The spatial scope of airline competition

Transcription

1 The spatial scope of airline competition Mark Lijesen a, Christiaan Behrens a,b, a Department of Spatial Economics, VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands b Tinbergen Institute, Gustav Mahlerplein 117, 1082 MS Amsterdam, The Netherlands Abstract Airlines compete on city pair markets. Alternative city (or airport) pairs may act as imperfect substitutes if not too far away. We measure airline s best responses to establish the extent to which airport pairs are substitutes. The use of best responses intuitively relates to the nature of oligopoly games and relies on very general assumptions. The main benefit of this measure is that we do not have to define the relevant market a priori, as its boundaries follow from firms (not) responding to one another. We illustrate our approach by analysing passenger transport competition between the United Kingdom and mainland Europe. Taking into account the spatial scope and airline heterogeneity, we find that the vast majority of city pair markets is less competitive compared with a symmetric Cournot duopoly. We furthermore show how supply by air carriers between the United Kingdom and the European mainland is affected by the high speed rail link between London and Paris/Brussels. Keywords: inter- and intramodal competition, airline competition, imperfect substitutes, relevant market, high speed rail JEL codes: D22, D43, L10, L93, R41 This research is supported by Advanced ERC Grant OPTION # Corresponding author. Fax , phone addresses: m.g.lijesen@vu.nl (Mark Lijesen), c.l.behrens@vu.nl (Christiaan Behrens) Preprint submitted to EARIE conference March 15, 2016

2 1. Introduction To what extent does a flight between Paris and London compete with a flight between Brussels and Manchester? How fierce is the competition between full service airlines, low cost carriers and high speed rail? We develop and empirically test a flexible measure that adequately reflects the competitiveness of airline markets taking into account the presence of imperfect substitutes. Earlier studies in aviation, particularly Brander and Zhang (1990); Oum et al. (1993); Fischer and Kamerschen (2003), apply the conduct parameter method and find that airline conduct resembles Cournot behaviour in duopoly routes in the US. Fageda (2006) finds that competition in Spanish aviation is less competitive, as he also takes monopoly routes into account. None of these studies accounts for the possibility that routes (i.e. airport pairs) may be imperfect substitutes. The main contribution of our analysis is that we determine relevant alternatives empirically, rather than predefining the relevant market. In aviation, the geographical boundaries of the market are often approximated by the catchment areas of airports. Catchment areas are generally defined as circles around an airport (Marcucci and Gatta, 2011). Apart from the geographical aspect, we take into account that airlines of a different signature may have a stronger or weaker response. This information can be helpful in determining the relevant market, which is important for regulators when assessing market power, e.g. in the case of a proposed merger. A special case of the relevant market definition is related to competition between airlines and high speed rail. Existing empirical evidence on rail-air interdependence is route specific, see, e.g., Gonzalez-Savignat (2004), Park and Ha (2006), and Behrens and Pels (2012), or lacks theoretical support, see, e.g., Dobruszkes et al. (2014). Our approach follows the intuition embedded in game theoretical oligopoly models, without having to specify the actors and their behaviour in much detail. Firms best responses to each other s output reflect the extent to which they compete with each other, as well as the intensity of the competition between them. Best responses in equilibrium can be empirically 2

3 determined at the level of pairs of firm-product combinations, allowing to obtain firm-pair specific responses. Firms that do not respond to each other, can be considered as not being in each other s relevant market. For a symmetric Cournot oligopoly, the measure following our approach equals the inverse of the number of firms, which serves as a useful benchmark. To empirically determine this measure, we estimate a hurdle model for airline-route output levels, consisting of a logit model for the decision whether to fly a certain route and a count data model for the number of seats offered. We account for product differentiation by distinguishing between types of airlines, as well as through the distance between airports on both sides of the route. We apply this model to short haul airline markets in Europe. These markets provide several challenges that put our approach to a serious test. Unlike in the US, publicly available data is very limited for European airline markets. Airline markets exhibit both observed and unobserved product differentiation, both in terms of the airports that airlines fly from and in terms of the level of service. Moreover, cost differences are likely to be present and the behaviour of some of the airlines (i.e. the network carriers) is likely to be affected by their network structure. Specifically in our study area, the high speed rail connection between London and mainland Europe should also be taken into account. We find that the vast majority of airline markets in our sample is less competitive than a homogeneous Cournot duopoly, but more competitive than a monopoly. Furthermore, we show that the impact of a change in capacity on the high speed rail link between London and mainland Europe is substantial and has a wider geographical scope in mainland Europe. The remainder of this paper is organized as follows. We develop the theoretical and empirical framework in section 2. The study area, data and estimation strategy are outlined in section 3. We present and discuss our empirical results in section 4. In section 5 we present the computed indicators, followed by a conclusion in section 6. 3

4 2. Theoretical and empirical framework 2.1. Theory The aim of this section is to derive a measure that reflects strategic interaction between firms, using only a small number of widely accepted assumptions. The measure is quite similar to the conduct parameter (see Bresnahan (1989) for an overview), but we avoid the empirical problems brought forward by Corts (1999), by focusing on best responses rather than attempting to estimate an elasticity-adjusted Lerner index. Our measure does not require the researcher to define the relevant market a priori, as it follows naturally from the analysis. Consider an industry where n profit maximizing firms face a downward sloping aggregate demand curve and have non-negative marginal costs. Furthermore, we assume that the level of demand is positive if price equals marginal costs. In a model with these characteristics, the best response function of every firm provides information on the extent to which it competes with other firms. A zero slope reflects no response, which would imply that the firms do not compete with each other. This can be measured at the level of individual (pairs of) firms, and can be aggregated to the level of markets. Since Q = q j + i j q i, we can express the market response in equilibrium as: Q q j = 1 + i j q i q j, (1) where Q denotes total market output, q i the output for product i and the upper bars equilibrium values. 1 Note that we do not define any market boundaries in the equation above. If firms are not in the same market, q i / q j = 0, meaning that only relevant competitors are taken into account. 1 In our empirical application, we define q i as the output of an airline on a specific origin-destination pair. 4

5 For a competitive market as well as a Bertrand oligopoly market, we know: Q/ q j = 0 j, whereas it takes a unity value in the case of a monopoly or a cartel. In a homogeneous symmetric Cournot market, the outcome would be 1/n, as we show in appendix A. This implies that our measure has a very straightforward interpretation: The market is as competitive as a symmetric Cournot market with 1/ Q q j firms would be. The often used Hirschman-Herfindahl index (HHI) has the same feature, albeit that the HHI measures concentration rather than competitive responses Empirical model Our theoretical framework provides an expression for the slope of the best response function in equilibrium. We now translate this theoretical finding into an expression that we can estimate and test empirically. We assume that airlines set their schedules without knowing the new schedule of their competitors and base their decision on the current schedule. Under the common assumption that the slope of a firm s best response function in equilibrium does not depend on that firm s level of output, we write the equilibrium output of any firm-market pair i as the sum of the products of the slopes and quantities of all other firms outputs in the previous period, plus a constant: 2 q i,t = A + j i q i q j q j,t 1, (2) where A reflects a set of control variables including a constant, which we will specify later on. For now, we would like to stress that q i / q j depends (among others) on the level of substitutability of products i and j. We distinguish between two sources that affect this level; the geographical distance between the routes and the signature of the airline. Geographical distance matters because the catchment areas of airports sometimes overlap. 2 Given the assumption that the slope of the best response function does not depend on the level of output, this is equivalent to the sum of the integrals of the best response functions. 5

6 The closer the airports are, the larger this overlap is. We choose not to use predefined multiple airport regions, but use a distance decay function to account for the impact of distance on substitutability. We define: q i q j = B ij e λ d ij, (3) where B ij denotes the strategic interaction parameter of interest, d ij the distance between both origin airports plus the distance between both destination airports of flights i and j, and λ a distance decay parameter. In our set-up, the B ij parameter is the semi-elasticity with respect to the competitor s output if d ij equals zero. Due to summation over alternatives, the distance decay parameter can not be estimated directly, but has to be chosen based on model fit. With respect to the signature of airlines, we are mainly interested in how this signature affects the response to other airlines behaviour. We expect similar firms to respond in a similar manner and hence have a homogeneous B ij parameter. The set M contains all airlines and M = F M f. In other words, each airline belongs exclusively to one of the F groups, f=1 for which we use indices f. This allows us to write the summation of (3) for a homogeneous group f as: i q i = B ij q j i e λ d ij. (4) Using separate subscripts for airlines and origin-destination pairs, we define the relationship between the equilibrium supply q in period t of firm v in group f on route r serving origin 6

7 origin and destination dest, as follows: 3 q f vr,t =B fo ln q f vr,t 1 + B f + B fhsr s s r q vs,t 1 e λ dsr + F B fh h=1 w v w M h s q ws,t 1 e λ dsr q hsr s,t 1 e λ dsr + B GDP GDP r,t + µ v + µ year + µ r + µ dest,t + ε vr,t, (5) with q f vr,t 1 denoting the lag of dependent variable and ε vr,t the airline route specific error term. 4 The second RHS term denotes the group specific reactions to airline v s own lagged output on other routes, whereas the third RHS term captures airline v s reaction to the output of all other competitors. The reaction is group specific based on the group airline v belongs to. The fourth RHS term denotes the group specific reaction of airline v to the output of the high speed rail link. The fifth RHS term controls for economic growth by adding the weigthed average of the GDP of the origin and destination countries. The remaining variables are dummy variables for every airline, year, airport pair and mainland airport-period combination (e.g. CDGJan2009) in the data. The combination of the lag structure and the controls used, adequately deals with possible problems regarding the direction of causality and omitted variables. 3. Empirical Setting 3.1. Aviation between the UK and mainland Europe We test our theoretical framework by examining the aviation industry, in particular, we analyze flights between the United Kingdom on the one hand and Belgium, France, Germany, 3 We assume that the shift in equilibrium value is caused by an exogenous change that has no direct influence on the best response of the firm itself. If the exogenous change does have a direct influence on the best response of the firm at stake, that effect will be captured by the error term and hence not affect the parameter estimates. 4 Not taking the log would result in an so-called explosive feedback model (Blundell et al., 2002). Taking the log implies that if q f vr,t 1 equals 0, qf vr,t also equals 0. In our set up this is no drawback since we exclude these observations in the second step of the hurdle model. 7

8 The Netherlands, and Switzerland on the other hand. 5 Figure 1 provides a map of our study area and the airports in our sample. Civil aviation markets provide a great opportunity to illustrate our framework, as capacity decisions reflect strategic choices in a quantity game. 6 Moreover, product differentiation is a common feature of civil aviation, both in terms of branding and product quality and in terms of access to the nodes in the network. Other factors that might influence the intensity of competition in aviation are cost differences, imperfect information, conjectural variations, airport capacity restrictions and the place that a specific link may have in the broader network of an airline. Furthermore, imperfect substitutes are available, in the form of high speed rail, conventional rail or road transport. 7 Both the UK and mainland Europe have a fairly high density of airports, as well as good infrastructure to access these airports. This allows travelers to choose from several airports on both sides of the trip. Any flight between an airport pair is therefore considered to be an imperfect substitute to a flight between any other airport pair. This raises the question to what (geographical) extent substitution is present. A flight from London Luton to Paris Charles de Gaulle is likely to compete with a flight from London Heathrow to Paris Orly. But to what extent do these flights compete with a flight from Manchester to Amsterdam? Our analysis is able to answer that question empirically by looking at firms best responses. This allows us to endogenously determine the relevant market. Moreover, we can assess the geographical scope of the impact of the High speed rail links to London on air routes. As explained in the previous section, the signature of the airline plays also a role. In the analysis, we distinguish between 4 types of airlines; full service airlines, low cost carriers, regional airlines and other airlines. The classification is provided in Appendix B. One can 5 Airports that do not have landside access to other airports are excluded from the analysis. 6 Airlines set their schedules for 6-months periods. Once the schedule is set, capacity may be altered slightly by applying smaller or larger plains, but most of the adjustments are made through advanced pricing mechanisms. 7 A special feature of our study area is that the UK is not accessible by road or conventional rail. We assume that ferries are too distinct from airlines to take into account. 8

9 Figure 1: Study area imagine that similar airlines respond stronger to each other than to airlines with a different signature. Moreover, our study area holds the international hub airports of Europe s 4 biggest full service airlines, and it is feasible that these airlines base their capacity choices on their intercontinental network; the flights of these airlines are used by passengers flying within our study area, but also by passengers connecting on one of these hub airports Data Table 1 provides the core descriptives of our data set. We obtain monthly aviation service levels for , using OAG Market Analysis (OAG, 2011), for the rail schedules we use the European Rail Timetable (Thomas Cook, 2011). We obtain GDP figures from Eurostat (Eurostat, 2015). The base year for the GDP index is We weight this index over the origin and destination country using absolute GDP levels. As a measure for the proximity of 9

10 Table 1: Descriptives. Variable Route-airline Total Total observations Mean Standard deviation combinations observations (Seats>0) (Seats>0) (Seats>0) Seats FSA (monthly) ,432 6,983 12,015 11,125 Seats LCC, (monthly) ,884 13,255 5,174 4,350 Seats RA, (monthly) 53 4,452 2,470 8,001 8,168 Seats Other, (monthly) 86 7, ,707 1,354 GDP (index) ,992 23, routes, we add up the Eucledian distance between the airports on both sides of the route. 8 Table 1 shows that full service airlines in our sample serve a total of 148 route-airline combinations. With 84 time periods in our data, this leads to 12,432 observations. Many of the observations have zero values however, since not every route-airline combination was served every month. There are 6,983 observations with a positive capacity level for full service airlines and the average number of monthly seats offered was slightly more than 12,000 (i.e. about 70 Boeing s a month). For low cost carriers, the number of observations is much higher, but the mean number of seats per observation is lower, suggesting that -in our study area- low cost carriers fly more routes at a lower output level than full service airlines. The latter is not surprising, as the hubs of the four largest full service airlines are within our study area. The descriptives also reveal that the other airlines are a small and very heterogeneous group. Despite their large number (see Appendix B), they serve a low number of routes and offer a low number of seats compared to the other airlines in our sample Estimation strategy The estimation of (5) uses the monthly number of seats provided by carrier v on route r as the dependent variable. Although the data are monthly, we specify delayed variables by taking the value of that variable one year ago, i.e. in the same month a year ago. The number of potential route-carrier combinations is much bigger than the actual route-carrier 8 For example the distance between routes Amsterdam-Manchester and Rotterdam Liverpool is defined as the Eucleadian distance between Amsterdam and Rotterdam (46 km) plus the distance between Manchester and Liverpool (39 km) and hence amounts to 85 km. The mean distance within our sample is 768 kilometers, with a standard deviation of 333 km. Mean and standard deviation are based on the unweighted average of all elements in the distance matrix, including high speed rail stations. 10

11 combinations where flights are offered. We account for this excessive number of zero-valued observations in our analysis by estimating a hurdle model. In the first step, we estimate a logit model and in the second step a zero truncated negative binomial count model. This two step model relaxes the assumption that the zeros and positive outcomes come from the same data generating process (Cameron and Travedi, 2010). In other words, we see the decision to quit or enter a route as a different process than adjusting the number of seats or monthly flights to changes in the competitive environment. The binomial count model has the set of explanatory variables as defined in (5). The logit model differs by excluding the lagged dependent variable and the route dummies and including a variable indicating whether or not the airline already serves other destinations from the UK-airport on that route. 4. Estimation results and interpretation Table 2 provides the results of the second step of the hurdle model for three different levels of distance decay parameter λ (the first step can be found in Appendix C). The levels of distance decay are chosen such that the effect reduces to 0 at 900 km (model (1), 500 km (2), or 150 km (3)). The difference between the three models seems not to be too large in terms of parameter values and their significance or in terms of model fit, but we do note that some parameters are statistically significant in model (2) and (3) but not in model (1). Within-group responses for full service airlines, low cost carriers and regional airlines are significant and negative and their absolute values are larger than those for between group-responses. Responses regarding other airlines are generally not significant, which is caused by the highly heterogeneous nature of this group. Judging by the lack of statistical significance, full service airlines do not seem to react to the actions of regional airlines, whereas the latter do not respond to the output of low cost carriers. The parameter for the low cost response to full service airlines is significant only in models (2) and (3). 11

12 Table 2: Zero truncated negative binomial model, seats (1) (2) (3) λ = λ = 0.01 λ = 0.05 B FSA (0.0755) (0.152) (0.761) B FSA,FSA (0.0775) (0.132) (0.195) B FSA,LCC (0.0447) (0.0868) (0.176) B FSA,RA (0.134) (0.196) (0.223) B FSA,Other (0.357) (0.643) (4.385) B LCC (0.105) (0.225) (1.928) B LCC,FSA (0.0691) (0.138) (0.313) B LCC,LCC (0.0592) (0.135) (0.438) B LCC,RA (0.140) (0.216) (0.412) B LCC,Other (0.415) (0.797) (1.936) B RA (0.368) (0.561) (2.215) B RA,FSA (0.0952) (0.132) (0.221) B RA,LCC (0.107) (0.261) (1.034) B RA,RA (0.250) (0.393) (0.836) B RA,Other (1.024) (2.151) (9.019) B Other (46.50) (86.46) (2896.7) B Other,FSA (0.537) (1.261) (5.892) B Other,LCC (0.305) (1.047) (7.033) B Other,RA (1.099) (1.923) (1.319) B Other,Other (3.185) (8.850) (8704.9) B FSA,HSR (0.0442) (0.0662) (0.298) B LCC,HSR (0.0478) (0.0797) (1.414) B RA,HSR (0.0563) (0.0849) (0.353) B Other,HSR (0.518) (1.875) (59.33) B FSA,Lag(Seats) (0.0319) (0.0342) (0.0373) B LCC,Lag(Seats) (0.0164) (0.0164) (0.0167) B RA,Lag(Seats) (0.0381) (0.0366) (0.0392) B Other,Lag(Seats) (0.166) (0.139) (0.107) GDP ( ) ( ) ( ) Dispersion parameter (0.0285) (0.0285) (0.0285) Observations ll Standard errors in parentheses p < 0.05, p < 0.01, p < The estimated coefficients represent the semi-elasticities when the summed distance between the two origin and two destination airports equals 0. 9 To facilitate interpretation, we 9 To scale the parameter estimates, all explanatory variables -except for the group specific reactions to 12

13 take the Manchester-Frankfurt market as an example and assume that the full service airline, Lufthansa, marginally adjusts its seats, e.g. adds 1 seat a month. The low cost carrier in this market, Flybe, supplies about 4,500 seats a month. Hence, in model (2) in table 2, the coefficient B LCC,F SA = implies a decrease of about ( 0.457/10, 000) 4, seats a month by Flybe. This effect would be smaller when distance between the OD pairs increases. Using the estimated results, we can calculate best responses at the route-carrier level, e.g. how does KLM on Manchester-Amsterdam react to a capacity increase of Lufthansa on Manchester-Frankfurt? These values represent the slope of the equilibrium output, q i / q j, and are expected to vary between 0 and 1/n. For some route-carrier pairs, the best response was positive rather than negative however, and all these cases relate to flights leaving from London. We note that distance is not a perfect indicator for access and egress time, especially in the case of London, where five airports are located in and around a dense metropolitan area. We stress that the relevant market concept is more than a geographical concept; it also depends on the signature of the airlines involved, as well as on their relative size. This can be demonstrated by figures 2 and 3, representing a 1-seat output increase on the Manchester Frankfurt route by Lufthansa and Flybe respectively. It is immediately clear from figures 2 and 3 that the relevant market for the full service airline (Lufthansa) is different from that of the low cost carrier (Flybe), despite the fact that they serve the exact same route. So far, we have been silent about the impact of high speed rail. Looking at the high speed rail connection between the UK and mainland Europe, we can determine the relevant market for both links to Paris and Brussels, respectively in a similiar way that we did for airlines. Figure 4 indicates the strength of the intermodal competition between air and own output on the same route and the GDP- are divided by 10,

14 Q q = and market response = j Germanwings: Flybe: MAN KLM: BHX AMS LHR LCY BA: DUS CGN BA: Crossair: Flybe: BA: FRA ZRH Figure 2: Best respones to Lufthansa s capacity on MAN-FRA ( 0.005), λ = high speed rail by showing the impact of adding one seat to the output of the high speed rail between London and Brussels. Although the effects on individual route-carrier combinations are fairly small, the impact of high speed rail on aviation is substantial, especially if one keeps in mind that the capacity of a train is considerably larger than that of an airplane. We also note that the geographical impact in the UK is limited to London, whereas it spreads out considerably on the European mainland. 5. Market responses on short haul airline markets in western Europe From the best responses presented in the previous section, we can derive market responses as defined in (1). We choose to determine the market response at the city pair level rather than the airport level, as we feel that this better reflects the choices made by consumers. 14

15 Q q = and market response = j MAN BHX LH: LHR LCY LH: LH: DUS LH: LH: BA: FRA Figure 3: Best responses to Flybe s capacity on MAN-FRA ( 0.005), λ = Q q j = KLM: BA: BMI: LHR LCY STN VLM: U2: VLM: RTM AMS LGW FR: EIN BA: DUS BMI: BRU SNB: BA: AF: BA: CDG Figure 4: Best responses to HSR capacity on London-Brussels ( 0.005), λ =

16 Table 3: Competitiveness ranking by city-pair level, for different distant decay values. Rank λ = λ = 0.01 λ = London-Antwerp [-0.347] London-Amsterdam [-0.126] London-Paris [0.175] 2 London-Frankfurt [-0.101] London-Antwerp [0.112] London-Frankfurt [0.287] 3 London-Dusseldorf [-0.081] London-Frankfurt [0.116] London-Amsterdam [0.288] 4 Manchester-Brussels [-0.044] London-Dusseldorf [0.142] London-Grenoble-Isere [0.388] 5 London-Amsterdam [-0.025] London-Paris [0.216] London-Munich [0.539] 6 London-Paris [0.086] London-Rotterdam [0.242] London-Dusseldorf [0.697] 7 London-Cologne [0.133] London-Brussels [0.281] London-Hamburg [0.737] 8 Manchester-Antwerp [0.154] London-Cologne[0.382] London-Geneva [0.751] 9 London-Stuttgart [0.189] East Midlands-Brussels[0.427] Liverpool-Amsterdam [0.765] 10 East Midlands-Brussels [0.199] Birmingham-Amsterdam [0.437] Manchester-Paris [0.799] Edinburgh-Toulouse [0.965] Edinburgh-Toulouse [0.997] Liverpool-Nimes [0.999] 214 Edinburgh-Nice [0.967] Exeter-Rennes [0.997] Bristol-Marseille [0.999] 215 Glasgow-La Rochelle [0.969] Manchester-Brest [0.999] London-Limoges [0.999] This choice is not fundamental, it merely determines the level at which best responses are weighted. For the case of MAN-FRA, the market response for the city pair is a weighted average of the market responses to an output increase by Lufthansa at that city pair and the market responses to an output increase by Flybe at that city pair and equals Despite the fact that the route between the cities is served by two carriers and the availability of a fair number of imperfect substitutes, the level of competitiveness of this market is low. Table 3 presents the top 10 and bottom 3 most competitive city pairs in our sample for different levels of the distance decay parameter λ. Several city pairs in the table have negative market responses, especially for the lowest value of λ. The values for London-originating flights might be downward biased as discussed before. The ranking of city pairs does however make sense, as the high ranking city pairs indeed have larger numbers of carriers serving them and have centrally located mainland airports, implying the presence of relatively close substitutes. On the lower end of the ranking we see city pairs that have at least one relatively isolated airport, so that alternatives are located further apart. Figure 5 presents the market responses, ranked by their magnitude for different levels of the distance decay parameter λ. By means of comparison, we also plot the HHI as it would commonly be calculated, i.e. based on the number of seats by airline at the city pair level. Recall that both the market response and the HHI can be interpreted as the inverse of the number of symmetric Cournot firms that would yield an equally competitive market. 16

17 market response / HHI λ = λ = 0.01 λ = 0.05 HHI Rank Figure 5: market response versus HHI on city-pair level, ranked by magnitude. This implies that, for λ = 0.01, about 90 percent of the markets, representing 33.7 percent of all output, in our sample is less competitive than a symmetric Cournot duopoly would be. Note that the HHI suggests that about two-thirds of the city pairs are monopoly markets, whereas for the market responses that we measured, this depends strongly on how strong the distance decay is. For the high level of distance decay, adjacent markets hardly play a role and the market response rapidly approaches unity, even earlier than the HHI. For λ 0.01, the market response is well below unity for most markets that we would consider monopoly markets if looked at in isolation, suggesting that they are subject to some competition from imperfect substitutes. Table 4 provides the correlation between the market responses for different levels of distance decays and the HHI. Despite the similarity in interpretation, the correlation between HHI and market responses is not impressive. Given that the market responses are based on less restrictive assumptions, this suggests that the HHI provides an inadequate approximation of competition at the city pair level and could hence lead to incorrect conclusions if used for policy advice. The correlations between the market responses with different levels of distance decay are higher, but still reveal that the chosen level of distance decay influences 17

18 Table 4: Correlation between competition measures. λ = λ = 0.01 λ = 0.05 HHI λ = λ = λ = HHI the outcomes and should hence be treated with some care. 6. Conclusion We measure the intensity of competition between product pairs by the best responses in equilibrium in short haul airline markets in Europe. Using best responses to measure the intensity of competition intuitively relates to the nature of oligopoly games and requires just a few assumptions, all of which are widely accepted and used. This implies that the resulting measure is very general and likely to be applicable in many markets. Moreover, and quite uniquely, our indicator does not require any market definition a priori, as the boundaries of the relevant market can be derived from the disaggregated inputs to the indicator. This has the added advantage that our analysis may be used to determine the relevant market, e.g. in the case of merger control. We empirically derive best responses in equilibrium from data of airlines offering direct flights between the UK and the mainland Europe. We show how the relevant market for any specific connection can be determined, based on the estimated best responses of the competitors of the airline offering the connection. We show how both the distance between alternative airports and the signature of the airline affect those best responses. In the case of the high speed rail, airline responses to the high speed rail also provide information on the modal substitution potential of high speed rail. Finally, we calculate and present the market response on the city pair level. The results suggest that the vast majority of the city pair markets is less competitive than a symmetric Cournot duopoly. Moreover, comparing the market response to the HHI suggests that the latter does not correctly measure the level of 18

19 competition in the markets under consideration. The development of our new indicator opens up a wide variety of opportunities for further research. First of all, our conjecture that the indicator can be used in many market types, calls for a more in-depth investigation. These investigations may be aimed at adopting the indicator in the case of e.g. contestable markets, monopolistic competition, markets with information asymmetry, markets with uncertainty and so on. 19

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22 Appendix A. Analytical treatment for Cournot markets Appendix A.1. The Homogenous Cournot case with n players In this section, we analytically derive q i / q j for the case of a n-firm Cournot market with homogeneous products. All firms face individual marginal costs c i and the same inverse demand function: p = α β i q i. (A.1) The first order conditions for firm i is now: α β j i q j 2q i c i = 0. (A.2) solving the system of n equations with n unknowns yields: q i = α nc i + c j j i. (A.3) n + 1 The equilibrium outcome expressed in A.3 obviously does not contain the putputs of the other firms. We can use any variable that directly affects the best response of firm j and will hence both affect q i and q j to analytically derive q i / q j in equilibrium. Using marginal costs of firm j, we get: q i q j = q i c j / q j c j. (A.4) And hence: q i = 1 q j n + 1 / n n + 1 = 1 n. (A.5) 22

23 Appendix A.2. Exploration of the properties of the heterogeneous Cournot case In this section, we analytically derive q i / q j for the case of a heterogenous 3-firm Cournot market. In this example, imperfect substitution is causing deviations from the standard Cournot case, other causes can be treated in a similar way. Consider a 3-firm oligopoly, where firms i, j and k produce their own variant of a good. The following inverse demand function for good i is assumed to hold: p i = α i β i q i γ ij q j γ ik q k. (A.6) with parameters α i and β i strictly positive and γ ij = γ ji. For γ ij > 0, goods i and j are substitutes. The parameters provide information on the degree of substitutability. If α i = α j and β i = β j = γ ij, goods i and j are perfect substitutes. For β i β j > γij 2 > 0, goods are imperfect substitutes. Firms maximize profits by setting quantities and have linear cost functions. From the first order condition of firm i s profit maximization problem, we can derive firm i s best response function in output: q i = α i c i 2β i γ ij 2β i q j γ ik 2β i q k. (A.7) Deriving similar best responses for all other firms and solving the system of 3 equations and 3 unknowns, we find equilibrium outputs for al firms. 10 We can now derive the slope of the best response in equilibrium: q i = 2β kγ ij γ ik γ jk. (A.8) q j 4β i β k γik 2 The slope of the best response of firm in equilibrium, as represented by (A.8) coincides with the same term on the right hand side in (1) and quantifies the intensity of competition 10 Full expressions are available upon request. 23

24 between firms i and j. The case of full symmetry (i.e. all β s and γ s equal) yields the outcome of 1/3, and a market response of 1/3, which is consistent with the homogenous case in the previous section. 24

25 Appendix B. Classification of carriers Table B.1: Carriers classification Full Service Airlines (FSA) Low Cost Carriers (LCC) Regional Airlines (RA) Other Air France Air Berlin Aer Lingus Aer Annan British Airways BMI baby BMI British Midland Air Europa KLM-Royal Dutch Airlines Britannia Airways Brussels Airlines Air Exel Netherlands Lufthansa German Airlines EasyJet Swiss Internation Air Lines Air Scotland EasyJet Switzerland VLM Airlines Air Turquoise Fybe British European Air Wales Flyglobespan Astraeus Germanwings Baboo Hapag-Lloyd Express Cirrus Airlines Jet2.com Condor Flugdienst Ryanair Darwin Airline Thomsonfly DBA Luftfahrtgesellschaft mbh Transavia Airlines Duo Airways Ltd TUIfly Eastern Airways EUjet European Air Express First Choice Airways Hamburg International Helvetic Airways Mytravel Airways OLT Ostfriesische Lufttransport Palmair ScotAirways SkySouth Thomas Cook Airlines Titan Airways V Bird Vladivostock Air 25

26 Appendix C. Result of logit estimation Table C.1: Logit model, seats (1) (2) (3) λ = λ = 0.01 λ = 0.05 B FSA (0.173) (0.265) (1.310) B FSA,FSA (0.152) (0.189) (0.261) B FSA,LCC (0.178) (0.296) (0.660) B FSA,RA (0.312) (0.310) (0.467) B FSA,Other (2.252) (3.899) (8.144) B LCC (0.268) (0.543) (4.764) B LCC,FSA (0.149) (0.223) (0.428) B LCC,LCC (0.153) (0.284) (1.004) B LCC,RA (0.376) (0.495) (1.761) B LCC,Other (1.934) (3.801) (6.755) B RA (0.719) (0.980) (6.543) B RA,FSA (0.218) (0.323) (0.258) B RA,LCC (0.303) (0.625) (2.696) B RA,RA (0.698) (0.993) (1.964) B RA,Other (3.414) (5.305) (17.41) B Other (36.27) (75.64) (581.5) B Other,FSA (0.664) (1.000) (2.953) B Other,LCC (0.512) (1.018) (2.489) B Other,RA (1.720) (2.879) (7.998) B Other,Other (6.251) (11.94) (27.67) B FSA,HSR (0.0499) (0.0575) (0.219) B LCC,HSR (0.0640) (0.0981) (1.030) B RA,HSR (0.0966) (0.135) (0.474) B Other,HSR (0.489) (0.919) (81.93) GDP ( ) ( ) ( ) Already serving UK airport (0.0326) (0.0324) (0.0324) Observations AIC ll Standard errors in parentheses p < 0.05, p < 0.01, p <