CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

9.2 METHODOLOGY BEHIND 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

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

9.3.2.2 Model Calibration—Existing Households Without Appliance ..................... 9-6

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

9.4 EFFECT OF INCREASED PURCHASE PRICE ON SHIPMENTS ............................. 9-8

9.5 AFFECTED STOCK ..................................................................................................... 9-10

9.6 EFFECT OF CANDIDATE STANDARD LEVEL ON SHIPMENTS 

FORECAST ................................................................................................................... 9-11

LIST OF TABLES

Table 9.3.1 Portable Dehumidifiers: Historical Shipments, Domestic plus Imports .............. 9-4

Table 9.3.2 Product Calss Marke Share of Dehumdifiers ....................................................... 9-7

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

LIST OF FIGURES 

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

Figure 9.3.2 Whole-home Dehumidifier: Survival and Retirement Functions ........................ 9-6

Figure 9.3.3 Dehumidifiers: Historical and Base-Case Shipments Forecast ........................... 9-7

Figure 9.3.4 Dehumidifiers: Disaggregated Shipments Forecast for Base Case ...................... 9-8

Figure 9.6.1 Shipments Forecasts for Base Case and Each Standards Case .......................... 9-11

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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. This chapter describes the data and methods the U.S. Department of Energy 

(DOE) used to forecast annual product shipments and presents results for dehumidifiers 

considered for this standards rulemaking. Because DOE did not have shipment data for each

product classes, total historical shipments of portable and whole-home dehumidifiers were 

estimated and then separated by market share of each product classes. 

To project shipments for dehumidifiers, DOE used a shipments model that is calibrated 

with historical shipments data. The shipments model estimates shipments to specific market 

segments, 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 on the 

consumer purchase decision.

 The shipments model was developed as a part of the national impacts analysis (NIA) 

spreadsheet. Appendix 10A discusses how to access the NIA spreadsheet and provides basic 

instructions for its use. 

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

presents the methodology behind the shipments model; section 9.3 describes the data inputs and 

model calibration; section 9.4 discusses impacts on shipments from changes in product purchase 

price; section 9.5 discusses the affected stock; and section 9.6 presents the shipments forecast for 

one of the candidate standard levels (CSL) that DOE considered. 

9.2 METHODOLOGY BEHIND 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 

projection. As represented by the following equation, the two primary market segments for 

dehumidifiers are installations in exiting households without dehumidifiers and replacements. 

ShipDEF(j) = RplDEH (j) + FTODEH (j)

 Where:

ShipDEH(j) = total shipments of dehumidifiers in year j, 

RplDEH(j) = units of dehumidifiers retired and replaced in year j, and 

FTODEH(j) = shipments to existing households without dehumidifiers in year j. 

DOE’s shipments model takes an accounting approach, tracking market shares of each 

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

9-1 
models estimate shipments due to replacements using sales in previous years and assumptions 

about the lifetime of dehumidifiers. Estimated sales attributable to replacements in a given year 

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

previous years that remain in the stock. As described in chapter 8 of this preliminary technical 

support document (TSD), DOE determined the useful service life of dehumidifiers. DOE then

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

how DOE estimated replacement shipments.

)1()( ∑ ∑ )(

0

1

__

_

jStockjRpl Ship ageprobRtr

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 to estimate 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, whereby older, less efficient units may 

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

DOE estimated replacements using product retirement functions that it developed based 

on product lifetimes. 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

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. 

9-2 
 The retirement probability is the difference in the survival function from one year to 

another. 

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

data starting from a specific year. The start year depends 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: 

)1()1,( _ agejStock == jShip

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 ageprob =++ × 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, that 

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

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

of the units will be retired and removed from the stock, triggering the shipment of a new unit. 

9.3 DATA INPUTS AND MODEL CALIBRATION 

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

dehumidifiers. 

9.3.1 Historical Shipments

For portable dehumidifiers, DOE used data on historical shipments (domestic shipments

plus imports) to calibrate its shipments model for dehumidifiers. DOE’s sources for historical 

shipments data were (1) DOE’s previous rulemaking for dehumidifiers1

, and (2) data provided 

by the Association of Home Appliance Manufacturers (AHAM) for the period 1999 – 20112. 

Table 9.3.1 summarizes the historical data on portable dehumidifier shipments.

9-3 
Table 9.3.1 Portable Dehumidifiers: Historical Shipments, Domestic plus Imports

Year Shipments 

(thousands) Year Shipments (thousands) Year Shipments (thousands)

1972 461 1986 555 2000 975

1973 646 1987 704 2001 806

1974 586 1988 673 2002 799

1975 392 1989 605 2003 1,311

1976 440 1990 743 2004 1,672

1977 314 1991 745 2005 1,957

1978 442 1992 803 2006 1,456

1979 685 1993 983 2007 2,004

1980 673 1994 1,059 2008 1,558

1981 536 1995 1,003 2009 1,700

1982 440 1996 977 2010 1,552

1983 437 1997 820 2011 1,368

1984 591 1998 1,031

1985 588 1999 950

Source: 1999–2011: AHAM Data Submittal, 2012. 1972–1998: DOE’s Previous Rulemaking for Dehumidifiers. 

DOE assumed that whole-home shipments started from 2004, and the shipments 

accounted for about 1 percent of the portable dehumidifiers market. 

9.3.2 Markets and Model Calibration 

 The market for dehumidifiers is comprised primarily of replacement units for products 

that have been retired from service. Total dehumidifiers shipments are represented by the 

following equation:

ShipDEF(j) = RplDEH (j) + FTODEH (j)

 Where: 

ShipDEH (j) = total shipments of dehumidifiers in year j, 

RplDEH(j) = units of dehumidifiers retired and replaced in year j, and 

FTODEH(j) = shipments to existing households without dehumidifiers in year j. 

The sections below discuss these markets in further detail. 

9-4 
9.3.2.1 Replacements

DOE used an accounting method that tracks the total stock of units by vintage to 

determine shipments to the replacement market. DOE estimated a stock of dehumidifiers by 

vintage by integrating historical shipments starting from 1972. Over time, some units are retired 

and removed from the stock, 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 portable dehumidifier fails, DOE used a product survival function based on a lifetime 

distribution having an average value of 11.0 years. To determine when a whole-home 

dehumidifier fails, DOE used a product survival function based on a lifetime distribution having 

an average value of 19.01 years. For a more complete discussion of dehumidifier lifetimes, refer 

to section 8.2.2.6 of chapter 8 in this preliminary TSD. Figure 9.3.1 and Figure 9.3.2 show the 

survival and retirement function that DOE used to estimate replacement shipments for each 

dehumidifier type. 

Figure 9.3.1 Portable Dehumidifier: Survival and Retirement Functions

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Lifetime Dist. for Portable Dehumidifiers

% of Retiring

% of Surviving

9-5 
Figure 9.3.2 Whole-home Dehumidifier: Survival and Retirement Functions

9.3.2.2 Model Calibration—Existing Households Without Appliance

To calibrate the estimated shipments with the historical data, DOE introduced into the 

model a market segment identified as existing households without dehumidifiers, also 

referred to as FTOs. DOE estimated that 0.34 percent of existing households without a 

dehumidifier would annually purchase this product over the period 2019─2048. 

9.3.3 Base-Case Shipments

Figure 9.3.3 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. 

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Lifetime Dist. for Whole-home Dehumidifiers

% of Retiring

% of Surviving

9-6 
Figure 9.3.3 Dehumidifiers: Historical and Base-Case Shipments Forecast

DOE’s base-case shipments model for dehumidifiers used the aggregate shipments, i.e. 

the shipments for all seven product classes, as the basis for its forecasts. In other words, DOE did 

not develop a separate shipments model for each dehumidifier product class. As provided in 

Table 9.3.2, DOE based market shares for each of the seven product classes. DOE used the 

average market shares over the period 2012 – 2048 to disaggregate forecasted shipments into 

each of the seven dehumidifier product classes. 

Table 9.3.2 Product Class Market Share of Dehumidifiers

Year

Product Class (pints/day)

≤20.00 20.01-

30.00

30.01-

35.00

35.01-

45.00 >45.00

≤ 8.0ft3 

Case 

Volume 

(Wholehome)

>8.0ft3

Case 

Volume 

(Wholehome)

Pre2004* 33.7% 23.4% 21.1% 21.8% 0.0% 0.0% 0.0% 

Post2004** 29.0% 23.4% 21.1% 21.8% 3.7% 0.7% 0.3% 

*Source: DOE’s previous rulemaking for dehumidifiers, 2009; **Source: AHAM Data Submittal, 2012 

(≤20.00 pints/day dehumidifiers); DOE’s previous rulemaking for dehumidifiers (20.01 - ≥45.00 pints/day 

dehumidifiers); Manufacture interview, 2013 (whole-home dehumidifiers). 

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

3.0000

3.5000

Shipments (million)

Year

Shipment - Historical and Projected

Historical

Projected

9-7 
Figure 9.3.4 Dehumidifiers: Disaggregated Shipments Forecast for Base Case 

9.4 EFFECT OF INCREASED PURCHASE PRICE ON SHIPMENTS

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

leads 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. Appendix 9A explains the method DOE 

used to quantify the effects of the above variables.

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 product prices and 

shipments 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 appliances. 

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

 when 

comparing appliance prices and 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 

during 1980–2002 to evaluate broad market trends and conduct simple regression analyses. The 

data indicate that there has been an increase in appliance shipments and a decrease in appliance 

a 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. Consumers are much more concerned with 

the higher purchase prices.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Shipments (million)

Year

Replacement Units New Units

9-8 

 
purchase price and operating costs during the period. Household income also increased 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 using the following expression. 

Income

PVOCPP

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 (that is, less than 1.0). DOE’s regression analysis 

suggests that the relative price elasticity of demand, averaged for the three appliances, is -0.34. 

Thus 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 effects of three factors (purchase price, 

operating cost, and household income), the effect of any single factor is mitigated by changes to

the other two. 

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 subject to simple 

statistical analysis. More importantly, 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 consumer preferences may have occurred during that 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 consider 

30-year 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 shortterm value. It was unable to identify sources specific to household durable goods, such as 

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

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

automobiles.3, 4 That study showed that the automobile price elasticity of demand changes 

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

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

9-9 
after the price change. Table 9.4.1 shows the relative change in the price elasticity of demand for 

automobiles over time. 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 Table 9.4.1, DOE performed a linear interpolation to obtain the relative price

elasticity.

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

Number of Years After Price Change

Change in elasticity 

relative to first year

1 2 3 5 10 20

1.00 0.78 0.63 0.44 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)()( ) _

_ _ _ _ jejMjNIjRpljShip RP j pSTD = BASE 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, 

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

case, 

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. 

9.5 AFFECTED STOCK

The affected stock is the in-service stock of a 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 between the base case 

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

the effect that new product shipments have on the appliance stock because of a standard level. 

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

year the standard takes effect, as described by the following equation.

∑

_

1

_

)()( )(

j Std yr

age

Aff p p jShipjStock p ageStock

=

= +

Where:

9-10
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 for 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 of this 

preliminary TSD, DOE assumed that new energy efficiency standards will 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 SHIPMENTS 

FORECAST

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

candidate standard levels (CSLs). For all CSLs, shipments are forecasted to increase—the effects 

from the increase in product purchase prices offsets the effects from decreased operating costs, 

resulting in a net increase in shipments. 

Figure 9.6.1 shows total projected shipments of dehumidifiers in the base case and under 

each standards case. 

 Figure 9.6.1 Shipments Forecasts for Base Case and Each Standards Case

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Shipments (million)

Base Case CSL 1 CSL 2 CSL 3 CSL 4

9-11
REFERENCES

1 DOE–Energy Efficiency and Renewable Energy. Energy Conservation Program for Consumer 

Products: Technical Support Document: Energy Efficiency Program for Consumer 

Products and Commercial and Industrial Equipment, Residential Dishwashers, 

Dehumidifiers, and Cooking Products, and Commercial Clothes Washers. 2009. 

Washington, D.C. (Last accessed October 10, 2013.) 

<http://www1.eere.energy.gov/buildings/appliance_standards/residential/cooking_produc

ts_final_rule_tsd.html> 

2 Association of Home Appliance Manufacturers. AHAM Data on Portable Dehumidifiers 

 for DOE Efficiency Standards Rulemaking, November 12, 2012. Letter to Building 

 Technologies Program, U.S. Department of Energy. 

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

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

4 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. www.osti.gov/bridge/servlets/purl/929429-Vm1S9X/929429.pdf. (Access 

May 2013.) 

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