Evidence from the Airline Industry

ABSTRACT

MUTUAL FORBEARANCE AND PRICE DISPERSION: EVIDENCE FROM THE AIRLINE INDUSTRY

by Christopher Alan Granquist

We replicate the reduced-form analyses of Evans and Kessides (1994) and Ciliberto and Williams (2014) to find empirical evidence of multimarket contact increasing price levels in a market. We then apply the fixed-effects model to price dispersion but find inconclusive results. We follow in the footsteps of Ciliberto and Williams to use gate ownership at an airport as an instrumental variable. We find evidence of the power of the instruments through first-stage regressions and strength tests. The application of the instrumental variables provides interesting but inconclusive results for both price levels and price dispersion. MUTUAL FORBEARANCE AND PRICE DISPERSION: EVIDENCE FROM THE AIRLINE INDUSTRY

Thesis

Submitted to the

Faculty of Miami University

in partial fulﬁllment of

the requirements for the degree of

Master of Arts in Economics

Christopher Alan Granquist

Miami University

Oxford, Ohio

2020

Advisor: Dr. Charles Moul

Reader: Dr. Jonathan Wolff

Reader: Dr. Mark Tremblay

c 2020 Christopher Alan Granquist This thesis titled

MUTUAL FORBEARANCE AND PRICE DISPERSION: EVIDENCE FROM THE AIRLINE INDUSTRY

Christopher Alan Granquist

has been approved for publication by

Farmer School of Business

and

Department of Economics

Dr. Charles Moul

Dr. Jonathan Wolff

Dr. Mark Tremblay Table of Contents

1 Introduction 1 1.1 Introduction ...... 1

2 Literature Review 1 2.1 Multimarket Contact ...... 1 2.2 Price Dispersion ...... 2 2.3 Related Markets ...... 3 2.4 Contemporary Work ...... 3 2.5 Contribution ...... 4 2.6 Data Sources ...... 4 2.7 Observations ...... 5 2.8 Dependent Variables ...... 6 2.9 Control Variables ...... 7 2.10 Multimarket Contact ...... 8 2.11 Instrumental Variables ...... 10

3 Results 11 3.1 Model ...... 11 3.2 Replication ...... 12 3.3 Price Dispersion ...... 12 3.4 First Stage Regressions ...... 13 3.5 Instrumental Variable Regressions ...... 14

4 Conclusion 15 4.1 Conclusion ...... 15

iii List of Tables

1 Summary Statistics ...... 19 2 Number of Common Markets in 2014 Q1 ...... 20 3 Average Contact Summary Statistics ...... 20 4 Log Average Price OLS Regression ...... 21 5 Gini Coefﬁcient OLS Regression ...... 22 6 Scaled Standard Deviation OLS Regression ...... 23 7 First-Stage Regression onto Average Contact I ...... 24 8 First-Stage Regression onto Average Contact II ...... 25 9 IV Regression ...... 26

iv 1 Introduction

1.1 Introduction

The reduction in competition due to threat of retaliation across an increasing number of markets by a pair of oligopolistic firms, known as mutual forbearance, is a well-documented economic phe- nomenon. While classic economic theory emphasizes unilateral market power in a single market, firms in the modern world span many markets, and from competition across markets arises a new game for the firm. Microeconomic theory suggests that a pair of firms may more successfully en- gage in tacit collusion when competing across multiple markets, and empirical literature reinforces this idea. The potential effects of collusion are well established. Chiefly, collusion may maintain higher prices than in a competitive market, and likewise collusion may enable a greater degree of price discrimination within a market. If price discrimination lowers the market quantity of goods below the equilibrium without price discrimination, overall market welfare will decrease. Hence, effects on both price and price discrimination from multimarket contact may decrease welfare. The airline industry is a favored industry of empirical industrial organization due to publicly available data and well-defined markets. Evidence for the effect of multimarket contact and its role in facilitating collusion begins with Evans and Kessides (1994),henceforth EK, who use airline data to find evidence of a positive effect of multimarket contact on prices. At the same time, Borenstein and Rose (1994), hereafter BR, use the airline industry to investigate the effects of competition on price dispersion. We believe it is a natural extension to use airline industry data to examine the effect of multimarket contact on price dispersion. We replicate models from the literature, and then apply the models to price dispersion as an independent variable.

2 Literature Review

2.1 Multimarket Contact

The microeconomic theory of multimarket contacted was formalized by Bernheim and Whinston (1990), hereafter BW. BW produce an irrelevance result for multimarket contact; competition across markets would not affect firm strategy under assumptions of identical markets, identical firms, and constant returns to scale. In the absence of these assumptions, competition across markets may have an effect on firm strategies. EK argue that the airline industry is an ideal industry to test for multimarket contact. The hub system for airlines encourages airport dominance, which differentiates production costs across markets. Firms also sort into national, regional, or low-cost carriers, with varying access to capital and production costs across markets. Finally, there are significant returns to scale since the cost of flying only marginally increases between flying a single passenger to flying at full capacity.

1 EK then test the hypothesis that prices in the airline industry are affected by multimarket competition using panel data from 1984 to 1988. EK use an OLS regression on log prices on a suite of controls and a constructed variable to measure multimarket contact, controlling for fixed effects. The multimarket contact variable constructed in EK, labeled AverageContact, is an important con- struction in future works addressing multimarket contact in the airline industry. The results con- clude that empirical evidence upholds the BW theory of multimarket contact and tacit collusion, such that markets whose firms compete in a number of other markets find significantly higher prices overall as compared to markets whose firms face a low amount of multimarket contact. EK also find that the inclusion of market fixed-effects have a significant negative effect on the magnitude of multimarket contact. Ciliberto and Williams (2014), henceforth CW, reexamine multimarket contact in the airline industry by revisiting EK. Using updated data from 2004 to 2007 combined with survey data concerning gate leases, CW explore structural parameters of tacit collusion. The chief contribution of this paper provides a structural analysis of the effect of multimarket contact using evidence from the airline industry. Relevant to our paper, they replicate EK’s reduced-form analysis and CW but note that the AverageContact variable as constructed by EK is itself endogenous. CW then explore a wider variety of control specifications as well as using number of gates leased by a firm and their competition at airports in the market as an instrumental variable for the AverageContact regressor, finding that the IV method is needed to discern a significant effect of multimarket contact on average prices.

2.2 Price Dispersion

Concurrently to EK in 1994, BR investigate price dispersion in the airline industry. BR uses the Gini coefficient (defined in Section 3.4) as a measure of price dispersion. The results find that price dispersion cannot be entirely explained by cost variation and instead that price discrimination is driving a significant effect of price variation. BR further explain possible sources of price dispersion, emphasizing that price discrimination may increase in the face of increasing competition under a model of monopolistic competition. BR also use an OLS regression of Gini on a suite of controls as well as several variables to measure competition and then instrument the competition variable. The result of BR is a finding of a positive association of competition within a market to price dispersion, of which a significant portion of the price dispersion is attributed to price discrimination. Gerardi and Shapiro (2009), henceforth GS, revisit BR, using panel data and replicated cross- sectional data to find contrasting results to BR. Similar to BR, GS use an OLS regression of Gini on controls and various measures of competition, and then instrument the competition variable. GS’s results suggest that the actual effect of competition on price dispersion is negative, in line with standard oligopoly theory, and that the difference between BR and GS may be reconciled by

2 omitted variable bias in the cross-sectional work of BR. Speciﬁcally the effect of omitting distance may cause a signiﬁcant positive bias to the effect of competition on price dispersion. This error is roughly caused by weak instruments, which GS are able to handle with a more appropriate set of instruments alongside panel data methods.

2.3 Related Markets

Empirical evidence of the effect of multimarket contact extends beyond the airline industry. Jans and Rosenbaum (1997), for example, investigate the effect of multimarket contact on pricing in the cement industry. Jans and Rosenbaum examine panel data over 16 years for 25 points in the cement industry to find a significant effect of multimarket contact, specifically finding an increase in multimarket contact relating to an increase in prices above marginal cost. Parker and Roeller (1997) examine the mobile telephone industry, in part considering the effect of multimarket contact. Parker and Roeller are able to explain part of noncompetitive prices in the mobile telephone duopoly markets of 1983 by the effect of multimarket contact as well as cross- ownership. Fernandez and Marin (1998) use evidence from the Spanish hotel industry to analyze multimarket contact and similarly find an explanation of noncompetitive prices by multimarket contact. They furthermore find evidence that omitting multimarket contact causes omitted variable bias on the effect of competition.

2.4 Contemporary Work

Several recent working papers address price dispersion using EK’s multimarket contact model. Chiang and Liou (2018) explicitly examine the effect of contact across markets on price dispersion in the airline industry using EK’s average contact variable as a regressor to the Gini coefficient as used in BR. Chiang and Liou find results varying based on market size and find that larger markets are more susceptible to increases in price dispersion from multiple sources, as well as finding that multimarket contact and price dispersion behave in opposite directions. Kim, Kim, and Tan (2019) produce a similar effort, explicitly using EK’s Average Contact variable to explain the Gini coefficient as a proxy for price dispersion. Kim, Kim, and Tan demon- strate specific interest in the effect of Southwest Airlines and find that, when Southwest Airlines is present on a route, multimarket contact fails to have a significant effect on price dispersion. How- ever, in the absence of Southwest, price dispersion decreases in a market as firms in the market exhibit more competition across markets.

3 2.5 Contribution

We contribute to the literature by examining the effect of multimarket contact on price dispersion. We provide results for the effect of multimarket contact on price dispersion through both ﬁxed-effect and instrumental variable regressions. As a secondary contribution to the literature, we formally address the endogeneity concerns raised by CW through ﬁrst-stage regressions and strength testing of instruments and our multimarket contact variable.

2.6 Data Sources

We draw the majority of our data from the Bureau of Transportation Statistics’ DB1B database. The DB1B is a 10% random sample of flight itineraries from reporting carriers. A flight itinerary is a schedule of airline transit for a consumer, including data on origin, destination, layover airports, carriers, passengers, market fare, and other parameters of interest. Reporting carriers may be either operating carriers, which provide the actual service of the flight, or ticketing carriers, which perform the itinerary transaction to the consumer. Operating carriers may differ from ticketing carriers as some contracted regional airlines do not ticket consumers directly but instead fly under aliases for multiple national carriers. Skywest Airlines, for example, has contracts with American Airlines, United Airlines, Delta Airlines, and Alaskan Airlines. We note that the DB1B itinerary information comes from reporting carriers, which arbitrarily may be either operating carriers or ticketing carriers. We also construct original measures for absolute distance between airports, airline hub status by airport, and airline gate leasing information by airport. Hubs are used by airlines to concentrate operations, and the hub status of an airport is designated by carriers. Gate leasing data are originally constructed. When available, we observe the total number of gates at an airport, number of common-use gates at an airport, and number of gates leased to each airline at an airport. We would ideally use information from airport competition plans submitted to the Federal Aviation Administration (FAA) combined with information obtained directly from airports. The Wendell H. Ford Aviation Investment and Reform Act for the 21st Century, colloquially known as AIR21, mandated that medium and large hubs, as defined by the FAA, are required to submit competition plans to the FAA. These competition plans include information on gate leasing procedures, airport expansion, access to common-use gates, and other leasing information. An update letter to the FAA must be sent by each competition-plan-covered airport annually, and new plans may be triggered on condition. These federal regulations help ensure accuracy of our gate leasing data as drawn from airport information. We note that competition plans are not readily available from the FAA, and must be collected individually. Furthermore, competition plans are erratically located and available, making it realistically impossible to scrape for competition plan data, let alone find consistent annual entries. We therefore consult the FAA competition plan cov-

4 ered airports that have been updated in 2014 or later. To accommodate airports for which no recent competition plans are available, we then scrape information from airport websites of current gate use by airline for available airports. This data is cross-referenced with the competition plans that both have airport gate lease information and are updated since 2014 according to the FAA. Though we only obtain three plans with useable data (Honolulu, Minneapolis-St. Paul, and St. Louis), the competition plans corroborate the information given by the airlines accurately, and hence we obtain the gate lease information for the 22 airports whose gate ownership information can be gleaned with some level of confidence. Due to the above information constraints, we only observe one instance of data for each airport and airline across all time periods. We reference the Government Accounting Office (GAO, 1990) report, as used by CW. This report states that 41% of gate leases are for over twenty years of duration, 25% for eleven to twenty years of duration, and 22% for three to eleven years of duration. Berry (1990) suggests that airports sign long-term leases to aid in capital investment while main- taining low-interest on debt issues and that airlines sign long-term leases to integrate the airport into a network. We also note that it is difficult for airlines to adjust airport leases, as termination is bilateral and subleasing is expensive due to imposed limits by airports (Ciliberto and Williams 2010). As an example of the inability of unilateral termination, Ciliberto and Williams describe an incident where, prior to 2010, Dallas Love airport declined an attempt by American Airlines to terminate a gate lease early, and the latter was forced to maintain payments until lease expiration in 2011. The limited access to modifications to airport capital combined with the limit on sublease fees discourage airlines from subleasing out to competitors. We finally note that gate capital is resistant to demand shocks in a single market, as single markets rarely generate a significant portion of the revenue from the airport as compared to the value of other markets in the airline’s network at that airport.

2.7 Observations

We use the DB1B to generate observations indexed by time, firm, and market. We define a market as a unidirectional route between two airports. For example, Chicago O’Hare (ORD) to Atlanta (ATL) is considered one route, and ATL to ORD is considered a distinct route. After filtering data, some markets are dropped while the converse market is not dropped, which drives some portion of variation in our data. We omit observations that are zero price, zero distance, or are based on a single passenger. We observe data quarterly from 2014 to 2018, generating twenty periods. We index quarter-yearly periods by t ∈ {1,...,T}, with T = 20. We observe thirteen significant carriers across our observations. We use carrier, airline, and firm as interchangeable notation in this paper. We drop airlines that do not report at least 1000 passengers in at least one period. Our remaining observed airlines are Alaskan Airlines (AS), American Airlines (AA), Delta Airlines (DL), Frontier Airlines (F9), Mesa Airlines (YV), Shuttle

5 America (S5), SkyWest Airlines (OO), Southwest Airlines (WN), Spirit Airlines (NK), Sun Coun- try Airlines (SY), Trans States Airlines (AX), United Airlines (UA), and US Airways (US). We note that, through 2014, US Airways was in the process of being merged with America Airlines. We therefore do not have reliable gate leasing information on US Airways, nor does it appear in the majority of our observations. We identify the national carriers as American Airlines, Delta Airlines, and United Airlines; the low-cost carriers as Southwest Airlines, Frontier Airlines, Spirit Airlines, and Trans State Airlines; and the regional carriers as Alaskan Airlines, SkyWest Airlines, Sun Country Airlines, Shuttle America, and Mesa Airlines. We index ﬁrm by j ∈ {1,...,J}, with J = 13. Finally, we observe gate leasing data from airports. We are limited to these airports as a re- striction of major or large hubs with recently updated competition plans so that gate leasing information observed may be reliable. Our deﬁnition of a market as a unidirectional route between two airports therefore generates 484 possible markets. However, 22 of these markets are same-city pairs, such as ORD to ORD, and we exclude uninteresting data. Generally, we index market by m ∈ {1,...,M}, with M = 462. Therefore, an observation is at the airline-city-pair-quarter level,

indexed jmt. After ﬁltering by observations with nonzero prices, distances, and within-observation standard deviations, we generate 37,639 observations. We list our summary statistics for all gener- ated variables in Table 1. The observed airports include Albequerque (ABQ), Anchorage (ANC), Atlanta (ATL), Nashville (BNA), Buffalo (BUF), Baltimore-Washington (BWI), Cleveland (CLT), Dallas-Fort-Worth (DFW), Honolulu (HNL), Houston (IAH), Kansas City (MCI), Miami (MIA), Minneapolis-Saint-Paul (MSP), New Orleans (MSY), Chicago O’Hare (ORD), Palm Beach (PBI), Philadelphia (PHL), San Antonio (SAT), Seattle (SEA), Santa Ana (SNA), St. Louis (STL), and Tampa (TPA).

2.8 Dependent Variables

We create three dependent variables of interest. We first create average prices as a replication effort for EK and CW. We then create two measures of price dispersion: the Gini Coefficient, as used by BR, and scaled within-observation standard deviation. The DB1B observes market fare by itinerary. As per CW, we discard extreme-priced observations below $25 and above $2500. We also halve the listed market fare for round-trip itineraries. We then calculate the simple average of market fares indexed by firm-market-period and deflate fares by the Consumer Price Index to 2014$ standard. Price has a mean of 171.56, a standard deviation of 88.49, and a median of 152.42 in our data. Our primary topic of interest in this paper is examining the effect of multimarket competition on price dispersion. Hence, we similarly generate a Gini Coefficient at the firm-market-period level using market fares as observed in the DB1B. The Gini Coefficient is mathematically defined as twice the area between the 45-degree line of absolute equality and the Lorenz Curve when

6 sorting by prices as a function of passengers. The Lorenz Curve, in this context, is the cumulative amount of fares paid by the lowest x% of passengers. The Gini Coefficient is bounded between zero and one, with zero being perfect inequality in a market and one being perfect equality. In context, a zero Gini would represent all fares in a market being paid by a single passenger, and conversely a one would represent every passenger paying the same fares. Therefore, as described in BR, we use the Gini Coefficient as a measure of price dispersion. This measure is equivalent to twice the expected absolute difference between two randomly drawn ticket prices (GS, 2009). Gini has a mean of 0.206, a standard deviation of 0.093, and a median of 0.225. As another measure of price dispersion, we construct within-observation scaled standard deviations. Given that the DB1B is a 10% sample of flight itineraries, we may observe multiple itineraries for each of our carrier/city-pair/quarter level observations. Hence, we may expect to see variation in the market fare of each itinerary, and hence can construct the standard deviation of all market fares indexed by firm, market, and period. We define this standard deviation of market fares across itineraries in a working observations as the within-observation standard deviation. It reflects price dispersion within one carrier/city-pair/quarter observation similar to the Gini coefficient, and hence we expect both Gini coefficient and within-observation standard deviation to behave in a similar way. We denote within-observation standard deviation as sd, and it has a mean of 114.06, a standard deviation of 77.37, and a median of 107.14. We then scale the standard deviation by average price of the observation. Considering the variation in price increases as price increases, scaling standard deviation by price allows a measure of strict variation that may be compared across observations with varying price levels. We formally construct our dependent variable as ln(sd + 1) − ln(price).

2.9 Control Variables

We construct a number of control variables from EK and CW. These controls include distance, round-trip percentage, direct-flight percentage, hub, route market share, airport market share, HHI, and network size. Distance is the absolute linear distance between two airports. Distance is an important com- ponent of consumer travel decisions. Distance may have a nonlinear relationship, however, as air travel becomes an increasingly attractive mode of transport relative to alternative forms of travel as distances increase. Therefore, we follow the literature and also include a measure of distance squared log(Distance)2 to account for this non-linearity. Distance has a mean of 1659.2, a standard deviation of 1215.1, and a median of 1198.7. RoundTrip is the percentage of passenger itineraries which are round-trip. A round trip is an itinerary in which the flight and return flight are purchased together. We include the fraction of flights in one firm-market-period observation that are round trip. Direct is the percentage of itineraries which are direct flights. A direct flight is an itinerary that flies straight between origin

7 and destination airport without any layovers. We include the fraction of flights in one firm-market- period observation that are direct. Hubs are airports that are central to a network for an airline. Hub status is designated by airlines; we construct our measure of hubs by airline designation. HubEither is a dummy variable with a value of one if either the origin or destination airport is a hub. We note that HubEither is the control used by CW. HubEither has a mean of 0.263, a standard deviation of 0.440, and a median of 0. Note that a median of 0 is reasonable in context, as any given airport is not likely to be a hub for any given carrier. RouteMktShare is a simple measure of route market share observed at the firm-market-time level. We define it as specified in EK and CW as the percentage of quantity of passengers served in one market in one period by an airline. RouteMktShare is a simple measure of competition across routes, and is similar to the measures of competition used by BR. Similarly, HHI is the Herfindahl-Hirschman Index (HHI) of one market in one period. The HHI of a market measures the level of concentration in a market. It is mathematically formulated as the sum of the square of market shares of all firms in the market. We calculate shares as 100 times the fraction of quantity of passengers served by an airline relative to the total amount of passengers served in the market. Hence, HHI is bounded between 1 and 10,000, where 1 is perfect competition and 10,000 is monopoly in the market. RouteMktShare has a mean of 0.207, a standard deviation of 0.267, and a median of 0.077. We also construct a measure of market share at an airport. Similar to the hub variables, we generate three controls of airport market share: share at the origin airport (AptShareOrigin), share at the destination airport (AptShareDest), and average share between both endpoint airports (AptShareAvg). The airport market share for an airport is calculated as the fraction of passengers served by an airline in a period relative to the total number of passengers, and hence is observed at the firm-market-period level. EK use AptShareAvg as their measure of airport market share. In our data, AptShareAvg has a mean of 0.152, a standard deviation of 0.038, and a median of 0.119. Network is a measure of the firm’s network size for the origin airport. This is measured as the fraction of routes an airline serves at an airport relative to the total possible routes at the airport. Network has a mean of 0.614, a standard deviation of 0.311, and a median of 0.614.

2.10 Multimarket Contact

EK create a measure of average route contact as an attempt to capture the amount of cross-market contact of all firms operating in a specific market. We label this measure AverageContact. For any given market m in period t, there are fmt firms operating in the market. Let D jmt be a dummy variable that has a value of one if firm j is operating in market m at time t. We construct a matrix

8 At = (a jkt) for each market-time pair, with

M a jkt = ∑ D jmtDkmt for j,k ∈ {1,...,J} m=1

Thus each element in matrix A is the number of markets concurrently served by airlines j and k in market m and period t. The diagonal of this matrix is the total number of routes served by airline j in market m at time t, since j = k. From this, we construct our AverageContact variable.

1 J J AverageContactmt = ∑ ∑ a jkmtD jmtDkmt [ fmt( fmt − 1)]/2 j=1 k= j+1

This measure represents the average amount of contact in market m across all markets between any two firms operating in the market m at time t. We note the properties of this measure as described in EK. A monopolistic route will have an average contact value of zero. AverageContact is also positively correlated with firm size, since large firms will operate across more markets. It also only measures the exposure of airlines in the market to other airlines by route presence, not magnitude of the exposure. Table 2 provides an illustration of the number of contact between firms in first quarter 2014. To provide an example for intuition, suppose the ORD to ATL route is served by only American Airlines, United Airlines, and Southwest Airlines. Suppose American and United compete against each other on 300 routes, American and Southwest 200 routes, and United and Southwest 100 routes. Then our measure of multimarket contact for the ORD-ATL route would be calculated as: 1 AverageContact = (300 + 200 + 100) = 200 [3(3 − 1)]/2

We note that AverageContact is a difficult measure to interpret at a glance. It roughly coincides with as the average amount of contact between any pair of firms in a market and period. Hence, before scaling, a one unit increase in AverageContact may be effectively interpreted as the average number of routes that any two firms share in a market increasing by one. Table 3 provides a comparison on summary statistics of AverageContact as compare to EK and CW, which both use the same measure of multimarket contact as in this paper. We find in our data a mean of AverageContact of 0.19, a median of 0.18, and a standard deviation of 0.07 when scaled to the level of EK. Ciliberto and Williams (2014) discuss the likely endogeneity behind prices, market shares, and average contact. Since we consider only a reduced-form analysis by regressing our dependent variables directly onto average contact, our endogeneity concern is of average multimarket contact. Ciliberto, Murry, and Tamer (2018) observe that market-specific multimarket contact may be endogenous due to unobservables correlated with pricing, entry, and exit decisions. Since for any

9 given time the average contact across all firms is fixed, variation across markets originates from the set of operating firms in a market. Variation within a market across time is driven by a change in set of operating firms and a change in multimarket contact. This variation comes from market structure and it may be correlated with the unobservables mentioned prior in CW. As Griliches and Mairesse (1995) argue fixed effects perform poorly when endogeneity is driven at a market and time level, CW suggest that instrumental variables should be used to address the possible endogeneity present in AverageContact.

2.11 Instrumental Variables

As per Ciliberto and Williams (2014), we intend to use the access to gates at an airport as an instrumental variable. While CW consider only the average gates across origin and destination, we seperately consider the two variables. We construct OwnGatesOrig as the percentage of gates leased by a carrier at the origin airport, OwnGatesDest as the percentage of gates leased by a carrier at the destination airport, and OwnGatesAvg as the average percent of gates leased by a carrier at the origin and destination airports. We also construct LCCGatesOrig, LCCGatesDest, and LCCGatesAvg similarly using low-cost carrier leases. As mentioned in our data sourcing, we assume gate leases are resistant to shocks, subleases, and termination, and therefore are unlikely to change over the course of our sample despite only being observed at one period. Summary statistics for instrumental variables are described in Table 1. We also obtain information specifically on Southwest Airline’s gate leasing. This information is provided directly by Southwest Airlines on the airport information section of their website. The information provided largely coincides with the data offered by the competition plans and airport websites. As Southwest tends to have a significant effect in airline literature and the fact the Southwest dominates our low-cost carrier’s category, we create three final measures of gate ownership. WNGatesAvg represents the average percent of gates leased at the origin and destination airport by Southwest. WNGatesOrig and WNGatesDest represent the percentage of gates leased by Southwest at the origin and destination airport respectively. Ciliberto and Williams use only the average percentages of gate leases at both endpoints. While the qualitative concept backing percentage of gate leases is valid, they fail to express the power of the instrumental variables. Without first-stage regressions or power tests for the IVs, it is difficult to justify why a specific suite is chosen. We explore the strength various combinations of instrumental variables and the resulting effect on multimarket contact to validate the formal power of the instrumental variables, as well as to select the most appropriate instruments to use.

10 3 Results

3.1 Model

We replicate our model from the reduced-form model of CW. The base model regresses our dependent variable of interest onto the AverageContact variable, a set of controls, and ﬁxed-effects. We also follow CW in an instrumental variable model of the same form: dependent variables regressed onto the AverageContact variable, a set of controls, and ﬁxed-effects. We describe our OLS model as:

ln(Price) = β ∗ AverageContactmt + γ ∗Controls + α j + δm + µt + ε jmt

Where β is the coefficient of our multimarket contact measure, γ is a row vector of coefficients for our vector of controls, α j,δm,andµt are fixed effects for firm, market, and period respectively, and ε jmt is an idiosyncratic error term. Following the literature, we choose four sets of controls and fixed-effects. The first set includes ln(Distance), ln(Distance)2, Direct, RoundTrip, AptShareAvg, RouteShare, and HHI, alongside period fixed-effects and carrier fixed-effects. This is the base model used in EK, replicated by CW in column 1 of Table 3. This set does not include market fixed-effects, so un-instrumented results are likely to be biased, but we include it as a point of comparison to the literature. Our second set of controls include Direct, RoundTrip, AptShareAvg, RouteShare, HHI, and market, carrier, and period fixed-effects. This coincides with column 3 of Table 3 of EK, and represents our first simple market fixed-effects set. We remove distance and squared distance from the set of regressors, as EK, due to multicollinearity with the market fixed-effects. We recognize that AptShareAvg, RouteShare, and HHI may be endogenous themselves. We again follow the precedent of CW to create alternative measures of relative market share. We create our third set of controls as Direct, RoundTrip, RouteShare, HHI, and Network with market, carrier, and period fixed-effects, replacing AptShareAvg from the second set with Network. We furthermore generate our fourth set of controls as Direct, RoundTrip, Network, and Hub. These controls coincide with column 3 of Table 3 of CW. Aside from our replication results, we discard the third set of regressors and consider only the fourth. We note that our instrument data is limited to market-carrier variation, with no variation across time. It is therefore best to think of route fixed-effects and and instruments as subsitute identifica- tion strategies. Hence, we generate three additional sets of controls that will be used solely in our IV model. These additional sets of controls simply replicate the last three sets of controls, except market fixed-effects are dropped and log(Distance) and log(log(Distance)2) are reinstated.

11 3.2 Replication

We replicate the reduced-form market fixed-effect results of multimarket contact on price levels of EK Table 3 and CW Table 3. We display our log price results in Table 4 and note comparisons of our coefficients of AverageContact to the suitable comparison from literature. The first column, using our first set of controls, identifies a significant coefficient of AverageContact on log price of 1.034 with standard error of 0.032. We recognize the importance of market-fixed effects as evidenced by EK, and hence recognize the strong possibility of upward bias that will be partially corrected via market fixed-effects and instrumental variables. The results are comparable to Table 3 column 1 of EK, who find OLS results of 1.140 for AverageContact with a standard error of 0.032. Our second set of controls finds a coefficient of multimarket contact on log prices of 0.123 with standard error of 0.033. This set of controls is comparable to CW Table 3 column 1, which displays a coefficient of 0.161 for AverageContact with a standard error of 0.050. Our third set of controls is compared to CW Table 3 column 3 finds a similar coefficient to the previous controls of 0.119 with a standard error of 0.033. Our final set of controls replicates Table 3 column 3 of CW, who find a coefficient of -0.017 with standard error of 0.003. In their reduced form analysis, simply using market fixed-effects with the chosen set of controls provides CW with a negative and near-zero coefficient for AverageContact, which would contradict the findings of EK and the hypothesis of mutual forbearance. This spurs a question of endogeneity of AverageContact, which CW answers using instrumental variables. We, however, do not find the same results. We note that our markets are not directly comparable to the markets used by CW due to limitations on instrument data, but our fourth set AverageContact coefficient of 0.125 with standard error of 0.033 follows closely in line with its two sibling control groups. Hence, we recognize the more present endogeneity concerns of CW without finding the same questionable results in the fixed-effect regressions. Our replication work is reasonably similar overall to the comparable literature. We recognize the potential for remaining endogeneity concerns of AverageContact, but reinforces the work of EK to suggest that market fixed-effects correct for a significant amount of endogeneity present and hence believe it is a suitable model to analyze the effect of multimarket contact on priced dispersion.

3.3 Price Dispersion

Our chief hypothesis is that mutual forbearance induced by multimarket contact will increase the price dispersion, to complement the demonstrated increase in price levels as evidenced in the literature. Hence, we use the same model as for price levels to test for price dispersion in the reduced form, described for the Gini coefﬁcient as

12 Gini = β ∗ AverageContactmt + γ ∗Controls + α j + δm + µt + ε jmt

And for the scaled standard deviation of prices:

ln(sd + 1) − ln(Price) = β ∗ AverageContactmt + γ ∗Controls + α j + δm + µt + ε jmt

The empirical strength of the model in explaining price dispersion appears to sufficiently provide a reasonable approximation of the direction of multimarket contact on the price levels. We use two measures of price dispersion, as noted in the Section 2. Our regression results for the Gini coefficient are displayed in Table 5, and our results for within-observation standard deviation scaled by price are displayed in Table 6. The coefficient of AverageContact for the first control set is -0.023 with standard error of 0.006. We find an identical coefficient of -0.023 in our fourth regression, with an increased standard error of 0.009. We only find insignificant results for the second and third control sets. This result is contradictory to our hypothesis, and is similarly concerning to the market fixed-effect results found in CW. For scaled standard deviation, all four regressions yield insignificant results for the coefficient of AverageContact. The first three regressions find insignificant coefficients of 0.013, 0.014, and 0.011 respectively, while the final set of controls identifies an insignificant -0.003 coefficient. No results approach statistical significance. We note several interesting features of the fixed-effect analysis. First, the regressions that do not include market-fixed effects are consistent with the other results for both Gini and standard 1 deviation. This is in contrast to the sharp decrease of 10 that the literature and our own analysis finds for log price. The R2 values for Gini coefficient are also significantly smaller than for the log price regressions. These factors indicate the potential for some underlying endogeneity of a greater extent than we find for price levels, and hence we follow CW in suggesting a treatment of instrumental variables may be needed.

3.4 First Stage Regressions

CW suggests the use of airport gate leases as an instrumental variable for AverageContact. Rhetor- ically, gate leases appear to be a sufficiently powerful IV due to apparent exogeneity and relation to both AverageContact and prices. CW, however, provide no quantitative evidence to support its choice of instruments. To justify the use of gate ownership as instruments, we construct first-stage regressions for all of our control sets alongside the Hausmann and Stock-Yogo strength tests for instrumental variables. We specify our first-stage regressions as

13 AverageContactmt = Instruments jm ∗ βIV +Controls jmt ∗ βCtrl + u jmt

Where βIV is the row vector of coefficients for our set of instruments, βCtrl is the row vector of controls for our set of controls, and u jmt is an idiosyncratic error term. We display the full first stage regressions with control coefficients in the appendix. The results are consistent and uninteresting across the controls, and hence we focus on the coefficients for gate ownership for our first set of controls. The first-stage model regresses AverageContact onto the chosen suite of instrumental variables, a set of control variables, and the appropriate fixed-effects. From our choice regression in Table 7 and Table 8, we run two tests of instrumental variable power. We first run the Hausman Test for exogenous regressors. The test uses residuals ν of our first-stage regression to test the null hypothesis δ = 0 for the auxiliary regression DepVar = AverageContact ·β +νδ. Rejecting the null hypothesis would suggest that the multimarket contact variable is endogenous and the use of instruments may be necessary. We find strong rejection rates for a null hypothesis in every specification. As evidenced by EK and CW, the AverageContact variable is visibly endogenous and requires some control for endogeneity. However, as we are aware of the endogeneity present in multimarket contact as suggested by the literature, our greater concern is the endogeneity present in AverageContact after market fixed effects have been controlled for. In order to control for this endogeneity through instruments, we require a strength test of our instruments. We use the Stock-Yogo Test for weak instrumental variables. The Stock-Yogo Test is an F-test with null hypothesis that our vector of coefficients for instrumental variables in our first-stage regression, βIV , is equivalent to the zero vector. Rejection of the null hypothesis suggests that our instrumental variables have explanatory power in our AverageContact variable, with rejection requiring an F-statistic of 10. We note that in our two specifications with four instrumental variables the distribution may be distorted into requiring a greater F-statistic than 10 (Stock and Yogo 2002).

3.5 Instrumental Variable Regressions

As an alternative to our fixed-effect results, we use OwnGatesOrigin, OwnGatesDestination, SWGatesOrigin, and SWGatesDestination as instrumental variables for AverageContact. Our instrumental variable model uses the same four control specifications as the fixed-effects model in addition to the three control sets with market fixed-effects removed. The full results are displayed in the appendix. However, we note extreme unexpected values from the control specifications including market fixed-effects and drop those regressions from our results of interest. We display our results for price levels with instrumental variables in Table 9. Results for multimarket contact are substantially decreased from the fixed-effect model, now demonstrating significant negative coefficients for AverageContact. The specification identifies a coefficient of

14 -2.156 with standard deviation of 0.750. These results are contradictory to the results found in the literature and theory. CW finds an amplified positive effect of multimarket contact on prices, which is expected in the face of mutual forbearance. However, the decrease in results does fit the statistical negative trend of the coefficient of AverageContact as more endogeneity is controlled for, as can be seen when market fixed-effects are introduced in our own analysis or EK. We recognize that our data set is more limited and covers a different span of time as compared to CW, but our results are nevertheless inconclusive. Conversely, instrumental variables have the reverse effect on the Gini coefficient. As displayed in Table 9, the coefficients for AverageContact on the Gini coefficient have increased and are now positive for all four sets of controls. though all four sets of controls are insignificant. We find a coefficient for AverageContact on the Gini coefficient of 0.218 with standard error of 0.121. The effect of instruments on within-observation scaled standard deviation is less pronounced. All coefficients are still insignificant. The set identifies a coefficient of 0.081 with standard error of 0.174. Our overall results for price dispersion using instrumental variables are insignificant and inconclusive. However, an interesting trend does emerge from all IV models: the instrumental variables scale the coefficient of AverageContact and invert the sign. Our results do not provide significant conclusions even internally compared, but we note this interesting trend.

4 Conclusion

4.1 Conclusion

We test the hypothesis that increased multimarket contact will result in increased price levels and price dispersion in a market. We use a fixed-effects model and an instrumental variable model to identify the effect of multimarket contact, finding contrasting results. Our fixed-effect model follows the literature and finds a significant positive association between multimarket contact and prices and an insignificant negative association between multimarket contact and price dispersion. Our instrumental variable model finds insignificant effects across the board, but it finds a negative association between multimarket contact and prices and positive association between multimarket contact and price dispersion. Overall, we find no conclusive evidence of the effect of mutual forbearance on price dispersion, but do find interesting trends when controlling for additional endogeneity.

15 References

[1] Bernheim, B.D. and Whinston, M.D. “Multimarket Contact and Collusive Behaviour.” RAND Journal of Economics, Vol21(1)(1990), pp. 1-26. [2] Berry, S. “Estimation of a Model of Entry in the Airline Industry.” Econometrica, Vol60(4)(1992), pp. 889-917. [3] Bilotkach, V. “Multimarket Contact and Intensity of Competition: Evidence from an Airline Merger.” Review of Industrial Organization Vol 38(1)(2011), pp. 95-115. [4] Borenstein, S. “Hubs and High Fares: Dominance and Market Power in the U.S. Airline In- dustry.” RAND Journal of Economics, Vol20(3)(1989), pp. 344-365. [5] Borenstein, S. and Rose, N. “Competition and Price Dispersion in the U.S. Airline Industry.” Journal of Political Economy, Vol102(4)(1994), pp. 653-683. [6] Chiang, P. and Liou, T. “Does multimarket contact affect price dispersion? Evidence from the airline industry.” Working paper, 2018. [7] Ciliberto, F., Murry, C., and Tamer, E. “Inference on Market Power in Markets with Multiple Equilibria.” Working paper, 2020. [8] Ciliberto, F. and Williams, J. “Limited Access to Airport Facilities and Market Power in the Airline Industry.” Journal of Law and Economics, Vol53(3)(2010), pp. 467-495. [9] Ciliberto, F. and Williams, J. “Does multimarket contact facilitate tacit collusion? Infer- ence on conduct parameters from the airline industry.” RAND Journal of Economics, Vol45(4)(2014), pp. 764-791. [10] Dai, M., Liu, Q., and Serfes, K. “Is the Effect of Competition on Price Dispersion Nonmono- tonic? Evidence from the U.S. Airline Industry.” The Review of Economics and Statistics, Vol96(1)(2014), pp. 161-170. [11] Evans, W. and Kessides, I. “Living by the ’Golden Rule’: Multimarket Contact in the U.S. Airline Industry.” Quarterly Journal of Economics, Vol109(2)(1994, pp. 341-366. [12] Fernandez, N. and Marin, P.L. “Market Power and Multimarket Contact: Some Evidence from the Spanish Hotel Industry.” Journal of Industrial Economics, Vol 46(1)(1998), pp. 302-315. [13] Gerardi, K.S. and Shapiro, A.H. “Does Competition Reduce Price Dispersion? New Evidence from the Airline Industry.” Journal of Political Economy, Vol117(1)(2009), pp. 1-37. [14] Griliches, Z. and Mairesse, J. “Production Functions: The Search for Identiﬁcation.” Working paper, 1995.

16 [15] Jans, I. and Rosenbaum, D. “Multimarket Contact and Pricing: Evidence from the U.S. Ce- ment Industry.” International Journal of Industrial Organization, Vol15(3)(1997), pp. 391- 412. [16] Kim, Kim, and Tan. “Tacit Collusion and Price Dispersion in the Presence of Southwest Airlines.” Working paper, 2019. [17] Parker, P.M. and Roeller, L.H. “Collusive Conduct in Duopolies: Multimarket Contact and Cross-Ownership in the Mobile Telephone Industry.” RAND Journal of Economics, Vol28(2)(1997), pp. 304-322. [18] Stock, J.H. and Yogo, M. “Testing For Weak Instruments in Linear IV Regression.” Identiﬁ- cation and Inference for Econometric Models, 2005.

17 Appendix: Airline Websites

ABQ - https://www.abqsunport.com/terminal-maps/ ANC - https://www.anchorage-airport.com/terminals.php ATL - https://www.airport-atl.com/terminals.php BNA - https://flynashville.com/flights/airline-information BUF - https://www.buffaloairport.com/airport-guide/terminal-map BWI - https://www.baltimore-airport.com/bwi-terminal.php: :text=Baltimore%20Airport%20(BWI) %20has%20a,transportation%20facilities%20in%20its%20core. CLT - https://www.airport-charlotte.com/terminal.php DFW - https://www.airport-dallas.com/terminals.php HNL - https://airports.hawaii.gov/hnl/flights/airlines/ IAH - https://www.airport-houston.com/terminals.php MCI - https://www.flykci.com/flight-information/airlines-at-kci/ MIA - http://www.miami-airport.com/airline-information.asp MSP - https://www.mspairport.com/airport/terminal-information MSY - https://www.new-orleans-airport.com/terminal.php ORD - https://www.flychicago.com/business/CDA/factsfigures/Pages/facility.aspx PBI - http://www.pbia.org/guide/airlines/ PHL - https://www.philadelphia-airport.com/terminals.php SAT - https://www.san-antonio-airport.com/terminals.php SEA - http://www.worldairportguides.com/seattle-tacoma-sea/terminals.php SNA - https://www.ocair.com/flightinformation/airlines STL - https://www.saint-louis-airport.com/terminals.php TPA - https://www.tampa-airport.com/terminal.php

18 Table 1: Summary Statistics

19 Table 2: Number of Common Markets in 2014 Q1

Table 3: Average Contact Summary Statistics

20 Table 4: Log Average Price OLS Regression

21 Table 5: Gini Coefﬁcient OLS Regression

22 Table 6: Scaled Standard Deviation OLS Regression

Notes: Dependent variable is calculated as ln(sd +1)/ln(price), where sd is the standard deviation of price of all itineraries in a period-route-carrier observation, and price is the average price of all itineraries in a period-route- carrier observation. All regressions control for firm and period fixed-effects. Heteroskedastic robust standard errors in parantheses. * significance at the 10% level, ** significance at the 5% level, *** significance at the 1% level.

23 Table 7: First-Stage Regression onto Average Contact I

Notes: All regressions control for firm and period fixed-effects. Heteroskedastic robust standard errors in parantheses. * significance at the 10% level, ** significance at the 5% level, *** significance at the 1% level. Critical values for the Stock-Yogo and Hausmann tests are at least 10, but critical values may inflate due to the number of regressors.

24 Table 8: First-Stage Regression onto Average Contact II

25 Table 9: IV Regression