Domestic airline alliances and consumer welfare

Transcription

1 RAND Journal of Economics Vol. 39, No. 3, Autumn 2008 pp Domestic airline alliances and consumer welfare Olivier Armantier and Oliver Richard This article investigates the consumer welfare consequences of the recent code-share agreement between Continental Airlines and Northwest Airlines. We develop a discrete choice model based on individual flight characteristics. This structural model recognizes that consumers (i) may have heterogeneous preferences for flight attributes, and (ii) may face different prices for the same flight. The empirical methodology also deals with the measurement error problem stemming from the absence of consumer-level data on prices. The estimation results suggest that, whereas the codeshare agreement did not impact consumers significantly on average, it increased the average surplus of connecting passengers but decreased the average surplus of nonstop passengers. Interestingly, the magnitude of our welfare results may be attributed in large part to changes in product characteristics other than prices. 1. Introduction Code-share agreements, whereby an airline can market seats on some of its partners flights, have been a common practice in the airline industry for the past 30 years. Yet, recent alliances among major domestic carriers in the United States represent a significant development in code-share practices. 1 Airline executives have publicly emphasized that their customers are the beneficiaries because these new alliances deliver more choices, more frequencies, and more Federal Reserve Bank of New York, Université de Montréal, CIRANO, CRT, and CIREQ; olivier.armantier@ny.frb.org. U.S. Department of Justice; oliver.richard@usdoj.gov. We are very grateful to Jan Brueckner, Jerome Foncel, Marc Fusaro, Marc Ivaldi, Darin Lee, Soiliou Daw Namoro, Ariel Pakes, Craig Peters, Jean-Francois Richard, Charles Romeo, Jeremy Verlinda, Gregory Werden, Dean Williamson, and Cliff Winston for insightful comments. Armantier would like to thank the Universitat Pompeu Fabra, and the Institut d Analisi Economica, where part of this research was conducted. We also thank seminar participants at the 2004 ESEM in Madrid, 2005 AEA meetings in Philadelphia, 2005 IIOC in Atlanta, Michigan Business School, Université demontréal, University of Maryland, University of Miami, Drexel University, Antitrust Division at the U.S. Department of Justice, Université de Laval, and the University of California at Santa Cruz. All remaining errors are ours. The views expressed in this article are those of the authors and do not represent the views of the U.S. Department of Justice, the Federal Reserve Bank of New York, or the Federal Reserve System. 1 See, for example, Continental Airlines and Northwest Airlines in 1999, US Airways and United Airlines in 2003, and Continental Airlines, Delta Airlines, and Northwest Airlines in Copyright C 2008, RAND. 875

2 876 / THE RAND JOURNAL OF ECONOMICS destinations to the traveling public. 2 Consumer advocates, however, are concerned that these agreements may reduce competition and consumer welfare. Because alliances may be challenged by policymakers if they harm consumers, it is important to evaluate the precise impact of this new form of code-share agreements on consumers. In the present article, we apply a discrete choice model to an original set of data, and we analyze the consumer welfare consequences of the first significant domestic code-share agreement among major U.S. carriers, the 1999 alliance between Continental Airlines (CO) and Northwest Airlines (NW). 3 Code-share agreements have been traditionally implemented to enable an airline to sell tickets in new markets without having to operate any additional aircraft. For instance, major airlines have long-standing regional code-share agreements at their hub airports with commuter carriers that serve smaller markets. Likewise, U.S. airlines faced with restrictions on entry in foreign markets (cabotage laws) have formed international alliances with foreign carriers that allow them to market flights within their partners domestic network. These alliances have been shown to benefit consumers, as they not only allow the partner airlines to market new destinations but they also typically lead to lower prices and higher passenger volumes. 4 These findings, however, may not extend to recent agreements between U.S. carriers, such as CO and NW, as they present distinctive features. In contrast with regional agreements, the CO-NW alliance spans the entire United States and involves major airlines competing across similar networks. In contrast with international alliances, CO and NW face no restrictions on entry in the United States, and they must compete in prices as they do not have antitrust immunity. Although it generated much controversy at policy levels, the CO-NW code-share agreement was implemented in 1999 without being challenged by the U.S. Department of Transportation, or the U.S. Department of Justice. 5 Arguably, this agreement, as well as the other domestic codeshare agreements that followed, remains subject to additional investigation under the antitrust laws, should evidence of significant consumer harm be brought forward. Few studies, however, have examined how the CO-NW agreement affected consumers. 6 Armantier and Richard (2006) provide evidence suggesting that the CO-NW alliance had mixed effects on consumers. In particular, they find that the implementation of the code-share agreement in a market was accompanied by a drop in average prices, but also by an increase in the average price paid by nonstop passengers. Armantier and Richard (2006), however, are unable to draw unambiguous conclusions because their reduced form analysis (i) cannot formally aggregate gains and losses across passengers and markets, and (ii) focuses exclusively on prices and passenger volumes, 2 From John Dasburg, Northwest Airlines president and CEO: Our customers are the beneficiaries because this alliance gives them choice choice in destinations, in schedules, in service options and in rewards. From Gordon Bethume, chairman and CEO of Continental Airlines: Our alliance demonstrates how consumers can win when two companies work together to provide our customers a dramatically larger range of services than either of us could offer on our own. We will deliver more choice, more frequencies, and more destinations to the traveling public. Source: Detroit Metro News, December In addition to their effect on consumers, the new form of domestic code-share agreements initiated by CO-NW raises a number of important and challenging questions. For instance, Armantier and Richard (2006) describe the effect of such an agreement on competition and prices. Ito and Lee (2007) analyze the reasons why airlines enter into such agreements. Finally, Netessine and Shumsky (2005) discuss how revenues are shared between code-share partners. In the present article, we focus exclusively on the effect of these agreements on consumer welfare. 4 See, for example, Brueckner and Whalen (2000), Park and Zhang (2000), as well as Brueckner (2001, 2003) for insightful discussions of international alliances. See Bamberger, Carlton, and Neumann (2004) for valuable insights on the regional code-share agreements between CO and America West, as well as NW and Alaska Airlines, which were implemented in In parallel to the announcement of the code-share agreement, NW acquired a controlling voting interest in CO. Although the terms of the code-share agreement were not challenged, the U.S. Department of Justice sued in October 1998 to challenge NW s equity acquisition, effectively blocking NW from exercising any control while the suit was pending. The matter was settled in November 2000, as NW divested most of its voting interest in CO. 6 See, for example, Ito and Lee (2007) for an analysis of code-sharing and airfares, as well as the General Accounting Office s reports T-RCED entitled Proposed Domestic Airline Alliances Raise Serious Issues and RCED entitled Effects on Consumers from Domestic Airlines Alliances Vary. See also Whalen (1999) and Armantier and Richard (2003) for welfare analyses of hypothetical domestic alliances.

3 ARMANTIER AND RICHARD / 877 which prevents them from taking into consideration additional benefits stemming from (e.g.) the introduction of new flights or the improvements in the attributes of existing flights. To measure adequately the multidimensional implications of the CO-NW code-share agreement on consumer welfare, we propose in the present article a mixed logit discrete choice approach for the decision problem of the airline consumer. There are few comparable discrete choice applications in the airline literature, with the notable exceptions of Peters (2006) and Berry, Carnall, and Spiller (2006). 7 These articles analyze a passenger s decision to purchase a ticket on any one of the flights proposed by an airline on a specific itinerary (e.g., a seat on any one of NW s nonstop flights between JFK, and LAX). Consumers are therefore assumed to value the aggregate characteristics of an airline s flights within an itinerary (e.g., the number of flights in the itinerary), rather than the characteristics of the specific flight on which the passenger actually travels (e.g., the actual price paid, the time of departure, and the duration of travel). As discussed in Armantier and Richard (2006), the CO-NW agreement may affect the number as well as the characteristics of individual flights in a market. Therefore, we need a model of consumer decisions at the flight level if we are to measure properly the various effects of the agreement on consumer welfare. We develop a model of consumer utility in which a consumer decides to purchase a seat on a specific flight based on that flight s attributes. In doing so, we recognize that consumers may have heterogeneous and possibly correlated preferences for flight attributes. Finally, unlike most discrete choice models developed for market-level data, our model accounts for the fact that the price of a flight may differ across consumers (depending, e.g., on the date of purchase). We apply the model to a primary sample consisting of flight schedule and ticket price data for the period that precisely identifies code-share flights. In this application, we encounter a measurement error problem, as the prices of the different flights in a market are not observed perfectly at the consumer level. To address this problem empirically, we acquired an auxiliary sample of airline tickets that provides detailed price, flight, and passenger information (e.g., dates of purchase and travel, flight schedule, and Saturday night stayover). The primary and auxiliary samples are then used in conjunction to estimate jointly the distribution of the measurement error and the discrete choice model. The results suggest that the implementation of the code-share agreement did not impact consumers significantly on average. This finding contrasts with (e.g.) Brueckner and Whalen (2000) and Bamberger, Carlton, and Neuman (2004), who show that international and regional code-share alliances benefit consumers. We also find that, although neutral on average, the CO-NW code-share agreement did not impact all consumers equally. In particular, whereas the alliance increased the average surplus of passengers on connecting flights, the average surplus of nonstop passengers dropped significantly. Finally, our results highlight the importance of taking into consideration factors other than prices when analyzing consumer welfare. Indeed, our analysis reveals that, after the CO-NW code-share in a market, consumers benefit from lower average prices but are harmed by changes in other flight attributes, such as the duration of travel or whether the flight is nonstop and takes off during peak hours. The article is structured as follows. We outline in Section 2 the basics of the CO-NW code-share agreement. The discrete choice model is introduced in Section 3, and we discuss in Section 4 its estimation in the presence of measurement errors in prices. In Section 5, we describe the primary and auxiliary samples. We discuss the estimation results in Section 6, and their economic implications in Section 7. In Section 8, we present the consumer welfare results. We test in Section 9 the robustness of the results to alternative specifications. Finally, we conclude in Section 10 with a discussion of the implications of our analysis for antitrust reviews of airline alliances and mergers. 7 Prior discrete choice analyses that did not adopt the mixed logit approach include in particular Morrison and Winston (1986, 1995), as well as Berry (1990).

4 878 / THE RAND JOURNAL OF ECONOMICS 2. The CO-NW code-share agreement In January 1998, CO and NW announced their intention to form a code-share agreement that included the U.S. market. Under the terms of the agreement, each airline is able to market seats on some of its partner s flights. The code-share flights are then listed twice in schedules, once by each airline with its own flight number and airline code. Moreover, the partners agree to coordinate flight schedules and operations to provide seamless service on code-share flights (e.g., one-stop check-in, automatic baggage transfers). The carrier operating the code-share flight determines seat availability for the marketing partner, but each airline commits to set prices competitively. All sales revenues go to the operating carrier. The marketing partner gets only a booking fee to cover handling costs (as travel agents do). Finally, the airlines agree to implement linkages in their frequent-flyer programs. 8 Executives at CO-NW emphasized that their alliance would benefit consumers by (i) expanding the number of flights offered, (ii) opening new markets to their consumers, and (iii) improving the attributes of existing flights in markets in which they already operated. They claimed that their alliance would promote competition over the United States by creating a fourth network to compete with the existing Big Three airlines in the U.S....Over 150 cities, 2,000 city-pairs, and three million passengers will gain a new airline competitor and new online connections through the alliance. 9 To illustrate these claims, and to understand how the code-share agreement can affect consumers, consider three airports A, B, and C. Assume that CO (respectively, NW), operates flights in market A-B (respectively, B-C), but not in market B-C (respectively, A-B). The alliance enables CO-NW to pair their existing flights, and thereby offer code-share flights in market A-C that connect through airport B. The partners can therefore expand the number of flights they offer in market A-C without having to operate a new aircraft. In particular, if market A-C was not served by either CO or NW before the agreement, then the alliance enables CO-NW to open this market to their consumers. Of course, traveling between A and C was previously possible by purchasing two different tickets, one from CO and one from NW. These so-called interline flights, however, are rare in practice (see Morrison and Winston, 1995), as they typically entail unfavorable features and, in particular, higher prices due to double marginalization. 10 In contrast, CO-NW can propose code-share flights in market A-C at a lower price and with seamless service. Finally, consumers may also benefit from shorter transit and travel times on code-share flights, as CO-NW were allowed to coordinate their flight schedules. The economic evidence available at the time seemed to support the claim that code-share alliances benefit consumers. Morrison and Winston (1995), for instance, provide evidence that customers dislike interline flights, whereas Park (1997) explains how airline alliances might enhance flight options and social welfare. Park and Zhang (1998, 2000), as well as Brueckner and Whalen (2000), then show how international alliances between U.S. and foreign carriers had allowed the alliance airlines to expand flight options and markets served. They also provide evidence of lower prices in transatlantic markets in which these alliances competed. Lastly, Bamberger, Carlton, and Neuman (2004) give evidence that regional alliances in the United 8 These reciprocal linkages allow a customer to use her frequent-flyer miles accumulated with one airline to book awards with the other airline, but combining mileage across programs to redeem awards was not allowed in the CO-NW agreement. Hence, a consumer may find it preferable to keep accumulating points in a single program and, thus, book seats on code-share flights through her preferred airline. 9 Statement by Hershel I. Kamen, from Continental Airlines, to the U.S. Senate, June 4, In contrast with an online flight, an interline flight consists of two independent products, each marketed and operated separately by different airlines. Double marginalization occurs because each airline in an interline flight maximizes the profits from its own product independently of the other airline. See Brueckner and Whalen (2000) as well as Brueckner (2003) for evidence of the double marginalization problem in international code-share agreements. Additional unfavorable features of interline flights often include the need for double booking, multiple check-ins, longer distances between connecting gates, higher probability of lost luggage, and uncertainty regarding the carriers responsibilities.

5 ARMANTIER AND RICHARD / 879 States allowed the partner airlines to expand the number of markets in which these airlines competed, resulting in lower average fares for consumers in those markets. Nevertheless, the CO-NW proposal, given its distinctive scope and its focus on the entire U.S. market, generated much controversy at policy levels, prompting numerous hearings on its competitive implications. Concerns were primarily expressed about the possibility for the agreement to lower the incentives of CO and NW (i) to enter markets in which only one of the partners already operated, (ii) to maintain competing flights in markets in which they jointly operated, and (iii) to compete in prices. In October 1998, the U.S. Congress granted the Department of Transportation (DOT) the authority to delay the implementation of domestic alliances pending a review of their effects. In November 1998, the DOT decided to allow the implementation of the alliance without a formal investigation, after CO and NW consented not to code-share flights in markets between their respective hub airports. The DOT, as well as the U.S. Department of Justice, presumably retained the right, however, to challenge the agreement after data became available, to ensure that the alliance does not harm the public and is not anti-competitive. In Armantier and Richard (2006), we report on some of the changes that followed the January 1999 implementation of the CO-NW code-share agreement. We summarize here the findings most relevant to the present analysis. By 2000, CO and NW code-shared in 26% of their combined markets. They chose to code-share mainly in markets they already served prior to the alliance. More specifically, at least one of CO or NW was present in 1998 in 88% of the code-shared markets. In that regard, the CO-NW alliance differs notably from traditional regional and international agreements, in which the partners essentially code-share flights in markets where none of them would otherwise operate. The alliance also appears to have enabled the partners to exploit the geographical complementary in the location of their hubs. In particular, 64% of NW s code-share passengers connect through CO s southern hub (Houston), whereas 64% of CO s code-share passengers connect through NW s northern hubs (Minneapolis and Detroit). When CO-NW code-shared in a market in 2000, (i) an average of 9% of their passengers traveled with a code-share ticket, (ii) virtually all code-share passengers (96%) traveled on connecting itineraries, and (iii) the number of connecting flights offered in the market increased by 15%, on average, whereas the number of nonstop flights remained essentially unchanged. This increase in connecting flights is mostly attributable to CO-NW (+29% on average), although their competitors also increased their number of connecting flights by 5% on average. Lastly, we found that the alliance had mixed effects on prices. Indeed, after the implementation of the agreement in a market, average fares for connecting flights declined by 5%, whereas average fares for passengers traveling nonstop increased by 11%. These variations in prices seem consistent with the conjecture that CO-NW have used the introduction of code-share connecting flights as a way to price discriminate more effectively between passengers with different willingness to pay for nonstop and connecting flights (see Ito and Lee, 2007 for a similar conjecture). The mixed results in Armantier and Richard (2006) did not allow us to draw any consumer welfare conclusions for the CO-NW alliance. Indeed, the reduced form analysis adopted does not provide the means to compare the relative gains and losses to consumers across markets, and it does not account for additional potential benefits, such as the introduction of new products or the improvement of existing products. 11 In the present article, we propose a discrete choice model of consumer decisions that quantifies the multidimensional welfare implications of the CO-NW code-share agreement. 11 In particular, note that a pre- and post-alliance comparison of flight attributes, such as the duration of a flight or the time spent in transit at an intermediate airport, based on scheduling data publicly available could be misleading. Indeed, such a comparison would identify variations across the products supplied by the airlines, but not necessarily across the products actually selected by the consumers. This drawback, however, does not apply to our discrete choice analysis, because we model the consumers decisions based on the products characteristics.

6 880 / THE RAND JOURNAL OF ECONOMICS 3. A discrete choice model We start by formalizing some of the concepts on which we build our model. Following Berry, Carnall, and Spiller (2006), we define a market as a round-trip travel from an origin airport to a destination airport, with a departure date within a specific quarter. 12 Markets are defined directionally. For instance, a round-trip in a given quarter from Pittsburgh to Miami, and a roundtrip from Miami to Pittsburgh in the same quarter, are two different markets. A product in a market is a ticket for a seat on a sequence of flights offered daily that link the origin to the destination, and the destination to the origin. The product is nonstop if it consists of a single nonstop flight each way. If the product requires at least one transfer at an intermediate airport, then the product is said to be connecting. A product belongs to an airline itinerary, where the airline is the carrier selling the ticket, and the itinerary is the sequence of airports that are part of the round-trip (origin, destination, and intermediate transfer airports, if any). When the airline marketing the product differs from the airline actually operating one of the flights in the product, then the product is a code-share. In contrast, the flights in an interline product are not only operated but also marketed by two different airlines. As explained below, the consumer s choice set, denoted J, is composed of products j = 0,..., J, where j = 0 identifies an outside good representing the decision of the consumer not to purchase any of the J airline products in the market. The outside good is assumed to encompass all means of transportation between the origin and destination airports other than airlines. Following convention, the mean indirect utility of the outside good will be normalized to 0 when we estimate the discrete choice model. Following Berry (1990) and Berry, Carnall, and Spiller (2006), we assume that the market size N is proportional to POP t, the geometric mean of the population in quarter t at the metropolitan areas for the airports in the market (source: U.S. Census data for ). In addition, we specify the proportionality factor to allow for exogenous variations in the market size over time. In other words, we define N = (φ 0 + φ 1 t) POP t, where (φ 0, φ 1 )are parameters to be estimated. To define a manageable choice set J, we assume that a consumer is initially endowed with an exogenous type τ characterizing in particular her time of purchase, dates of travel, class of travel, and airports of origin and destination. For each product, a consumer is then quoted a specific price consistent with her type. 13 A market therefore consists of N heterogeneous consumers who choose among the same set of J + 1 products, but each consumer faces a different vector of prices. In other words, a consumer in our model does not choose her time of purchase, travel dates, class of travel, and market. She only selects one of the J + 1 alternatives based on their characteristics and the prices specifically quoted to her. We recognize that our model imposes some restrictions on the consumers possible choices. In particular, a passenger with a given type (e.g., a business passenger) cannot purchase certain tickets (e.g., a coach or a discount ticket). To devise a less restrictive model, one could assume that the components of τ characterize the product rather than the consumer. A consumer would then select not only her flight but also her dates of travel, airports of origin and destination, class of travel, and time of purchase. However, one would then face a classic dimensionality problem, as the large number of alternatives would make the discrete choice model intractable. Although it may not be fully consistent with the airlines complex pricing practices, we believe that our model is a tractable and reasonable approach to study the demand side of the airline industry. The indirect utility derived by consumer i from product j is given by U i, j = α i P i, j + Y δ j i + Z λ + ξ j j + ε i, j, (1) 12 To facilitate the presentation, we omit in the remainder of this section the subscript referring to the market under consideration. We therefore concentrate on the decision of a consumer in a given market. 13 We therefore implicitly assume that a product is always available to a consumer, albeit not at any price. This assumption is partially supported by the fact that flights were rarely sold out during our sample period (e.g., on average, 71% of seats available on domestic flights in 2000 were actually booked). In addition, overbooking is a common practice in the rare instances in which a flight is sold out.

7 ARMANTIER AND RICHARD / 881 where P i, j is the price of product j quoted to consumer i; (Y j, Z j ) are vectors of product characteristics; ξ j represents the product characteristics that are unobservable to the econometrician (e.g., effect of advertisement, local reputation); (α i, δ i ) are unobservable random and possibly nonindependent coefficients specific to consumer i; λ is a vector of deterministic parameters; and ε i, j is an error term independently and identically distributed (hereafter i.i.d.) from a type-i extreme value distribution, representing the unobserved idiosyncratic preferences of consumer i for product j. Following convention, ε i, j is assumed to be independent of all other random variables. Note that, unlike most discrete choice models developed for market-level data, we allow for P i, j to vary across consumers. Each consumer in the market purchases the good that maximizes her indirect utility. This optimization problem leads to the well-known logistic probability that consumer i purchases product j: exp ( α i P i, j + Y j π i, j (P i ) = δ i + Z λ + ξ ) j j exp ( j J α i P i, j + Y j δ i + Z j λ + ξ ), (2) j where P i is the vector of all prices quoted to consumer i. The market share of product j may then be written as the average purchase probability across all consumers in the market: [ exp ( α i P i, j + Y j s j = E δ i + Z λ + ξ ) ] j j, (3) j J exp ( α i P i, j + Y j δ i + Z j λ + ξ j ) where the expectation operator E[.] is taken over the random variables (α i, δ i, P i ). In our sample, we only observe market shares at the airline-itinerary level, not at the product level. Therefore, we must rewrite accordingly the theoretical market shares at the airline-itinerary level. This transformation, however, requires an additional assumption in order to estimate the model. Indeed, we have to assume that all products j within an airline-itinerary k have the same unobserved characteristics ξ k. This assumption may be considered reasonable, because the characteristics traditionally unobserved in the airline industry (e.g., effect of advertisement, quality of service, or local reputation) usually apply at the airline-itinerary level, rather than at the flight level. 14 The airline-itinerary market shares may then be written S k = [ s j = E exp ( j k α i P i, j + Y δ j i + Z λ + ξ ) ] j k, (4) j k k K j k exp ( α i P i, j + Y j δ i + Z j λ + ξ k ) where j k denotes a product j that belongs to an airline-itinerary k, and K denotes the set of all airline itineraries. 4. Measurement error In the data available from the DOT (Databanks 1A and 1B), which we use to construct our primary sample, we do not observe P i, j, the price quoted for each product to each consumer. Instead, as further explained in Section 5, we can infer an estimate of the average purchased price P k across all products j within the airline-itinerary k. Such a data limitation is not specific to the airline industry. Indeed, the prices quoted for unchosen alternatives are often unavailable to the analyst. In most applications of discrete choice models, the average purchased price is used as a proxy for the unobserved price variable. This approach may be considered reasonable when the prices quoted for a product do not vary significantly across consumers. In our application, however, it is difficult to argue that P k is a legitimate proxy for P i, j. Indeed, (i) ticket prices 14 This definition of the unobserved characteristic is equivalent to that in Berry (1990), Peters (2006), and Berry, Carnall, and Spiller (2006). This does not imply, however, that the discrete choice models in these articles are equivalent to the one presented here. Indeed, consumers in our model select the flight they prefer based on that flight s characteristics, rather than their favorite airline itinerary based on average attributes.

8 882 / THE RAND JOURNAL OF ECONOMICS within the same airline itinerary vary markedly across consumers and products (e.g., prices often increase five-fold depending on the date of purchase), and (ii) unlike the average quoted price P k, the average purchased price P k depends on consumers decisions, and it is therefore endogenous to the discrete choice model. To illustrate the possible adverse consequences of measurement errors in our discrete choice model, suppose first that we observe the average quoted price P k. Let us denote the measurement error by e i, j = P i, j P k. Substituting P k + e i, j for the unobserved price variable P i, j in the indirect utility function (1) yields U i, j = α i P k + Y j δ i + Z j λ + ξ k + ε i, j where ε i, j = α i e i, j + ε i, j. (5) A possible approach to deal with the measurement error may consist of assuming that the compounded error term ε i, j is i.i.d. with a type-i extreme value distribution. When appropriate, this assumption enables one to write the traditional logit choice probabilities as a function of the average quoted price P k. To be valid, however, this approach requires the following two conditions to be satisfied: first, e i, j must be uncorrelated with the product characteristics (Y j, Z j, ξ k ); and second, α i cannot be random and consumer specific. Otherwise, ε i, j is no longer i.i.d., which is a necessary condition to derive the traditional logit choice probabilities. In our application, both conditions are unlikely to be satisfied. Indeed, α i, the consumer marginal utility for the price, is likely to vary randomly depending (e.g.) on the consumer s budget or the purpose of the trip. Likewise, we will see that, within the same airline itinerary, the price of a ticket on a flight with attractive characteristics (e.g., a peak-hour departure) is more likely to exceed its corresponding average airline-itinerary price P k. Because it prevents the analyst from solving the discrete choice model, this form of measurement error cannot be addressed directly with standard techniques such as the instrumental variables method. We now propose an alternative approach. Suppose that the distribution of e i, j, the measurement error for product j, is characterized by a general additively separable model of the form e i, j = P i, j P k = 1 ( A j ) + 2 (B i ) + u i, j, (6) where product j belongs to the airline-itinerary k; A j and B i are vectors of product and consumer characteristics; 1 (.) and 2 (.) are functions; and u i, j is an independently distributed mean zero error term. 15 If this conditional distribution was known, then we could solve the measurement error problem directly by replacing P i, j in the utility function (1) by P k + 1 (A j ) + 2 (B i ) + u i, j.in fact, observe that because the individual-specific effect α i 2 (B i ) enters (1) additively, it cancels out when we derive the choice probabilities (2). As a result, we would only need to replace P i, j by P k + 1 (A j ) + u i, j in (1). The market share in (3) may then be written [ ) ] s j = E k K exp ( { ( ) } α i P k + 1 A j + ui, j + Y δ j i + Z λ + ξ j k j k exp ( { ( α i P k + 1 A j ) + ui, j } + Y j δ i + Z j λ + ξ k ), (7) where E[.] is taken with respect to (α i, δ i ) and the u i, j s. In most applications, the conditional distribution of the measurement error in (6) is unknown. It may nevertheless be estimated in many situations. For instance, suppose that we have access to a random sample of quoted prices P i, j, along with their corresponding product and passenger characteristics (A j, B i ). In this situation, we could first estimate the model in (6). Then, we would replace P i,j in the utility function (1) by P k + 1 (A j ) + u i, j. Finally, we would use the estimated distribution of the u i, j s to integrate them out of (7). 15 The objective here is not to model an inverse demand function for airlines products. In particular, the model in (6) takes the average airline-itinerary price P k as data, not as a variable to be explained. In addition, we make no attempt at modelling the complex yield management practices used by airlines to price their products.

9 ARMANTIER AND RICHARD / 883 Unfortunately, (6) cannot be estimated with our primary sample. Indeed, as explained in Section 5, we only observe a subsample of purchased rather than quoted prices, and these purchased prices P i,j cannot be matched to the corresponding product and passenger characteristics (A j, B i ). In fact, to the best of our knowledge, a random sample of quoted prices P i, j along with (A j, B i ) does not exist for the airline industry. 16 What we were able to acquire is an auxiliary sample of prices for products that have been purchased, along with their corresponding product and passenger characteristics (A j, B i ). Although this auxiliary sample is not sufficient by itself to estimate directly the model in (6), we can combine it with the primary sample to recover the measurement error distribution. Indeed, using Bayes rule, we can express the conditional distribution of purchased prices as a function of the conditional distribution of quoted prices derived from (6) (i.e., P i, j = P k + e i, j ), and the probabilities of purchase derived from the discrete choice model. As shown in the Appendix, we can then jointly estimate the discrete choice model (which depends on the distribution of the measurement error) and the measurement error distribution (which depends on the choice probabilities), and thereby address the measurement error problem. Before we conclude this section, we must recognize that, compared to the traditional discrete choice approach, our method to deal with the measurement error problem requires additional assumptions to be valid. Let us now discuss some of these key assumptions. 17 First, after controlling for all relevant product and consumer attributes (A j, B i ), the distribution of the measurement errors must be invariant whether we consider a market in the auxiliary or in the primary sample. 18 Second, the measurement error distribution in (6) must be correctly specified. In particular, the individual effect 2 (B i ) must be additively separable. Third, u i, j must be independent of (α i, δ i ), the consumer marginal utilities for the products characteristics in the discrete choice model. In other words, after controlling for the individual characteristics B i,the marginal utilities (α i, δ i ) should be irrelevant to explain the price quoted to a consumer. As we shall see in Section 5, this assumption finds some support in our application from the fact that airlines typically only observe the characteristics B i at the time they quote a price to a consumer. Fourth, u i, j must be independent of ξ k, the product unobserved characteristics. Observe, however, that u i, j is by construction mean independent of ξ k in our application, because the unobserved characteristic is defined at the airline-itinerary level. 19 In addition, we shall see in Section 5 that we model the variance of u i, j as a function of P k, which should be correlated with ξ k. As a result, the independence of u i, j and ξ k may be reinterpreted into a weaker condition: u i, j may depend on ξ k, but only through the average price P k. 5. The data The primary sample. The primary sample consists of data on flight schedules and purchased prices obtained, respectively, from the Official Airline Guide (OAG) and the DOT. The OAG data list the time and itinerary for all flights supplied by commercial U.S. airlines. The DOT data are the Origin-Destination Survey Databank 1B. This databank is a 10% random sample of tickets sold by U.S. airlines for travel in a quarter. The only information provided by a ticket is the purchased price and the corresponding airline itinerary. In other words, a purchased 16 A possible alternative would be for the analyst to construct artificially a sample of prices by asking for quotes for different products at different points in time. This approach, however, would not generate a random sample of quoted prices, as it would ignore the consumers actual timing of decisions. In other words, the prices collected would not necessarily reflect the prices quoted to actual consumers at the time they made their purchase decision. 17 The entire set of assumptions under which the model is estimated is specified in the Appendix. 18 Unfortunately, this invariance hypothesis cannot be tested directly because prices in the primary sample cannot be matched to a specific product. A series of less formal tests, conducted at the airline-itinerary level, suggests no significant difference between the measurement error distributions in the primary and auxiliary samples (see Armantier and Richard, 2004). 19 This statement remains valid in the more general case in which the unobserved product characteristic ξ j and the average price P j are both defined at the product level.

10 884 / THE RAND JOURNAL OF ECONOMICS TABLE 1 Descriptive Statistics for the Primary Sample: Data for Mean Standard Minimum Maximum Per market (1,077 observations) Number of passengers a 5, , , , Number of products Mean price ($, in 100s) Number of airline itineraries Number of airlines POP (in 1,000,000s) GMP ($, in 100,000s) b (0.21) 0.34 MILES (in 1,000s) Per airline itinerary (17,764 observations) Number of passengers a , , Number of products PRICE ($, in 100s) Per product (177,454 observations) NONSTOP PEAK TRAVELTIME (minutes, in 100s) TRANSITTIME (minutes, in 100s) HUB INTHUB AIRPORTSHR a Predicted quarterly average from DB1B (i.e., value observed in Databank 1B multiplied by 10). b On a per-capita basis. Calculated as deviation from sample mean across markets. price P i,j cannot be matched with the consumer i who purchased it, nor with the product j it corresponds to. A purchased price P i,j can only be matched with the airline itinerary that includes product j. Nevertheless, Databank 1B can be used to derive the market share and the average purchased price per airline itinerary. In addition, a key feature of Databank 1B, relative to the routinely used Databank 1A, is that it reports each of the operating and marketing carriers, which enables one to identify separately online, code-share, and interline tickets. The primary sample is partitioned into two subsamples, with exactly the same structure but covering two different time periods. The first subsample consists of 160 airport-pairs served by CO and/or NW between 1998 and The data are for the 1st quarters of , and the 3rd quarters of (7 quarters in total). This subsample includes a total of 18 airlines supplying 177,764 products across 1,077 markets (see Table 1 for descriptive statistics). 20 CO-NW code-share in 100 of the 160 airport-pairs, and they do not code-share in the other 60 airport-pairs. The estimation of the discrete choice model and the consumer welfare analysis will rely essentially on this first subsample, as it spans the January 1999 implementation of the CO-NW code-share agreement. The second subsample has been constructed to span the same set of markets as the auxiliary sample. It consists of 63 domestic airport-pairs in the 4th quarter of 2002, and it includes a total 12 airlines supplying 13,743 products. This second subsample will be used exclusively in conjunction with the auxiliary sample to estimate the distribution of the measurement error. Let us now turn to the definition of the variables composing the vectors of product characteristics Y j and Z j in the consumer s indirect utility (1). In doing so, we assume that (i) a code-share flight marketed by the two partners constitutes two distinct products; and (ii) the airline-specific characteristics of a code-share product pertain to the marketing airline. The 20 A description of the criteria used to construct our sample may be found on Armantier s website at sceco.umontreal.ca/liste_personnel/armantier/index.htm. For instance, we use Borenstein and Rose s (1994) guidelines to screen for unusually high and low ticket prices.

11 ARMANTIER AND RICHARD / 885 first assumption is supported by the fact that, under the terms of their agreement, code-share flights are marketed separately by the two partners. In particular, CO and NW have pledged to compete in prices on code-share products. 21 The second assumption is supported by the fact that (i) consumers may be unaware at the time of purchase that the product they are booking is a code-share; and (ii) consumers often do not know the exact obligations and level of commitment of the operating airline. 22 In other words, one may reasonably assume that, when purchasing a ticket, a consumer considers the attributes of the airline with which she is contracting. Finally, note that we considered different partitions of the variables across the Y j and Z j vectors to estimate the model. We present below the partition that provided the best fit on a 25% random sample of our data. Variables with a random parameter. The variables in Y j include the following attributes of product j: PEAK j is a variable indicating whether the departure times for the outbound and inbound flights in a nonstop product are scheduled during peak travel hours (i.e., 5 am to 9 am, or 4pmto8pm). 23 We include this variable as we acknowledge that some passengers, such as business travelers, may have higher valuations for peak-hour products (see Morrison and Winston, 1995). NONSTOP j is a dummy variable equal to 1 if product j is nonstop. This fixed effect measures a consumer s valuation for not having to deal with the hassles of a stop at an intermediate airport, such as a higher probability of lost luggage, delays, or missed connections. AIRPORT SHR j is the share of passenger enplanements at the endpoint airports in the market for the airline marketing product j. Following Borenstein (1989, 1991), we recognize that a consumer s valuation of an airline s product may be affected by the airline s presence at the airports in the market. For instance, dominance at an airport confers an airline greater visibility in flight offerings, counter space, and gate access. HUB j is a dummy variable equal to 1 if the origin airport in the market is a hub for the airline marketing product j. This variable is taken to capture the advantages the hub airline may offer to passengers. Such advantages include a greater array of airport services (e.g., lounges, and greater counter and gate access), more options in case of flight delays or cancellations, and a greater array of options and destinations for frequent-flyer rewards (see Borenstein, 1989, 1991; Evans and Kessides, 1993; Morrison and Winston, 1995). The random parameters (α i, δ i ) associated with (P i, j, Y j ) are assumed to be determined by the system of equations α i = a 0 + b 0 GMP + ω i,0 and δ i,l = a l + b l GMP + ω i,l l {1,...,4}, (8) where the error terms ω i,l (l = 0,..., 4) are jointly normally distributed with mean zero and variance σ 2 l ; and GMP is the annual average per-capita gross metropolitan product across both metropolitan areas in the market. 24 Moreover, we allow a consumer s marginal utility for the price to be correlated with her marginal utility for the peak-hour and nonstop characteristics; that is, we specify that Cov(ω i,0, ω i,1 ) = ρ 1 and Cov(ω i,0, ω i,2 ) = ρ 2, where ω i,0, ω i,1, and ω i,2 are the 21 See Armantier and Richard (2006) for evidence that the alliance airlines indeed appear to compete in prices on code-share products. 22 During our sample period, airlines and travel agents were not required to inform consumers that the flight they were booking was code-shared and might not be operated entirely by the marketing airline. 23 PEAK j = 1 if the departure times for both the outbound and inbound itineraries are scheduled during peak hours; PEAK j = 0.5 if only one of the itineraries is scheduled during peak hours; and PEAK j = 0 otherwise. Empirical tests suggest that the variable PEAK j is not relevant for connecting products. Finally, note that we also estimated the model after decomposing PEAK j in two dummy variables, one for the outbound flight and one for the inbound flight. The estimation results and the economic implications did not vary significantly. 24 The source for the GMP variable is the U.S. Conference of Mayors (usmayors.org). Note also that the variable GMP is defined in deviation from its mean, so that a l (l = 0,..., 4) may be interpreted as an unconditional mean.

12 886 / THE RAND JOURNAL OF ECONOMICS error terms associated with the random parameter of, respectively, P i, j, PEAK j, and NONSTOP j in equation (8). Indeed, some passengers may simultaneously place a lower emphasis on price and a greater emphasis on nonstop travel and peak-hour departures. Variables with a deterministic parameter. The variables in Z j include the following attributes of product j: AIRLINE j is an M 1 vector of dummy variables, where M is the number of different airlines in the primary sample. If airline m markets product j, then the mth component of AIRLINE j is equal to 1, and all other components are equal to 0. This variable accounts for a consumer s valuation of an airline s overall reputation, service, and frequent-flyer programs. TRAVEL TIME j is the scheduled travel time (in minutes) across the outbound and inbound itineraries (i.e., it includes all flight times and airport transit times, if any). Our hypothesis is that, all else equal, passengers prefer shorter flights. INT HUB j is a variable denoting whether the intermediate transfer airports in a connecting product are hub airports for the airline marketing product j. 25 When intermediate transfers occur at a hub airport, a passenger may benefit from more convenient counter and lounge access, and from a greater availability of alternate flights in case of missed or cancelled connections. TRANSIT TIME j is the scheduled airport transit time (in minutes) at intermediate airports (if any). We include this variable because time spent at an intermediate airport may be perceived as an additional inconvenience by passengers. CS CONW PROD j and CS CONW MKT j are two dummy variables identifying the implementation of the CO-NW code-share agreement at the product and market levels. CS CONW PROD j equals 1 when product j is code-shared by CO-NW, and CS CONW MKT j equals 1 for all CO-NW products in markets in which they code-share. These variables should capture any fixed effect associated with code-sharing, such as differences in reputation and/or travel experience. Note that we decided to create two code-share variables, because it is unclear whether consumers in our sample were aware of the implementation of the agreement at either the product or market level. CS REG j is a dummy variable accounting for regional code-share agreements. It is equal to 1 when product j is code-shared by either CO and America West, or NW and Alaska Airlines. This variable may reveal whether the new form of code-share agreements initiated by CO-NW may be distinguished from regional agreements. INTERLINE j is a dummy variable equal to 1 when the product is an interline. Note that unlike the code-share variables, the interline variable is only defined at the product level. Indeed, passengers necessarily know that they are purchasing an interline ticket, as it requires two different bookings. This variable should enable us to test whether, beyond observed differences (e.g., higher average prices for interline tickets), code-share and interline products are perceived in a similar manner by the public. STRIKE NW j is a dummy variable equal to 1 in the third quarter of 1998 for all NW flights in markets where NW competed. This variable should capture the impact of the strike launched by NW employees during that period. YEAR j and SUMMER j are, respectively, a time trend and a seasonal dummy variable accounting for any variations in the valuation of airline travel over time. The auxiliary sample and the measurement error specification. The auxiliary sample consists of ticketing data obtained from the SABRE Group, which offers the world s largest computer reservation system through more than 50,000 travel agents as well as the Internet 25 INT HUB j = 1 if the intermediate airports in the outbound and inbound itineraries are hubs for the airline; INT HUB j = 0.5 if only one of the intermediate airports is a hub; and INT HUB j = 0 otherwise. Once again, decomposing INT HUB j in two dummy variables does not significantly affect the results.