Philippe Gagnepain

Pedro L Marín

The e¤ects of airline alliances: What do the aggregate data say? 1

Keywords: Alliance, airline, cross-price elasticities. JEL: L11, L13, L41

We consider an empirical model of worldwide airline alliances that we apply to a large set of companies for the period 1995-2000. Using observations at the network level, we estimate a cost, capacity, and demand system that accounts for crossprice elasticities. Our contribution consists in evaluating airlines'strategical interactions through the window of …rms' network interconnections. We consider networks coincidences and potential connections with all their rivals. The results allow us to classify all company pairs as either complements or substitutes. We shed light on the fact that many airlines involved in the same alliance are potential substitutes.

Introduction

Using aggregate data at the airline level, we analyze worldwide airline alliances. We suggest that airlines inside alliances cut prices by 5% on average. We also propose an empirical model that allows us to evaluate to which extent two airlines'networks are substitutes.

We suggest that a signi…cant number of airlines enrolled in the same alliances o¤er services which can be considered as substitutes, and this could lead to anti-competitive practices.

We also evaluate price cost margins for each alliance and shed light on whether these margins obey some Nash pricing behavior.

There is increasing evidence suggesting that strategic alliances between otherwise independent …rms have become commonplace in a wide variety of industries. According to [START_REF] Oster | Modern Competitive Analysis[END_REF], a strategic alliance could be de…ned as an arrangement in which two or more …rms combine resources outside the market in order to accomplish a particular task or set of tasks. In the airline industry, deregulation has triggered several waves of alliances between worldwide airlines. Alliances between airlines are mainly designed to achieve ‡eet rationalization, expansion and rationalization of network structure as well as greater exploitation of cost economies. In particular, international airlines have the opportunity to extend their networks to foreign countries by entering an alliance agreement with a foreign airline. By coordinating their services or production processes, alliance partners can o¤er greater convenience to consumers, including access to connecting services, greater e¢ ciencies and procedural operations in ticketing, ground handling and baggage handling, expanded route networks and connecting options.

Airlines can engage as well in cooperative pricing, while enjoying antitrust immunity.

Strategic alliances in the airline industry have attracted more antitrust attention than any others. 1 Many types of alliances have been adopted by airlines, ranging from agreements that involve relatively little cooperation such as frequent ‡yer programs to agreements commonly known as code sharing practices that involve the sharing of costly assets such as planes, terminals, counters, crews and more (see [START_REF] Oum | Airline alliances: Current status, Policy issues, and Future Directions[END_REF], for more details on the forms of alliances in the airline industry). Code sharing arrangements have been until very recently the most popular form of alliance adopted by airlines. In this case, two companies operating two connecting routes o¤er an interline trip that is ticketed as 1 The European Commission Article 81 and 82 Treaty states that the Commission can exempt an alliance if it considers that the economic e¢ ciencies and overall bene…ts of the transaction outweigh the anti-competitive e¤ects.

The rest of the paper is organized as follows: The next section presents a discussion of the data we use and the associated methodology. Section 3 proposes to construct airlines' network substitution indexes. Section 4 presents the basic capacity, demand and cost ingredients which are inherent to our airline model. Section 5 focuses on the empirical implementation of the model. In particular, functional forms and the estimation procedure are presented. We develop in this section the procedure we use in order to model the price demand interactions between the di¤erent companies' networks of our dataset. Section 6 discusses our estimation procedure. In particular, we present the instruments we use to proxy airlines'fares in the demand equation. Section 7 is dedicated to the description of the dataset and the construction of the variables. Section 8 presents the estimation results. Section 9 proposes an evaluation of competitive forces in the industry. Finally, Section 10 concludes.

Discussing the data and the model

In what follows we specify a model of airlines' behavior that entails estimating the international demand faced by each airline as well as its technology. The ideal modelling approach consists in working at the airline-route level. This approach has been followed by [START_REF] Borenstein | Hubs and High Fares: dominance and market power in the U.S. airline industry[END_REF], [START_REF] Oum | The E¤ects of airline Codesharing Agreements on Firm Conduct and International Airfares[END_REF], [START_REF] Brueckner | The Price E¤ects of International Airline Alliances[END_REF], [START_REF] Brueckner | The Economics of International Codesharing: An Analysis of Airline Alliances[END_REF][START_REF] Brueckner | International Airfares in the age of Alliances: the e¤ects of Codesharing and Antitrust Immunity[END_REF], or [START_REF] Whalen | A panel data analysis of code-sharing, antitrust immunity, and open skies treaties in international aviation markets[END_REF], where a speci…c market is an origin destination pair. Given that airlines take di¤erent price and capacity decisions on each market they operate, working at the airline-route level allows the researcher to observe and account for each market characteristics such as the number and identity of the competitors, the length of the route, or the prices of each product available.

In this paper, we are interested in shedding light on alliance e¤ects on airlines'behavior at a more aggregate level, i.e., at the airline level. Our motivation is twofold: First, the researcher focusing on non-U.S. airlines is usually constrained by the quality of the data available, which makes any work at the airline-route level unfeasible. 2 Second, we aim 2 Data at the airline-route level are provided by the U.S. Department of Transportation. The database allows observing only interline trips where at least one route segment is ‡own on a U.S. airline. This implies for instance that it contains information on the United-Lufthansa or United-SAS pairs, but it does not on the routes jointly operated by Lufthansa and SAS. Data at the airline-route level for airlines outside the U.S. are in general very limited. For instance, the world air transport statistics published by the International Civil Aviation Organization (ICAO) and the Air Transport Association (IATA) do not contain observations on ticket prices at the route level.

at advocating the idea that airlines may take corporate and strategic decisions at the entire network level. An airline enters an alliance in order to expend its network overseas to destinations points that it could not reach otherwise, because of the high …xed costs induced, or because most countries do not permit cabotage by foreign companies. The decision of an airline to join an alliance and eventually …nd appropriate solutions to reorganize its productive structure a¤ects its operating costs and the demand it faces at the network level. Airlines serve a large number of interconnected routes that form a network. Sometimes consumers buy a company's service in one single route (what is known as a direct ‡ight) but very often they buy sets of (normally two or three) interconnected routes (indirect ‡ights through one or two hubs). Additionally, when buying a ticket in an individual route, frequent consumers take into account the company's network size and characteristics, since this a¤ects the ‡exibility to make further interconnections if needed, exchange tickets, take alternative routes and even enjoy frequent ‡yer prizes and discounts. Scope economies among routes and network e¤ects (almost) impose a common policy to all the routes served by a given airline. 3In other words, we aim at proposing a di¤erent approach based on aggregate data which attempts to derive lessons at the airlines'network level rather than the route level.

We propose two main contributions: First, we test for the impact of the formation of alliances on airlines annual prices and costs. We suggest that price reductions due to alliances are strong enough so that they can be identi…ed through annual prices. We …nd no empirical evidence however of a direct e¤ect of alliances on airlines' operating costs. Second, we propose an original demand framework that accounts for the intensity of competition in each airline's main hub. In particular, we account for the proportions of overlapping and connecting route kilometers between two airlines' main hub. We identify a substitution index cut-o¤ above which two airlines'networks can be considered as substitutes.

The dataset has been constructed for the period 1995-2000 from raw data included in reports. The companies under study are worldwide airlines with special attention to the U.S. and the E.U. airlines, which usually constitute the main alliance partners. Some of the airlines belong to international alliances and some others operate as independent airlines. The dataset includes observations for a total of 55 airlines, as shown in table 1.

Table 2 presents a list of the di¤erent alliances members.

A measure of network substitution

We propose a methodology based on airlines' total networks. We de…ne …rst in this section a measure of substitution between two airlines'networks. To illustrate our aim, we present an example in Figure 1, where …ve airlines operate services on …ve networks. Some networks have no overlapping routes: This is the case for instance of network 1 and 2, which have a city (I) in common, but no overlapping routes. These two networks are said to be complements. As the number of overlapping route kilometers between two networks increases, so does the degree of substitutability between them. Networks 1 and 3 have one route in common; in particular, they share two cities, B and I. Networks 1 and 4 have two routes in common, given that they both operate at cities B, I, and H. Finally, networks 1 and 5 share all routes (cities A, B, I, and H), which makes them perfect substitutes.

Hence, counting the number of route kilometers that two networks have in common allows us to derive a substitutability index between two networks. This in turn enables us to shed light on the degree of substitutability between two (average products of) airlines.

Note however that, due to data restriction, we do not have detailed information on the activity of airlines on each route they operate. We are nevertheless able to observe airlines' operations in their respective hub. This is a potential drawback, since we do not observe the entire activity of an airline, but we are con…dent that the observation of airlines' activity through their hubs provides a fair instrument, as the hub is the center of gravity of airlines'operations. 4In …gure 2, we illustrate how the measure of the airlines'network substitutability can be translated at the level of airlines'hubs. Consider two airlines 1 and 2 with respective hubs H 1 and H 2 ; from which they operate their services. In 2.a., the number of overlapping routes between 1 and 2 is at its minimum level, i.e., airline 1 (2 resp.) does not propose any service in 2's (1's resp.) network besides the route that links H 1 and H 2 . The two airlines'services are said to be complementary in this case, and it is very much alike the case of networks 1 and 2 in Figure 1. In 2.b., Airline 1 (2 resp.) may decentralize a share of its operations to H 2 (H 1 ), increasing thus the degree of substitutability between 1 and 2's operations. This situation is similar to the networks pairs 1-3 and 1-4 above.

Finally, in 2.c., both companies' hubs coincide, setting the degree of substitutability of both activities at the maximum level, as in the case of the network pair 1-5 above.

We construct our substitution index as follows: Consider two airlines i and j. We suggest that the degree of substitutability (complementarity resp.) between the total operations of two airlines i and j increases (decreases resp.) with the share of route kilometers departing from i and j's hubs and that i and j have in common. De…ne O ij as airline i's hub route kilometers also served by airline j. Likewise, de…ne O ji as airline j's hub route kilometers also served by airline i. Moreover, denote as T i (T j ) the total hub route kilometers for airline i ( j). Hence, the substitution index is de…ned

as O i j = (O ij +O ji )
(T i +T j ) : Note that a higher degree of substitution between i and j implies therefore that O i j increases.

We proceed in a similar fashion to construct a complementarity index between both airlines i and j. De…ne as C ij the quantity of airline i's hub route kilometers not served by airline j; and C ji the quantity of airline j's hub route kilometers not served by airline i. Provided with these components it is possible to de…ne C i j = (C ij +C ji ) (T i +T j ) : Hence, a higher degree of complementarity between i and j implies therefore an increase of C i j .

Moreover, C i j = 1 O i j .

From our 55 airlines, we determine all the possible airline pairs. Out of the 1485 possibilities, 444 pairs are characterized by overlapping activities. We calculate the substitution index O i j for each of them. Table 3 presents a list of the 87 airline pairs with the highest indexes. Some of these airline pairs present high substitution indexes because they operate from the same hub. This is the case for instance of All Nippon and Japan airlines (Hub: Tokyo), British Airways and Virgin Atlantic (Hub: London), Aeromexico and Mexicana (Hub: Mexico City), or Air Europa and Spanair (Hub: Madrid). Other pairs operate from distinct hubs located in the same domestic markets: Delta and TWA (Hubs: Atlanta and St Louis), and Air Canada and Canadian Airlines (Toronto and Calgary) for instance. Finally, one observes pairs of airlines with distinct hubs located in di¤erent countries. High substitution indexes in this case imply that these airlines operate a signi…cant share of their total activity in their competitor's hub. Examples are Qantas and Thai (Hubs: Sydney and Bangkok), and British Airways and United (Hubs: London and Chicago).

Determining whether two airlines' operations can actually be considered as substitutes or complements requires the de…nition of a substitution index cut-o¤. This can be achieved through the estimation of a demand function for world airlines'operations, which constitutes the core of the analysis presented in this paper.

Cost, capacity, and demand

An airline o¤ers a speci…c capacity determined by the total number of seats available in the airplanes, and the total mileage performed. Based on this supply and prices, consumers make optimizing travel decisions that consist of a particular number of trips. Hence, as already suggested by numerous authors, passenger-trips are not as much under the control of operators, and airlines are concerned by the capacity to produce a potential for trips (See [START_REF] Berechman | Public Transit Economics and Deregulation Policy[END_REF]. In other words, costs and revenues are driven by two di¤erent variables that are closely related. It is thus crucial to disentangle the capacity supplied, Q, and the level of transport services requested by the customers, q.

Since the capacity supplied must at least meet the highest peaks of tra¢ c, demand never saturates the network capacity on average. On the other hand, the capacity must be adjusted to the level of demand, so the former is endogenous to the latter. Here we do not present a complete model of optimal provision of transport services. Instead, we simply introduce a reduced form of a technical adjustment process between capacity and demand according to the relation that we specify as follows:

Q i = (q i ; ); (1)
where is a vector of parameters to be estimated. This equation just approximates how engineers adjust the network size and structure to the demand level on annual basis.

For the speci…cation of the demand function, we follow the classical guidelines. Assume that from consumer n's indirect utility associated with the consumption of air transportation we can derive the individual long-run demand function:

q i (p i ; p j ; m i ; ); i = 1; :::; N; j 6 = i;

(2)

where is a vector of parameters. Firm i's aggregate demand q i depends on its own price, p i , competitors'prices p j , as well as market exogenous characteristics m i . A limited number of competitors meets in each route, with the combination of competitors changing from one route to another. Di¤erent competitors supply alternative products which di¤er in time schedule, number of stops, availability of interconnections with other ‡ights, etc.

In addition, at the two ends of each route start other routes that can be served by the same or a di¤erent set of airlines. Accordingly, the services o¤ered by di¤erent airlines can be regarded either as imperfect substitutes or complements. By assuming the same pricing policy for all the routes served by one company, we are implicitly saying that p j represents the price asked by the di¤erent …rms in the market, and this price accounts for the fact that the routes served by …rms are complements or substitutes of those served by …rm i. The price elasticity associated with this reduced-form demand corresponds to an estimate of the long-run elasticity, when capacity has been fully adjusted.

Moreover, airlines are endowed with a given technology. In order to provide a given amount of service, Q i , an airline must buy variable inputs, namely, labor, L i and materials, M i , which productivity depends on network exogenous characteristics, z i . The production process and its underlying technology can be implemented through a long-run dual cost function. Denoting by w L and w M the price of labor and materials, the cost function is:5

C i = C(Q i ; ! i ; z i ; t; ALL i ; ); ( 3
)
where t is a trend, and is a vector of parameters denoting technology. Note moreover that we test for the alliance e¤ect on the company's costs. ALL i is a dummy variable that takes value 1 if the observed airline is part of an alliance, and 0 otherwise.

Our econometric model comprises three equations in a block-recursive structure, so that each equation can be estimated separately. The lower level provides the demand of transport that explains the demand (usage) of transport in terms of the transportation price, which is endogenous, and needs to be proxied. We will go back to this point below.

The middle level is constituted by Equation ( 1) that provides a relationship between demand and capacity (or supply). This equation just says that, at each period, one can identify the engineering function that has been used to set up the network structure in terms of size. The upper level is made of the cost function, which relates cost to capacity and to other elements like the inputs prices and the e¤ect of alliances.

Note that we do not attempt to estimate …rms'pricing strategy simultaneously with our aforementioned equations. The reason is that, since we work at the aggregate level, making any assumption on the "average" pricing conduct of airlines would not help to improve the quality of our estimates. We will provide further discussion on this aspect in Section 9.

Empirical implementation

The next step consists in proposing speci…c functional forms for our three equations. In particular, we explain how our demand function identi…es the cross price e¤ects between each pair of airlines observed in our database.

The demand equation corresponding to (2) is speci…ed in linear form as follows

q i = 1i + 2i p i + X j6 =i i j p j + m m i + u qi , i; j = 1; :::; N; (4)
where u qi is an error term. Notice that we allow the intercept 1i and the own-price e¤ects 2i to vary across airlines. Moreover, we account for …rms' cross-price speci…c e¤ects i j . These characteristics imply a matrix of own and cross-price e¤ects @q i @p j that can only be estimated imposing some constraints. Following the approach suggested by [START_REF] Jaumandreu | Modelling Price Competition Across Many Markets (An Application to the Spanish Loans Market)[END_REF], we assume that own-price and cross-price e¤ects must follow some pattern.

First, we assume that the intercept and the total own-price e¤ect of each airline are proportional to the size of its own network. Accordingly, we de…ne 1i = 0 + 1 N ET i and 2i = 2 N ET i , i.e., we assume that the own rate e¤ect of an airline depends on the size of its operations.

Second, the total cross-price e¤ect of a rival j depends on the extent to which j's network is a substitute or a complement to i's network. We therefore weight airlines' coincidences and potential connections with all their rivals. In particular, we de…ne i j = 3 O i j + 4 C i j , where 3 and 4 are the common cross-price e¤ects and O i j and C i j are the two overlapping and connecting indexes de…ned above. We expect 3 and 4 to be positive and negative respectively, i.e., a higher proportion of overlapping route kilometers O i j (connecting route kilometers C i j resp.) between two airlines i and j makes it more likely for these airlines to be substitutes (complements resp).

De…ning p o ij = O i j p j , and p c ij = C i j p j , expression (4) can be transformed into an equation with only two cross-price parameters 3 and 4 to be estimated,

q i = 0 + 1 N ET i + 2 N ET i p i + 3 X j6 =i p o ij + 4 X j6 =i p c ij + m m i + u qi , i; j = 1; :::; N: (5)
Note that the whole matrix of own and cross-price e¤ects can be recovered from this estimation for a given set of values of N ET i , the O i j and C i j variables, and the coe¢ cients. Moreover, we de…ne the cut-o¤ value O i j from which two airline i and airline j can be considered as substitutes: We need i j > 0, i.e., O i j > O i j = 4 3 4 . Likewise, two airlines are complements when O i j < O i j = 4 3 4 . We turn now to the two other equations. We assume a Cobb-Douglas speci…cation for the cost function in (3). This speci…cation retains the main properties desirable for a cost function and provides a su¢ ciently precise description of the technology, while remaining tractable for our purpose. 6 The cost function is then speci…ed as

C i = 0 ! 1 Li ! 2 M i Q 3 i z i exp( t t + A ALL i + u ci ) (6)
where u ci is an error term. Homogeneity of degree one in input prices is imposed, i.e.,

z i = N ET 4 i ASL 5 i : (7)
Note that the average stage length measures the length of the average route operated by an airline while the network size adds the lenght of all routes of the airline's network.

With respect to the relationship between demand, q i, and supply, Q i , represented in (1), we assume the following functional form,

Q i = 0 q 1 i exp(u Qi ); (8)
where u Qi is an error term.

Estimation

We estimate the sequential system of equations ( 5), ( 6) and (8). Since prices p i in the demand equation ( 5) are endogenous, we need to …nd some instruments. We use as instruments for p i a trend t, the national private consumption in the airline's country of origin, P RIV i , the size of population of the airline's country of origin, P OP i , wages ! Li , a measure of competition COM P i , and a dummy indicating whether the airline belongs to an alliance or not, ALL i (All these variables are discussed in more details in the next section). Hence, we estimate the following additional equation:

p i = p (ALL i ; P RIV i ; P OP i ; ! Li ; COM P i ; t; ) , i = 1; :::; N; (9)
where is a vector of parameters. Several comments are worth emphasizing: First, note that we test whether alliances have any impact on the global average price set by airlines using a simple dummy, in a similar fashion as in the cost equation. This procedure is similar to the one used by Brueckner and Whalen (2001) and [START_REF] Whalen | A panel data analysis of code-sharing, antitrust immunity, and open skies treaties in international aviation markets[END_REF] with two di¤erences: They measure the e¤ects of codesharing and immunity agreements on prices while we rather focus on the e¤ect of being a member of an alliance without specifying with precision the nature of the agreement. Moreover, as already mentioned, these authors work at the route (market) level while we focus on economic indicators aggregated at in the cost function and for evidence on their e¤ects on airlines' productivity. A measure of airport concentration was included in an alternative speci…cation but it turned out to be highly correlated with the size of the network.

the network level. Note however that they consider that the codesharing and immunity agreements apply to all the products o¤ered by airlines while in practice these agreements are e¤ective in some speci…c markets only. In a sense, this "generalization" of airlines' cooperative behaviors generates an average e¤ect on prices that is, to some extent, similar to our measures.

Second, entering an alliance is a decision of the airline and this has several consequences in our model: We should proxy the alliance variable A i since it is most probably endogenous. This is however a di¢ cult task due to the fact that very few instruments are left in our database. We run several logit estimations on the choice of entering an alliance and obtained results where a trend, airlines'wages, and the (1995) airlines'network size signi…cantly a¤ect the probability to enter an alliance. Unfortunately, these instruments create important collinearity problems once prices are proxied in the demand equation.

We therefore decided to discard the idea of proxying the decision to enter an alliance.

Further comments on the logit estimation results are provided in section 8.

Another consequence is that the overlapping and connection indexes O i j and C i j may themselves be decision variables of airlines. In order to avoid endogeneity problems at this level, we keep both O i j and C i j …xed over time, i.e., we use the initial 1995 indexes to proxy the degree of substitution and connection between airlines over the whole period of observation.

Finally, we compute several robustness checks to test the validity of our estimates of own and cross price elasticities. We show that the own elasticities do not vary much when prices are proxied or not. We also try other speci…cations of the demand equation. In particular, we replace N ET i in the expression of the constant and the own price parameter by the number of airline's ‡ights departures DEP i and the number of routes ROU T ES i .

We suggest that these changes entail minor variation in the results.

Variables de…nition

The variables have been constructed as follows. In the cost function, total costs (C i ), production (Q i ), wages (! Li ), and average stage length (ASL i ) correspond to total operating expenses, seat-kilometers available, ‡ight crew salaries and maintenance and overhaul expenses over number of employees, and total aircraft kilometers over total aircraft de-partures (DEP i ), respectively. With respect to total costs, companies report one single …gure that corresponds to passengers, freight and mail activities. The distribution of operations among these three activities can vary signi…cantly among companies. However, it is easy to obtain information on the total number of tons-Kilometers performed that correspond to passengers (including baggage), freight and mail, respectively. We multiply total costs reported by each company by the share of tons-kilometers performed corresponding to passengers in order to compute our cost variable (C i ).

The variable N ET i is the total number of route kilometers an airline operates on all its di¤erent routes (ROU T ES i ). Finally, the price of materials (! M i ) has been constructed

as the average fuel prices at the airline's home country and at the OECD, weighted by the company's domestic and international operations respectively.

On the demand side, demand (q i ) corresponds to passenger-kilometers performed, and prices (p i ) are measured as passenger revenues over passenger-kilometers performed.

The home country exogenous characteristic m i is domestic private consumption P RIV i .

Finally, t the time trend, is equal to one in 1995 and incremented by one each year.

We also construct a competition index COM P i for each airline i, which accounts for the number and the intensities of coincidences of i's network with other airlines' networks. We have de…ned previously the substitution index

O i j = (O ij +O ji ) (T i +T j )
as the share of route kilometers departing from two airlines i and j's hubs and that i and j have in common. Summing O i j over all airlines j which coincide with i, we obtain a measure of the competition index, COM P i = P j O i j for airline i. Thus, airline i faces a higher competitive pressure if COM P i increases, i.e., if i shares a higher quantity of route kilometers with its competitors.

Finally, we need to construct a variable to account for the alliance e¤ects in the price and cost equations. Airlines cooperate with partners who are the members of the same alliance, i.e., ONE, SKY, STAR, WINGS, and QUAL. We construct a dummy ALL i which takes value one if the observed airline is a member of any of these alliances, and zero otherwise. Note that it is implicitly assumed that being a member of one of these alliances entails that an airline sets cooperative prices in all the markets where it is present.

Demand elasticity and costs

Tables 5 to 11 provide the results for the econometric model. Prior to estimating the demand function (5), we need to obtain estimated prices pi through the price equation ( 9). As a by-product, we test several price determinants, as presented in Table (5). We obtain price outcomes that are similar to the empirical results obtained by [START_REF] Brueckner | The Price E¤ects of International Airline Alliances[END_REF] and [START_REF] Whalen | A panel data analysis of code-sharing, antitrust immunity, and open skies treaties in international aviation markets[END_REF], although these authors work at a more disaggregated level, i.e., on a market (route) basis. First, note that prices decrease at an annual rate of 4 to 7% as suggested by the trend. Second, prices are higher, on average, if the domestic private consumption inside the home country of the observed airline is more important.

Third, the size of the population of the home country of the observed airline and the price are inversely related, which suggests that this variable is a potential proxy for the quantity of passengers-kilometers carried.

Note that the average wage paid to the employees of the airline is not a relevant determinant of the price, suggesting that a direct connection between airlines'prices and costs is potentially loose. Whether or not an airline is a member of an alliance has a signi…cant impact. On average, prices are 5 to 6% lower under alliances. This is an interesting result, given the highly aggregated nature of the data. Although airlines establish strategic price interactions on a market to market basis, prices reductions are important enough so that these reductions can be identi…ed in annual average prices at the airline level. Interacting the alliance variable with our measure of competition yields the expected negative results, i.e., prices are lower for alliance members facing a higher competitive pressure.

As suggested previously, we also estimate the decision of airlines to enter an alliance. 8 Replacing ALL i in the price equation by this estimated probability reduces signi…cantly the magnitude of the alliance e¤ect (-1% instead of -5%), although the alliance outcome remains negative and highly signi…cant. This suggests a potential endogeneity bias: Airlines entering alliances may enjoy lower costs than those not entering. In particular, the former may be more e¢ cient and/or larger …rms. Not accounting for this issue may lead to an overstatement of the alliance e¤ects on prices.

From the di¤erent price speci…cations in Table 5, we derive measures pi which are in- 8 The estimated probability to enter an alliance is Pr = 30:62 troduced in our demand equation. Tables 6-8 present the results for the demand equation.

Table 6 shows the results of the demand equation ( 5). In Tables 7 and8, we produce alternative estimates obtained from the estimation of (5) where N ET i is replaced by the number of routes, ROU T ES i , and the number of departures DEP i , respectively. All the coe¢ cients have the expected signs. As expected, demand increases signi…cantly with the size of the network, the number of aircraft departures, or the number of routes operated.

Likewise, private consumption growth a¤ects positively demand. The own price parameter 2 is negative and signi…cant, and do not vary much depending on whether the size of the network, the number of routes, or the number of departures enter the speci…cation of the own price demand elasticity. Note moreover that, from Table 6, plugging into the demand function the real observed price p i (Column A) or the estimated pi (Columns I to V) do not a¤ect much 2 . With respect to cross price estimates, it appears that 3 ( 4 resp.) is positive (negative resp.) and signi…cant. This result suggests that a higher proportion of overlapping route kilometers between two airlines i and j makes it more likely for these airlines to be substitutes. Likewise, a higher proportion of connecting route kilometers between two airlines i and j makes it more likely for these airlines to be complements.

From the estimation of the own price parameter 2 obtained in Tables 678, we evaluate the own price demand elasticity as ii = 2 N ET i p i q i : We obtain estimates between 1:51 and 1:99 for the average airline over the period considered.9 More interestingly, using the cross price demand parameters 3 and 4 , we derive the substitution cut-o¤

O i j = 4 3
4 above which two airlines can be considered as substitutes. From the demand results c 3 and c 4 obtained in Table 6 (7 and 8 resp.), the cut-o¤ O i j is 0.180 (0.113 and 0.077 resp.)10 Hence, substitute airline pairs are those for which O i j 0:180 (0.113 and 0.077 resp.) in Table 3, i.e., we identify 12 substitute airline pairs (31 and 57 resp.), which represents 2.7% (6.9 and 12.8% resp.) of the airline pairs characterized by overlapping activities.

Table 9 identi…es the pairs of airlines whose services are substitutes. Airlines pairs which are members of the same alliances over 1995-2000 are underlined. Airline pairs which become members of the same alliance after our period of observation are underlined and in italic. Interestingly, a signi…cant number of pairs of substitute airlines belongs to the same alliance, which may lead to softer competition and higher prices. Among the pairs with the highest substitution index are SAS and Thai, (Star Alliance from 1997), Continental and Delta (Skyteam from 2004), or Canadian Airlines and Cathay (OneWorld from 1999). Note also the presence of the pair American Airlines-British airways (OneWorld since 1998) which required antitrust immunity on transatlantic routes in 1997 and 2001 without success, or the pair Lufthansa-United which got granted antitrust immunity in 1997 under very speci…c restrictions on some particular routes such as Washington/Frankfurt and Chicago/Frankfurt.11 More recently, the European Commission opened two antitrust proceedings against these four airlines together with other members of Star Alliance (Air Canada and Continental) and OneWorld (Iberia) in relation to cooperation on transatlantic routes. 12 The Commission is willing to assess whether cooperation among these airlines may lead to restrictions of competition on certain routes.

These cases illustrate that a methodology based on network substitution such as the one presented in this paper may be a relevant tool for regulators when deciding whether or not two airlines should be allowed cooperative arrangements. We turn to the capacity and cost side of our results.

Table 10 presents the demand-capacity relationship. Again, the coe¢ cients are signi…cant and have the expected sign. Table 11 presents the estimates for the cost function. All the parameters are signi…cant and have the expected sign. Costs increase with wages and production. The production process is characterized by increasing returns to scale since the production parameter 3 is signi…cantly lower than 1. The coe¢ cient of the time trend is negatively signed, suggesting the presence of technological progress. Airlines' network size and average stage length have a negative impact on operating cost. Thus, companies with larger networks and/or longer routes enjoy a signi…cant cost advantage.

Finally, we also introduce in the cost function our alliance (ALL) dummy variable to test whether airlines'operating costs are reduced if airlines enter into cooperative agreements.

The results suggest that alliances have no direct e¤ect on cost since the ALL e¤ect is not signi…cant.

Hence, it seems that alliances between airlines reduce prices signi…cantly but they have no direct e¤ect on costs. We expect however alliances to have a positive impact on the quantity of passengers kilometers carried [START_REF] Whalen | A panel data analysis of code-sharing, antitrust immunity, and open skies treaties in international aviation markets[END_REF], which in turn leads to a decrease of airlines' average costs due to the presence of economies of density. Thus, alliances mostly increase the ‡ow of passengers inside the existing network, and thus reduce airlines'costs, but they do not a¤ect airlines'cost technology.

The competition e¤ect of alliances

We propose now to discuss further our previous …ndings in light of the average competitive behavior of each airline. Provided with the demand, capacity, and cost estimates, we measure the degree of competition in the industry after the introduction of alliances.

We evaluate alliances'marginal costs and margins and shed light on whether the pricing behavior of airlines which are members of alliances is similar to a hypothetical Nash pricing behavior.

Provided with the cost and demand ingredients, each airline solves the following program, max

q i i = q i p i C(Q i ; ! i ; z i ); (10)
where q i is the optimal quantity to be chosen, and Q i = (q i ; ). The …rst order condition for …rm i, which entails Nash pricing, is given by

p i 0 (q i ) M C i p i = q i p i @p i @q i ; (11)
where

M C i = @C i @Q i and 0 (q i ) = @Q i @q i :
Using the estimates of the cost, capacity and demand system obtained in the previous section, we can evaluate the price-cost margins

M i = p i 0 (q i ) M C i p i
, and test these margins against those that could be obtained if airlines obeyed to Nash behavior, as described by the right-hand side of (1). Under Nash, …rms set prices independently, since each …rm i only cares for its own demand q i .13

From the expressions of demand (5), capacity (8) and costs (6), the price …rst-order condition under Nash behavior can be rewritten as

p i 1 Q i q i M C i p i = q i p i 1 1 : (12)
Through the estimation of the cost function, the marginal costs M C i can be easily

recovered since M C i = 3 C i Q i .
Putting them together with our estimate of the capacitydemand elasticity 1 , as well as the observed values for supply, demand and prices, we are able to evaluate the price-marginal cost margin M i set by each airline. We refer to M i as the actual margin since it directly depends on the observation of p i , q i , Q i , C i and the parameters 1 and 3 .

Table 12 presents the estimated values for marginal costs M C i , and margins M i , for all …rms and alliances. Several results are worth emphasizing.

First, the average airline enjoys a positive margin. Second, distinguishing companies belonging to alliances from companies outside alliances, it seems that companies within alliances obtain higher margins. However, these companies set lower prices and face lower marginal costs. Note that this latter result (lower marginal costs) is not inconsistent with the non-signi…cant alliance e¤ect on costs which is presented in Table 11. Indeed, the alliance e¤ect in Table 11 is in principle independent of any airline characteristics, while the average marginal cost for alliance members computed in Table 12 is conditional on airline characteristics. As discussed in the previous section, alliance members may enjoy lower marginal costs because alliances are potentially clubs which gather more e¢ cient and/or larger companies, compared to those outside alliances.

Third, note that prices, marginal costs, and margins vary signi…cantly across alliances.

A striking result is the average margin of Quali ‡yer which is close to 0. This could be related to the negative pro…t obtained by some of its airlines for several years, illustrating the …nancial di¢ culties of the alliance, which stopped its operations in 2001 after the bankruptcies of Swissair and Sabena.

Using our estimates for the demand equation, note that, as suggested by the righttions of the conduct parameter through the pricing rule may lead to signi…cant underestimation of market power. Similarly, imposing a speci…c conduct and estimating costs may lead to over or underestimation of costs when perfect competition or monopoly are assumed respectively. On the contrary, estimates are quite insensitive to the assumed demand functional form. hand side of Equation ( 11), Nash behavior would entail an average margin M T N for all the airlines in the sample equal to 0:707. On average, the industry's actual margin M T = 0:122 does not entail pure Nash behavior. It is also worth distinguishing airlines that belong to alliances and those that do not. We have suggested that companies within alliances were setting the highest margins. We also calculate an average individual Nash margin for each group. Note that, from the ratio q i =p i , evaluated at the average observation of the sample, it can be seen that the airlines within alliances meet demand on a more inelastic portion of the curve than other companies. Hence, pure Nash behavior for companies inside alliances entails a margin M A N equal to 0.950, while for other companies the margin, M N A N , is equal to 0.677. The values of these actual margins lie below the individual Nash behavior margins. Hence, individual Nash behavior is not met for any set of companies. We can as well evaluate an average Nash margin for each alliance. Airlines inside these alliances show a behavior that is di¤erent from individual Nash. According to our results, Airlines in SkyTeam and Star Alliance are those characterized by the less competitive behavior.

Note that Star Alliance (OneWorld resp.) includes six (…ve resp.) airlines whose networks are substitutes to other airlines'networks inside the same alliance. We present in the lower half of the table individual estimates for these companies, which are American Airlines, British Airways, Qantas, Cathay, Canadian Airlines, United, Lufthansa, All Nippon, SAS, Thai, and Mexicana. Note that, compared to the average airline inside an alliance, a majority of them enjoy higher margins, since they bene…t from marginal costs advantages and/or they set higher prices. Comparing the real margins to individual Nash margins suggests that Lufthansa, Mexicana, SAS, and Thai have the less competitive behavior.

Conclusion

After worldwide liberalization of the airline market, competition has led …rms to start forming alliances. Economic studies have proposed that alliances between airlines whose networks can be regarded as substitutes should result in softer competition and higher prices. At the same time, alliances between …rms whose networks can be regarded as complements should result in lower prices due to cost reductions. The former type of alliance should be avoided, but the latter should be promoted.

This study sheds light on these issues. Our contribution consists in evaluating airlines'strategical interactions through the window of …rms'network interconnections. To estimate cross-price elasticities for all the networks of our database, we consider airlines' networks coincidences and potential connections with all their rivals. The results allow us to classify all company pairs as either complements or substitutes, and predict price cost margins.

Our results suggest that a signi…cant number of companies that are allied between 1995 and 2000 can cooperate on routes that were jointly served before, so that many members'networks can be considered as substitutes.

At the same time, we show that, on average, alliance members propose lower prices than airlines outside alliances. We suggest that this negative impact of alliances on prices does not correspond necessarily to a change in airlines'pricing once they are part of an alliance. We rather believe that alliances are clubs of large and e¢ cient companies, in which the members are able to set lower prices because they enjoy lower costs.

  Digest of Statistics published by International Civil Aviation Organization (ICAO), World Air Transport Statistics published by International Air Transport Association (IATA), and Economic Outlook published by the Economics and Statistics Department of the Or-ganization for Economic Cooperation and Development (OECD) as well as airlines annual

  31) W AGES. Standard errors are in parenthesis.

FIGURE

  FIGURE 1: Network overlapping

Table 4

 4 presents descriptive statistics.

TABLE 1 :

 1 List of airlines included in the Dataset

	Airline	Seats-kil.	Airline	Seats-kil.
	United Airlines	272,380,784	Aeromexico	16,770,044
	American Airlines	250,920,342	Mexicana	15,942,627
	Delta Airlines	224,202,461	Finnair	13,409,143
	Northwest	153,461,676	Olympic	13,157,697
	British Airways	144,535,575	TAP	12,837,742
	Japan Airlines	112,853,559	Continental Micronesia	9,200,909
	Continental Airlines	108,316,288	Aer Lingus	8,662,699
	Lufthansa	103,576,477	Avianca	7,275,610
	U.S. Air	95,375,781	LOT	6,707,159
	Air France	94,723,686	Air Lanka	6,628,365
	All Nippon Airways	79,336,012	Air Europa	4,987,922
	Qantas	78,106,832	British Midland	4,819,388
	KLM	70,075,874	Spanair	4,682,385
	TWA	59,716,643	Braathens	4,536,869
	Cathay Pacific	56,506,464	Malev	4,029,375
	Air Canada	51,470,679	Cyprus Airways	3,889,153
	Alitalia	51,433,485	Air UK	3,393,372
	Thai Airways	47,788,381	Meridiana	3,316,857
	Iberia	43,128,693	Mea Air Liban	3,233,606
	Swissair	38,245,227	Gb Airways	1,770,826
	America West	37,929,149	Jersey European	1,228,033
	Canadian Airlines	35,288,169	Croatia Airlines	1,020,691
	Varig	35,199,155	Maersk Air	727,783
	SAS	31,500,448	Lithuanian Airlines	623,836
	Virgin Atlantic	26,642,135	Estonian Air	408,050
	Alaska Airlines	25,589,388	Air Baltic	268,564
	Japan Air system	22,201,996	Air Botswana	109,663
	Sabena	20,714,658
	Note: Seats-kilometers supplied: Average between 1995 and 2000.

TABLE 3 :

 3 Overlapping pairs

	Airline Pair	Index	Airline Pair	Index
	All Nippon -Japan Airlines	0.5641	Air France -Japan Airlines	0.0907
	Delta -TWA	0.3860	British Airways -United	0.0859
	Aeromexico -America West	0.3484	Lufthansa -Thai	0.0854
	SAS -Thai	0.3358	All Nippon -Sabena	0.0834
	Continental -TWA	0.3118	Japan Air System -Northwest 0.0827
	Air UK -Spanair	0.3063	United -Virgin	0.0827
	Continental -Delta	0.2670	Delta -Swissair	0.0826
	British Airways -Virgin	0.2400	British Airways -Delta	0.0825
	Aeromexico -Mexicana	0.2383	British Airways -Qantas	0.0812
	Continental Micro. -Japan Air Sys.	0.1858	Qantas -United	0.0799
	Air Europa -Spanair	0.1829	Alitalia -TWA	0.0786
	Japan Airlines -United	0.1812	Air France -Thai Airways	0.0779
	Olympic -TWA	0.1795	Continental -Mexicana	0.0773
	Mexicana -USAIR	0.1539	Continental -Virgin	0.0757
	Air UK -British Midland	0.1536	Delta -Virgin	0.0752
	Qantas -Thai	0.1522	Japan Airlines -Virgin	0.0752
	British Airways -Continental	0.1518	Air Europa -Iberia	0.0735
	American -Delta	0.1501	Japan Airlines -Lufthansa	0.0734
	Canadian Airlines -Cathay	0.1413	Delta -SAS	0.0713
	Japan Airlines -Northwest	0.1374	Air Canada -British Airways 0.0698
	Delta -Lufthansa	0.1364	Continental -Japan Air sys.	0.0698
	Air Canada -Canadian Airlines	0.1355	Air UK -KLM	0.0693
	Aeromexico -Iberia	0.1314	Air Europa -TWA	0.0689
	Olympic -Thai	0.1307	Swissair -Varig	0.0686
	All Nippon -Northwest	0.1288	British Airways -USAIR	0.0680
	Continental -SAS	0.1263	Delta -Sabena	0.0669
	Alitalia -Thai	0.1261	TAP -TWA	0.0660
	TAP -Varig	0.1242	Delta -United	0.0656
	Japan Airlines -Japan Air System	0.1191	Air France -TWA	0.0647
	American -Continental	0.1178	Air France -All Nippon Airw 0.0641
	Mexicana -United	0.1173	Continental -Lufthansa	0.0640
	American -British Airways	0.1126	Japan Air System -United	0.0637
	British Airways -Thai	0.1116	Air France -United	0.0636
	Lufthansa -United	0.1101	Cont. Micro. -Japan Airl.	0.0631
	American -United	0.1066	Iberia -Varig	0.0630
	Northwest -Qantas	0.1049	Japan Airlines -Thai	0.0626
	All Nippon -Qantas	0.1046	Cathay -Swissair	0.0624
	All Nippon -Virgin	0.1028	Air Canada -Iberia	0.0620
	Japan Airlines -Qantas	0.0988	Olympic -Qantas	0.0619
	Continental Micronesia -Northwest	0.0987	All Nippon -Cont. Micro.	0.0618
	All Nippon -United	0.0980	Delta -Varig	0.0614
	Aeromexico -Continental	0.0948	American -Lufthansa	0.0613
	Cathay -Qantas	0.0930	Iberia -TWA	0.0613
	Air UK -Cathay	0.0922	…
	Note: Only the first 87 over a total of 444 overlapping airline pairs are presented here.

TABLE 4 :

 4 Descriptive statistics (Annual data, 1995-2000, 55 airlines)

	Variable	Mean	Stand. Dev.	Min	Max
	Costs (10 3 $)	2,465,913	172,663	11,820	14,901,114
	Wages ($)	14,969	510	773	59,094
	Price Fuel (index)	162.68	1.94	88.21	283.76
	Price ticket ($/Pass.kil)	0.117	0.003	0.032	0.303
	Production (Seats-kil)	45,906,516	3,450,119	96,609	284,044,940
	Demand (Pass-kil)	32,439,265	2,469,556	50,994	204,149,480
	Network size (kil)	271,083	14,508	1,467	1,075,683
	Av. Stage Length (kil)	1,385	57	277	8,978
	# Routes	193.58	9.56	1.52	809.57
	# Departures	177,587	12,315	4,029	968,893
	Priv. Cons. (index)	1443.70	117.44	1.29	6683.8
	Competition (index)	0.619	0.029	0.001	1.964
	Alliance	0.118
	OneWorld	0.027
	Star Alliance	0.060
	Wings	0.061
	SkyTeam	0.009
	Qualiflyer	0.021

TABLE 5 :

 5 Prices

	Variable	I	II	III	IV	V
	CONST	-4.70 ***	-1.01	-2.65 ***	-4.65 ***	-4.69 ***
		(0.26)	(2.19)	(0.07)	(0.25)	(0.29)
	TREND	-0.07 ***	-0.06 ***	-0.04 ***	-0.06 ***	-0.06 ***
		(0.01))	(0.01)	(0.01)	(0.01)	(0.01)
	PRIV	0.41 ***	0.41 ***		0.39 ***	0.40 ***
		(0.05)	(0.04)		(0.04)	(0.05)
	POP		-0.22 *
			(0.13)
	WAGES			0.04
				(0.03)
	ALL				-0.05 **	-0.06 ***
					(0.02)	(0.02)
	ALL×COMP					-0.06 *
						(0.03)
	Error Dev.	0.09 ***	0.09 ***	0.09 ***	0.09 ***	0.09 ***
		(0.003)	(0.003)	(0.003)	(0.02)	(0.003)
	R Squared	0.96
	Mean Log-likelihood	1.92
	# of observations	330	330	330	330	330

Note: Standard errors are in parenthesis.

*** Significant at the 1% level;

** significant at the 5% level; * significant at the 10% level.

TABLE 6 :

 6 Demand I (Network)

	Variable	Par	A	I	II	III	IV	V
	CONST		0.97 **	1.04 **	1.03 **	1.09 **	0.99 **	0.98 **
			(0.47)	(0.47)	(0.47)	(0.47)	(0.47)	(0.48)
	NET		0.21 ***	0.22 ***	0.22 ***	0.22 ***	0.22 ***	0.22 ***
			(0.01)	(0.02)	(0.01)	(0.01)	(0.01)	(0.01)
	NET×OWN PRICE		-0.88 ***
			(0.15)
	NET×OWN PRICE 2			-0.95 ***	-0.96 ***	-0.98 ***	-0.94 ***	-0.94 ***
				(0.16)	(0.16)	(0.17)	(0.16)	(0.16)
	PRICE_O		0.77 **	0.73 **	0.73 **	0.72 **	0.75 **	0.75 **
			(0.32)	(0.35)	(0.32)	(0.33)	(0.32)	(0.32)
	PRICE_C		-0.17 **	-0.18 **	-0.18 **	-0.18 **	-0.17 **	-0.17 **
			(0.07)	(0.07)	(0.07)	(0.07)	(0.07)	(0.07)
	PRIV		0.25 **	0.28 **	0.28 **	0.25 **	0.28 **	0.28 **
			(0.11)	(0.11)	(0.11)	(0.11)	(0.11)	(0.11)
	Error Dev.		0.22 ***	0.22 ***	0.22 ***	0.22 ***	0.22 ***	0.22 ***
			(0.01)	(0.01)	(0.01)	(0.01)	(0.01)	(0.01)
	R 2		0.76
	Own Price Elasticity		-1.73	-1.77	-1.77	-1.78	-1.79	-1.78
			(0.11)	(0.11)	(0.11)	(0.10)	(0.11)	(0.11)

Note: Standard errors are in parenthesis.

*** Significant at the 1% level;

** significant at the 5% level; * significant at the 10% level.

TABLE 7 :

 7 Demand II (Departures)

	Variable	Par	I	II	III	IV	V
	CONST		1.06 ***	1.05 ***	1.06 ***	1.02 ***	1.00 ***
			(0.34)	(0.34)	(0.33)	(0.34)	(0.34)
	DEP		0.29 ***	0.29 ***	0.29 ***	0.29 ***	0.29 ***
			(0.01)	(0.01)	(0.01)	(0.01)	(0.01)
	DEP×OWN PRICE		-1.48 ***	-1.49 ***	-1.53 ***	-1.48 ***	-1.48 ***
			(0.14)	(0.14)	(0.14)	(0.14)	(0.14)
	PRICE_O		2.02 ***	2.02 ***	2.01 ***	2.03 ***	2.03 ***
			(0.19)	(0.19)	(0.19)	(0.19)	(0.19)
	PRICE_C		-0.17 ***	-0.17 ***	-0.17 ***	-0.17 ***	-0.16 ***
			(0.05)	(0.05)	(0.05)	(0.05)	(0.05)
	PRIV		-0.02 ***	-0.01 ***	-0.02 ***	-0.02 ***	-0.02 ***
			(0.005)	(0.005)	(0.005)	(0.006)	(0.005)
	Error Dev.		0.15 ***	0.15 ***	0.15 ***	0.15 ***	0.15 ***
			(0.006)	(0.005)	(0.006)	(0.06)	(0.005)
	R 2		0.88
	Own Price Elasticity		-1.53	-1.53	-1.51	-1.53	-1.54
			(0.11)	(0.11)	(0.10)	(0.11)	(0.11)

Note: Standard errors are in parenthesis.

*** Significant at the 1% level;

** significant at the 5% level; * significant at the 10% level

TABLE 8 :

 8 Demand III (Routes)

	Variable	Par	I	II	III	IV	V
	CONST		1.06 **	1.05 **	1.14 **	1.02 **	1.01 **
			(0.47)	(0.47)	(0.47)	(0.47)	(0.47)
	ROUTES		0.26 ***	0.26 ***	0.27 ***	0.26 ***	0.26 ***
			(0.02)	(0.02)	(0.02)	(0.02)	(0.02)
	ROUTES×OWN PRICE		-1.35 ***	-1.35 ***	-1.41 ***	-1.33 ***	-1.33 ***
			(0.19)	(0.19)	(0.20)	(0.19)	(0.19)
	PRICE_O		1.39 ***	1.39 ***	1.37 ***	1.41 ***	1.41 ***
			(0.30)	(0.30)	(0.30)	(0.30)	(0.30)
	PRICE_C		-0.19 ***	-0.18 **	-0.20 ***	-0.18 **	-0.18 **
			(0.07)	(0.07)	(0.07)	(0.07)	(0.07)
	PRIV		0.07 ***	0.07 ***	0.07 ***	0.07 ***	0.07 ***
			(0.006)	(0.006)	(0.006)	(0.006)	(0.006)
	Error Dev.		0.21 ***	0.21 ***	0.21 ***	0.21 ***	0.21 ***
			(0.008)	(0.008)	(0.008)	(0.01)	(0.01)
	R 2		0.77
	Own Price Elasticity		-1.99	-1.98	-1.99	-1.99	-1.98
			(0.12)	(0.12)	(0.12)	(0.12)	(0.12)

Note: Standard errors are in parenthesis.

*** Significant at the 1% level;

** significant at the 5% level; * significant at the 10% level.

TABLE 10 :

 10 Demand-Capacity relationship

	Variable		Parameter
	CONST		1.58 ***
			(0.28)
	q		0.92 ***
			(0.01)
	Error Dev.	0.05 ***
			(0.002)
	R 2		0.99
	Note:	Standard errors are in parenthesis.
	*** Significant at the 1% level;	** significant at
	the 5% level;

*

significant at the 10% level.

TABLE 11 :

 11 Cost function

	Variable		A	A2
	CONSTANT	-4.95 ***	-4.99 ***
			(0.24)	(0.25)
	WAGE		0.24 ***	0.24 ***
			(0.02)	(0.02)
	Q		0.93 ***	0.93 ***
			(0.02)	(0.02)
	NET		-0.07 **	-0.07 **
			(0.03)	(0.03)
	ASL		-0.38 ***	-0.38 ***
			(0.04)	(0.04)
	TREND		-0.15 ***	-0.15 ***
			(0.03)	(0.03)
	ALL			-0.03
				(0.06)
	Error Dev.	0.30 ***	0.30 ***
			(0.01)	(0.01)
	R 2		0.97
	Note:	Standard errors are in parenthesis.
	*** Significant at the 1% level;	** significant at the 5% level;

*

significant at the 10% level.

TABLE 12 .

 12 Marginal costs, prices, and margins.

	Price	MC	Real Margin Nash Margin

Notes: Price: One passenger-kilometer in Dollars. MC: One seat-kilometer in Dollars.

Standard errors are in parenthesis.

Corresponding author. Departamento de Economía, Universidad Carlos III de Madrid, C/ Madrid 126, 28903-Getafe (Madrid), Spain, e-mail: philippe@eco.uc3m.es

This type of aggregate approach has been mostly used by authors measuring the e¤ects of the European airline deregulation on airlines'costs reductions. This is the case for instance in[START_REF] Good | US Airline Deregulation: Implications for European Transport[END_REF],[START_REF] Neven | Rent Sharing in The European Airline Industry[END_REF][START_REF] Brueckner | The Economics of International Codesharing: An Analysis of Airline Alliances[END_REF],[START_REF] Röller | Capacity and Product Market Competition: Measuring Market Power in a Puppy-Dog'Industry[END_REF], Marín (1998), and[START_REF] Gagnepain | Regulation and Incentives in European Aviation[END_REF].

If a carrier has several hubs (which is the case of many American carriers), the most important hub in terms of supply is accounted for. A detailed description of all companies'hubs as well as the level of supply operated from each of them is available upon request.

We originally estimated a long run cost function where capital was regarded as a variable input. Accordingly, a measure for the price of capital was computed from the companies'accounting data and included in the cost function. This variable was not signi…cant at any con…dence level.

+

= 1. We assume that z i includes measures of airlines'network size, N ET i , and average stage length, ASL i , 7 and has the following shape:6 See Marín (1998) for details on the same choice for the airline industry 7 See Marín (1998) andNeven et al. (2001) for discussions on the introduction of these two variables

A survey by[START_REF] Oum | Concepts of price elasticities of transport demand and recent empirical estimates[END_REF] on price elasticities of air transport demand suggests that empirical …ndings obtained during the 80s usually lie between -4.51 and -0.4.

We keep the worst case scenario from each table.

Note issued by the U.S. Department of Transportation on the 20th May 1996.

European Commission MEMO/09/168. 20th April 2009.

By estimating cost and demand functions, we are able to generate direct measures of the price-cost margins. This approach follows the spirit of[START_REF] Genesove | Testing Static Oligopoly Models: Conduct and Cost in the Sugar Industry, 1890-1914[END_REF], which shows that direct estima-

grateful to Jordi Jaumandreu for very constructive discussions, as well as Quim Beltrán for superb research assistance. Finally, funding from the Fundación Ramón Areces and Ministerio de Educación y Ciencia (SEJ2004-00670 and SEJ2007-66268) is gratefully acknowledged.

if the two components were served by one single airline. welfare have identi…ed various counter powered e¤ects. Oum, Park, and Zhang

Abstract:

We consider an empirical model of worldwide airline alliances that we apply to a large set of companies for the period 1995-2000. Using observations at the network level, we estimate a cost, capacity, and demand system that accounts for crossprice elasticities. Our contribution consists in evaluating airlines'strategical interactions through the window of …rms' network interconnections. We consider networks coincidences and potential connections with all their rivals. The results allow us to classify all company pairs as either complements or substitutes. We shed light on the fact that many airlines involved in the same alliance are potential substitutes. Keywords: Alliance, airline, cross-price elasticities. JEL: L11, L13, L41.