WORKING 

 PAPERS

Slow Market Adjustment to Tax Changes: 

Evidence from the Market for Used Wide-body Commercial Aircraft

Loren Smith

WORKING PAPER NO. 289

May 2007

___________________________________________________________________________

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author to protect the tentative character of these papers.

______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
Slow Market Adjustment to Tax Changes: Evidence from the 

Market for Used Wide-body Commercial Aircraft 

Loren K. Smith1

May 8, 2007 

Abstract 

Investment tax credits are generally implemented to stimulate investment in new goods. 

However, in the case of durable goods, such policies may also affect secondary markets for used 

goods. Using a simple theoretical model, I show that an exogenous shock to the price of new 

durable goods (e.g., a change in tax policy) causes an increase in price and a decrease in the 

number of transactions in used good markets. After describing the theoretical model and its 

predictions, I use transaction and price data for new and used wide-body commercial aircraft to 

show that the data is qualitatively consistent with the predictions of the theoretical model. Given 

a 10 percent increase in the price of new goods, the price of used goods increases 15-20 percent, 

and used goods are kept longer on average before they are sold in secondary markets. 

 

1

 I would like to thank Paul Sullivan, Keith Brand, Dan Hosken and Simon Anderson for their helpful 

comments and suggestions. The opinions expressed in this paper are those of the author and do not 

necessarily represent those of the FTC or its individual commissioners. Correspondence: Federal Trade 

Commission, 601 New Jersey Ave., Washington, DC 20001. Email: lsmith2@ftc.gov. 

0
1 Introduction 

Investment tax credits are often designed to stimulate investment in new goods. However, 

tax programs may also affect secondary markets for used durable goods. This paper characterizes 

the effects of exogenous changes in the prices of new durable goods on prices and holdings. In 

1986, a 10 percent tax credit given to purchasers of new commercial aircraft was removed, which 

effectively increased price of new aircraft. I use a simple theoretical model to predict the effect 

that such a price change in the new good market will have on markets for used durable goods, and 

then show that the data is consistent with the theory using price and probit regression models. 

In this work, I use the theoretical model to show that an investment tax credit, such as the one 

removed by the Tax Reform Act of 1986 (TRA86, hereafter), not only affects investment in new 

durable goods, but also affects prices and quantities sold of used durable goods. Specifically, the 

theoretical model shows that when the price of new durable goods increases, the price of used 

durable goods should increase as well, but to a lesser extent. Furthermore, under the assumption 

that the density of consumer tastes for newness is upward sloping, owners of durable goods are 

more likely to hold a good for a longer period after the price of new goods increases, than they 

were before the price increase. 

The model developed here is a simplification of richer models like those developed in Rust 

(1985) and Konishi and Sandfort (2002). The theoretical framework used is very similar to those 

employed by Anderson and Ginsburgh (1994) and Hendel and Lizzeri (1999). I assume that 

durable goods are useful for only two periods, and that the only source heterogeneity among 

goods is the physical depreciation of a good in its first and second periods of use. That is, all new 

goods are homogeneous and all goods physically depreciate at the same rate. Thus, all used 

goods are also homogeneous as well. Equilibrium with positive quantities of both new and used 

goods results because of heterogeneity in consumers’ preferences for quality (newness), and 

transaction costs. Using a similar model, Hendel and Lizzeri (1999) identifies the extent to which 

“lemons” exist in used goods markets as compared to heterogeneity in the physical depreciation 

of different brands of goods. Specifically, they find that Japanese automobiles hold their value 

better in used markets than their American counterparts because they degrade less quickly, and 

not because of the existence of relatively more lemons among American automobiles. Anderson 

and Ginsburgh (1994) use a similar framework to characterize the ability of manufactures to 

(second-degree) price discriminate against consumers of used goods by altering the durability of 

their products. 

1
 Using transaction data from Back Aviation solutions and price data from Avmark 

Incorporated, I use this exogenous shock to the price of new durable goods to show that the data 

qualitatively supports the predictions of the theoretical model. First, I specify a price regression 

to show that the exogenous increase in the price of new durable goods brought on by TRA86 

results in a smaller but significant increase in the price of used goods. Second, I estimate two 

Probit regression equations that show that transactions of used aircraft slow after the 

implementation of TRA86, which is consistent with the theoretical model’s prediction that 

owners of used aircraft will hold their assets longer after an increase in the relative price of new 

goods. 

 

2 Tax Reform Act of 1986 

Prior to the Tax Reform Act of 1986 (TRA86 hereafter), purchasers of new capital assets, like 

aircraft, received an investment tax credit (ITC) of 6-10 percent. The tax credit was 10 percent 

for all wide-body commercial aircraft. This 10 percent discount was designed to spur investment 

in new durable goods. TRA86 brought about three significant changes that could impact 

investment by airlines in new commercial aircraft, (1) it eliminated the 10 percent ITC on the 

purchase of new aircraft, (2) it increased the length of time over which depreciation benefits are 

realized on aircraft from five to seven years from when they are new, and (3) it reduced the 

corporate tax rate from 46 percent to 34 percent. The first two changes instantly increased the 

cost of owning new aircraft relative to used aircraft. The third change reduced airlines’ tax 

burden, which could possibly increase investment in aircraft (both new and used). This paper 

predicts and estimates the effects of the increase in the relative price of new aircraft on 

equilibrium prices and quantities in the used market. 

3 Model

 The following simple two-period model illustrates how, under certain assumptions, prices 

and quantities of used durable goods sold change with an exogenous shock to the price of new 

durable goods. 

2
3.1 Information 

Let there be an arbitrarily large number of time periods indexed t =1, 2,...,T . Durable 

goods are useful for at most two periods. Therefore, at time t, there are at most 2 vintages of a 

good in the market. At the beginning of each time period, consumers know the quality of new 

goods and the condition of used goods carried over from the previous period. The only source of 

heterogeneity across goods is deterioration from aging. Therefore, all goods of the same vintage 

are homogeneous. Given the price of new goods, equilibrium prices and owners of used goods 

are determined by a perfectly competitive market for used goods. 

 The market consists of manufacturers, consumers, and scrappers. The focus of this study 

is on dynamics and equilibrium in used markets. Therefore, manufacturer and scrapper behavior 

is greatly simplified and treated as exogenous (and known to consumers). 

3.2 Scrappers 

Scrappers have an infinitely elastic demand for all vintages of durable goods at a fixed 

price P. In other words, they are always willing to purchase any amount of any vintage of the 

good at a price of P per unit. For simplicity, and without loss of generality, I set P = 0. 

3.3 Manufacturers 

The price of a new good, Pt , is exogenously determined at time t by manufactures. 

Manufacturers provide as many new goods as are demanded at Pt . The stock of used goods 

available to airlines at time t is determined by the number of new goods demanded at time t-1. 

The location of all new and used goods and the prices of used goods are then determined by 

equilibrium. 

3.4 Consumers 

 Consumers are indexed . I assume the number of consumers in the market is 

arbitrarily large and constant over time. Consumers can own at most one durable good in each 

period. At time t, one year-old goods have quality 

i =1,..., N

t 1 q − =ν , and new goods have quality 

3
t q = + ν k .

2

 Consumer i’s preference for quality is measured by the parameter θi . Consumer 

preferences,θi , are distributed F with associated density f such that f >0 everywhere on the 

relevant support. 

The utility received by consumer i at time t is determined by the good they own when 

they enter the period (if they own one), the good they choose in the current period (if they choose 

one), and the prices of new and used goods. As is shown in Anderson and Ginsburgh (1994), if 

there are no changes in the quality of new or used goods (i.e., ν and k ), or in the price of new or 

scrapped goods, over any two-period span there are only four choices that can possibly be optimal 

for consumers (for simplicity, I assume the discount factor is zero): 

1. Consumer i buys a new good and sells a used good in each period: 

 V nn k P P c i in ( , 2( ) ) = [θ ν +−+−u ], 

where c is a transaction cost associated with purchasing a good. 

 

2. Consumer i buys a new good and holds it for two periods: 

 V nu k P c ii n ( , 2 ) =θ ν ( +−− ) . 

3. Consumer i buys a used good in each period: 

 V uu P c i i ( , 2 ) = [θ ν − −u ]. 

4. Finally, consumer i does not consume either new or used goods: 

 Vi (0,0 0 ) = . 

 Any combination of segments of the market defined by the above payoffs may (or may 

not) exist in equilibrium. 

 

2

 I assume a deterministic rate of depreciation for durables. Previous work, e.g., Rust (1985) and Konishi 

and Sandfort (2002), has allowed for more general depreciation patterns. More generality in the 

depreciation of durables does not change the point I am illustrating with the model developed here. 

4
3.5 Equilibrium and Some Implications 

I assume that the secondary market for used goods is perfectly competitive. Equilibrium 

prices of used goods and the owners of new and used goods are determined by the price of new 

goods set by manufacturers. Characterization of all of the possible equilibria of the model is 

given in great detail in Anderson and Ginsburgh (1994). For this study, I will focus on equilibria 

where markets for both new and used goods exist, and prices of new and used goods are positive. 

For a secondary market for used good to exist and the price of used good be positive, the supply 

of used goods (i.e., those buying a new good in every period) and the demand for used goods (i.e., 

those buying a used good in every period) must be equal. Given the distribution of consumer 

tastes for quality, F, the equilibrium condition can be expressed 

2 2 1 P Pc P Pc Pc n u nu u F FF

k k ν

⎛ ⎞ ⎛ ⎞⎛ −+ −− + −=− ⎜ ⎟ ⎜ ⎟⎜ ⎝ ⎠ ⎝ ⎠⎝⎞

⎟

⎠

. (1) 

Using the equilibrium condition given by equation (1), the following results can be 

derived. 

Claim 1 – 

1 0

2

u

n

dP

dP

< <

Proof – By the implicit function theorem, 

2 2

2 2 2

nu nu

u

n nu nu u

P Pc P Pc f f dP k k

dP P Pc P Pc Pc k ff f k k ν ν

⎛ ⎞⎛ ⎞ −+ −− ⎜ ⎟⎜ ⎟ + ⎝ ⎠⎝ ⎠ = ⎡ − + − −⎤ + ⎛ ⎞⎛ ⎞ ⎛ ⎜ ⎟⎜ ⎟ ⎜ + + ⎢ ⎥ ⎣ ⎦ ⎝ ⎠⎝ ⎠ ⎝

⎞

⎟

⎠

, which is between 0 and 1/2. 

Claim 1 states that when the price of a new good increases $1, the price of used goods 

may not increase at all, and will increase by no more than $0.50. Given the simplicity of the 

theoretical model, in particular the fact that goods are only useful for two periods, the quantitative 

results are not too meaningful. What is more important is the qualitative result that when the 

price of new goods increase, the model predicts that the price of used goods will increase, but to a 

lesser extent. 

5
Claim 2 – If the density of consumer preferences for quality, f, is increasing 

(decreasing), the proportion of consumers holding goods for two periods is increasing 

(decreasing) in the price of new goods. 

Proof – The proportion of consumers holding used goods for two periods is given by, 

2 2 P Pc P Pc nu nu H F F

k k

⎛ ⎞⎛ −+ −− = − ⎜ ⎟⎜ ⎝ ⎠⎝⎞

⎟

⎠

, and 

1 2 2 1 2 ( )0 u nu nu

n n

dH dP P P c P P c f f dP k dP k k

⎛ ⎞⎡ − + − −⎤ ⎛ ⎞⎛ ⎞ = − ⎜ ⎟ − > < ⎢ ⎥ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎣ ⎦ ⎝ ⎠⎝ ⎠ if the term in square 

brackets is positive (negative), which is true when f x '( ) > <( ) 0

 

 for all x’s in the relevant 

domain. 

Claim 2 can be interpreted to mean that as the density of consumers with a high 

preference for quality becomes tighter and/or the density of consumers with a low preference for 

quality becomes more dispersed, the proportion of consumers holding goods for two periods will 

more likely increase when the price of new goods increases. This observation provides some 

insight into the market for wide-bodied commercial aircraft. In the market for wide-body jets, 

there are relatively few airlines that purchase the majority of new wide-body commercial aircraft, 

which is consistent with a tight distribution of consumers with a high preference for quality. 

Moreover, there are numerous purchasers of used wide-bodies that purchase aircraft at widely 

varying times in their lifecycle, which is consistent with a widely dispersed density of consumers 

with a low preference for quality. Therefore, the distribution of consumer tastes is apparently 

increasing and one might anticipate the number of airlines holding used aircraft for longer 

durations to increase if the price of new aircraft increases, ceteris paribus. 

 

4 Data 

 

In this section, I present an overview of the data. The transaction data were provided by 

Back Aviation Solutions (BAS), and the price data were provided by Avmark Incorporated (AI).3

 

3

 I thank Todd Pulvino at the Kellogg Business School for providing me with this data. 

6
4.1 Transaction Data 

The transaction data give detailed information about every aircraft that was registered to 

fly in the past 60 years at several points in each aircraft’s lifecycle. Importantly for this study, the 

data provide a rich set of information for each aircraft in the sample when it is new and whenever 

it is sold in the secondary market, including the buyer and seller of the aircraft. 

 Although the data includes information on many types of aircraft, this study focuses on 

the nearly 3000 wide-body commercial aircraft active during the fifteen-year period spanning 

1978-1993. The study is narrowed to wide-body jets for several reasons. First, wide-bodies are 

arguably the most important segment of the commercial aircraft market. Wide-body commercial 

jets generated more revenue in both primary and secondary markets than all other types of aircraft 

combined during the relevant time period. Second, wide-bodies are less likely to be substitutes 

for alternative types of aircraft, such as narrow body aircraft and regional jets, since during the 

sample period wide-body jets were used predominantly for transoceanic routes and were the only 

type of aircraft capable of flying routes of such lengths. Finally, narrowing my attention to widebodies is consistent with other studies in the literature (see e.g., Smith (2007) and Benkard 

(2005)). 

 The data provided by BAS also include several observed attributes for each aircraft. The 

attributes are as general as the aircraft’s make and model, and as detailed as the height of the 

aircraft’s cargo door in centimeters. Airlines carefully consider the technical specifications of an 

aircraft prior to purchase, and carefully monitor each aircraft’s condition as it ages. Therefore it 

is reasonable to assume that the observed attributes of aircraft influence aircrafts’ values to 

airlines. 

4.2 Price Data

The price data include actual transaction prices for 700 of the almost 3000 new and used 

aircraft sold in new and used markets during the time period 1978-1993. Prior to 1993, U.S. air 

carriers were required by law to report the price of any new or used aircraft they purchased or 

sold. Therefore, most of the missing prices are for transactions involving airlines outside of the 

7
U.S.4

 The remaining missing prices are for transactions that took place in 1993, but were 

reported on tax filings in 1994. Aircraft prices were reported to the Department of Transportation 

and/or the Federal Aviation Association and assembled by AI. 

5 Empirical Framework 

 Using the data described above, I design some reduced form empirical models to 

investigate the possibility that (1) equilibrium prices of aircraft changed significantly after 

TRA86, and (2) that the length of time that airlines hold aircraft is affected by the change in tax 

structure. 

5.1 Prices 

The theoretical model presented in Section 3 suggests that if TRA86 increases the prices 

airlines pay for new wide-body aircraft, the prices of used aircraft are likely to increase as well, 

but to a lesser extent. To attempt to identify the extent to which TRA86 may have affected prices 

in the used market, I specify the following regression, 

2

1 2 3 4

5 6

86

86 86 .

jt jt jt jt t jt

jt t jt t j x ijt

P AGE AGE AGE DTRA DNEW

DNEW DTRA DUSED DTRA X

ββ β β

β β βε

= + +× + +

× +× + +

(5.1) 

The dependent variable, Pjt , is the natural logarithm of the observed transaction price of aircraft j

when it was sold at time t. The variable DTRA86 is equal to one if the sale took place in 1986 or 

after. Recalling that the tax policy change was enacted in 1986, β5 and β6 measure the 

difference in the average price of aircraft after the policy change relative to before the policy 

change for new and used aircraft respectively, controlling for airplane model-specific effects (the 

X’s), price declines associated with aircraft aging (AGE), and any differences in the price declines 

associated with aircraft aging before and after the policy change ( β3 ). 

 One reasonable criticism of the specification given by equation (5.1) is that the policy 

dummy variable simply reflects a trend in prices that occurred over the sample period that has 

 

4

 There are over 300 airlines outside of the U.S. that owned a wide-body jet at one time or another during 

the sample period. 

8
nothing to do with the policy. Therefore, I also estimate a second specification of the regression 

equation given by equation (5.1) plus a linear time trend. 

 Another possibly misleading artifact of the data is that though the policy took effect in 

January of 1986, discussions of a policy change began sometime in 1985. As a result, it is 

unclear whether airlines’ ownership behavior in 1985 was affected by the policy or not. 

Therefore, I also estimate a third specification of the model that throws out all sales made in 

1985. 

5.2 Transactions

In addition to effects on the prices of used goods, under specific assumptions about the 

distribution of consumer preferences for newness, the model also predicts that aircraft will more 

likely be held longer after the tax change than they were before the tax change. Specifically, 

since there are relatively few airlines purchasing the majority of new wide-body commercial 

aircraft, and there are many purchasers of used wide-body jets with perhaps widely varying 

preferences for quality (or newness), one might expect the number of airlines holding used 

aircraft for longer durations to increase if the relative price of new aircraft increases due to the tax 

change. 

 To evaluate this hypothesis, I estimate two Probit models. In the first specification, I use 

24,618 observations (including over 3,000 sales) occurring between 1978-1993 involving aircraft 

ages 2-15 to estimate the parameters of the equation 

() ( )

( )

15

1

2

15

13

2

Pr 1

1 86

ijt it jt k

k

jt t k j x ijt

k

Sold AGE k

AGE k DTRA X

α β

β β ε .

−

=

+

=

=+ = +

=× + +

∑

∑

 (5.2) 

Since the data contain many observations and sales, I am able to estimate 142 parameters, 

including 10 seller-specific fixed effects, parameters for a full spline in age before and after the 

tax program, and aircraft characteristics and several model-vintage fixed effects (the X’s). 

β15 28 − β are the parameters of interest for evaluating the hypothesis that airlines’ hold used 

aircraft longer after the TRA86. 

 Again, a reasonable criticism of the specification given by equation (5.2) is that the 

policy dummy variable simply captures a trend in the frequency of secondary market transactions 

9
occurring over the sample period that have nothing to do with the policy. Therefore, I also 

estimate a Probit specification given by equation (5.2) plus a linear time trend. 

 Also, since discussions of a policy change began sometime in 1985, it is unclear whether 

airlines’ ownership behavior in 1985 was affected by the policy or not. Therefore, I also 

estimate a third specification of the model that throws out all sales made in 1985. 

Another possible criticism of the above specification is that the periods before and after 

the tax change are too long, and therefore, the parameters of interest are capturing period-specific 

effects other than those brought on by the policy change. Such concerns may be alleviated 

somewhat if the results are similar when the model is evaluated at points in time only soon before 

and immediately after the tax change.5

 Estimation of the second Probit specification uses 3,640 

(about 300 sales) observations occurring in 1984 and 1986 involving aircraft ages 2-15. Sticking 

with the notion that the announcement of a policy change sometime in 1985 may have indirectly 

affected airline investment behavior in 1985, 1984 is used instead. The second Probit estimation 

equation is given by 

( ) ( )

2

Pr 1 2 3 86 . ijt jt jt t jt j x ijt Sold AGE AGE DTRA AGE X = + × + ++ β β ββ ε (5.3) 

The data used for this specification contain too few observations to reliably estimate a complete 

spline in age and its interaction with the policy variable, like was done in the specification given 

by equation (5.2). Alternatively, the more parsimonious specification given by equation (5.3) is 

quadratic in age. The parameter that captures the effect of the policy in this specification of this 

model is β 2 . A negative estimate of β 2 indicates that older aircraft are less likely to be sold 

after the policy change than they were before. 

6 Results 

 The estimation results are generally consistent with the predictions of the theoretical 

model outlined in section 3.5. 

6.1 Price Regression Results 

 

5

 I would have liked to have been able to do something similar with the price regressions, but there were 

too few observed prices to make this possible. 

10
 

 To evaluate the price regressions described in Section 5.1, I use 564 sales of wide-body 

aircraft ages 1-15 for the first two specifications, and 501 sales of wide-body aircraft ages 1-15 

for the last specification. The results of the price regressions are given in Table 6.1. Neither the 

addition of the time trend in Specification 2 or the exclusion of sales made in 1985 in 

Specification 3 seem to have a meaningful effect on the parameter estimates or the regressions’ 

quality. Therefore, I summarize the results of all of the specifications of the price regression 

together. The small and insignificant coefficient on the interaction of the TRA86 and new 

dummy variables indicate that the transaction prices of new aircraft do not differ significantly 

before and after the implementation of TRA86. Therefore, accounting for the 10 percent tax 

credit, the price of new aircraft effectively increased approximately 10 percent after the policy 

was enacted in 1986. The regression results indicate that the price of used aircraft increase 

between approximately 15 and 20 percent after the policy took effect, after controlling for model 

and age effects. 

The theoretical model predicts that when the price of new aircraft increase the price of 

used aircraft may increase but not more than half as much. However, the predictions of the 

theoretical model are made in level (not percentage) terms. The regression approximates the 

average price before TRA86 of a new Boeing 747-100 to be 64.5 million real (1982-1984) dollars 

(effectively $58 million after the realization of the 10 percent investment tax credit), a five yearold aircraft of the same model has a predicted average price of $36.6 million, and a 10 year-old 

747-100 has a predicted average price of $25.6 million. After the implementation of TRA86 the 

average price of a five year-old 747-100 increases to approximately $41-42.8 million (a $5.4-7.2 

million increase), and the average price of a 10 year-old 747-100 increases to $29.4-30.6 million 

(a $3.8-5.0 million increase). The price increases for the used models predicted by the data are 

higher than those predicted by the theoretical model presented in Section 3. There are a few 

possible explanations that may explain the under-prediction of price increases in used good 

markets by the theoretical model. First, the theoretical model assumes that aircraft are only 

useful for two periods. As the number of useful periods of the durable good increases in the 

theoretical model, so does the predicted price increases for used models relative to a price 

increase of new models. Second, the theoretical model only mimics price increases that occur 

due to a change in the investment tax credit. The actual TRA86 also increased the number of 

years over which depreciation benefits were realized by aircraft owners from the first 5 years of 

an aircraft’s life to the first 7 years of an aircraft’s life. This also increased the relative (to new 

aircraft) value of used aircraft. 

11
 

6.2 Probit Results 

 The results of the first three Probit specifications are given in Table 6.2. The introduction 

of the time trend in the second specification does not effect the estimated correlation between the 

policy dummy variable and the probability of an aircraft being sold in the used market 

qualitatively; however the time trend does affect the magnitude of the estimated correlations. The 

coefficient estimates on the interactions of the age dummy variables and the policy dummy 

variable (a dummy variable that equals one in 1986 and after) indicate that airlines are generally 

more likely to hold used aircraft longer after the implementation of TRA86. Specifically, in 

Specification 1, almost all of the coefficients are negative and most are significant. On average 

(across different ages of aircraft), the policy decreases the probability an aircraft will be sold in 

used markets by approximately 3 percent. The results are similar for Specification 2, but the 

magnitude and statistical significance of the results are reduced. Specification 3 excludes 

transactions made in 1985, since the announcement of the policy may have affected airline 

behavior even before the policy was put in place. Though none of the coefficients on the 

interaction of the policy variable and various aircraft ages differ statistically between 

Specifications 2 and 3, it does appear that the point estimates of Specification 3 are slightly more 

negative, indicating that given the exclusion of data from 1985, the Probit model predicts a more 

significant estimated dampening of secondary market transactions after TRA86 was put in place. 

The only non-negative (though insignificant) coefficient on the policy interactions in all of the 

specifications presented in Table 6.2 is on the interaction of seven year-old aircraft with the 

TRA86 dummy. This is likely a result of the fact that the depreciation schedule for commercial 

aircraft was extended from five to seven years by TRA86, which might have made seven years a 

new focal point for the sale of a used aircraft. The results of the first set of Probit regressions also 

indicate that longer aircraft and aircraft with greater fuel capacities are more likely to be sold in 

used markets, while longer range aircraft are more likely to be held by their current owners. 

Also, the fact that Eastern and Northwest airlines tend to keep aircraft relatively longer before 

selling them in used markets is reflected in the relatively large and negative coefficients on their 

respective dummy variables. 

 The results of the final Probit specification, which focuses on aircraft holdings in the 

years 1984 and 1986, are given in Table 6.3. The results of the regression further support the idea 

that used aircraft sales slowed after the implementation of TRA86. Specifically, the negative and 

significant coefficient on the interaction of age and a dummy variable for observations in 1986 

12
indicates that used aircraft of every age from 2 to 15 are less likely to be sold in 1986 than they 

were in 1984. 

 The results of the Probit regressions presented above are consistent with the predictions 

of the theoretical model if the density of consumer tastes for quality (newness) is increasing. This 

is consistent with the notion that all buyers have different tastes for quality and the fact that there 

are very few buyers buying the majority of new aircraft, while there are many buyers of used 

aircraft. This is appears to be true in the data. New aircraft are often bought several at a time, 

and over 80 percent of new aircraft are purchased by 20 airlines, while there have been over 300 

owners of used wide-body aircraft within the relevant time period. 

7 Conclusions 

The theoretical model characterized above, as well as the price and discrete choice regression 

models estimated in this paper are designed to show that an investment tax credit like the one 

removed by TRA86 not only affects investment in new durable goods, but also affects prices and 

quantities of aircraft held in used durable good markets. Specifically, the simple theoretical 

model shows that when the price of new durable goods increases, the price of used durable goods 

should increase to a lesser extent. Furthermore, under the assumption that the density of 

consumer tastes for quality is upward sloping, owners of durable goods are more likely to hold a 

good for two periods after the price of new goods increases, than they were before the price 

increase. 

 The results of the theoretical model are generally consistent with the data on sales of used 

wide body aircraft. The price regression model shows that the average transaction price of used 

aircraft increases approximately 15-20 percent after the implementation of TRA86. In addition, 

the two Probit regression models developed in the paper show that transactions of used aircraft 

generally slow after the implementation of TRA86. This supports the prediction of owners of 

used aircraft holding their assets longer after the implementation of TRA86 than they did before. 

13
References 

[1] Anderson, S. P., and V. P. Ginsburgh (1994), “Price Discrimination via Second-hand 

Markets,” European Economic Review, 38, 23-44. 

[2] Benkard, C. L. (2004), “A Dynamic Analysis of the Market for Widebodied Commercial 

Aircraft,” Review of Economic Studies, 71:3. 

[3] Hendel, I., and A. Lizzeri (1999), “Adverse Selection in Durable Goods Markets,” 

American Economic Review, 89:5, 1097-1115. 

[4] Konishi, H., and M. T. Sandfort (2002), “Existence of Stationary Equilibrium in the 

Markets for New and Used Durable Goods,” Journal of Economic Dynamics & Control, 

26, 1029-1052. 

[5] Rust, J. (1985), “Stationary Equilibrium in a Market for Durable Assets,” Econometrica, 

53:4, 783-805. 

[6] Smith, L. K., (2006), “Dynamics and Equilibrium in a Structural Model of Commercial 

Aircraft Ownership,” FTC Working Paper No. 280. 

14
Table 6.1 

Log Price Regression 

Age and Vintage Parameters 

Variable Specification 1 Specification 2 Specification 3 

Constant 3.7258* 

(0.1909) 

3.7798* 

(0.1995) 

3.8139* 

(0.2022) 

New 0.1150 

(0.1597) 

0.1199 

(0.1598) 

0.3891 

(0.2639) 

DNew DTRA × 86 -0.0129 

(0.1507) 

0.0140 

(0.1535) 

-0.2208 

(0.2649) 

DUsed DTRA × 86 0.1471* 

(0.0753) 

0.1774* 

(0.0820) 

0.1967* 

(0.0908) 

Age -0.1000* 

(0.0146) 

-0.0982* 

(0.0148) 

-0.0957* 

(0.0158) 

Age DTRA × 86 0.0090 

(0.0071) 

0.0084 

(0.0071) 

0.0146 

(0.0085) 

2 Age 0.0019* 

(0.0008) 

0.0019* 

(0.0008) 

0.0014 

(0.0010) 

Time NA -0.0065 

(0.0070) 

-0.0119 

(0.0074) 

n = 564 for Spec. 1 and Spec. 2, n = 501 for Spec. 3; 

2 R = 0.8409 for Spec. 1, for Spec. 2 and for Spec. 3; 2 R = 0.8411 2 R = 0.8390

* - indicates significance at the 5 percent level 

15
Table 6.1 

Log Price Regression 

Aircraft Model Parameters 

Variable Specification 1 Specification 2 Specification 3 

747-100 0.3515 

(0.1852) 

0.3106 

(0.1903) 

0.3152 

(0.1937) 

747-200 0.4707* 

(0.1807) 

0.4449* 

(0.1828) 

0.4330* 

(0.1849) 

747-Special 0.0183 

(0.1917) 

-0.0084 

(0.1938) 

-0.0651 

(0.1980) 

747-400 0.7554* 

(0.1784) 

0.7542* 

(0.1784) 

0.7533* 

(0.1801) 

767-200 -0.0146 

(0.1808) 

-0.0261 

(0.1813) 

-0.0325 

(0.1832) 

767-300 0.1087 

(0.1762) 

0.1036 

(0.1763) 

0.0998 

(0.1780) 

DC10-100 -0.2234 

(0.1834) 

-0.2588 

(0.1873) 

-0.2550 

(0.1896) 

DC10-200 0.1789 

(0.1808) 

0.1520 

(0.1833) 

0.1170 

(0.1854) 

DC10-300 -0.2926 

(0.2294) 

-0.3243 

(0.2320) 

-0.2749 

(0.2353) 

MD11 0.4559* 

(0.2024) 

0.4650* 

(0.2027) 

0.4725* 

(0.2047) 

L-1011-1 -0.5610* 

(0.1842) 

-0.5915* 

(0.1871) 

-0.5518* 

(0.1897) 

L-1011-503 -0.4506* 

(0.1896) 

-0.4755* 

(0.1915) 

-0.7733* 

(0.2343) 

L-1011-500 -0.2114 

(0.1859) 

-0.2306 

(0.1870) 

-0.2835 

(0.1897) 

L-1011-200 -0.1686 

(0.2280) 

-0.1754 

(0.2280) 

-0.1857 

(0.2304) 

A300-B220 -0.1339 

(0.2171) 

-0.1669 

(0.2200) 

-0.1900 

(0.2224) 

A300-B410 -0.1596 

(0.1816) 

-0.1791 

(0.1828) 

-0.1995 

(0.1849) 

A300-C4 -0.2693 

(0.3027) 

0.2991 

(0.3041) 

-0.3313 

(0.3073) 

A310-200 0.0174 

(0.2523) 

-0.0100 

(0.2540) 

-0.0313 

(0.2570) 

A310-220 -0.0164 

(0.2062) 

-0.0309 

(0.2069) 

-0.0482 

(0.2090) 

A310-300 -0.0521 

(0.1927) 

-0.0450 

(0.1929) 

-0.0433 

(0.1950) 

* - indicates significance at the 5% level. 

16
Table 6.2 

Probit Model 1 

Characteristics and Airline Specific Effects 

Variable Specification 1 Specification 2 Specification 3 

Coefficient Marginal 

Effect 

Coefficient Marginal 

Effect 

Coefficient Marginal 

Effect 

Constant -2.1396* 

(0.1620)

NA -10.2422* 

(0.6650)

NA -10.0423* 

(0.6832) 

NA 

Fuel 

Capacity 

4.46e-06* 

(1.36e-06)

3.88e-07* 

(1.19e-07) 

4.71e-06* 

(1.41e-6)

2.73e-07* 

(8.28e-07)

4.61e-06* 

(1.46e-06) 

2.68e-07* 

(8.62e-08) 

Range -1.62e-05 

(1.23e-05)

-1.14e-06 

(1.07e-07) 

-1.67e-05 

(1.25e-6)

-9.67e-07 

(7.26e-07)

-1.86e-05 

(1.30e-05) 

-1.08e-06 

(7.60e-07) 

Length 0.0040* 

(0.0015)

0.00034* 

(0.00013) 

-0.0036* 

(0.0017)

-0.00021* 

(0.0001)

-0.0032 

(0.0018) 

-0.00019 

(0.0001) 

Eastern 

Airlines 

-0.9216* 

(0.1602)

-0.0383* 

(0.0024) 

-0.9344* 

(0.1634)

-0.0241* 

(0.0018)

-1.0509* 

(0.1855) 

-0.0249* 

(0.0017) 

TWA -0.3628* 

(0.1156)

-0.0233* 

(0.0052) 

-0.3666* 

(0.1156)

-0.0151* 

(0.0033)

-0.3579* 

(0.1254) 

-0.0149* 

(0.0036) 

Delta 

Airlines 

0.1975* 

(0.0804)

0.0201* 

(0.0094) 

0.2074* 

(0.0818)

0.0145* 

(0.0068)

0.2208* 

(0.0839) 

0.0157* 

(0.0071) 

USAir -0.1661 

(0.0906)

-0.0126* 

(0.0059) 

-0.2332* 

(0.0939)

-0.0109* 

(0.0035)

-0.1894* 

(0.0962) 

-0.0092* 

(0.0039) 

United 

Airlines 

-0.1681* 

(0.0834)

-0.0128* 

(0.0055) 

-0.1934* 

(0.0829)

-0.0094* 

(0.0034)

-0.1825* 

(0.0845) 

-0.0090* 

(0.0035) 

Continent

al Airlines 

0.2417* 

(0.1085)

0.0257* 

(0.0139) 

0.2324* 

(0.1085)

0.0168* 

(0.0096)

0.2495* 

(0.1110) 

0.0184* 

(0.0101) 

American 

Airlines 

-0.2403* 

(0.0872)

-0.0173* 

(0.0051) 

-0.2502* 

(0.0877)

-0.0116* 

(0.0032)

-0.2551* 

(0.0907) 

-0.0118* 

(0.0033) 

Northwest 

Airlines 

-0.7621* 

(0.1368)

-0.0358* 

(0.0028) 

-0.7731* 

(0.1362)

-0.0227* 

(0.0019)

-0.7923* 

(0.1393) 

-0.0229* 

(0.0020) 

Piedmont 

Airlines 

0.4190* 

(0.0802)

0.0513* 

(0.0130) 

0.4174* 

(0.0816)

0.0369* 

(0.00098)

0.4005* 

(0.0879) 

0.0338* 

(0.0102) 

Time NA NA -1.2811* 

(0.0945)

-0.0743* 

(0.0037)

-1.2377* 

(0.0966) 

-0.0719* 

(0.0039) 

Also included in the probit models summarized by this and the following table were dummy 

variables for every model-vintage combination (e.g., Boeing 747 that was new in 1985, Boeing 

767 that was new in 1986, etc.). 

N = 24618 -- * - indicates significance at the 5 percent level 

17
Table 6.2 

Probit Model 1 

Aircraft Age Effects Before and After 1986 

Variable Specification 1 Specification 2 Specification 3 

Coefficient Marginal 

Effect 

Coefficient Marginal 

Effect 

Coefficient Marginal 

Effect 

 Age = 3 -0.7580* 

(0.0986) 

-0.0387* 

(0.0027) 

1.4354* 

(0.1986) 

0.2417* 

(0.0562)

1.4172* 

(0.2028) 

0.2366* 

(0.0569)

 4 -0.6266* 

(0.0932) 

-0.0347* 

(0.0031) 

2.8401* 

(0.2820) 

0.7319* 

(0.0795)

2.6989* 

(0.2890) 

0.6876* 

(0.0882)

5 -0.5434* 

(0.0896) 

-0.0318* 

(0.0033) 

4.1987* 

(0.3716) 

0.9616* 

(0.0216)

4.0576* 

(0.3804) 

0.9524* 

(0.0276)

 6 -0.5203* 

(0.0915) 

-0.0309* 

(0.0035) 

5.4961* 

(0.0915) 

0.9900* 

(0.0025)

5.2575* 

(0.4758) 

0.9883* 

(0.0037)

 7 -0.6705* 

(0.1066) 

-0.0358* 

(0.0032) 

6.6203* 

(0.5603) 

0.9925* 

(0.0013)

6.2651* 

(0.5726) 

0.9917* 

(0.0015)

8 -0.4682* 

(0.0998) 

-0.0288* 

(0.0042) 

8.1011* 

(0.6517) 

0.9943* 

(0.0011)

7.8384* 

(0.6657) 

0.9942* 

(0.0011)

9 -0.3080* 

(0.0991) 

-0.0213* 

(0.0053) 

9.5465* 

(0.7450) 

0.9957* 

(0.0009)

9.2166* 

(0.7617) 

0.9956* 

(0.0010)

10 -0.2223* 

(0.1015) 

-0.0163* 

(0.0062) 

10.9087* 

(0.8387) 

0.9963* 

(0.0008)

10.5615* 

(0.8571) 

0.9962* 

(0.0009)

11 -0.2603* 

(0.1097) 

-0.0186* 

(0.0062) 

12.1457* 

(0.9335) 

0.9966* 

(0.0008)

11.7344* 

(0.9548) 

0.9963* 

(0.0009)

12 -0.0257 

(0.1097) 

-0.0022 

(0.0092) 

13.6623* 

(1.0281) 

0.9968* 

(0.0008)

13.1639* 

(1.0518) 

0.9963* 

(0.0009)

13 -0.0926 

(0.1226) 

-0.0075 

(0.0092) 

14.8691* 

(1.1238) 

0.9968* 

(0.0008)

14.4838* 

(1.1512) 

0.9964* 

(0.0009)

14 -0.0778 

(0.1432) 

-0.0064 

(0.0110) 

16.1554* 

(1.2200) 

0.9965 

(0.0008)

15.8372* 

(1.2518) 

0.9963 

(0.0009)

15 0.1352 

(0.1608) 

0.0131 

(0.0173) 

17.6525* 

(1.3156) 

0.9959 

(0.0009)

17.277* 

(1.3525) 

0.9956 

(0.0009)

2*DTRA86 -1.5960* 

(0.1142) 

-0.0468* 

(0.0016) 

-0.3758* 

(0.1454) 

-0.0157* 

(0.0045)

-0.4280* 

(0.1463) 

-0.01717* 

(0.0042)

3*DTRA86 -0.4171* 

(0.1335) 

-0.0260* 

(0.0057) 

-0.1435 

(0.1335) 

-0.0073 

(0.0060)

-0.2231 

(0.1367) 

-0.0106 

(0.0053)

4*DTRA86 -0.3801* 

(0.1248) 

-0.0244* 

(0.0056) 

-0.1389 

(0.1250) 

-0.0071 

(0.0056)

-0.1400 

(0.1311) 

-0.0072 

(0.0059)

5*DTRA86 -0.3853* 

(0.1265) 

-0.0246* 

(0.0056) 

-0.1847 

(0.1260) 

-0.0091 

(0.0052)

-0.2278 

(0.1329) 

-0.0108 

(0.0051)

6*DTRA86 -0.3883* 

(0.1314) 

-0.0247* 

(0.0058) 

-0.2353 

(0.1305) 

-0.0110 

(0.0049)

-0.2240 

(0.1400) 

-0.0106 

(0.0054)

7*DTRA86 0.0596 

(0.1283) 

0.0054 

(0.0123) 

0.1744 

(0.1285) 

0.0118 

(0.0101)

0.2648 

(0.1380) 

0.0195 

(0.0126)

8*DTRA86 -0.1081 

(0.1204) 

-0.0086 

(0.0088) 

-0.0246 

(0.1206) 

-0.0014 

(0.0067)

-0.0685 

(0.1281) 

-0.0037 

(0.0066)

9*DTRA86 -0.0702 

(0.1139) 

-0.0058 

(0.0088) 

-0.0102 

(0.1143) 

-0.0006 

(0.0065)

-0.0320 

(0.1221) 

-0.0018 

(0.0067)

10*DTRA86 -0.2555* 

(0.1190) 

-0.0181* 

(0.0067) 

-0.2144 

(0.1198) 

-0.0102 

(0.0046)

-0.2601 

(0.1282) 

-0.0120 

(0.0046)

11*DTRA86 -0.0742 

(0.1192) 

-0.0061 

(0.0092) 

-0.0372 

(0.1202) 

-0.0021 

(0.0065)

-0.0627 

(0.1340) 

-0.0034 

(0.0069)

12*DTRA86 -0.5095* 

(0.1233) 

-0.0294* 

(0.0043) 

-0.4831* 

(0.1245) 

-0.0182* 

(0.0029)

-0.4598* 

(0.1416) 

-0.0178* 

(0.0034)

13*DTRA86 -0.4559* 

(0.1325) 

-0.0274* 

(0.0051) 

-0.4272* 

(0.1340) 

-0.0169* 

(0.0034)

-0.5580* 

(0.1566) 

-0.0199* 

(0.0031)

14*DTRA86 -0.5213* 

(0.1503) 

-0.0298* 

(0.0051) 

-0.4907* 

(0.1526) 

-0.0184* 

(0.0034)

-0.7367* 

(0.1793) 

-0.0227* 

(0.0026)

15*DTRA86 -0.6259* 

(0.1637) 

-0.0329* 

(0.0045) 

-0.5945* 

(0.1661) 

-0.0203* 

(0.0030)

-0.8402* 

(0.2166) 

-0.0238* 

(0.0025)

2 year-old aircraft prior to 1986 are the comparison group. N = 24618 

Standard errors are in parentheses -- * - indicates significance at the 5 percent level 

18
Table 6.3 

Probit Model 2 

Includes Data for Only 1984 and 1986 

Variable Coefficient Marginal Effects 

Constant -1.1879* 

(0.1636) 

NA 

Fuel Capacity 6.99e-06* 

(2.46e-06) 

8.75e-07* 

(3.08e-08) 

Range 8.33e-06 

(2.49e-05) 

1.04e-07 

(3.12e-06) 

Length -0.0017 

(0.0025) 

-0.0002 

(0.0003) 

Age D× 1984 -0.0583 

(0.0391) 

-0.0073 

(0.0049) 

Age DTRA × 86 -0.0902* 

(0.0410) 

-0.0113* 

(0.0051) 

2 Age 0.0077* 

(0.0022) 

0.00097* 

(0.00027) 

Boeing 747 -1.7667* 

(0.3009) 

-0.1941* 

(0.0342) 

Boeing 767 -1.0910* 

(0.2167) 

-0.0697* 

(0.0064) 

Airbus A-300 -0.5586* 

(0.1694) 

-0.0515* 

(0.0113) 

Douglas DC-10 -1.0846* 

(0.2236) 

-0.0922* 

(0.0138) 

Lockheed L-1011 -0.9145* 

(0.2013) 

-0.0707* 

(0.0095) 

The comparison group is Airbus A-310. 

n = 3460 ; log− =− likelihood 883.20 ; ( ) 2 χ 11 186.52 =

* - indicates significance at the 5 percent level 

19