Multiple equilibria and deterrence in airline markets.

Ciliberto, Federico ; Zhang, Zhou

I. INTRODUCTION

In this article, we propose a new empirical methodology to determine whether firms strategically deter new potential entrants. In particular, we use a longitudinal dataset from the U.S. airline industry to estimate three different models for entry games with very general forms of heterogeneity between U.S. carriers in airline markets: a simultaneous game with complete information and two sequential games with or without strategic entry deterrence. In a sequential game with entry deterrence, an incumbent decides whether to incur a cost to deter potential entrants. The main objective of our article is to test which of these three models of strategic behavior provides the best fit to the data and from that to determine if other models could dominate the static model that is so often used in modeling entry games. We aim to provide a methodology that is practical to answering the crucial question of whether firms strategically deter new entrants and leave to future work how the firms are able to do so.

As Ellison and Ellison (2011) point out, the economic investigation of whether firms make strategic investments to deter entry is a central theme in industrial organization, because competition ensures that prices are in the long run reflective of the marginal cost of a product or service if entry is not artificially impeded. However, the number of empirical studies investigating strategic deterrence is very limited. Kadiyali (1996), which is the closest paper to ours, estimates the post-entry demand and cost functions of two firms by estimating a menu of different games and choosing the game that fits the data best. With these demand and cost estimates, she concludes that the incumbent was forced to accommodate the entrant because the profit the incumbent would have made under a deterrence strategy was lower than the profit it made under accommodation. Kadiyali's strategy relies on identifying one particular post-entry game that is being played in all markets. In our article, as we will explain in more detail shortly, in each market and at each point in time, firms play a predetermined game, which is one out of a menu of three: simultaneous-move, sequential-move, and a deterrence game. We also allow for firm heterogeneity, which leads to multiple equilibria in the number and identity of firms; this allows for a more general framework for examining deterrence. Other papers in the deterrence literature include Ellison and Ellison (2011) and Goolsbee and Syverson (2008). Ellison and Ellison (2011) test a theoretical prediction of the relationship between investment and market size--a relationship that differs depending on whether or not firms deter potential entrants. Their approach is very transparent but the results are statistically weak. Goolsbee and Syverson (2008) identify deterrence by looking at changes in incumbent behavior that result from exogenous changes in potential entry behavior. Differently from these two papers, our article explicitly allows for multiple equilibria and for firms to decide between deterrence and accommodation. There are also dynamic structural models of deterrence, including Sweeting (2013), Williams (2012), Chicu (2013), and Snider (2009). These dynamic models allow forward-looking behavior by firms; however, none of these papers allow for multiple equilibria.

We start from the observation that in any theory of entry deterrence, the incumbent can prevent the entry of competitors but only at a cost or investment that the incumbent could avoid if entry were instead accommodated. We call these costs the "deterrence investments" (Bernheim 1984). Then, we exploit the theory developed in Bernheim (1984), where the definition of deterrence investment is intentionally ambiguous so as to abstract from the complex issues that arise with particular theories of entry deterrence and to focus on the fundamental trade-off that the incumbent faces. Firms can make deterrence investments to block the entry of profit-lowering competitors, and deterrence investments include all investment that raise barriers to entry, but these investments are costly. Our objective is to estimate the costs of deterrence investments and compare them with the profits made by the firm when they do not deter their competitors; we then predict whether or not firms make these investments when they face the threat of new entry.

We model the interaction among airlines as a repeated static entry game, where we allow for very general forms of heterogeneity, which lead to multiple equilibria. In the same spirit as Kadiyali (1996), we estimate a menu of different games to choose the one that fits the data best. The first game is a repeated static simultaneous move entry game with complete information. This is akin to the game studied by Ciliberto and Tamer (2009), except that airlines interact repeatedly over time. The second game is a repeated static game, where firms can face two scenarios, depending on the exogenous history of the game. In each time period, there are two stages. In the first stage, if there was a single incumbent in the previous period, that incumbent moves first. In the second stage, all remaining firms move simultaneously. The results from this game depend upon the exogenous history of the game, and in the case that there were no incumbents (or several incumbents) in the previous period, the result is identical to the simultaneous-move game. Finally, we consider a game where the firms can make deterrence investments in a sequential-move game, where all airlines are considered potential entrants. Thus, the model that allows only for simultaneous-move games is a subgame of the one that allows for sequential-move games depending on the game history, which is a subgame of the one that allows for firms playing a sequential-move game to also make deterrence investments.

The main concern with our approach is that we study strategic deterrence using a repeated static game rather than a dynamic game. In a dynamic game, the firms would take into account the current period's profit as well as a stream of discounted future profits, and the firm would be willing to pay a higher deterrence cost. Therefore, to the extent that the returns to deterrence in each period come over a number of periods, our estimates of the deterrence cost may be too small.

However, there are several advantages to our approach. First, as discussed below, we do find that the model with sequential games with strategic deterrence provides the best fit to the data and conclude that the results support the hypothesis of the existence of strategic entry deterrence. Hence, the concern about the possible downward bias induced by the use of a repeated static game rather than a dynamic game is mitigated by the results we find. Second, a repeated static game allows us to model very general forms of heterogeneity among firms, and for multiple equilibria, which are features that, so far, have not been dealt with in dynamic games. In this sense, our approach should be thought of as complementary to one that estimated the game among airlines as a dynamic game.

To identify deterrence investments, we use changes in firms' entry decisions over time. The idea is to compare entry decisions across similar markets whose market structures change differently over time. In particular, if there are two markets that have identical observable and unobservable characteristics, and in one there is only one incumbent over time, while in the other there are periods with two firms, then it must be the case that the incumbent in the first market does deter new entrants. Using this simple idea, we estimate the costs that incumbents must face to make "deterrence investments" and determine if there are some airlines that systematically prevent new entry.

Data are from the Origin and Destination Survey (DB1B), which is a 10% sample of airline tickets from reporting carriers. These are quarterly data from 2004, and they are organized by market, year, and quarter. The panel data provide the variation needed to identify both the competitive effect of the firms' entry ([delta]) and the cost of the deterrence investments (c). First, we observe entry in markets where there are no incumbents (or there is more than one incumbent), and there we will assume that firms play a simultaneous-move game. We also observe entry in markets where there is only one incumbent, and there we will assume that firms play a sequential-move game. Therefore, we identify c separately from 5. Second, the set of competitors vary by market, so it is possible to allow firms to have heterogeneous competitive effects and deterrence costs.

The estimation is largely based on Tamer (2003) and Ciliberto and Tamer (2009), who propose a methodology to estimate a game among airlines in a one-shot static simultaneous-move game. The fundamental idea behind their methodology, which we will briefly review in the article, is that even in the presence of multiple equilibria, one can estimate sets of parameters of the profit functions that correspond to models with different equilibrium selection rules. Tamer (2003) and Ciliberto and Tamer (2009) show that one can construct upper and lower bounds for the probabilities that the various equilibrium outcomes can take and then choose the parameters that minimize an appropriately defined distance between these lower and upper bounds and the empirical probabilities. Methodologically, the difference here is that when firms can play a sequential move or deterrence game, there will be almost always be a unique equilibrium. However, because in some markets firms play a simultaneous-move game, we still will only be able to estimate sets of parameter values, and so we will not be able to achieve point identification.

We find that the model where firms make deterrence investments fits the data much better than a model where firms play a simultaneous or sequential-move game. Thus, we cannot reject the hypothesis that incumbents deter entrants in the airline industry. In addition, we show that the profits incumbents can make if they move first are larger than those that they can make if the game is played simultaneously. The study of the differences in profits is meant to provide a sense of the magnitude of the benefits of strategic deterrence.

This result is stronger, as one would expect, when incumbents can deter new entrants. Finally, we find that all firms deter new entrants, with the exception of United Airlines. Remarkably, United Airlines was under bankruptcy protection during the period of analysis, suggesting that its deterrence investments were not credible. This last result underscores the importance of modeling firms as heterogenous competitors.

Our article contributes to two important literatures. First, we contribute to the literature on the estimation of entry games with complete information (Berry 1992; Bresnahan and Reiss 1990; Ciliberto and Tamer 2009; Mazzeo 2002) by allowing firms to play a simultaneous or sequential-move game and to deter new entrants. Bresnahan and Reiss (1990) and Berry (1992) considered a sequential- and a simultaneous-move game as alternatives to describe the interaction between car dealers and airlines. However, Bresnahan and Reiss (1990) and Berry (1992) maintained that firms were playing the same game, whether simultaneous or sequential-move, in all markets. Here, the selection of the type of game played is a function of the past history of the game, and thus firms play sequential- and simultaneous-move games across different markets and time. Second, we contribute to the literature on deterrence, which we discussed above.

The article is organized as follows. Section II describes anecdotal evidence of deterrence in the airline industry. Section III describes the model and econometric methodology. Section IV provides information on the data, and Section V details the identification strategy. Section VI presents the estimation results, and Section VII compares counterfactual profits under each type of game. Section VIII concludes.

II. ANEDOCTAL EVIDENCE OF STRATEGIC DETERRENCE

In 1999, the Transportation Research Board, a unit of the National Research Council, prepared a report on entry and competition in the U.S. Airline Industry. As part of this extensive and informative report, the Transportation Research Board provided a list of informal complaints received by the Department of Transportation from new entrant airlines about unfair exclusionary practices between March 1993 and May 1999.

Table 1 summarizes the list of informal complaints received by the Department of Transportation by the Complaining Party, always a Low Cost Carrier (LCC); by the party against whom the complaint was filed, always a national carrier; the quarter when the complaint was filed; and the markets which were involved in the complaint.

Table 1 provides three fundamental insights on the nature of competition between low cost carriers and national carriers.

First, some national airlines show much more aggressive behavior against new entrants than others. In particular. Delta, Northwest, American, and Continental have used aggressive competitive behavior in several markets and over time. One telling case involved Northwest's behavior toward Reno Air. In 1993, Reno Air announced that it would enter the Reno-Minneapolis/St Paul market, which, at that time, was not served on a nonstop basis by Northwest. After Reno's entry, Northwest announced that it would not only start nonstop service between Reno and Minneapolis/ St Paul, but it would also enter three of Reno Air's existing nonstop markets: Reno-Seattle, Reno-Los Angeles, and Reno-San Diego. Northwest would also match Reno Air's fares in all markets.

Second, the markets where national carriers have reacted aggressively against low cost carriers were always markets out of the hub of the national carrier. In light of Spence (1977) and Dixit (1980), this is not surprising, since national carriers make large sunk investment costs at their hubs. Spence and Dixit show that incumbents might strategically invest in capacity to deter new entrants, and this is exactly what national carriers might be doing at their hubs. Airlines make sunk investment costs in their hubs through the signing of long-term leases for the use of gates and check-in positions, and participation in the costs of airports' expansions and modernizations.

Finally, the markets that are mentioned in Table 1 are mainly markets between a hub and a medium-sized Metropolitan Statistical Area (MSA), such as Mobile, Des Moines, or Jacksonville. The markets in which national carriers show aggressive behavior toward low cost airlines are not markets between the largest MSAs in the United States.

III. THE ENTRY GAME PLAYED BY THE AIRLINES: ESTIMATION

The theoretical literature on deterrence is vast. Both Spence (1977) and Dixit (1980) provide theoretical arguments for deterrence. Spence (1977) shows that entry can be deterred by the mere existence of capacity; Dixit (1980) extends the argument and shows that since investment in capacity can alter the outcomes in the post-entry game, there can be incentives to invest in capacity in order to deter potential entrants. There are many variations on this basic theoretical model. Fudenberg and Tirole (1984) add advertising and show that an incumbent's low advertising pre-entry is a credible threat of deterrence, because it allows the incumbent firm to cut prices if a competitor were to enter. Judd (1985) allows for multiproduct incumbent firms, and he allows these firms to exit after entrants enter the market; he shows that intensive post-entry competition may facilitate entry, because the multi-product incumbent firms are more likely to exit the market. Bulow et al. (1985) show that the incentives for a firm to engage in deterrence differ depending on whether potential competitors' goods are substitutes or complements. In particular, when goods are strategic complements, firms may underinvest in capital in order to reduce future competition. Bernheim (1984) extends the basic model to allow firms to enter over multiple periods. In this case, he shows the counterintuitive result that policies that are intended to increase competition, such as subsidizing entry, can have the opposite effect. Finally, Anderson and Engers (2007) do not focus on deterrence, but they develop a theoretical model that solves the problem in the standard Stackelberg model where the order of moves is exogenously specified. In their model, firms compete over entry time. In our analysis, the order of moves is exogenous, but it changes across markets and time.

In this article, we use the practical solution proposed by Bernheim (1984), which we have discussed in the introduction. More specifically, we assume that the game played by the airlines is played repeatedly over time. In each period, airlines know each other's strategies and payoffs; thus, this is a complete information game. A strategy profile in this game tells each firm under what conditions to enter into a market, and it will depend on the nature of the game that the firms play (i.e., whether the game is simultaneous- or sequential-move).

Formally, there are I airlines, indexed by i = 1, ..., I, that must decide whether to enter into the market at time t = 1, ..., [infinity]. Let [y.sub.imt] = 1 if firm i enters in market m at time t and [y.sub.imt] = 0 otherwise. The entry decisions [y.sub.mt] are observed but the profits made by the firms, [[pi].sub.mt], are unobservable. The set of potential entrants is constant across markets and time. There are seven potential entrants, which we will discuss later.

The data consist of a random sample of market-firm-time specific observations ([y.sub.mt], [X.sub.mt]). Let [[epsilon].sub.mt] = ([e.sub.1mt], ..., [[epsilon].sub.Imt]) be a mean zero random variable that is uncorrelated with [X.sub.mt] and has a known (up to a finite dimensional parameter [OMEGA]) distribution F[OMEGA] x [[epsilon].sub.mt] = ([e.sub.imt], ..., [e.sub.Imt]) is known to the players but unobserved to the econometrician, which is why we have a game of complete information. The shocks need to be independent of the observable market and firm characteristics; otherwise, we would have to formalize the observable characteristics as endogenous outcomes of the strategic game that firms play, which is clearly beyond the scope of this article.

The unobservable error [[epsilon].sub.int] is modeled as follows:

[[epsilon].sub.imt] = [v.sub.m] + [[xi].sub.mt] + [[eta].sub.im] + [[zeta].sub.imt].

[v.sub.m] represents market unobservables that are market specific and constant over time; it captures, for example, the fact that in market m there is a large share of business passengers. [[xi].sub.mt] is a market shock that changes over time, and which affects firms in market m in the same way; for example, changes in the demand for travel over time. [[eta].sub.im] is a time-invariant market-specific airline shock to allow different firms to face different unobservables in the same market; for example, some airlines might see a larger share of business passengers in the same market than other airlines do. Finally, [[zeta].sub.imt] are time-variant, firm-specific shocks. (1)

[X.sub.mt] is a k x I matrix of k exogenous determinants of entry decisions, both market- and carrier-specific. It includes both a vector of market characteristics that are common among the firms in market m and a vector of firm characteristics that enter into the profits of all the firms in that market.

A. Simultaneous-Move Game

The instantaneous profit function is written as follows:

[[pi].sub.imt] = [X'.sub.imt] [alpha] + [summation over (j[not equal to]i)] [[delta].sub.j] [y.sub.jmt] + [[epsilon].sub.imt].

The observed part of the profit is known up to a finite dimensional parameter vector [theta] [equivalent to] ([alpha], [delta]).

An important feature of the profit function in this article is the presence of [[delta].sub.j], which summarizes the effect that airline j has on i's profits. (2) In particular, notice that this function depends directly on the identity of the firms (y/s, j [not equal to] i). This allows for general heterogeneity in competitive effects, which is especially important for low cost airlines that have different operating methods than the major carriers. (3) If we assume that firms play a simultaneous-move game in all markets and in all periods, then this is simply the model in Ciliberto and Tamer (2009) applied to panel data rather than to cross-section data. We refer to that paper for the detailed description of the estimation methodology. Here, we provide a brief summary.

The statistical model associated with the simultaneous-move game is as follows:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

with entry decisions corresponding to

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

and j = 1, ..., l. Thus, this is a simultaneous system of discrete choice equations. The problem with the estimation of such a model is that in general it has multiple equilibria. Tamer (2003) proposed a methodology to identify sets of parameters of the model for the case of two firms choosing between two decisions (e.g., whether or not to enter into a market) and Ciliberto and Tamer (2009) provided a practical methodology to estimate sets in the case of many firms making multiple decisions. In particular, Ciliberto and Tamer (2009) show that Model (1) provides the following inequality restrictions on regressions:

(3) [H.sub.1] (x, [theta]) [less than or equal to] Pr (y|x) [less than or equal to] [H.sub.2] (x, [theta]),

where Pr(y|r) is a [2.sup.I] vector of choice probabilities that we consistently estimate using the data, and we interpret the inequalities element by element. The H's are functions of [theta] and the distribution function [F.sub.[OMEGA]], where [OMEGA] is part of the vector [theta]. As Ciliberto and Tamer (2009) explain, the identified set, [[THETA].sub.I], is then the set of parameter values that obeys the inequality restrictions for all x almost everywhere and represents the set of economic models that is consistent with the empirical evidence. For a given parameter value, the estimator is based on minimizing the distance between this vector of choice probabilities and the set of predicted probabilities.

We estimate Model (1) using a sharp two-step minimum distance estimator.

First, we estimate the conditional choice probabilities nonparametrically, using a simple frequency estimator. Then, we estimate the identified set [[THETA].sub.I] using the simulation procedure provided in Ciliberto and Tamer (2009). In practice, we simulate random draws of [v.sub.m], [[xi].sub.mt], [[eta].sub.im], and [[zeta].sub.imt] from four independent normal distributions with mean zero and variance equal to 1.

B. Sequential-Move Game

We now consider the case when firms face two different scenarios depending on the exogenous history of their previous interactions. More specifically, we will maintain that at each time t and in each market m, there are two stages. In the first stage, the incumbent moves first. In the second stage, all other firms move simultaneously. Therefore, the scenario the firm faces at time i + 1 depends on the observed market structure at time t. If there was a single incumbent in the previous period then that firm moves first. If there was no incumbent (or several incumbents), the result is the same as the simultaneous-move game. (4)

In the event that there was an incumbent in the previous period, one firm makes its entry decision before the other firms choose theirs, and all other firms can observe the first mover's choice. Thus, in a sequential-move game with a single incumbent in the previous period, the followers' actions are conditional on the first mover's actions. When firms face this scenario, then they use the subgame-perfect Nash equilibrium solution concept to solve the game they play. A subgame-perfect Nash equilibrium is a combination of firm's strategies [y.sup.*.sub.mt] such that no firm can unilaterally benefit from choosing a different strategy at any stage of the game.

When there is at least one subgame-perfect pure strategy equilibrium where incumbent firm h makes non-negative profits, then the statistical model for the sequential-move game is given as follows:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Otherwise, if there is no subgame-perfect equilibrium with incumbent h in the market, the statistical model is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

To illustrate the type of game that firms play at each period, consider Table 2, which presents several possible scenarios with two airlines (American and Delta) in one particular market. In the first quarter of 1998, neither of the two airlines was serving this particular market. Therefore, in the second quarter of 1998, there was no incumbent, and thus the two airlines moved simultaneously in the second stage, and the result is the same as the simultaneous-move game. Among the possible realizations, the airlines ended up in the one where American entered into the market, while Delta did not enter. In the third quarter of 1998, American is now the incumbent and moves first, and Delta follows. The interpretation of the game in the other quarters is analogous.

Consider now the game played in the third quarter of 1998 by the two firms. American was the incumbent in the second quarter, and thus American must decide whether or not to enter before Delta makes its decision. To determine the one-shot equilibrium of the game, the game is solved through backward induction. First, we determine the Nash pure strategy equilibria in the second stage of the game, the one where only Delta must decide whether to enter, given the decision made by American. Then, we determine whether in the second stage equilibrium "chosen" by Delta, American makes non-negative profits. If there is such an equilibrium (or more) in the second stage, American can pick it by moving first.

Consider, for example, the situation where there are two equilibria in the case where there was no incumbent in the previous period, and both American and Delta move simultaneously. Let the categorical variable [y.sub.AA] = 1 if American is in the market, otherwise [y.sub.AA] = 0. Similarly, [y.sub.DL] = 1 if Delta is in the market. Let the first equilibrium be = (0,1): American does not enter, while Delta enters into the market. Let the second equilibrium of the last stage game be ([y.sub.AA], [y.sub.DL]) = (1,0): American enters, Delta does not enter. In the case that American was the incumbent in the previous period, there will be a unique equilibrium. ([y.sub.AA], [y.sub.DL]) = (1,0).

The two scenarios that the firms face are based on whether or not there was an incumbent in the previous period. They have the same payoffs but they possibly have different equilibria. The set of equilibria when there is an incumbent in the previous period is a subset of the set of equilibria when there is no incumbent in the previous period. This observation leads to the discussion concerning the estimation.

If the firms play a sequential-move game in a market when there is an incumbent in the previous period, and there is a unique equilibrium, then the inequalities (3) hold with equality. The way we derive the equalities and inequalities is conceptually analogous to the way that Ciliberto and Tamer (2009) derive the inequalities for the simultaneous-move game.

First, we estimate nonparametrically the empirical probability of each market structure as in the first step for the estimation of the parameters in the simultaneous-move game, except that now we need to include the information on whether or not there is an incumbent, and its identity.

Then, we determine the scenario the firm faces based on the exogenous history of the game. In particular, we determine for each market m in each period t the equilibria of the simultaneous-move game. Then, we determine whether there is at least one equilibrium where the incumbent (e.g., American) is in the market among these simultaneous-move equilibria. As in the example above, if there is such an equilibrium, then the incumbent will move first and will be able to select this equilibrium. Clearly this process is only applied if there is an incumbent in the market; otherwise, we solve the game as if it were a simultaneous-move game.

C. A Game of Strategic Deterrence

Generally, the fact that one airline, say American, has the first-mover advantage does not imply that there exists a subgame-perfect equilibrium where American is in the market. This only occurs if there is one subgame-perfect equilibrium where American is in the market. This is where the role of strategic deterrence comes into play. Following Bemheim (1984), we will assume that an incumbent can opt to deter new entrants when the game is sequential. An incumbent firm i can make deterrence investments by paying a deterrence cost [c.sub.i] at time t and ensure that it will be a monopolist at time t + 1.

To understand the role of the deterrence investments, consider again the example of the strategic interaction between American and Delta illustrated in Table 2. In the third quarter of 1998, American must decide first whether to deter new entrants. If American pays a deterrence cost [c.sub.AA], then American can deter new entrants and make the expected value of the stream of future profits when the firm is a monopolist today, [[pi].sup.M.sub.AA]. American's value to entry would then be given by [[pi].sup.M.sub.AA] - [c.sub.AA]. If American does not pay the deterrence cost, then the airlines play the sequential game just described.

American will deter new entrants if: (1) the cost of deterrence is lower than the monopoly value to entry and (2) the profit that American makes under deterrence, [[pi].sup.M.sub.AA] - [c.sub.AA], is not smaller than the lowest value to entry that American would make in any of the subgame-perfect equilibria of the sequential game played by airlines should American not deter new entrants. Thus, American might not deter new entrants even when it could do so. (5)

In the sequential-move game where firms can make deterrence investments we proceed as follows. As in the sequential-move game, we first estimate the empirical probability of each market structure conditional on whether one of the firms was a single incumbent in the previous period. So the first stage nonparametric estimates are the same in the case when we allow firms to play a sequential-move game and when we allow them to make deterrence investments.

Then, we solve the game as if the firms were playing a sequential-move game; that is, as if they did not have the possibility to make deterrence investments. We then compute the profits of the incumbent in each of the subgame-perfect equilibria of the sequential game. Among all these profits we choose the one where the incumbent makes the lowest profit. Next, we compute the "deterrence profit," given by the profit that the incumbent would make as a monopolist, and we subtract the deterrence cost c. We compare the "deterrence profit" of the incumbent to the lowest profit that the incumbent would make in the equilibria of the sequential game. If the "deterrence profit" is lower, then the incumbent plays a sequential game; if the profits minus the deterrence costs are non-negative, the incumbent incurs the deterrence cost and deters new entrants.

If there is a subgame-perfect equilibrium where incumbent firm h makes non-negative profits and where the profits are larger than those that incumbent firm h would make with deterrence investments, then the statistical model for the deterrence game is written as:

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

If, however, firm h, the first mover, makes higher profits when it deters new entrants, then the statistical model is given as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

IV. DATA AND VARIABLES

A. Data

The main data are from the Airline Origin and Destination Survey (DB1B) from the year 2004; these data include details on each domestic itinerary, including operating carrier, origin carrier, origin and destination airports, number of passengers, distance, and the fare. We merge this dataset by operating carrier with the T-100 Domestic Segment Dataset, which contains domestic market data by air carriers, origin, and destination airports for passengers enplaned. Unlike the DB1B dataset, the T-100 is not a sample; it reports all domestic flights in a given month of the year. From the merged dataset, we drop tickets with flights that have a frequency that is less than weekly, and we also drop tickets with flights for which there is no record in the T-100 Segment. We then clean the dataset as described in Ciliberto and Tamer (2009). (6) The unit of observation in the cleaned dataset is by market-carrier-year-quarter. Since we are only interested in knowing whether or not a carrier served a market, we construct an indicator variable that equals 1 if the carrier serves the market and 0 otherwise. Therefore, the unit of observation is by market-year-quarter in the final dataset. Time is denoted by t, and a unit of observation is individually denoted by the triple jmt.

We define a market as a trip between two airports, regardless of intermediate transfer points and direction of flight. Thus, the entry decision of an airline means that the airline starts a nonstop or connecting service between two airports. Table 1, which lists informal complaints about unfair exclusionary practices, provides insights on the nature of competition between low cost carriers and national carriers, and we use these insights to determine the relevant markets. We merge our data with demographic information from the U.S. Census Bureau for all MSAs of the United States. We then rank airports by the MSA's market size. To maintain exogeneity of selection of markets to the observed patterns of entry, we include all markets out of the top 150 MSAs as ranked by their population. (7) We then drop all markets where the two endpoints are both in the top 30 MSAs. (8) We also include markets that are temporarily not served by any carrier, where the number of observed entrants is equal to zero. (9)

We consider five national carriers (American, Continental, Delta, Northwest, United). As in Ciliberto and Tamer (2009), we build a categorical variable Medium Airlines, [MA.sub.mt], that is equal to 1 if either America West, US Air, Alaska, or Southwest is in market m at time t. (10) Small, low cost earners are present in only a few markets. Rather than dropping these carriers from the market analysis because we cannot identify their impact on the entry decisions of competitors, we group them in a meaningful way in order to capture the impact of their presence. To this end, we construct an indicator variable, Low Cost Carrier Small, [LCC.sub.MT], which is equal to 1 if one or more low cost carriers are present in the market, and 0 otherwise. Carriers are denoted by i. We exclude all markets in which one of the carriers has a hub at either endpoint.

As in Ciliberto and Tamer (2009), the entry decision in each market for each airline is interpreted as a " marginal" decision, and the airline's network structure is taken as given. This marginal approach to the study of airline markets is also used in the literature that studies the relationship between market concentration and pricing. For example, Borenstein (1989) does not include prices in other markets out of Atlanta (e.g., ATLORD) to explain fares in the market ATL-AUS.

B. Variables

Following Berry (1992), we use the carrier's Airport Presence at the market's endpoints to construct measures of carrier heterogeneity. We compute a carrier's ratio of markets served by the carrier out of an airport over the total number of markets served out of an airport by at least one carrier. We then average the carrier's airport presence at the two endpoints to define the carrier's Airport Presence. (11)

A firm- and market-specific measure of cost is not available. To proxy for the cost that a carrier incurs in order to serve a particular market, we construct a measure of the opportunity fixed cost of serving a market. To do this, we first compute the sum of the geographical distances between a market's endpoints and the carrier's closest hub. (12) Then, we compute the difference between this distance and the nonstop distance between the two airports, and we divide this difference by the nonstop distance. This ratio can be interpreted as the percentage of the nonstop distance that must be traveled if the airlines were to use a connecting flight instead of a nonstop flight to serve the market. This is a good measure of the opportunity fixed cost of serving a market, because it measures the cost of the best alternative to nonstop service, which is a connecting flight through the closest hub. This measure is associated with the fixed cost of providing airline service because it is a function of the total capacity of a plane but does not depend on the number of passengers transported in a particular flight. We denote this variable as Cost.

We include six control variables. Three are demographic variables. (13) We calculate Market Size as the geometric mean of the city populations at the market endpoints in order to measure the size of the potential market. We use average per capita incomes (Per Capita Income) and the average rates of income growth (Income Growth Rate) of the cities at the market endpoints to measure the strength of the economies at the endpoints. The other three control variables are geographical variables. Market Distance is the nonstop distance between the endpoints. The distance from each airport to the closest alternative airport (Close Airport) controls for the strength of passengers' alternative option, which is to fly from a different airport to the same destination. (14) Finally, we also include the sum of the distances from the market endpoints to the geographical center of the United States (US Center Distance). This variable controls for the fact that, just for purely geographical reasons, cities in the middle of the United States have a larger set of close cities than cities on the coasts or cities at the borders with Mexico and Canada. (15)

Table 3 presents summary statistics for the exogenous variables that determine entry. (16) All the variables are means within a market.

In order to run the estimation and compute the confidence intervals using Chernozhukov, Hong, and Tamer (2007), we discretize the continuous variables. Variables could be discretized in quartiles or deciles; here, we discretize the variables using extremely fine discretizations so that the discrete variables have the same means and standard deviations as the continuous variables.

V. IDENTIFICATION

A. Identification of Strategic Deterrence

There are at least three reasons why one firm might be a monopolist for a long period of time in a market that are completely unrelated to strategic deterrence.

First, a firm might have a particularly high market-carrier shock, allowing it to operate as a monopolist over a long period of time. To address this possibility, we use the basic idea that one bad shock to a firm cannot explain why a firm never enters in a market where American is the incumbent. If the other firm is profitable on average, then that firm should enter unless American deters its entry. To allow for deterrence from a high market-carrier shock, we include r\im.

Second, there might only be space for one firm in the market, in the sense that two firms would not be able to both make non-negative profits. However, if this is the case, then we should see no pattern in the identity of the monopolist over time. Third, there might be multiple equilibria with different number of firms in a market, and we might simply observe the equilibrium with one firm rather than one with two or more firms. Table 4 illustrates how we plan to identify strategic deterrence from these other two possibilities.

There are two firms that compete against each other in one market, and for simplicity of exposition, we again consider American and Delta as the two competing firms. At time 0, neither firm is present in the market, because neither firm makes non-negative profits. Then at time 1, there is a positive shock to the profits of both firms and either one but not both of the firms can enter into the market, and American enters. At time 2, there is another positive shock to the profits of both firms, and now both American and Delta can profitably enter into the market. However, we observe only American in the market. At time 3, there is a negative shock to the profits of both firms and American must exit the market. At time 4, there is a positive shock to both profits and either one but not both of the firms can enter into the market and this time Delta enters. At time 5, there is another positive shock to both profits and both American and Delta enter into the market.

American was able to prevent the entry of Delta when American was the incumbent, while Delta was not able to prevent the entry of American when Delta was the incumbent.

Table 4 lists hypothetical possible situations in a deterrence game between two airlines. A negative value of [c.sub.i] indicates that there is a positive cost of deterrence, and a negative [[delta].sub.j] indicates that competitor j has a negative effect on i's profits. Table 4 implies that American must face lower deterrence costs than Delta and that American did deter Delta from entry at time t = 2. The last column of Table 4 shows how the identification strategy discussed in the first two columns of Table 4 can be used to identify the cost that airlines must incur to deter new entrants. Since American deterred Delta from entry at time t = 2, then it must be that [[pi].sup.M.sub.AA] + [c.sub.AA] > [[pi].sup.M.sub.AA] + [[delta].sub.DL], that is the value to entry of American in this market when it deters Delta is higher than the value to entry of American as a duopolist. On the contrary, [[pi].sup.M.sub.DL] + [c.sub.DL] > [[pi].sup.M.sub.DL] + [[delta].sub.AA], Delta's value to entry as a monopolist in this market is not large enough to justify the deterrence costs. The variation across and within markets identifies [[pi].sup.M.sub.AA], [[pi].sup.D.sub.AA], [[pi].sup.M.sub.DL], [[pi].sup.D.sub.DL], [c.sub.AA], and [c.sub.DL].

The critical feature of this stylized model is that the incumbent faces a trade-off. The incumbent can deter new entrants, but only at a cost [c.sub.i]. Whether the incumbent will actually deter new entrants depends on the characteristics (and unobservables) of the market and of the new entrant.

The critical variation that is needed for the econometric analysis concerns new entry and exit. In order to identify the role of strategic deterrence, it is crucial to see firms entering in markets that were not previously served by any airline and firms entering in markets that are already served by other airlines. This variation in the market structure within markets over time separately identifies the effect of strategic deterrence from the role that sunk costs, operating costs, and demand changes have on market structure. Table 5 illustrates this type of variation in the data.

There are 756 new entries over the time period considered. Some patterns are clear from the table. First, most of these new entries occur where there is more than one incumbent in the market or where there are no incumbents. Only 20% of the new entries were in markets where there was only one incumbent. Second, low cost carriers enter disproportionately in markets where there are other incumbents. Finally, there is less entry by the national airlines where a LCC is the only incumbent in the market.

B. Exclusion Restrictions

We assume that the unobservables are not correlated with our exogenous variables. We consider a reduced form profit function, where all of the control variables (e.g., population and distance) are maintained to be exogenous.

The main difficulty of estimating Model (1) is given by the presence of the competitors' entry decisions, since it is a simultaneous move entry game. Theorem 2 in Ciliberto and Tamer (2009) shows that we can identify the parameters with an exclusion restriction consisting of a variable that enters firm i's profit but not firm j's. If this variable has wide support (i.e., a large degree of variation), then this reduces the size of the identified set. We have two variables that work as exclusion restrictions: Airport Presence and Cost.

VI. RESULTS

We present the results for the empirical specifications in the same order as the statistical models in Section III. We present the results for the (repeated static) simultaneous, sequential, and deterrence games. Then we compare the results across the various specifications.

In our results, we report superset confidence regions that cover the truth, [[theta].sub.l], with a pre-specified probability. This parameter might be partially identified. Since, in general, these models are not point identified, and since the true parameter, along with all parameters in the identified set minimize a nonlinear objective function, we report confidence regions that cover the true parameter value and that can be used as consistent estimators for the bounds of the partially identified parameter [[theta].sub.I]. In each table, we report the cube that contains the confidence region that is defined as the set that contains the parameters that cannot be rejected as the truth with at least 95% probability. (17)

Column 1 of Table 6 presents the results of the estimation of a static simultaneous-move game. Here, the effect of American's entry is different from the effect of Delta's entry on other airlines. However, American's entry affects all its competitors in the same way. For example, [[delta].sub.AA] [not equal to] [[delta].sub.DL]. The effect of American on all of its competitors is included in [-11.589,-9.597], while the effect of Continental is included in [-13.816,- 11.926]. This implies that the entry of a second competitor is less likely if Continental enters the market than if American does. The negative effect of the entry of an LCC on the probability of entry of another competitor is even stronger, as it is included in [-18.954,- 16.335]. Overall, LCCs have the strongest negative effect on competitors, as was also found in Ciliberto and Tamer (2009). American has the weakest effect, while the other airlines are comparable ([-12.436,-10.834] for Delta, [-12.681, -11.103] for the MA type, [-12.910,-11.190] for Northwest, and [-12.801,- 10.324] for United). In general, the results in column 1 of Table 6 do not provide any support for the hypothesis that larger airlines are more aggressive than low cost airlines. Instead, low cost airlines are the most aggressive in the market, since it is much less likely that other firms enter when they are present.

Next, market presence, the measure of heterogeneity, has a strong positive sign and is included in [11.422, 13.233]. The higher the percentage of markets that one airline serves out of an airport, the more likely it is that a firm enters into a market. This is consistent with previous work (Berry 1992; Ciliberto and Tamer 2009). The distance from the hub of an airline (our measure of fixed costs) is negatively associated with entry ([-2.408, -0.868]), which we expected. Both of these results are robust across the three columns in Table 6.

The remaining rows of column 1 in Table 6 present the results for the control variables. The effect of market distance is included in [0.772,1.362], which implies that entry is more likely when the distance between cities is larger. The effect of market size is included in [1.711,2.407], which implies that larger markets are more likely to be served. Markets whose endpoint cities are seeing their incomes increasing are more likely to be served ([0.646,1.469]). Markets between cities that have multiple airports are less likely to be served, ceteris paribus. This does not imply, of course, that cities with multiple airports are less likely to be served; it just says that airlines are not likely to serve two markets out of the same city. These four results are robust across the three specifications. Then, there are two results concerning the distance from the geographical center of the United States and the distance among airports of a city. Neither of these results is robust to changes in the specifications, and it is thus difficult to draw a clear interpretation.

We calculate the goodness of fit by taking the percentage of realized observations that were correctly predicted by the model. For example, in the simultaneous game, if the realized observation is any one of the multiple equilibria predicted by the model, we consider that observation as correctly predicted. In the deterrence game, if there was not a single incumbent in the previous period, then all firms move simultaneously and the model predicts multiple equilibria. As in the simultaneous game, we consider the observation as correctly predicted if it is one of the equilibria the model predicts. If there is a single incumbent in the previous period, and the model predicts deterrence, then the resulting predicted equilibrium is unique and is counted as correctly predicted if it matches the observation in the data.

The fact that additional parameters are estimated in the deterrence game does not, by itself, account for the increased goodness of fit. For example, suppose there is a market in which we see either American or Continental but not both over a certain period of time. In the sequential-move game, this would suggest that given the competitive effects of those two airlines, the market can only support one firm, and the model would predict exactly that: either American or Continental, but not both, and this would predict behavior in this market well. In the deterrence model, we would predict that there would be persistence in the identity of the firm that is unexplained by the unobservable. That is, if we saw American in the market at time t - 1, the model would predict only American to be in the market at time t. In this way, the predictions in the deterrence model are more restrictive than the predictions in the other two models that allow for multiple equilibria. The fact that we are able to predict more observations correctly under the deterrence model strongly suggests that airlines do, indeed, deter new entrants.

Column 2 of Table 6 presents the results of the estimation of the game where firms can play sequentially. Recall that this is the framework where the type of game that firms play depends on the exogenous history of the game. If there is a single incumbent, then the firms play a sequential-move game. Otherwise, the firms play a simultaneous-move game. The estimation results in column 2 are quite similar to those presented in column 1 of Table 6. The only relevant difference is in the magnitude of the strategic effects for the larger firms, but the differences are not statistically significant as the intervals overlap. Similarly to the simultaneous game, we calculate the goodness of fit by calculating the percentage of realized observations that are correctly predicted by the sequential game model. Using the estimated parameters, we predict when incumbents would move first, thereby restricting the equilibria to those in which the incumbent serves the market. When the realized equilibrium is one of our predicted equilibrium, we consider that observation as being correctly predicted. In the sequential-move game, we do slightly worse in our predictions, though the difference is not significant.

Column 3 of Table 6 presents the results when firms can make deterrence investments. This is the first set of the central results of the article. The results are very rich and we have designed Figure 1 to go over them in two steps. First, we discuss how the "competitive effects," 5, differ in column 3 from columns 1 and 2. Then, we discuss the estimation results for the cost of the deterrence investments, c.

First, we observe that the competitive effects are, in some cases, larger in magnitude in column 3 than they were in columns 1 and 2. For example, we find that the effect of American on its competitors is now in [-13.722,- 11.155] while before it was in [-11.589,-9.597]. Thus, it is larger (in absolute value) and statistically different. We find similar results for Continental and Delta. Remarkably, we find the opposite for the low cost carriers, as now their effect on competitors is in [-15.590, -12.490], while in column 1, it was in [-18.954, -16.335]. The results for MA, Northwest, and United are similar across the three columns. In the simultaneous-move game, the competitive effect of the presence of a low cost carrier has a larger effect than any other airline.

However, if we allow for deterrence, the estimate of the competitive effect overlaps those of all of the other airlines. This has important implications for policy. For example, the static model suggests that decreasing the cost of entry to only low cost carriers would decrease prices more than decreasing cost of entry to all airlines. However, if there is persistence in the market that is explained by deterrence, then there is no reason to treat low cost carriers differently than any other airline. These are interesting results and indicate that allowing for deterrence investments can lead to different estimates of the competitive effects than when we do not allow for firms to deter, which in turn informs policy.

Now, consider the estimates of the costs of deterrence. These costs are crucial for our analysis, because the higher they are, the less likely it is that a firm deters new entrants. We find that American can deter the entry of new firms in its markets by paying deterrence costs included in [-7.458, -3.441], These costs are lower than the competitive effects of any of American's rivals (the lowest is Northwest, which is included in [-12.989, -10.561]). This implies that American would definitively pay the deterrence cost if it had the option to do so. The analysis is the same for all the other firms except for United, whose costs of deterrence overlap the competitive effects of American, Continental (though by little), LCCs, MA, and Northwest. This implies that United would only make deterrence investments if facing the potential competition of Delta. We will return to this finding below.

Overall, these results are striking and indicate that all firms have an incentive to make deterrence investments, though they face different costs of doing so. (18)

To determine the fit of the model to the data, we estimate the model under the deterrence parameters and predict when firms would deter entrants. When firms deter, we predict only one equilibrium (the incumbent remains in the market as a monopolist). When the incumbent does not deter, the firm still has a first-mover advantage and the firms play a sequential game. Under these assumptions, we correctly predict almost half of the observed outcomes. Since the deterrence game restricts many market predictions to a single equilibrium (incumbents deter the majority of the time) instead of allowing for multiple equilibria as in the simultaneous and sequential games, the increased goodness of fit provides strong evidence that firms are, in fact, using deterrence investments.

[FIGURE 1 OMITTED]

VII. COMPARING PROFITS ACROSS TYPES OF GAMES

The results in this section compare the profits made in the deterrence game to those made in the sequential game and the profits made in the sequential game to those made in the simultaneous-entry game. Because we can only identify the profits up to a scale, we follow Bresnahan and Reiss (1990) and use the ratios of profits in the different games to gauge the economic importance of being a first mover in the context of sequential-move and deterrence games. We calculate these ratios by comparing the deterrence profits under the deterrence scenario to the sequential profits using the parameters in the sequential-move game (column 2 of Table 6). (19) In the remaining analysis we use the parameter values where the distance function is minimized and simulate 1,000 errors and compute the profits. The ratios of these profits are reported in Tables 7 and 8.

We begin with the simultaneous-move game and we use the parameters in column 1 of Table 6. We first check if there is a unique equilibrium because in that case we have one profit for each firm in the equilibrium. If there are multiple equilibria, then for each incumbent firm we consider three possibilities: (1) the highest profit that the firm makes among all the possible equilibria; (2) the lowest profit, which can be zero if the firm is not in the unique equilibrium or if the firm is not in at least one of the multiple equilibria; and (3) the case where the equilibrium is selected randomly, with equal probabilities across equilibria.

For sequential-move equilibria without deterrence investments, equilibrium profits are calculated using the parameters estimated in column 2 of Table 6. As discussed above, the incumbent moves first but we do not allow for the incumbent to choose the specific resulting equilibrium. For example, suppose American is the incumbent. If there are multiple duopoly equilibria, American can choose to be one of the firms in the market, but it cannot choose its competitor. Therefore, we report bounds on the sequential profit, where the lower bound is the minimum profit the incumbent could make in the sequential game and the upper bound is the maximum profit the incumbent could make in the sequential game. The reported sequential profit is the average profit for the incumbent firm.

For equilibria in the game with deterrence investments, we use the parameter estimates in column 3 of Table 6. As before, we simulate the games 1,000 times and take the average profit that each firm makes when it chooses to deter.

Table 7 reports the ratio of sequential profits to simultaneous profits. The simultaneous equilibrium profit is calculated using three different methods, as explained above. In column 1, the values have a range that falls below 1 for most firms, which implies that firms, on average, actually do better when they are able to choose the best possible equilibrium in the simultaneous game than in a sequential game. The second column in Table 7 reflects the "worst case" simultaneous profits, where each simultaneous equilibrium is chosen as the lowest profit for the firm, and we find, as expected, that the profits made in the sequential game are substantially higher than the worst-case scenario of the simultaneous game. (20)

The third column in Table 7 reports the ratio of sequential profits to simultaneous profits when the simultaneous equilibrium is chosen at random from all possible equilibria. The randomized simultaneous profits provide perhaps the most informative ratio in the sense that the randomized profits reflect the average profits a firm would make in the simultaneous game, if the simultaneous game were played many times. For example, American makes, on average, somewhere between 0.441 and 2.896 times as much profit when it plays a sequential game versus a simultaneous game where the simultaneous equilibrium is truly chosen randomly.

Table 8 reports the ratio of deterrence profits to sequential profits, where the deterrence profit is calculated in two different ways. A firm either compares the profit when it deters to its maximum possible profit in the sequential game (columns 1 and 2), or it compares the deterrence profit to its minimum possible profit in the sequential game (columns 3 and 4). In the first column, we compare the deterrence profit to the maximum sequential profit. In the third column, we compare the deterrence profit to the minimum sequential profit. (21)

When American decides to deter based on its maximum possible profit in the sequential game, it makes 1.677 times as much profit in the deterrence game compared to its best profit in the sequential game and deters 92% of the time when it is an incumbent. The remainder of the time, the firm plays the sequential game. When comparing its deterrence profit to the minimum possible sequential profit, American makes, on average, 11.001 times more profit when it chooses to deter. It still enters the market 92% of the time. For all firms except United, the decision to deter does not change when comparing the minimum to maximum sequential profits. (22) This implies that the profits in the sequential game are generally much lower than when firms choose to deter.

Our results that are reported in Table 8 suggest that (with the exception of United), when an airline can deter new entrants, it will almost always do so. If this is true, this has implications for many policies, including merger analysis. Suppose we have a market where there are three airlines, American, Continental, and Delta. Under the simultaneous model, a merger between American and Continental would change the competitive effect of the new merged airline. This may result in Delta entering the market less often, but only through the competitive effect; moreover, if the competitive effect of the new merged airline is less than the sum of the competitive effects of American and Continental, then Delta may be present in the market more often. If, however, the new merged airline is able to deter, then it will do so over 90% of the time, and Delta will enter the market substantially less, and there would be fewer options for the consumers in that market.

Last, we examine the bounds on the ratio of profits for different pairs of firms. (23) These results are reported in Table 9. The columns compare the profits of various firms to American's profits. The first row shows these ratios in the simultaneous game, the second row for the sequential game, and the third row for the deterrence game.

In the simultaneous game, Continental and Delta both make higher profits than American does, with Continental's estimate of profits at 1.27 to 3.58 times American's. The results are similar for Delta, and the upper bound on these two ratios is quite high. In the simultaneous game, United makes about the same profit as American, and low cost carriers appear to make less than American does, with the lower bound at 0.089. This lower bound on low cost carriers' profits is very low, indicating that the simultaneous game may not give the best measure of actual airline profits. Since Continental and Delta both make more than American, and United makes about the same amount, these results also imply that low cost carriers are the least profitable firms in the industry.

The results for the sequential game differ somewhat from those in the simultaneous game. Continental and Delta are still estimated to make higher profits, but at a lower ratio. The estimate for the low cost carriers is more reasonable, with the lower bound at 0.350 and the upper bound at 1,242. In this game, United makes less than American rather than close to the same amount. Overall, these estimates give the ratios of profits across firms to be much closer together than the simultaneous game.

In row three, the results of the deterrence differ from both the simultaneous and sequential game in two important ways: first, the ranges estimated on the ratios are much tighter than the other two games; second, the overall range of profits is lower, with the lowest bound at 0.612 (for United) and the highest at 1.59 (for Delta). In the deterrence game, Continental is estimated to make about 84% of the profit that American does, while in the other two games. Continental is estimated to make at least 25% more than American. LCCs, on the other hand, are estimated to make more than American (and therefore Continental and United) in the deterrence game, which is reasonable. The results from these ratios across games provide further evidence that the deterrence game provides the best fit to the data.

VIII. CONCLUSIONS

We use a practical approach of estimation to determine whether firms make investments to raise barriers to deter new entrants. The objective of the estimation is to quantify the cost of "deterrence investments" (Bernheim 1984) and relate them to the monopoly profits that firms make when they successfully deter new entrants and the profits that they would make as accommodating oligopolists. We model firms as playing different types of games depending on the exogenous history of the game in each market. We find that the data are consistent with a model where firms make deterrence investments. This provides evidence that the static assumption made in entry game models would understate profits made in the airline industry. Also, we find that the profits incumbents can make if they move first are larger than those that they can make if the game is played simultaneously. This result is stronger, as one would expect, when incumbents can deter new entrants. Finally, we find that all firms deter new entrants, with the exception of United Airlines.

There are several limitations to our work which we leave for future research. First, and most obviously, we find that firms make deterrence investments, but we do not characterize the nature of those investments. This avenue of research is clearly important for policy interventions. Second, we consider a repeated static game where the history of the game in each period is exogenous. Flowever, firms are likely forward looking when they make their investment decisions. This avenue of research is important to exactly quantify the cost of deterrence. However, the benefit of deterrence should be even higher if we allow for its benefit to extend over time, because firms would be able to maintain their position as incumbents longer. Therefore, we can still think of our estimates as providing a measure for what would be the best case scenario for airlines that wanted to make the case that they do not deter new entrants. Since we do find evidence of strategic deterrence even in a repeated static game, we would expect our findings to be even stronger in a dynamic game. ABBREVIATIONS LCC: Low Cost Carrier MSA: Metropolitan Statistical Area

doi: 10.1111/ecin.12381

Online Early publication August 8, 2016

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FEDERICO CILIBERTO and ZHOU ZHANG *

* We would like to thank Victor Aguirregabiria. Michael Mazzeo, Steven Stern. Andrew Sweeting, Elie Tamer, and Jonathan Williams for valuable comments. We thank Ed Hall and the University of Virginia Alliance for Computational Science and Engineering, who have given us essential advice and guidance in solving many computational issues. All remaining errors are our own. Research support from the Bankard Fund for Political Economy at the University of Virginia is gratefully acknowledged.

Ciliberto: Department of Economics, University of Virginia. Charlottesville. VA 22904. Phone 434-9246755, Fax 4349822904, E-mail ciliberto@virginia.edu

Zhang: Seattle, WA. Phone 908-868-3183, E-mail zhou.zhang@gmail.com [Correction added on 7 September 2016, after first online publication: The author's affiliation has been removed due to company policy. The company has in no way been involved in this research.]

(1.) We maintain that the scale of the components is the same. In Ciliberto and Tamer (2009), it was maintained that the scale of all the components was the same except for one specification, where they estimated a covariance matrix for the individual component, here denoted by [[zeta].sub.jmt]. Even in that covariance matrix, one of the variances had to be normalized to 1. In this article, for computational simplicity, we have not run any specification where the individual component is free.

(2.) Ideally one would want a more general model where firms have different effects on each other, but that has a much larger set of parameters, and we have already the deterrence costs to estimate. We do not have a sense of the magnitude of the bias that is introduced by imposing symmetry, but we presume that the bias would affect both the deterrence cost estimates and the competitive effects, and we presume that the key results of the article would stand.

(3.) Boguslaski, Ito, and Lee (2004) examine entry patterns by Southwest Airlines in order to identify which carriers are most vulnerable to competition from Southwest.

(4.) To allow for a deterrence game to be played when more than one incumbent is present would complicate the modeling considerably. The key difficulty is that there would be an incentive for either incumbent to free ride on the other one, so to avoid the cost of deterrence while enjoying the benefits of having an additional entrant in the market. In addition, the benefits from deterrence would be smaller, since two firms would be now in the market, and thus the costs would have to be smaller as well. We cannot envision a pure strategy equilibrium where both firms incur the deterrence costs, unless we model the game between the firms as one where long-run collusion strategies can be chosen by the firms, which is well beyond the scope of our article. Overall, we believe that Bernheim's model, with only one incumbent firm as the case where deterrence can occur, is the most realistic in this context.

(5.) In principle, we could specify the investment costs as functions of market and firm characteristics. We leave that to future work. Notice, however, that we cannot specify the investments as continuous choice, as this would lead to a model where firms make both discrete and continuous decisions simultaneously, which is well beyond the scope of this article.

(6.) In particular, we drop: (1) Tickets with more than six coupons; (2) Tickets involving U.S.-nonreporting carrier flying within North America (small airlines serving big airlines) and foreign carrier flying between two U.S. points; (3) Tickets that are part of international travel; (4) Tickets involving noncontiguous domestic travel (Hawaii. Alaska, and Territories); (5) Tickets whose fare credibility is questioned by the DOT; (6) Tickets that are neither one-way nor round-trip travel; (7) Tickets including travel on more than one airline on a directional trip (known as interline tickets); (8) Tickets with fares less than 20 dollars; (9) Tickets in the top and bottom five percentiles of the year-quarter fare distribution. We define a firm as serving a market if it transported at least 20 passengers in one quarter, as in Ciliberto and Tamer (2009).

(7.) Following Borenstein (1989), we assume that flights to different airports in the same metropolitan area are in separate markets.

(8.) The list of the MSAs is available from the authors.

(9.) To distinguish markets that are almost never served by any carrier from markets that are only temporarily not served by any carrier, we proceed as in Ciliberto and Tamer (2009). Using the data from 1996 to 2007, so for a longer period of time than the one we use in the estimation, we compute the number of quarters that a market has been served by at least one carrier, for each market, m. We drop all markets that were not served in at least 50% of the quarters in the full dataset.

(10.) As explained in Ciliberto and Tamer (2009), an important issue is how to treat regional airlines that operate through code sharing with national airlines. If the regional carrier is independently owned and issues tickets, then we treat it as an independent carrier.

(11.) In the case of the Medium Airlines (MA), we first compute the airport presence for USAir, Alaska, Southwest, and America West, and then we take the maximum of the three. In the case of the LCC, we first compute the airport presence of each of the low cost carriers, and then again we take their maximum.

(12.) Data on the distances between airports, which are also used to construct the variable Close Airport are from the dataset Aviation Support Tables: Master Coordinate, available from the National Transportation Library. To construct the measure of Cost we consider the following hub airports: Dallas Fort Worth and Chicago O'Hare for American; Cleveland. Houston International, and Newark for Continental; Atlanta. Cincinnati, and Dallas Fort Worth for Delta: Phoenix and Las Vegas for America West; Minneapolis and Detroit for Northwest; Denver and Chicago O'Hare for United; Charlotte, Pittsburgh, and Philadelphia for USAir. To derive the measure of Cost for the Medium Airlines (MA) we take the minimum among the distances that we compute for Continental, USAir, America West, and Northwest. Southwest does not really have major hubs; it uses several airports, among which we consider Chicago Midway, Baltimore, Las Vegas, Houston Hobby, Phoenix, Orlando. With the exception of ATA, LCCs do not have hubs in the same sense that we mean for the largest carriers. To construct a measure of the cost, we computed the (minimum) distance from airports where LCCs had a meaningful presence.

(13.) Data are from the Regional Economic Accounts of the Bureau of Economic Analysis, downloaded in February 2005.

(14.) For example, Chicago Midway is the closest alternative airport to Chicago O'Hare. Notice that for each market we have two of these distances, since we have two endpoints. Our variable is equal to the minimum of these two distances. In previous versions of the paper, we addressed the concern that many large cities have more than one airport. For example, it is possible to fly from San Francisco to Washington on nine different routes. In a previous version of the paper, we allowed the firms' unobservables to be spatially correlated across markets between the same two cities. In the estimation, whenever a market was included in the subsample that we drew to construct the parameter bounds, we also included any other market between the same two cities. This is similar to adjusting the moment conditions to allow for spatial correlation. In our context, it was easy to adjust for it since we knew which of the observations were correlated, that is, ones that had airports in close proximity.

(15.) The location of the mean center of population is from the Geography Division at the U.S. Bureau of the Census. Based on the 1990 census results, that was located in Crawford County. Missouri.

(16.) Several variables, such as prices or market shares are excluded because they are endogenous. For example, markets with a larger number of firms are more likely to see lower prices. We only include variables that are predetermined or clearly exogenous to the entry decision.

(17.) Not every parameter in the cube belongs to the confidence region. This region can contain holes but here we report the smallest "cube" that contains the confidence region.

(18.) Deterrence costs may vary for a number of reasons. Mahoney and Wilson (2014) show there are interactive effects between airlines' networks and consumers' preferences across airports, and this interaction may lead to heterogeneity in deterrence costs across airlines.

(19.) In a typical counterfactual, we would compare profits of the deterrence game under the deterrence scenario to the sequential profits under the parameters estimated in the deterrence game. Instead, we compare the profits assuming the different menu of games the firms could be playing.

(20.) MA is never able to enter the market in the worst case scenario, so the lower bound of simultaneous profits is zero for this firm.

(21.) Note that Table 8 shows that if firms compare the deterrence profit to a sequential game, most firms (except United) deter over 90% of the time. In fact, three firms, including low-cost carriers, deter 100% of the time. This is perhaps surprising, considering that complaints received by the Department of Transportation of aggressive behavior are usually filed by low cost carriers. However, the fact that low cost carriers are the complainants and the prediction that they deter new entrants 100% of the time are not necessarily contradictory. Since low cost carriers serve fewer markets than the national airlines, they have a greater incentive to complain about aggressive behavior against them, especially if they are constantly facing one particular airline. National airlines, on the other hand, face many different low cost firms in few markets, which would decrease the incentive to complain against any particular low cost airline in any particular market.

(22.) The exception is United. United deters much more when comparing the deterrence profit to the minimum sequential profit versus the maximum sequential profit. This could be due to the fact that United faces the highest cost of deterrence, and so would be more sensitive to the relative benefit of deterrence. It could also be the case that the range of profits United makes in the simultaneous game is greater than for the other airlines.

(23.) We show the results for four pairs of firms. The results with the remaining firms are similar and are available on request from the authors. TABLE 1 Informal Complaints Received by the Department of Transportation Complaining Complained Period Markets Involved in the Party Against Complaint AccessAir Northwest (NW) 3/1999 Markets between New York, Los Angeles, and Des Moines and Moline/Quad Cities/Peoria AccessAir Delta, NW, TWA 5/1999 Markets between New York, Los Angeles, and Des Moines and Moline/Quad Cities/Peoria AirTran Delta 8/1998 General Kiwi Continental 2/1998 Niagara-Newark Valuejet Northwest 3/1997 Atlanta-Memphis Valuejet Delta 2/1997 General (e.g., Atlanta-Mobile) Frontier United 1/1997 General (e.g., Denver-Los Angeles) Spirit Northwest 11/1996 Detroit-Philadelphia, Detroit-Boston Vanguard American 10/1996 DFW and Kansas City, Phoenix, Cincinnati, Wichita Air South Continental 3/1996 Newark and Charleston, Columbia, Myrtle Beach Vanguard Northwest 8/1995 Minneapolist and Chicago Midway, Kansas City Valuejet USAir 3/1995 Washington Dulles and Florida, Hartford, Boston. Valuejet Delta 12/1993 Markets out of Atlanta, in particular to Jacksonville. Memphis Reno Air Northwest 3/1993 Reno-Minneapolis Note: From the Special Report 255: "Entry and Competition in the U.S. Airline Industry Issues and Opportunities," Transportation Research Board, National Research Council, July 1999. TABLE 2 The Game Played by Airlines in One Particular Market Time (quarter/year) Airline 1/1998 2/1998 3/1998 AA 0 1 1 DL 0 0 1 Type of game -- Simult. Sequential AA moves first Time (quarter/year) Airline 4/1998 1/1999 2/1999 AA 1 0 0 DL 1 1 1 Type of game Simult. Simult. Sequential DL moves first Note: Observable and unobservable market conditions change over time. TABLE 3 Summary Statistics, by Airline Variables AA CO Airline 0.298 (0.457) 0.259 (0.438) Airline incumbent 0.044 (0.205) 0.072 (0.258) Airline entry 0.034 (0.182) 0.020(0.140) Airport presence 0.344(0.157) 0.227(0.187) Cost 0.576 (1.154) 0.536(1.017) Market distance U.S. center distance Closest airport Market size (population) Change income market Number of airports Number of markets Number of quarters Number of observations Variables DL LCC Airline 0.466 (0.499) 0.141 (0.348) Airline incumbent 0.173 (0.378) 0.002 (0.046) Airline entry 0.046 (0.209) 0.014(0.120) Airport presence 0.530 (0.207) 0.127 (0.083) Cost 0.645 (1.297) 0.510(1.220) Market distance 0.815 (0.477) U.S. center distance 1.220 (0.427) Closest airport 0.347 (0.212) Market size (population) 1.998(0.995) Change income market 4.089 (0.313) Number of airports 1.611 (0.550) Number of markets 844 Number of quarters 4 Number of observations 3,376 Variables MA NW Airline 0.230(0.421) 0.255 (0.436) Airline incumbent 0.010(0.098) 0.065 (0.247) Airline entry 0.038 (0.190) 0.036 (0.188) Airport presence 0.219(0.123) 0.283 (0.180) Cost 0.266 (0.475) 0.868(1.606) Market distance U.S. center distance Closest airport Market size (population) Change income market Number of airports Number of markets Number of quarters Number of observations Variables UA Airline 0.227(0.419) Airline incumbent 0.022 (0.145) Airline entry 0.035 (0.184) Airport presence 0.275 (0.138) Cost 0.803 (1.469) Market distance U.S. center distance Closest airport Market size (population) Change income market Number of airports Number of markets Number of quarters Number of observations TABLE 4 Occurrence of Strategic Deterrence Identity of Possible Firms Firms in Observed Profits of Time Equilibrium in the Data the Firms 0 0 0 (0,0) 1 AA or DL AA ([[pi].sup.M.sub.AA], 0) 2 AA and DL AA ([[pi].sup.M.sub.AA] + [c.sub.AA], 0) 3 0 0 (0,0) 4 AA or DL DL (0, [[pi].sup.M.sub.DL]) 5 AA and DL AA and DL ([[pi].sup.M.sub.AA] + [[delta].sub.DL], [[pi].sup.M.sub.DL] + [[delta].sub.AA]) Note: Possible Firms in Equilibrium indicates the identity of the firms that could be making non-negative profit in equi- librium. Actual Firms in Equilibrium indicates the identity of firms that are observed in the data. TABLE 5 Variation in Entry and Exit One Incumbent New AA CO DL LCC MA NW UA No More Than Entry Incumbent One Incumbent AA -- 6 6 0 0 8 4 19 73 CO 3 -- 11 0 2 1 1 7 43 DL 14 16 -- 0 3 3 3 58 57 LCC 0 1 4 -- 0 2 0 5 37 MA 9 4 16 0 -- 5 3 17 73 NW 5 5 11 0 1 -- 4 26 72 UA 7 1 9 0 2 9 -- 16 74 Total 38 33 57 0 8 28 15 148 429 New Total Entry AA 116 CO 68 DL 154 LCC 49 MA 127 NW 124 UA 118 Total 756 TABLE 6 Regression Results Simult. Move Game Seq. Move Game Coefficient Bounds Coefficient Bounds American, [[delta].sub.AA] 1-11.589 -9.597] [-10.880 -7.231] Continental, [[delta].sub.CO] [-13.816 -11.926] [-12.831 -9.111] Delta, [[delta].sub.DL] [-12.436 -10.834] [-11.956 -8.692] LCC, [[delta].sub.LCC] [-18.954 -16.335] [-16.202 -12.464] MA, [[detla].sub.MA] [-12.681 -11.103] [-10.837 -7.610] Northwest, [[delta].sub.NW] [-12.910 -11.190] [-12.687 -9.206] United, [[delta].sub.UA] [-12.801 -10.324] [-11.157 -7.232] Deterrence cost AA, [c.sub.AA] Deterrence cost CO, [c.sub.CO] Deterrence cost DL, [c.sub.DL] Deterrence cost LCC, [c.sub.LCC] Deterrence cost MA, [c.sub.MA] Deterrence cost NW, [c.sub.NW] Deterrence cost UA, [c.sub.UA] Market Presence [11.422 13.233] [8.680 9.988] Min Cost Hub [-2.408 -0.868] [-2.029 -1.344] Market Distance [0.772 1.362] [0.718 1.372] From Center [-1.304 -0.502] [-0.517 0.055] Min Distance [-1.513 0.159] [0.608 2.449] Market Size [1.711 2.407] [1.198 1.683] Change Income [0.646 1.469] [0.513 1.713] Number Airports [-1.726 -0.799] [-0.661 0.049] Constant [-1.613 1.544] [-3.318 0.254] Function Value 1735.521 1881.632 Goodness of Fit 0.37 0.34 Number Obs 3,376 3,376 Deterrence Game Coefficient Bounds American, [[delta].sub.AA] [-13.722 -11.155] Continental, [[delta].sub.CO] [-15.870 -13.052] Delta, [[delta].sub.DL] [-16.778 -13.984] LCC, [[delta].sub.LCC] [-15.590 -12.490] MA, [[detla].sub.MA] [-14.263 -11.254] Northwest, [[delta].sub.NW] [-12.989 -10.561] United, [[delta].sub.UA] [-13.011 -10.618] Deterrence cost AA, [c.sub.AA] [-7.458 -3.441] Deterrence cost CO, [c.sub.CO] [-10.430 -8.526] Deterrence cost DL, [c.sub.DL] [-3.990 -0.258] Deterrence cost LCC, [-7.791 -2.679] [c.sub.LCC] Deterrence cost MA, [c.sub.MA] [-9.684 -5.554] Deterrence cost NW, [c.sub.NW] [-2.576 0.392] Deterrence cost UA, [c.sub.UA] 1-13.535 -9.692] Market Presence [7.678 10.637] Min Cost Hub [-1.102 -0.636] Market Distance [8.030 9.285] From Center [1.601 2.873] Min Distance [2.636 3.619] Market Size [2.402 3.320] Change Income [1.927 3.696] Number Airports [-5.481 -4.134] Constant [-1.408 3.915] Function Value 1724.826 Goodness of Fit 0.49 Number Obs 3,376 TABLE 7 Ratio of Sequential to Simultaneous Profits Best Case Worst Case Randomized Simultaneous Simultaneous Simultaneous Profits Profits Profits AA [0.123 0.941] [1.957 14.955] 10.326 2.494] CO [0.161 0.907] [0.906 5.123] [0.417 2.354] DL [0.242 0.872] [1.812 6.518] [0.493 1.774] LCC [0.042 1.128] [7.733 209.447] [0.167 4.529] MA [0.006 0.547] -- 10.029 2.606] NW [0.123 0.992] [1.105 8.883] [0.365 2.932] UA [0.074 0.738] [0.792 7.911] [0.233 2.325] TABLE 8 Ratio of Deterrence to Sequential Profits Compared to % Times Compared to % Times Max Profit in Firm Deters Min Profit Firm Sequential in Sequential Deters game game AA 1.947 0.920 15.290 0.920 CO 1.344 0.971 7.743 0.971 DL 2.114 0.971 7.618 0.971 LCC 2.059 1.000 55.773 1.000 MA 4.660 1.000 415.605 1.000 NW 2.376 1.000 19.106 1.000 UA 2.202 0.226 17.840 0.700 TABLE 9 Ratio of Firm Profits across Games CO/AA DL/AA Simultaneous [1.269 3.574] [1.578 3.358] Sequential [1.224 1.6551 [1.464 3.109] Deterrence [0.838 0.845] [1.549 1.589] LCC/AA UA/AA Simultaneous [0.089 1.036] [0.873 1.295] Sequential [0.350 1.242] [0.524 0.685] Deterrence [1.278 1.313] [0.612 0.774]