Christian Bontemps
email: christian.bontemps@tse-fr.eu

Kevin Remmy
email: remmy@uni-mannheim.decompasslexecon.

Johnny Wei

Jiangyu Wei

Ex-post Evaluation of the American Airlines-US Airways Merger: a structural approach

Keywords: merger, airlines, network, structural model, nested logit, airfare, demand, supply

In this paper, we estimate a structural model of the domestic US airline market to analyze the eect of the recent merger between American Airlines and US Airways. Our results show that, between 2011 and 2016, a substantial fuel price drop in conjunction with changes in consumer preferences toward direct ights completely rationalizes the observed decrease in prices. However, we estimate that, during the same period, more than half of the consumer welfare increase is due, on top of these environmental changes, to the ex-post optimization of the networks of the newly merged airline and of its competitors.

Introduction

Over the last 25 years, the US airline industry has faced a drastic reduction in the number of legacy carriers operating on the domestic market through two merger waves; one following the 9/11 crisis and the other due to the global nancial crisis of 2008 (see [START_REF] Philippon | The Great Reversal[END_REF]. Thus, the six legacy carriers in operation in 2005 have now consolidated into three legacy carriers: American Airlines, Delta Airlines and United Airlines (see [START_REF] Carlton | Are legacy airline mergers pro-or anti-competitive? Evidence from recent US airline mergers[END_REF]. The last merger occurred between American Airlines and US Airways, who announced their intention to merge in 2013. The announcement followed two years of American Airlines operating under bankruptcy protection. It created one of the world's largest airlines and drew considerable attention from all stakeholders.

As a result, the antitrust division of the US Department of Justice (DoJ), along with several state attorneys general, led a lawsuit in August 2013 seeking to block the merger. The main argument was that the merger would considerably lessen competition and increase fares, resulting in harm to consumers (see [START_REF] Peterman | The Future of Airline Mergers after the US Airways and American Airlines Merger[END_REF].

From the theoretical literature, we know that two opposing forces exist in horizontal mergers in oligopolistic markets. On the one hand, the number of competitors decreases and may lead to a monopoly in some specic markets or a quasi-monopoly if the competitors oer products that are not close substitutes (such as a connecting ight versus a direct one). Monopolization was a major concern of the DoJ when ling the lawsuit. On the other hand, a merger may induce some cost reduction through the rationalization of the network (i.e., exploiting the economies of scale or density generated from a more extensive network), or through the reduction in sta or aircraft maintenance to eliminate redundant entities. These cost reductions can impact the prices charged to consumers. Finally, competitors that are more aggressive on prices can react by entering some markets where there is possible room for competition. In addition, a larger network post-merger can be benecial to consumers who can reach more destinations.

In this paper, we evaluate the eect on prices and consumer surplus of the merger between American Airlines and US Airways through the estimation of a structural model of the US domestic airline industry. In doing so, we propose an ex-post evaluation of this merger. During the period studied (2011 to 2016), the fuel price dropped by almost two-thirds, causing a drop in the marginal cost of more than 10%. Additionally, the dierent airlines reacted to this new merger by rationalizing their networks. Indeed, the new entity eliminated overlaps and connecting ights when there were direct ights already proposed. Competitors did the same. Furthermore, this period saw the entry of a number of low-cost carriers (LCCs), who took advantage of new slot availabilities and reduced competition due to the merger. Indeed, one merger remedy was for the newly merged entity to sell slots at several airports, mainly at the Ronald Reagan International Airport and LaGuardia Airport. The slot divestiture at LaGuardia allowed Southwest Airlines and JetBlue to buy slots there for the rst time. 1 Finally, consumer preferences changed and the willingness to pay for ying directly increased over the period, a shift already noticed by [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF] during a former period. Accounting for these changes is crucial in an ex-post analysis of a merger, therefore, nding a reference scenario for conducting a dierence-in-dierences analysis may be somewhat challenging.

Estimating a structural model allows us to disentangle eects directly related to the merger from those that occurred independently.

We use pre-and post-merger fares data from the US Department of Transportation from the second quarter of both 2011 and 2016. In our main analysis, we estimate that airfares should have dropped on average by 6.73% and, therefore, consumer surplus should have increased by around 6.67%, had the supply of ights been the same in 2016 as in 2011. This assumption states that there is no merger and no further entry from LCCs or any other airline but allows for changes in fuel price and consumer preferences. When comparing the 2011 and 2016 data directly, we observe an average decrease in prices of 6.59% and an average increase in consumer surplus of 14.35%. As a result, we can overwhelmingly attribute the decrease in prices observed between 2011 and 2016 to changes in marginal costs and preferences. The merger and the entry/exit decisions of both the new entity and its competitors slightly increased prices and considerably increased consumer surplus by proposing more direct ights. However, it is very dicult to predict what would have been the entry/exit decisions between 2011 and 2016 without such a merger.

As detailed below in the literature review, ex-post merger analyses have traditionally been conducted with reduced-form models. We employ a structural approach in this paper. There has been a considerable debate about the advantage of estimating a reduced-form model rather than a structural model. Both have their advantages and drawbacks and can be seen as complementary.

They have their own sets of implicit or explicit assumptions, in terms of the behavior of the economic agents, linearities of the functional forms, and the stationarity of the environment over the period considered. Most of the empirical literature using structural models has focused on simulating the impact of mergers on prices and welfare before the merger has occurred. The rst step consists of estimating the demand and supply sides of the industry. The second step is to use these estimations to simulate the merger impact (see, among others, [START_REF] Berry | Some applications and limitations of recent advances in empirical industrial organization: Merger analysis[END_REF][START_REF] Nevo | Measuring Market Power in the Ready-to-Eat Cereal Industry[END_REF][START_REF] Peters | Evaluating the performance of merger simulation: Evidence from the US airline industry[END_REF] using pre-dened scenarios. However, ex-post merger analyses have been receiving increasing attention, both from policymakers and researchers [START_REF] Buccirossi | A short overview of a methodology for the ex-post review of merger control decisions[END_REF][START_REF] Ilzkovitz | Ex Post Economic Evaluation of Competition Policy: The EU Experience[END_REF]. We contribute to this literature by decomposing the dierence in price and consumer surplus between 2011 and 2016 into dierent ctitious steps, such as changes in consumer preferences and marginal costs that are not directly caused by the merger, the merger itself, and the entry/exit reactions of both the newly merged entity and the other airlines. To the best of our knowledge, we are the rst to employ such a structural decomposition. We also contribute to the literature studying airline mergers by separating price eects from market structure eects ex-post.

Following earlier structural work [START_REF] Chen | Mergers and product quality: Evidence from the airline industry[END_REF][START_REF] Gayle | How much do consumers really value air travel on-time performance, and to what extent are airlines motivated to improve their on-time performance?[END_REF], we estimate a nested logit model. Then, with estimates in hand, we perform several counterfactual exercises to evaluate the merger between American Airlines and US Airways. First, we simulate the no-merger case, keeping the market structure constant, but letting the demand and supply parameters take on their 2016 values. Doing so allows us to isolate changes in preferences and marginal costs unrelated to the merger. We nd substantial heterogeneity in price and consumer surplus changes across market structures. Markets where both merging parties oered direct ights before the merger saw signicant increases in consumer surplus. This increase is mainly due to changes in the merging entity's network and the entry of competitors. On the contrary, markets where only one of the merging parties was present saw consumer surplus decrease. This decrease is mainly due to the exit of either the merged entity or competitors. Overall, consumer surplus increased due to the merger and the entry/exit decisions of airlines.

The remaining part of the paper is structured as follows. Section 2 reviews the relevant literature.

Section 3 introduces the data used and presents a descriptive analysis of the eect of the merger.

Section 4 presents the demand and supply model and the estimation method. Section 5 analyzes the estimates using the 2011 and 2016 waves of the DB1B data. Section 6 presents the counterfactual analysis of our merger simulation and Section 7 concludes. The Supplemental Material available online2 contains appendices that provide a robustness check of our results and more details about our GMM estimation method.

Literature review

This paper relates and contributes to several strands of literature. First, there exists a vast literature on merger simulation using structural estimations of demand and supply. [START_REF] Hausman | Competitive analysis with dierenciated products[END_REF] simulate a merger in the beer industry. [START_REF] Nevo | Measuring Market Power in the Ready-to-Eat Cereal Industry[END_REF] simulates a merger in the ready-to-eat cereal sector, using a random coecients model à la BLP (1995). [START_REF] Ivaldi | Quantifying the eects from horizontal mergers in european competition policy[END_REF] simulate a merger between two truck producers, Volvo and Scania, using a nested logit demand estimation. [START_REF] Björnerstedt | Does Merger Simulation Work? Evidence from the Swedish Analgesics Market[END_REF] propose a post-merger comparison of a merger simulation in the Swedish Analgesics Market by comparing simulated prices and actual prices. We contribute to this literature by extending ex-post merger analysis to consider changes in market structure, as well as considering pure price eects.

Second, a large literature studies past mergers in the airline industry, mostly in reduced form. [START_REF] Borenstein | Airline mergers, airport dominance, and market power[END_REF] looks into the mergers that occurred in the mid-1980 in an ex-post way and detects anti-competitive eects of the mergers. Similar evidence of price increases is also revealed by [START_REF] Werden | The eects of mergers on price and output: Two case studies from the airline industry[END_REF], [START_REF] Kim | Mergers and market power: Evidence from the airline industry[END_REF][START_REF] Kim | Mergers and market power: Evidence from the airline industry[END_REF][START_REF] Morrison | Airline mergers: A longer view[END_REF] when examining other mergers in the same period. [START_REF] Bilotkach | Multimarket Contact and Intensity of Competition: Evidence from an Airline Merger[END_REF] studies the eects of multi-market contact on frequency following the merger between US Airways and America West. [START_REF] Luo | The price eects of the delta/northwest airline merger[END_REF] studies the price eects of the Delta/Northwest merger using regression techniques. Building on Bajari et al.'s (2007) approach, [START_REF] Benkard | Simulating the dynamic eects of horizontal mergers: U.s. airlines[END_REF] study the eects of horizontal mergers from a dynamic perspective. Following [START_REF] Nevo | Measuring Market Power in the Ready-to-Eat Cereal Industry[END_REF]) approach, Peters (2006) conducts merger simulations for ve mergers in the airline industry and makes a comparison between the simulated prices and the actual post-merger prices, as in [START_REF] Björnerstedt | Does Merger Simulation Work? Evidence from the Swedish Analgesics Market[END_REF]. Some recent studies investigate the eect of a merger on product quality [START_REF] Mazzeo | Competition and service quality in the US airline industry[END_REF][START_REF] Rupp | Does competition inuence airline on-time performance[END_REF][START_REF] Prince | Multimarket contact and service quality: Evidence from on-time performance in the US airline industry[END_REF][START_REF] Chen | Mergers and product quality: Evidence from the airline industry[END_REF][START_REF] Rupp | Mergers and Product Quality: A Silver Lining from De-Hubbing in the US Airline Industry[END_REF]. [START_REF] Bontemps | Price Competition and Endogenous Product Choice in Networks: Evidence from the US Airline Industry[END_REF] propose a two-stage model endogenizing carriers' choices of their networks and use it to predict the change post-merger network structures. Several papers investigate the American Airlines-US Airways merger. Using dierences-in-dierences (DID), [START_REF] Carlton | Are legacy airline mergers pro-or anti-competitive? Evidence from recent US airline mergers[END_REF] claim that the recent legacy mergers, including that of American Airlines and US Airways, were pro-competitive. More recently, [START_REF] Das | Eect of Merger on Market Price and Product Quality: American and US Airways[END_REF] simulates the merger of American Airlines and US Airways, using ex-ante simulation and estimating the marginal cost reduction necessary to t the actual 2016 prices. He examines the eects of this merger on product quality and price, using both DID and merger simulation methods. [START_REF] Ciliberto | Market structure and competition in airline markets[END_REF] extend the merger simulation approach by allowing endogenous entry decisions and also examine the merger between American Airlines and US Airways.

We contribute to this literature in dierent ways. Contrary to [START_REF] Benkard | Simulating the dynamic eects of horizontal mergers: U.s. airlines[END_REF][START_REF] Ciliberto | Market structure and competition in airline markets[END_REF]; [START_REF] Bontemps | Price Competition and Endogenous Product Choice in Networks: Evidence from the US Airline Industry[END_REF] who make ex-ante predictions about post-merger market structures, we provide an ex-post analysis of changes in market structure. Also, we disentangle changes in prices and consumer surplus directly related to the merger from those not related to the merger and caused by exogenous changes in preferences and costs. Then, we contribute to this literature by documenting large changes in preferences and costs between 2011 and 2016. Here, we connect to the work of [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF].

Finally, our paper connects to the literature on the structural estimation of demand and supply, which is now the reference in the new empirical industrial organization (IO) literature. Since [START_REF] Berry | Automobile prices in market equilibrium[END_REF] developed a random coecients model, many papers have applied the discrete-choicetype demand models to airline markets. [START_REF] Berry | Airline hubs: costs, markups and the implications of customer heterogeneity[END_REF] use a random coecients model to study the role of hubs. [START_REF] Armantier | Domestic airline alliances and consumer welfare[END_REF] measure the welfare outcomes of the codeshare agreement. [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF] investigate the factors that aect airlines' protability by comparing demand and supply outcomes between 1999 and 2006. [START_REF] Ciliberto | Does multimarket contact facilitate tacit collusion? Inference on conduct parameters in the airline industry[END_REF] examine the potential collusive behavior in the US airline industry and nd evidence that carriers with little multi-market contact do not cooperate in setting fares. Ruiz-Pérez (2019) considers the underlying common ownership structures of airlines by nancial institutions and studies how it aects entry decisions and price competition. [START_REF] Gayle | How much do consumers really value air travel on-time performance, and to what extent are airlines motivated to improve their on-time performance?[END_REF] estimate a nested logit for the demand for air transport and evaluate the impact of airlines' on-time performances.

3 Data and descriptive analysis

Data and summary statistics

The primary data source we use in our paper is the DB1B database provided by the US Department of Transportation, available online. 3 It consists of a 10% random sample of ticket records for the US domestic airline market in a given quarter. Since we are interested in the demand and supply sides before and after the merger, we select two samples from before and after the merger, respectively.

The pre-merger sample comes from the second quarter of 2011, more than one year before American Airlines and US Airways ocially announced their intent to merge (February 2013). The postmerger sample comes from the second quarter of 2016, more than one year after the Federal Aviation Administration granted a single operating certicate for US Airways and American Airlines (April 2015). 4We exploit the tables "Ticket" and "Market" of this database, keeping the tickets corresponding to the trips between the top 49 US metropolitan areas ("cities" hereafter).5 Both one-way tickets and return tickets are in the nal sample. Following the usual treatment of these data (see, for example, [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF], the tickets with more than one stop and multiple operating or ticketing carriers are deleted. We deate the prices in the 2016 data and all prices are in real 2011 US$. In our work, we dene a market t ∈ T as a non-directional city pair, with T collecting all city pairs in our sample. A non-directional market implies that a ight from A to B and a ight from B to A are in the same market. Also, we do not model the competition between the dierent airports in a given city.

In a given market, dierent airlines may propose dierent products. Airlines can choose to oer a direct ight between the origin and destination (OD). Alternatively, they can provide a one-stop ight with a connection at an intermediate airport. We dene a product on the itinerary level. Two ights oered by the same airline with the same endpoints but with a dierent connecting airport are two dierent products. This product denition explains why we have many more one-stop than direct products in our sample (see Table 3). A product in a given OD market is therefore a trip by air proposed by a given airline, with or without a connection and, if the ight is connecting, the identity of the connecting city.

Table 1 provides some summary statistics at the product level. The average price decreased by 6.59% from $194.33 in 2011 to $181.52 in 2016. Since we only keep the observations with at most one stop, the number of stops varies between zero and one, and the mean values show that most of the products are direct ights (see also Table 3). Connections is the maximum number of cities that an airline oers direct service to out of the two OD cities. 6 [Include Table 1] We present some market-level statistics in Table 2. Compared to 2011, the number of products per market increased in 2016. As expected, the number of rms per market decreased from 2011 to 2016. Entry by competitors of the merging entities did not compensate for losing one legacy carrier in most of the markets considered in our sample. The trend of having more direct passengers underlined in [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF] has continued through our sample period.

[Include Table 2] 3.2 A descriptive analysis of the merger: impact on the network First, we propose a descriptive analysis of the network of the main airlines before and after the merger. We consider the major carriers (United Airlines (UA), Delta Airlines (DL), American Airlines (AA), US Airways (US), and Southwest Airlines (WN)) separately. We collect the remaining carriers into a group called LCC. 7 Table 3 displays the main carrier-level statistics in 2011 and 2016. 6 If an airline oers direct service to ve cities out of endpoint A and direct service to 15 cities out of endpoints B, Connections is equal to 15.

7 These low-cost carriers are Alaska Airlines (AS), JetBlue Airways (B6), Allegiant Air (G4), Frontier Airlines (F9), Spirit Airlines (NK), Sun Country Airlines (SY), US 3,000 Airlines (U5), AirTran Airways (FL), and Virgin America (VX). Between 2011 and 2016, AirTrans merged with Southwest Airlines, and US 3,000 Airlines ceased operations, meaning they are no longer part of our sample in 2016.

Before the merger, American Airlines and US Airways were not as large as the two other major airlines, Delta and United Airlines. However, the merger helped AA overtake Delta and United in terms of passengers and markets served. It is also noteworthy that Southwest Airlines was the largest airline in terms of passengers served, despite serving fewer markets. This fact reects Southwest's dierent policy, which mostly oers direct ights. Between 2011 and 2016, the share of legacy carriers has continued to decrease, a trend observed during the last 20 years.

[Include Table 3] In Tables 4 and5, we display some descriptive statistics of the main airlines' networks for 2011 and 2016. For 2011, we also create a ctive entity, "AA + US", by combining all the direct ights of the individual rms, thus eliminating all duplicate products. Here, a city is a node of the network, and a link between two cities exists if an airline operates a direct ight between at least one airport in each of these two cities. The rst two lines report the number of cities connected by each airline and the number of links. At rst glance, it is clear that the networks are not fully connected, thanks to the (partial) hub and spoke system operated by the major airlines. Southwest, historically a point-to-point operator, has more links than the major airlines. However, we do see a trend in the rationalization of the networks of major airlines. Delta had 326 direct ights from these cities in 2011 and only 287 (around 12% less) in 2016. The ctive entity AA+US in 2011 would have oered 468 direct ights. However, American Airlines only oers 427 direct ights in 2016, connecting all the cities in our sample. This decrease suggests that AA altered its network by cutting some direct routes and making full use of US Airways' former hubs.

Similarly, the average path length (the path length between two cities is the minimum number of links necessary to join these two cities)8 slightly increased during this period for all airlines. In contrast, the average degree (i.e., the average number of cities directly connected to a given city) for the legacy carriers decreased because some direct routes were cut. Finally, the average closeness, which measures the inverse of the average length to reach any city from a given one) decreased since the average path length increased.

[Include Tables 4 and5] Next, we focus on some node-level characteristics. For each merging party, in 2011 and 2016, we calculate the centrality measures (degree and closeness)9 by city and rank them accordingly. The gures are reported in Table 6. We focus on the top-ve nodes for each merging airline in 2011.

Unsurprisingly, these top-ve nodes coincide with each carrier's hubs. In an airline network, a rm can select some central airports as "hubs" that link to many other airports. In 2011, American Airlines had six hubs: Chicago (ORD), Dallas (DFW), Los Angeles (LAX), New York (JFK, LGA), and Miami (MIA). US Airways had four hubs: Charlotte (CLT), Philadelphia (PHL), Phoenix (PHX), and Washington (DCA). JFK is the fth most important node in US Airways' network.

The most inuential nodes in American Airlines' network in 2016 include the pre-merger hubs of both airlines. Thus, we see that the merged entity fully integrated US Airways' former hubs. From Figure 2 compared to Figure 1, we can see that the network of the merged entity was much more well-connected compared to 2011, thanks to the merger. In particular, the new American Airlines was able to expand its business along the east coast, which was a major reason to seek a merger with US Airways.

Overall, this section shows that there were signicant changes to the post-merger network of the merged entity. Thus, it is crucial to take into account these changes in an ex-post analysis of the merger.

[Include Table 6] [Include Figures 1 and2] 3.3 A descriptive analysis of the merger: impact on prices Table 7 displays the mean price in 2011 and 2016 as a function of the market structure. Overall prices decreased by 6.59%. At rst sight, the merger may have led to this price decrease. However, as mentioned before, fuel prices substantially decreased between 2011 and 2016, aecting marginal costs. These marginal cost changes need to be controlled for, in order to study the merger's price eects. This price change is however heterogeneous among markets. A few markets exhibit a price increase, mainly when only one of the two entities was present. It is often said that US Airways was behaving more aggressively pre-merger than the other legacy carriers.10 This behavior may positively aect prices post-merger if the merged entity no longer acts as aggressively. However, these markets concern only around 12% of the passengers of our sample. In the next section, we introduce our structural model to disentangle the direct merger eect on these prices from the changes in preferences and marginal costs.

[Include Table 7] 4 Model

To examine consumer and rm behavior in the US airline industry, we build and estimate a structural model of demand and supply for ights. On the demand side, the goal is to identify consumer preferences for dierent ight characteristics and their price elasticity. On the supply side, the goal is to determine how specic product attributes aect the marginal cost of serving a given ight.

Once estimated, the model allows us to perform a rich set of counterfactuals to analyze the eect of mergers.

We make two critical assumptions. First, we assume that airlines take their network of segments to serve as given. Endogenizing network choices poses a burden, both conceptually and computationally, and is outside of the scope of this paper. However, we are evaluating the merger ex-post, so we observe the post-merger network structure and account for it. Second, we refrain from modeling airlines' frequency and capacity choices. The rationale behind this decision is that we are mainly interested in how mergers aect prices and network structure.

Demand

We model demand using a nested logit demand model [START_REF] Berry | Estimating discrete-choice models of product dierentiation[END_REF]. In this section, we present the main results, which are known in the empirical IO literature but are reported here to be selfcontained. In market t, the consumer can choose to either y between the two cities by choosing one of the inside products (direct and one-stop ights) j ∈ J t or to consume the outside option (product 0), which means traveling by other means or not traveling at all. Following the literature on demand estimation in airline markets, the inside products are grouped into the rst nest whereas the second nest is only composed of the outside option. The utility of consumer i in market t from purchasing product j ∈ J t (an inside product) is

u ijt = x jt β -αp jt + ξ jt + ε ijt (λ), (1)
where x jt is a vector of observed product attributes, p jt is the price of the product, and ξ jt represents product attributes unobserved by the researcher. 11 We normalize the utility of purchasing the outside option (product 0) to u i0t = η i0t where η i0t is an identically and independently distributed (across consumers) "logit error" following the terminology of [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF]. ε ijt (λ) is an idiosyncratic taste shock for product j in market t unobserved by the researcher. We assume it follows the distribution necessary to yield the familiar nested logit market share function, i.e., a generalized extreme value distribution. The nesting parameter λ ∈ (0, 1) governs the substitution patterns between the two nests. As λ approaches 0, all substitution occurs within the nests. When λ approaches 1, the model collapses into a simple logit model. We dene θ d ≡ (β, α, λ) to be the vector of parameters to be estimated.

When λ ∈ (0, 1], the share of people choosing product j ∈ J t in market t among the set of people consuming an inside product, the within-group share, is given by

s j|f,t (x t , p t , ξ t ; θ d ) = exp (δ jt /λ) k∈Jt exp (δ kt /λ) , (2)
with δ jt = x jt β -αp jt + ξ jt being the "mean utility" of product j.

The percentage of people ying in market t is

s f t (x t , p t , ξ t ; θ d ) = j∈Jt exp (δ jt /λ) λ 1 + j∈Jt exp (δ jt /λ) λ , (3)
which allows us to dene the market share of product j = 0 proposed in market t as

s jt (x t , p t , ξ t ; θ d ) = s j|f,t (x t , p t , ξ t ; θ d ) × s f t (x t , p t , ξ t ; θ d ). (4)
Similarly, the market share of the outside option is equal to

s 0t (x t , p t , ξ t ; θ d ) = 1 1 + j∈Jt exp (δ jt /λ) λ . (5)
A manipulation of equations ( 2) to (5) gives us a linear estimating equation (see [START_REF] Berry | Estimating discrete-choice models of product dierentiation[END_REF]):

ln( s jt s 0t ) = x jt β -αp jt + (1 -λ) ln(s j|f,t ) + ξ jt . (6)
All terms in equation ( 6) but ξ jt and θ d being observed, one can estimate θ d ≡ (β, α, λ) by regression techniques, ξ jt playing the role of the error term. However, since the demand-side unobservables, ξ jt , realize before rms choose prices, there is a correlation between prices and these unobservables, and similarly, between ξ jt and the within-group share s j|f,t . Typically, a more demanded product (i.e. with a higher value of ξ jt ) is priced higher at equilibrium and has a higher market share. Therefore, equation ( 6) can be estimated by 2SLS. A discussion of the choice of product attributes and instruments is provided in Section 5.

Supply

We model the static prot-maximizing price decisions of all the airlines in each market t. We assume that they play a Nash-Bertrand pricing game. For each market t, the prot maximization of airline f determines its pricing strategy. Observe that an airline may oer more than one product; for example, a direct ight and one-stop ight through its hub. Therefore, each rm chooses the set of prices p f t of the products they oer in each market t to maximize max

p f t Π f t ≡ j∈J f t (p jt -mc jt )s jt (x t , p t , ξ t ; θ d )M t , (7)
where J f t collects all products oered by rm f in market t with ∪ f ∈F J f t = J t . Also, mc jt is the marginal cost of oering product j and M t is the market size of market t (dened here as the geometric mean of the population at the endpoint metropolitan areas). Together, s jt M t give the number of consumers (passengers) choosing product (ight) j in market t. The rst-order condition with respect to the price of product j writes

∂Π f t ∂p jt = s jt (x t , p t , ξ t ; θ d ) + k∈J f t (p kt -mc kt ) ∂s kt ∂p jt (x t , p t , ξ t ; θ d ) = 0, (8)
giving us the standard trade-o between reducing the price to gain a higher market share and increasing the price to collect a higher markup, while internalizing the eect of product j's price on other products oered by the rm in the same market.

The market shares are observed from the data and their derivatives with respect to prices can be estimated from the estimation of the demand. Therefore, the previous equation allows us to estimate the markups (or equivalently, the marginal costs) for all products proposed by all rms.

For counterfactual analysis, we want to explain how markups are dependent on product attributes.

Therefore, we specify the marginal cost function for product j as

mc jt = w jt θ s + ζ jt , (9)
with w jt a vector of observed marginal cost shifters and ζ jt a marginal cost shock not observed by the researcher. The vector of parameters to be estimated is θ s . The choice of the product attributes in the marginal cost equation is detailed below. Equation ( 9) can be estimated by OLS.

Estimation procedure

As explained above, the parameters of the demand side need to be estimated with Instrumental

Variables (for both the price and the within-group share), whereas the parameters of the marginal cost specication only require OLS techniques. However, observe that the marginal costs in (9) are estimated from the demand side and not observed. We should take this uncertainty into account while computing the standard errors of the estimated θ s . Standard econometric procedures are available to correct for this parameter uncertainty.

However, estimating demand and supply jointly allows us to take into account the potential correlation between demand shocks and marginal cost shocks. Therefore, the joint estimation increases eciency, resulting in shorter condence intervals for both the demand and marginal cost parameters, θ d and θ s . Therefore, we estimate the demand and supply-side jointly using the Generalized Method of Moments (see [START_REF] Hansen | Large Sample Properties of Generalized Method of Moments Estimators[END_REF]. Since we have linear models for both the demand and the supply, estimating both sides jointly comes at a negligible computational burden.

More details are given in Appendix C.2.

5 Results and analysis

Specication

On the demand side, we let the utility of purchasing a product depend on several attributes. We select them following the literature [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF][START_REF] Ciliberto | Does multimarket contact facilitate tacit collusion? Inference on conduct parameters in the airline industry[END_REF]. The attributes we consider are the mean price, Price, which is endogenous, the number of stops (Stops)

to account for the fact that consumers value direct and one-stop ights dierently, and the maximum number of direct connections oered out of the endpoints (Connections). An airline serving more destinations out of an airport can enhance the value of frequent yer programs, for instance. We also include the distance (in thousand miles) between the endpoint cities (Distance) and its square (Distance2 ) to allow for distance to aect utility non-linearly. Finally, we include a set of carrier dummies to capture consumer preferences for dierent airlines.

On the supply side, we let the marginal cost depend on the number of stops (Stops), a hub dummy (Hub) equal to one if an endpoint or connecting airport is a hub for the airline, zero otherwise, and the distance (in thousand miles) between the endpoint cities (Distance). We allow for two sets of parameters: one for short and medium-haul ights (radial distance less than 1,500 miles) and another for long-haul ights (distance higher than 1,500 miles). We do so to account for the fact that airlines use dierent types of aircraft for these two types of routes. As for the demand side, we also include carrier dummies to pick up systematic marginal cost dierences across airlines.

Instruments

Since the demand-side unobservables, ξ jt , realize before rms choose prices, there is a correlation between prices and these unobservables. Also, the within-group share s j|g,t in equation ( 2) is a function of price and hence endogenous. We build instruments in the spirit of [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF], which are a variant of the instruments proposed by [START_REF] Berry | Automobile prices in market equilibrium[END_REF]. The idea behind these instruments is that close substitutes in the space of products' attributes constrain a product's price.

Functions of rival rm product attributes then serve as a proxy for the level of competition a given product faces. Similarly, attributes of other products produced by the same rm will aect pricing behavior (see equation ( 8)). In this vein, we use the percentage of rival products that are direct ights, the total number of rival products, the percentage of direct ights in a market, the number of competitors, and a dummy indicating whether a market is a monopoly. We also employ exogenous cost shifters, such as dummies, indicating that at least one of the endpoints is a hub and the number of direct connections oered out of the endpoints. Finally, we include interactions between the instruments.

Results

We present the estimation results for our GMM estimation of the demand side and the supply side in Table 8. Following the standard GMM procedure, we select our instruments, being mindful that including too many instruments may lead to biased estimates but that incorporating a sucient number of them guarantees the stability of our estimates, provided the overidentication test is not rejected by the data. With our nal choice of instruments, the degree of overidentication is equal to 5 for the 2011 data and 4 for the 2016 data. The J-test statistics are equal to 4.43 and 5.69, respectively and, therefore, we do not reject the overidentication test, for the usual test levels (5% or 1%). Also, we report the F-test statistics for the rst stage of the 2SLS demand estimation to assess that our instruments are not weak. The values are equal to 479 and 683 for the price in 2011 and 2016, and 845 and 1009 for the within-group market share s j|g . These results give us strong reasons to believe that we do not face any problems related to weak instruments (see [START_REF] Stock | A Survey of Weak Instruments and Weak Identication in Generalized Method of Moments[END_REF] and that both our estimates and the estimated standard errors are reliable.

[Include Table 8]

The nesting parameter λ lies between zero and one, and is statistically signicant, suggesting that substitution between the inside and outside products exists. In other words, when the price of a ight increases, passengers may decide to switch to another inside product or to not y at all. The price coecients for both years are negative, which aligns with our expectations and standard economic theory. We report the (mean) own price elasticity estimates in Table 9 with their corresponding 95% asymptotic condence interval. 12 The absolute values of the estimates of own-price elasticities are lower in 2016 than in 2011 though the dierence is not statistically signicant. Therefore, we can-not reject the assumption that the price elasticity is the same in 2011 and 2016. [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF] nd an increase in price elasticities between 1999 and 2006 and attribute it to the emergence of search engines and online ticketing services. Both factors have increased customers' ability to gather information and compare prices. However, as customers were already accustomed to online service and air travel during the 2010s, a stability in price elasticity is plausible.

The distance estimates imply a U-shape dependence of utility on distance. Most of the literature nds an inverse U-shape. However, most of the products in our dataset have a distance value corresponding to the increasing part of the distance function. This nding is consistent with the estimates of [START_REF] Ciliberto | Does multimarket contact facilitate tacit collusion? Inference on conduct parameters in the airline industry[END_REF] who have a similar denition of the products. Most of their observations also lie on the increasing part of the inverse U-shape function. Moreover, in our robustness analysis (see Appendix B), including only the distance does not modify the outcomes of our model. Finally, we still get the U-shape across several other robustness checks that we present in the same appendix.

A negative estimate of the number of stops shows passengers' preference for direct ights. Note that the variable Stops is not conditional on distance, so it measures the disutility incurred by a consumer while holding distance constant. We also display the connection semi-elasticity in Table 9, as well as its 95% condence interval. It measures the percentage change in a product's demand when a direct ight becomes a connecting ight, ceteris paribus. We nd that consumers have a higher aversion toward indirect ights in 2016, in line with a trend already found by [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF] who exploit data from 1999 and 2006. It is dicult to directly compare our values (61.5% for 2011 and 70.9% for 2016) with those estimated in Berry and Jia (2010) because we do not have the same denition of products nor the same model. However, we do have the same order of magnitude.

The eect of an airline's network size on consumers' utility, captured by Connections, is positive. One reason for this nding is that more ights increase the attraction of loyalty programs to customers. With a larger number of connections at an airport, a carrier can also provide better service and more convenient gate access for customers [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF]. The carrier-specic bution and by reporting the 25th and 975th values.

taste parameters suggest that, in 2011, American Airlines and US Airways were more popular than Delta Airlines. Nonetheless, Delta Airlines became more popular in 2016 than the merged entity American Airlines. Note that the reference group for both years is United Airlines.

We allow for two sets of marginal cost parameters: one for short-distance markets and the other for long-distance markets. There exist two opposite eects of the number of stops on marginal costs. On the one hand, connecting airports could generate economies of scale by transporting more passengers, which lowers the marginal cost. On the other hand, the extra volume of trac would cause higher coordination and management costs and lead to additional fuel consumption at landings and takeos, which increases the marginal cost. Hence, the coecient's sign reects the trade-o between these two eects [START_REF] Berry | Airline hubs: costs, markups and the implications of customer heterogeneity[END_REF][START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF]. There is no statistical evidence of economies of scale, even for long routes in 2011. The coordination cost eect seems to dominate any economies of scale. The same reasoning can apply to the hub parameters since hubs mostly function as connecting points. Unlike most previous literature, our results suggest that ights involving hubs have a higher cost, which implies the increasing cost of coordination and fuel prevails over the scale economies. Marginal cost also increases with distance, even for the long routes.

Tables 10 and11 show average prots, prices, marginal costs, and markups at dierent levels in both years, respectively. These tables reveal that the marginal costs of connecting ights are indeed higher than for direct ights. The marginal cost of operating a direct ight has decreased by 13.4%

between 2011 and 2016 (following the fuel price drop), whereas the marginal cost of operating a connecting ight has remained broadly the same. Also, as expected, LCCs have lower marginal costs, which aligns with the supply estimates.

Marginal costs for all airlines decreased substantially except for Southwest and Delta Airlines.

The marginal costs of the LCCs decreased more because the share of fuel cost in their operating cost is higher. Airlines were more "protable" in 2016 than in 2011.

One of the reasons raised by the DoJ in its attempt to block the merger between American Airlines and US Airways was the fear of increasing coordinated eects, such as an increase in tacit collusion. [START_REF] Ciliberto | Does multimarket contact facilitate tacit collusion? Inference on conduct parameters in the airline industry[END_REF] give evidence that multimarket contact may facilitate tacit collusion in a Bertrand price setting. Also, the merged entity internalizing its pricing externality becomes less aggressive in its pricing behavior toward its remaining competitors (see [START_REF] Porter | Mergers and coordinated eects[END_REF][START_REF] Ivaldi | Assessment of post-merger coordinated eects: Characterization by simulations[END_REF], essentially acting as if facing a higher marginal cost. The DoJ argued that US Airways had a more aggressive pricing behavior toward the other legacy carriers when it oered a connecting ight in a market in which one or more legacy carriers were operating directly. After having carefully investigated the mean Lerner Index of the airlines in dierent market congurations, we have not been able to nd any statistical evidence of these dierences in behavior, either before or after the merger.13

Analysis of marginal costs

The main argument for allowing a merger often relies on cost savings that counterbalance the upward pressure on pricing due to reduced competition. We take advantage of having marginal cost estimates pre-and post-merger to quantify how the marginal costs of the new American Airlines are related to the two production technologies of the two merging entities.

First, we compare the distributions of marginal costs for American Airlines and US Airways pre-and post-merger. The results are displayed in Figure 3. As illustrated in Tables 10 and11, we observe a shift toward the left of the distribution mainly driven by the drop in fuel price (see also Figure 4, which displays the distributions for Delta Airlines, United Airlines and SouthWest Airlines).

[Include Figures 3 and4]

Our objective is to compare the distribution of marginal costs for US Airways and American

Airlines pre-and post-merger. As illustrated above, directly comparing these distributions would be misleading due to the changes in fuel price between 2011 and 2016. Therefore, for every ight proposed by US Airways or American Airlines in 2011, we need to impute a value for what would have been the marginal cost of the same product, had US Airways and American not merged between these dates.

To do so, we estimate the distribution of marginal costs for ights proposed by Delta Airlines and United Airlines in 2011 and in 2016. We assume that the rank of the marginal cost of a ight proposed by US Airways or American Airlines in 2011 would have stayed constant in 2016. For example, if the marginal cost of a ight proposed by US Airways corresponds to the median of the marginal costs of ights proposed by Delta Airlines and United Airlines in 2011, its imputed value for 2016 is the median of the distribution of marginal costs of ights proposed by Delta Airlines and United Airlines in 2016. This scenario appears to be the most plausible to impute the marginal cost values for counterfactuals that are not observed. [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF] proceed similarly to input the unobserved component ξ jt in their counterfactuals. 14 We apply this procedure for direct and connecting ights separately.

Figure 5 displays the new distributions (direct ights on the left panel, connecting ights on the right panel). The distribution of American Airlines in 2016 seems to be a mix between the two former distributions. To test it formally, we run a Kolmogorov-Smirnov test to decide which distribution ts the distribution of the marginal costs of the new American Airlines in 2016 best. We consider ve candidates: the distribution of American in 2011 "translated" to 2016, the distribution of US in 2011 "translated" to 2016, the distribution which corresponds to the maximum of the two previous distributions, the distribution corresponding to the minimum, and the average of these two distributions. Remember that, pre-merger, American Airlines and US Airways were proposing approximately the same number of ights. The average represents a union of the two former technologies without any cost reduction.

[Include Figure 5]

The corresponding test statistics are reported in Table 12. The critical value for a 5% level test is 1.35, meaning we reject all tests but the rst one and the average for the direct ights, and we reject all tests but the average for the connecting ights. Therefore, it seems plausible under our assumptions that the merger-related eciency gains take time to materialize. In 2016, claiming that the production technology of the new entity is just the union of the production technologies of the two former entities is not rejected by the data. In fact, the administrative burden of combining two rms, as well as the need to synchronize baggage handling operations, and the decision of the DoJ to force American Airlines to maintain some ights (in particular from/to the former hubs of US Airways) have generated some frictions which have so far prevented the new entity from improving on its production costs.

14 See section V.C of [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF], pages 34-35.

[Include Table 12] 6 Counterfactuals

As illustrated in Table 7, the mean price of a ticket has decreased in the markets we consider between 2011 and 2016. 15 However, many changes occurred in the meantime. In particular, marginal costs decreased, largely due to the drop in fuel price. 16 We estimate a 13.4% marginal cost decrease for a direct ight. Also, the preferences of consumers have shifted toward direct ights and, in 2016, more than 80% of passengers take direct ights in our sample. In our counterfactual analysis, we aim to disentangle the eects of each change that occurred between 2011 and 2016. Our structural model is ideally suited for carrying out such a decomposition.

6.1 Deriving the change in prices due to changes in marginal costs and demand First, we would like to estimate what the prices of the ights proposed in 2011 would be had they been proposed in 2016. This is Scenario 1, and our objective is to compare the outcome of this scenario with the reality of 2016. In this scenario, there is no merger between US Airways and American Airlines. Also, all airlines propose the same products as in 2011 (no entry/exit by anybody) and compete as in 2011. However, marginal costs and consumer preferences change.

To do so, we take the estimates θ d and θ s of both the demand and marginal cost of 2016 and recompute the utility and marginal cost for each ight proposed in 2011 but evaluated with the 2016 preferences and costs. The natural question that arises is how to impute the new value of the unobserved product attribute ξ jt . Indeed, ξ jt plays a crucial role in determining the utility and, consequently, the market share of the corresponding product. As mentioned in [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF], the dierence between ξ jt in 2016 and ξ jt in 2011 "is a combination of changes in taste and 15 We recall that all prices are expressed in 2011 US$ 16 From 3.3 US$ per gallon to 1.20 US$ per gallon for the USA Daily Spot Prices for Kerosene. Source: USA Energy Information Administration. https://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm changes in unobserved product characteristics". We impute the new value of ξ jt in our scenario by keeping its rank constant, as in [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF].

To be more specic, we estimate the demand for 2011 and 2016 from which we can recover the distribution of the ξ's for both years studied. If ξ, for a given product, corresponds to the rst quartile of the distribution in 2011, the imputed value for Scenario 1 is the rst quartile of the distribution estimated in 2016. More generally, if the quantile of ξ is γ, the imputed value is the quantile γ of the distribution estimated in 2016. We do the same for imputing the 2016 value of the ζ's, the unobserved cost shocks.17

Table 13 displays the percentage changes in sales-weighted prices (weighted by the number of passengers in each market) and consumer surplus. Overall, we see that prices have decreased by around 6.59%, but would have decreased by 6.73% between 2011 and 2016 because of changes in marginal costs and preferences. In terms of prices, the merger (jointly with its impact on airlines strategies) slightly increased prices. However, in the previous section, we provide evidence that the merged entity has not yet realized any cost savings from the merger. 18 On the other hand, consumer surplus has increased by 14.35%. Less than half of this increase can be attributed to the changes in preferences and marginal costs, suggesting that the merger (and the rationalization of airlines' networks) did increase consumer surplus. In the next part, we present additional scenarios to estimate these networks' eects.

[Include Table 13] 6.2 Decomposition of the merger steps

We consider additional scenarios to disentangle the pure merger eect from changes in the networks of the dierent airlines. However, it would be fair to say that we are not able to distinguish which entries of competitors (LCC in particular) are directly linked to the merger and which would have occurred nevertheless. We consider three scenarios to lead us from the outcome of Scenario 1 to the actual situation in 2016.

Scenario 2: AA and US merge

In Scenario 2, we assume joint prot maximization by American Airlines and US Airways, but keep the set-up of Scenario 1 otherwise. The only dierence between Scenario 1 and Scenario 2 is that the merged entity now internalizes the eects of changing prices on all products proposed by American Airlines and US Airways. This scenario allows us to back out the pure price eect of the merger (see Appendix C.1 for further details).

Scenario 3: the new American Airlines updates its network

In Scenario 3, we update Scenario 2 by allowing the new entity "American Airlines" to reoptimize its network. We do so by updating its product oerings to those actually proposed in 2016. Similarly, we update the error terms of demand and supply, ξ jt and ζ jt , to the actual estimates from 2016 for the products oered by American Airlines. Note that we restrict the product oerings of all other rms to remain as those we observe in 2011. Hence, we have a data set in which we combine the products oered by the new American Airlines in 2016 with those oered by competitors in 2011. Doing so allows us to isolate the impact of the merging rm's post-merger network re-alignment.

Scenario 4: Competitors update their network

We move from the outcome of Scenario 3 to the actual market situation in 2016 with Scenario 4. Here, we allow competitors to update their networks. We do so by updating their product oerings to those we observe in 2016. We also use their 2016 estimates for the error terms of both demand and supply, which allows us to estimate the eect of the changes in competitors' product oerings. However, it is dicult to know which fraction of this change is actually a pure reaction to the merger and which would have occurred absent the merger. Disentangling these forces would require a model that endogenizes the market structure, which is beyond the scope of this paper.

These scenarios allow us to perform a detailed step-by-step evaluation of the merger. Having pre-and post-merger data means we do not have to rely on ad-hoc assumptions regarding the post-merger network structure. [START_REF] Ciliberto | Market structure and competition in airline markets[END_REF] and [START_REF] Bontemps | Price Competition and Endogenous Product Choice in Networks: Evidence from the US Airline Industry[END_REF] both show that such ad-hoc assumptions strongly drive the analysis. Both also provide ways to take into account changes in network structure in an ex-ante analysis where post-merger data is not (yet) available.

Tables 14 and15 display the percentage changes in sales-weighted prices (weighted by the number of passengers in each market) and consumer surplus across scenarios. Column 2 in the consumer surplus table reports the observed changes between 2011 and 2016. The rst line recaps the information across markets. Then, we decompose the changes according to the market situation in 2011, as in Table 13.

[Include Tables 14 and15]

Overall, we see that prices did not vary much when the networks were updated. In Scenario 2, mechanically, prices increase because one competitor vanished, but this increase was very small (+0.05%). This is mainly because, often, the merging entities were competing with at least two other big competitors. Also, there was little overlap in the networks of American Airlines and US Airways, especially when considering direct ights. In Scenario 3, when American Airlines is rationalizing its post-merger network, prices increase slightly (+0.12%) and in Scenario 4, they decrease only very slightly. Overall, the merger and the re-optimization of airlines' strategies induced a price increase of +0.15%.

On the other hand, consumer surplus has increased, especially in Scenario 4. We saw in Scenario 1 that less than half of the consumer surplus increase is due to the drop in marginal costs and changes in preferences. Most of the remaining part is due to the competitors of American Airlines adapting to the new situation by entering new markets and increasing competition.

This global analysis hides heterogeneity across dierent market structures, especially for the consumer surplus. We see that in markets where both American Airlines and US Airways were present before the merger, consumer surplus increased by more than in the no-merger scenario.

Again, this nding underlines the fact that competitive pressure and new entries (or threats of entries) kept prices from increasing too much. Also, stronger consumer tastes for a more extensive network and an expanded network post-merger led to higher consumer surplus.

On the other hand, consumer surplus absent the merger would have been higher in markets where only one of the merging parties was present before the merger. Consumers in these markets saw less new entry of competitors, which may explain this result.

Finally, we see that in markets where neither merging party was present, the re-optimization of the competitors' networks harms consumers considerably (-31.23% change in consumer surplus).

However, this only concerns 26 markets (0.2% of the passengers), some of which saw airlines leave for reasons that may be unrelated to the merger.

Conclusion

In this paper, we study the merger between American Airlines and US Airways and in particular, its impact on the US domestic market connecting the top metropolitan areas. Fuel prices dropped substantially in the period under scrutiny, having a high impact on production costs.

We estimate a structural model of demand for and supply of dierentiated products from the US Department of Transportation data collecting a 10% random sample in the second quarters of 2011 and 2016. We nd that the mean price has decreased by 6.59% but estimate that, without the merger, the mean price would have dropped by 6.73%. The merger with rms' subsequent reactions and adaptations to the new consumer tastes explain the gap. It is worth noting that, following [START_REF] Berry | Tracing the woes: An empirical analysis of the airline industry[END_REF], the shift in consumer preferences toward direct ights -which tend to be more expensive -has continued. This trend also explains part of this relative increase in prices. In addition, we do not nd evidence of any cost savings in the merging entities.

Breaking down the results by market structure, we nd that consumers in markets where both American and US Airways were present in 2011 beneted from the merger, even if prices did not change because of that. This fact is mainly due to the entry of LCCs and to a lesser extent, a more extensive network of the merged entity. On the other hand, consumers in markets where only one of the merging parties was present would have enjoyed a higher consumer surplus without a merger.

Overall, these ndings suggest that merger remedies, such as slot divestiture at LaGuardia, that gave LCCs and Southwest Airlines slots worked well.

In our simulations, entry of either low-cost or other legacy carriers often osets the eect of a decrease in the number of legacy carriers. We nd this pattern mainly in markets where the two merging entities were both operating before the merger. Modeling the endogeneity of the entry behavior is beyond the scope of this paper. It has been tackled by [START_REF] Ciliberto | Market structure and competition in airline markets[END_REF] and requires the use of moment inequalities to endogenize these decisions. There is, however, the necessity to provide empirical researchers with tools to deal with it while using standard econometric techniques, at the price of adding some assumptions, such as in the entry game literature.

Finally, it is worth noting that doing our simulation ex-post allows us to consider the shifts in both supply and demand. Merger analysis is often conducted ex-ante and rarely done ex-post.

Having pre-and post-merger data enables us to decompose the eect of the merger. It also prevents us from having to make ad-hoc assumptions on the post-merger network structure that have been shown to strongly inuence the analysis.

A Tables and Figures Notes: In these gures, the size of the node is constructed based on the normalized degree value of each node, and the width of the curve representing a link between two cities is associated with the number of passengers traveling through such a route. Red nodes in the graphs indicate the hubs for the airline. Most of the thick curves in the gures involve the hubs, and most large nodes are red suggesting that the hubs indeed undertake a higher volume of trac. Besides, as the graphs suggest, the hubs of American Airlines were more evenly distributed while US Airways emphasized its business more along the east coast. Overall, Dallas could be the most important node for American Airlines, and Charlotte was the most inuential node for US Airways. Supplement to "Ex-post evaluation of the American Airlines-US Airways merger: a structural approach" by Christian Bontemps, Kevin Remmy and Jiangyu Wei

B Robustness checks

In this section, we document some robustness checks. We discuss the choice of instruments then, the scenario for imputing the values in the counterfactual analysis. In the main text, we have selected our set of instruments in order to have a minimum degree of overidentication to get optimal and stable estimates, while not rejecting the overidentication test. In this robustness analysis, we report the demand side estimates and some estimates for other choices of sets of instruments. We use the following sets: We build these ve instrument sets for both year's data. The results are reported in Tables 16 and17. We also display the estimated elasticities as well as the overall price changes calculated from the counterfactual analysis of Scenario 1. We also add a column of results where we omit the distance squared in the product attributes, combining this specication with the optimal set of instruments chosen in the paper (IV1 for 2011 and IV4 for 2016). Indeed, we observe that the utility to y is an increasing function of the distance for most of the products of our sample. It seems natural to check whether introducing the distance linearly in the utility function changes the results.

The rst column (OLS) holds estimates from a nested logit model where we do not instrument for price nor the within-group share of products. For these non consistent estimates, we notice that the price coecient is biased towards zero, which is expected as the true coecient is negative and the correlation between the unobserved product attribute and the price positive (more demanded products are higher priced).

For 2011, we see that the estimates are relatively robust for the rst three columns. Then, the estimates become very unprecise, especially with IV3 (only one degree of overidentication). IV4 is rejected by the J-test. IV5 is not but gives very large condence intervals for the parameters. Overall, the estimates of elasticities and counterfactual are relatively robust.

For 2016, the estimates are also sensitive to changes in the instrument sets. Note that here, the column "IV 4" is the default specication used in the main part of the paper and provide the more Supplementary Appendix -page 1 accurate estimates. However, the estimates using the sets "IV 1" and "IV 2" does not seem to be be admissible from an economic point of view. Also, we reject the J test for these two cases.

We see that for 2011 and 2016, we recover a U-shaped dependence of utility on distance and that not including the square slightly changes the estimates but not the outcomes of the model. C Details on the estimation procedure C.1 Details on the supply-side + scenario 2

The rst-order conditions with respect to the prices of the products oered in market t are given by equation ( 8), for all j ∈ J t . We can stack the rst order conditions to get the following matrix/vector equality:

s t + ∆ t [p t -mc t ] = 0 Jt , (C.1)
where s t and mc t are vectors collecting the market shares and marginal costs, respectively, of products oered in market t. The matrix ∆ t is of dimension J t × J t and holds own-and cross-price derivatives, with

∆ kl,t =          ∂s lt ∂p kt if k, l ∈ J f t , 0 otherwise. (C.2)
Observe that s t , ∆ t depend on the product attributes of all products proposed in the market, including the prices and the marginal cost of each product depends on its attributes. When one knows the demand function and the marginal cost, the price can be derived from looking at the xed point of equation (C.1). For example, assume that in market t, one rm oers products 1 and 2 and another rm oers product 3, the prices of these three products solve the following FOC system (omitting the product attributes): When setting the prices of its products, rm 1 takes p 3 as "given" and endogeneizes the impact of a change in p 1 on both s 1 and s 2 . It does not take into account the impact of p 1 on s 3 . When setting the price of product 3, rm 2 only solves one equation:

s 3 + ∂s 3 ∂p 3 (p 3 -mc 3 ) = 0.
Supplementary Appendix -page 2

Figure 1 :

 1 Figure 1: Networks of American Airlines (AA) and US Airways (US) (2011)

Figure 2 :

 2 Figure 2: Networks of Merged Entities Before and After Merger

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3: Distribution of estimated Marginal Costs for direct ights of US and AA pre and post-

IV 1 :

 1 Instrument set for 2011 used in the main specication IV 2: Instrument set for 2011 without interaction variables IV 3: The three instruments which are used in common for both 2011 and 2016 IV 4: Instrument set for 2016 used in the main specication IV 5: Instrument set for 2016 without interaction variables

  p 1 , p 2 , p 3 ) s 2 (p 1 , p 2 , p 3 ) s 3 (p 1 , p 2 , p 3 ) p 1 , p 2 , p 3 ) ∂s 2 ∂p 1 (p 1 , p 2 , p 3 ) 0 ∂s 1 ∂p 2 (p 1 , p 2 , p 3 ) ∂s 2 ∂p 2 (p 1 , p 2 , p 3

Table 14 :

 14 The mean values for the price and number of stops are weigthed by the number of passengers.Number of stops varies between zero and one due to sample selection. Connections is the maximum number of connections at the segment endpoints (origin and destination). Product share is the market share among the ying options, excluding the outside option. Market prices by scenario and market structure in 2011

	A.1 Tables
	Note that in the following tables, AA stands for American Airlines, UA stands for United Airlines,
	US stands for US Airways, DL stands for Delta Airlines, WN stands for Southwest and LCC stands
	for all the other carriers.
		Table 1: Product-level descriptive statistics
	Variable	Mean (2011) std dev. (2011) Mean (2016) std dev. (2016)
	Price (100 USD)	1.94	0.97	1.82	0.91
	Number of Stops	0.15	0.34	0.12	0.32
	Connections (100)	0.34	0.14	0.36	0.15
	Distance (1000 miles)	1.06	0.78	1.09	0.77
	Product share	0.37	0.14	0.34	0.13
	Observations	17540		19295
	Notes:

Table 15 :

 15 Market consumer surplus by scenario and market structure in 2011

	Market structure 2011 Change 2011-2016		Changes in%
			Scenario 1	Scenario 2	Scenario 3	Scenario 4
			Changes in	AA and US	AA updates its	Competitors
			preferences and	merge	network	update their
			marginal costs			networks
	Overall
		+14.35%	+6.67%	-0.27%	+1.23%	+6.18%
	AA and US present
	3 rms	34.96%	+8.02%	-0.05%	+9.49%	+14.17%
	4 rms	24.68%	+8.90%	-0.41%	+4.22%	+10.31%
	5 rms	15.86%	+5.08%	-0.31%	+1.14%	+9.35%
	AA or US present
	1 rm	18.67%	+35.78%	0.00%	+12.44%	-22.27%
	2 rms	1.40%	+19.64%	0.00%	-0.04%	-15.21%
	3 rms	3.49%	+19.33%	0.00%	-3.36%	-10.26%
	4 rms	-2.83%	+11.32%	0.00%	+0.15%	-12.84%
	None present
	None present	-16.66%	+17.18%	0.00%	+3.42%	-31.23%

(a) Network of AA (2011) (b) Network of US (2011)

Table 16 :

 16 Demand-side variables with dierent instruments: year 2011

		OLS	IV 1	IV 1	IV 2	IV 3	IV 4	IV 5
	Mean utility
	Intercept	-5.137	-3.332	-4.184	-3.306	-3.004	-3.357	-2.597
		(0.037) (0.187)	(0.117)	(0.190)	(0.685)	(0.196)	(0.320)
	Price	-0.299	-1.723	-1.484	-1.742	-1.938	-1.703	-2.203
		(0.008) (0.120)	(0.094)	(0.121)	(0.469)	(0.124)	(0.211)
	Stops	-0.959	-1.397	-1.620	-1.369	-1.218	-1.320	-1.015
		(0.023) (0.056)	(0.047)	(0.056)	(0.163)	(0.056)	(0.082)
	OriginConn	2.206	3.721	3.154	3.807	4.379	3.878	5.152
		(0.062) (0.289)	(0.238)	(0.292)	(1.024)	(0.296)	(0.478)
	Distance	-0.189	-0.293	0.434	-0.291	-0.301	-0.307	-0.315
		(0.028) (0.060)	(0.048)	(0.060)	(0.069)	(0.059)	(0.072)
	Distance2	0.057	0.224		0.226	0.258	0.228	0.300
		(0.007) (0.024)		(0.024)	(0.069)	(0.024)	(0.037)
	Nesting	0.637	0.711	0.734	0.704	0.675	0.686	0.635
	Parameter (λ)	(0.003) (0.014)	(0.012)	(0.014)	(0.071)	(0.024)	(0.035)
	Carrier FEs
	AA	0.305	0.356	0.313	0.358	0.383	0.364	0.416
		(0.024) (0.047)	(0.043)	(0.048)	(0.063)	(0.047)	(0.058)
	DL	0.125	0.150	0.144	0.154	0.156	0.154	0.159
		(0.020) (0.039)	(0.036)	(0.040)	(0.043)	(0.039)	(0.048)
	US	0.203	0.620	0.591	0.623	0.661	0.605	0.711
		(0.023) (0.049)	(0.044)	(0.049)	(0.110)	(0.049)	(0.066)
	WN	-0.342	-0.896	-0.802	-0.910	-1.030	-0.917	-1.190
		(0.021) (0.073)	(0.063)	(0.074)	(0.246)	(0.075)	(0.118)
	LCC	0.662	-0.030	0.040	-0.026	-0.058	0.020	-0.098
		(0.026) (0.056)	(0.049)	(0.056)	(0.141)	(0.058)	(0.084)
	Statistics
	J-statistic	N/A	4.433	8.8314	0.410	0.0379	45.480	0.359
	Degree of overidentication N/A	5	5	3	1	4	2
	Ftest Price	N/A	54.8	66.8	76.7	105.0	84.7	93.5
	Ftest Nest share	N/A	847.12	853.5	1098.8	938.1	505.9	715.5
	Elasticities
	Own-price elasticity		4.17	3.510	4.24	4.86	4.22	5.78
	95% CI		(3.56,4.80)	(3.07,3.98)	(3.63,4.87)	(2.19,8.42)	(3.45,4.99)	(4.41,7.39)
	Con. semi-elasticity		0.615	0.656	0.608	0.573	0.597	0.517
	95% CI		(0.584,0.639) (0.634,0.674) (0.577,0.634) (0.472,0.611) (0.567,0.623) (0.456,0.558)
	Scenario 1
	∆ Price		-6.73%	-6.64%	-6.65%	-5.55%	-7.01%	-4.33%

See also https://money.cnn.com/2013/11/12/news/companies/us-airways-american-airlines-antitru st/index.html.

It can be downloaded from https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/by/bontemp s/bontemps_remmy_wei_suppl_mat.pdf

See the website, https://www.transtats.bts.gov

Aircraft with the US Airways livery ceased to y in October 2015.

We keep the metropolitan areas with population over one million inhabitants.

A direct ight has a path length of one, a connecting ight, through a hub, a path length of two.

As for Tables4 and 5, we do not report the betweenness as it does not provide any noteworthy information.

We have not been able to nd strong statistical evidence after the analysis of our estimated results. See subsection 5.3, last paragraph.

In the following x t , p t and ξ t denote the vector of collected x jt , p jt and ξ jt , across all inside products proposed in market t.

The condence intervals are calculated by simulating 1000 draws of the parameter θ d from its asymptotic distri-

These tables are available upon request directly from the authors.

See Berry and Jia (2010), Section V.C .

An interesting avenue for future research would be to investigate whether any cost savings have been realized later.

We would like to thank the Guest Editors and two anonymous referees for helpful comments. Special thanks to Sara Crompton Meade and Mariane Bontemps for proofreading. Funding from the French National Research Agency (ANR) under the Investments for the Future program (Investissements d'Avenir, grant ANR-17-EURE-0010) is gratefully acknowledged.

Supplementary Appendix -page 4

However, its market share, s 3 , depends on the prices of all the products proposed in the market (here p 1 , p 2 and p 3 ).

In Scenario 2, we simulate the case were both AA and US are merging. Imagine AA is rm 1 in the example above and US is rm 2, the new entity needs to take into account that, when it changes p 1 , it impacts s 1 , s 2 , like before, but, also s 3 . The new equilibrium prices satisfy the following system:

Therefore, for this counterfactual, we need to update the matrices ∆ t for all markets and solve for the new equilibrium prices using xed-point algorithms.

C.2 Estimation procedure

We estimate the demand and supply-side jointly using the Generalized Method of Moments (see [START_REF] Hansen | Large Sample Properties of Generalized Method of Moments Estimators[END_REF]. Since we employ a nested logit model on the demand side, estimating both sides jointly comes at a negligible computational burden. We form moments that are interactions of the demand-and supply-side shocks with exogenous instruments introduced above.

On the demand side (see equation ( 6)), the linearity of the system allows us to express the unobservable ξ jt as a function of the demand parameters θ d and the explanatory variables. We then obtain the moment conditions by interacting the resulting demand-side unobservables with instruments:

where z d jt is a k 1 × 1 vector of instruments. On the supply-side (see equation ( 9)), the supply-side unobservable ζ jt , is the dierence between the implied marginal costs from equation ( 8) and their deterministic part, w jt θ s . We can then form moment conditions in the same way we did on the demand side:

where z s jt is a k 2 × 1 vector of instruments, in fact the product attributes. We build sample analogs of the moment conditions by averaging rst across products within a given market and then across markets:

Supplementary Appendix -page 5 with θ = (θ d , θ s ). ḡ(θ) is a (k 1 + k 2 ) × 1 vector of means. The GMM objective function to be minimized (with respect to θ) is a distance of ḡ(θ) to 0, i.e.:

f (θ) = ḡ(θ) Ωḡ(θ),

with Ω a positive denite weighting matrix. We employ a two-step procedure in which we obtain a rst set of estimates using an initial weighting matrix (the identity) before getting the nal set of estimates using an estimate of the optimal GMM weighting matrix. Supplementary Appendix -page 6