6-1

CHAPTER 6: SHIPMENTS ANALYSIS

6.1 INTRODUCTION

Central air conditioner and heat pump (CAC-HP) shipment estimates are a necessary input

for national energy savings calculations.

In this chapter we describe an accounting model for projecting annual CAC-HP shipments

that accounts for:

C Combined effects of price, operating cost, and income on annual U.S. shipments.

C Market segments (e.g., new housing, replacement decisions, and non-owners adding

a CAC-HP).

C Decisions to repair rather than replace.

C Age categories of CAC-HP.

All calculations are performed on a series of Microsoft Excel spreadsheets which are accessible over

the Internet. The shipments model is incorporated into a larger spreadsheet model that forecasts

national energy savings and net present value. Access to and basic instructions for the spreadsheets

are discussed in Chapter 7 on the National Energy Savings and Net Present Value Analysis.

6.1.1 Definition of Market Segments and Ownership Categories

The CAC-HP shipments model described herein segments both CAC-HP owners and CACHP purchases into different categories. The different types of CAC-HP owners (e.g. new housing,

regular CAC-HP owners, and non-owners) are faced with different types of CAC-HP purchase

decisions and purchase motivations. On the other hand, the different CAC-HP purchasers are

motivated to purchase a CAC-HP for different reasons. Because of these differences within

households and the CAC-HP market, we segment both markets and ownership into different

categories. To the extent a model can portray the different behaviors and stock flows of the different

market segments, the better it portrays the reality of the CAC-HP market. Additionally, by

disaggregating the market and utilizing specific known features of the different market segments,

the behavior of the model is constrained to match real market conditions and is more likely to behave

in ways consistent with actual market behavior. 

As described in Chapter 5, the Life-Cycle Cost and Payback Period Analysis acounts for the

use of residential-type central air conditioners and heat pumps in commercial buildings. But for

purposes of forecasting shipments, only the residential housing market is considered. Although

ignored in the shipments model, commercial applications are accounted for in the National Energy

Savings and Net Present Value Analysis by adjusting the annual energy consumption of central airconditioning and heat pump equipment to reflect their use in commercial buildings. More details

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on the annual energy consumption adjustment are provided in Chapter 7.

In this shipment forecast model, households with air conditioning equipment are classified

into a Central Air-Conditioning (CAC) households and a Heat Pump (HP) households using the

relative market share of the different types of equipment. The two types of systems are further

classified as split or package systems according to the relative market shares of the system type. The

shipment forecast model first calculates the over-all dynamics of the combined CAC-HP market

Households in this combined market are further divided into four different ownership categories,

while consumer purchases of CAC-HP are divided into five different market segments. The four

CAC-HP ownership categories are: 1) new housing, 2) existing housing with a regular CAC-HP, 3)

housing without a CAC-HP, and 4) housing with an extended life CAC-HP. We refer to the

population of CAC-HP in each ownership category as the stock of CAC-HP of that category.

Meanwhile the different types of CAC-HP purchases are divided into five separate market

segments as follows:

• New Housing Market: When new homes are completed, they will result in the purchase

of new CAC-HPs.

• Early (Discretionary) Replacement Market: Even before a CAC-HP breaks down, about

29% of CAC-HP owners replace the existing CAC-HP because they want an updated

model, because of remodeling, or for other miscellaneous reasons. 

• Regular Replacement Market: Most CAC-HP purchases result from the replacement of

an existing CAC-HP that has broken down after the completion of its useful life. 

• Extra Repair Market: Under conditions of high costs for new CAC-HP a few consumers

will rebuild or repair a broken down CAC-HP (thus extending its lifetime) rather than

purchasing a new CAC-HP. Eventually, even extended life CAC-HPs breakdown and

are replaced.

• Remodeling Market: When people change residence or remodel their homes they may

install new air conditioning equipment. 

The ownership categories reflect the type of CAC-HP that a consumer has, while the markets

segments reflect the reasons for purchasing a new CAC-HP.

The CAC-HP Shipments Model keeps track of the population of each type of CAC-HP and

CAC-HP purchase. Events and consumer decisions influence how the stock and supply of CAC-HP

flow from one category to another. Decisions which are economically influenced are modeled with

econometric equations. 

Figure 6.1 shows the detailed flow diagram for the CAC-HP Shipments Model. 

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Houses with

CAC or HP Problems? EarlyReplacement? No No

Yes

Yes

Buy CAC or HP

Houses

with

CAC or HP

Repair or

Replace? Replace

Regular or

Extra Repair? Repair Regular

Houses with

Extended Lifetime

CAC or HP

Did CAC or HP

Break Down? Yes

Houses

with

Extended

Lifetime

CAC or HP

Extra Repair

New Houses Purchase

CAC or HP? Yes

House w/o

CAC or HP

Remodeled

Houses

Purchase

CAC or HP?

No

No

No

Figure 6.1 Flow Diagram for CAC/HP Shipments Model

As depicted in Figure 6.1, households are faced with a series of decisions of whether or not

the current unit will be replaced, or whether a new unit will be purchased. The types of households

are illustrated with rectangles, and the decisions to which the households are subjected are indicated

by the arrows. Each branch of a decision or event tree is illustrated with a diamond which has one

input arrow, and two output arrows. The decisions to which each category of households (and their

CAC-HP unit) are subjected are described below: 

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New households are those households which represent a net increase in housing stock (new

housing construction less housing stock removed from the market). These households are faced with

the decision of whether or not to get a new CAC-HP with the house. 

For households with existing regular units, the first question is whether or not the current unit

is having operational problems (i.e. needs repair). If the unit is without problems then the consumer

must decide if he or she wants to purchase a unit for other discretionary reasons. If the unit has

operational problems, then the consumer must decide if the unit is to be repaired or replaced. If the

consumer makes an extra repair to avoid purchasing a new unit, then the model assumes that the

repair extends the unit lifetime by six years. 

For households without CAC-HPs a small fraction (at most a few percent) of consumers will

decide to become new CAC-HP owners in a given year.

Households with extended lifetime CAC-HPs are those households that have extended the

lifetime of their unit through an extra repair when the unit last broke down. When the CAC-HP

breaks down yet again, the consumer will have to have it replaced..

In section 6.1.3 we review the economics durables sales forecasting literature; section 6.2

describes the details of the mathematical structure of the model, while section 6.3 discusses the

modeling of economic consumer decisions, and section 6.4 presents the model results. 

6.1.2 Shipments Model Features

We have incorporated a variety of features in the CAC-HP shipments model in order to

provide more detailed predications and accounting the forecasts. 

Detailed accounting of different market segments and CAC-HP ownership categories: The

model accounts for a variety of market dynamics including changes in repair behavior and

extending the life of CAC-HPs through extra repairs. 

Purchase price, operating cost, and income elasticities: The model includes consumer

responsiveness to purchase price, operating costs, and income. Assumptions about the interrelation of different economic factors are used to determine the relative importance while overall sensitivities are calibrated with historical shipments data. 

Incorporation of repair rates and early (discretionary) replacements: The current shipments

model utilizes data from a study on heat pump service life to establish both CAC-HP repair rates

and the proportion of early (discretionary) replacements1.

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The purpose of the model is to provide the best estimates possible for future CAC-HP

shipments that are consistent with the recent history of CAC-HP shipments, and with current CACHP market structure and consumer preferences. 

While we endeavored to include a diverse set of features in the shipments model, there were

some features which for the sake of simplicity and accuracy were not included. In particular there

we did not include either a fuel switching elasticity nor regional housing shifts. We do however

discuss later in this chapter estimates of the relative impacts of these factors and show that they are

relatively small. 

6.1.3 Review of Other Published Research

We performed a review of recent literature on forecasting purchases of consumer durables

in order to evaluate studies regarding price and features sensitivities and their application to long

term sales forecast models. We report on eight relevant studies published from 1990 to the present.

In this literature, a standard measure of consumer sensitivity to features of the products and

the market is sales elasticity. Elasticity is the parameter that relates the relative change in a feature

(such as price, P) to the relative change in sales. For example:

Δ S S = e ⋅ Δ P P (6.1)

where ÄS/S is the relative change in sales, ÄP/P is the relative change in price, and g is the elasticity.

Elasticities are generally negative numbers ranging from 0 to -3. A product which has an elasticity

-2 will experience a 2% drop in sales for a 1% increase in price.

According to the marketing and sales forecasting literature, consumer price response and

elasticity varies dramatically depending on the type of trade-offs being made, the time scale over

which sales variations are being measured, the type of durable being examined, and the stage of

development of the particular durables market in question. 

The greatest price sensitivity is observed when consumers are being asked to make trade-offs

between price, brand, and features in an unconstrained market where the consumer has the choice

of different brands and makes of product. In this context, which is most relevant to marketing

decisions, the choice of from whom to buy a product is highly sensitive to the price being charged

by that particular manufacturer. Price/features trade-offs are typically applied to set prices for

different product classes according to the over-all value that consumers place on other features

relative to price2.

In the long-term sales forecast literature, elasticities are much smaller than those observed

in short term sales or product choice applications. This reflects the difference between a long-term

perspective (whether to own a CAC-HP) and a short-term one (which unit to purchase and when to

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buy). Furthermore, durables undergo a time dependent price sensitivity as they go from introduction

to acceptance in the overall market3 4 5. Research that examines the change in elasticities over time6

finds that for clothes dryers and appliances that are deemed ‘necessities’ (i.e. have a high market

penetration) that ‘elasticities are either constant, not statistically different from zero, or decline

toward the later stages of the adoption life cycle’7. These results are based on fitting models with

elasticity to historical data on shipments and sales of major appliances. 

Since the introduction of standards could potentially cause long term structural changes in

prices and features, we consider the results from the long term sales forecast literature most relevant

to the present CAC-HP shipments modeling effort. It is expected that elasticities will be smaller than

what is found when consumers are evaluating brand or features choices. 

6.2 METHOD

6.2.1 Definitions

The model is organized in terms of three classes of items: Stocks, Events, and Decisions.

These different classes are defined as follows: 

6.2.1.1 Stock

A Stock is the number of households with a particular CAC-HP of a particular category. The

main property of a stock is that it evolves over the course of the year by aging one year and by

increasing or decreasing in response to inflows and outflows produced by events and decisions. The

four permanent stocks in the model are new households, households with CAC-HPs, the households

without CAC-HPs, and households with rebuilt or extended-life CAC-HPs. In addition to the

permanent stocks, there are temporary stocks of CAC-HPs in need of repair, repaired CAC-HPs,

rebuilt CAC-HPs, and retired CAC-HPs. All of the temporary stocks are allocated to one of the four

permanent stocks within the one year computational time step of the model. 

6.2.1.2 Events

Events are things that happen to a stock that can change the status of a portion of that stock,

but do not depend on economic conditions. Events do not depend on market conditions, but are

dependent on the properties of the stock. The main event in the model is CAC-HP problem

development or breakdown. For regular CAC-HP, whether or not a unit develops problems that

require a repair is an event. For extended-life units, whether the unit suffers from a final breakdown

is another event. 

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6-7

6.2.1.3 Decisions

Decisions are consumer reactions to events and market conditions. Decisions are described

in terms of probabilities that typically depend on the type of stock, the age of the CAC-HP, the

incremental cost of the decision, and market conditions. The probability of two subsequent decisions

in the same year is equal to the product of the two individual decision probabilities. The dependence

of decision probabilities on price and market conditions is given by an econometric logit equation:

ln

Prob

Prob

Price - PWF* OS

1 -

æ

è

ç

ö

ø

÷ = + ×

æ

è

ç

ö

ø

a b ÷

Income

(6.2)

where Prob is the probability of the decision, and where the right hand side of the equation

represents the utility of the decision. The coefficients b represents the consumer sensitivity to

changes in product life-cycle cost relative to income. The constant term a is an offset for the utility

which calibrates the utility to the value of the market share in a reference year. Price is the purchase

price in the current year, while PWF is the present worth factor given the consumer market discount

rate for savings versus purchase price trade-offs. OS is the operating savings relative to a unit of the

average efficiency of units sold in1998, and Income is the household income. 

The details of model calibration and selection of parameters for the consumer decision model

are presented in Section 6.3.1.

6.2.2 Purchases from New Housing

6.2.2.1 Definition

Purchases from net new housing are defined as those purchases that arise from a net increase

in the total housing stock. 

6.2.2.2 Approach

The decision tree shown in Figure 6.2 illustrates the approach taken for modeling new

housing purchases.

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6-8

House movals HouseCompletion House House Re s Remod els Stock = + − Δ (6.4)

 New Houses

Purchase CAC/HP ?

Yes No

Buy New Join Houses

Unit without a CAC/HP

Figure 6.2 Decision Tree for New Housing

Purchases

U New Homes = EMS New Homes HouseCompletions

⋅ Prob ⋅ (6.3)

U Removals = HouseRemovals ⋅U Stock Saturation (6.5)

Data is available for the market saturation of new households with CAC-HP units up to 1997

from the Residential Energy Consumption Survey (RECS)8. This market share is projected into the

future using a logit probability of purchase equation as described in section 6.3. 

The equations for estimating the purchases from new housing are as follows:

Where,

UNew Homes = New CAC and HP purchases for new home,

ProbNew Homes = the probability of purchase of CACs and HPs for new homes,

HouseCompletions = the housing completions, and

EMS = the eligible market share for either CAC and HP (this is 90% of all new

housing).

For any given year, there are a certain number of CAC and HP systems which are removed

during the course of remodels and housing demolitions. Thus, there must be an accounting of the

number of CAC-HP units which have been removed from the equipment stock before they have

reached the end of their useful life. It is assumed that the number of CAC-HP units removed is equal

to the number of housing demolitions multiplied by the current stock saturation of CAC-HP. The

equations for estimating housing demolitions and the number of CAC-HP units removed with the

demolitions are as follows: 

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6-9

U year age U year age

U

U

moval tired

moval

age

tired

age

Re Re

Re

Re

( , ) = ( , )⋅

∑

∑

=

=

1

30

1

30 (6.6)

Where,

HouseRemovals = The net housing stock that is either demolished or has a remodel that

would remove an old CAC-HP product,

HouseRemodels = Housing stock that has a remodel that may remove an old CAC-HP

product,

ÄHouseStock = change in the housing stock,

URemovals = CAC or HP stock removed with demolished housing stock, and

UStock Saturation = CAC or HP stock saturation.

When the units are removed from the stock, we must assume a particular age distribution.

We assume the age distribution is the same as that for replacements, namely:

Where,

URemovals (year ,age) = CAC or HP stock removed with demolished housing stock of a given

age in a given year, and

URetired (year ,age) = number of CAC or HP units retired of a given age in a given year.

6.2.2.3 Current Assumptions

It is assumed that the relative size of the eligible markets for CAC and HP are in fixed

proportion (primarily due to the climate and geography). We used the relative size of CAC and HP

market shares in total sales from 1978 to 1997 to determine this ratio9. Figure 6.3 shows the market

share of heat pumps in air conditioning product sales from 1978 to 1997, and as one can see from

the figure, there is no discernable trend, and the level remains at about 23%. 

 EE-RM-STD-98-440 COMMENT 311
6-10

Hea t Pump M arke t Sha re in S a le s

0 %

5 %

10%

15%

20%

25%

30%

1978 1983 1988 1993 1998

Year

Market Share

2 3 % L e ve l H is t o ric a l M a rk e t Sha re

Figure 6.3 Market Share of Heat Pumps relative to Total Central Air Conditioner and

Heat Pump Sales

6.2.3 Existing Housing with a Regular CAC-HP

6.2.3.1 Definition

Existing housing with regular CAC-HP are those existing households that have a CAC-HP

unit, and whose unit has not had an extra repair that extends the life of the CAC-HP unit. 

6.2.3.2 Approach

The decisions involved with the replacement and repair of regular CAC-HPs in existing

housing are illustrated in Figure 6.4. The figure shows that several decisions and events affect the

replacement of an existing CAC-HP with a new or used machine.

 EE-RM-STD-98-440 COMMENT 311
6-11

Houses with CAC/HP

Are there problems? 

Yes No

Repair or Replace Unit

Replace Unit? Early?

Replace Repair Yes No

Buy New

Unit Regular or Buy New Keep Existing 

Extra Repair Unit Unit

 Extra Regular

Extend Keep Existing 

Unit Life Unit

Figure 6.4 Decision Tree for Replacement and Repair of Regular CACHP Units in Existing Housing 

For a household with an existing CAC-HP unit, the first question is whether or not the unit

has problems and needs repair. If the unit needs repair, the consumer will then decide whether to

repair the machine or replace it. If the machine is repaired, then the decision is evaluated to see if

it is an ‘extra’ repair for a machine that under normal economic conditions would have been

replaced. If it is an extra repair, then the CAC-HP is assumed to have its life extended by six years.

If the machine does not have any problems, the consumer still may replace the CAC-HP early

(before breakdown). These discretionary purchases are referred to as early replacements. According

to a 1987 heat pump survey data10, about 29% of CAC-HP units are replaced early. Table 6.1

provides the reasons from the survey for why heat pump owners replace their equipment. The

percentage of early replacements (29%) are based on all reasons excluding ‘Unit Failure’ and ‘Don’t

Know/No Answer’.

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Table 6.1 Reasons for Replacing Heat Pumps

Reason for Replacement Percentage of Respondents a

Unit Failure 55.6%

Efficiency Upgrade 8.6%

Service Problems 7.9%

Unit Aging 4.6%

Improved Comfort 4.6%

Maintenance Personnel 0.7%

Natural Disaster 0.7%

Advertising/Sales Promotion 0.0%

Other 2.0%

Don’t Know/No Answer 47.0%

a Multiple responses cause total to exceed 100%.

The decisions and events in the decision tree are modeled with probability functions. We

therefore need four relative probability functions to model this purchase decision process:

1. The probability that an existing CAC-HP has a problem.

2. The probability of replacing, or repairing a machine as a function of age.

3. The probability of an early replacement of a machine without problems.

4. The probability that a CAC-HP is not replaced.

1. The probability that an existing CAC-HP has a problem and needs repair is based on the

same 1987 heat pump survey that is used to estimate early replacements. In the survey, data is

presented on the life of the original compressor11. For purposes of this analysis, the survival function

of the original compressor is used to establish the probability that an existing CAC-HP has a problem

and needs repair. Figure 6.5 shows the survival function of the original compressor. It should be

noted that the 1987 heat pump survey established a survival function for the original compressor only

out to its median lifetime (14.5 years). Linear extrapolation was used to determine the remaining

portion of the function.

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6-13

Pr ( , )

Pr

( Pr ( , )) Re .Re

Re

ob year age

ob

ob year age pair vs tire

Needs pair

Survival

=

1−

(6.7)

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18

Age of Unit

Probability

Figure 6.5 Probability Function that an Existing CAC-HP has a

Problem

2. The probability of Repair vs. Replace (replace and retire are used interchangeably) is

subject to market variations and changes as described by a probability of purchase equation:

Where,

ProbRepair vs. Retire (year, age) = Probability of repair vs. retire,

ProbNeeds Repair = probability of needing repair (as shown in Fig. 6.5) , and

ProbSurvival (year,age) = probability of survival (as shown in Fig. 6.6).

Again, the 1987 heat pump survey12 is used to establish the probability of a CAC-HP unit

needing repair. The probability of survival is based on the survival function in the 1987 survey for

the total heat pump system. Figure 6.6 shows the heat pump survival function. It should be noted

that the 1987 heat pump survey established a survival function for the entire heat pump system only

out to its median lifetime (19 years). Linear extrapolation was used to determine the remaining

portion of the function.

 EE-RM-STD-98-440 COMMENT 311
6-14

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25

Age of Unit

Probability

Figure 6.6 Survival Probability Function for CAC-HP Units

The probability that a CAC-HP has a problem and needs repair was presented earlier (Figure

6.5). Thus, as presented in Eqn. 6.7, the probability function for determining whether to repair or

replace a CAC-HP units is based on the probability functions for needing repair (Figure 6.5) and

survival (Figure 6.6).

If proportionally more machines are being repaired than in the reference year of 1996, then

those machines repaired above and beyond the reference level have their life extended by six years.

In the model, this is done by moving the machine to the stock of extended lifetime machines, and

using a survival probability function for this stock which is shifted by six years. 

3. For the probability of early retirement, a simple linear function describes the relative

probability of a discretionary CAC-HP replacement over time. This function is assumed to be zero

at age zero and to increase linearly with CAC-HP age. The slope of this function is chosen so that

the relative proportion of discretionary replacements vs. all replacements in the model output is

consistent with the 1987 heat pump survey data discussed previously (i.e., 29% is 1987). CAC-HP

purchases that result from a change of residence are not considered to be ‘replacements’.

Figure 6.7 shows the probabilities for the different decisions and events as a function of

CAC-HP age for the model calibration year of 1987. For most of the age of the unit, the most likely

disposition of an existing CAC-HP is for it to be kept. There is a significant probability of repairs

for much of the machine’s life. Meanwhile, as the CAC-HP becomes old the likelihood of

replacement becomes dominant. Throughout the units’ life, there is some probability of an early

replacement. Though in any given year the probability of an early replacement may be small, the

cumulative effect of this small probability is approximately 29% of total CAC-HP sales.

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Relative Probability of Decisions/Events

0.0

0.2

0.4

0.6

0.8

1.0

1 4 7 10 13 16 19 22 25

Age of Unit

Probability 

Replace

Repair

Early Replacement

No Action

Figure 6.7 Relative Probability of Regular Replacement, Repair, Early

Replacement and No Action as a Function of CAC-HP Age

for 1987

Pr ( , ) Pr ( , )

Pr ( , )

Re Re .Re

Re .Re

ob year age ob year age

ob age

Xtra pairs tirevs pair

tirevs pair

=

− 1996 (6.11)

The equations describing the details of the disposition of the existing units are as follows:

U Needs Repair ( year, age) = ProbNeeds Repair ( year, age) ⋅ U Stock ( year, age) (6.8)

U Retired ( year, age) = ProbRetire vs. Repair ( year, age) ⋅ U Needs Repair ( year, age) (6.9)

U year age ob year age U year age U year age Early Early stock Needs pair ( , ) = Pr ( , )⋅[ ( , ) − Re ( , )] (6.10)

U year age ob year age U year age

if ob elseU

Extra pairs Xtra pairs Needs pair

Xtra pairs Xtra pairs

Re Re Re

Re Re

( , ) Pr ( , ) ( , )

( Pr )

= ⋅

> 0 = 0

(6.12)

Where,

UNeeds Repair (year, age) = The number of regular units of a given age that need repairs

in a given year,

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6-16

ProbNeeds Repair (age) = the probability that a regular CAC-HP unit of a given age

needs repair (this function is independent of year),

UStock (year, age) = the number of regular units of a particular age in a given

year, 

URetired (year, age) = the number of regular units retired,

Prob Retire vs Repair (year, age) = the relative probability that a regular CAC-HP which needs

repair will be retired,

UEarly (year, age) = the number of CAC-HP units that are replaced early,

ProbEarly (year, age) = the probability that a CAC-HP will be replaced early, 

ProbXtra Repairs (year, age) = the probability that a CAC-HP that needs repair received

extra repairs that extended its lifetime, and

UXtra Repairs (year, age) = the number of regular CAC-HPs that received lifetimeextending repairs. 

6.2.3.3 Current Assumptions

There are several important assumptions made in modeling the replacement and repair of

existing units. These include:

• The needs-repair (or problems) probability function is independent in time. We also

assumed that when compressor breaks down is when a unit needs repair. To

reiterate, this probability function is based on the survival function of the original

compressor as established by the 1987 heat pump survey.

• When a machine breaks down, it is either repaired or replaced.

• All early replacements result in the purchase of a new machine.

• If a greater proportion of machines with problems obtain repairs in the future than

they did in 1996, then the additional population of repaired machines have an

extended lifetime which is six years greater than the regular CAC-HP lifetime. 

• For machines that do not experience problems, the relative probability of an early

replacement is zero for a new machine and increases linearly with CAC-HP age.

6.2.4 Remodeled Households

6.2.4.1 Definition

Remodeled households are those households that purchase a new CAC-HP system due to

remodeling work. 

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U year ob year House year Remodel NewHousin g Remodel ( ) = Pr ( )⋅ ( ) (6.13)

House year A House year Remodel Remodel Completions( ) = ⋅ ( ) (6.14)

 Remodeled Houses

Purchase CAC-HP? 

Yes

No

Buy New Remain without 

CAC-HP CAC-HP

Figure 6.8 Decision Tree for Remodeled

Housing

6.2.4.2 Approach

The approach taken to model purchase decisions by households undergoing remodels that

may effect CAC-HP purchases is shown in Figure 6.8. The household has only one decision:

whether or not it is going to purchase a unit.

For this, we just assume an annual probability of purchase which varies according to the economic

probability of purchase model. We utilize the same purchase probability function used in the new

housing market. 

The relatively simple dynamics of the decision by a remodeling household deciding to buy

a unit is described by one equation:

Where,

U Remodel (year) = The number of remodeling households that purchase CAC-HP units

in a given year,

Prob New Housing (year) = the probability that a household will purchase a CAC-HP in a given

year if it is in the new housing or remodel market, and

House Remodel (year) = the number of remodeling households in a given year. 

And the number of remodel households is assumed to be proportional to new housing completions

and is therefore described by the following equation: 

 EE-RM-STD-98-440 COMMENT 311
6-18

Where,

ARemodel = The coefficient that determines the size of the remodel market relative to housing

completions. 

6.2.4.3 Current Assumptions

The probability that a remodeling household will purchase a CAC-HP in a given year is

assumed to be proportional to the number of housing completions (which measure construction

activity), and saturation of CAC-HP in new housing. The over-all size of the market is described

by a calibration constant which is set based on data from the Air Conditioning, Heating, and

Refrigeration (ACHR) News. For both the CAC and HP markets, the ACHR News estimates that

14% of shipments in 1992 went to the “add-on” market (we assume here that the remodeling market

corresponds to the “add-on” market described by the ACHR News)13. The 14% value was used as

calibration point to estimate the size of the remodel market.

6.2.5 Housing with an Extended-Life CAC-HP

6.2.5.1 Definition

These households have CAC-HP units that have received more repairs than what was normal

in the reference year of 1996. It is therefore assumed that the lifetime of these CAC-HPs has been

extended by these extra repairs. 

6.2.5.2 Approach

The input of this particular stock of CAC-HPs comes from regular CAC-HP households that

have made extra repairs on their equipment. Once an extra repair has been made, it is assumed that

no more repairs will be made after the next machine breakdown. 

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Houses with Extended Life Units

Are there problems? 

Yes,

 Replace

 Unit No

 Buy New Keep Existing 

 Unit Unit

Figure 6.9 Decision Tree for Housing with

Extended Life Units

0.0

0.2

0.4

0.6

0.8

1.0

5 10 15 20 25 30

Age of Unit

Survival Probability 

Figure 6.10 Survival probability function for extended life units

Figure 6.9 illustrates the decision tree for the stock of extended-life CAC-HP units. Note that

these CAC-HP units are already quite old because they are regular CAC-HPs that have received extra

repairs near breakdown. The main event in this decision tree is whether or not the machine has

problems. This probability function is just a shifted version by six years of the survival probability

function for regular CAC-HPs and is illustrated in Figure 6.10. 

 EE-RM-STD-98-440 COMMENT 311
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UXR year age UXR year age UXR year age

U year age

Stock Stock tired

Xtra pairs

( , ) ( , ) ( , )

( , )

Re

Re

= − − − − −

+ − −

1 1 1 1

1 1

(6.16)

UXRRetired ( year, age) = ProbXR Retire (age) ⋅ UXRStock ( year, age) (6.15)

In terms of equations, the dynamics of the extended-life CAC-HPs can be described as

follows: First the retirement of the CAC-HPs is calculated simply with the retirement (replacement)

probability function (shown in Figure 6.10). 

Where,

UXR Retired (year, age) = The number of extended-life CAC-HP units of a particular age

retired in a given year,

Prob XR Retire(age) = the probability that an extended-life CAC-HP of a given age will

be replaced or retired (based on the extended survival function in

Figure 6.10), and

UXR Stock(year, age) = the number of extended-life CAC-HP units of a given age in a

given year.

Then the stock accounting is done such that the change in stock is the number of regular

CAC-HPs that get extra repairs minus the stock that is returned: 

Where,

U Xtra Repairs (year, age) = the number of regular CAC-HP units of a particular age that

received extra repairs in a given year. 

6.2.5.3 Current Assumptions

There are several assumption of the extended-life CAC-HP modeling. These include: 1)

Extended life CAC-HPs are never repaired again; 2) The extended-life CAC-HPs have a lifetime that

is six years greater than that of the regular units; and 3) The retirement probability function is

independent of time.

6.2.6 Accounting Equations

For conducting the shipment forecasts, we specify a series of equations that define the

dynamics and accounting of the different types of CAC-HP stocks. For new housing the equation

describing the stock of new housing is trivial. The stock of new housing is the number of housing

starts.

Meanwhile the most complicated accounting equation is that which describes the accounting

of the existing stock of regular CAC-HP units.

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Ustock ( year, age = 1) = U New ( year − 1) (6.17)

U year age U year age U year age

U year age U year age

U year age

Stock Stock tired

Early Xtra pairs

movals

( , ) ( , ) ( , )

( , ) ( , )

( , )

Re

Re

Re

= − − − − −

− − − − − −

− − −

1 1 1 1

1 1 1 1

1 1

(6.18)

UXRStock UXRStock UXR

U

year age year age year age

year age

( , ) ( , ) ( , )

( , )

= − − − − −

+ − −

1 1 1 1

1 1

Retired

Xtra Repairs

(6.19)

For the stock of regular CAC-HP units we have two equations which describe the accounting

of the population. The first equation says that the number of one-year old units is simply equal to

the number of new CAC-HP units purchased the previous year:

Meanwhile the next equation describes the accounting for CAC-HPs of the different, older age

categories:

Where,

year = The year that the stock is being estimated,

U Stock (year, age) = the population of regular CAC-HP in existing housing of a

particular age, 

U New (year) = the number of CAC-HP purchases in a particular year,

U Retired (year, age) = the number of regular CAC-HP units from a particular age

category that were replaced in a given year because of problems

that had occurred,

U Early (year, age) = the number of regular CAC-HP units that are replaced early from

a particular age category in a given year for discretionary reasons,

UEarly (year) = the total number of early replacements (of all age categories) of

regular CAC-HP units in a given year,

U Xtra Repairs (year,age) = the number of regular CAC-HPs that have received lifetimeextending repairs (these machines get transferred to the extended

lifetime stock), and

U Removals (year,age) = the number of CAC-HPs of a particular age that have been

removed with the demolished housing stock in a given year.

Eqn. 6.18 indicates that the number of CAC-HP in a particular age category is equal to the

number of CAC-HPs in the younger age category of the previous year minus the number of CAC-HP

retired or replaced early. 

Then for the stock accounting for the extended life machines (those that have received extra

repairs), we have the following:

Where,

UXR Stock (year, age) = The number of CAC-HP units in a given year of a given age

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U year U year age UXR year age

U year age U year U year

New tired tired

Early el New New Home

( ) ( , ) ( , )

( , ) ( ) ( )

Re Re

Remod

= +

+ + + −

(6.20)

group that belong to the stock of machines that have received

extra repairs, These extra repairs have extended the life of the

machine,

UXR Retired (year, age) = the number of machines of a particular age that are retired from

the extra repair stock in a given year, and

U Xtra Repairs (year, age) = the number of regular CAC-HP units of a particular age in a given

year that receive repairs that extend the machine life in a given

year.

Eqn. 6.19 says that the stock of extended life CAC-HPs comes from regular CAC-HP units

which receive extra repairs when they break down. This stock then ages, and is removed as it is

retired due to additional repair problems. 

Eqn. 6.20 says that number of non-owner households is the number of households minus the

number of regular CAC-HP owners minus the number of extended life CAC-HP owners. 

The CAC-HP purchase are related to changes in the different CAC-HP stocks as follows:

Where,

U New (year) = The number of new CAC-HP purchases in a given year,

U Remodel (year) = the number of CAC-HP units purchased by households undergoing

remodeling

In the rest of this report we will describe in more detail how this accounting approach is

implemented to forecast CAC-HP shipments.

6.3 MODEL

In order to estimate the impact of standards-induced price and features changes it is necessary

to have a model which describes consumer decisions. 

6.3.1 Logit Probability of Purchase Model

6.3.1.1 Logit Equation

The mathematical building block for the modeling of consumer decision probabilities is the

logit probability of purchase model. In this model, the probability of purchase depends on the utility

of the CAC-HP, Util, which depends on the attributes of the appliance. This purchase probability

is constrained to be between 0 and 1, and relative changes in the probability of purchase are

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¶

¶

Prob

Prob = Util ⋅ (1− Prob)

(6.21)

Prob =

+

Util

Util

e

1 e

(6.25)

¶Util = b × ¶

æ

è

ç

ö

ø

÷

Price - PWF* OS

Income

(6.22)

ln

Prob

Prob

Price - PWF*OS

1-

æ

è

ç

ö

ø

÷ = + ×

æ

è

ç

ö

ø

a b ÷

Income

(6.23)

Util = a + b×

æ

è

ç

ç

ö

ø

÷

÷

Price - PWF* OS

Income

(6.26)

proportional to changes in the utility of the appliance. These theoretical requirements for the

decision probability function can be satisfied by requiring that the probability of purchase function

satisfies the following equation:

where Prob = decision probability, and MUtil is the differential change in utility which is a linear

function of the CAC-HP attribute variables. The factor of (1-Prob) on the right hand side of the

equation enforces the condition that the probability of purchase never exceeds 1. 

We can solve the above equation for the probability function assuming a particular functional

form of the utility in terms of the attribute variables:

where the differential change in utility is equal to a linear function of differential changes in price,

operating savings and features changes. Substituting Eqn. 6.22 in Eqn. 6.21 and then integrating we

obtain:

or

Prob

Price-PWF*OS) Income

=

+

- + ×

æ

è

ç

ö

ø

÷

é

ë

ê

ù

û

ú

1

1

a b

e

(

(6.24)

where a is a constant of integration determined by the values of the probability at initial market

conditions. This can also be written as:

Where,

Thus, the above equations define the logit probability of purchase model. 

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6.3.2 Determination of Market Shares

In the shipments model for CAC-HP, there are important interactions and constraints

imposed by the interaction between different sub-markets. For this reason the CAC-HP shipments

model first solves for the sales of all central air conditioning products, and then divides the markets,

sales, and stocks between different product types.

Usually, houses get only one central air conditioning system which is either a central air

conditioner with gas heating, or a heat pump which provides both cooling and heating services. In

addition, central air conditioning systems and heat pump systems come as either split systems or as

packaged systems. If all four product types are modeled independently, then it is possible for the

total saturations of the systems to exceed one, and an important over-all constraint to sales and stocks

may not be satisfied. We therefore first solve for sales of all air conditioning systems, and then

divide households and sales between CAC and HP. Then for each of CAC and HP we divide

households and sales into split vs. package systems. We also allocate different proportions of sales

and stocks to different regions of the country and to commercial buildings so that we can calculate

the proper weighted averages of heating and cooling energy use.

6.3.2.1 Eligible Market Share for AC

Some parts of the U.S. do not require any air conditioning, and how cheap they may become

central air conditioning systems will not reach 100% saturation. This implies that the eligible market

for central air conditioning systems is less than 100%. To estimate the size of the eligible market

we do two fits to historical data. One fit is for housing stock saturations over time, while the other

is for new housing over time. The eligible market in the housing stock is less than that for new

housing because old house designs in some parts of the country may not allow for upgrades to central

air conditioning systems. We estimate the size of these eligible markets by fitting a logit market

saturation model (with price/income as the primary economic driver for consumer decisions) to the

historical saturations. When we do this fit, we find that the best fit value for the housing stock

eligible market is approximately 80% while that for new single family housing is approximately

90%. Figure 6.11 shows the logit market saturation model fits to central air conditioning system

saturation with 80% and 90% maximum eligible markets for housing stock and new single family

housing respectively.

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Stock and New Housing AC Saturations

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

1970 1975 1980 1985 1990 1995 2000

Year

Saturation

Historical Stock Historical New SF Homes

New SF Home Fit Housing Stock Fit

Figure 6.11 Central AC System Saturations in New Single Family Housing

and Housing Stock: Comparison of Data and Logit Function Fits

6.3.2.2 Market Share for CAC versus HP

Once the over-all market share for central air conditioning systems is properly modeled, the

next task is to divide sales and saturations between simple central air conditioning systems and heat

pump systems. During the early stages of introduction of the technology, there was a fairly complex

market dynamics between central AC and heat pumps. This is because central AC is a simpler

technology that entered the market first and it took some time for heat pumps to attain consumer

acceptance and mature as a technology. But referring back to Figure 6.3, after 1978, the relative

market share of heat pumps in all central air conditioning systems settled into a reasonably constant

value centered around 23%. We therefore use a fixed 23% market share for the size of the heat

pump market relative to all central AC products.

6.3.2.3 Market Share of Split vs. Package systems

The detailed dynamics between packaged and split systems sales is largely beyond the scope

of the shipments forecast study. We therefore for the sake of modeling simplicity, assumed fixed

relative market shares of split vs. package systems for both CAC and HP. The criteria that we used

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for selecting the relative market shares of split vs. packaged CAC and HP products is that the

selected market shares should produce roughly correct shipments values in the late 1990's for

packaged system sales. The relative market share values that satisfy this criteria is 88% split versus

packaged heat pumps and 90% split versus. packaged CAC. The difference between the optimal

values for the model and the relative market shares in currently observed sales comes from the fact

that relative market shares of packaged systems are declining over time, and some packaged systems

are being replaced with split systems. The mathematical structure of the model assumes that

packaged systems are replaced with packaged systems. For the model to capture the declining

market share of packaged systems it therefore must use a low value of the packaged system market

share for the forecast to compensate for the fact that some of the replacement market is being

satisfied by split systems rather than packaged systems. 

6.3.2.4 Regional Market Shares

In order to calculate energy use amounts and operating expenses, it is necessary to have an

estimate of the regional distribution of the different air conditioning products. We calculate the

fraction of products in each of the nine Census divisions utilizing household saturation data from the

RECS 1997 survey14. We also obtain from RECS the approximate average annual operation of such

products (in units of hours at peak load) from the regional average energy use, the regional average

efficiency and the mean capacity of such systems.

6.3.3 Price

The CAC-HP shipments model initially calculates shipments and stocks for all central air

conditioning products and then divides these into the different product sub-markets according to

fixed market shares that assume very low inter-product elasticities. In calculating the price, and

operating cost over time, a weighted average of different products is taken to estimate the effective

unit price for the CAC-HP market and these unit prices must be projected forward and backward in

time with the appropriate price indices. This section describes some of the details of how these price

averages and projections are made. 

6.3.3.1 Average Price Accounting

For modeling total CAC-HP shipments a weighted average price is used that is the average

price for all CAC-HP products over all efficiency levels. The price vs. efficiency model is provided

by the Engineering analysis, where those efficiencies less than 10 SEER are assumed to be the same

price as 10 SEER. To project prices from 1998 to 1969 the Unitary AC producer price index is used,

while the all items consumer price index is used to measure inflation and convert prices to real 1998

dollars. Prices are also averaged for the appropriate efficiency level distribution.

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6.3.3.2 Historical Operating Cost Estimates

Because the shipments model is integrated with the National Energy Savings calculation, a

detailed calculation of the operating costs and energy use is made. This calculation includes keeping

an accounting of energy use that is disaggregated by the nine Census Divisions, and the distribution

of efficiency levels for each year of interest. As the spreadsheet model was reaching the

computational limits of Microsoft Excel spreadsheets, we did not simultaneously calculate the

energy use for all four product classes and take the weighted-average. The operating cost

calculations are therefore for the particular product of interest relative to a reference year of 1998.

6.3.3.3 Post-Standard Price Scenarios

To calculate the average price of the CAC-HP units after the standard (and the average energy

use), assumptions must be made about the distribution of different efficiency level market shares

after a performance standard is implemented. There are three assumptions or efficiency scenarios

regarding post-standard efficiencies.

The first efficiency scenario is what we call the NAECA scenario which is a modification

of the roll-up scenario. In the NAECA scenario, the market shares are those of the roll-up scenario

except that 6% market share that would be at the standard SEER level is distributed equally amongst

the next three higher SEER levels. 

The second efficiency scenario is what we call the “roll-up” scenario. This is where all of

the market shares for SEER levels above the standard stay the same both pre- and post-standard, but

the market share at the standard level is the sum of the current market shares for all of those

efficiencies less than or equal to the standard SEER level.

The third efficiency scenario is what we call the “shift” scenario where the relative

distribution of efficiencies stays the same, but the market shares for the different efficiencies simply

shift with the standard. For example if the standard is a SEER 12 standard, this is two SEER levels

higher than the current 10 SEER standard and the market shares for the different SEER levels shift

up two SEER levels. For example the market share for the 12 SEER level would be what the current

market share for the 10 SEER level is, and the market share for the 13 SEER level post-standard

would be the market share for the current 11 SEER level., etc. 

These three efficiency scenarios allow us to examine the sensitivity of the results regarding

the details of the post-standard efficiency distribution. The shift scenario represents the high price

and high efficiency post-standard efficiency distribution, the roll-up represents the lower price and

lower efficiency scenario, and the NAECA scenario represents a medium case. These efficiency

scenarios are discussed in greater detail in Chapter 7.

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6.3.4 Model Calibration

There are several parameters that require calibration in the CAC-HP shipments model. These

include the amplitude of the early replacement function, the size of the remodel market, the relative

importance of savings and price in the consumer decision model, and the over-all sensitivity of

purchases to price/income. In addition we examine the question of whether or not there is a

measurable fuel switching elasticity and whether regional housing shift effects are significant. 

6.3.4.1 Remodels and Early Replacements

In the shipments model we model purchases due to remodels as a market that is correlated

to the new housing market, and we describe the size of this market with a single coefficient that

determines the size of the eligible remodel market relative to new housing completions. From the

Air Conditioning, Heating, and Refrigeration News, we have a relatively recent estimate of the

remodel market as 14% of all sales15. We therefore set the coefficient of the remodel market size

by the condition that the amount of remodel market sales between 1990 and 1996 average

approximately 14%. After we make this adjustment and tune other parameters in the model, the

exact value may drift slightly but it remains between 13% and 15%.

For the early replacement market, an ASHRAE paper reports that approximately 29% of total

sales are early replacements in 198716. We therefore set the amplitude of the early replacement

probability function to replicate this figure in the model results. 

6.3.4.2 Market Discount Rate

The market discount rate is a quantitative description of how consumers trade off purchase

price and operating savings in their purchase decisions. We do not have concrete, precise data on

the market discount rate for consumer decisions for air conditioning products. The one piece of

information that we have is that more than 75% of consumers in today’s market purchase units at

minimum efficiency, and that this implies that the implicit consumer discount rate for consumer

decisions is fairly large. We assume a discount rate for consumer decisions half way between a one

and two year payback which corresponds to 75%. The shipments forecast is relatively insensitive

to the precise value of this discount rate. Changing it from 75% to 25% changes the sales forecast

for a 12 SEER standard less than 1%.

6.3.4.3 Price/Income Elasticity

After the implicit discount rate for consumer decisions is set, the effective price of the

appliance is calculated as Price - PWF * OS, where Price is the purchase price, PWF is the present

worth factor corresponding to the discount rate, and OS is the annual operating savings relative to

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a baseline operating cost obtained from the 1997 shipment-weighted efficiency. We then scale this

by dividing by average household income and use the effective price divided by income as the

primary driver for economic decisions. As described above, there is a coefficient that determines the

sensitivity of consumer decisions with respect to this parameter. We assume that the coefficient in

the logit decision model is the same in all markets (new housing, remodels, replacements, and early

replacements), and we calibrate this last coefficient by minimizing the root mean square (RMS)

deviation between the shipments model estimates and the historical shipments data for all central

conditioning products between 1970 and 1996. 

6.3.4.4 Evaluation of Fuel Switching Elasticity

Measurement of a fuel switching elasticity requires some data which shows a correlation

between price differences and changes in market share. But as Figure 6.3 shows, the relative market

share of heat pump in central air conditioning sales has stayed relatively constant over the past 20

years. In addition we have little data on the relative prices of heat pumps versus a combination

central air conditioner/gas furnace system. There has been some changes in the relative price of gas

and electricity as fuels, with the peak of gas prices relative to electricity being in 1983. But there

is no corresponding peak in heat pump market share at this time. We therefore conclude that there

is no measurable fuel switching elasticity, and we set the fuel switching elasticity to zero in the

model. 

6.3.4.5 Regional Shift Effects

In this section we provide a brief sensitivity analysis of the size of regional housing shift

effects on the shipments results. To estimate the size of possible regional shifts we can compare the

the relative market share of housing stock in the four Census divisions between 1980 and 1990. We

find that the market share of households in the Northeast decreased from 21.7% to 20.5%, that

Midwest household market share decreased from 25.9% to 24.2%, that Southern household market

share increased from 32.9% to 34.6%, and Western household market share increased from 19.3%

to 20.6%17. From these statistics it seems that there is a slow long term shift from the Northeast and

Midwest to the South and West. To the extent the shifts are to the Pacific division of the Western

region, such housing shifts do not increase energy use, but to the extent the shifts are to the South,

this may imply a greater number of average cooling hours for systems sold in the future. To calculate

the size of the potential impact, we take 2% of the Northeast market share of central air conditioners

for the Mid Atlantic Census division and shift this market share to the West South Central Census

division and calculate how much of an impact this has on energy savings from a 12 SEER standard

for Split Air Conditioners. Without this market share shift, the energy saved from a standard is 2.31

quadrillion Btu, while with the regional shift the savings is 2.35 quadrillion BTU, less than a 2%

change in energy savings. This probably over-estimates the change in energy savings since our

calculation is for a fixed housing market shift that occurs before the standard comes into effect,

rather than a more gradual shift over time. In addition, the West South Central Census division has

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the highest air conditioner energy use, while the housing shift would be distributed across the three

divisions that comprise the Southern Census region. 

We therefore conclude that the small impact on energy savings estimates does not justify the

computational complication that would be necessary to include a more precise calculation of the

gradual housing shifts that may occur over the post-standard evaluation period between 2006 and

2030. 

6.4 RESULTS

6.4.1 Trial Standard Levels

Shipments results are generated based on Trial Standard Levels (TSL). The TSLs are based

on the following: 1) efficiency levels identified in the supplemental Advance Notice of Proposed

Rulemaking (ANOPR) published in November, 1999, 2) the efficiency level identified as the

Maximum Technologically Feasible level, and 3) a combination of efficiency levels for different

product classes that has potentially positive impacts on consumers and the Nation.

Based on the preliminary analyses performed in the supplemental ANOPR, it was observed

that uniform efficiency levels for all product classes ranging from 11 to 13 SEER appeared to result

in the greatest economic benefits to both consumers and the Nation. Consequently, it was announced

in the supplemental ANOPR to further consider and conduct analyses for 11 SEER,12 SEER, and

13 SEER, for each product class.

In selecting candidate standard levels, the Process Rule requires the consideration of

equipment which has the most energy efficient combination of design options. The highest efficiency

level that is “technologically feasible” is known as “Max Tech.” The Maximum Technologically

Feasible level for each product class is assumed to be 18 SEER. As has been noted in Chapters 4 and

5 of this TSD, in conducting the economic analyses for this “Max Tech” standard level, the greatest

production cost multiplier data for each product class and efficiency level available was 15 SEER.

Extrapolation of 15 SEER data to 18 SEER was believed to be unjustified. Consequently, the

economic analyses for the 18 SEER case are all based on the 15 SEER cost multipliers, therefore,

the economic results represent, at best, a lower bound to the actual values.

In addition to considering equipment which has the most energy efficient combination of

design options, other criteria for selecting candidate standard levels include: the combination of

design options with the lowest life-cycle costs; and standard levels that incorporate noteworthy

technologies or fill in large gaps between efficiency levels of other candidate standards levels. In

this case the LCC results for different product classes show positive savings for consumers (although

not necessarily the minimum savings) and fill in the gap between uniform efficiency levels for the

candidate standard levels. 

 

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Based on these criteria, shipments results are presented for the following five TSLs:

• TSL 1: 11 SEER for all product classes,

• TSL 2: 12 SEER for all product classes,

• TSL 3: 12 SEER for air conditioners and 13 SEER for heat pumps,

• TSL 4: 13 SEER for all product classes, and

• TSL 5: 18 SEER for all product classes.

6.4.2 Shipment Results

The model provides a rather detailed picture of possible standards impacts on purchases,

replacement, and repair of CAC-HP. Figures 6.12 through 6.14 show the shipments results for the

five TSLs based on ARI cost data, a survival function yielding an 18 year average equipment life,

and electricity price forecasts from the Annual Energy Outlook (AEO) 2000 Reference Case. Three

sets of results are provided based on the NAECA (Figure 6.12), Roll-up (Figure 6.13), and Shift

(Figure 6.14) efficiency scenarios. Historical data points are also provided in each of the Figures to

show how closely the shipments models agree with historical data. 

Under all efficiency scenarios shipments drop in the first year that standards become effective

as some consumers forego the purchase of more efficient air conditioners and heat pumps due to

their higher purchase price. With progressively higher TSLs, product efficiency and product

purchase price increase, resulting in a greater number of consumers foregoing the purchase of more

efficient equipment. Forecasted shipments differences are slight between the three efficiency

scenarios. Because the Roll-up efficiency scenario assumes the lowest number of high efficiency

units beyond the minimum standard level, forecasted shipments are greatest under this efficiency

scenario as a smaller number of consumers are foregoing the purchase of new equipment. The Shift

efficiency scenario assumes the largest number of high efficiency units beyond the minimum

standard level and, as a result, this efficiency scenario forecasts the fewest shipments. Shipments

forecasted under the NAECA efficiency scenario fall in between those forecasted under the Roll-up

and Shift efficiency scenarios.

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0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1950 1960 1970 1980 1990 2000 2010 2020 2030

Year

Shipments (millions)

Historical

Base case

TSL 1

TSL 2

TSL 3

TSL 4

TSL 5

Figure 6.13 Combined Central Air Conditioner and Heat Pump Shipment Forecasts

based on Roll-up Efficiency Scenario and AEO2000 Reference Case

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1950 1960 1970 1980 1990 2000 2010 2020 2030

Year

Shipments (millions)

Historical

Base case

TSL 1

TSL 2

TSL 3

TSL 4

TSL 5

Figure 6.12 Combined Central Air Conditioner and Heat Pump Shipment Forecasts

based on NAECA Efficiency Scenario and AEO2000 Reference Case

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0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

1950 1960 1970 1980 1990 2000 2010 2020 2030

Year

Shipments (millions)

Historical

Base case

TSL 1

TSL 2

TSL 3

TSL 4

TSL 5

Figure 6.14 Combined Central Air Conditioner and Heat Pump Shipment Forecasts

based on Shift Effciency Scenario and AEO 2000 Reference Case

6.4.2.1 Sensitivity to AEO2000 Forecasts

Sensitivities were conducted on the impact of different AEO2000 forecasts on the shipment

forecasts. Figure 6.15 shows how the base case shipments forecast under the NAECA efficiency

scenario is impacted by the AEO2000 Low Growth Case and AEO2000 High Growth Case.

Shipments forecasts based on the Low Growth Case result in lower shipments relative to the

Reference Case while the High Growth Case results in greater shipments. The impact of the Low

Growth and High Growth Cases on the base case shipments forecasts under the Roll-up and Shift

efficiency scenarios are relatively the same as that under the NAECA efficiency scenario. In turn,

the impact of the different AEO forecasts on the five TSL forecasts are also similar to the impact on

the base case forecast under the NAECA efficiency scenario. Also of note in Figure 6.15, the slight

dip in forecasted shipments after 1999 is due to a corresponding dip in new housing completions as

forecasted by AEO2000.

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0

1

2

3

4

5

6

7

8

1995 2000 2005 2010 2015 2020 2025 2030

Year

Shipments (millions)

AEO High Growth

AEO Reference

AEO Low Growth

Figure 6.15 Sensitivity of Base Case Shipments, NAECA Efficiency Scenario to AEO2000

Forecasts

6.4.3 Shipment Scenarios

As discussed in Chapter 5 on the Life-Cycle Cost and Payback Period Analysis, two

scenarios were investigated where lower estimates of the manufacturer costs and system lifetime

were analyzed. These scenarios are investigated to determine their impact on the shipment forecasts.

All shipment scenarios are conducted only with the NEACA efficiency scenario and AEO2000

Reference Case.

6.4.3.1 Manufacturer Cost Scenario

The manufacturer cost scenario involves replacing the cost estimates submitted by ARI with

those from the reverse engineering analysis. Table 6.2 shows the percentage change in the annual

shipment forecasts from substituting the ARI-based manufacturer costs with those from the reverse

engineering analysis. For all TSLs, there are a greater number of shipments forecasted under the

reverse engineering manufacturer cost scenario. Because the reverse engineering manufacturer cost

estimates are lower than those from ARI, there is less of an increase in central air conditioner and

heat pump purchase prices. Thus, fewer consumers forego an equipment purchase.

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Table 6.2 Shipments Impact from Reverse Engineering Manufacturer Cost Scenario

Percentage Change from Shipments Forecasts based on ARI Manufacturer Costs

Year Base Case TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

2000 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2001 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2002 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2003 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2004 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2005 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2006 0.0% 0.3% 0.9% 1.2% 2.8% 6.8%

2007 0.0% 0.3% 0.8% 1.1% 2.4% 6.6%

2008 0.0% 0.3% 0.8% 1.0% 2.1% 6.3%

2009 0.0% 0.3% 0.8% 1.0% 1.8% 6.1%

2010 0.0% 0.3% 0.7% 0.9% 1.5% 5.7%

2011 0.0% 0.3% 0.7% 0.9% 1.5% 5.6%

2012 0.0% 0.3% 0.7% 0.9% 1.4% 5.3%

2013 0.0% 0.2% 0.6% 0.8% 1.3% 5.0%

2014 0.0% 0.2% 0.6% 0.8% 1.3% 4.8%

2015 0.0% 0.2% 0.6% 0.8% 1.3% 4.6%

2016 0.0% 0.2% 0.6% 0.7% 1.2% 4.3%

2017 0.0% 0.2% 0.6% 0.7% 1.2% 3.8%

2018 0.0% 0.2% 0.5% 0.7% 1.2% 3.0%

2019 0.0% 0.2% 0.5% 0.7% 1.2% 2.5%

2020 0.0% 0.2% 0.5% 0.7% 1.2% 2.0%

2021 0.0% 0.2% 0.5% 0.7% 1.2% 1.7%

2022 0.0% 0.2% 0.5% 0.7% 1.2% 1.5%

2023 0.0% 0.2% 0.5% 0.7% 1.2% 1.5%

2024 0.0% 0.2% 0.5% 0.7% 1.2% 1.7%

2025 0.0% 0.2% 0.5% 0.7% 1.2% 1.8%

2026 0.0% 0.2% 0.5% 0.7% 1.2% 2.0%

2027 0.0% 0.2% 0.5% 0.7% 1.2% 2.2%

2028 0.0% 0.2% 0.5% 0.7% 1.2% 2.3%

2029 0.0% 0.2% 0.5% 0.7% 1.3% 2.6%

2030 0.0% 0.2% 0.6% 0.7% 1.3% 2.9%

6.4.3.2 Lifetime Scenario

The lifetime scenario is based on a retirement function yielding an average lifetime of 14

years in which no compressor replacement occurs. The shorter lifetime is based on the assumption

that most, if not all, consumers when faced with replacing a failed compressor would choose to

replace the entire system rather than replace the compressor in a relatively old system. Table 6.3

shows the percentage change in the annual shipment forecasts based on the use of a 14-year average

lifetime retirement function. For all TSLs as well as the base case, there are greater number of

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shipments forecasted. Because units are being retired earlier (14 years on average versus 18 years),

more shipments are forecasted. 

Table 6.3 Shipments Impact from 14-year Average Lifetime Scenario

Percentage Change from Shipments Forecasts based on ARI Manufacturer Costs

Year Base Case TSL 1 TSL 2 TSL 3 TSL 4 TSL 5

2000 3.8% 3.8% 3.8% 3.8% 3.8% 3.8%

2001 5.8% 5.8% 5.8% 5.8% 5.8% 5.8%

2002 6.5% 6.5% 6.5% 6.5% 6.5% 6.5%

2003 7.5% 7.5% 7.5% 7.5% 7.5% 7.5%

2004 7.8% 7.8% 7.8% 7.8% 7.8% 7.8%

2005 7.8% 7.8% 7.8% 7.8% 7.8% 7.8%

2006 7.7% 8.0% 8.3% 8.5% 9.8% 17.0%

2007 7.3% 7.6% 7.9% 8.1% 9.1% 16.2%

2008 7.1% 7.5% 7.8% 8.0% 8.8% 15.6%

2009 7.5% 7.9% 8.3% 8.4% 9.0% 15.6%

2010 8.1% 8.4% 8.8% 8.9% 9.4% 15.3%

2011 9.0% 9.4% 9.8% 9.9% 10.3% 16.0%

2012 9.6% 9.9% 10.3% 10.4% 10.8% 15.8%

2013 9.7% 10.0% 10.3% 10.4% 10.8% 15.0%

2014 9.5% 9.8% 10.1% 10.2% 10.5% 13.9%

2015 9.4% 9.7% 9.9% 10.0% 10.3% 13.0%

2016 9.4% 9.6% 9.8% 9.9% 10.1% 12.0%

2017 9.1% 9.3% 9.5% 9.6% 9.8% 11.0%

2018 8.5% 8.7% 8.9% 8.9% 9.1% 9.5%

2019 8.2% 8.3% 8.5% 8.5% 8.7% 8.5%

2020 8.1% 8.2% 8.3% 8.3% 8.5% 7.8%

2021 8.0% 8.1% 8.2% 8.2% 8.3% 7.2%

2022 7.9% 8.0% 8.0% 8.1% 8.1% 6.7%

2023 8.0% 8.1% 8.1% 8.1% 8.1% 6.7%

2024 8.1% 8.2% 8.2% 8.2% 8.1% 6.7%

2025 8.2% 8.2% 8.1% 8.1% 8.1% 6.7%

2026 8.1% 8.1% 8.1% 8.1% 8.1% 7.1%

2027 8.0% 8.0% 8.0% 8.0% 8.0% 7.3%

2028 7.8% 7.9% 7.9% 7.9% 8.0% 7.6%

2029 7.7% 7.8% 7.9% 7.9% 8.0% 8.1%

2030 7.7% 7.8% 7.9% 7.9% 8.1% 8.7%

6.4.4 Sales and Shipments Impacts of Efficiency-Induced Price Changes

Figures 6.16 through 6.19 show the impacts relative to existing minimum efficiency

equipment (i.e., 10 SEER) on forecasted equipment sales and shipments due to different efficiency

levels (i.e., 11 through 13 SEER and 18 SEER) by product class under the NAECA efficiency

scenario and AEO2000 Reference Case. To note, the Shipments Model forecasts equipment sales

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-30%

-20%

-10%

0%

10%

20%

30%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Ship - 2006-2030

Ship - 2006

Sales - 2006-203

Sales - 2006

Figure 6.16 Impacts of Increased Efficiency for the year 2006 and

Average Impacts over the period 2006 to 2030 for Split A/C

Sales and Shipments

in millions of dollars while shipments are forecasted in millions of units. Results are not shown by

Trial Standard Level as each of the product classes are affected differently by changes in efficiency.

In the figures, both the impacts at the year the efficiency level is assumed to become effective (2006)

and the average impacts over the forecast period (2006 to 2030) are illustrated. For all classes, sales

and shipment impacts for the 11 SEER efficiency level are well within 5% of the base case. For both

HP classes, sales and shipment impacts for the 12 SEER efficiency level are also within 5% of the

base case. Larger sales and shipments impacts are forecast for all other efficiency levels. 

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-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Ship - 2006-2030

Ship - 2006

Sales - 2006-203

Sales - 2006

Figure 6.17 Impacts of Increased Efficiency for the year 2006 and

Average Impacts over the period 2006 to 2030 for Split Heat

Pump Sales and Shipments

-30%

-20%

-10%

0%

10%

20%

30%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Ship - 2006-2030

Ship - 2006

Sales - 2006-203

Sales - 2006

Figure 6.18 Impacts of Increased Efficiency for the year 2006 and

Average Impacts over the period 2006 to 2030 for Package

A/C Sales and Shipments

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-50%

-40%

-30%

-20%

-10%

0%

10%

20%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Ship - 2006-2030

Ship - 2006

Sales - 2006-203

Sales - 2006

Figure 6.19 Impacts of Increased Efficiency for the year 2006 and

Average Impacts over the period 2006 to 2030 for Package

Heat Pump Sales and Shipments

The biggest factor that influences the size of the potential standards-induced changes is the

actual installed consumer price increase that is induced by the standard. If price increases are large,

the shipments volume decreases almost proportional to the price increase, but because the price

elasticity is less than one, price increases result in increased gross sales dollar volume. The net

financial impact of these opposing effects is examined in more detail in the manufacturing impact

analysis (Chapter 8). 

Some of the measures that consumers might take to avoid the purchase of a new higherpriced CAC-HP keep them out of the market for only a relatively short period of time. Therefore

there is some recovery from the initial shipments drop that might be seen in the year a new efficiency

level first takes effect. It is forecasted that the long term average shipments drop is approximately

40% and 35% less for CAC and HP, respectively, than the drop which might be seen in the first year

that the efficiency level takes effect.

6.4.5 Impacts on Mean Age, Mean Lifetime, Early Replacements, and Total Repairs of CACHP 

Figures 6.20 through 6.23 illustrate the estimated relative impacts on the mean age of CACHP, the mean CAC-HP lifetime, the early replacement of CAC-HP, and the total volume of CAC-HP

repairs. These are average impacts over the time period of 2006 to 2030. These four different

measures of CAC-HP retention measure different types of consumer reactions to higher potential

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-50%

-40%

-30%

-20%

-10%

0%

10%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Age

Lifetime

Repairs

Replace

Figure 6.20 Average Impacts on Mean Age, Mean Lifetime, Early

Replacements, and Total Repairs over the period 2006 to 2030 for

Split A/C

CAC-HP prices. Impacts are shown by product class in the following figures and have determined

only under the NAECA efficiency scenario and AEO2000 Reference Case.

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-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Age

Lifetime

Repairs

Replace

Figure 6.21 Average Impacts on Mean Age, Mean Lifetime, Early

Replacements, and Total Repairs over the period 2006 to 2030 for

Split Heat Pumps

-50%

-40%

-30%

-20%

-10%

0%

10%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Age

Lifetime

Repairs

Replace

Figure 6.22 Average Impacts on Mean Age, Mean Lifetime, Early

Replacements, and Total Repairs over the period 2006 to 2030 for

Package A/C

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-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

10%

11 12 13 14 15 16 17 18

SEER

Relative Impact

Age

Lifetime

Repairs

Replace

Figure 6.23 Average Impacts on Mean Age, Mean Lifetime, Early

Replacements, and Total Repairs over the period 2006 to 2030 for

Package Heat Pumps

The increase in repair rate measures the impact of consumers who perform an extra repair

on their CAC-HP rather than retire the machine. As shown in Figures 6.20 through 6.23, such

repairs increase with increased efficiency. This increase is primarily due to the corresponding

decrease in consumers that replace their machines early. 

The extended lifetime of CAC-HP reflects repairs that consumers might undertake to extend

the lifetime of CAC-HP. Such extended repairs will have a delayed effect on the average lifetime

of a CAC-HP, and only a relatively small fraction of machines will receive such extended repairs.

An extra repair extends the life of a 18.4 year old machine by at most six years. The most significant

impact of increased efficiency on lifetime is illustrated at the 18 SEER efficiency level. For example

in Figure 6.20 for Split A/C, the 18 SEER efficiency level increases the mean lifetime by

approximately 6% or just over one year.

The increase in mean age of a CAC-HP illustrates both the impacts of extra repairs and a

decrease in consumers replacing their systems early. The proportion of older machines increases

slightly, and this results in a slight increase in the average age of machines. Again, it takes several

years for extra repairs to have a significant impact on the CAC-HP age distribution, so the averaged

impact over the period is significantly smaller than the peak age increase which occurs several years

after implementation of the standard. 

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11. Bucher, M.E., C.M. Grastataro, and W.R. Coleman, Heat Pump Life and Compressor

Longevity in Diverse Climates. ASHRAE Transactions, 1990. 96(1): p. 1567-1571.

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