.50

7.00

7.50

8.00

8.50

9.00

2014 2019 2024 2029 2034 2039 2044

Shipments (Millions)

Base Case

TSL 1 

TSL 2 

TSL 3, TSL 4 

TSL 5 

TSL 6 
9-16

9.7.2 Room Air Conditioners

Figure 9.7.2 compares the shipments forecasts for the base case and TSL 1 through 6 for 

units less than 6,000 Btu/h without reverse cycle and with louvered sides. In Figure 9.7.2, the 

difference between the base case and standard level shipments forecasts depicts the annual 

shipments reductions caused by the standard levels. For all standard levels, shipments are 

forecasted to decrease compared to the base case; the effects from the increase in product 

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

shipments. Similar effects are seen for the other room air conditioner product classes.

Figure 9.7.2 Room Air Conditioners, < 6,000 Btu/h Without 

Reverse Cycle and With Louvered Sides: Base Case 

and Trial Standards Level Shipments Forecasts
9-17

REFERENCES

1. Association of Home Appliance Manufacturers, AHAM Data on Room Air Conditioners 

and Clothes Dryers. 2009 

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

Washington, DC. 

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

Washington, DC. 

4. Statistical Review. Appliance Magazine, April, 1990 

5. Statistical Review. Appliance Magazine, April, 1992 

6. Statistical Review. Appliance Magazine, April, 1993 

7. 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/> 

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

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

9. 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>