Nonlinear pricing strategies and competitive conditions in the airline industry.

Hernandez, Manuel A. ; Wiggins, Steven N.

I. INTRODUCTION

Many industries use nonlinear pricing based on product attributes. One industry where this practice is long recognized is domestic airlines. While price dispersion in the industry has been widely studied, data limitations have prevented analysis investigating the impact of competitive conditions on price dispersion linked to nonlinear pricing as opposed to variation in costs. This paper uses a novel data set that allows us to investigate how nonlinear pricing strategies vary with market structure. We construct a ticket menu using standard categories of tickets, including first class tickets, business class tickets, fully refundable tickets, nonrefundable tickets, and nonrefundable, restricted tickets. These categories exhibit substantially different prices and are available across all types of routes. We investigate both how market concentration and the competitive pressures generated by Southwest and other low cost carriers impact the relative fares within the ticket menu.

Using traditional measures of concentration, including both Herfindahl-Hirschman Index (HHI) and discrete measures used in other studies of airlines (competitive, duopoly, and monopoly), we observe only a modest impact of concentration on relative fares. The discrete measures appear to be more informative, indicating that concentration primarily reduces the relative fares for high end (first class) tickets on monopoly routes. We identify a puzzle regarding the pricing of high end fares under monopoly. The evidence does not support a more general relationship between concentration and other fares.

We find considerably stronger evidence regarding the impact of Southwest on the fare structure. While previous studies show that Southwest's presence reduces mean fares, our results provide a much richer picture. The results show that Southwest's presence reduces low end fares but actual and potential competition from Southwest also generally leads to a substantial compression of the entire fare structure. Competition from other low cost carriers also affects the fare structure, but does not lead to a compression of fares.

Our analysis ties into several literatures. Our work is closely related to the theoretical work on nonlinear pricing and imperfect competition (see, e.g., Rochet and Stole 2002; Stole 1995). (1) Generically, however, there is no natural empirical implementation of these models for testing. More specifically, in these models consumers differ in two dimensions, brand loyalty and their marginal preference for quality. The results of these papers show that the relationship between competition and high versus low prices turns on the correlation between consumers' preferences for quality and their "brand loyalty." Unfortunately, these models generally predict monotonicity, so that prices exhibit either a wider or narrower spread related to competition (Busse and Rysman 2002). Our results, in contrast, show that higher prices are reduced on highly concentrated routes, but that intermediate prices are at most modestly affected. The results for actual and potential competition from Southwest generally support the predictions of Rochet and Stole (2002) that increased competition will lead to fare compression.

Our study is also related to the empirical work on competition and price dispersion in airline markets. There is an extensive body of work regarding the relationship between market concentration and airline price dispersion. The empirical evidence on this matter is mixed. In a seminal paper, Borenstein and Rose (1994) examine concentration and price dispersion, using cross-sectional variation in market concentration and dispersion to identify the relationship between the two. They show that airlines offer highly dispersed prices; the expected absolute difference in fares between two randomly chosen passengers on the same airline and route is 36% of the average price. The authors also find that price dispersion decreases with market concentration. Hayes and Ross (1998), in turn, do not find a clear relationship between market structure and price dispersion. More recently, Gerardi and Shapiro (2009) and Gaggero and Piga (2011) find evidence that fare dispersion of airline prices increases with market concentration. (2) Of particular interest is Gerardi and Shapiro (2009), who use time-series variation in concentration to identify its relationship with fare dispersion. They argue that cross-sectional identification of the effects of concentration may suffer from omitted variable bias. This finding is of particular interest because our data are cross-sectional.

In contrast to these papers, our analysis contributes to an understanding of fare dispersion, but approaches the issue using groups of tickets that are used by airlines to create fare/ticket restriction menus. (3) These data are more refined than earlier work that measures dispersion using a simple Gini coefficient. Our menu approach permits an examination of relative fares using comparably restricted tickets across markets. This fare menu approach offers greater control for ticket quality and several distinct metrics of fare differences using the relative pricing of different groups of comparable tickets. These more refined data show that the relationship between the fare structure and competition is more complex than previous studies would indicate. Still, we are restricted to a single cross-section, which requires caution in the interpretation of results.

Our paper also contributes to the literature regarding the impact of Southwest Airlines and other low cost carriers by examining the effect of those carriers on relative prices within the fare menu. Previous studies show that Southwest's presence has a substantial impact on mean fares (see, e.g., Brueckner, Lee, and Singer 2010; Goolsbee and Syverson 2008; Morrison 2001). These studies consider separately actual competition from Southwest, potential competition where Southwest offers service at both endpoints but not on the route itself, and adjacent competition where Southwest offers service to the same city-pair but at least one endpoint is to a different airport in the same city. We follow a similar categorization to analyze how Southwest impacts relative prices within a menu of fares. We use the same categories to evaluate other low cost carriers.

The remainder of the paper is organized as follows. Section II presents the empirical model. Section III describes the data. Section IV presents and discusses the main estimation results and performs alternative estimations to evaluate the robustness of the results. Section V concludes.

II. EMPIRICAL MODEL

This section presents our empirical model of the relationship between market structure and the fare ratios of various ticket types. Our goal is to analyze whether competitive conditions affect a carrier's nonlinear pricing strategy. This analysis involves examining the effect of market concentration and the presence of low cost carriers on relative prices, controlling for cost and other market-specific effects. The cornerstone of our model regards our ability to link specific groups of ticket restrictions to particular fares, which differs significantly from previous work using the Origin and Destination Survey (DB 1B) from the U.S. Department of Transportation, which does not contain data on ticket characteristics, load factors, and specific flights. (4)

Airlines provide a menu of ticket restrictions with associated fares on their various routes and allow travelers to self-select by purchasing different types of tickets. (5) A key feature of this fare structure is that the basic menu of ticket types (restrictions) is the same across routes, even when routes exhibit different levels of competition. (6) This commonality permits us to analyze the relationship between the relative prices of various types of tickets and competitive conditions.

The ticket menu consists of five ticket quality categories ordered by cabin, refundability, and ticket restrictions. More specifically, Group 1 includes first class tickets while Group 2 includes business class tickets. Group 3 includes fully refundable coach class tickets. Group 4 includes nonrefundable tickets without travel or stay restrictions, and Group 5 includes nonrefundable tickets that also entail travel and/or stay restrictions. (7) We define the lowest priced Group 5 tickets as the base group and examine the variation in the ratios of the fares associated with higher quality tickets to Group 5 tickets.

A. Identification

Our identification strategy relies on the cross-sectional relationship between these fare ratios and competitive conditions while controlling for cost and market factors. Our ticket-level analysis allows us to incorporate numerous, widely used controls that affect airline fares. While our data is limited to a single cross-section, our unique data set permits us to introduce various controls that have been unavailable in prior work. Most important, our data permit the construction of the fare menu so that relative fares include control for ticket quality. In addition, we also have other data that permits control for flight level data including a flight's estimated load factor at ticket sale, days in advance a ticket was purchased, and time and day-of-week of departure. These controls allow us to account more accurately for possible differences in opportunity cost across tickets that enhance the econometric reliability of the estimation.

Naturally, we cannot rule out potential unobservable differences across routes regardless of the inclusion of a broad set of cost and market controls. Although cross-route variation in the costs of removing or adding ticket restrictions, which represent the key characteristics varying across our ticket groups, seems implausible, there still may be unobservable differences across routes correlated with market structure and relative pricing strategies that could be biasing our results.

B. Model Specification

The model postulates fares as a function of group dummies for fare type, market concentration, carrier market share on the route, the presence of low cost carriers, hubbing, and a set of controls at the ticket, flight, and market level. The central variables of interest are the group dummies that capture the fare premia associated with higher quality tickets as compared to base group fares.

We estimate two log-linear fare equations. In the first baseline equation we do not interact quality premia with market structure. In the second equation we do such an interaction, allowing quality premia to vary with market structure and with the low cost carrier and hub dummies. We refer to the first equation as the no interaction model and to the second equation as the interaction model.

The log-linear fare equation of the no interaction model is given by

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [p.sub.ijkt] is the fare per mile of ticket (itinerary) i charged by carrier j on route k at time t, [q.sub.fi] is a dummy variable for Group f fare, f - 1, ..., 4, mkt[structure.sub.k] is the route market structure measured through either HHI or categorical variables for monopoly, duopoly and competition, [mktshare.sub.jk] is the carder market share on the route, [LCC.sub.j] is a vector of variables indicating the presence of low cost carriers on the route, [HUB.sub.jk] is a vector of dummies to indicate the carrier has a hub on the route, and [X.sub.ijkt] is a vector of ticket, flight, and route controls. We specify the error term to have a carder effect [[alpha].sub.1j], a random route effect [K.sub.1k] common to all carders on a route, and a white noise error [[epsilon].sub.ijkt].

The log-linear fare equation of the interaction model is given by

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The parameters of interest are [[beta].sub.f1] in Equation (1) and [[delta].sub.f1], [[delta].sub.f3], [[delta].sub.f6], and [[delta].sub.f8] in Equation (2), where f = 1, ..., 4. The magnitude of the coefficients [[beta].sub.f1] and [[delta].sub.f1] approximates the quality premium of Group 1 through Group 4 fares as compared to Group 5 fares, the lowest fares. The signs of [[delta].sub.f3], [[delta].sub.f6], and [[delta].sub.f8] indicate how these premia vary with market concentration, the presence of low cost carriers and hubs. Table S1 in the Supporting Information provides a full description of all variables used in the analysis.

Carrier market share on a route and route concentration are both included because, as shown by Borenstein (1989), these variables can have distinct effects on fares (see also Stavins 2001). An increase in market concentration on a route would be expected to increase all fares, but an increase in a given carder's share could lead to a separate effect increasing only that carrier's fares.

Following Mordson (2001), Lee and Luengo-Prado (2005), Goolsbee and Syverson (2008), and Brueckner, Lee, and Singer (2010), we separately account for the presence of Southwest and other low cost carriers. The existing literature indicates that Southwest and other low cost carders represent distinct and somewhat different types of competitive pressure, affecting the level of fares. We address how such competitive pressure can also have a distinct effect on the distribution of fares. We account for both the presence and potential presence of these carriers on the route and at adjacent airports, considering that low cost carriers may operate from alternative airports.

Previous studies have also shown that hubs may affect fares, raising the distinct possibility that they may differentially impact particular groups of fares. In particular, hubbing may lessen competition through frequent flyer programs and long-term leases on gates and airports facilities, leading to differential pricing at hubs (Borenstein 1989; Evans and Kessides 1993; Lee and Luengo-Prado 2005). For example, carriers may extract additional hub premiums from travelers who purchase high end fares who may also be active participants in frequent flyer programs. We account separately for passengers who originate at a hub and those whose destination is a hub.

Our data set further permits to control for flight-level scarcity as studied in theoretical analyses of scarcity pricing in airlines. Theories of scarcity pricing developed by Dana (1998, 1999a, 1999b) and Gale and Holmes (1993) indicate that prices will vary with load factor. (8) Variations in the load factor of a flight may reflect both changes in capacity utilization and in the perceived probability that demand will exceed capacity. Accordingly, we account for time of purchase, flight level load factor deviations, and peak departure times. Days before departure reflect the fact that flights gradually sell out, and remaining fares are typically higher. (9) We measure load factor deviations by first measuring mean load factor for each day prior to departure by carrier-route. For a given itinerary, we then measure deviations in the actual load factor from this baseline for a given flight and day on which a ticket was purchased. Positive deviations reflect greater scarcity and the reverse for negative deviations. These controls reflect Dana's approach. We also include a peak departure variable corresponding to Monday through Friday from 7-10 a.m. and 3-7 p.m., considering that Gale and Holmes (1993) emphasize scarcity associated with busy flight times. Our analysis reveals systematically higher load factors at these times.

The analysis also includes market controls for cost and demand conditions widely used in the literature. We account for slot-controlled airports which are likely to raise the costs of serving a market (Borenstein 1989). (10) Similarly, we include market variables for distance, average population and per capita income at the endpoint cities, a tourism index, and the absolute temperature difference between the origin and destination. (11) Both the tourism index and the absolute temperature difference are used to control for tourist effects and, potentially, for differences in the relative demand for different fare types. The tourism index is a proxy of the proportion of leisure travelers to each destination (Borenstein 1989; Borenstein and Rose 1994). A larger absolute temperature difference between the origin and destination might also indicate a higher proportion of leisure travelers on the route (Brueckner, Dyer and Spiller 1992; Stavins 2001).

C. Endogeneity Issues

In Equations (1) and (2) both market share and HHI are potentially endogenous. Market share is endogenous both because fares and share may influence each other and because unobservable route characteristics may influence both. To the extent that market share is endogenous, the route HHI is also endogenous. We begin by using the same instruments and procedures found in the studies of Borenstein (1989) and Borenstein and Rose (1994), and then introduce additional controls to address remaining issues. We also consider potential differences in routes to evaluate whether such differences are systematic.

We instrument a carrier's market share using the carrier's geometric average of its enplanement shares (share of boarded passengers) at the two endpoint airports, where the average shares are calculated omitting the route in question. Enplanement shares at endpoint airports measure the carriers' portion of total boarded passengers at the endpoints, reflecting the degree to which passengers may be familiar with or prefer travel on a particular carrier at those endpoints. High endpoint enplanement shares are closely related to high shares on individual routes. This instrument preserves the portion of high shares common to the endpoint airports but should not be correlated with idiosyncratic route-specific share effects because it is calculated using endpoint shares of boarded passengers for all routes from the endpoint airports. Further, since high enplanement shares at the endpoints are not influenced by fares on a given route, then enplanements are not likely to be simultaneously determined with fares on a particular route that is excluded from the enplanement share calculation.

The use of this instrument, however, raises the possibility of an airport specific effect. High enplanement shares could be related to a common preference for a carrier's flights related for example to frequent flyer loyalty. There is no complete solution to this potential selection issue, but we address it in two ways.

First, to control for the potential preference of frequent flyers and its potential correlation with enplanement shares, we introduce two hub variables as compared to the single variable found in the literature. We use both an overall hub variable, which takes a value of one for all passengers on the hub route, and an origin hub variable, which takes a value of one only when passengers originate from a carrier's hub. These variables should control for routes where there would be a strong preference for the hub carrier's flights. (12)

These instruments and controls though may not fully resolve unobserved route characteristics that may influence the estimates. There is an inherent limitation in attempting to instrument for market shares because shares may be associated with other unobservable factors that may lead to dominance and higher prices. For example, while the hub variables may attenuate the effects of frequent flyer programs, they cannot offer such control on nonhub routes. The implication is that the share coefficient may, to some extent, reflect the effects of such preferences so that it is important to note that the coefficient for market share could in part reflect the influence of these factors.

In addition, there may also be unique characteristics of highly concentrated routes, which leads to our second approach. Our results indicate that the primary effects of concentration on prices are found on the most concentrated, monopoly routes. Consequently, we investigate the potential similarities and differences between these monopoly routes and other routes in our sample in an attempt to identify other important factors that set such routes apart (see Section IV).

If share is endogenous, then HHI is also endogenous. We can readily calculate an instrument for HHI if one assumes that the above instrument for market share is valid and that the concentration of traffic among other carriers-that is, the distribution of remaining shares among those carriers--does not depend upon a carrier's own fares. Using this assumption, the endogenous portion of HHI is that part associated with the firm's own share. Accordingly, one can develop an instrument by estimating the firm's share in a first stage regression using the instrument described above. Using the fitted values from this regression one can then rescale other firms' shares to ensure that overall shares continue to add to one. We can then calculate a predicted HHI using the estimated share from the first stage regression and these rescaled shares. (13) This predicted HHI is a valid instrument for HHI using the assumptions described above.

This instrument is subject to limitations similar to those described above for the market share instrument. Large shares for a carrier could be associated with unobserved demand factors that affect all departures from an airport so that the HHI coefficient in part reflects these effects. These effects should be more muted because the HHI is calculated using all shares, but one should interpret these coefficients recognizing that one cannot rule out these effects. We also include instruments for the interaction terms between HHI and the dummy variables for fare types that consist of the same instruments interacted with the corresponding dummy variables.

Southwest's presence on a route is also potentially endogenous (see also Goolsbee and Syverson 2008). In our analysis we categorize Southwest's presence into four groups: routes served by Southwest, routes where Southwest serves both endpoint airports but not the route, routes where Southwest offers adjacent service (at least one endpoint is to a different airport in the same city), and routes where Southwest does not offer service to at least one of the cities (see Brueckner, Lee and Singer 2010; Goolsbee and Syverson 2008; Morrison 2001). In principle there exists a fifth category where Southwest is a potential entrant into adjacent service, but Goolsbee and Syverson find that such potential entry does not affect prices. The source of endogeneity concerns the selection bias and potential endogeneity regarding routes Southwest actually enters as compared to those where it is simply a potential entrant. The same taxonomy and interpretation applies to other low cost carriers.

We adopt two strategies for addressing this issue. First, our results, which are similar to those of Goolsbee and Syverson (2008), show that Southwest's effects are similar for routes where Southwest offers service and where they offer potential service (i.e., they serve both endpoints, but not the route). This finding suggests that the effect arises because Southwest serves both endpoint airports. We confirm this interpretation by re-estimating the basic equation using a single variable that takes a value of one whenever Southwest serves both endpoint airports. This variable is clearly exogenous since Southwest's decision to serve each endpoint is unlikely to be endogenous to the fares on a particular route from the airport, or characteristics associated with a single route from that airport. This approach does not rule out a selection mechanism where the routes differ from other routes in the sample. Our second strategy is to compare the route characteristics for routes where Southwest is an actual or potential competitor compared to other routes.

For low cost carriers the data indicate only modest effects of those carriers when they actually serve a route and similar modest effects on the distribution of fares. Given the lack of instruments, and the fact that we mainly use low cost carriers as a control, we re-estimate the equation using a single variable that takes a value of one when low cost carriers serve both endpoints. We further recognize the potential endogeneity of other control variables, including the tourism index and load factor deviations. Due to the lack of valid instruments we can only acknowledge this issue and caution that one should interpret our results accordingly.

III. DATA

A. Ticket Transactions Data

The main data source of this paper is a census of airline ticket transactions from a major computer reservation system (CRS). The data set consists of tickets purchased between June and December 2004 for travel in the fourth quarter of that year. It includes tickets purchased directly from airlines, including their websites, and through travel agents and online travel sites. Overall, the data represent approximately 30% of all domestic ticket transactions in the United States. For each ticket sold or itinerary, we have information on the fare paid, origin and destination, segments (coupons) involved in the itinerary, carrier and flight number, cabin and booking class, and dates of purchase, departure, and return.

Due to confidentiality reasons, the major CRS vendor did not provide information on ticket restrictions. Consequently, the transaction data set was merged to historical data from a travel agent's CRS containing a large subset of fares offered for travel in the last quarter of 2004. (14) For each fare in this second data set, we have information on origin and destination, carrier, booking class, departure date from origin, advance purchase requirements, refundability, travel restrictions, and maximum or minimum stay restrictions. The matching procedure, described more fully by Puller, Sengupta, and Wiggins (2009), matches an itinerary from the transaction data set to a fare from the travel agent's data set based on route, carrier, and fares. The matching process ensured that fares matched within 2% and that the itinerary matched advance purchase requirements and travel and stay restrictions. (15)

Following the literature, we define a route as an airport-pair, regardless of direction, and restrict attention to direct one-way and roundtrip itineraries. This restriction follows Goolsbee and Syverson (2008) and Gerardi and Shapiro (2009) but was needed in our case because it is not possible to match multi-leg trips in the original data set with ticket restrictions from the second data set. (16) We also exclude tickets that involve travel with different airlines (interline tickets) and tickets with different ticketing and operating carriers. Prices are measured as roundtrip fares and the fare for one-way tickets is doubled. To avoid holiday peaks, we drop transactions involving travel on Thanksgiving, Christmas, and New Year. (17) We also follow the literature by eliminating fares of less than 20 dollars (ten for one-way tickets), which presumably represent the handling charges for frequent-flyer tickets.

The data set includes tickets for travel on American, Continental, Delta, Northwest, United, and US Airways. These legacy carriers individually transported more than 5% of all domestic travelers during the fourth quarter of 2004. Southwest also carried more than 5% of all domestic travelers, but we exclude Southwest tickets because we only have limited information for those tickets and Southwest does not use the fare menu that is central to the analysis. The data set also includes tickets for flights operated by AirTran, Alaska, America West, ATA, Frontier, Hawaiian, Midwest, Spirit, and Sun Country.

The analysis restricts attention to matched itineraries where there are at least one thousand observations per route and one hundred observations per carrier-route. This restriction results in 878,169 tickets on 246 routes and 460 carrier-routes. The list of routes is reported in Table $2. It is important to note that while we restrict the tickets used in our analysis, all market structure variables include all carriers and tickets.

As noted, we group tickets into five categories. Table S3 shows that fares decline with the quality decreases that occur as we move from Group 1 to Group 5. The data in the table were calculated using carrier route percent deviations from mean fare per mile by ticket category for the legacy carriers. These percent deviations were then averaged across routes for the corresponding carriers. Group 1, Group 2, and Group 3 fares are generally above the average fare per mile charged by a carrier while Group 4 and Group 5 fares are below the average. These data reveal sharp differences in the fares of the various groups, a finding that is confirmed in the regression analysis below, which controls for numerous other factors. The five-type fare structure together with dummy variables for time of purchase and one-way travel and carrier fixed effects explain on average 76% of the fare variation in each of the routes analyzed.

B. Market Level Variables

We also use various market level variables similar to those used in previous airline studies. Market share and the market structure measures are derived from the T-100 Domestic Segment Database from the Bureau of Transportation Statistics (BTS). This data set contains domestic, nonstop segment data reported every month by all U.S. carriers. As noted by Gerardi and Shapiro (2009), who also work with nonstop itineraries, there are limitations to this approach, but this data source most closely matches the concentration of the sales of tickets in our sample.

For market concentration, we include the HHI. We also follow Borenstein and Rose (1994) and use as an alternative a set of discrete concentration measures. Under that approach we categorize routes into monopoly (greater than 90% of nonstop passengers for a single carrier), duopoly (two carriers with greater than 90%), and competitive (the remainder).

Turning to low cost carriers, we use a 5% market share threshold in defining actual presence for Southwest and other low cost carriers. This threshold eliminates seldom used, highly circuitous routes. Adjacent competition by these carriers is defined as a case where these carriers serve a city-pair but at least one endpoint is to a different airport in the same city (see Morrison 2001). We follow Goolsbee and Syverson (2008) who measure potential competition by these carriers as a setting where the carrier operates at the two endpoint airports but does not fly the route. While they find that such potential competition is important, they do not find that potential entry involving adjacent airports is significant.

Table 1 presents descriptive statistics. Roundtrip fares range from 62 dollars for a Las Vegas (LAS)-Los Angeles (LAX) trip on American to $4,806 for a San Francisco (SFO)-New York-Kennedy (JFK) trip on United. The average fare paid is 457 dollars or 31.3 cents per mile. The percentage of tickets sold in Group 1 through Group 5 is, respectively, 5%, 7%, 12%, 28%, and 47%. Roughly 60% of the tickets are bought in the last 2 weeks prior to departure, and 25% are purchased in the last 3 days. More than 80% of itineraries involve travel to/from a hub, 74% of itineraries are for roundtrip travel, and 65% of the tickets involve travel during peak times. There is direct competition from Southwest for 9% of the itineraries and competition from other low cost carriers for 34% of the itineraries. Twelve percent of the sample tickets are on monopoly routes, 48% on duopoly routes, and 40% on competitive routes. Eighteen percent of routes are monopolies, 48% are duopolies, and the remaining 34% are competitive markets. These distributions are similar across various distances.

Figure 1 provides a preliminary overview of the value of the menu pricing approach in analyzing the relationship between market concentration and pricing. The figure graphs the relationship between concentration and the ratio of various Group fares to the lowest, Group 5 fares. The graph indicates a more complex relationship than provided by a simple Gini coefficient. Panel A uses discrete market structure categories and shows that the average fare per mile of Group 1 (first class) decreases relative to Group 5 in monopolies. On competitive and duopoly routes the ratio of Group 1 to Group 5 fares is approximately 5.8 while on monopolistic routes the ratio is less than 4.6. The ratio of Group 2 (business class) to Group 5 fares also decreases, but only moderately. In contrast, the ratio of Group 3 to Group 5 fares increases in highly concentrated markets, from two in competitive and duopoly markets to 2.7 in monopoly markets. Group 4 fares relative to Group 5 fares do not seem to vary with market structure conditions (the ratio fluctuates around 1.5). This relative pricing pattern also holds when using HHI, as illustrated in the bottom figure. (18)

Table 2 offers additional insights about the relative pricing pattern described above. The table reports absolute fares in cents per mile by fare type and market structure using both market structure categories and concentration ranges. Interestingly, the decrease in the ratio of Group 1 to Group 5 fares on monopoly routes is mainly driven by fare reductions for first class tickets. On competitive and duopoly routes Group 1 fares average between 94 and 97 cents per mile while on monopoly routes these fares average about 74 cents per mile. Group 5 fares, in turn, fluctuate around 18-19 cents per mile with varying market structure conditions. Business class (Group 2) fares also show a moderate decrease in highly concentrated routes. Group 3 fares, on the other hand, show an important increase from 31-32 cents per mile on competitive and duopoly routes to 43 cents per mile on monopoly markets, which explains the increase in the ratio of Group 3 to Group 5 fares. Group 4 fares also increase in more concentrated markets, but to a lesser extent. Hence not all fares necessarily rise or follow a similar pattern with increased concentration, which reinforces the complex relationship between market structure and pricing behavior in the industry.

Figure 2 provides, in turn, some insights regarding the potential impact of Southwest on relative fares within the ticket menu. The figure reports average price ratios by fare type, day of purchase, and Southwest direct presence on the route. We find that the ratio of Group 1, Group 2 and Group 3 fares to the lowest, Group 5 fares are smaller on routes where Southwest directly operates versus routes where Southwest is not present. On average, the price ratios are 25%-35% smaller on routes with Southwest presence. Interestingly, the differences in relative fares persist, or in the case of Group 2 become more accentuated, as we approach the departure date. The ratio of Group 4 to Group 5 fares, in contrast, does not show much variation across different days prior to departure with Southwest presence.

IV. ESTIMATION RESULTS

This section presents the estimation results and evaluates robustness. The fare equations specified in (1)and (2)are estimated by both ordinary (OLS) and two-stage least squares (2SLS). The 2SLS approach is required to address the potential endogeneity of the carrier market share and the route HHI. (19) We treat carrier effects as fixed and route effects as random. Route effects are treated as random to permit inclusion of route-specific variables, such as market structure.

A. No Interaction Model

Table 3 presents the results for the base, no interaction model. These results show the basic fare premia for various groups compared to Group 5, Model 1 measures market concentration using HHI while Model 2 uses the categorical variables. Carrier fixed effects are omitted for ease of presentation. As in Goolsbee and Syverson (2008) and Gerardi and Shapiro (2009), the reported standard errors are robust and clustered at the route level to control for correlation of errors on a route.

Turning to the power of our instruments, while we do not have overidentifying restrictions with which to test the exogeneity of the instruments, we do examine under- and weak identification of our instruments. The test results are presented at the bottom of Table 3. The tests reported are the LM and Wald versions of the Kleibergen and Paap (2006) rk statistic. The LM under-identification test rejects at the 1% level of significance the null hypothesis that the excluded instruments are not correlated with the presumably endogenous regressors while the F weak-identification test suggests that the instruments are not weakly correlated with the endogenous explanatory variables.

The estimation results for the group variables show the price premia for various groups after controlling for cost and market-specific factors. The quality premium over Group 5 fares increases progressively from Group 4 through Group 1 fares. In the first model, where we use HHI as the measure of market concentration, the 2SLS results indicate that Group 4 through Group 1 fares per mile are, on average, 35%, 54%, 204%, and 398% higher than Group 5 fares. In the second model, where we use categorical variables to measure market concentration, the corresponding premia are very similar: 35%, 54%, 202%, and 402%.

The coefficients of the control variables generally have the expected signs and are in most cases statistically significant in both models. Average fares, however, do not show much variation with the market structure measures. Further insight into this result can be found in the study of Borenstein (1989), which found offsetting effects regarding the impact of HHI on low (20th percentile) and high (80th percentile) fares. (20)

Regarding the impact of low cost carriers on fares, we observe that Southwest has larger effects than other low cost carriers. We find that direct, potential, and adjacent competition from Southwest all significantly reduce fares. In particular, direct competition from Southwest reduces fares by about 29%, and both potential and adjacent competition reduces fares by 21%. Other low cost carriers, however, only have a significant negative effect on prices (of 15%) when they directly serve the route. (21) Hubs, in turn, have a positive effect on fares. The results show that fares per mile on routes where the operating carder has a hub at either endpoint are about 15% higher than thres on routes not involving a carrier's hub.

[FIGURE 2 OMITTED]

Concerning the remaining coefficients, we focus on Model 2 for ease of exposition. The results show that both the time of purchase and one-way tickets have an important effect on ticket prices. Tickets bought closer to departure time are typically more expensive than those bought further in advance. More specifically, travelers who purchase a ticket 0-6 days in advance end up paying between 22% and 24% more per mile than those who purchase a ticket more than 21 days in advance. Passengers who purchase one-way tickets pay 18% more than half the price of roundtrip fares. The results further indicate that the load factor and peak time variables are statistically significant, but their economic magnitudes are small. A one standard deviation increase in the deviation of load factor from its mean at the time of ticket purchase (0.2) only increases the fare per mile by 2%. Tickets that involve travel during peak times of the day are approximately 3% more expensive than those during off-peak times.

Most of the coefficients of the market variables are consistent with the literature. The presence of a slot-controlled airport increases average fares by about 13%. Distance between endpoints and a higher population at the endpoint cities decreases the average fare per mile. The tourism variables are designed to account for the proportion of leisure travelers on a route, but only the tourism index is statistically significant and it is economically small. A one standard deviation increase in the tourism index (0.03) results in a 4% decrease in the average fare per mile.

B. Interaction Model

We now turn our attention to the relationship between the quality premia and market structure. Table 4 presents the estimation results for this interaction model. As above, Model 1 uses the HHI while Model 2 uses categorical concentration variables. For later comparison we begin by only interacting concentration with the quality variables (base interactions). We then further interact the ticket quality measures with a full set of dummies for Southwest, other low cost carriers, and hubs (full interactions). We note without further discussion that the estimated coefficients of the control variables here are similar to those in Table 3.

The Model 1 results show a statistically significant effect of HHI on the Group 1 premium. The relative premia of the other group fares do not seem to vary with changes in the level of concentration. Further insight into this result is provided by Model 2, which uses discrete concentration measures. Those results show that the Group 1 premium falls only on monopoly routes. We also observe a marginally significant increase (in the base interactions model) in the relative premium of Group 3 fares on monopoly routes. Group 2 relative fares moderately decrease on duopoly routes while the Group 4 premium remains unchanged.

Hence the results for traditional measures of concentration show only a weak, limited relationship between the structure of fares and concentration as summarized in Table 5. Panel A of the table reports predicted premia over Group 5 fares for various categories and levels of concentration. The panel reveals largely modest differences as concentration changes with the exception of Group 1 fares, which appear to be driven by the most concentrated, monopoly routes.

Our data present a more complete view of fare structure than is available from other studies using Gini coefficients or other single statistics regarding dispersion, and indicate only a limited relationship between concentration and fare structure. In particular, our results indicate that when using a fare menu approach the primary effect of concentration is for the highest priced tickets on monopoly routes. This result, also observed in the preliminary analysis (see Figure 1), is something of a puzzle given a monopolist's market power. The result may be indicative of a more complex relationship between the fare structure and concentration than previous studies would suggest. Because this result is found only on a limited number of routes, and for monopolies, the result naturally raises a possible selection issue regarding these routes, which we deal with in the next subsection. (22) For now we turn to Southwest.

The regression results in Table 4 show a very substantial effect of Southwest on the level and structure of fares. In particular, Southwest direct or potential presence both reduces the base fare, by approximately 15%, and compresses the entire fare structure. Comparing the two parts of Panel B in Table 5 reveals that the premium over Group 5 falls by at least one-half; in the case of Group 2 and Group 3 fares the premia substantially vanish or is even reversed. (23) Consequently, Southwest actual or potential presence appears to significantly change the fare structure of legacy carriers.

The more surprising feature of the results is that Southwest has a larger impact on high end fares than on low end fares. A possible explanation for the observed fare compression is that legacy carriers are simply trying to compete with Southwest, which operates with a fairly compressed fare structure. In addition, Southwest may be competing with legacy carriers for business travelers by offering important time savings in terms of higher flight frequencies and better on-time performance. Figure S1 compares the average flight frequency and on-time performance of Southwest versus legacy carriers on all routes in our sample where both directly compete (21 routes). The comparison is based on the airline on-time performance data provided by the BTS. We consider both all flights during our period of analysis and only flights during peak times (weekdays 7-10 a.m. or 3-7 p.m.) where we could expect a higher presence of business travelers. We observe that Southwest offers, on average, nearly one additional flight per day than legacy carriers operating on the same routes (10.9 vs. 10.1 flights per day). Similarly, Southwest shows a better on-time performance than legacy carriers for most of the indicators considered. Except for departure delays, Southwest shows lower flight arrival delays (10.6 vs. 11.9 min per flight), elapsed time (10.3 vs. 10.9 s per mile traveled) and cancellations (0.6% vs. 0.8% of flights cancelled) during any time of the day. (24) These differences persist when considering only peak hours. Hence, business travelers may be willing to accept fewer amenities to achieve the larger time savings provided by Southwest.

The results obtained are also in line with the results of Snider and Williams (2011) who find that direct low cost competition compresses the fare distribution; yet our results do not extend to low cost carriers other than Southwest as discussed next. Our results further tie with the results of Alderighi et al. (2012) for the European aviation market. They find that competition of low cost carriers reduces both business and leisure fares of full-service carriers in a quite uniform manner, with an emphasis on mid-segment fares. The remaining issues regarding Southwest, as above regarding monopoly routes, concern potential endogeneity of Southwest presence and sample selection issues regarding the routes it serves, which we address more fully in the following subsection.

Competition from other low cost carriers and airline hubs has a considerably smaller impact on fares. Direct competition from other low cost carriers leads to lower base fares, as well as Group 3 fares, but somewhat higher premia for first and business class fares. The increased premia for First and business class ranges from 50 to 150 percentage points. These results would appear to be driven by changes in the composition of passengers that airlines serve once some passengers opt to use low cost carriers. Specifically, low cost carriers compete vigorously for price sensitive customers, and legacy carriers respond by raising prices on the less price sensitive customers who remain. This result indicates that the different type of competitive pressure exerted by Southwest and other low cost carriers on fare levels, found in previous studies, also extends on to the fare structure. Southwest seems to further compete with legacy carriers for business travelers.

Airlines also increase their fares generally for flights serving their hubs, but the structure of fares is only modestly different in those settings. The hub variable, defined as one for a hub origin or destination, indicates an approximate 14% increase in base fares. The interactions of this variable with the group dummies are generally positive but not significant (except for Group 2 fares), which indicates a reasonably uniform increase in fares. The separate dummy for a hub as an origin, which measures the differential effect of passengers whose trips originate at a hub but arrive at a nonhub airport, is also insignificant. The conclusion is that fares increase for hub service but the basic structure generally remains unchanged.

The regression results in Tables 3-5 provide three important results. First, the quality premium over Group 5 fares declines progressively as we move from Group 1 (first class) through Group 4 fares, which confirms the asserted price/quality ticket differences. Second, traditional measures of concentration are related to this fare structure only in that first class premia fall substantially on monopoly markets, a puzzling result that differs significantly from the Busse and Rysman (2005) investigation of Yellow Pages advertising. Third, Southwest presence, particularly direct and potential presence, is associated with a substantial reduction in all fares and a general compression of the entire fare structure. Competition from other low cost carriers and hubbing do not generally impact the fare structure.

C. Sample Selection and Endogeneity

The fact that our findings focus on discrete city-pairs raises the issue of whether there are unidentified route characteristics that lead to a sample selection bias that could separately account for the results. Table $5 presents the available summary statistics comparing both monopoly versus nonmonopoly routes, and comparing routes that vary according to Southwest's competitive presence. These data cannot, of course, fully address the possibility that there are other unidentified differences across routes. The data, however, indicate that in terms of observables the routes seem to be similar. (25)

The remaining econometric issue regarding Southwest and other low cost carriers regards whether the actual provision of service on a route is correlated with unobservable route characteristics that could also influence airline prices. Note that the impact of Southwest on average prices is similar simply if Southwest operates at both endpoint airports. Because service at both endpoint airports consists of decisions involving a large number of routes, Southwest's decision to offer service at the endpoint airports is unlikely to reflect demand on the individual routes. Accordingly, we can avoid endogeneity by constructing a dummy variable that takes a value of one if Southwest is present at both endpoint airports. We use a similar, but separate variable for other low cost carriers. The estimation results under this alternative specification are reported in Table $6. The estimated effects of Southwest and other low cost carriers in this specification remain similar, but somewhat smaller than those found in Table 4. While neither the original specification nor this specification is ideal, in the absence of valid instruments the results suggest that potential endogeneity is unlikely a source of substantial bias.

Finally, the potential route selection bias can also be addressed in two albeit incomplete ways. One way is to break down the sample into more homogenous subsamples based on distance and number of passengers, and determine if the results hold up within the subsamples. We observe that most of our central findings regarding the decrease in the relative premium of Group 1 tickets on monopoly routes and the impact of Southwest on the fare structure hold. (26) The second way is to identify the variables varying within a route using a first-step estimation with routes fixed effects and then identify the remaining controls at the route level with the between estimator. Most of our main results also hold under this alternative estimation procedure. (27)

D. Alternative Measures of Market Structure and Functional Form

The analysis above measures market concentration and the presence of low cost carriers using T-100 Domestic Segment data. These data sets are only for direct flights, which is consistent both with our sample based on direct itineraries, and Gerardi and Shapiro (2009). One could argue, however, for broader measures that include both direct and connecting service. Both types of measures have been used in prior work. We use as an alternative a widely used, broader measure that includes up to four coupons (one-stop service) from DB1B. (28) For comparison, in the T-100 data used above, 84 routes are competitive, 119 are duopolies, and 43 routes are monopolies. With the alternative DBIB data, 124 routes are competitive, 100 are duopolies and 22 are monopolies.

Using these alternative measures of market structure, the basic regression results do not change. Table $7 presents the estimation results using these alternative measures. The magnitude of the control variable coefficients changes little and the measured impact of concentration on the structure of fares is generally unchanged. Southwest presence, particularly direct presence, also seems to compress the entire fare structure. The upper panel of Table $8 (panel A) summarizes all these results. Overall, the price premia for these estimations change little as compared to those found above.

We also investigate the robustness of the results to functional form by re-estimating Equation (2) using fare per mile as the dependent variable instead of its logarithm. Table S9 presents the estimation results. The results show that the effect of both the control variables and the variables of interest are in most cases similar to those above. The signs and significance levels of the measured changes in the price premia are qualitatively similar as is the measured impact of market structure and Southwest presence. As shown in the lower panel of Table $8 (panel B), the changes in fare premia between competitive to highly concentrated markets are also similar to those found in the estimations above. Southwest direct or potential presence also significantly reduces (and reverses in several cases) the relative premium of the group fares.

In sum, the alternative measures of market structure and alternative functional form broadly support the central findings that the ratio of first class to the lowest fares significantly decreases on monopoly routes, while Southwest direct and potential presence generally compresses the entire fare structure. The results seem not sensitive to a variety of alternative estimations.

V. CONCLUDING REMARKS

This paper has investigated the relationship between competitive conditions and nonlinear pricing in the airline industry. Our unique, ticket level data set enabled us to construct a fare menu, and then examine how the premia for various types of fares is influenced by changes in market concentration and the presence of Southwest and other low cost carriers. The menu consisted of five categories of tickets ranging from first class to restricted, nonrefundable tickets.

The estimation results show a limited relationship between the fare menu and traditional measures of concentration. The highest-quality fares (first class tickets) decrease relative to low-quality fares in highly concentrated (monopoly) routes. This is a puzzling result given a monopolist's market power, which further suggests that the relationship between the fare structure and market concentration is more complex than prior studies would suggest.

In contrast, there is strong evidence that Southwest's presence has a large and important effect on both the level and distribution of fares. In particular, we observe that actual and typically potential competition from Southwest both lowers all fares and compresses the entire fare structure, forcing higher end fares down toward the lowest fares. Competition from other low cost carriers also reduces low end fares, but competition from these carriers appears to be associated with more fare dispersion. Hence Southwest exerts a kind of different type of competitive pressure than other low cost carriers and seems to further compete with legacy carriers for business travelers by offering important time savings.

Finally, we recognize that since our identification strategy is cross-sectional there still may be other unobservable differences across routes correlated with market structure and relative pricing strategies that could impact our results. The analysis considered various differences in routes and did not find important differences, but one cannot rule out the possibility that route level unobservables influence the results. Accordingly, one should interpret the results with some caution given the results of Gerardi and Shapiro (2009) who found that the cross-sectional analysis of Borenstein and Rose (1994) was likely impacted by such an omitted variable bias.

ABBREVIATIONS

BTS: Bureau of Transportation Statistics

CRS: Computer Reservation System

HHI: Herfiudahl-Hirschman Index

doi: 10.1111/ecin.12045

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Table S1. Description of Variables

Table S2. Routes by Market Structure

Table S3. Average Percent Deviations from the Average Fare per Mile by Ticket Type and Legacy Carrier, Percent Differences Calculated at Carrier-Route Level

Table S4. Distribution of Tickets by Ticket Type, Legacy Carrier and Southwest Direct or Potential Presence

Table S5. Route Characteristics by Market Structure and Southwest Presence

Table S6. Log of Fare Per Mile Regressions, Interaction Models (Alternative Specification with Single Dummies for Low Cost Carriers' Presence at Endpoint Airports)

Table S7. Log of Fare Per Mile Regressions, Interaction Models (Measures of Market Structure Derived from DBIB)

Table S8. Predicted Quality Premia of Various Fares to Group 5 by Market Structure and Southwest Presence (Alternative Estimations)

Table S9. Fare Per Mile Regressions, Interaction Models

Figure S1. Flight Frequency and On-Time Performance of Southwest versus Legacy Carriers (Calculations Based on the Routes Where Southwest Directly Competes with Legacy Carriers).

(1.) Refer to the study of Stole (2007) for an extensive survey of models on nonlinear pricing and imperfect competition.

(2.) See also the study of Stavins (2001), who uses marginal implicit prices of ticket restrictions as a proxy for price discrimination and concludes that price discrimination decreases with concentration. Her study, however, only focuses on two ticket restrictions and on a limited number of routes.

(3.) Our analysis is more in line with Busse and Rysman (2005) who examine the relationship between competition and price schedules offered for display advertising in Yellow Pages directories.

(4.) The load factor measures how much of a flight's passenger carrying capacity is used at a particular point in time.

(5.) On this matter, Puller, Sengupta, and Wiggins (2009) find evidence that theories in which ticket characteristics segment customers and facilitate price discrimination may play a major role in airline pricing. Sengupta and Wiggins (2011) also reveal that ticket characteristics explain much of the variation in airline fares.

(6.) Our data also indicate that the distribution of ticket types is generally similar across routes and does not vary with market structure.

(7.) Certainly, there are numerous ticket classes and associated restrictions within flights. We use these five groups to represent the major categories of tickets, and these categories capture the major differences among ticket types and fares.

(8.) These theories argue that airline pricing can be explained in a context of costly capacity, perishable goods, and demand uncertainty.

(9.) We include dummy variables for number of days in advance the ticket was purchased: 0-3 days, 4-6 days, 7-13 days, and 14-21 days.

(10.) Slot-controlled airports during our period of analysis include Washington-National (DCA), New York-Kennedy (JFK), and New York-La Guardia (LGA).

(11.) The tourism index is the share of accommodation earnings to personal income at the destination city of the itinerary.

(12.) We also separately control for potential competition to account for a carrier's potential dominance. Potential competition is measured by the geometric mean of the combined shares of firms with less than a 1% share in the endpoint airports; these firms have a presence at an airport and can expand if circumstances warrant, limiting airport dominance by larger carriers on the route. The inclusion of this regressor, however, does not materially affect our estimation results.

(13.) Following the study of Borenstein and Rose (1994), we do not use instruments for the monopoly and duopoly dummies. We are unaware of valid instruments for these variables.

(14.) The travel agent's data set is incomplete because some of the posted fares are usually deleted after a certain period of time, although not in a systematic way.

(15.) The matching procedure appears to match at a somewhat lower rate at the lower end of the fare distribution, but generally the matched tickets (our working sample) are representative of the census of airline ticket transactions from a major CRS. The sample statistics for the matched observations and all observations in the original transaction data set are also similar for the variables where they can be compared.

(16.) Fares for multileg trips are complex and this additional complexity meant that we were unable to match multileg fares.

(17.) We exclude travel on the Wednesday prior to Thanksgiving through the following Sunday. We also exclude all travel beginning on December 22 through the end of year.

(18.) Routes are divided into three groups when using HHI: less than or equal to 0.5, between 0.5 and 0.8, and greater than 0.8. Similar results hold if one uses the definitions of monopoly, duopoly, and competition by Verlinda (2005).

(19.) A Hausman test also indicates that the corresponding variables are likely correlated with the error term at a 10% significance level.

(20.) To investigate this issue further we sought to replicate his specification with our data by omitting the hub variable and our ticket group variables, which he did not have available. While the coefficient for HHI remains statistically insignificant at conventional levels, the coefficient for market share is positive and highly significant, comparable to Borenstein's findings. As the group variables clearly measure important ticket heterogeneities, the results suggest that one must include them in the evaluation of the relationship between market structure and price.

(21.) There are several reasons why other low cost carriers could have a smaller effect on tares than Southwest, including a lower number of seats offered, less brand recognition, a less extensive network, and others as well.

(22.) The decrease in the Group 1 relative premium in monopoly routes could also reflect a missing variable problem. For example, it is possible that older planes with fewer amenities are assigned to less competitive routes, as that, part of the relative decrease in first class tickets could be because of the lower quality service offered to first class passengers. This possibility further ties with the decrease in absolute Group I fares in monopoly routes outlined in the preliminary analysis. Unfortunately, the lack of more detailed information prevents us to formally account for this potential effect.

(23.) Interestingly, on routes with Southwest direct or potential competition, most legacy carriers also exhibit a much higher share of either Group 3 or Group 2 tickets, relative to routes without Southwest presence. As shown in Table $4, on routes with Southwest direct or potential presence, Group 3 tickets represent 34%, 25%, and 22% of the total tickets in American, United, and Delta, versus 8%, 9%, and 2% on other routes; the share of Group 2 tickets in Northwest, in turn, is 29% on routes with Southwest presence versus 14% on other routes.

(24.) Departure and arrival delays are the difference between the flight scheduled and actual departure and arrival times. Elapsed time is the time computed between gate departure and gate arrival divided by route distance.

(25.) Comparing monopoly versus nonmonopoly routes, the largest differences are found regarding slot controlled airports and proportion of connecting service. Still, even these are modest differences. In the Southwest data there are substantial differences regarding Southwest presence in any form and slot controlled airports--Southwest does not serve these routes. In addition, routes where Southwest offers direct competition are slightly shorter, exhibit a higher tourism index, and have smaller populations. One cannot rule out that such routes might have different elasticities. Note, however, that routes where Southwest is a potential competitor are generally longer, have a lower Tourism index, and populations roughly equal to the sample mean. Our results show that the estimated effect of Southwest presence is comparable for both sets of routes, which would suggest that these differences are not the source of the observed effects.

(26.) By distance, we divided the routes into less than 600 miles, between 600 and 1,200 miles, and more than 1,200 miles; by passengers carried, we divided the routes into less than 200,000 passengers, between 200,000 and 350,000 passengers, and more than 350,000 passengers. The decrease in the relative premium of Group 1 fares on monopoly routes is significant in most subsamples and specifications. Southwest coefficients, particularly those accounting for Southwest direct presence, are also mostly of the same sign as in the main results when statistically significant. The results regarding Southwest potential competition become weaker in certain subsamples (short and long distance routes) and are sometimes reversed.

(27.) The decrease in the premium of Group 1 over Group 5 fares on monopoly routes is significant across all specifications and the coefficients regarding Southwest direct presence are uniformly of the same sign as in the main results. We also only observe one significant sign reversal in the case of Southwest potential competition (for the relative premium of Group 4 fares).

(28.) We follow previous investigators who have used DBIB to calculate concentration (see, e.g., Borenstein 1989; Borenstein and Rose 1994). We use tickets with up to four coupons--one-stop service--and exclude tickets that involve open-jaws and circular trips. Open-jaws involve a gap in the trip, while a circular trip is a trip where the outbound itinerary differs from the return, which indicates more than one possible destination. Using these data, we construct shares, and then define the market structure measures using these shares and the criteria established above.

MANUEL A. HERNANDEZ and STEVEN N. WIGGINS*

* We thank the valuable comments of Li Gan, James Griffin, Justine Hastings, Qihong Liu, Aviv Nevo, Steven Puller, Nicholas Rupp, and seminar participants at the International Industrial Organization Conference, Universidad Autonoma de Nuevo Leon (UANL), Southern Economic Association Annual Meeting, the Allied Social Science Association Annual Meetings, and the PERC Applied Microeconomics Workshop at Texas A&M University. We would also like to thank Anirban Sengupta for help in acquiring and developing the data. Finally, we would like to thank Wesley Wilson and three anonymous referees for their many useful comments. The usual disclaimer applies.

Hernandez: Markets, Trade and Institutions Division, IFPRI, Washington, DC 20006. Phone 202-862-5645, Fax 202467-4439, Email m.a.hernandez@cgiar.org

Wiggins: Department of Economics, Texas A&M University, College Station, TX 77843. Phone 979-845-7383, Fax 979-847-8757, Email swiggins@tamu.edu

TABLE 1
Summary Statistics for Variables in Analysis

                               Mean       SD       Min       Max

Fare (dollars)                   457      464        62      4,806
Fare per mile (cents)           31.3     32.0       3.4      305.9
Dummies for ticket type
Group 1                         0.05     0.22      0.00       1.00
Group 2                         0.07     0.26      0.00       1.00
Group 3                         0.12     0.33      0.00       1.00
Group 4                         0.28     0.45      0.00       1.00
Group 5                         0.47     0.50      0.00       1.00
Market structure
  variables
Market share                    0.57     0.26      0.00       1.00
HHI                             0.56     0.20      0.19       1.00
Monopoly                        0.12     0.33      0.00       1.00
Duopoly                         0.48     0.50      0.00       1.00
Competitive                     0.40     0.49      0.00       1.00
Low cost carriers and
  hubbing
Southwest on route              0.09     0.28      0.00       1.00
Southwest potential entry       0.03     0.18      0.00       1.00
Southwest on adjacent           0.11     0.31      0.00       1.00
  route
Low cost carrier on route       0.34     0.47      0.00       1.00
Low cost carrier potential      0.10     0.31      0.00       1.00
  entry
Low cost carrier on             0.30     0.46      0.00       1.00
  adjacent route
Hub for carrier                 0.83     0.38      0.00       1.00
Hub for carrier at origin       0.50     0.50      0.00       1.00
Ticket and flight controls
Adv0_3                          0.25     0.44      0.00       1.00
Adv4_6                          0.14     0.35      0.00       1.00
Adv7_13                         0.21     0.41      0.00       1.00
Adv14_21                        0.16     0.36      0.00       1.00
Adv22_over                      0.23     0.42      0.00       1.00
One-way                         0.26     0.44      0.00       1.00
Load factor deviation           0.01     0.20     -1.08       1.23
  from mean
Peak time                       0.65     0.48      0.00       1.00
Market controls
Slot-controlled airport         0.21     0.40      0.00       1.00
Distance (miles)               1,020      654       185      2,704
Population (thousands)         7,259    3,655     1,521     15,834
Per capita income             38,693    3,461    31,811     48,150
  (dollars)
Temperature difference          9.61     6.77      0.10      26.70
                                0 01     0.03      0.00       0.13
# observations                                             878,169

Note: For a detailed description of the variables refer to Table
SI in the Supporting Information.

TABLE 2
Absolute Fares Per Mile by Ticket Type and Market Structure

                      Market Structure

            Competitive     Duopoly   Monopoly

          Cents Per Mile

Group 1        96.9          93.9       73.5
Group 2        75.1          69.4       67.6
Group 3        30.6          32.4       43.1
Group 4        26.2          28.0       28.9
Group 5        18.7          19.2       18.3
Total          29.1          32.2       35.2

                               HHI

            HHI [less       0.5 < hhi
          than or equal   [less than or
            to] 0.50      equal to] 0.8    HHI > 0.8   Total

Group 1       96.8             92.3          80.1       92.6
Group 2       73.0             67.0          71.8       71.5
Group 3       32.2             30.6          46.5       33.0
Group 4       26.9             27.0          30.3       27.4
Group 5       19.1             18.3          19.7       18.9
Total         29.0             30.4          41.1       31.3

Notes: Group 1: first class tickets; Group 2: business class
tickets; Group 3: refundable full coach and coach tickets;
Group 4: nonrefundable tickets without travel or stay restrictions;
Group 5: nonrefundable tickets with travel and/or stay restrictions.
Absolute fares are a weighted average of fares by flying distance
for each market structure category and concentration range (HHI).
Market structure categories defined according to Borenstein and
Rose (1994).

TABLE 3
Log of Fare Per Mile Regressions, No Interaction Models

                                         Model 1: HHI

                                      OLS           2SLS

                                     Dependent Variable:
                                     Log of Fare Per Mile

Group 1                            1.611 ***      1.605 ***
                                    (0.039)        (0.037)
Group 2                            1.114 ***      1.111 ***
                                    (0.058)        (0.058)
Group 3                            0.431 ***      0.429 ***
                                    (0.049)        (0.049)
Group 4                            0.302 ***      0.299 ***
                                    (0.027)        (0.026)
Market share                         0.039          0.157
                                    (0.068)        (0.107)
HHI                                  -0.012        -0.094
                                    (0.077)        (0.100)
Monopoly
Duopoly
Southwest present                  -0.341 ***    -0.338 ***
  (Actual competition)              (0.047)        (0.047)
Southwest present at endpoints     -0.226 ***    -0.237 ***
  (Potential competition)           (0.045)        (0.044)
Southwest on adjacent route        -0.230 ***    -0.225 ***
  (Adjacent competition)            (0.051)        (0.050)
LCC present                        -0.166 ***    -0.164 ***
  (Actual competition)              (0.034)        (0.033)
LCC present at endpoints             0.029          0.029
  (Potential competition)           (0.041)        (0.041)
LCC on adjacent route                -0.023        -0.019
  (Adjacent competition)            (0.025)        (0.025)
Hub for carrier                    0.151 ***      0.128 ***
  (At origin or destination)        (0.036)        (0.030)
Hub for carrier at origin           0.037 *        0.036 *
                                    (0.021)        (0.021)
Adv0_3                             0.219 ***      0.219 ***
                                    (0.016)        (0.016)
Adv4_6                             0.199 ***      0.200 ***
                                    (0.014)        (0.013)
Adv7_13                            0.161 ***      0.161 ***
                                    (0.015)        (0.014)
Adv14_21                           0.079 ***      0.079 ***
                                    (0.010)        (0.010)
One-way                            0.166 ***      0.168 ***
                                    (0.012)        (0.013)
Load factor deviation              0.122 ***      0.122 ***
  from mean                         (0.010)        (0.010)
Peak time                          0.025 ***      0.025 ***
                                    (0.006)        (0.006)
Slot-controlled airport            0.134 ***      0.126 ***
                                    (0.029)        (0.029)
Log distance                       -0.709 ***    -0.712 ***
                                    (0.019)        (0.018)
Log population                     -0.132 ***    -0.124 ***
                                    (0.019)        (0.019)
Log per capita income                -0.076        -0.073
                                    (0.182)        (0.183)
Log temperature difference           -0.006        -0.007
                                    (0.017)        (0.017)
Tourism index                      -1.496 **     -1.482 ***
                                    (0.202)        (0.198)
Constant                           9.459 ***      9.394 ***
                                    (1.939)        (1.937)
Underidentification test:
  Kleibergen-Paap rk LM stat.                       10.26
  Chi-square (1) P-value                           (0.001)
Weak identification test:
  Kleibergen-Paap rk                                7.50
  Wald F stat.
# observations                      878.169        878,169
R-squared                            0.814          0.813

                                     Model 2: Structural
                                         Categories

                                     OLS          2SLS

                                     Dependent Variable:
                                     Log of Fare Per Mile

Group 1                           1.616 ***    1.613 ***
                                   (0.039)      (0.037)
Group 2                           1.109 ***    1.106 ***
                                   (0.057)      (0.056)
Group 3                           0.434 ***    0.432 ***
                                   (0.049)      (0.049)
Group 4                           0.303 ***    0.302 ***
                                   (0.027)      (0.027)
Market share                        0.009        0.038
                                   (0.059)      (0.087)
HHI
Monopoly                            0.070        0.048
                                   (0.045)      (0.059)
Duopoly                             -0.022       -0.030
                                   (0.020)      (0.020)
Southwest present                 -0.330 ***   -0.329 ***
  (Actual competition)             (0.048)      (0.047)
Southwest present at endpoints    -0.235 ***   -0.240 ***
  (Potential competition)          (0.041)      (0.040)
Southwest on adjacent route       -0.238 ***   -0.235 ***
  (Adjacent competition)           (0.052)      (0.051)
LCC present                       -0.161 ***   -0.161 ***
  (Actual competition)             (0.034)      (0.034)
LCC present at endpoints            0.024        0.025
  (Potential competition)          (0.039)      (0.039)
LCC on adjacent route               -0.015       -0.013
  (Adjacent competition)           (0.024)      (0.024)
Hub for carrier                   0.156 ***    0.148 ***
  (At origin or destination)       (0.036)      (0.030)
Hub for carrier at origin          0.037 *      0.036 *
                                   (0.021)      (0.021)
Adv0_3                            0.217 ***    0.217 ***
                                   (0.017)      (0.016)
Adv4_6                            0.197 ***    0.198 ***
                                   (0.014)      (0.013)
Adv7_13                           0.159 ***    0.160 ***
                                   (0.014)      (0.014)
Adv14_21                          0.077 ***    0.077 ***
                                   (0.010)      (0.009)
One-way                           0.166 ***    0.167 ***
                                   (0.012)      (0.013)
Load factor deviation             0.123 ***    0.123 ***
  from mean                        (0.010)      (0.010)
Peak time                         0.025 ***    0.025 ***
                                   (0.006)      (0.006)
Slot-controlled airport           0.121 ***    0.118 ***
                                   (0.028)      (0.027)
Log distance                      -0.713 ***   -0.714 ***
                                   (0.018)      (0.018)
Log population                    -0.128 ***   -0.125 ***
                                   (0.018)      (0.018)
Log per capita income               -0.022       -0.023
                                   (0.182)      (0.180)
Log temperature difference          -0.004       -0.005
                                   (0.017)      (0.018)
Tourism index                     -1.440 **    -1.441 ***
                                   (0.199)      (0.197)
Constant                          8.875 ***    8.861 ***
                                   (1.936)      (1.915)
Underidentification test:
  Kleibergen-Paap rk LM stat.                    10.66
  Chi-square (1) P-value                        (0.001)
Weak identification test:
  Kleibergen-Paap rk                             11.55
  Wald F stat.
# observations                     878,169      878,169
R-squared                           0.815        0.814

Notes: White robust standard errors reported in parentheses,
clustered on route. Fare per mile = roundtrip fare (in cents) /
(2 x nonstop origin to destination mileage). All regressions
include carrier fixed effects. Market share and HHI instrumented
using the same instruments as Borenstein (1989) and Borenstein
and Rose (1994). The under-and weak identification tests for
the instruments are the LM and Wald versions of the Kleibergen
and Paap (2006) rk statistic and are heteroskedastic-robust.

* Significant at 10%; ** significant at 5%; *** significant
at 1%.

TABLE 4
Log of Fare Per Mile Regressions, Interaction Models

                                   Model 1: HHI

                                 Base Interactions

                                OLS           2SLS

                                Dependent Variable:
                                Log of Fare Per Mile

Group 1                        1.814 ***     1.835 ***
                               (0.079)       (0.089)
Group 2                        1.049 ***     1.053 ***
                               (0.114)       (0.175)
Group 3                        0.336 *       0.276
                               (0.169)       (0.196)
Group 4                        0.336 ***     0.320 ***
                               (0.062)       (0.061)
Market share                   0.044         0.170 **
                               (0.068)       (0.078)
HHI                            -0.007        -0.102
                               (0.081)       (0.114)
Monopoly
Duopoly
Group 1*HHI                    -0.369 **     -0.418 **
                               (0.161)       (0.175)
Group 2*HHI                    0.090         0.080
                               (0.157)       (0.250)
Group 3*HHI                    0.183         0.295
                               (0.256)       (0.308)
Group 4*HHI                    -0.062        -0.037
                               (0.099)       (0.109)
Group l*Monopoly
Group l*Duopoly
Group 2*Monopoly
Group 2*Duopoly
Group 3*Monopoly

Group 3*Duopoly
Group 4*Monopoly
Group 4*Duopoly
Southwest present              -0.336 ***    -0.332 ***
  (Actual competition)         (0.047)       (0.049)
Southwest present at           -0.232 ***    -0.244 ***
  endpoints
  (Potential competition)      (0.042)       (0.041)
Southwest on adjacent route    -0.225 ***    -0.217 ***
  (Adjacent competition)       (0.052)       (0.050)
LCC present                    -0.167 ***    -0.165 ***
  (Actual competition)         (0.035)       (0.034)
LCC present at endpoints       0.030         0.031
  (Potential competition)      (0.041)       (0.042)
LCC on adjacent route          -0.022        -0.019
  (Adjacent competition)       (0.025)       (0.027)
Hub for carrier                0.151 ***     0.127 ***
  (At origin or destination)   (0.036)       (0.030)
Hub for carrier at origin      0.037 *       0.037 *
                               (0.021)       (0.021)
Group l*SW present
Group 2*SW present
Group 3*SW present
Group 4*SW present
Group 1*SW potential entry
Group 2*SW potential entry
Group 3*SW potential entry
Group 4*SW potential entry
Group 1*SW adjacent route
Group 2*SW adjacent route
Group 3*SW adjacent route
Group 4*SW adjacent route
Group l*LCC present
Group 2*LCC present
Group 3*LCC present
Group 4*LCC present
Group 1*LCC potential entry
Group 2*LCC potential entry
Group 3*LCC potential entry
Group 4*LCC potential entry
Group 1*LCC adjacent route
Group 2*LCC adjacent route
Group 3*LCC adjacent route
Group 4*LCC adjacent route
Group l*Hub
Group 2*Hub
Group 3*Hub
Group 4*Hub
Group l*Hub at origin
Group 2*Hub at origin
Group 3*Hub at origin
Group 4*Hub at origin
Adv0_3                         0.219 ***     0.220 ***
                               (0.016)       (0.016)
Adv4_6                         0.199 ***     0.200 ***
                               (0.014)       (0.013)
Adv7_13                        0.161 ***     0.161 ***
                               (0.014)       (0.014)
Adv14_2l                       0.079 ***     0.079 ***
                               (0.010)       (0.010)
One-way                        0.166 ***     0.168 ***
                               (0.012)       (0.013)
Load factor deviation          0.123 ***     0.123 ***
  from mean                    (0.010)       (0.010)
Peak time                      0.025 ***     0.025 ***
                               (0.006)       (0.006)
Slot-controlled airport        0.134 ***     0.125 ***
                               (0.030)       (0.030)
Log distance                   -0.710 ***    -0.714 ***
                               (0.019)       (0.018)
Log population                 -0.131 ***    -0.120 ***
                               (0.020)       (0.021)
Log per capita income          -0.068        -0.065
                               (0.183)       (0.184)
Log temperature difference     -0.006        -0.008
                               (0.017)       (0.017)
Tourism index                  -1.497 ***    -1.476 ***
                               (0.204)       (0.201)
Constant                       9.360 ***     9.287 ***
                               (1.962)       (1.965)
Underidentification test:
  Kleibergen-Paap                            10.21
    rk LM stat.
  Chi-square (1) P-value                     (0.001)
Weak identification test:
  Kleibergen-Paap                            7.45
  rk Wald F stat.
# observations                 878,169       878.169
R-squared                      0.814         0.814

                                   Model 1: HHI

                                 Full Interactions

                                OLS           2SLS

                                Dependent Variable:
                                Log of Fare Per Mile

Group 1                        1.616 ***     1.625 ***
                               (0.116)       (0.121)
Group 2                        0.837 ***     0.683 ***
                               (0.132)       (0.262)
Group 3                        0.710 ***     0.668 ***
                               (0.182)       (0.225)
Group 4                        0.309 ***     0.284 ***
                               (0.059)       (0.061)
Market share                   0.011         0.122
                               (0.066)       (0.076)
HHI                            0.028         -0.059
                               (0.082)       (0.108)
Monopoly
Duopoly
Group 1*HHI                    -0.330 *      -0.364 **
                               (0.166)       (0.172)
Group 2*HHI                    0.150         0.381
                               (0.166)       (0.310)
Group 3*HHI                    -0.094        -0.020
                               (0.207)       (0.282)
Group 4*HHI                    -0.074        -0.030
                               (0.090)       (0.102)
Group l*Monopoly
Group l*Duopoly
Group 2*Monopoly
Group 2*Duopoly
Group 3*Monopoly
Group 3*Duopoly
Group 4*Monopoly
Group 4*Duopoly
Southwest present              -0.166 ***    -0.166 ***
  (Actual competition)         (0.046)       (0.047)
Southwest present at           -0.147 ***    -0.159 ***
  endpoints
  (Potential competition)      (0.049)       (0.048)
Southwest on adjacent route    -0.169 ***    -0.167 ***
  (Adjacent competition)       (0.040)       (0.040)
LCC present                    -0.149 ***    -0.148 ***
  (Actual competition)         (0.038)       (0.039)
LCC present at endpoints       -0.010        -0.008
  (Potential competition)      (0.053)       (0.053)
LCC on adjacent route          -0.046        -0.042
  (Adjacent competition)       (0.033)       (0.033)
Hub for carrier                0.138 ***     0.118 ***
  (At origin or destination)   (0.044)       (0.043)
Hub for carrier at origin      0.032         0.032
                               (0.021)       (0.020)
Group l*SW present             -0.319 ***    -0.320 ***
                               (0.087)       (0.087)
Group 2*SW present             -0.569 ***    -0.509 ***
                               (0.093)       (0.146)
Group 3*SW present             -0.472 ***    -0.467 ***
                               (0.098)       (0.103)
Group 4*SW present             -0.207 ***    -0.202 ***
                               (0.040)       (0.042)
Group 1*SW potential entry     -0.265 **     -0.256 **
                               (0.122)       (0.120)
Group 2*SW potential entry     -0.395 ***    -0.412 ***
                               (0.096)       (0.091)
Group 3*SW potential entry     -0.323 **     -0.318 ***
                               (0.125)       (0.121)
Group 4*SW potential entry     0.026         0.031
                               (0.061)       (0.059)
Group 1*SW adjacent route      0.225 ***     0.215 ***
                               (0.070)       (0.069)
Group 2*SW adjacent route      0.100         0.141
                               (0.088)       (0.114)
Group 3*SW adjacent route      -0.624 ***    -0.610 ***
                               (0.091)       (0.096)
Group 4*SW adjacent route      0.122 *       0.129 *
                               (0.073)       (0.070)
Group l*LCC present            0.135 **      0.131 **
                               (0.054)       (0.054)
Group 2*LCC present            0.412 ***     0.452 ***
                               (0.096)       (0.113)
Group 3*LCC present            -0.316 ***    -0.315 ***
                               (0.099)       (0.096)
Group 4*LCC present            -0.051        -0.044
                               (0.048)       (0.048)
Group 1*LCC potential entry    0.063         0.070
                               (0.157)       (0.154)
Group 2*LCC potential entry    0.054         0.026
                               (0.102)       (0.099)
Group 3*LCC potential entry    -0.051        -0.050
                               (0.117)       (0.114)
Group 4*LCC potential entry    0.011         0.005
                               (0.068)       (0.070)
Group 1*LCC adjacent route     0.194 ***     0.189 ***
                               (0.055)       (0.054)
Group 2*LCC adjacent route     0.107         0.158
                               (0.070)       (0.103)
Group 3*LCC adjacent route     -0.045        -0.045
                               (0.072)       (0.072)
Group 4*LCC adjacent route     0.046         0.047
                               (0.039)       (0.040)
Group l*Hub                    0.070         0.078
                               (0.096)       (0.096)
Group 2*Hub                    0.203 **      0.168 *
                               (0.098)       (0.098)
Group 3*Hub                    0.104         0.100
                               (0.079)       (0.077)
Group 4*Hub                    0.055         0.049
                               (0.049)       (0.051)
Group l*Hub at origin          0.005         0.004
                               (0.048)       (0.047)
Group 2*Hub at origin          0.004         0.006
                               (0.102)       (0.103)
Group 3*Hub at origin          0.032         0.030
                               (0.064)       (0.063)
Group 4*Hub at origin          0.005         0.005
                               (0.052)       (0.051)
Adv0_3                         0.246 ***     0.246 ***
                               (0.017)       (0.017)
Adv4_6                         0.221 ***     0.221 ***
                               (0.014)       (0.014)
Adv7_13                        0.162 ***     0.161 ***
                               (0.014)       (0.014)
Adv14_2l                       0.082 ***     0.082 ***
                               (0.010)       (0.010)
One-way                        0.144 ***     0.148 ***
                               (0.011)       (0.011)
Load factor deviation          0.128 ***     0.129 ***
  from mean                    (0.010)       (0.010)
Peak time                      0.025 ***     0.025 ***
                               (0.005)       (0.005)
Slot-controlled airport        0.118 ***     0.107 ***
                               (0.029)       (0.029)
Log distance                   -0.702 ***    -0.706 ***
                               (0.020)       (0.019)
Log population                 -0.132 ***    -0.123 ***
                               (0.021)       (0.021)
Log per capita income          -0.029        -0.029
                               (0.170)       (0.170)
Log temperature difference     -0.010        -0.012
                               (0.017)       (0.017)
Tourism index                  -1.586 ***    -1.556 ***
                               (0.224)       (0.224)
Constant                       8.919 ***     8.881 ***
                               (1.794)       (1.786)
Underidentification test:
  Kleibergen-Paap                            10.28
    rk LM stat.
  Chi-square (1) P-value                     (0.001)
Weak identification test:
  Kleibergen-Paap                            7.80
  rk Wald F stat.
# observations                 878,169       878,169
R-squared                      0.829         0.829

                                      Model 2:
                               Structural Categories

                                  Base Interactions

                                 OLS           2SLS

                                Dependent Variable:
                                Log of Fare Per Mile

Group 1                        1.642 ***     1.638 ***
                               (0.041)       (0.042)
Group 2                        1.205 ***     1.203 ***
                               (0.069)       (0.069)
Group 3                        0.400 ***     0.396 ***
                               (0.077)       (0.078)
Group 4                        0.282 ***     0.281 ***
                               (0.026)       (0.026)
Market share                   0.006         0.055
                               (0.055)       (0.087)
HHI
Monopoly                       0.057         0.033
                               (0.044)       (0.057)
Duopoly                        -0.037 *      -0.046 *
                               (0.021)       (0.027)
Group 1*HHI
Group 2*HHI
Group 3*HHI
Group 4*HHI
Group l*Monopoly               -0.417 ***    -0.415 ***
                               (0.095)       (0.094)
Group l*Duopoly                -0.003        -0.002
                               (0.052)       (0.052)
Group 2*Monopoly               -0.039        -0.036
                               (0.101)       (0.101)
Group 2*Duopoly                -0.198 **     -0.202 **
                               (0.084)       (0.082)
Group 3*Monopoly               0.229 *       0.232 *
                               (0.132)       (0.131)
Group 3*Duopoly                0.032         0.035
                               (0.068)       (0.069)
Group 4*Monopoly               -0.052        -0.053
                               (0.069)       (0.069)
Group 4*Duopoly                0.055 *       0.055 *
                               (0.030)       (0.030)
Southwest present              -0.321 ***    -0.320 ***
  (Actual competition)         (0.048)       (0.047)
Southwest present at           -0.237 ***    -0.242 ***
  endpoints
  (Potential competition)      (0.038)       (0.037)
Southwest on adjacent route    -0.233 ***    -0.231 ***
  (Adjacent competition)       (0.053)       (0.052)
LCC present                    -0.162 ***    -0.162 ***
  (Actual competition)         (0.036)       (0.036)
LCC present at endpoints       0.018         0.018
  (Potential competition)      (0.039)       (0.038)
LCC on adjacent route          -0.025        -0.024
  (Adjacent competition)       (0.024)       (0.023)
Hub for carrier                0.157 ***     0.148 ***
  (At origin or destination)   (0.035)       (0.029)
Hub for carrier at origin      0.036 *       0.036 *
                               (0.019)       (0.019)
Group l*SW present
Group 2*SW present
Group 3*SW present
Group 4*SW present
Group 1*SW potential entry
Group 2*SW potential entry
Group 3*SW potential entry
Group 4*SW potential entry
Group 1*SW adjacent route
Group 2*SW adjacent route
Group 3*SW adjacent route
Group 4*SW adjacent route
Group l*LCC present
Group 2*LCC present
Group 3*LCC present
Group 4*LCC present
Group 1*LCC potential entry
Group 2*LCC potential entry
Group 3*LCC potential entry
Group 4*LCC potential entry
Group 1*LCC adjacent route
Group 2*LCC adjacent route
Group 3*LCC adjacent route
Group 4*LCC adjacent route
Group l*Hub
Group 2*Hub
Group 3*Hub
Group 4*Hub
Group l*Hub at origin
Group 2*Hub at origin
Group 3*Hub at origin
Group 4*Hub at origin
Adv0_3                         0.221 ***     0 222 ***
                               (0.017)       (0.017)
Adv4_6                         0.198 ***     0 199 ***
                               (0.014)       (0.013)
Adv7_13                        0.159 ***     0.159 ***
                               (0.014)       (0.014)
Adv14_2l                       0.077 ***     0.077 ***
                               (0.009)       (0.009)
One-way                        0.165 ***     0.166 ***
                               (0.012)       (0.013)
Load factor deviation          0.123 ***     0.123 ***
  from mean                    (0.010)       (0.010)
Peak time                      0.025 ***     0.025 ***
                               (0.006)       (0.006)
Slot-controlled airport        0.115 ***     0.112 ***
                               (0.028)       (0.027)
Log distance                   -0.718 ***    -0.719 ***
                               (0.016)       (0.016)
Log population                 -0 119 ***    -0.116 ***
                               (0.019)       (0.019)
Log per capita income          0.049         0.049
                               (0.176)       (0.173)
Log temperature difference     -0.004        -0.005
                               (0.017)       (0.017)
Tourism index                  -1.396 ***    -1.399 ***
                               (0.200)       (0.199)
Constant                       8.092 ***     8.068 ***
                               (1.881)       (1.860)
Underidentification test:
  Kleibergen-Paap                            10.65
    rk LM stat.
  Chi-square (1) P-value                     (0.001)
Weak identification test:
  Kleibergen-Paap                            12.10
  rk Wald F stat.
# observations                 878,169       878,169
R-squared                      0.817         0.817

                                      Model 2:
                               Structural Categories

                                 Full Interactions

                                OLS           2SLS

                                Dependent Variable:
                                Log of Fare Per Mile

Group 1                        1.488 ***     1.485 ***
                               (0.097)       (0.098)
Group 2                        1.000 ***     0.997 ***
                               (0.092)       (0.093)
Group 3                        0.673 ***     0.668 ***
                               (0.130)       (0.131)
Group 4                        0.260 ***     0.260 ***
                               (0.038)       (0.037)
Market share                   0.032         0.039
                               (0.054)       (0.077)
HHI
Monopoly                       0.082 *       0.047
                               (0.046)       (0.058)
Duopoly                        -0.018        -0.031
                               (0.022)       (0.026)
Group 1*HHI
Group 2*HHI
Group 3*HHI
Group 4*HHI
Group l*Monopoly               -0.346 ***    -0.347 ***
                               (0.104)       (0.103)
Group l*Duopoly                -0.027        -0.026
                               (0.059)       (0.059)
Group 2*Monopoly               0.082         0.090
                               (0.116)       (0.120)
Group 2*Duopoly                -0.116        -0.119 *
                               (0.074)       (0.072)
Group 3*Monopoly               0.133         0.136
                               (0.107)       (0.106)
Group 3*Duopoly                -0.062        -0.057
                               (0.058)       (0.059)
Group 4*Monopoly               -0.070        -0.071
                               (0.061)       (0.061)
Group 4*Duopoly                0.043         0.042
                               (0.031)       (0.030)
Southwest present              -0.153 ***    -0.153 **
  (Actual competition)         (0.048)       (0.047)
Southwest present at           -0.153 ***    -0.161 **
  endpoints
  (Potential competition)      (0.043)       (0.044)
Southwest on adjacent route    -0.176 ***    -0.172 **
  (Adjacent competition)       (0.042)       (0.042)
LCC present                    -0.138 ***    -0.139 **
  (Actual competition)         (0.042)       (0.042)
LCC present at endpoints       -0.007        -0.006
  (Potential competition)      (0.052)       (0.051)
LCC on adjacent route          -0.044        -0.041
  (Adjacent competition)       (0.033)       (0.031)
Hub for carrier                0.143 ***     0.130 ***
  (At origin or destination)   (0.046)       (0.042)
Hub for carrier at origin      0.034         0.033
                               (0.021)       (0.021)
Group l*SW present             -0.332 ***    -0.331 ***
                               (0.092)       (0.091)
Group 2*SW present             -0.572 ***    -0.565 ***
                               (0.089)       (0.088)
Group 3*SW present             -0.460 ***    -0.458 ***
                               (0.097)       (0.096)
Group 4*SW present             -0.209 ***    -0.210 ***
                               (0.040)       (0.040)
Group 1*SW potential entry     -0.261 **     -0.258 **
                               (0.112)       (0.111)
Group 2*SW potential entry     -0.447 ***    -0.444 ***
                               (0.091)       (0.090)
Group 3*SW potential entry     -0.325 ***    -0.314 ***
                               (0.107)       (0.107)
Group 4*SW potential entry     0.053         0.055
                               (0.053)       (0.053)
Group 1*SW adjacent route      0.232 ***     0.228 ***
                               (0.075)       (0.074)
Group 2*SW adjacent route      0.028         0.028
                               (0.093)       (0.092)
Group 3*SW adjacent route      -0.636 ***    -0.632 ***
                               (0.092)       (0.092)
Group 4*SW adjacent route      0.138 *       0.138 **
                               (0.070)       (0.069)
Group l*LCC present            0.106 *       0.101 *
                               (0.060)       (0.060)
Group 2*LCC present            0.397 ***     0.401 ***
                               (0.107)       (0.107)
Group 3*LCC present            -0.305 ***    -0.306 ***
                               (0.098)       (0.097)
Group 4*LCC present            -0.049        -0.048
                               (0.047)       (0.047)
Group 1*LCC potential entry    0.081         0.086
                               (0.156)       (0.154)
Group 2*LCC potential entry    -0.042        -0.042
                               (0.105)       (0.104)
Group 3*LCC potential entry    -0.070        -0.071
                               (0.113)       (0.111)
Group 4*LCC potential entry    0.008         0.006
                               (0.070)       (0.070)
Group 1*LCC adjacent route     0.193 ***     0.191 ***
                               (0.055)       (0.055)
Group 2*LCC adjacent route     0.098         0.102
                               (0.068)       (0.069)
Group 3*LCC adjacent route     -0.037        -0.038
                               (0.069)       (0.068)
Group 4*LCC adjacent route     0.040         0.039
                               (0.039)       (0.038)
Group l*Hub                    0.069         0.071
                               (0.098)       (0.098)
Group 2*Hub                    0.195 **      0.189 **
                               (0.086)       (0.086)
Group 3*Hub                    0.117         0.116
                               (0.076)       (0.076)
Group 4*Hub                    0.050         0.049
                               (0.048)       (0.048)
Group l*Hub at origin          0.001         0.000
                               (0.050)       (0.050)
Group 2*Hub at origin          -0.003        -0.002
                               (0.080)       (0.080)
Group 3*Hub at origin          0.020         0.020
                               (0.062)       (0.062)
Group 4*Hub at origin          0.005         0.005
                               (0.053)       (0.052)
Adv0_3                         0.244 ***     0.244 ***
                               (0.018)       (0.017)
Adv4_6                         0.218 ***     0.218 ***
                               (0.015)       (0.014)
Adv7_13                        0.158 ***     0.159 ***
                               (0.014)       (0.013)
Adv14_2l                       0.080 ***     0.080 ***
                               (0.010)       (0.009)
One-way                        0.145 ***     0.146 ***
                               (0.011)       (0.011)
Load factor deviation          0.128 ***     0.128 ***
  from mean                    (0.010)       (0.010)
Peak time                      0.025 ***     0.025 ***
                               (0.005)       (0.005)
Slot-controlled airport        0.095 ***     0.091 ***
                               (0.027)       (0.026)
Log distance                   -0.711 ***    -0.713 ***
                               (0.018)       (0.018)
Log population                 -0.117 ***    -0.112 ***
                               (0.020)       (0.020)
Log per capita income          0.069         0.070
                               (0.169)       (0.166)
Log temperature difference     -0.009        -0.010
                               (0.017)       (0.017)
Tourism index                  -1.465 ***    -1.467 ***
                               (0.217)       (0.215)
Constant                       7.823 ***     7.783 ***
                               (1.782)       (1.759)
Underidentification test:
  Kleibergen-Paap                            10.69
    rk LM stat.
  Chi-square (1) P-value                     (0.001)
Weak identification test:
  Kleibergen-Paap                            13.21
  rk Wald F stat.
# observations                 878,169       878,169
R-squared                      0.832         0.832

Notes: White robust standard errors reported in parentheses,
clustered on route. Fare per mile = roundtrip fare (in cents) / (2
x nonstop origin to destination mileage). All regressions include
carrier fixed effects. Market share and HHI instrumented using the
same instruments as Borenstein (1989) and Borenstein and Rose
(1994). The under- and weak identification tests for the
instruments are the LM and Wald versions of the Kleibergen and Paap
(2006) rk statistic and are heteroskedastic-robust.

* Significant at 10%; ** significant at 5%; *** significant at 1%.

TABLE 5
Predicted Quality Premia of Various Fares to Group
5 by Market Structure and Southwest Presence

                           Model 1: HHI

             HHI Tenth      HHI Median    HHI Ninetieth
            Percentile     (HHI = 0.51)     Percentile
           (HHI = 0.34)                    (HHI = 0.89)

A. Base interactions

Group 1        444%            406%            332%
Group 2        194%            199%            208%
Group 3         46%            53%             71%
Group 4         36%            35%             33%

B. Southwest presence

Southwest direct or potential competition

Group 1        208%            189%            152%
Group 2         29%            37%             59%
Group 3        -20%            -20%            -20%
Group 4         17%            17%             15%

No Southwest direct or potential competition

Group 1        448%            414%            348%
Group 2        223%            245%            298%
Group 3         76%            76%             74%
Group 4         39%            38%             37%

               Model 2: Structural Categories

           Competitive   Duopoly    Monopoly

A. Base interactions

Group 1       414%         413%       240%
Group 2       233%         172%       221%
Group 3        49%         54%         87%
Group 4        32%         40%         26%

B. Southwest presence

Southwest direct or potential competition

Group 1       194%         187%       108%
Group 2        36%         21%         49%
Group 3       -17%         -22%        -5%
Group 4        17%         22%         9%

No Southwest direct or potential competition

Group 1       431%         417%       275%
Group 2       273%         231%       308%
Group 3        79%         69%        105%
Group 4        37%         43%         28%

Notes: Group 1: first class tickets; Group 2; business class
tickets; Group 3: refundable full coach and coach tickets; Group 4:
nonrefundable tickets without travel or stay restrictions; Group 5:
nonrefundable tickets with travel and/or stay restrictions. Market
structure categories in Model 2 defined according to Borenstein and
Rose (1994).

FIGURE 1
Relative Fares by Ticket Type and Market Structure

Market structure categories

                Group 1      Group 2      Group 3      Group 4
               / Group 5    / Group 5    / Group 5    / Group 5

Competitive       5.88         4.54         2.03         1.43

Duopoly           5.81         4.15         1.99         1.54

Monopoly          4.55         3.94         2.71         1.56

HHI

HHI <= 0.50       5.92         4.31         2.11         1.46

0.5 < HHI         5.77         4.20         1.92         1.53
<=0.8

HHI > 0.8         4.78         3.93         2.68         1.53

Note: Group 1: first class tickets: Group 2: business class
tickets: Group 3: refundable full coach and coach tickets: Group 4:
nonrefundable tickets without travel or stay restrictions: Group 5:
nonrefundable tickets with travel and/or stay restrictions.
Relative fares are a weighted average of relative fares by flying
distance for each market structure category (top figure) and
concentration range (bottom figure). Market structure categories
defined according to Borenstein and Rose (1994).

Note: Table made from line graph.