Domestic Airline Alliances and Consumer Welfare Olivier Armantier and Oliver Richardy February 2008

Abstract

This paper 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 ‡ight characteristics. This structural model recognizes that consumers i) may have heterogeneous preferences for ‡ight attributes, and ii) may face di¤erent prices for the same ‡ight. 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, while the code-share agreement did not impact consumers signi…cantly on average, it increased the average surplus of connecting passengers, but it decreased the average surplus of nonstop passengers. Interestingly, the magnitude of our welfare results may be attributed in large part to changes in products characteristics other than prices. Keywords: Discrete Choice; Consumer Welfare; Structural Estimation; Airline Alliances. JEL Classi…cations: D12, D60, C51, C15, L93.

Federal Reserve Bank of New York, Université de Montréal, CIRANO, CRT, and CIREQ. E-mail: [email protected]. y Assistant Chief, Economic Litigation Section, Economic Analysis Group, Antitrust Division, US Department of Justice, Washington, DC 20530. E-mail: [email protected]. 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 Cli¤ Winston for insightful comments. Olivier 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 de Montréal, University of Maryland, University of Miami, Drexel University, Antitrust Division at the US Department of Justice, Université de Laval, and the University of California at Santa Cruz. All remaining errors are ours. The views expressed in this paper 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.

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1. Introduction Code-share agreements, whereby an airline can market seats on some of its partners’ ‡ights, have been a common practice in the airline industry for the past thirty years. Yet, recent alliances among major domestic carriers in the U.S. represent a signi…cant development in code-share practices.1 Airline executives have publicly emphasized that their “customers are the bene…ciaries”because these new alliances “deliver more choices, more frequencies, and more destinations to the traveling public.”2 Consumer advocates, however, are concerned that these agreements may reduce competition and consumer welfare. Since alliances may be challenged by policy makers 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 paper, we apply a discrete choice model to an original set of data, and we analyze the consumer welfare consequences of the …rst signi…cant 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 ‡ights within their partners’ domestic network. These alliances have been shown to bene…t 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 …ndings, however, may not extend to 1

See e.g. Continental Airlines and Northwest Airlines in 1999, US Airways and United Airlines in 2003, and Continental Airlines, Delta Airlines, and Northwest Airlines in 2003. 2 From John Dasburg, Northwest Airlines president and CEO: “Our customers are the bene…ciaries 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 o¤er on our own. We will deliver more choice, more frequencies, and more destinations to the traveling public.” Source: Detroit Metro News, 12/1998. 3 In addition to their e¤ect 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 e¤ect 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 paper, we focus exclusively on the e¤ect of these agreements on consumer welfare. 4 See e.g. 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 1994-1995.

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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 U.S. and involves major airlines competing across similar networks. In contrast with international alliances, CO and NW face no restrictions on entry in the U.S., 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 code-share agreements that followed, remains subject to additional investigation under the antitrust laws, should evidence of signi…cant consumer harm be brought forward. Few studies, however, have examined how the CO-NW agreement a¤ected consumers.6 Armantier and Richard (2006) provide evidence suggesting that the CO-NW alliance had mixed e¤ects on consumers. In particular, they …nd 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, which prevents them from taking into consideration additional bene…ts stemming from (e.g.) the introduction of new ‡ights or the improvements in the attributes of existing ‡ights. To measure adequately the multidimensional implications of the CO-NW code-share agreement on consumer welfare, we propose in the present paper 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 papers analyze a passenger’s decision to purchase a ticket on any one of the ‡ights proposed by an airline on a speci…c itinerary (e.g. a seat on any one of NW’s nonstop ‡ights between JFK and LAX). Consumers are therefore assumed to value the aggregate characteristics of 5

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, e¤ectively 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 e.g., Ito and Lee (2007) for an analysis of code-sharing and airfares, as well as the General Accounting O¢ ce’s reports T-RCED-98-215 entitled “Proposed Domestic Airline Alliances Raise Serious Issues”, and RCED-99-37 entitled “E¤ects on Consumers From Domestic Airlines Alliances Vary”. See also Whalen (1999), and Armantier and Richard (2003) for welfare analyses of hypothetical domestic alliances. 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).

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an airline’s ‡ights within an itinerary (e.g. the number of ‡ights in the itinerary), rather than the characteristics of the speci…c ‡ight on which the passenger actually travels (e.g. the actual price paid, the time of departure, the duration of travel). As discussed in Armantier and Richard (2006), the CO-NW agreement may a¤ect the number as well as the characteristics of individual ‡ights in a market. Therefore, we need a model of consumer decisions at the ‡ight level if we are to measure properly the various e¤ects of the agreement on consumer welfare. We develop a model of consumer utility in which a consumer decides to purchase a seat on a speci…c ‡ight based on that ‡ight’s attributes. In doing so, we recognize that consumers may have heterogeneous and possibly correlated preferences for ‡ight attributes. Finally, unlike most discrete choice models developed for market level data, our model accounts for the fact that the price of a ‡ight may di¤er across consumers (depending, e.g., on the date of purchase). We apply the model to a primary sample consisting of ‡ight schedule and ticket price data for the period 1998 to 2001 that precisely identi…es code-share ‡ights. In this application, we encounter a measurement error problem as the prices of the di¤erent ‡ights 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, ‡ight, and passenger information (e.g. dates of purchase and travel, ‡ight schedule, Saturday night stay-over). 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 signi…cantly on average. This …nding contrasts with (e.g.) Brueckner and Whalen (2000), and Bamberger et al. (2004), who show that international and regional code-share alliances bene…t consumers. We also …nd that, although neutral on average, the CO-NW code-share agreement did not impact all consumers equally. In particular, while the alliance increased the average surplus of passengers on connecting ‡ights, the average surplus of nonstop passengers dropped signi…cantly. Finally, our results highlight the importance of taking into consideration factors other than prices when analyzing consumer welfare. Indeed our analysis reveals that, after CO-NW codeshare in a market, consumers bene…t from lower average prices, but they are harmed by changes in other ‡ight attributes, such as the duration of travel, or whether the ‡ight is nonstop and takes o¤ during peak-hours. The paper 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 4

to alternative speci…cations. Finally, we conclude in Section 10 with a discussion of the implications of our analysis for antitrust reviews of airline alliances and mergers.

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 ‡ights. The code-share ‡ights are then listed twice in schedules, once by each airline with its own ‡ight number and airline code. Moreover, the partners agree to coordinate ‡ight schedules and operations to provide seamless service on code-share ‡ights (e.g. one-stop check-in, automatic baggage transfers). The carrier operating the code-share ‡ight 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-‡yer programs.8 Executives at CO-NW emphasized that their alliance would bene…t consumers by i) expanding the number of ‡ights o¤ered, ii) opening new markets to their consumers, and iii) improving the attributes of existing ‡ights in markets in which they already operated. They claimed that their alliance would promote competition over the U.S. 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 a¤ect consumers, consider three airports A, B and C. Assume that CO (respectively, NW) operates ‡ights 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 ‡ights, and thereby o¤er codeshare ‡ights in market A-C that connect through airport B. The partners can therefore expand the number of ‡ights they o¤er 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, travelling between A and C was previously possible by purchasing two di¤erent tickets, one from CO and one from NW. These so called “interline”‡ights, however, are 8

These reciprocal linkages allow a customer to use her frequent-‡yer 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 …nd it preferable to keep accumulating points in a single program and, thus, book seats on code-share ‡ights through her preferred airline. 9 Statement by Hershel I. Kamen, from Continental Airlines, to the U.S. Senate, 06/04/98.

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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 ‡ights in market A-C at a lower price and with seamless service. Finally, consumers may also bene…t from shorter transit and travel times on code-share ‡ights, as CO-NW were allowed to coordinate their ‡ight schedules. The economic evidence available at the time seemed to support the claim that codeshare alliances bene…t consumers. Morrison and Winston (1995), for instance, provided evidence that customers dislike interline ‡ights, while Park (1997) explained how airline alliances might enhance ‡ight options and social welfare. Park and Zhang (1998, 2000), as well as Brueckner and Whalen (2000), then showed how international alliances between U.S. and foreign carriers had allowed the alliance airlines to expand ‡ight options and markets served. They also provided evidence of lower prices in transatlantic markets in which these alliances competed. Lastly, Bamberger et al. (2004) gave evidence that regional alliances in the U.S. 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 ‡ights 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 e¤ects. 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 ‡ights 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 become available, to ensure that the alliance does not harm the public and is not anticompetitive. 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 10

In contrast with an online ‡ight, an interline ‡ight consists of two independent products, each marketed and operated separately by di¤erent airlines. Double marginalization occurs because each airline in an interline ‡ight maximizes the pro…ts 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 ‡ights 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.

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here the …ndings most relevant to the present analysis. By 2000, CO and NW codeshared in 26% of their combined markets. They chose to code-share mainly in markets they already served prior to the alliance. More speci…cally, 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 di¤ers notably from traditional regional and international agreements, in which the partners essentially code-share ‡ights 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), while 64% of CO’s code-shares 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 travelled with a code-share ticket, ii) virtually all code-share passengers (96%) travelled on connecting itineraries, and iii) the number of connecting ‡ights o¤ered in the market increased by 15%, on average, whereas the number of nonstop ‡ights remained essentially unchanged. This increase in connecting ‡ights is mostly attributable to CO-NW (+29% on average), although their competitors also increased their number of connecting ‡ights by 5% on average. Lastly, we found that the alliance had mixed e¤ects on prices. Indeed, after the implementation of the agreement in a market, average fares for connecting ‡ights declined by 5%, while average fares for passengers travelling nonstop increased by 11%. These variations in prices seem consistent with the conjecture that CO-NW have used the introduction of code-share connecting ‡ights as a way to price discriminate more e¤ectively between passengers with di¤erent willingness to pay for nonstop and connecting ‡ights (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 bene…ts, such as the introduction of new products, or the improvement of existing products.11 In the present paper, we propose a discrete choice model of consumer decisions that quanti…es the multi-dimensional welfare implications of the CO-NW code-share agreement. 11

In particular, note that a pre and post alliance comparison of ‡ights attributes, such as the duration of a ‡ight 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, since we model the consumers’ decisions based on the products’characteristics.

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3. A Discrete Choice Model We start by formalizing some of the concepts on which we build our model. Following Berry et al. (2006), we de…ne a market as a round-trip travel from an origin airport to a destination airport, with a departure date within a speci…c quarter.12 Markets are de…ned directionally. For instance, a round-trip in a given quarter from Pittsburgh to Miami, and a round-trip from Miami to Pittsburgh in the same quarter are two di¤erent markets. A product in a market is a ticket for a seat on a sequence of ‡ights o¤ered 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 ‡ight 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 di¤ers from the airline actually operating one of the ‡ights in the product, then the product is a code-share. In contrast, the ‡ights in an interline product are not only operated, but also marketed by two di¤erent airlines. As explained below, the consumer’s choice set, denoted J , is composed of products j = 0; :::; J, where j = 0 identi…es 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 et al. (2006), we assume that the market size N is proportional to P OPt , 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 1998-2001). In addition, we specify the proportionality factor to allow for exogenous variations in the market size over time. In other words, we de…ne N = ( 0 + 1 t) P OPt , where ( 0 ; 1 ) are parameters to be estimated. To de…ne a manageable choice set J , we assume that a consumer is initially endowed with an exogenous type 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 speci…c price consistent with her type.13 A market therefore 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 ‡ights were rarely sold out during our sample period (e.g. on average, 71% of seats available on domestic ‡ights in 2000 were actually booked). In addition, “overbooking” is a common practice in the rare instances in which a ‡ight is sold out.

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consists of N heterogeneous consumers who choose among the same set of J + 1 products, but each consumer faces a di¤erent 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 speci…cally 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 characterize the product rather than the consumer. A consumer would then select not only her ‡ight, 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: Ui;j =

i Pi;j

+ Yj0

i

+ Zj0 +

j

+ "i;j

(3.1)

;

where Pi;j is the price of product j quoted to consumer i; (Yj ; Zj ) are vectors of product characteristics; j represents the product characteristics that are unobservable to the econometrician (e.g. e¤ect of advertisement, local reputation); ( i ; i ) are unobservable random and possibly non-independent coe¢ cients speci…c to consumer i; is a vector of deterministic parameters; and "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, "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 Pi;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: i;j

(Pi ) = P

exp

j 0 2J

exp

i Pi;j

+ Yj0

i Pi;j 0

+

i

+ Zj0 +

Yj00 i

+

Zj0 0

j

+

;

(3.2)

j0

where Pi 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

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market:

"

sj = E P

exp

j 0 2J

exp

i Pi;j

+ Yj0

i Pi;j 0

i

+ Zj0 +

+ Yj00

i

j

+ Zj0 0 +

j0

#

;

(3.3)

where the expectation operator E [:] is taken over the random variables ( i ; i ; Pi ). 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 k . This assumption may be considered reasonable, since the characteristics traditionally unobserved in the airline industry (e.g. e¤ect of advertisement, quality of service, or local reputation) usually apply at the airline-itinerary level, rather than at the ‡ight level.14 The airline-itinerary market shares may then be written " # P 0 0 X i Pi;j + Yj i + Zj + k j2k exp P sj = E P Sk = ; (3.4) 0 0 j2k i Pi;j 0 + Yj 0 i + Zj 0 + k0 k0 2K j 0 2k0 exp where j 2 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 Pi;j , the price quoted for each product to each consumer. Instead, as further explained in Section 5.1, we can infer an estimate of the average purchased price Pk across all products j within the airline-itinerary k. Such a data limitation is not speci…c 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 signi…cantly across consumers. In our application, however, it is di¢ cult to argue that Pk is a legitimate proxy for Pi;j . Indeed, i) ticket prices within the same airline-itinerary vary markedly across consumers and products (e.g. prices often increase 5-fold depending on the date of purchase); and ii) unlike the average quoted 14

This de…nition of the unobserved characteristic is equivalent to that in Berry (1990), Peters (2006), and Berry et al. (2006). This does not imply, however, that the discrete choice models in these papers are equivalent to the one presented here. Indeed, consumers in our model select the ‡ight they prefer based on that ‡ight’s characteristics, rather than their favorite airline-itinerary based on average attributes.

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price P k , the average purchased price Pk 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 …rst that we observe the average quoted price P k . Let us denote the measurement error by ei;j = Pi;j P k . Substituting P k + ei;j for the unobserved price variable Pi;j in the indirect utility function (3.1) yields: Ui;j =

iP k

+ Yj0

i

+ Zj0 +

k

+e "i;j

where e "i;j =

i ei;j

+ "i;j :

(4.1)

A possible approach to deal with the measurement error may consist in assuming that the compounded error term e "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 satis…ed: …rst, ei;j must be uncorrelated with the product characteristics (Yj ; Zj ; k ); and second, i cannot be random and consumerspeci…c. Otherwise, e "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 satis…ed. Indeed, 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 ‡ight with attractive characteristics (e.g. a peak-hour departure) is more likely to exceed its corresponding average airline-itinerary price P k . Since 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 ei;j , the measurement error for product j, is characterized by a general additively separable model of the form, ei;j = Pi;j

Pk =

1

(Aj ) +

2

(Bi ) + ui;j

;

(4.2)

where product j belongs to the airline-itinerary k; Aj and Bi are vectors of product and consumer characteristics; 1 (:) and 2 (:) are functions; and ui;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 Pi;j in the utility function (3.1) by P k + 1 (Aj ) + 15

The objective here is not to model an inverse demand function for airlines’products. In particular, the model in (4.2) takes the average airline-itinerary price P k as data, not as a variable to be explained. In addition, we make no attempt at modeling the complex “yield management”practices used by airlines to price their products.

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(Bi ) + ui;j . In fact, observe that since the individual speci…c e¤ect i 2 (Bi ) enters (3.1) additively, it cancels out when we derive the choice probabilities (3.2). As a result, we would only need to replace Pi;j by P k + 1 (Aj ) + ui;j in (3.1). The market share in (3.3) may then be written " # exp i P k + 1 (Aj ) + ui;j + Yj0 i + Zj0 + k sj = E P ; (4.3) P 0 0 i P k0 + 1 (Aj 0 ) + ui;j 0 + Yj 0 i + Zj 0 + k0 k0 2K j 0 2k0 exp 2

where E [:] is taken with respect to ( i ; i ) and the ui;j ’s. In most applications, the conditional distribution of the measurement error in (4.2) is unknown. It may nevertheless be estimated in many situations. For instance, suppose that we have access to a random sample of quoted prices Pi;j , along with their corresponding product and passenger characteristics (Aj ;Bi ). In this situation, we could …rst estimate the model in (4.2). Then, we would replace Pi;j in the utility function (3.1) by P k + b 1 (Aj ) + ui;j . Finally, we would use the estimated distribution of the ui;j ’s to integrate them out of (4.3). Unfortunately, (4.2) cannot be estimated with our primary sample. Indeed, as explained in Section 5.1, we only observe a sub-sample of purchased rather than quoted prices, and these purchased prices Pi;j cannot be matched to the corresponding product and passenger characteristics (Aj ;Bi ). In fact, to the best of our knowledge, a random sample of quoted prices Pi;j along with (Aj ;Bi ) 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 (Aj ;Bi ). Although this auxiliary sample is not su¢ cient by itself to estimate directly the model in (4.2), 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 (4.2) (i.e. Pi;j = P k + ei;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 re16

A possible alternative would be for the analyst to construct arti…cially a sample of prices by asking for quotes for di¤erent products at di¤erent 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 re‡ect the prices quoted to actual consumers at the time they made their purchase decision.

12

quires 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 (Aj ; Bi ), 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 (4.2) must be correctly speci…ed. In particular, the individual effect 2 (Bi ) must be additively separable. Third, ui;j must be independent of ( i ; i ), the consumer marginal utilities for the products’ characteristics in the discrete choice model. In other words, after controlling for the individual characteristics Bi , the marginal utilities ( i ; i ) should be irrelevant to explain the price quoted to a consumer. As we shall see in Section 5.2, this assumption …nds some support in our application from the fact that airlines typically only observe the characteristics Bi at the time they quote a price to a consumer. Fourth, ui;j must be independent of k , the product unobserved characteristics. Observe, however, that ui;j is by construction mean-independent of k in our application, since the unobserved characteristic is de…ned at the airline-itinerary level.19 In addition, we shall see in Section 5.2 that we model the variance of ui;j as a function of P k , which should be correlated with k . As a result, the independence of ui;j and k may be re-interpreted into a weaker condition: ui;j may depend on k , but only through the average price P k .

5. The Data 5.1. The primary sample The primary sample consists of data on ‡ight schedules and purchased prices obtained respectively from the O¢ cial Airline Guide (OAG) and the DOT. The OAG data list the time and itinerary for all ‡ights supplied by commercial U.S. airlines. The DOT data is 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 price Pi;j cannot be matched with the consumer i who purchased it, nor with the product j it corresponds to. A purchased price Pi;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 17

The entire set of assumptions under which the model is estimated is speci…ed in the Appendix. Unfortunately, this invariance hypothesis cannot be tested directly since prices in the primary sample cannot be matched to a speci…c product. A series of less formal tests, conducted at the airlineitinerary level, suggests no signi…cant di¤erence 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 j and the average price P j are both de…ned at the product level. 18

13

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 in two sub-samples, with exactly the same structure, but covering two di¤erent time periods. The …rst sub-sample consists of 160 airportpairs served by CO and/or NW between 1998 and 2001. The data are for the 1st quarters of 1998 through 2001, and the 3rd quarters of 1998 through 2000 (7 quarters in total). This sub-sample 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 …rst sub-sample, as it spans the January 1999 implementation of the CO-NW code-share agreement. The second sub-sample 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 sub-sample will be used exclusively in conjunction with the auxiliary sample to estimate the distribution of the measurement error. Let us now turn to the de…nition of the variables composing the vectors of product characteristics Yj and Zj in the consumer’s indirect utility (3.1). In doing so, we assume that i) a code-share ‡ight marketed by the two partners constitutes two distinct products; and ii) the airline-speci…c characteristics of a code-share product pertain to the marketing airline. The …rst assumption is supported by the fact that, under the terms of their agreement, code-share ‡ights 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 di¤erent partitions of the variables across the Yj and Zj vectors to estimate the model. We present below the partition that provided the best …t on a 25% random 20

A description of the criteria used to construct our sample may be found on Armantier’s website at http://www.sceco.umontreal.ca/liste_personnel/armantier/index.htm. For instance, we use Borenstein and Rose (1994)’s guidelines to screen for unusually high and low ticket prices. 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 ‡ight they were booking was code-shared and might not be operated entirely by the marketing airline.

14

sample of our data. 5.1.1. Variables with a Random Parameter The variables in Yj include the following attributes of product j: - P EAKj is a variable indicating whether the departure times for the outbound and inbound ‡ights in a nonstop product are scheduled during peak travel hours (i.e. 5am to 9am, or 4pm to 8pm).23 We include this variable as we acknowledge that some passengers, such as business travellers, may have higher valuations for peak-hours products (see Morrison and Winston 1995). - N ON ST OPj is a dummy variable equal to 1 if product j is nonstop. This …xed e¤ect 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. - AIRP ORT _SHRj 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 a¤ected by the airline’s presence at the airports in the market. For instance, dominance at an airport confers an airline greater visibility in ‡ight o¤erings, counter space, and gate access. - HU Bj 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 o¤er to passengers. Such advantages include a greater array of airport services (e.g. lounges, greater counter and gate access), more options in case of ‡ight delays or cancellations, and a greater array of options and destinations for frequent-‡yer rewards (see Borenstein 1989, 1991, Evans and Kessides 1993, Morrison and Winston 1995). The random parameters ( i ; i ) associated with (Pi;j ; Yj ) are assumed to be determined by the system of equations: i

= a0 + b0 GM P + ! i;0

and

i;l

= al + bl GM P + ! i;l

8l 2 f1; ::; 4g ;

(5.1)

where the error terms ! i;l (l = 0; :::; 4) are jointly normally distributed with mean zero and variance 2l ; GM P is the annual average per capita gross metropolitan prod23

P EAKj = 1 if the departure times for both the outbound and inbound itineraries are scheduled during peak hours; P EAKj = 0:5 if only one of the itineraries is scheduled during peak hours; and P EAKj = 0 otherwise. Empirical tests suggest that the variable P EAKj is not relevant for connecting products. Finally, note that we also estimated the model after decomposing P EAKj in two dummy variables, one for the outbound ‡ight, and one for the inbound ‡ight. The estimation results and the economic implications did not vary signi…cantly.

15

uct 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 hours and nonstop characteristics; that is, we specify that Cov (! i;0 ; ! i;1 ) = 1 and Cov (! i;0 ; ! i;2 ) = 2 , where ! i;0 , ! i;1 and ! i;2 are the error terms associated with the random parameter of respectively Pi;j , P EAKj , and N ON ST OPj in equation (5.1). Indeed, some passengers may simultaneously place a lower emphasis on price, and a greater emphasis on nonstop travel and peak-hours departures. 5.1.2. Variables with a Deterministic Parameter The variables in Zj include the following attributes of product j: - AIRLIN Ej is a M 1 vector of dummy variables, where M is the number of di¤erent airlines in the primary sample. If airline m markets product j, then the mth component of AIRLIN Ej 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-‡yer programs. - T RAV EL_T IM Ej is the scheduled travel time (in minutes) across the outbound and inbound itineraries (i.e. it includes all ‡ight times and airport transit times, if any). Our hypothesis is that, all else equal, passengers prefer shorter ‡ights. - IN T _HU Bj 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 bene…t from more convenient counter and lounge access, and from a greater availability of alternate ‡ights in case of missed or cancelled connections. - T RAN SIT _T IM Ej is the scheduled airport transit time (in minutes) at intermediate airports (if any). We include this variable since time spent at an intermediate airport may be perceived as an additional inconvenience by passengers. - CS_CON W _P RODj and CS_CON W _M KTj are two dummy variables identifying the implementation of the CO-NW code-share agreement at the product and market levels. CS_CON W _P RODj equals 1 when product j is code-shared by CONW, and CS_CON W _M KTj equals 1 for all CO-NW products in markets in which they code-share. These variables should capture any …xed e¤ect associated with codesharing, such as di¤erences in reputation and/or travel experience. Note that we decided 24 The sources for the GM P variable is the U.S. Conference of Mayors (http://www.usmayors.org). Note also that the variable GM P is de…ned in deviation from its mean, so that al (l = 0; :::; 4) may be interpreted as an unconditional mean. 25 IN T _HU Bj = 1 if the intermediate airports in the outbound and inbound itineraries are hubs for the airline; IN T _HU Bj = 0:5 if only one of the intermediate airports is a hub; and IN T _HU Bj = 0 otherwise. Once again, decomposing IN T _HU Bj in two dummy variables does not a¤ect signi…cantly the results.

16

to create two code-share variables, since it is unclear whether consumers in our sample were aware of the implementation of the agreement at either the product or market level. - CS_REGj 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. - IN T ERLIN Ej 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 de…ned at the product level. Indeed, passengers necessarily know that they are purchasing an interline ticket, as it requires two di¤erent bookings. This variable should enable us to test whether, beyond observed di¤erences (e.g. higher average prices for interline tickets), code-share and interline products are perceived in a similar manner by the public. - ST RIKE_N Wj is a dummy variable equal to 1 in the third quarter of 1998 for all NW ‡ights in markets where NW competed. This variable should capture the impact of the strike launched by NW employees during that period. - Y EARj and SU M M ERj are respectively a time trend and a seasonal dummy variable accounting for any variations in the valuation of airline travel over time. 5.2. The Auxiliary Sample and the Measurement Error Speci…cation The auxiliary sample consists of ticketing data obtained from the SABRE Group, which o¤ers the world’s largest computer reservation system through more than 50,000 travel agents, as well as the internet (Travelocity). These data include 55,223 tickets with a departure date in October 2002 across 63 airport-pairs.26 Each ticket lists the ticket price, the purchase date, the travel dates, the ‡ight times, and the class as well as the sub-class of travel. After testing di¤erent models, we …nd that the best speci…cation for the measurement error model (4.2) is to have 1 (Aj ) linear, and 2 (Bi ) decomposed into a linear combination of indicator functions Di , an individual random e¤ect i , and a time random e¤ect t . As a result, (4.2) may be written ei;j = Pi;j

Pk =

1 Aj

+

2 Di

+

i

+

t

+ ui;j

;

(5.2)

where the components of Aj =(P EAKj , T RAV EL_T IM Ej , T RAN SIT _T IM Ej ) are de…ned in identical fashion to their analog in the discrete choice model; t identi…es the departure date of consumer i; Di consists of three sets of dummy variables representing six di¤erent classes of travel (i.e. …rst, business, coach, discount with or without a 26

Note that since the auxiliary sample is not a time series, and does not overlap with the implementation of the CO-NW code-share agreement, we cannot use it directly to estimate the discrete choice model.

17

Saturday night stay-over, and “super saver”), six levels of advance purchase (from less than 2 days to more than 30 days), and three levels of travel duration (from less than 2 days to more than 7 days);27 and ui;j is a normally distributed mean zero error term exhibiting heteroskedasticity in the form V ar(ui;j ) = 2u P k . Descriptive statistics for the variables used in (5.2) are provided in Table 2. The consumer random e¤ect i is assumed to be normally distributed with mean zero and variance 2 i . Observe, however, that the auxiliary sample does not possess a panel structure. Indeed, we only observe a single purchase decision for each consumer. To estimate the distribution of the random e¤ect i we therefore de…ne di¤erent groups of consumers corresponding to the di¤erent possible combinations of the dummy variables in Di (e.g., the group of …rst class passengers travelling for less than two days and purchasing their tickets less than two days in advance). The random parameter i then takes the same value for all passengers within a group, which enables the estimation of the distribution of i . Finally, although we will relax this assumption in Section 9, we initially assume that i is independent of ( i ; i ) the marginal utilities for the product characteristics in the discrete choice model. We …nd that the time random e¤ect t follows an AR(1) process of the form t = ' t 1 + t where j'j < 1, and t is a normally distributed error term with mean zero and variance 2 . As a result, prices in a market are correlated across departure dates. In particular, if we denote d the number of days separating the departure dates of two passengers i and i0 who travel in the same market, then the correlation between the prices quoted to these consumers is inversely proportional to d. More speci…cally, we …nd that cor(Pi;j ; Pi0 ;j 0 ) = 'd = (1 '2 ) when products j and j 0 belong to the same market, and cor(Pi;j ; Pi0 ;j 0 ) = 0 otherwise.28 To conclude, observe that the speci…cation of the measurement error is consistent with the airlines’ pricing practices. Indeed, one of the basic principle behind “yield management”is to price discriminate based on the consumer characteristics observable at the time of purchase. In other words, consumers are grouped in di¤erent “price buckets” based on the characteristics included in Di , i.e. their class of travel, trip duration, and advance purchase. In this context, it is not unreasonable to assume, as we did in Section 4, that ui;j is independent of ( i ; i ). Indeed, in contrast with the observable 27

More speci…cally, the variables F IRST , BU SIN ESS, COACH, DISCOU N T _SAT , DISCOU N T , and SU P ER_SAV ER are equal to 1 when the passenger class of travel is respectively …rst, business, coach, discount with or without a Saturday night stay-over, or “super saver”. The variable BOU GHT _a_T O_b_DAY S equals 1 when the passenger bought his ticket between a and b days prior to its departure. The variable T RIP _a_T O_b_DAY S equals 1 when the duration of the trip is between a and b days. To guarantee E [ei;j ] = 0 we actually use the variables in deviation from their airline itinerary average in (5.2). 28 We estimate this two-way panel data model with serial correlation with the maximum likelihood approach developed by Karlsson and Skoglund (2004).

18

characteristics Di , the marginal utilities are not directly revealed by consumers when they ask airlines for a price quote. Since Di is discrete, the error term ui;j may then be interpreted as the variation in the price of a product across consumers with almost identical characteristics. For instance, the error term will capture the di¤erence in the price paid by two passengers with identical characteristics (Di ; i ), but with slightly di¤erent travel or purchase dates. This price di¤erence is assumed to re‡ect exogenous day-to-day variations in the demand for airline travel.

6. The Estimation Results 6.1. The Measurement Error Distribution We report in Table 3 the estimation outcomes for the measurement error distribution.29 Let us …rst concentrate on the vector of parameters 1 associated with the product characteristics Aj . The components of 1 are all signi…cantly di¤erent from zero at either a 5% or 10% signi…cance level. In particular, the estimation results indicate that, all else equal, prices for ‡ights departing during peak-hours are higher than their airlineitinerary average. Moreover, we …nd that, within an airline-itinerary, prices decrease with the time spent in transit at an intermediate airport, while they increase with the total travel time.30 The latter result may re‡ect the added cost incurred by an airline when ‡ying longer distances. We now turn to the deterministic component of the individual characteristics Bi . We …nd, as expected, that prices rise signi…cantly when moving to a superior class (e.g. from coach to business class). Prices are also signi…cantly higher than average when the ticket is bought closer to the travel date and, to a lesser extent, when the trip lasts only a few days. It appears, however, as indicated by the insigni…cant parameters in Table 3, that prices remain essentially constant when the ticket is acquired at least 21 days in advance, or when the trip lasts for more than 3 days. In fact, we can see in Table 3 that the remaining parameters are left essentially unchanged, when we re-estimate the model without these insigni…cant parameters.31 The standard error ($48:8) of the consumer speci…c random e¤ect i represents nearly 13% of the average price in our sample. In other words, after controlling for observed 29

Observe that for obvious identi…cation reasons, we have excluded the variables T RIP _7_T O_365_DAY S and BOU GHT _30_T O_365_DAY S when estimating the model. The consumer of reference is therefore a passenger travelling for more than 7 days, and purchasing her ticket at least 30 days in advance. 30 This result does not imply that we predict cheaper prices on nonstop ‡ights than on connecting ‡ights. Indeed, our model only enables the comparison of prices for ‡ights within the same itinerary. 31 We use this re-estimated model consisting only of signi…cant parameters when substituting P k +ei;j for the unobserved price variable Pi;j in the utility function (3.1).

19

individual characteristics, we are still able to capture a signi…cant amount of the price variation across types of consumers. The estimation also reveals that prices in a market appear to be positively correlated across departure dates. Indeed, both and ', the parameters of the AR(1) process followed by the time random e¤ect t , are found to be signi…cantly di¤erent from zero. In particular, our results suggest that (all else equal) the correlation between the prices of two tickets quoted for consecutive dates of departure in the same market is roughly 0:41. Finally, we …nd evidence of heterogeneity in the data since the parameter is signi…cantly greater than zero. In summary, the results for the auxiliary model show that the measurement error ei;j = Pi;j P k is strongly correlated with the product characteristics, and varies markedly across consumers. These …ndings therefore con…rm that the measurement error in the price variable cannot be ignored when we estimate the discrete choice model. 6.2. The Discrete Choice Model Estimation results for the discrete choice model are provided in Tables 4 and 5.32 Let us …rst concentrate on the estimation of the random parameters ( i ; i ). In the second column of Table 4, we can see that the estimated mean values al of these random coe¢ cients are all signi…cantly di¤erent from zero, and they have the expected signs. For instance, we …nd that consumers dislike higher prices and prefer nonstop ‡ights, scheduled during peak-hours, from a hub-airline with a large airport share. In the third column of Table 4, we report how GM P , the per capita gross metropolitan product, a¤ects the random coe¢ cients ( i ; i ). We …nd that consumers in markets with high GM P are less sensitive to prices, and they have a greater valuation for the N ON ST OP , P EAK, AIRP ORT _SHR, and HU B characteristics. This result is consistent with the fact that these attributes are usually of greater importance to passengers travelling for business. The last column in Table 4 provides the standard deviations l for the random coe¢ cients ( i ; i ). These standard deviations are all signi…cantly di¤erent from zero, thereby con…rming that consumers have heterogeneous valuations for these product characteristics. Note that the standard deviations on the P EAK, and N ON ST OP variables are high relative to their estimated mean coe¢ cient al . As explained in Berry et al. (2006), this indicates that consumers with high marginal utility for these attributes will tend to substitute towards products with similar attributes. Finally, we report at the bottom of Table 4 the estimate of 1 (respectively 2 ), the correlations between a consumer’s marginal utility for the P RICE and N ON ST OP characteristics (respectively P RICE and P EAK characteristics). We …nd that the valuation of P RICE is highly and negatively 32

The standard deviations in these tables are asymptotically robust, and they have been corrected for simulation errors (see Berry et al. 1995).

20

correlated to the valuation of P EAK and, to a lesser extent, to that of N ON ST OP . The estimated correlations therefore indicate that the passengers that are less sensitive to prices have a higher marginal utility for nonstop ‡ights scheduled during peak-hours. Let us now turn to Table 5, where the estimation results for the deterministic parameters are presented. We …nd that the parameters associated with the variables T RAV EL_T IM E and T RAN SIT _T IM E are signi…cantly smaller than zero. In other words, consumers seem to prefer shorter ‡ights, and they experience an additional disutility when spending time in transit at an intermediate airport. We also …nd that connecting passengers prefer to transit through the hub airports of the airline from which they bought their ticket (i.e. the parameter of IN T _HU B is positive and significant). These e¤ects are interesting since, to the best of our knowledge, they have not been previously identi…ed econometrically. In addition, they appear to support Morrison and Winston’s (1995) conjecture that the increase in transit time (as a fraction of total travel time) that followed deregulation adversely impacted consumers. We report in Table 5 that the parameter of the product level code-share dummy variable is signi…cantly lower than zero (see CS_CON W _P ROD). In other words, we …nd evidence of a disutility for ‡ights code-shared by CO-NW. This estimated disutility is in fact non-negligible when compared to the estimated parameters of the airline dummy variables for CO and NW in Table 5. Indeed, we …nd that the passengers’valuation of a CO and NW product drops respectively from 0:123 to 0:089, and from 0:092 to 0:058, when the partners code-share the product. The agreement, however, does not appear to have a¤ected the reputation of the non-code-share CO-NW products in markets in which the partners code-share. Indeed, the parameter of the market level code-share dummy variable is not signi…cantly di¤erent from zero (see CS_CON W _M KT in Table 5). We conjecture that the disutility for CO-NW code-share products may be explained by a combination of factors. First, some passengers may dislike the fact that their ‡ights are not entirely operated by the airline from which they purchase their ticket. Second, some passengers may dislike the fact that they do not know how the two partners share responsibilities in case of refunds, delays, cancellations, or lost luggage. Third, codeshare products are often more congested, which may negatively impact passengers loyal to either CO or NW.33 The estimation outcomes show no discernible e¤ects for regional code-share and interline products. Indeed, the parameters of the variables CS_REG and IN T ERLIN E are not signi…cantly di¤erent from zero in Table 5. Therefore, unlike CO-NW code-share products, we …nd no evidence supporting the conjecture that regional code-share and 33

Note, that these results are not su¢ cient to conclude unambiguously about the consequences of the code-share agreement on consumers. They only suggest that the reputation of CO and NW declines when they code-share a product. As we shall see, consumer surplus may still increase due to the creation of new products, or the improvement of existing products.

21

interline products are perceived by the public as being signi…cantly di¤erent from other products. This implies in particular that, after controlling for the higher prices of interline tickets, the additional features of interline products listed in Section 2 (e.g. double checking and double booking) do not appear to a¤ect consumers’utility. Moreover, observe that the strike launched by NW employees in the third quarter of 1998 does not appear to have penalized the demand for NW products, as the parameter associated to the variable ST RIKE_N Wj is found to be insigni…cant. This last set of results, however, should be interpreted with caution since we only possess a small number of observations for the regional code-share, interline, and strike variables. The estimated values for the airline dummy parameters in Table 5 appear sensible, and broadly consistent with airline rankings at the time, such as the 2000 Airline Quality Ratings.34 For instance, the dummy parameters are relatively higher for Southwest and Delta Airlines, and lower for TWA (whose assets were acquired out of bankruptcy by American Airlines in 2001). The parameters on the small regional carriers are mostly insigni…cant, maybe due to the fact that we have relatively few observations on these airlines. The parameter associated with the SU M M ER dummy variable is signi…cantly greater than zero, thereby suggesting a seasonal e¤ect with higher valuations for airline travel in the summer than in the winter. In contrast, we …nd no evidence of a time trend as the parameters of the three annual dummy variables are all insigni…cant. Finally, our results suggest that the market size N , de…ned in Section 3, expanded exogenously since the parameter 1 is signi…cantly greater than zero in Table 5.

7. Economic Implications We now turn to the economic implications of the estimated parameters. Note that although not directly related to the main object of the paper (i.e. the consumer welfare consequences of the CO-NW code-share agreement), the results presented in this Section present a major economic interest in their own right. Indeed, to the best of our knowledge, some of the premiums estimated here are unique in the economic literature on airlines. We …rst conduct some simulations to examine the consequences of increasing prices across all products by 10%. We …nd that such an increase in price would lower the probability that a consumer purchases an airline product by 11:02%.35 Airline passengers would also be less likely to travel with a nonstop ‡ight ( 3:61%), and to use a hubairline ( 4:68%). As a result, although prices increase by 10% in the simulation, the average price actually paid by passengers only increases by 6:21%. These simulation 34 35

Source: The Airline Quality Rating for 2000 at http://www.aqr.aero/aqrreports/2001aqr.pdf. All the premiums estimated in this section are signi…cant at a 5% signi…cance level.

22

results seem sensible as they suggest that passengers substitute high-priced nonstop and hub-airline ‡ights for either cheaper ‡ights or the outside good. We also conduct some simulations to evaluate the level of the “hub-premium”. We …nd that a hub-airline can charge a fare up to 8:73% higher than non-hub-airlines for a ‡ight taking-o¤ from its hub, but with otherwise identical characteristics. The magnitude of the hub-premium, although slightly smaller, is consistent with Berry et al. (2006). Likewise, we …nd that, all else equal, consumers are willing to pay an extra 6:29% on average to ‡y with one of American, Delta or United Airlines (the “Big 3” airlines in the U.S. market). This result may be explained in part by the marketing e¤orts undertaken by these airlines to generate consumer loyalty (e.g. these airlines have the most popular frequent-‡yer programs). Moreover, our simulations indicate that passengers are willing to disburse 16:51% more for a nonstop ‡ight, and an additional 4:70% if that nonstop ‡ight takes o¤ during peak-hours.36 Hence, ‡ying nonstop appears to be the attribute for which passengers are willing to pay the most. Finally, to reduce by 10% the duration of their travel (roughly 30 minutes each way on average), or by 10% the time spent in transit at an intermediate airport (roughly 8 minutes each way on average), consumers are willing to pay a fare that is higher by 4:94% and 1:88%, respectively. These e¤ects, although modest, are signi…cant statistically, and they should not be ignored when analyzing certain aspects of the airline industry, such as (e.g.) the consequences of deregulation (see Morrison and Winston 1995). Table 6 displays the average own and cross-price elasticities of market shares implied by the results. To facilitate the discussion, we report the average elasticities for …ve groups of airlines: i) CO and NW (the “Alliance” airlines); ii) American, Delta and United Airlines (the “Big Three”); iii) US Airways, TWA (the “Other Majors”); iv) Southwest and America West (“WN-HP”);37 and v) the “Regional” group that encompasses the remaining smaller carriers. Note …rst that the magnitudes of the elasticities are generally consistent with previous …ndings in the airline industry.38 As one may expect, the “Big Three” have the lowest own-price elasticity (in absolute terms), while the market shares of the “WN-HP” and “Regional” groups are the most sensitive to price. Note also that the own-price elasticity of the “Alliance”airlines lays between the “Big Three”and the “Other Majors”groups. The cross-elasticities in Table 6 show that a price increase by any other group of airlines mostly bene…ts the “WN-HP” and “Regional” airlines groups, while it leaves the market shares of the “Big Three” essentially 36

The 16:51% average for nonstop ‡ights incorporates changes in both ‡ight and transit times. By grouping Southwest and America West together, we are not implying that these two carriers are similar. It simply happens that their respective own and cross-price elasticities are comparable in our sample markets. 38 See Oum, Gillen and Noble (1986), as well as Whalen (1999) for aggregate demand elasticities estimated from log-linear demand functions, and Peters (2006) for a discrete choice estimation of elasticities. 37

23

una¤ected. In summary, the estimation results and their economic implications appear sensible, and they attest to the ability of our discrete choice model to capture consumer behavior in the airline industry.

8. Consumer Welfare Analysis In this Section, we exploit the fact that our primary sample spans the implementation of the 1999 CO-NW code-share agreement to compare the pre and post alliance expected consumer surplus for each airport-pair in our sample.39 Observe that this approach allows us to aggregate the multidimensional implications of the code-share agreement on consumers (e.g. changes in prices and other product characteristics, introduction of new products). In the absence of wealth e¤ects, the expected surplus of a consumer in a market (i.e. an airport-pair during a speci…c quarter) may be written as (see e.g. McFadden 1981, Small and Rosen 1981): 1 ECS = E Ui;j , (8.1) i

where j = ArgM axUi;j denotes the product selected by consumer i, Ui;j is the utility j2J

function in (3.1), i is the marginal utility of income, and the expectation operator E [:] is taken with respect to ( i ; i ; Pi ; "i;j ). To evaluate numerically (8.1), we simulate ui;j , ! i;l , and "i;j , the error terms in respectively the measurement error equation (5.2), the marginal utility equation (5.1), and the utility function (3.1).40 These welfare simulations 39

The pre alliance (respectively, post alliance) consumer surplus in a given airport-pair is calculated as the average of the expected consumer surplus across all quarters in our sample preceding (respectively, following) the implementation of the code-share agreement in that airport-pair. In the period following the implementation of the agreement in a market, we only take into consideration the quarters during which CO-NW code-share. In other words, if the partners stop code-sharing in a market, then we ignore the quarters following that decision. Moreover, in markets in which the partners never code-share, we compare the consumer surplus before and after January 1999, date at which the agreement became e¤ective. 40 Under the logit framework, (8.1) may be integrated analytically with respect to "i;j (see e.g. McFadden 1981, or Small and Rosen 1981). This approach is more e¢ cient to evaluate the expected consumer surplus as it does not require to simulate "i;j . We prefer, however, to rely h on simulations iof "i;j . Indeed, this approach allows us to calculate conditional expectations such as E 1i Ui;j j Zj = z , the expected surplus of consumers who purchased products with a speci…c characteristic Zj = z. In particular, we will be able to contrast the welfare of passengers who selected a connecting or a nonstop product. In addition, we will be able to take advantage of the linearity of the utility function to approximate the contribution of each characteristic to the consumer surplus. the contribution of Zj to the i h For instance,

. Note that our simulations suggest expected consumer surplus may be approximated by E 1i Zj0 that the cost of evaluating the expectation with respect to "i;j numerically rather than analytically in

24

are conducted under the following assumptions: i) j captures unobserved variations in product characteristics, not variations in consumers taste, ii) the quality of the outside good remains constant over the sampling period, and iii) the expansion of the market size is exogenous. Thus, when we evaluate the consumer surplus, we set the unobserved characteristics j at their values estimated in Section 6, we include the seasonal dummy variables, and we control for the exogenous market expansion by setting 1 = 0 in the market size equation (see Section 3).41 As indicated in Table 7, our model predicts that the individual consumer surplus decreased by 1:51% on average after CO-NW code-shared in a market. This decrease, however, is not statistically signi…cant, and it is not signi…cantly lower than in markets in which CO-NW never code-share (i.e. +0:56%). When we account for endogenous variations in passenger volumes, we …nd a modest 3:44% gain in total consumer surplus after the partners code-share in a market. This gain is signi…cantly greater than zero, but it is not signi…cantly di¤erent from the 2:86% increase in total consumer surplus observed in markets in which CO-NW never code-share. In other words, it would seem that the CO-NW code-share agreement had virtually no impact on consumers. This result, however, is somewhat misleading. Indeed, a more detailed analysis reveals that the e¤ects of the code-share agreement were not equally shared across consumers. In particular, the last two columns in Table 7 indicate that after CO-NW code-share in a market the individual consumer surplus of nonstop passengers declined by 5:90%, while the individual consumer surplus of connecting passengers increased by 2:45%, on average (both of these estimates, as well as their di¤erence, are signi…cant at a 5% level). This asymmetric e¤ect may be attributed in part to the variations in the prices paid by these nonstop and connecting passengers. Indeed, as in Armantier and Richard (2006), we see in the primary sample that after the implementation of the agreement in a market, the price paid for a connecting product decreased on average by 5:97%, while the price paid for a nonstop product increased on average by 10:26%. Interestingly, we …nd that these changes in the distribution of prices led some consumers to adjust their travelling patterns. In particular, our simulations indicate that some passengers substituted nonstop products, which became more expensive after the agreement took e¤ect in a market, in favor of cheaper connecting alternatives. Our results thus suggest that, although consumers were not signi…cantly a¤ected on average after (8.1) is marginal (the mean square error is of the order of 0.05%). Finally, note that, when evaluating (8.1) numerically, we use the same sequence of draws f! i;l gi;l for all markets. Likewise, we use the same sequence of draws fui;j ; "i;j gi when product j is available in two di¤erent quarters. 41 The annual dummy variables (Y EAR1 ; Y EAR2 ; Y EAR3 ) are not included in the welfare simulations as their parameters were found to be insigni…cant. Note also that keeping the unobserved characteristics at their pre alliance levels, not including the seasonal dummy variables, and/or allowing for the markets’ exogenous expansion, change (occasionally signi…cantly) the estimated values of the consumer surplus. The general conclusions of the paper, however, remain una¤ected.

25

the implementation of the code-share agreement in a market, connecting passengers saw their surplus increase on average, while nonstop passengers experienced a drop in average consumers surplus. We feel it is important to insist on the fact that the magnitude of the consumer welfare results cannot be imputed solely to variations in average prices. In particular, observe that, according with Armantier and Richard (2006), prices in our primary sample were in fact 4:40% lower on average after CO-NW code-shared in a market.42 In addition, when we decompose the variations in the individual consumer surplus into di¤erent sources, we …nd that consumers essentially bene…ted from lower prices after CONW code-shared in a market (see Table 8 where the principal sources of variations are reported). In other words, an analysis focusing solely on aggregate prices, and thereby ignoring variations in other characteristics (as it is often the case in policy reviews of alliances and mergers) would have erroneously concluded that the code-share agreement was bene…cial to consumers. Table 8, however, shows that the gains from lower prices are more than o¤set by losses generated by other product characteristics. Our simulations indicate that these losses may be traced in large part to the changes in travelling patterns. In particular, we have seen that after the implementation of the agreement in a market, some passengers substitute from nonstop products, which became more expensive, in favor of connecting alternatives, whose prices decreased on average.43 As a result, some product attributes, such as nonstop, peak-hours or travel time, do not contribute as much to the surplus of a consumer. This result therefore illustrates the importance of taking into consideration the variations in all product attributes, not only prices, when analyzing consumer welfare (see Richard 2003 for a similar argument). Finally, we conclude this Section by noting that the e¤ects of the agreement are not con…ned to markets in which CO-NW code-share. In particular, the alliance appears to a¤ect nonstop passengers in markets with nonstop ‡ights used as a portion of a codeshare product. To illustrate, consider a connecting code-share product linking airports A and C, through airport B. In other words, a passenger purchasing this code-share product would travel with two nonstop ‡ights, one from A to B, and the other from B to C. Until now, we have only analyzed the e¤ect of the agreement in code-share markets such as A-C. However, since the code-share product involves nonstop ‡ights in A-B and B-C, the implementation of the agreement in market A-C also has collateral e¤ects on nonstop passengers in markets A-B and B-C. In fact, when we isolate such nonstop passengers in our sample, we …nd that both their individual and total consumer surplus 42

In comparison, prices remained unchanged on average in markets in which CO-NW did not codeshare. 43 In fact, our simulations suggest that this substitution e¤ect may be imputed almost equally to rising non-stop fares and falling connecting fares.

26

declined signi…cantly by respectively 7:03% and 11:28%.44 This result may be considered relevant from a policy analysis perspective, as it illustrates how the implementation of an agreement in a market may have collateral consequences on consumers in other markets.

9. Robustness and Alternative Speci…cations We test in this Section the robustness of the results we just presented by comparing our benchmark model to some alternative speci…cations. We start by considering the consequences of ignoring the fact that consumers are quoted di¤erent prices for the same product. In other words, we now ignore the measurement error problem, and re-estimate the discrete choice model proposed in Section 3 under the constraint: Pi;j = Pk for any consumer i and any product j belonging to the airline-itinerary k. For parsimony, we only report in Table 9 the estimation outcomes for the most relevant variables, as well as the most important economic implications. According with intuition, passengers appear to be signi…cantly less price sensitive when prices are forced to remain constant across consumers (see Model 1 in Table 9). As a result, the airlines’ own-price elasticities are now signi…cantly smaller (in absolute terms), while the hub and nonstop premiums are considerably in‡ated. Observe also that the remaining estimated parameters either i) di¤er signi…cantly from those obtained in Section 7 with our benchmark model, ii) become insigni…cant (see P EAK), or iii) do not have the expected signs (see T RAV EL_T IM E). Moreover, although the consumer surplus appears to vary in the same direction after the implementation of the code-share agreement, the magnitude of the e¤ect di¤ers signi…cantly from the benchmark model. To test which speci…cation …ts the data better, we follow the approach developed by Singleton (1985) for non-nested hypotheses. In other words, we create a structural model nesting as special cases both the benchmark and this alternative model. The P-value of the alternative against the benchmark is 3:712E 4, while the P-value of the benchmark against the alternative is 0:313. In other words, one may clearly reject the alternative model in favor of the benchmark. These results therefore con…rm that ignoring the measurement error in the price variable, and thereby assuming that the price of a product does not vary across consumers, leads to signi…cant biases both in the point estimates and in their economic implications. We also test the consequences of ignoring the di¤erence between quoted prices and purchased prices. In other words, we now control for the measurement error problem by estimating the distribution of purchased prices around their mean, instead of the 44

Again, our simulations suggest that these losses may be attributed in large part to the sharp increase in the price paid for these nonstop ‡ights (on average, +9:47% across all airlines, and +15:07% for CONW ‡ights). We conjecture that the price increases may re‡ect the added demand for seats on these nonstop ‡ights generated by the in‡ux of CO-NW code-share passengers.

27

distribution of quoted prices around their mean. To do so, we estimate the discrete choice model and the measurement error distribution in (5.2) under the assumptions that Pi;j = Pi;j and P k = Pk . Observe that in this case the estimation procedure is simpler, as it may be conducted sequentially instead of jointly. Indeed, as the measurement error distribution does not depend anymore on consumers’ choices, we can …rst estimate it using only the data from the auxiliary sample. Then, we can substitute this estimated measurement error model in the market share equation (3.3), and estimate the discrete choice model separately using the 1998-2001 data in the primary sample. We can see in Table 9 (Model 2) that the parameters of the measurement error distribution are all smaller when estimated with the alternative instead of the benchmark model.45 In other words, we …nd that the unconditional distribution of purchased prices is more concentrated than the distribution of quoted prices. This result is consistent with the fact that, all else equal, consumers tend to purchase products in the lower tail of the distribution of quoted prices. We also …nd that the only parameters varying signi…cantly between the two models are the class of travel, the advance purchase and, more speci…cally, the random individual e¤ect. In other words, the di¤erence between the quoted and purchased price distributions around their respective means is essentially captured by individual characteristics. The fact that these individual characteristics do not enter the discrete choice model explains why the two speci…cations produce very similar estimates for the parameters of the discrete choice model. In addition, observe that the economic implications and the consumer welfare predictions remain essentially unchanged. In fact, a speci…cation test reveals that the benchmark model cannot be accepted against the alternative at the usual signi…cance levels.46 Therefore, ignoring the di¤erence between purchase and quoted prices would have lead to biases in the measurement error distribution, but it would have been essentially without consequences on the estimation of the discrete choice model and on the economic implications. We now verify whether ( i ; i ), the consumers’ marginal utilities for the product attributes in the discrete choice model, are correlated with Bi , the consumers’ individual characteristics in the measurement error model. To do so, we assume that 3 = cor (! i;0 ; i ), where ! i;0 is the error term in equation (5.1) characterizing the marginal utility on price i , and i is the component of Bi that captures the individual random e¤ect in the measurement error equation (5.2). We estimate that b3 = 0:128 with a standard error of 0:073. According with intuition, 3 is positive suggesting that consumers facing higher than average prices are slightly less sensitive to prices. The magnitude of the e¤ect, however, is only signi…cant at the 10% signi…cance level, and 45

This observation is in fact valid for all parameters, even those not reported in Table 9. The P -value of the alternative against the benchmark is 3:410E 3, while the P -value of the benchmark against the alternative is 2:104E 2. 46

28

it is modest from an economic perspective. In fact, observe that the other estimated parameters, as well as the economic implications, are nearly identical to those obtained in Section 7 with the benchmark model (see Model 3 in Table 9). In other words, ignoring the slight correlation between the consumers’marginal utilities and their individual characteristics is essentially of no consequences on the conclusions of the paper. Following Peters (2006), and Berry et al. (2006), we now test whether the di¤erent options covered by the outside good (e.g. travel by automobile or train) are comparable to those of the inside goods (i.e. airline travel). To do so, we add to our benchmark model a nest for the outside good. The additional nest parameter, estimated at 0:835 with a standard error of 0:169, is not signi…cantly di¤erent from 1, thereby rejecting the presence of a nest for the outside good. This result contrasts with Peters (2006), and Berry et al. (2006). We conjecture that this may be explained by the fact that we consider a richer model at the ‡ight level, which already captures ‡exible substitution patterns across ‡ights. In contrast, models developed at the airline-itinerary level may require the introduction of a nest to capture similar substitution patterns. Note also that neither the estimated parameters, nor the economic implications change signi…cantly when a nest for the outside good is added to the benchmark speci…cation (see Model 4 in Table 9). We now test whether the data may be explained by a simpler logit model without random parameters. The only di¤erence with the benchmark model is that preferences for the product’s attributes are now constrained to be deterministic and common to all consumers (i.e. ( i ; i ; ) = ( ; ; )). The results in Table 9 (see Model 5) indicate a signi…cant variation in the parameters’estimates, although no obvious trend may be detected. Likewise, the economic interpretations and the consumer welfare predictions di¤er notably from the benchmark model, even if they are of the same signs. To test whether marginal utilities parameters may be considered deterministic, we adopt the extension to the general method of moment framework of the Wald test (see e.g., Newey and West 1987). We …nd a P-value of 6:824E 5, thereby indicating that one may reject the alternative model in favor of the benchmark. In other words, we …nd that ignoring the heterogeneity in consumers’valuations a¤ects the parameters’estimates and their economic implications. The outcome of an instrumental variable estimation is contingent on the validity of the instruments used. In the Appendix, we provide statistical tests indicating that the instruments used to estimate the benchmark model cannot be considered weak. In addition, we test here the sensitivity of the results by considering a new set of six instruments re‡ecting various ‡ying and operating costs incurred by the airlines.47 The 47

The six cost variables are de…ned as follow: F U EL_COST accounts for fuel and oil operating expenses; P ERS_COST accounts for ‡ying personnel operating expenses (e.g. pilots and co-pilots);

29

number of new instruments is not su¢ cient to identify fully the model. Therefore, we combine these cost variables with the instruments we already used to estimate the benchmark model. The results presented for Model 6 in Table 9 indicate that both the point estimates and the economic consequences remain virtually unchanged when we augment the set of instruments with proxies for the airlines’marginal costs. These results therefore provides some support for the validity of the instruments used in the estimation of the benchmark model. Finally, we check the sensitivity of the results to the speci…cation of the market size. Following Berry (1990) and Berry et al. (2006), we now assume that the market size does not vary exogenously. In other words, we re-estimate the benchmark model under the constraint that N = 0 P OPt , where P OPt is the geometric mean of the population in quarter t at the metropolitan areas for the airports in the market. The results reported for Model 7 in Table 9 indicate that most of the estimated parameters and economic implications do not vary signi…cantly from those obtained in Section 7 with the benchmark model. The only signi…cant di¤erence (at a 10% level only) is for the variation in total consumer surplus. This was anticipated since we controlled for the exogenous variations in the market size when we conducted the consumer welfare simulations with the benchmark model. Nevertheless, these results demonstrate that the estimation of the discrete choice and measurement error models are not sensitive to the de…nition of the market size. To summarize, the benchmark model appears to be robust to alternative speci…cations, thereby supporting our results pertaining to the consumer welfare consequences of the CO-NW code-share agreement.

10. Conclusion The objective of the paper was to quantify the consumer welfare consequences of the 1999 domestic code-share agreement between Continental Airlines and Northwest Airlines. To address this problem adequately, we developed a discrete choice model based on individual ‡ight attributes, since a code-share agreement a¤ects the number as well as the characteristics of the ‡ights o¤ered. Our model accounts for the facts that airline consumers may have heterogeneous valuations of a ‡ight’s attributes, and that the price for the same ‡ight varies across consumers depending (e.g.) on the date of purchase. F LY IN G_OT HER_COST accounts for all other ‡ying operations cost (e.g. taxes, insurance, landing fees); M AIN T _COST accounts for maintenance costs; P AX_COST accounts for passengers service costs (e.g. ‡ight attendants, food); …nally, ALL_OT HER_COST represents all other operating costs (e.g. promotion, depreciation). Note that each of these variables is computed on a per-mile basis and then multiplied by the mileage of the airline-itinerary. Hence, values for each variable vary by quarter, by airline and by itinerary. Source: Bureau of Transportation Statistics.

30

This approach introduces a measurement error problem, as prices for each possible ‡ight and consumer are not observed in publicly available databases. To address this problem, we estimated jointly with the discrete choice model the distribution of the measurement error using a detailed auxiliary sample of ticketing data. We …nd that a consumer’s valuation of an airline product is signi…cantly a¤ected by a number of ‡ight attributes, including the price, the ‡ight duration, or the time spent in transit at an intermediate airport. Our results also reveal that there is substantial heterogeneity in the valuation of ‡ight attributes across consumers. More importantly, our results suggest that on average the 1999 CO-NW alliance had no signi…cant impact on consumers. This is not to say, however, that the agreement had a neutral e¤ect on all consumers. Indeed, we …nd that, after the agreement took e¤ect in a market, the surplus of passengers on connecting ‡ights increased signi…cantly, whereas the surplus of passengers on nonstop ‡ights declined sharply. Overall, our analysis of the CO-NW code-share agreement does not seem to provide su¢ cient evidence suggesting the need to review existing domestic code-share agreements on the ground that they negatively a¤ect consumers. Traditionally, policy reviews of domestic code-share agreements (and more generally, alliances and mergers), such as the 1999 CO-NW, the 2003 Delta-CO-NW, and the 2003 United-US Airways agreements, have focused almost exclusively on the overlap in markets served by the alliance partners, and on the potential for collusion in prices in code-share markets.48 Yet, our study demonstrates that, in spite of lower average prices, consumers were harmed by variations in product characteristics such as the duration of travel or the time of departure.49 Moreover, our results indicate that the implementation of the CO-NW agreement in a market may have generated collateral loses for nonstop passengers in non code-share markets. Our …ndings therefore suggest that policy reviews of code-share agreements i) should place a greater emphasis on changes in product attributes other than price, and ii) should consider the impact of the alliances in markets other than those in which they will be implemented. More generally, our paper highlights some key distinctive features of this new form of domestic code-share alliances, as compared to previous regional and international code-share alliances. The latter bene…ted consumers by opening new markets, and by eliminating the need to travel with tickets purchased from di¤erent airlines (see Brueckner and Whalen 2000, Brueckner 2003). In contrast, the CO-NW agreement 48

See, e.g., the Statement by Joel I. Klein, Assistant Attorney General at the Antitrust Division of the U.S. Department of Justice, before the Committee on Commerce, Science, and Transportation of the United States Senate concerning Competition in the Airline Industry, in Charleston S.C. on March 12, 1999. 49 In fact, an analysis focusing solely on prices may have led us to conclude erroneously that the code-share agreement positively impacted the consumer surplus per passenger.

31

opened few new markets. In fact, it essentially increased the number of connecting ‡ights o¤ered by CO-NW, which in turn a¤ected prices and passengers’‡ying patterns. As our analysis indicates, once we aggregate the consequences of these changes, it is not apparent that the CO-NW domestic alliance yielded bene…ts to consumers. Finally, the methodology developed in this paper, and in particular the method devised to address the measurement error problem on the price variable, should be of more general interest to analyze di¤erent aspects of the airline industry. In the past decade alone, major events such as mergers, bankruptcies, the emergence of low cost airlines, or the September 11 terrorist attack have signi…cantly a¤ected the mix of products o¤ered across airline markets. Since our discrete choice approach provides a better accounting of the multi-dimensional implications of changes in ‡ight attributes, it may help better quantify the consequences of such events on the welfare of airline consumers.

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33

Oum, T., Gillen, D. and Noble, S.E., 1986, “Demands for Fareclasses and Pricing in Airline Markets”, Logistics and Transportation Review, 22, 195-222. Park, J., 1997, “The E¤ect of Airline Alliances on Markets and Economic Welfare”, Transportation Research, 33, 181-195. Park, J. and Zhang, A., 1998, “Airline Alliances and Partner Firms’Output”, Transportation Research, 34, 245-255. Park, J. and Zhang, A., 2000, “An Empirical Analysis of Global Airline Alliances: Cases in North Atlantic Markets”, Review of Industrial Organization, 16, 367-384. Peters, C., 2006, “Airline Merger Simulation”, The Journal of Law and Economics, 49, 627-649. Richard, O., 2003, “Flight Frequency and Mergers in Airline Markets”, International Journal of Industrial Organization, 21, 907-922. Richard, J.F. and Zhang, W., 1998, “E¢ cient high-dimensional Monte-Carlo importance sampling”, University of Pittsburgh, Mimeo. Singleton, K., 1985, “Testing Speci…cations of Economic Agents’Intertemporal Optimum Problems in the Presence of Alternative Models”, Journal of Econometrics, 30, 391-413. Small, K. and Rosen, H., 1981, “Applied Welfare Economics with Discrete Choice Models”, Econometrica, 49, 105-130. Stock, J.H. and Yogo, M., 2005, “Testing for Weak Instruments in IV Regression”, in Identi…cation and Inference for Econometric Models: A Festschrift in Honor of Thomas Rothenberg, Andrews, D. W. K. and Stock, J. H. , eds., Cambridge University Press, 80–108. Whalen, T., 1999, “The Welfare E¤ects of Domestic Airline Alliances”, University of Illinois Urbana-Champaign, mimeo.

12. Appendix : The Inference Method We present in this appendix the inference method used to estimate jointly = ( 1 ; 2 ) 2 , where 1 is the vector of unknown structural parameters characterizing the discrete choice model (see Section 3), and 2 is the vector of unknown parameters characterizing the distribution of the measurement error in the price variable (see Section 4). As we shall see, our approach is an extension of the well known GMM technique developed by Berry, Levinsohn, and Pakes (1995) (BLP, hereafter), whereby we essentially add a new set of moments to identify the measurement error distribution. We start with some notations. When necessary, we will di¤erentiate Pi;j , the price of product j quoted to a consumer with individual characteristics Bi , and Pi;j , the price of product j when it is purchased by this consumer. Likewise, gi;j (:) and gi;j (:) denote the distributions of, respectively, Pi;j and Pi;j conditional on the product and consumer 34

characteristics (Aj ; Bi ). The “star” superscript will be used to distinguish a random variable (e.g. Pi;j ) from its corresponding observation (e.g. Pi;j ). Recall that gi;j (:) has been assumed to be characterized by Pi;j = P k + ei;j = P k +

1

(Aj ) +

2

(Bi ) + ui;j

(12.1)

;

while the probability that a consumer i purchases a product j in an airline-itinerary k is given by: i;j

(Pi ) = P

k0 2K

exp P

j 0 2k0

i Pi;j

+ Yj0

exp

i Pi;j 0

i

+ Zj0 + +

Yj00 i

+

k Zj0 0

+

:

(12.2)

k0

where j 0 2 k 0 denotes a product j 0 that belongs to an airline-itinerary k 0 , and K denotes the set of all airline-itineraries. Let us also summarize the observations at our disposal. For each market in the primary sample, we observe the characteristics Aj ; Yj ; Zj for every product in that market, as well as the market share and the average purchased price Sk ; Pk for every airline-itinerary in that market.50 The variables we do not observe in the primary sample are i) the product unobservable characteristics k , ii) the individual and the average prices quoted Pi;j ; P k , iii) the individual purchased prices along with their corresponding characteristics (Pi;j ; Aj ; Bi ); and iv) the consumers’ characteristics ( i ; i ; Bi ). Finally, we observe in the auxiliary sample the individual purchased prices Pi;j along with the corresponding product and consumer characteristics Aj ; Bi . We now list the assumptions under which we estimate the benchmark model in Section 6. First, the conditional price distribution in (12.1) is correctly speci…ed. In particular, the individual e¤ect 2 (Bi ) is additively separable, and the ui;j ’s are independently distributed.51 Second, the individual random e¤ect Bi is independent of the marginal utilities ( i ; i ).52 Third, the error terms "i;j , ui;j , and k are independent of all other random variables. Fourth, after controlling for all relevant product and consumer attributes (Aj ; Bi ), the distributions gi;j (:) and gi;j (:) are invariant whether we consider a market in the auxiliary or in the primary sample. Let us also outline our general estimation strategy. How to implement this strategy will be explained next. The estimation method basically consists in four parts. First, 50 Recall that the primary sample consists of panel data observed for di¤erent markets (i.e. di¤erent airport-pairs over di¤erent quarters). For the ease of presentation, we have omitted the market subscript in the …rst part of this Appendix. 51 Note that the distribution of the ui;j ’s can depend on the observable P k ; Aj . This is the case for instance in our application as we assume that the variance of ui;j is a function of P k . 52 Once again, this assumption may be relaxed. In particular, we consider in Section 9 a situation in which Bi is correlated with i .

35

we estimate the conditional distribution of quoted prices in (12.1). Second, we replace each price Pi;j in the choice probability (12.2) by P k + b 1 (Aj ) + ui;j , which yields i;j

(Pi ) = P

k0 2K

n o 0 0 b P + (A ) + u i k 1 j i;j + Yj i + Zj + k n o b 0 0 0 exp P + (A ) + u + Yj00 i + Zj0 0 + i k 1 j i;j j 0 2k0

exp P

(12.3) k0

(recall that i b 2 (Bi ) cancels out of (12.3) as it enters the utility function additively). Third, we evaluate the market shares at the product and airline-itinerary levels, X sj = E [ i;j (Pi )] and Sk = sj , (12.4) j2k

using the distribution of ( i ; i ) and the marginal distributions of the ui;j ’s, as they have been assumed to be independent. Fourth, we estimate the discrete choice model by comparing Sk , the airline-itinerary market share observed in our data, with Sk , its theoretical counterpart we just calculated. As explained in Section 4, however, this estimation strategy cannot be implemented sequentially. Indeed, we cannot estimate (12.1) directly since we observe purchased prices rather than quoted prices. Below, we explain how we can use Bayes rule to express the distribution of purchased prices as a function of the discrete choice model and the distribution of quoted prices. The discrete choice model and the conditional distribution of prices in (12.1) can then be estimated jointly. To understand our application of Bayes rule, observe …rst that the distribution of the purchased price Pi;j may be expressed as a conditional distribution of the form gi;j Pi;j = gi;j Pi;j = Pi;j j i;j , where i;j characterizes the event “a consumer with characteristics Bi purchases product j”. Under our independence assumptions, the probability of occurrence of this event may be written Pr ( i;j ) = E [ i;j (Pi )], where i;j (Pi ) is the choice probability in (12.3), and E [:] denotes the expectation with respect to ( i ; i ) and the ui;j ’s. Likewise, the probability that a consumer with characteristics Bi purchases product j when she is quoted a price Pi;j = Pi;j , may be written Pr i;j j Pi;j = E i;j (Pi ) j Pi;j = Pi;j , where E [:] denotes the expectation with respect to ( i ; i ), and the ui;j 0 ’s (j 0 6= j). Using Bayes rule, we can now express the distribution of purchased prices conditional on (Aj ; Bi ) as a function of the choice probabilities and the conditional distribution of quoted prices: (Pi ) j Pi;j = Pi;j gi;j Pi;j = Pi;j : E [ i;j (Pi )] (12.5) Let us now turn to the joint inference method. Observe that if we knew k ; P k for all airline-itineraries, then we would be in a position to estimate jointly the discrete

gi;j Pi;j =

Pr

i;j

E j Pi;j gi;j Pi;j = Pi;j = Pr ( i;j )

36

i;j

choice and measurement error models. Indeed, we could simulate in (12.3) ( i ; i ) and the ui;j ’s from their respective distributions to evaluate numerically E [ i;j (Pi )] and E i;j (Pi ) j Pi;j = Pi;j for any given Pi;j , and thereby characterize the purchased prices density gi;j Pi;j in (12.5). We could then estimate the parameters of the measurement Y error distribution by (e.g.) maximizing the likelihood gi;j Pi;j ; for the purchased prices Pi;j observed in the auxiliary sample. Concurrently, following BLP’s approach, we could estimate the parameters of the discrete choice model by comparing Sk , the airlineitinerary market shares observed in the primary sample, with Sk ( ), the corresponding theoretical market shares calculated numerically for a speci…c parameter value . Unfortunately, the pairs k ; P k are not directly observable in the data. Nevertheless, for any parameter value , they can be inferred from the observed market shares and average purchased prices Sk ; Pk . Indeed, extending the now traditional BLP’s approach, let us de…ne the vectors ( ) and P ( ), each of dimension K, solution of the system of non-linear equations Sk

;P;

= Sk

Pk

;P;

= Pk

8k = 1; :::; K

(12.6)

where Sk ; P ; and Pk ; P ; are respectively the theoretic market share and the average purchased price on airline-itinerary k, both obtained numerically for a speci…c value of ; P k ; .53 Observe that BLP only have to solve the …rst set of equations (i.e. Sk ( ; ) = S k ), since they assume that the components of P are observed. After this transformation, we can de…ne two i.i.d sequences and two sets of moment conditions.54 First, from the data in the primary sample, we can de…ne the sequence m;k ( ) ; m;k m;k , where m and k identify respectively the markets and the airline-itineraries, and m;k is an appropriate vector of instrumental variables verifying dim ( m;k ) dim ( 1 ). We then obtain the traditional BLP’s moment conditions: E

m;k m;k

( ) =0.

In addition, from the data in the auxiliary sample, we can de…ne the sequence Pi;j i;j . The second set of moment conditions is then simply provided by the individual score 53

The average price paid for a product in airline itinerary k may be written as Pk =

P j2k Pj sj P ; j2k sj

where

Pj = E [Pi;j ] is the expected purchased price of product j obtained numerically from its distribution in (12.5). 54 To de…ne unambiguously the estimator we re-introduce here the market subscript.

37

function derived from the purchased prices distribution E

@ ln gi;j (Pi;j ; ) = 0 . @ 2

The GMM estimator is based upon the empirical counterpart of the previous orthogonality conditions:

bGM M = Arg minB 0 2

1

B

where

0

P

m;k B B=@ X @ @

i;j

m;k m;k

2

( )

ln gi;j Pi;j ;

1

C A ,

(12.7)

and is a symmetric positive de…nite weighting matrix that may be chosen optimally in order to minimize the variance of the estimator. In practice, the optimal matrix is approximated by the covariance of an initial estimate of , in which is set equal to the identity matrix. We conclude this Appendix with some practical considerations speci…c to our application. First, given the structure of our samples, we evaluate the two sets of moment conditions in (12.7) using two di¤erent sets of markets. Indeed, as explained in Section 5, the primary sample is partitioned in two sub-samples. The …rst sub-sample, a time series between 1998 and 2001, covers the 1999 implementation of the CO-NW code-share agreement. The second sub-sample, for the fourth quarter of 2002, has been speci…cally constructed to span the same set of markets as the auxiliary sample. As a result, the …rst set of moment conditions (generated by the discrete choice model) is evaluated with data from the …rst sub-sample; while the second set of moment conditions (generated by the measurement error model) is evaluated with data from the second sub-sample and data from the auxiliary sample. The estimated parameter bGM M , however, is clearly a function of both the primary and auxiliary samples. When we estimate our benchmark model in Section 6, we include in the vector of instruments m;k all of the exogenous variables presented in Section 5, except for the average price and airport-share variables as they may be correlated with the unobserved product characteristics. Following (e.g.) Berry et al. (1995) and Nevo (2000), instruments for the price variable also include lagged prices (using a 2-quarter lag), as well as the average characteristics of the other products supplied by the same …rm in the same market, and by other …rms in the same market. A well known limitation of this now traditional approach to deal with the price endogeneity is that it is only valid under the assumption that the products’characteristics are predetermined. In the airline industry, this assumption …nds some support in the fact that ‡ight schedules are published in advance, and adjustments in response to variations in consumers’demand are virtually inexistent. Nevertheless, since the validity of these instruments cannot be established 38

formally, we test in Section 9 the robustness of our results using an alternative set of instruments that captures changes in marginal costs. Finally, the instruments for the airport-share variable include the average number of itineraries o¤ered by the airline at the endpoint airports, as well as the corresponding airport-share of the airline with a lag of two quarters.55 A critical issue that comes into play when evaluating the market shares is the fact that the expectations in (12.4) involve two sets of relatively high dimensional integrals. The …rst set is associated with the random parameters ( i ; i ), and the second set is associated with the vector of error terms ui;j . Although these integrals do not have a closed form solution, they may be approximated numerically with arbitrary precision. For instance, one could replace the expectations by empirical means of simulated points. Such an approach, however, would be prohibitively time-consuming in our application given the relatively high dimension of the integrals involved. To circumvent partially this problem, we take the following steps: i) we approximate numerically the …rst set of integrals with the E¢ cient Importance Sampling method (see Richard and Zhang 1998, or Liesenfeld and Richard 2001); and ii) we approximate the second set of integrals by generating extensible lattice points modi…ed by the baker’s transformation (see Hikernell et al. 2000). The estimation of the discrete choice model is conducted in parallel on several workstations using Fortran and the mathematical library IMSL. To reduce further computational time, we have adopted most of the recommendations in Berry (1994), Berry et al. (1995), and Nevo (2000) to optimize the computer code. In particular, following Berry (1994), the unknown vector of parameters 1 has been partitioned in two, depending on whether or not its components enter the model linearly. The computational burden, however, remains quite signi…cant (the estimation procedure takes nearly a month to converge) because of the relatively large sample size and high dimensional integrals involved in the market shares.

55

We …nd no evidence suggesting that our instruments are weak. Indeed, the …rst stage F statistics of the excluded instruments for the price and airport share endogenous variables are respectively 14:836 and 21:653. In addition, the Cragg-Donald (1993) statistic is 18:053, which is greater than the critical value provided by Stock and Yogo (2005) for usual signi…cance levels. As a result, it appears that we can reject the null hypothesis of weak instruments.

39

13. Tables

Table 1 Descriptive Statistics for the Primary Sample. Data for 1998-2001. Mean

Std.

Minimum

Maximum

Per Market (1,077 observations) Number of passengers 1

5,514.55

4,480.24

1,800.00

44,250.00

Number of products

164.77

90.63

9.00

660.00

Mean price ($, in 100s)

3.81

1.08

1.47

9.34

Number of airline-itineraries

16.49

11.62

1.00

62.00

Number of airlines

5.26

1.99

1.00

10.00

POP (in 1,000,000s)

2.34

0.95

0.77

6.57

GMP ($, in 100,000s)

0.00

0.09

(0.21)

0.34

MILES (in 1,000s)

1.42

0.63

0.16

2.58

2

Per Airline-Itinerary (17,764 observations) Number of passengers 1

334.34

1,065.92

10.00

24,310.00

Number of products

9.99

12.01

1.00

156.00

PRICE ($, in 100s)

3.76

1.83

0.27

26.42

Per Product (177,454 observations) NONSTOP

0.09

0.28

0.00

1.00

PEAK

0.03

0.15

0.00

1.00

TRAVELTIME (minutes, in 100s)

6.68

1.91

1.00

13.06

TRANSITTIME (minutes, in 100s)

1.17

0.52

0.00

3.00

HUB

0.12

0.32

0.00

1.00

INTHUB

0.82

0.36

0.00

1.00

AIRPORTSHR

0.16

0.15

0.00

0.80

1

Predicted quarterly average from DB1B (i.e. value observed in Databank 1B multiplied by 10). 2 On a per capita basis. Calculated as deviation from sample mean across markets.

40

Table 2 Descriptive Statistics for the Auxiliary Sample (55,223 Tickets). Variable

Mean

PRICE ($, in 100s) PEAK TRAVEL_TIME (minutes, in 100s) TRANSIT_TIME (minutes, in 100s) FIRST BUSINESS COACH DISCOUNT DISCOUNT_SAT SUPER_SAVER

Variable

3.591 (3.483) 0.420 (0.395) 3.994 (2.332) 0.238 (0.510) 0.003 (0.056) 0.043 (0.204) 0.097 (0.296) 0.463 (0.499) 0.350 (0.477) 0.044 (0.205)

TRIP_0_TO_2_DAYS TRIP_3_TO_6_DAYS TRIP_7_to_365_DAYS

BOUGHT_0_TO_2_DAYS BOUGHT_3_TO_6_DAYS BOUGHT_7_TO_13_DAYS BOUGHT_14_TO_20_DAYS BOUGHT_21_TO_29_DAYS BOUGHT_30_TO_365_DAYS

Numbers in parenthesis refer to standard deviations.

41

Mean 0.423 (0.494) 0.450 (0.497) 0.127 (0.333)

0.099 (0.299) 0.170 (0.375) 0.179 (0.383) 0.166 (0.372) 0.138 (0.344) 0.249 (0.433)

Table 3 Estimation Results for the Measurement Error Model Variable

Estimate (Std.)

Variable

Estimate (Std.)

TRAVEL_TIME

5.175* (1.827)

5.183* (1.781)

BOUGHT_0_TO_2_DAYS ♠

256.161* (17.039)

265.082* (16.850)

TRANSIT_TIME

-1.341** (0.817)

-1.355** (0.830)

BOUGHT_3_TO_6_DAYS

144.121* (9.120)

148.289* (9.124)

PEAK

8.115* (1.902)

8.122* (1.879)

BOUGHT_7_TO_13_DAYS

56.218* (8.492)

52.414* (8.166)

FIRST

988.720* (38.961)

973.125* (37.856)

BOUGHT_14_TO_20_DAYS

14.271* (5.538)

16.805* (5.601)

BUSINESS

689.643* (32.012)

684.553* (31.620)

BOUGHT_21_TO_29_DAYS

7.260** (4.041)

__

COACH

186.064* (29.564)

198.71* (29.587)

σμ

48.798* (6.404)

48.862* (6.373)

DISCOUNT

15.157 (26.353)

__

σε

36.321* (11.498)

34.606* (9.760)

DISCOUNT_SAT

-126.282* (31.270)

-141.500* (33.217)

ϕ

0.366* (0.098)

0.358* (0.111)

SUPER_SAVER

-362.875* (41.658)

-354.821* (41.658)

σu

0.189* (0.021)

0.204* (0.020)

TRIP_0_TO_2_DAYS ♠

26.178* (2.953)

27.768* (3.008)

ζ

1.455* (0.017)

1.464* (0.019)

2.760 (3.825)

__

TRIP_3_TO_6_DAYS

i

* indicates parameters significant at a 5% significance level. ** indicates parameters significant at a 10% significance level. Numbers in parenthesis refer to standard errors. ♠ For identification purposes, the variables TRIP_7_TO_365_DAYS and BOUGHT_30_TO_365_DAYS are not included in the model.

Table 4 Estimation Results for the Discrete Choice Model Estimates for the Random Parameters (α i , δ i ) Variable

al

bl

σl

PRICE

-1.253* (0.111)

0.421* (0.075)

0.256* (0.053)

PEAK

0.352* (0.081)

0.111* (0.029)

0.145* (0.032)

NONSTOP

1.062* (0.126)

0.240* (0.090)

0.343* (0.087)

AIRPORT_SHR

0.179* (0.048)

0.064* (0.024)

0.039* (0.018)

HUB

0.807* (0.188)

0.065* (0.026)

0.074* (0.025)

ρ1

0.568* (0.145)

ρ2

0.279* (0.101)

* indicates parameters significant at a 5% significance level. Numbers in parenthesis refer to standard errors.

42

Table 5 Estimation Results for the Discrete-Choice Model Estimates for the Deterministic Parameter λ Variable

Estimate

Variable

*

Estimate

Variable

Estimate

*

TRAVEL_TIME

-0.205 (0.060)

Delta Airlines (DL)

0.256 (0.049)

Frontier Airlines (F9)

0.060* (0.028)

TRANSIT_TIME

-0.389* (0.101)

United Airlines (UA)

0.033 (0.027)

Vanguard Airlines (NJ)

0.007 (0.043)

INT_HUB

0.090* (0.034)

US Airways (US)

-0.020 (0.028)

Spirit Airlines (NK)

-0.005 (0.052)

CS_CONW_PROD

-0.034* (0.015)

TWA (TW)

-0.067* (0.026)

Western Pacific (W7)

-0.068 (0.054)

CS_CONW_MKT

-0.017 (0.025)

Southwest Airlines (WN)

0.266* (0.073)

SUMMER

0.034* (0.009)

CS_REG

0.074 (0.068)

America West (HP)

0.059 (0.041)

YEAR1 (1998) ♠

-0.012 (0.007)

INTERLINE

-0.121 (0.088)

Midway Airlines (JI)

0.017 (0.029)

YEAR2 (1999)

-0.004 (0.009)

STRIKE_NW

-0.026 (0.063)

AirTran Airways (FL)

0.051 (0.034)

YEAR3 (2000)

0.008 (0.007)

Continental Airlines (CO)

0.123* (0.026)

American Trans Air (TZ)

-0.025 (0.024)

φ0

6.418* (1.801)

Northwest Airlines (NW)

0.092* (0.023)

Midwest Express (YX)

-0.052* (0.024)

φ1

0.139* (0.066)

American Airlines (AA)

0.174* (0.034)

Sun Country Air (SY)

-0.063 (0.056)

* indicates parameters significant at a 5% significance level. Numbers in parenthesis refer to standard errors. ♠ For identification purposes, 2001 is used as the year of reference.

43

Table 6 Average Own and Cross Price Elasticity across Airline Groups CO-NW “Alliance”

AA-DL-UA “Big Three”

TWA-US “Other Majors”

WN-HP

Regional

CO-NW “Alliance”

-1.952* (0.161)

0.277* (0.068)

0.106* (0.042)

0.037 (0.047)

0.009 (0.051)

AA-DL-UA “Big Three”

0.092* (0.026)

-1.540* (0.148)

0.051 (0.038)

0.016 (0.041)

0.012 (0.042)

TWA-US “Other Majors”

0.111* (0.039)

0.186* (0.070)

-2.229* (0.206)

0.064 (0.079)

0.026 (0.068)

WN-HP

0.154* (0.064)

0.229* (0.086)

0.148* (0.062)

-2.604* (0.237)

0.042 (0.081)

Regional

0.295* (0.132)

0.350* (0.118)

0.278 (0.185)

0.313* (0.142)

-2.785* (0.250)

Notes: Row i column j indicates the percentage change in the market share of i when the price of j increases by one percent. Numbers in parenthesis refer to standard errors. Regional group includes: F9, JI, FL, NJ, NK, YX, TZ, W7, SY. See Table 5 for airline names. * indicates parameters significant at a 5% significance level.

Table 7 Variation in Consumer Surplus After CO-NW Code-Share in a Market (in %) Passengers Flying on Type of Airport-Pairs Individual Consumer Surplus Total Consumer Surplus

All Consumers

Connecting Flights *

Nonstop Flights

Code-Shared

-1.51 (1.26)

2.35 (1.08)

-5.90* (1.62)

Never Code-Shared

0.56 (1.32)

1.78 (0.98)

-0.99 (1.47)

*

*

Code-Shared

3.44 (1.45)

5.46 (1.32)

-3.76* (1.60)

Never Code-Shared

2.86* (1.39)

3.67* (1.35)

0.05 (1.44)

* indicates parameters significant at a 5% significance level. Numbers in parenthesis refer to standard errors.

Table 8 Decomposition of the Variation in the Individual Consumer Surplus After CO-NW Code-Share in a Market (in %) Effect of:

Price

Peak Hours

Nonstop

Travel Time

Transit Time

Variation in Consumer Surplus

0.56

-0.34

-1.26

-0.53

-0.28

44

Table 9 Estimation Outcomes and Economic Implications of Alternative Models Alternative models

Benchmark Model

Model 1

Model 2

Model 3

Model 4

Model 5

Model 6

Model 7

Prices do not Vary across Consumers

Purchased Prices Equal Quoted Prices

α i and Bi

Benchmark Model with a Nest for the Outside Good

Benchmark Model without Random Parameters

Alternative Instruments

Alternative Market Size

are Correlated

Measurement Error Model 5.183*

Travel_Time

_____

(1.781) 8.122

PEAK

*

_____

(1.879) *

973.125 (37.856)

First

_____

*

Trip_0_to_2_days Bought_0_to_2_days

27.768

_____

(3.008) *

265.082 (16.850)

_____

*

48.862

σμ

(6.373)

i

_____

4.884*

5.376*

4.708*

4.310*

4.978*

5.457*

(1.812)

(1.883)

(1.722)

(1.958)

(1.869)

(1.881)

*

*

*

*

*

8.338*

8.006

8.150

(1.925)

8.457

(1.927)

(2.035) 1021.774

(41.154)

(39.174)

(41.640)

*

*

967.735

25.166

(3.228) 247.720

28.872

(3.055) *

259.982

*

*

28.004

(3.215) *

246.487

7.980

(2.215)

*

927.837

*

7.528

(1.875)

955.004*

(51.654)

(38.612)

(35.521)

*

*

29.200*

(3.128)

(2.973)

18.309

(4.249) *

(1.962) *

892.043

*

217.492

*

987.037 26.439

251.867

*

269.029*

(17.297)

(18.231)

(16.546)

(21.280)

(16.198)

(17.467)

*

*

*

*

*

30.756

49.462

51.034

62.769

47.219

54.726*

(5.906)

(6.661)

(5.803)

(10.359)

(6.425)

(6.835)

Discrete Choice Model -1.253

PRICE ♠

*

(0.111) 0.352

PEAK ♠

TRAVEL_TIME

-1.322*

-1.861*

-1.168*

-1.082*

(0.187)

(0.126)

(0.096)

(0.151)

(0.176)

(0.116)

(0.103)

*

*

*

0.185

0.385

*

0.304*

(0.081)

(0.127)

(0.077)

(0.090)

(0.084)

(0.116)

(0.077)

(0.082)

*

*

*

*

*

*

*

1.098*

-0.205

*

1.640

(0.249)

1.101

0.337 1.026

0.326 0.950

0.719

1.113

(0.139)

(0.141)

(0.117)

(0.094)

(0.127)

(0.109)

*

*

*

-0.085

-0.220

*

-0.179*

0.065

-0.189

(0.060)

(0.084)

(0.063)

(0.065)

(0.071)

(0.085)

(0.064)

(0.075)

*

*

*

*

*

*

*

8.182*

6.418

φ0

-1.275*

0.339

(0.126)

P

-1.242*

-0.420 0.138

1.062

NONSTOP ♠

*

*

4.141

7.006

(1.801)

(2.304)

*

*

-1.497*

-0.229 6.386

(1.926)

-0.196 8.132

(1.714)

4.931

7.665

(2.184)

(1.542)

(1.889)

(2.471)

-1.532*

-1.619*

-1.887*

-1.510*

-1.481*

Economic Implications -1.540

-0.617

“Big Three” Own Price Elasticity

(0.148)

(0.221)

(0.165)

(0.133)

(0.154)

(0.212)

(0.145)

(0.163)

Hub Premium

6.29%

13.03%

6.17%

6.22%

5.78%

3.85%

6.34%

6.65%

Non-Stop Flight Premium

16.51%

22.94%

16.80%

15.98%

14.92%

9.30%

16.24%

17.12%

-1.51

-2.86

-1.45

-1.56

-1.08

-0.82

-1.58

-1.62

(1.26)

(1.77)

(1.22)

(1.19)

(1.45)

(1.78)

(1.30)

(1.27)

*

*

*

*

*

5.98*

(1.49)

(1.80)

% Variation in consumers surplus on code-share markets

Individual Total ♠

3.44

*

(1.45)

1.49

3.34

(1.82)

(1.41)

3.55

3.07

(1.49)

(1.50)

5.64

(1.87)

3.35

* indicates parameters significant at a 5% significance level. Numbers in parenthesis refer to standard errors. When the model includes random coefficients, the parameter reported corresponds to

45

al

, the mean value of the random coefficient..