A Dynamic Measurement Model of the European Airline Industry Using Competitive Market Power Variables

International Research Journal of Finance and Economics
ISSN 1450-2887 Issue 31 (2009)
© EuroJournals Publishing, Inc. 2009
http://www.eurojournals.com/finance.htm

A Dynamic Measurement Model of the European Airline
Industry Using Competitive Market Power Variables


Stamatis Kontsas
Technological Education Institution of Western Macedonia (Adjunct)
38, Leoforos K. Karamanli str., 54639, Thessalonica, Greece
E-mail: kontsas@otenet.gr

John Mylonakis
Hellenic Open University (Tutor)
10, Nikiforou str., Glyfada, 166 75, Athens, Greece
E-mail: imylonakis@vodafone.net.gr


Abstract

Traditional models of market power assume that the degree of market power can
accurately be assessed from models where either price or quantity competition are the only
endogenous variables. The scope of this paper is to investigate whether the inferred
significant degree of market power at the product market level is sensitive to the
introduction of an input variable, namely capacity. To test this assessment a structural
model is specified and estimated which accounts for competition in two variables: capacity
and prices in the European Airline Industry using data for the period of 1993-2007. Results
showed that some degree of market power exists and that firms’ market power is
significantly overestimated whenever capacity competition is not accounted for. Therefore,
it seems likely that most of the benefits from European liberalization will come from the
elimination of cost inefficiencies.


Keywords: Competitive market power, European Airline Industry, Market competition,
Product differentiation, Airlines Prices, Airplanes capacity
JEL Classification Codes: G140, D420, D430

1. Introduction
Traditional models of market power (Bresnahan, 1999) assume that the degree of market power can
accurately be assessed from models where either price or quantity competition are the only endogenous
variables. One of the conclusions of this literature is that significant market power, in the sense of price
costs margins, exists in some concentrated industries. In this paper a structural model is specified and
estimated which accounts for competition in two variables: capacity and prices.
Recently, more emphasis has been placed on the interactions between product market
competition and other "input" markets, such as R&D, advertisement, finance, labor, and capacity. By
endogenizing such input markets, which is often done by using a two-stage set-up, a number of
fundamental issues need to be reconsidered. Of particular interest is the effect of imperfect product
market competition on the demand for inputs. Another issue is that of endogenous costs and market

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International Research Journal of Finance and Economics - Issue 31 (2009)
130
structure (Sutton, 1991). A third area is anti-trust, where conventional wisdom of competition policy
may not hold, once another strategic variable is introduced (Fershtman and Gandal, 1994).
The scope of this paper is to investigate whether the inferred significant degree of market power
at the product market level is sensitive to the introduction of an input variable, namely capacity. In
other words, does endogenous capacity effect the conclusions about product market competition? If so,
one could attribute the above conclusion that "there is a great deal of market power, in the sense of
price cost margins, in some concentrated industries" (Bresnahan, 1999) to the fact that input markets
have not been properly endogenized.
To account for competition in input, as well as, output markets, this paper analysis a two-stage
setup. In the first stage firms make capacity decisions followed by a product-differentiated, price
setting game in the second stage. Since costs are endogenized through the first stage, this has important
implications for the measurement of market power in the product market. This model is applied to the
European airline industry using data for the period of 1993-2007.
The European airline industry is a particularly good "industry case" where this argument can be
tested. Firstly, there likely exists significant market power due to the regulatory aspects of the industry.
The reason for this cooperative duopoly structure in most markets has been created by bilateral
agreements between member states. In fact, the rationale for the "liberalization" program in the
European airline industry is based on the presumption to end monopolies and bring prices down to
"more competitive" level. A first and second package of measures introducing new competition rules,
relaxing price controls, and opening market, access where introduced in 1997 and 1999 respectively.
Over time the pressure resulted in a third package, leading towards an 'in principle' open intra-
European market by April 1st 1999. Many of the measures contained in these packages will take time to
implement. In addition, the question of third country access, i.e. opening up markets for competitors
from non-EC countries and vice-versa, is still to be addressed more completely and remains in the
public debate. The road to deregulation is still uncertain, but it is rather clear that the potential for
significant market power in the European airline industry existed. This paper intends to assess this
claim by measuring market power prior to major deregulations.
The second reason for why the European airline industry is well-suited for this study is that
capacity investments, such as in planes, are an important aspect of competition. It is argued that the
airline industry is one in which capacity investments (say in airplanes) are substantial. In addition,
there are frequent claims that "over-investment" in capacity has led towards considerable excess
capacity and consequently fierce product market competition. Furthermore, the two-stage set-up of our
model assumes that capacity (airplanes) is long-run decisions, whereas prices are short-run decisions.
Within the context of the airline industry this is not unreasonable, since planes must be ordered in
advance and delivery times may be lengthy.


2. Past Literature
The literature on measuring oligopolistic conduct includes mostly formulations that allow for only one
strategic variable, such as price or quantity (Iwata, 1994, Gallop and Roberts, 1999, Appelbaum, 2002,
Bresnahan, 1999). Specifically in the U.S. airline industry, market power has been studied by Brander
and Zhang (2000). They conclude that the Cournot model is much more consistent with the data in
general than either Bertrand or cartel behavior. Other important contributions on pricing in the airline
industry include Borenstein and Rose (2004) who analyze price dispersion on a given flight. The effect
of networks on competition and pricing are studied in Brueckner and Spiller (2001) and empirically
tested in Brueckner, Dyer and Spiller (2002). Evans and Kessides (1994) investigate the ability to
exercise market power in the airline industry through multimarket contact. They find that fares are
higher on routes where the competing carriers have inter-route contact. More recently, market power
through repeated interactions has been empirically tested for. Brander and Zhang (2003) estimate a
switching regime model for the U.S. airline industry based on the theory of repeated games. Firms are

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International Research Journal of Finance and Economics - Issue 31 (2009)
assumed to be implementing punishment strategies to enforce collusion in an uncertain environment
(Green and Porter, 1994)). Empirical observations would then be drawn from either a collusive or
punishment phase. Brander and Zhang reject the constant behavior models in favor of regime-
switching models, where the punishment phases are best described by Cournot competition. By
contrast, this paper focuses on the European airline industry, which is likely to display more collusive
behavior over the sample period studied.
A related strand of literature suggests that market power is quite significant in the U.S. airline
industry. Hurdle et al. (1999) and Whinston and Collins (2002) study the hypothesis of contestability
of the U.S. airline industry. Overall they find that the airline market is not contestable and that excess
profits are being earned. In addition, Berry (2000, 2002) and Borenstein (1999, 2000) argue that
airlines are able to increase average prices through strong airport presence and hub dominance.
This paper differs from the above literature by explicitly estimating a structural model which
accounts for competition in two variables: capacity and prices. The model has a two-stage setup. In the
first stage firms make capacity decisions followed by a product-differentiated, price setting game in the
second stage. Contrary to several other studies (Borenstein, 2000, Evans and Kessides, 1994), this
model is an aggregate model at the carrier level. Therefore, specific route effects or price
discrimination strategies are not considered. Since costs are endogenized through the first stage, this
has important implications for the measurement of market power in the product market. This model -
demand, cost (short and long run) and conduct – is estimated for the European Airline Industry using
data for the period of 1993-2007. A number of specification tests and reject a simple one-stage
specification in favor of the proposed two-stage set-up are performed. In particular, we find that
empirically the game is consistent with a fat-cat strategy. In other words, European Airlines overinvest
in capacities in order to be less aggressive. Regarding the measurement of market power in the product
market, some degree of market power exists is found. However, market power in the two-stage set-up
is significantly lower than in the more widely employed one-stage specification, which is consistent
with the direction of bias in fat-cat games. This illustrates that a firm's market power in the product
market is significantly overestimated whenever capacity competition is not accounted for.


3. A Model of Competition for the European Airline Industry
A simple two-stage game is specified where firms make capacity decisions in the first stage, followed
by a product-differentiated market game in prices. Therefore, capacity decisions are endogenized
which impacts on the marginal costs in the second stage and its inferred product market competition.
Product-differentiated and price-setting game is specified, where each carrier faces a demand of the
form, as following:
q (p ,p ,Z ),
i = 1,...N (1)
1
1
j
i
where: Ν is the number of carriers (or countries), q1 is the quantity demanded, p1 is a price index for
carrier i, and pj is a price index of the competitors prices. Zi is a vector of country-specific, exogenous
factors affecting demand. The time subscript for notational convenience is omitted. The implicit
duopoly assumption in (1) can be justified by the existence of bilateral agreements. While the
European carriers were engaged in moderate competition in Trans-Atlantic travel, the domestic
scheduled market remained heavily regulated through bilateral agreements until the mid-eighties. The
resulting duopolistic market structures created by the bilateral agreements also prevented new entry in
the intra-European market. The price elasticity implicitly defined in (1) is assumed to be negative. In
other words, small price elasticity implies that consumers consider carriers to be poor substitutes. It is
q
∂
q
∂
assumed that the own-price effect is larger than the cross-price effect, i.e.
1
1
−
>
> 0 .
p
∂
p
∂
i
1
It is through the cost structure that short-run and long-run decisions impact firms' profitability.
In the short run, firms can affect costs (as well as demand and profitability) only through changes in

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International Research Journal of Finance and Economics - Issue 31 (2009)
132
prices. In the long-run carriers can vary their cost structure through changes in the capital stock
(planes). Therefore, firm-level long-run costs are specified, as following:
−C (q (.),k ,lr,ω ) = C(q (.)lk ,ω ) + rk (2)
LR
i
i
i
i
i
i
i i
where: CLR(.) denotes the long-run cost function and C(.) the short-run cost function. Note that short-
run costs (or variable costs) depend only on quantity, given a capital stock (ki) and other fixed factor
prices (ω). In the long-run, the quasi-fixed factor (capital) becomes variable, that is capital can be
purchased at its factor prices r.
To endogenize the short- and long-run decisions, it is assumed that firms behave strategically: a
two-stage game is specified, where firms purchase capital in stage 1, followed by price decisions in
stage 2. Thus, in stage 2, each firm i solve the following program, as following:
max π = q (.)p − C(q (.)lk ,ω )
i
i
i
i
i
i
i
p
where: qi(.) is given in (1) and C denotes the short-run costs. Adopting a conjectural-variation
framework, where: θ = p
∂ / p
∂ , the corresponding first-order condition for firm i is given
i
i
by,
p − MC(.)
1
i
=
(3)
p
p
i
i
n − θ n
ij
ij
pi
q
∂ p
q
∂ p
where:
i
i
ii ≡ −
the own-price elasticity,
i
i
n ≡
is the cross-price elasticity
p
∂ q
ij
p
∂ q
i
i
i
i
andMC(.) ≡ C
∂ / q
∂ MC. Assuming that the parameter θ is identified, it can be estimated and
i
interpreted as the degree of coordination in a price-setting game. In particular, when θ = 0, behavior is
consistent with a Nash game in prices. In this case (3) reduces to the well-known relationship where
firms price according to their own elasticities. When θ<0 conduct is more competitive than Nash
behavior, with prices approaching marginal costs as θ ∞ . Collusive behavior is consistent with θ > 0.
Joint profit maximization, i.e. cartel pricing, is associated with a θ equal to one.
Let us denote the equilibrium prices defined by (3) as *
p (k ,l ) ji. The firms’ maximization
i
i i
problem for each firm i in stage 1 can then be written as,
*
*
*
*
*
max π = q (p ,p ,z )p − C (q (p ,p ,z )k lr,ω )
i
i
i
i
i
i
LR
i
i
j
i
i i
ι
ki
Omitting the functional arguments as well as the '*' for notational convenience, the
corresponding first-order condition is:
p
∂
⎡
p
∂
p
∂ ⎤
C
∂
i
i
i
q + (p − MC) Δ
+ Δ
−
− r = 0
i
i
⎢ i
i
⎥
i
k
∂
k
∂
k
∂
k
∂
i
⎣
i
i ⎦
i
q
∂
q
∂
q
∂
where:
i
i
Δ ≡
+
θ and
i
Δ ≡
are the respective partial demand elasticities including the
i
p
∂
p
∂
i
p
∂
i
i
i
conjectural variations. Note that under the assumptions on (1) Δi< 0 (since θ < 1). Making use of (3)
reduces the expression to,
p
∂
∂
j
C
(p − MC)Δ
−
− r = 0 (4)
i
j
i
k
∂
k
∂
i
i
As left with the direct effect of period one investment levels on costs,
k
−∂ / k
∂ − r and the
i
i
sequential strategic effect arising from the two-period set up,p − MC)Δ p
∂ / k
∂ . Whenever the
i
j
j
i
strategic effect is zero, there is no need to specify a two-stage setup, and only the direct effect of stage
one capacity decisions on (short-run) costs are considered. In this case (4) reduces to
C
−∂ / k
∂ = r and
i
i
both capacity and pricing decisions are modeled simultaneously. Note that C
∂ / k
∂ < 0 , since this is
i
the reduction in short-run costs from one more unit of capacity.

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International Research Journal of Finance and Economics - Issue 31 (2009)
Econometrically, the estimation of market power in such models would proceed by estimating
equations (1), (3), and (4) simultaneously. It is clear that estimation of equations (1) and (3) alone,
which assumes that capacity investment levels are exogenous, introduces simultaneity bias, and leads
to less efficient estimates. Furthermore, estimation of equations (1), (3) and (4) which ignores the
strategic two-stage set-up is subject to a potential misspecification in equation (4), leading towards
inconsistent estimates of market power and other elasticities. Below it is investigated whether the two-
stage set-up is appropriate by testing whether the sequential strategic effect is statistically significant.
Note that since(p − MC)Δ > 0 , the sequential strategic effect exists whenever p
∂ / k
∂ ≠ 0 .
i
j
j
i
Using the structure of the model we can solve explicitly for p
∂ / k
∂ . Implicit differentiation of (3)
j
i
with respect to ki and ki and solving, yields after some manipulations:
p
∂
∂
∂
j
MC
B
p
M
∂ C
A
i
=
and
=
(5)
2
2
2
2
k
∂
k
∂
A − B
k
∂
k
∂
A − B
i
i
i
i
MC
∂
where: A ≡ 2 −
Δ . Note that as long as MC
∂
/ p
∂ ≥ 0 . Then, A>0 and B>0 (this also guarantees
i
q
∂
i
i
that the second-order condition at stage 2 is satisfied). In addition, assuming own demand effect is
larger than the cross-demand effect, i.e. -Δi>Δj>0, we have that A>B which implies that the cross-
sequential strategic effect ( p
∂ / k
∂ ) is smaller in absolute value than the own-sequential effect
i
i
( p
∂ / k
∂ ). The fact that the own strategic effect dominates the cross strategic effect is a direct
j
i
consequence of the own-demand effect dominating the cross-demand effect. Finally, note that
sign{ p
∂ / k
∂
= sign p
∂ / k
∂
= sign M
∂ C / k
∂
.
i
i}
{ i j}
{
i}
Given the above, this relates to the taxonomy for two-stage games given in Fudenberg and
Tirole (1994). Since the second-stage game is in prices, strategic complements are obvious. According
to Fudenberg and Tirole (1994) this implies that whenever p
∂ / k
∂ > 0 there is a puppy-dog strategy,
i
i
which refers to a situation where firms under invest in capacity in order to be a less threatening rival.
Conversely, whenever p
∂ / k
∂ < 0 there is e a fat-cat strategy, where firms overinvest in order to be
i
i
less aggressive.
Since sign{ p
∂ / k
∂
= sign p
∂ / k
∂
= sign M
∂ C / k
∂
we have that MC
∂
/ k
∂ which is the
i
i}
{ i j}
{
i}
i
effect of capacity on the marginal costs in stage two, determines the sign and magnitude of how the
two-periods are linked. This is an important effect in the model, since whenever it is zero there is no
need to specify a two-stage game, since stage one variables have no impact on stage two decisions. In
this case the {sequential) strategic effect is zero and all choices are simultaneous. Whether the
sequential setup is relevant to estimate market power can therefore be tested through the significance of
MC
∂
/ k
∂ .
i
Moreover, the sign of MC
∂
/ k
∂ , will determine the direction of bias if a two-stage set-up is not
i
used. To illustrate this, let MC
∂
/ k
∂ < 0 , i.e. there is a fat-cat game where firms overinvest. Supposing
i
that in this case a certain amount of market power exists, this must be measured. Since market power in
the product market generally leads to increased capacity investment in stage one (Fershtman and
Gandal, 1994) marginal costs as well as prices will decline. From the second-order condition of stage 1
(Appendix), p
∂ / k
∂ − M
∂ C / k
∂ > 0 . In other words, marginal costs decline by more than prices when
i
i
i
capacity investment increases, which increases the price-cost margin. This implies that in the context
of (3) larger price-cost margin are associated with the same degree of market power θ. Consequently,
ignoring such feedbacks to the capacity stage, an upward bias in the measurement of market power
occurs.
The direction of bias is reversed whenever the capacity game is a puppy-dog. To see this let’s
assume that MC
∂
/ k
∂ > 0 , which implies that capacity increases marginal costs in stage two. From the
i

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International Research Journal of Finance and Economics - Issue 31 (2009)
134
second-order condition of stage 1 (Appendix), it stems that M
∂ C / k
∂ − M
∂ C / k
∂ < 0 that is marginal
i
i
costs increase by more than prices when capacity investment increases. This implies that smaller price-
cost margin is associated with the same degree of market power θ. The following remark summarizes
these arguments.
Remark: Whenever the capacity game can be categorized as a fat-cat (i.e. MC
∂
/ k
∂ > 0 and firms
i
overinvest) then a one-stage game would result in an upward bias in the measurement of
market power. Whenever the capacity game can be categorized as a puppy-dog
(i.e. MC
∂
/ k
∂ > 0 , and firms underinvest) then a one-stage game would result in a
i
downward bias in the measurement of market power. Finally, whenever MC
∂
/ k
∂ = 0 then
i
no bias exists. The sign and significance of MC
∂
/ k
∂ , a testable hypothesis follows.
i


4. Empirical Implementation
4.1. Functional Specification, Data and Estimation
The implementation of the above model involves the simultaneous estimation of the demand equation
(1) and the first-order conditions (3) and (4) subject to (8). The endogenous variables are therefore
prices, quantities, and capital (number of planes). The demand equation corresponding to (1) is
specified as follows,
q = α + α p + α p GDP + α GASOLINE + α GDP
i
0
1 i
2 j
i
3
i
4
i (1a)
+ α GCONS + α RAIL + α NETWORK + ε
5
i
6
i
1
i
ji
where: ε denotes the error term. The exogenous variables influencing demand are: an index of the price
of all other airlines (Pj), an index of the price of gasoline (GASOLINE), an index for the price of rail
transportation (RAIL), a measure of country size (GDP), a measure of economic activity - consumption
growth (GCONS), and a measure of the size of the carriers' network (NETWORK). The data and their
construction are described in more detail in Appendix. Summary statistics of the data are presented in
Table 1.

Table 1:
Data Statistics

Variable Mean
Minimum
Maximum
PI 1.151
0.740
1.855
QI 1.878
.5164
6.165
KI 90.652
23.500
241.000
PJ 1.137
0.768
1.364
PK 2.814
1.155
7.031
PL 2.454
0.368
4.583
PM 0.970
0.493
1.599
GASP 0.642
0.311
1.233
GDP 406.380
66.600
1488.210
GCONS 7.659
-0.900
23.700
PRAIL 0.048
0.0143
0.136
NETWORK 421.851
188.787
1072.390
PWTDEB 29.622
8.000
84.010
PTURBO 5.236
0
38.430
LOADF 63.805
53.489
72.700
STAGEL 11.478
6.495
19.313
Number of observations: 120

To complete the parameterization we must specify two more derivatives of the short-run cost
function (2). First, the short-run marginal cost equation ( C
∂ / q
∂ .) implicitly defined in (2) is assumed
i

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International Research Journal of Finance and Economics - Issue 31 (2009)
to be linear in capital, two factor prices: the price of labor and materials, as well as two cost
characteristics: the load factor and the stage length. That is,
C
∂ = MV = β +β k +β PL +β PM +βLOADF +β STAGEL
0
1 i
2
i
3
i
i
3
i
q
∂ i
Second, the effect of adding capacity to short-run marginal cost ( C
∂ / k
∂ .) is assumed to be
i
linear in output and two characteristics of capital: the percentage of wide-bodied planes in the fleet
(PWIDE), and the percentage of turboprop planes (PTURBO):
C
∂ = γ0 + γ q + γ PWIDE + γ PTURBO, (2a)
1 i
2
i
3
i
k
∂ i
This must be negative. Applying Roy's identity, the parameter on ki is constrained in the short-
run marginal cost equation to be equal to the parameter on output in the long-run marginal cost
equation, i.e. γ1=β1. Using the above functional specifications, we can substitute
Δ = α + θ ⋅(α + α GDP ) and MC into (3) yielding:
i
1
2
n
i
qi
p = β + β k + β PL + β PM + β LOADF + β STAGEL −
+ ε (3a)
i
0
1 i
2
i
3
i
4
i
5
i
2i
α + θ ⋅(α + α GDP )
1
2
22
i
where: ε2i is the error term. For the first-order condition for capacity investments in stage one (4) we
can substitute (2a) and (5) into (4), noting that under the above functional specifications A = 2 and Β =
-Δj/Δi, yielding:
Δ / Δ
j
i
(p − MC)Δ β
− γ − β q − γ PWIDE − γ PTURBO − r + ε = 0 (4a)
i
j i
2
0
1 i
2
3
i
3i
(Δ / Δ ) − 4
j
i
where: MC and Δi are as above and Δ = α + α GDP . Using these functional forms we estimate the
j
2
22
i
system of three equations (la), (3a), and (4a), which endogenize prices, output, and capacity, by
nonlinear three stage least squares. The results are presented in Table 2.

Table 2:
European Airlines - Two Stage Game

(Non-linear three-stage least squares estimates)
Variable Estimate
t-statistic
Demand Equation


INTERCEPT -1052.580
-2.16
Pi -1.284
-6.13
Pj 0.354
7.75
Pj*GDP -.065
-5.89
GASOLINE -.665
-.5.44
GDP 0.854
8.49
GCONS -0.798
-0.22
RAIL 0.487
7.87
NETWORK 0.167
1.76
Marginal Cost. (del dq.)


INTERCEPT -10.777
-0.52
Ki -0.024
-1.91
PL -17.329
-2.12
PM 4.615
0.70
LOADF 0.108
1.90
STAGEL -1.556
-1.52
Marginal Cost of Capital - ( C
∂ / k
∂ )
i


INTERCEPT 0.129
0.43
Qi -0.024
-1.91
PWTDE -9.086
-8.10
PTURBO 2.414
2.06
Behavioral Parameters

NASH Cartel
Θ
0.646 6.72
3.68

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International Research Journal of Finance and Economics - Issue 31 (2009)
136
4.2. Consistency Checks
Before interpreting the results, several consistency checks are performed on whether the theoretical
model is in line with the empirical estimates. These tests can be thought of as specification tests of
having chosen the "right" structure for the data in hand. Given that a considerable amount of structure
is imposed, there are a number of conditions which need to be satisfied but have not been imposed ex
ante. The purpose of this subsection is to investigate whether the "data reject the model".
As Table 2 shows, the demand estimates are in line with the maintained assumptions. Both the
own-price elasticity (-1.284) and cross-price elasticity (0.289 at sample mean) have the expected signs.
In addition, the maintained assumption that the own-price effect is larger in absolute value than the
cross-price effect is confirmed by the data at each sample point. Since this theoretical model of product
differentiation assumes that firms are monopolists in their respective niches, it follows that firms must
price in the elastic part of their linear demand schedules (Panzar and Rosse, 1987). The estimation in
Table 2 for the own-price elasticity of demand is -1.284 and therefore is consistent with the theory.
In addition, the estimates in Table 2 imply at all sample points that the partial own-demand
effect is negative (Δi< 0), which is sufficient for the second-order condition at stage 2 to be satisfied
(Appendix). Furthermore, the partial own demand effect (at all sample points) is larger in absolute
value than the cross-demand effect, i.e. -Δi>Δj>0. As mentioned in the previous section, this implies
that the cross-sequential strategic effect ( p
∂ / k
∂ ) is smaller in absolute value than the own-sequential
j
j
effect ( p
∂ / k
∂ ) and that they have the same sign.
i
i
Finally, there are some requirements for the stage one maximization problem to be well-
defined. A restriction that must be met is that the effect of capacity on short-run marginal costs is
negative, i.e. C
∂ / k
∂ < 0 , which ensures that the first-order condition (4) can be satisfied. In other
i
words, adding capacity must lower marginal costs in order for firms to have any incentive to invest in
capacity. Given the estimates in Table 2, it is found that C
∂ / k
∂ < 0 at all sample points. Furthermore,
i
the second-order condition for capital is also satisfied at all sample points, since
p
∂ / k
∂ − M
∂ C / k
∂ > 0 (Appendix).
i
i
i
In sum, the estimates in Table 2 are consistent with all the restrictions and maintained
assumptions of theoretical model developed above.

4.3. Interpretation of Parameters
The results given in Table 2 are interpreted in more detail. The price elasticity of demand is estimated
at -1.284 which indicates elasticity close to unity (in fact the estimate is statistically not significantly
different from one). As mentioned above, since a monopolist prices in the elastic part of a linear
demand function, the above finding is consistent with airlines exercising some degree of market power
in their respective market niches. The cross-price elasticity depends on GDP and is estimated at 0.289
(at the sample mean) which indicates that airlines are substitutes.
Many of the remaining parameters have the expected signs. For the demand equation GDP, the
price of railroad transportation and the size of the network all have positive and significant effects. The
price of gasoline has a negative effect on airline demand, indicating that automobiles and air travel are
complements. This might be explained by the fact that gasoline prices are highly correlated with fuel
prices. Consumption growth has a negative but insignificant effect on demand for air travel. The cost
parameters generally have the expected signs. For the marginal cost function capital has the expected
negative effect, the load factor raises marginal costs, whereas the stage length lowers marginal costs.
Unexpectedly, the price of labor has a negative effect on marginal costs, indicating a high degree of
factor substitution. Turning to the marginal cost of capital specification, we get the expected impact.
An increase in wide-bodied planes lowers marginal costs, and more turboprop planes raises marginal
costs.

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137
International Research Journal of Finance and Economics - Issue 31 (2009)
As already mentioned, the effect of capital on marginal costs, MC
∂
/ k
∂ , determines whether
i
the two-stage model can be reduced to a one-stage model. Since this effect is negative and significant
(t-stat of -1.91), a one-stage model in favor of the two-stage specification is rejected. In particular,
since MC
∂
/ k
∂ < 0 , it is found that empirically the game is consistent with a fat-cat strategy. In other
i
words, European airlines overinvest in capacities in order to be less aggressive. Moreover, using a one-
stage model without capacity competition, would lead to biased estimates of market power, since it
ignores the strategic linkages between competition in capacity and prices. Since empirically is found
that MC
∂
/ k
∂ < 0 , as well as, p
∂ / k
∂ − M
∂ C / k
∂ > 0 , it is expected the direction of bias to be
i
i
i
i
upward.
Turning to the measurement of market power in this two-stage set-up it is found that there is
some evidence to suggest that firms achieve market power through collusion. The estimated market
power index θ is .646. More importantly, it is significantly different from zero (Nash behavior), as well
as, one (Cartel behavior). Therefore, are rejected the hypothesis of Nash behavior (t-stat of 6.72), as
well as, Cartel behavior (t-stat of 3.68). This suggests that firms do exercise some form of market
power, although there is no evidence of cartel pricing. Using equation (3) the estimated mark-up over
marginal costs is equal to 91%, which is substantial. One measure of comparison is to compute the
mark-up for the case of Nash behavior. Setting θ = 0 (or equivalently ηij = 0) in (3) a mark-up of 78%
is obtained. Therefore, a 13% increase in the mark-up appears due to non-cooperative pricing in the
product market.
As already mentioned, ignoring the capacity stage would introduce an upward bias in the
measurement of market power. In order to quantify this bias in the context of the empirical
investigation at hand, it is interesting to compare the above results on market power to those which
would have obtained if one where to ignore the endogeneity of capital investment altogether. To do
this, the model is re-estimated reducing it to a one-stage, simultaneous move pricing game. In other
words we re-specify the first-order condition (3a) as:
qi
p = β + β PK + β PL + β PM + β LOADF + β STAGEL −
+ ε
i
0
1
i
2
i
3
i
4
i
5
i
2ι
α + θ ⋅(α + α GDP )
(3b)
1
2
22
i
where: k is replaced in (3a) with the price of capital PKi in order to have a well-specified marginal cost
function.
The new model to be estimated thus consists of equations (la) and (3b), which is the standard
two-equation structural model often used to measure market power. The estimated market power from
the one-stage set-up a substantially different: the market power index θ is now .944, which is
significantly higher than before and rather close to cartel behavior. In addition the direction of bias is
as expected.
To illustrate this bias in the estimated market power further, Table 4 summarizes the
comparison between the two alternative models in terms of mark-ups. As can be seen, the estimated
mark-up over marginal costs for the standard one-stage model is over 100%, which is almost 10%
higher than under the two-stage specification. By contrast, the difference in price-cost margins between
the two specifications for non-cooperative Nash behavior is very small, with only 2.5%. This implies
that while the two-stage model associates only some 13% of the estimated mark-up with non-
cooperative behavior, a standard one-stage model would attribute almost 20% of the mark-up with
collusion.

Table 3:
Market Power, Demand Elasticities and Price-Cost Margins under Alternative Specifications

Price-Cost Margin (under non-
Estimated Price-
Demand Elasticity

Market Power (θ)
cooperative behavior, θ = 0)
Cost Margin
(nii)
One-Stage Game
80.6%
100.1%
.94
1.24
Two-Stage Game
78.1%
91.3%
.65
1.28
The estimates reported in the demand equation are converted into elasticities. Number of observation: 120

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International Research Journal of Finance and Economics - Issue 31 (2009)
138
In sum, it appears that firms’ market power is significantly overestimated whenever capacity
competition is not accounted for.


5. Conclusions
The scope of this paper was to investigate whether the inferred significant degree of market power at
the product market level is sensitive to the introduction of an input variable, namely capacity. In other
words, does endogenous capacity effect the conclusions about product market competition?
To test this assessment a structural model was specified and estimated which accounted for
competition in two variables: capacity and prices. Then, this model -demand, cost (short and long run),
and conduct – was estimated for the European Airline Industry using data for the period of 1993-2007.
A number of specification tests were performed and reject a simple one-stage specification in favor of
a two-stage set-up. Regarding the measurement of market power in the product market, it was found
that some degree of market power exists. However, market power in the two-stage set-up was
significantly lower than in the more widely employed one-stage specification, which was consistent
with the direction of bias in fat-cat games. This illustrates that firms market power in the product
market was significantly overestimated whenever capacity competition was not accounted for and that
the Bresnahan’s claim that "there is a great deal of market power, in the sense of price cost margins, in
some concentrated industries" may partially be due to the fact that input markets were not been
properly endogenized.
There are several implications of the above findings. Combining these results with other
findings that European carriers have a substantial cost disadvantage vis-à-vis their U.S. competitors
(Good, Roller and Sickles, 1993) it seems likely that most of the benefits from European liberalization
will come from the elimination of cost inefficiencies. This is especially so in light of the above model
where market power is even smaller, once capacities are endogenized. Given that prices are not high
because of outright cartel pricing, airline prices in Europe might come down more gradually as
efficiency increases and market niches are abolished.

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