9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

9.2 DEFINITION OF MARKET SEGMENTS FOR THE SHIPMENTS ANALYSIS ....... 9-1

9.2.1 Fundamental Model Equations........................................................................................ 9-2

9.2.1.1 Replacement Shipments................................................................................. 9-3

9.2.2 Shipments to New Construction ...................................................................................... 9-4

9.2.3 Shipments to New Owners............................................................................................... 9-4

9.3 DATA INPUTS AND SUPPORTING CALCULATIONS ............................................ 9-4

9.3.1 Historical Shipments and Calculation of Replacement Shipments.................................. 9-4

9.3.1.1 Historical Shipments...................................................................................... 9-4

9.3.2 Shipments to New Construction ...................................................................................... 9-6

9.3.3 Shipments to New Owners............................................................................................... 9-6

9.3.3.1 Product Switching.......................................................................................... 9-7

9.4 IMPACT OF STANDARDS ON SHIPMENTS ............................................................. 9-8

9.4.1 Purchase Price Elasticity.................................................................................................. 9-8

9.4.2 Impact from Increase in Relative Price.......................................................................... 9-10

9.5 RESULTS ...................................................................................................................... 9-11

LIST OF TABLES

Table 9.3.1 Saturations of Residential Boilers in New Construction in 2020 ........................ 9-6

Table 9.3.2 Switch of Replacement Units During the 2020-2049 Period............................... 9-7

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

LIST OF FIGURES

Figure 9.3.1 Historical Shipments of Residential Boilers........................................................ 9-5

Figure 9.3.2 Product Switching Among Residential Boiler Product Classes .......................... 9-7

Figure 9.5.1 Historic and Projected Base Case Shipments Residential Boilers by 

Product Class ..................................................................................................... 9-11

Figure 9.5.2 Total Projected Shipments of Residential Gas-fired Hot Water Boilers in 

the Base Case and Each Standards Case............................................................ 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 project annual product shipments and presents results for residential boiler

product classes considered in this analysis.

The shipments model divides the shipments of residential boilers into specific market 

segments. The model starts from a historical base year and calculates retirements and shipments 

by market segment for each year of the analysis period. This approach produces an estimate of 

the total equipment stock, broken down by age or vintage, in each year of the analysis period. In 

addition, the product stock efficiency distribution is calculated for the base case and for each 

standards case for each product class. The stock distribution is used in the national impact 

analysis (NIA) to estimate the total costs and benefits associated with each efficiency level.

The shipments model was developed as a Microsoft Excel spreadsheet that is accessible 

on DOE’s Appliance and Commercial Equipment Standards website 

(http://www1.eere.energy.gov/buildings/appliance_standards/rulemaking.aspx?ruleid=62). 

Appendix 10-A discusses how to access and utilize the shipments model spreadsheet, which is

integrated into the spreadsheet for the NIA. This chapter explains how the shipments model is 

constructed and provides some summary output. The rest of section 9.1 describes the 

methodological approach. 

9.2 DEFINITION OF MARKET SEGMENTS FOR THE SHIPMENTS ANALYSIS 

The residential boiler shipments model considers three product placement channels 

(hereafter referred to as “channels”) as follows:

1. New housing: a certain fraction of new buildings acquire boilers in each future year. This 

fraction is defined as the new construction saturation, which varies by year, by region,

and by product class.

2. Existing owners (replacements): these are defined as existing buildings with boilers

installed. This category receives new shipments when existing equipment is replaced.

3. New owners: these are defined as existing buildings that acquire boilers for the first time 

during the analysis period. The new owners primarily consist of households that during a 

major remodel add hydronic heating using a gas-fired hot water boiler. Additionally, 

some households could decide to switch from a gas furnace to a boiler with hydronic air 

handler. For this analysis, new owners also include households switching between 

different boiler product classes.
9-2

9.2.1 Fundamental Model Equations

The fundamental dependent variable in the shipments model is the equipment stock,

which is represented as a function of analysis year (indexed by j), and equipment vintage or age 

(the equipment age is noted as a, and is equal to the analysis year minus the vintage). The stock 

function is adjusted in each year of the analysis period by new shipments coming in and broken 

or demolished equipment being taken out.

For existing stock:

Stock ( j, a) = Stock ( j −1, a −1) − Rem ( j, a) + Ship ( j −1, a −1) p p p p

Eq. 9.1

and for new shipments:

Stock ( j, a = 1) = Ship ( j −1). p p

Eq. 9.2

Where:

Stockp (j, a) = number of units of product class p and age a in analysis year j,

Remp (j, a) = number of units of product class p and age a removed in analysis year j, and

Shipp(j) = number of units of product class p shipped in year j.

Removals due to equipment failure contain a survival function fp(a) that is used to 

represent the probability that a unit of age a will survive in a given year; equivalently, the 

probability that this unit will fail is 1- fp(a).

Total removals in the base case are then:

Rem ( j a) [ f (a)] Stock ( j a) p p p , = 1− × , .

Eq. 9.3

In the standards case, there is also a second term that represents the extended repair stock 

that has been in use for six years following the repair date (see section 9.4.2 for discussion of

extended repair). 

Shipments are directed to one of the three channels:

Ship ( j) Rpl ( j) NC ( j) NO ( j) p = p + p + p

Eq. 9.4

Where:
9-3

Rplp(j) = number of units of product p replaced in year j, which depends on removed units and 

units in demolished buildings,

NCp(j) = number of units installed in new construction of product p in year j, and

NOp(j) = number of units shipped to “new owners” of product p in year j.

9.2.1.1 Replacement Shipments

The shipments model assumes that units that are taken from demolished buildings, 

Dem(j), are included in the mix of broken units Remp (j). As the demolished units do not need to 

be replaced, they are deducted from Remp(j) when calculating the required replacements, as 

represented by the following expression:

Rpl ( j) Rem ( j) Dem( j) p = p −

Eq. 9.5

When a boiler fails, it is removed from the stock or is repaired for extended use. The 

following retirement function rp(a) is used to represent the probability that a unit will fail at age 

a.

Rem ( j) r (a) Stock ( j a) p a p a = ∑ × ,

Eq. 9.6

Retirement functions and product lifetimes are discussed in more detail in chapter 8. 

In each year, equipment is removed from demolished buildings. As represented by the 

following expression, the shipments model assumes that the saturation of the equipment in the 

demolished buildings is the same as that of the overall building population.

Dem( j) = D( j)× sat(p, j −1)

Eq. 9.7

The number of demolished buildings is calculated by:

Eq. 9.8

D( j) = H _ Stock( j −1) + H _ Starts( j) − H _ Stock( j)

Where: 

H_Stock (j) = number of housing units in analysis year j,

H_Starts(j) = number of new housing units in year j,

D(j) = number of demolished buildings, 

Dem (j) = number of equipment units demolished in analysis year j, and

sat(p,j) = saturation of equipment of product class p for all buildings in year j.
9-4

9.2.2 Shipments to New Construction

DOE multiplied new construction market saturations by projections of new housing units 

to estimate shipments to the new construction channel. On a product class basis, the 

determination of shipments to new construction is represented by the following expression:

NC ( j) NC Starts res( j) NC Sat res ( j) NC Starts com( j) NC Sat com ( j) p = _ _ × _ _ p + _ _ × _ _ p

Eq. 9.9

Where: 

NC_Starts_res(j) = number of new residential housing starts in year j, 

NC_Sat_resp(j) = new residential housing saturation for product class p and year j, 

NC_Starts_com(j) = number of new commercial building starts in year j, and

NC_Sat_comp (j) = new commercial housing saturation for product class p and year j. 

9.2.3 Shipments to New Owners 

The third market segment consists of new owners of products in a given product class, 

and also includes an adjustment for switching to a different product class. Because there are no 

data on the extent of these phenomena, DOE estimated historical shipments to this market 

segment as a residual, using the following equation:

NO( j) = Shipment( j) − (RU( j) + NU( j))

Eq. 9.10

Where: 

j = year where historical shipment data is available

NO(j) = new owners (if positive) or adjustment for switching (if negative) for year j,

Shipment(j) = historical shipment in year j,

RU(j) = estimated replacement units in year j, and

NU(j) = new units for new homes in year j.

9.3 DATA INPUTS AND SUPPORTING CALCULATIONS

9.3.1 Historical Shipments and Calculation of Replacement Shipments

9.3.1.1 Historical Shipments

DOE used historical shipments data (i.e., domestic shipments and imports) to populate its 

shipments model for residential boilers. The historical shipments data for all gas and oil boilers 

were collected from Appliance Magazine (AM), Gas Appliance Manufacturers Association 
9-5

(GAMA)a and the Energy Star program.

2,3,4 DOE adjusted the historical shipment data reported 

by AM, GAMA, and the Energy Star and disaggregated residential gas and oil boilers into hot 

water boilers and steam boilers by using AHRI’s recent shipment information provided to DOE.

DOE also estimated that the fraction of electric hot water boilers is 3.4% and the fraction 

of electric steam boilers is the same with the fraction of gas-fired and oil-fired steam boiler based 

on the boiler units information derived from Energy Information Administration (EIA)’s 2009 

Residential Energy Consumption Survey (RECS 2009)8 and EIA’s 2003 Commercial Buildings 

Energy Consumption Survey (CBECS 2003).

9 Further details about historical shipments are 

described in appendix 9-B. Figure 9.3.1 summarizes the historical shipments data that DOE 

assembled. 

Figure 9.3.1 Historical Shipments of Residential Boilers

A fraction of residential boilers are shipped to commercial buildings; therefore, DOE 

considered the future shipments of residential boilers to commercial buildings in this analysis. 

DOE used RECS 2009 and CBECS 2003 to determine the number of residential boilers in 

residential and commercial applications. DOE estimated that residential boilers shipped to 

commercial buildings accounted for 7% of the total historical shipments of residential boilers. 

Details of the methodology to determine the fraction of residential boilers shipped to commercial 

buildings are described in appendix 9-B.

 

a Total shipments reported by AM and GAMA included commercial boilers with input between 300 kBtu/h and 450 

kBtu/h. Note that DOE adjusted for shipments from manufacturers that were not part of GAMA or currently part of 

AHRI.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

Historical shipments (million)

Steam Electric Boiler Hot Water Electric Boiler

Oil-fired Steam Boiler Oil-fired Hot Water Boiler

Gas-fired Steam Boiler Gas-fired Hot Water Boiler
9-6

9.3.2 Shipments to New Construction

DOE determined new residential housing and commercial building construction starts by 

using recorded data through 201210, 11 and projections from EIA’s Annual Energy Outlook 2013

(AEO 2013).12

DOE developed new housing boiler type market saturations from Characteristics of New 

Housing data from the U.S. Census Bureau,

13 RECS 2009, and CBECS 2003. DOE used 

historical new housing saturations for each boiler type to project future saturations for each class.

DOE used the U.S. Census data to estimate national saturations for gas boilers, oil boilers and 

electric boilers in new single-family houses in the 1999-2013 time period. DOE estimated future 

national saturations in single family houses using the average saturation in the 2010−2013 by 

Census division. It derived national saturation values over time using weights based on the AEO

2013 housing forecast of new single family (SF) starts by Census division. To estimate future 

saturations in multifamily (MF) and manufactured home (MH) for gas boilers, oil boilers and 

electric boilers, DOE used the average saturations in homes built in 1990-2009 (from RECS 

2009 data) that use each type of heating equipment.

Table 9.2.1 shows the projected market saturations of residential boilers by housing types 

in year 2020. DOE assumed that steam boilers are primarily a replacement product, so the new 

construction saturations for steam boilers were set equal to 0 percent.

Table 9.3.1 Saturations of Residential Boilers in New Construction in 2020

Product Class Single 

Family

MultiFamilyManufactured

Home

Commercial 

Buildings

Gas-fired Hot Water Boiler 1.09% 1.15% 0.00% 0.72%

Gas-fired Steam Boiler 0.00% 0.26% 0.00% 0.17%

Oil-fired Hot Water Boiler 0.19% 0.11% 0.00% 0.28%

Oil-fired Steam Boiler 0.00% 0.02% 0.00% 0.05%

Hot Water Electric Boiler 0.19% 0.08% 0.00% 0.08%

Steam Electric Boiler 0.00% 0.10% 0.00% 0.02%

9.3.3 Shipments to New Owners 

The new owners primarily consist of households that during a major remodel add 

hydronic heating using a gas-fired hot water boiler and households that choose to install a boiler 

for a hydronic air handler to replace a gas furnace. For this analysis, new owners also include 

households switching between different boiler product classes. 

To estimate future shipments to households that choose to install a boiler for a hydronic 

air handler to replace a gas furnace, DOE used information from the 2008 American Home 
9-7

Comfort Survey, which indicated that about 9% of new central boilers went to new owners.

14

Because the potential number of new owners is limited, DOE assumed that in the future this 

fraction would decrease to 3%.

9.3.3.1 Product Switching

For replacement units, DOE estimated product switching between different boiler product 

classes (steam to hot water and oil to gas) based on stakeholder input on market trends.

DOE estimated that 1% of steam oil boiler replacement units were replaced by steam gas boilers, 

1% of steam oil boiler replacement units were replaced by hot water oil boilers, and 1% of steam 

oil boiler replacement units were replaced by hot water gas boilers. Similarly, DOE estimated 

that 1% of steam gas boiler replacement units were replaced by hot water gas boilers and 1% of 

hot water oil boiler replacement units were replaced by hot water gas boilers. Figure 9.2.2

illustrates DOE’s product switching estimates between the residential boiler product classes.

Figure 9.3.2 Product Switching Among Residential Boiler Product Classes

The results from the shipments model for the switched units during the 2020-2049 period 

are summarized in Table 9.2.2 (negative value represents number of boiler units replaced by 

other product classes and positive value indicates number of boiler units used as replacements in

other product classes):

Table 9.3.2 Switch of Replacement Units During the 2020-2049 Period

Product classes

Net switch 

units 

(thousand)

Gas-Fired hot water boiler 42.611

Gas-Fired steam boiler -4.118

Oil-Fired hot water boiler -27.154

Oil-Fired steam boiler -11.340

Gas-Fired Hot 

Water Boilers

Oil-Fired Hot 

Water Boilers

Gas-Fired 

Steam Boilers

Oil-Fired 

Steam Boilers

1% of repl. units

1% of repl. units

1% of repl. units 1% of repl. units 1% of repl. units
9-8

9.4 IMPACT OF STANDARDS ON SHIPMENTS

For replacements, consumer purchase decisions are influenced by the purchase price and 

operating cost of equipment, and therefore may be different in the base case and under standards 

cases at different efficiency levels (ELs).

b These decisions are modeled by estimating the 

purchase price elasticity for boilers. The purchase price elasticity is defined as the change in the 

percentage of consumers acquiring a boiler divided by a change in the relative price (defined 

below) for that equipment. This elasticity, along with information obtained from the life-cycle 

cost (LCC) and payback period (PBP) analysis on the change in purchase price and operating 

costs at different ELs, are used in the shipments model to estimate the change in shipments under 

standards at different ELs.

9.4.1 Purchase Price Elasticity

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 

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

high implicit discount ratesc 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 + = =

Eq. 9.11

 b Because the percentage change in the cost of boilers due to amended residential boiler standards is relatively small, 

DOE assumed that the new construction market is unaffected by changes in either the total installed cost or 

operating costs of the equipment. That is, home builders are not likely to choose to not install a boiler if the installed 

cost rises by a small amount. c A high implicit discount rate with regard to operating costs suggests that consumers put a low economic value on 

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

concerned with higher purchase prices.
9-9

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 real prices, as opposed to nominal, and an implicit 

discount rate of 37 percent to estimate the present value of operating costs. The rate of 37 percent 

is based on a survey of several studies of different appliances suggests that the consumer implicit 

discount rate has a broad range and averages about 37 percent.

15

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

over the three appliances, is -0.34. This implies that a relative price increase of 10 percent results 

in a 3.4 percent decrease in shipments. Note that the relative price elasticity incorporates the 

impacts from purchase price, operating cost, and household income, so the impact from any 

single effect can be mitigated by changes in 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 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 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 projections of shipments and national impacts attributable to standards are

calculated for a lengthy time period, DOE needed to consider how the relative price elasticity is 

affected after a new standard takes effect. DOE considered the relative price elasticity, described 

above, to be a short-term 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.16 This study shows that the automobile price elasticity of demand 

changes in the years following a purchase price change, becoming smaller (more inelastic) until 

it reaches a terminal value around the tenth year after the price change. Table 9.3.1 shows the 

relative change in the price elasticity of demand for automobiles over time. DOE developed a 

time series of relative price elasticities based on the relative change in the automobile price 

elasticity of demand. For years not shown in Table 9.3.1, DOE performed a linear interpolation 

to obtain the relative price elasticity.
9-10

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

9.4.2 Impact from Increase in Relative Price 

Using the relative price elasticity, DOE was able to estimate the impact of the increase in 

relative price from a particular standard level. The impact, as shown in the equation below, is 

expressed as a percentage drop in market share for each year, dMSp

j. 

( )

( ) e (j) RP _base j

RP _std j dMS RP

p

p p

j ×































 = 1 −

Eq. 9.12

Where:

dMSp

j = percentage market share drop for class p, year j, 

RP_stdp(j)= relative price in the standards case for product class p, year j, 

RPp(j)= relative price in the base case for product class p, year j, and

eRP(j) = relative price elasticity in year j.

To model the impact of the increase in relative price from a particular standard level on 

boiler shipments, DOE assumed that the affected consumers would repair their equipment rather 

than replace it, extending the life of the product by 6 years. When the extended repaired units fail 

after 6 more years, they will be replaced with new ones. 

The model calculates the relative percentage market drop, dMSp

j, due to the equipment 

price increase from a particular standard level. The extended repair is only applicable to failed

equipment that was purchased before 2020.

The number of failed boilers that will be repaired instead of being replaced is calculated 

as follows: 

= ∑ ( )× − < a

p XRi Rem j, a dMSi for( j a) 2020

( ) = ∑ − + − ( ) −

a

i j Rpl j Re m( j,a ) XR XR Dem j 6

Eq. 9.13

Where:
9-11

dMSp

j = percentage market share drop for class p, year j, 

a = age of equipment,

j = year,

Rem(j,a) = retiring units in year j of age a,

XRj = extended repair units, year j,

Rpl(j) = replacement units in year j, and

Dem (j) = number of units gone with demolished buildings in analysis year j.

9.5 RESULTS

Figure 9.5.1 shows the historic and projected shipments of residential boilers by product 

class. The projected shipments of residential boilers show a slightly downtrend due to the flat 

housing start projection by AEO 2013 and decreasing saturation of residential boilers in single 

family homes. The shipments of gas-fired steam boilers, oil-fired hot water boilers, and oil-fired 

steam boilers slightly decrease over time due to the product switching from steam to hot water 

and from oil to gas. The shipment of gas-fired hot water boilers slightly increases due to the 

product switching and the associated shipments to new owners.

Figure 9.5.1 Historic and Projected Base Case Shipments 

Residential Boilers by Product Class

Figure 9.5.2 shows total projected shipments of gas-fired hot water boilers in the base 

case and under each standards case. Because the elasticity is modeled as a delayed replacement 

of boiler products, the projection for the ELs shows a decline in the early years, but an increase 

in later years once the delayed replacements are finally made. As explained above, the elasticity 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1960 1970 1980 1990 2000 2010 2020 2030 2040

Shipments (million)

Oil-fired Steam Boiler Oil-fired Hot Water Boiler

Gas-fired Steam Boiler Gas-fired Hot Water Boiler
9-12

parameter decreases over time, so the impact of the standards on shipments diminishes. See 

appendix 9-B for total shipment projections for other boiler product classes.

Figure 9.5.2 Total Projected Shipments of Residential Gas-fired 

Hot Water Boilers in the Base Case and Each 

Standards Case

0.170

0.175

0.180

0.185

0.190

0.195

0.200

0.205

0.210

2015 2020 2025 2030 2035 2040 2045 2050 2055

Shipments (million)

Base EL 1 EL 2 EL 3

EL 4 EL 5 EL 6
9-13

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