9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

9.2 APPROACH TO SHIPMENTS MODEL ....................................................................... 9-1

9.3 DATA INPUTS AND MARKET SEGMENTS.............................................................. 9-3

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

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

9.3.2.1 Replacements................................................................................................. 9-5

9.3.2.2 First-time Owners .......................................................................................... 9-5

9.3.2.3 Commercial Sector......................................................................................... 9-6

9.3.3 Base-Case Shipments....................................................................................................... 9-6

9.4 EFFECT OF INCREASED PURCHASE PRICE ON SHIPMENTS ............................. 9-6

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

9.6 EFFECT OF CANDIDATE STANDARD LEVEL ON PROJECTED 

SHIPMENTS ................................................................................................................... 9-9

LIST OF TABLES

Table 9.3.1 Historical Shipments of Room ACs (1972–2012)............................................... 9-4

Table 9.4.1 Change in Relative Price Elasticity following a Change in Purchase Price ........ 9-8

Table 9.6.1 Shipments Projected for Base Case and Each Standards Case, millions........... 9-10

LIST OF FIGURES

Figure 9.3.1 Portable ACs: Survival and Retirement Functions.............................................. 9-5

Figure 9.3.2 Portable ACs: Projected Shipments for Base Case by Market Segment ............. 9-6
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) related to potential energy efficiency 

standards. Estimated shipments also are required for the manufacturer impact analysis. This 

chapter describes the data and methods the U.S. Department of Energy (DOE) used to project

annual shipments of portable air conditioners (ACs) under base-case and standards-case 

efficiency levels. 

DOE estimated shipments for portable ACs using a shipments model calibrated with 

historical shipments data. The shipments model first estimates shipments for both of the 

residential and commercial sectors, and then disaggregates results to estimate individual sector.

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

accounts for the effects of changes in both purchase price and annual operating cost on the 

consumer purchase decision. The shipments model was developed as a part of the spreadsheet 

for the national impacts analysis (NIA). Appendix 10A describes how to access the NIA

workbook and provides basic instructions for its use. 

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

the approach to building the model; section 0 describes the data inputs and model calibration; 

section 9.4 discusses impacts on shipments from changes in product purchase price, operating 

cost, and household income; section 9.5 discusses the affected stock of portable ACs; and section 

9.6 presents the model results for various candidate standard levels for product efficiency.

9.2 APPROACH TO SHIPMENTS MODEL

DOE has developed national stock models to estimate annual shipments of various 

products under potential new energy efficiency standards. The models consider market segments 

as distinct inputs to projected shipments. Typically, the primary market segments are new home 

installations, replacements, and first-time owners. The following is the general equation for 

calculating product shipments to the three market segments. 

Ship ( j) Rpl ( j) NI ( j) 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,

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

FTOp(j) = number of product p purchased by first-time owners in year j.
9-2

For portable ACs, DOE did not consider the new construction market because this 

product, unlike some household appliances, is not commonly installed in new homes (unlike

central ACs). DOE included a market segment for purchases of portable ACs by first-time 

owners [or consumers who purchase an additional (rather than replacement) portable AC.]

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

product or product class, the vintage of units in the existing stock, and expected housing stock 

trends. The models estimate shipments attributable to replacements using sales in previous years 

and assumptions about the lifetime of the product. In a given year estimated sales attributable to 

replacements are equal to the total stock of the appliance minus the number of appliances sold in 

previous years that remain in the stock. The following equation shows how DOE estimates 

replacement shipments of consumer appliances.

( ) ( 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 develops 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 

calculations of both the NES and NPV, because the product operating cost for any year depends

on the age distribution of the stock. The dependence of operating cost on the product age 

distribution occurs under a standards-case scenario that produces increasing efficiency over time, 

whereby older, less efficient units may have higher operating costs, while younger, moreefficient units have lower operating costs.

DOE estimates replacements using product retirement functions developed from product 

lifetimes. DOE bases the retirement function on a Weibull distribution for the product lifetime. 

The shipments model assumes that no units are retired before reaching a minimum product 

lifetime, and all units are retired before exceeding a maximum product lifetime. For all products,

the models use a Weibull equation to determine the probability of retirement at a certain age.

e

x

P x

















 



( ) 

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 = age of appliance;
9-3

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 the 

next.

DOE calculates the total in-service stock of products by integrating historical shipments 

data starting from a specified year. The start year depends on the historical data available for 

each product. As units are added to the in-service stock, some 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:

( , 1) ( 1)

_

Stock j age   Ship 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 equal simply 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 of units also is 

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

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

in section 9.3. Over time, some units will be retired and removed from the stock, triggering the 

shipment of a new unit. 

9.3 DATA INPUTS AND MARKET SEGMENTS

The following sections describe the data inputs and market segments considered for 

portable ACs. Those data inputs are used in the general equations presented in section 9.2 for 

each market segment identified for portable ACs.

9.3.1 Historical Shipments

DOE used historical data regarding shipments of room ACs (domestic shipments and 

imports) to populate and calibrate its shipments model for portable ACs. DOE assumed that 
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shipments of portable ACs account for approximately 10 percent of the total shipments of room 

ACs.

1 DOE consulted two sources for historical shipments data for room AC: (1) for 1972–2009, 

DOE’s rulemaking for room ACs,

2

and (2) for 2010–2012, data from UBM, Market Research.

3

Table 9.3.1 presents the combined shipments data for 1972–2012.

Table 9.3.1 Historical Shipments of Room ACs (1972–2012)

Year Shipments 

millions Year Shipments millions Year Shipments millions

1972 4.15 1986 2.75 2000 6.50

1973 4.81 1987 3.68 2001 5.58

1974 3.78 1988 4.40 2002 6.15

1975 2.16 1989 4.68 2003 8.22

1976 2.16 1990 3.80 2004 8.08

1977 2.46 1991 2.56 2005 8.03

1978 3.16 1992 2.59 2006 10.06

1979 2.92 1993 2.80 2007 9.46

1980 2.44 1994 3.85 2008 9.09

1981 2.94 1995 4.00 2009 5.79

1982 2.27 1996 4.53 2010 6.42

1983 1.77 1997 3.84 2011 7.26

1984 2.98 1998 4.53 2012 7.55

1985 2.94 1999 6.29

Sources: For 1972–2009: DOE’s previous rulemaking for room ACs, 2011. 

 For 2010–2012: UBM, Market Research, 1954-2012.

9.3.2 Markets and Model Calibration

The market for portable ACs consists primarily of replacement units for products that 

have been retired. DOE’s shipments model also assumes that some existing households without a 

portable AC will purchase one (first-time owners). Total shipments of portable AC are 

represented by the following equation.

Ship ( j) Rpl ( j) FTO ( j)

pac



pac  pac

Where:

Shippac (j) = total shipments of portable ACs in year j, 

Rplpac (j) = replacement shipments in year j, and

FTOpac (j) = shipments to existing households that purchase a new portable AC in year j. 
9-5

The sections below discuss the market segments in further detail. 

9.3.2.1 Replacements

DOE determined shipments to the replacement market using an accounting method that 

tracks the total stock of units by vintage. Over time, as some units are retired and removed from 

stock, the shipment of a replacement unit is triggered. Depending on the vintage, a certain 

percentage of units will fail and need to be replaced every year. DOE determined the useful 

service life of portable ACs to estimate how long the appliance is likely to remain in stock. To 

determine when a unit fails, DOE used a survival function based on a product lifetime 

distribution having an average value of 10.5 years. For a more complete discussion of DOE's 

estimated lifetime of portable ACs, refer to chapter 8. Figure 9.3.1 shows the survival and 

retirement functions that DOE used to estimate replacement shipments.

Figure 9.3.1 Portable ACs: Survival and Retirement Functions

9.3.2.2 First-time Owners

To calibrate the modeled shipments with the historical data, DOE introduced a market 

segment for new purchases of portable ACs. It includes purchase of new units by households 

without portable ACs. DOE derived first-time owners through 2012, as the difference between 

the historic total shipments and the calculated replacement shipments. For 2013 through 2048, 

DOE estimated that 0.17 percent of households will purchase the product annually, as an initial 

purchase. 

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Lifetime Distribution for Portable AC

% Retiring

% Surviving
9-6

9.3.2.3 Commercial Sector

As described in chapter 8, DOE estimated that 1 percent of total portable AC shipments 

are used in the commercial sector. DOE used this percentage to estimate shipments to the 

commercial sector for all years in the analysis period.

9.3.3 Base-Case Shipments

Figure 9.3.2 presents projected shipments of portable ACs in the base case, divided into 

market segments. The leveling off in shipments projected by the model reflects the saturation of 

the potential market for this product.

Figure 9.3.2 Portable ACs: Projected Shipments for Base Case by 

Market Segment

9.4 EFFECT OF INCREASED PURCHASE PRICE ON SHIPMENTS

DOE conducted a literature review and an analysis of appliance price and efficiency data 

to estimate the combined effects on product shipments from increases in product purchase price, 

decreases in product operating costs, and changes to household income. Appendix 9-A provides 

a detailed explanation of the methodology DOE used to quantify the impacts from these 

variables.

Existing studies of appliance markets suggest that the demand for appliances is priceinelastic. Other information in the literature suggests that appliances are a normal good, so that 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Shipments (million)

Shipments by Market Segement

Replacements FTOs
9-7

rising incomes increase the demand for appliances, and that consumer behavior reflects relatively 

high implicit discount ratesa when comparing appliance prices and appliance operating costs. 

DOE used the available data for the period 1980-2002 on large appliance purchases 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. Because 

purchase decisions are sensitive to income, as well as to potential savings in the operating cost of 

the appliance, DOE combined the available economic information into one variable, termed the 

relative price. This variable was used in a regression analysis to parameterize historical market 

trends. 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 costs.

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

present value of operating costs.

DOE’s regression analysis suggests that the relative price elasticity of demand, averaged 

over the three appliances, is -0.34. Thus, for example, a relative price increase of 10 percent 

would result in a shipments decrease of 3.4 percent. Note that, because the relative price

elasticity incorporates the effects of three factors (purchase price, operating cost, and household 

income), the impact of any single factor is mitigated by changes in the other two.

A relative price elasticity of -0.34 is consistent with estimates of appliance price effects

in the literature. Nevertheless, DOE stresses that the measure is based on a small data set, using 

simple statistical analysis. More importantly, the measure is based on the 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 consumer preferences may have occurred during this period, but DOE did 

 

a An implicit discount rate refers to a rate than can be inferred from observed consumer behavior with regard to 

future operating cost savings realized from more-efficient appliances. An implicit discount rate is not a true discount 

rate because the observed consumer behavior is affected by lack of information, high transaction costs, and other 

market barriers. However, implicit discount rates can predict consumer purchase behavior with respect to energyefficient appliances. A high implicit discount rate with regard to operating costs means that consumer reflects a high 

discounting of future operating cost savings realized from more-efficient appliances. In other words, consumers are 

much more concerned with higher purchase prices.
9-8

not account for them in this analysis. Despite the uncertainties, DOE believes that its estimate of 

the relative price elasticity of demand provides a reasonable assessment of the effect that 

purchase price, operating cost, and household income have on product shipments.

Because DOE’s projections of shipments and national impacts from potential standards 

consider a 30-year period, DOE needed to consider how relative price elasticity is affected after a 

new standard takes effect. DOE considered the relative price elasticity developed above to be a 

short-term value, but was unable to identify sources specific to household durable goods, such as 

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

how the relative price elasticity changes through time, DOE relied on two studies pertaining to 

automobiles.4, 5 Those studies show that the price elasticity of demand for automobiles changes 

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

purchase price, 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 over time in 

the price elasticity of demand for automobiles. As shown in the table, DOE developed a time 

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

elasticity of demand for automobiles. For years not shown in the table, DOE performed a linear 

interpolation to obtain the relative price elasticity.

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

Years Following Price Change

1 2 3 5 10 20

Change in elasticity 

relative to first 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

Using the following equation, DOE estimated standards-case shipments by incorporating 

the effect of the relative price into the base-case shipments projection. 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 M j e j RP jSTD p



BASE p  BASE p

 RP 

Where:

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

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

MBASE_p(j) = first-time owners 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.
9-9

9.5 AFFECTED STOCK

For any energy efficiency rulemaking, the affected stock is the in-service stock of the 

appliance or product that is affected by a standard level. In addition to the projection of product 

shipments under the base case and each 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 effect that shipments of new 

products under a standard level have on the appliance stock. Therefore, the affected stock 

consists of those in-service units that are purchased in or after the year a standard takes effect, as 

described by the following equation.

∑

_

1

_

( ) ( ) ( )

j Std yr

age

Aff Stock pj Shippj 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 units (years), and

Std_yr = effective date of standard.

As required for the above equation, to calculate affected stock DOE must define the 

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

that any new energy efficiency standards for portable ACs would become effective in 2019.

Thus, all appliances purchased starting in 2019 are affected by the standard level. 

9.6 EFFECT OF CANDIDATE STANDARD LEVEL ON PROJECTED 

SHIPMENTS 

This section compares the shipments projected under the base case with those projected 

for all the candidate standard levels (CSLs) established for portable ACs. For all CSLs, 

shipments are projected to increase—the effects of the increase in product purchase price offset 

the effects of decreased operating costs, resulting in a net increase in shipments.

Table 9.6.1 shows total projected shipments of portable ACs in the base case and under 

each CSL.
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Table 9.6.1 Shipments Projected for Base Case and Each Standards Case, millions

CSL 2019 2025 2030 2035 2040 2045 2048

Base case 0.98 1.070 1.177 1.272 1.375 1.472 1.531

CSL 1 1.00 1.082 1.189 1.286 1.390 1.490 1.550

CSL 2 1.01 1.086 1.193 1.290 1.395 1.495 1.555

CSL 3 1.02 1.088 1.195 1.293 1.398 1.499 1.559

CSL 4 0.99 1.079 1.187 1.285 1.391 1.492 1.552
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REFERENCES

 

1 Natural Resources Canada (NRCan). Survey of Household Energy Use 2007: Detailed 

Statistical Report. Statistics Canada and NRCan, Ottawa ON. Report SHEU-2007. (Last 

accessed September 6, 2014.) 

<http://oee.nrcan.gc.ca/publications/statistics/sheu07/pdf/sheu07.pdf>. 

2 U.S. Department of Energy–Office of Energy Efficiency and Renewable Energy. Energy 

Conservation Program for Consumer Products: Technical Support Document: Energy 

Efficiency Standards for Consumer Products: Residential Clothes Dryers and Room Air 

Conditioners. April 2011. Washington, D.C. (Last accessed September 6, 2014.)

<http://www.regulations.gov/#!documentDetail;D=EERE-2007-BT-STD-0010-0053>.

3 UBM, Market Research. Appliance Historical Statistical Review 1954–2012. January 

2014. UBM, Hong Kong.

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

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

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

Appliances. 2008. Lawrence Berkeley National Laboratory: Berkeley, CA. Report No. 

LBNL 326E. OSTI ID: 929429. (Last accessed September 6, 2014.) 

< http://eetd.lbl.gov/sites/all/files/lbnl-326e.pdf>.