9-i

CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

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

9.1.1 Definition of Market Segments for the Shipments Analysis........................................... 9-1

9.1.2 Fundamental Model Equations........................................................................................ 9-2

9.2 DATA INPUTS AND SUPPORTING CALCULATIONS ............................................ 9-3

9.2.1 Historical Shipments and Calculation of Replacement Shipments.................................. 9-3

9.2.1.1 Historical Shipments...................................................................................... 9-3

9.2.1.2 Replacement Shipments................................................................................. 9-4

9.2.2 Shipments to New Housing ............................................................................................. 9-5

9.2.3 Shipments to New Owners and Adjustment for Switching ............................................. 9-5

9.2.4 Forecasting Condensing and Non-Condensing Market Shares ....................................... 9-6

9.3 IMPACT OF STANDARDS ON SHIPMENTS ............................................................. 9-6

9.3.1 Purchase Price Elasticity.................................................................................................. 9-6

9.3.2 Impact from Increase in Relative Price............................................................................ 9-8

9.4 RESULTS ........................................................................................................................ 9-9

`

LIST OF TABLES

Table 9.3.1 Change in Relative Price Elasticity Following a Purchase Price Change ........... 9-8

LIST OF FIGURES

Figure 9.2.1 Historical Shipments of HVAC Products with Furnace Fans.............................. 9-4

Figure 9.4.1 Historic and Forecast Base Case Shipments of HVAC Products With 

Furnaces Fans by Product Class ........................................................................ 9-10

Figure 9.4.2 Total Projected Shipments of HVAC Products With Furnaces Fans in the 

Base Case and Each Standards Case.................................................................. 9-10
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 furnace fan product 

classes being considered in this analysis. The shipments model divides the population of 

appliance users into specific market segments and estimates the shipment of new equipment to 

each of these segments. The model starts from a historical base year and calculates, for each year 

of the analysis period, both shipments and retirements by market segment. This approach 

produces an estimate of the total equipment stock, broken down by age or vintage, in each year 

of the analysis period. The product stock distribution is calculated for the base case and for each 

efficiency level of each product class. The stock distribution is used in the national impact 

analysis (NIA) to estimate the total dollar and energy costs and benefits associated with each 

efficiency level.

The vast majority of furnace fans are shipped pre-installed in furnaces and other heating, 

ventilating, and air conditioning (HVAC) products, so DOE estimated furnace fan shipments by 

projecting shipments of those products.

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/residential/central_ac_hp.html). 

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. The analysis incorporates a large number of components or market 

segments, describing different product classes, market sectors, and geographic regions; for 

simplicity, the methodology is explained in terms of a single product class for residential 

consumers for the country as a whole. 

9.1.1 Definition of Market Segments for the Shipments Analysis 

The furnace shipments model considers three product placement channels (hereafter 

referred to as “channels”) as follows:

1. New housing: a certain fraction of new buildings are assumed to acquire furnaces in the 

year of construction. This fraction is defined as the new construction saturation, which 

varies by year, by region, and by product type.

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

installed. This category receives new shipments when existing equipment is replaced.
9-2

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

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

have central air conditioning alone or central air conditioning and electric heating and 

choose to install a gas furnace.

9.1.2 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 ,a ) Rem (j,a) p = p − 1 − 1 − p

and for new units:

Stock (j,a ) Ship (j ). p = 1 = p − 1

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.

Shipments are directed to one of the three channels:

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

Where:

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

removals,

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.

Removals due to equipment failure contains two terms. In the first, a survival function 

fp(a) 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). The second term is the extended 

repair stock that has been in use for six years following the repair date. Total removals in the 

base case are then:
9-3

Rem (j,a) = [1 − f (a)]× Stock (j,a)+ ER _Stock (j,a2 = 6) p p p p

Where:

a2 = number of years since the equipment was repaireda

ER_Stockp(j, a2) = number of extended-repair units of product p replaced in year j.

, and

9.2 DATA INPUTS AND SUPPORTING CALCULATIONS

9.2.1 Historical Shipments and Calculation of Replacement Shipments

9.2.1.1 Historical Shipments

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

shipments model for furnace fan equipment. As part of its data submittal to DOE’s 2011 furnace 

standards rulemaking, the Air-Conditioning, Heating, and Refrigeration Institute (AHRI) 

provided historical shipments data over the 2005-2009 time period disaggregated into three

categories: (1) non-weatherized gas and mobile home gas furnaces, (2) oil-fired furnaces, and (3) 

weatherized gas furnaces.

2 Historical shipments for 1972-2005, except for weatherized gas 

furnace shipments, were also provided by the Gas Appliance Manufacturers Association 

(GAMA) from previous data submittals to the Lawrence Berkeley National Laboratory (LBNL).

2

DOE disaggregated mobile home gas furnace shipments from the gas furnace total by using a 

combination of data from the U.S. Census 3 and American Housing Survey (AHS).4 DOE used a 

similar method to determine mobile home electric furnace shipments. For electric furnaces, DOE 

used the historical estimates calculated in DOE’s 2011 furnace standards rulemaking. For 

weatherized gas furnaces, DOE used the 2005-2009 data provided by AHRI together with 

historical packaged central air conditioner shipments. For hydronic air handlers, DOE estimated 

that they represented less than 1% of the total furnace market and estimated historical shipments 

keeping this market share constant.

Disaggregated condensing and non-condensing shipments by region were available from 

1992 to 2009, and these data were used to estimate shipments before 1992. 

Figure 9.2.1 summarizes the historical shipments data that DOE assembled. 

 

a Based on data available from Decision Analyst consumer survey of central heating and cooling equipment owners, 

DOE was able to estimate that consumers expect a major repair to extend the lifetime of the equipment by around 6 

years.

1
9-4

Figure 9.2.1 Historical Shipments of HVAC Products with 

Furnace Fans

9.2.1.2 Replacement Shipments

When an equipment unit fails, it is removed from the stock. The following retirement 

function rp(a) is used to represent the probability that a unit will be broken at age a.

Re m (j) r (a) Stock (j,a) p a p = ∑ a ×

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 population.

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

Dem( j) = D( j)× sat(p, j −1)

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, 

0.0

1.0

2.0

3.0

4.0

5.0

1990 1995 2000 2005 2010

Historical Shipments (millions)

HAH

MHEF

MHGFc

MHGFnc

EF

OF

WGF

NWGFc

NWGFnc
9-5

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.

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) Re m (j) Dem(j) p = p −

9.2.2 Shipments to New Housing

DOE multiplied new construction market saturations by forecasts 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(j) NC _ Sat (j) p = ×

p

Where: 

NC_Starts (j) = number of new housing starts in year j, and

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

DOE determined new construction starts to the residential market segment, otherwise 

referred to as housing starts, by using recorded data through 2008 and projections from the DOEEnergy Information Administration (EIA)’s Annual Energy Outlook 2011 (AEO2011) for the 

period 2010–2035.8

 

DOE developed new housing market saturations from Characteristics of New Housing

data from the U.S. Census Bureau. DOE used historical new housing saturations for each furnace 

product class to project future saturations for each class. DOE used a 10-year average (2000-

2009) to estimate future saturations for non-weatherized gas (43.9%) and mobile home gas 

furnaces (30.7%), and a 5-year average from 2005-2009 to estimate future saturations for oil 

furnaces (0.4%).

9.2.3 Shipments to New Owners and Adjustment for Switching

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. In most cases, new 

owners consist of households that have central air conditioning alone, or central air conditioning 

and electric heating, and choose to install a gas furnace to augment or replace their existing 

equipment. 

DOE estimated historical shipments to this market segment using the following equation:
9-6

Where: 

j = year where historical shipment data is available

A(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,

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

To estimate future shipments to this market segment, DOE calculated the average 

shipments for this market segment in the past 3-4 years, and projected this quantity into the 

future.

9.2.4 Forecasting Condensing and Non-Condensing Market Shares

For non-weatherized gas and mobile home gas furnaces, the future market shares will be 

affected by the regional furnace standards that require compliance starting in 2013. The 

standards require that non-weatherized gas and mobile home gas furnaces sold in the North 

region must have a minimum annual fuel utilization efficiency (AFUE) of 90 percent, which 

requires them to be condensing furnaces. Therefore, all non-weatherized gas and mobile home 

gas furnaces shipments in the north from 2013 onward are assumed to be condensing furnaces. 

In the South region, condensing furnaces are not required, but some consumers may 

choose to purchase them anyway. DOE used the historical trend to estimate that condensing 

furnace shipments in the south increase from 28 percent in 2018 to 41 percent in 2047. This 

projection is similar to that used in DOE’s 2011 furnace standards rulemaking. 

9.3 IMPACT OF STANDARDS ON SHIPMENTS

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

operating cost of equipment, and therefore will likely be different in the base case and under 

different candidate standard levels (CSLs). These decisions are modeled by estimating the 

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

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

below) for that equipment. This elasticity and information obtained from the life-cycle cost 

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

under different CSLs are used in the shipments model to estimate the resulting change in 

shipments.

9.3.1 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 
9-7

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 ratesb 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 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.

5

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 

 

b 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.
9-8

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 DOE’s forecasts of shipments and national impacts attributable to standards is 

calculated for a lengthy time period, it 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.6 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.

Table 9.3.1 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

9.3.2 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 CSL. The impact, as shown in the equation below, is expressed as 

a percentage drop in market share for each year, dMSp

j , which is applied in the decision for 

replacement versus extended repair. 

( )

( ) e (j) RP _base j

RP _std j dMS RP

p

p p

j ×































 = 1 −

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
9-9

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

Because the percentage change in the cost of furnaces due to potential furnace fan 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 furnace if the installed cost rises by a small amount.

To model the impact of the increase in relative price from a particular CSL on furnace

shipments, DOE assumed consumers affected by an increase in total installed cost would repair

their equipment rather than replace it, extending the life of the product by six years. When the 

extended repaired units fail after six more years, they will be replaced with new ones. 

The model calculates, for each year after the standard, the relative percentage market 

drop, dMSp

j, due to the equipment price increase. The extended repair is only applicable to failed

equipment that is purchased before 2018. 

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

as follows: 

= ∑ ( )× − < a

p XRi Rem j, a dMSi for( j a) 2018

( ) = ∑ − + − ( ) −

a

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

Where:

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.

9.4 RESULTS

Figure 9.4.1 shows the historic and projected shipments of HVAC products with furnace 

fans by product class.

Figure 9.4.2 shows total projected shipments of HVAC products with furnace fans in the 

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

replacement of a furnace, the forecast for the CSLs shows a decline in the early years, but an 

increase in later years once the delayed replacements are finally made. Recall that the elasticity 

parameter decreases over time, so the impact of the standards on shipments diminishes.
9-10

Figure 9.4.1 Historic and Forecast Base Case Shipments of HVAC Products 

With Furnaces Fans by Product Class

Figure 9.4.2 Total Projected Shipments of HVAC Products With 

Furnaces Fans in the Base Case and Each Standards 

Case

0.0

1.0

2.0

3.0

4.0

5.0

1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045

Historical Shipments (millions)

HAH

MHEF

MHGFc

MHGFnc

EF

OF

WGF

NWGFc

NWGFnc

3.0

3.5

4.0

4.5

5.0

2015 2020 2025 2030 2035 2040 2045 2050

Shipments (millions)

Base

CSL1

CSL2

CSL3

CSL4

CSL5
9-11

REFERENCES

1. Decision Analysts, Homeowner “Spotlight” Report: Equipment Switching, Repair Profile 

and Energy Efficiency August, 2011. Arlington, Texas. 

<http://www.decisionanalyst.com/Syndicated/HomeComfort.dai>

2. Air-Conditioning Heating and Refrigeration Institute, Historical Shipments Data 

provided to Lawrence Berkeley National Laboratory, 2010.

3. U. S. Department of Commerce - Bureau of the Census, Characteristics of New Housing, 

2010. U.S. Census. (Posted June 2, 2010) (Last accessed August 7, 2010.) 

<http://www.census.gov/const/www/charindex.html>

4. U.S. Census Bureau: Housing and Household Economic Statistics Division, 2009 AHS 

National Data, 2009. HUD. (Last accessed September, 2011.) 

<http://www.huduser.org/portal/datasets/ahs/ahsdata09.html>

5. Train, K., Discount Rates in Consumers' Energy-Related Decisions. Energy: The 

International Journal, 1985. 10(12): pp. 1243-1253 

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

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