Savings That Hurt: Production Rationalization and Its Effect on Prices

Savings that hurt: Production rationalization and its effect on prices

Item Type Article

Authors Varela, Mauricio; Viswanathan, Madhu

Citation Varela, M, Viswanathan, M. Savings that hurt: Production rationalization and its effect on prices. J Econ Manage Strat. 2019; 1– 26. https://doi.org/10.1111/jems.12330

DOI 10.1111/jems.12330

Publisher WILEY

Journal JOURNAL OF ECONOMICS & MANAGEMENT STRATEGY

Download date 10/10/2021 16:39:26

Item License http://rightsstatements.org/vocab/InC/1.0/

Version Final accepted manuscript

Link to Item http://hdl.handle.net/10150/634956 Savings that Hurt: Production

Rationalization and its Effect on Prices*

Mauricio Varela Department of Economics, University of Arizona 1130 E Helen St, Tucson, AZ 85721

E-mail: [email protected]

Madhu Viswanathan Department of Marketing, Indian School of Business 1130 E Helen St, Tucson, AZ 85721

E-mail: [email protected]

September 1st, 2019

Running Head: Savings that Hurt

*We thank Stan Reynolds, Mark Walker and three anonymous reviewers for useful comments. All errors are our own. Abstract

Post-merger scenarios often lead to reallocation of resources and production across the

merged entity. Production rationalization, the process of reallocating production across facil-

ities so as to reduce total costs, results in ﬁrms equating marginal costs across markets. This

results in marginal costs, and hence prices, being higher in some markets and lower in others

than otherwise would be without production rationalization. This paper proposes a model of

competition that elicits these effects and the resulting consequences on consumer and producer

surplus. The paper also presents empirical evidence to show that production rationalization, in

the form of ﬂeet reoptimization, affected prices following the US Airways/American Airlines

merger. Prices of the merged ﬁrm increased 10% on routes typically served by US Airways

relative to routes typically served by American Airlines, and by 12% relative to US Airways’

rivals’ prices. Price-cost regressions conﬁrm such price hikes were likely due to ﬂeet reopti-

mization.

Keywords: production rationalization, merger effects, cost synergies, American Airlines

JEL Classiﬁcation: D40, L11, L40, L93 1

1. Introduction

Mergers often lead to large scale reallocation of resources and production across the merged enti- ties. This process, production rationalization, wherein the merged firm reoptimizes over both its previous and newly acquired resources, can lead to dramatic changes in both the internal operations of the firm as well as market outcomes. While scholars have extensively focused on identifying ways to optimally allocate resources and in general believe that such optimal reallocation leads to efficiency gains, there is very little study on the impact of such reallocation on consumers.

To illustrate why consumers may not necessarily gain from these reallocations and subsequent cost efficiencies, consider our context; the US Airways - American Airlines merger, wherein production rationalization in the form of fleet reoptimization occurs. Prior to the merger, US Airways utilized a fleet of fuel efficient Airbus aircraft for domestic operations. In contrast, American Airlines utilized the gas-guzzling McDonnell Douglas MD80s in addition to their fuel efficient Boeing aircraft. If US Airways had some under utilization in the operation of its Airbus aircraft, the merger would allow American Airlines to tap into US Airways’ underused fleet, retiring some MD80s and saving costs for the merged firm. Given the aggregate scale of the two airlines, it is possible that the number of consumers who could be served with the more efficient airplanes exceeds the available number of fuel efficient airplanes. In other words, it is entirely possible that the marginal consumer for American Airlines would continue to be served with MD80s while the marginal consumer for US Airways would now be served with MD80s instead of Airbus aircraft. Thus, the marginal cost of serving a US Airways customer would have increased, while the marginal cost of serving an American Airlines customer would have remained the same. Crucially, as prices are determined by the marginal consumer, prices for US Airways’ customers would have risen while prices for American Airlines’ customers would have remained flat, negatively affecting some consumers without benefiting others.1

How does production rationalization affect consumers? This is the question that we seek to answer in this paper. To do so, our paper develops a stylized model that formalizes the effects of production 2 rationalization on prices and uses this framework to guide an empirical analysis of production rationalization in the airline industry. In particular, we develop a stylized model to show how, due to the US Airways - American Airlines merger, production rationalization in the form of ﬂeet reoptimization could have increased prices for some customers without signiﬁcantly decreasing prices for others. We then empirically test the predictions from our stylized model using price and cost data for the US domestic airline industry.

Our empirical strategy consists of two steps. First, we use a Difference-in-Difference estimator to test for price changes before and after the merger. We find prices of the merged firm (i.e. AA/US) increased 10% more on predominantly US Airways routes2 than on predominantly American Air- lines routes. In addition, merging parties’ prices increased approximately 12% more than rivals’ prices on predominantly US Airways routes while prices increased only 6% more than rivals’ on predominantly American Airlines routes. We take this as strong evidence that the merger resulted in prices increasing for US Airways’ customers. Second, to show that such price increases were due to production rationalization, we correlate prices with the operating costs of McDonnell Dou- glas MD80s and Airbus A319s aircraft and find prices of the merging parties on predominantly US Airways routes track the costs of the A319 more closely than those of the MD80 prior to the merger, and vice-verse after the merger. In contrast, prices on predominantly American Airlines routes track the costs of the MD80 more closely than those of the A319 both pre- and post- merger. We take the reversal in the relationship between the operating costs of aircraft and price as strong evidence that production rationalization, in the form of fleet reoptimization, caused some of the price increases on US Airways’ operations and no price effects on American Airlines’ operations.

While we have focused on a merger scenario, production rationalization is not limited to mergers. Firms constantly reallocate resources, facilities and technologies in response to changes in supply, demand, regulatory, and technological conditions. Changes in trade deals, investments in infras- tructure, expansions in input markets, all facilitate production rationalization by making it easier for ﬁrms to move inputs across facilities. Identifying the impact of production rationalization in many of these circumstances is more challenging as reallocations and responses to changes are 3 more gradual. In contrast, mergers offer an ideal context to assess the impact of production rationalization due to the magnitude of changes and the relatively short duration these changes take to realize.

Our paper is mostly related to the literature on merger efficiencies and, to a lesser extent, to that on multi-market competition. Most literature on merger efficiencies focuses on the type and size of efficiencies that mitigate consumer welfare loss from reductions in competition. For example, see Farrell and Shapiro (1990) for the size of marginal cost efficiencies, Werden and Froeb (1998) on how merger efficiencies constrain future entry, and Stennek (2004) on information transfer as a form of efficiencies. This paper differs from Farrell and Shapiro (1990) and subsequent work in that it explores how variable cost synergies in and of themselves can be detrimental to consumers, absent any market power effects. Of course, increased market power would only exacerbate the welfare concerns described in this paper.

The literature on multi-market competition focuses on how cross-market supply spillovers (e.g. Bulow et al. (1985)) or conduct spillovers (e.g. Bernheim and Whinston (1990)) affect market outcome, with empirical work3 focusing mainly on showing how increases in multi-market contact increased collusive behavior between competitors. Our paper provides an alternate mechanism (production rationalization) to explain increases in prices that does not rely on competition. In particular, we argue that a merger generates the opportunity for rationalizing production across markets. Even if there are no reductions in competition, this rationalization has effects on the marginal cost of production in every market, altering prices, rivals’ responses, and consumer welfare.

The paper also adds to the growing empirical literature that evaluates merger effects post facto, and particularly in the airline industry (Luo (2014), Goolsbee and Syverson (2008), Kwoka and Schumilkina (2010), Gayle (2008), and Kim and Singal (1993)). Peters (2006) shows how price changes for five different airline mergers were mostly due to changes in unobserved costs (inferred from pricing decisions), and not so much as changes in market structure. Werden et al. (1991) specifically compares price changes following the Northwest-Republic and TWA-Ozark mergers across routes that suffered loss of competition relative to those that did not. They find prices 4 increased on select routes that did not suffer loss of competition. Unfortunately, as the main focus of their paper were routes that did suffer loss of competition, the authors do not explore further plausible causes for such price increases. Our paper provides one possible explanation for their findings.

Finally, the airline industry has been vastly used to illustrate various cross-market effects, including multi-market contact (e.g. Evans and Kessides (1994) and Ciliberto and Williams (2014)), density economies (e.g. Brueckner and Spiller (1994)), hub dominance (e.g. Borenstein (1989)), and endogenous network formation (e.g. Bamberger et al. (2004)). We add to this literature by detailing how production rationalization affects prices.

Our paper has implications for academics, public policy experts, and practitioners. For academics and policy experts, our study suggests that appropriate attention should be given to the impact of production rationalization and other multi-market externalities in merger analysis. The following quote summarizes the current position of the U.S.’ antitrust authorities on cost efﬁciencies accruing due to a merger.

“The Agencies have found that (...) efficiencies resulting from shifting production among facilities formerly owned separately, which enable the merging firms to reduce the incremental cost of production, are more likely to be susceptible to verification and are less likely to result from anti-competitive reductions in output.” U.S. Department of Justice and Federal Trade Commission (2010)

According to this, the Agencies (the FTC and the DOJ) give positive credit to efficiencies that are merger-specific and likely to result in reductions of incremental costs. They explicitly state that “shifting production among facilities formerly owned separately” are more likely to be credited than other forms of efficiencies. We suggest caution when analyzing such efficiencies, as production rationalization may result in higher incremental costs for some consumers, even though it results in lower incremental costs for others. Similarly, potential merging parties are cautioned against ignoring how savings in one market can be offset by higher costs in other markets.4 In particular, firms should deliberate the profitability of such cost efficiencies, as the resulting higher marginal 5 cost that one of the two merging parties incurs will result in lower profits for that firm, partially offsetting the profit gains accrued to the other firm (cf. Salant et al. (1983)).

The rest of the paper is organized as follows. In the following section we propose a simple theoretical model that formalizes how fleet reoptimization in the airline industry results in firms equating marginal cost across markets and how allowing for such production rationalization affects costs and prices. A more general model that formalizes these ideas to arbitrary industries is presented in the appendix. Section 3 explores evidence of price changes in the US airline industry following the American Airlines - US Airways merger and relates such price changes to the aforementioned theoretical model. Section 4 discusses briefly the implications for policy and firm behavior. Con- clusions follow.

2. The theory behind production rationalization

2.1 Production rationalization at its core

We first present a stylized model of airline pricing that illustrates how production rationalization can lead to higher prices and lower consumer welfare. Section A in the appendix extends this model to a more general setting and validates the main points discussed here. Before we proceed, it is useful to think of what can be considered demand and marginal cost in the airline context. In the airline industry, aggregate ‘output’ for flights is usually measured in seat-miles (total miles flown by each aircraft, weighted by the available seats on that aircraft). Airlines can affect the seat-miles for a particular market by adding more flights, by replacing the aircraft flown with larger aircraft, and by increasing flight distance (e.g. connecting at a farther hub). Of these, the most preferred and effective production lever that is available to airlines is to increase the number of flights.5 Thus the marginal cost of serving a market can be effectively seen as the marginal cost of adding an additional flight.

Consider a setting with two ﬁrms, American Airlines (AA) and US Airways (US), each operating as monopolists6 in distinct national markets. Let the demand for ﬂights for US Airways and American 6

Airlines be given by, respectively, DUS(p) = a− p and DAA(p) = s(a − p). Here, s captures Amer- ican Airlines’ relative higher demand from serving more and larger routes. To generate sales, firms must fly passengers over certain distances. Let US Airways’ cost of flying a passenger one mile be given by c, capturing the operating costs of flight –e.g. fuel, wages, maintenance, and selling costs.

Assume American Airlines’ costs are slightly higher, c + ∆, in accordance with American Airlines having an older, more inefficient, fleet. Additionally, assume that if US Airways were to merge with American Airlines, US Airways’ fleet would have a capacity limit of k seat-miles, capturing the maximum utilization achievable by the union of both firms. Finally, assume that prior to the merger neither airline is constrained by fleet limitations: both firms can add more flights if they so wished. That is, we assume US Airways has enough planes to serve its own consumers, but not sufficient to serve both its own and AA’s consumers.

Prior to the merger, firms maximize profits independently in each market. Equilibrium prices, quantities, and profits are:

a + c a − c a − c2 p? = D? = π? = (1) US 2 US 2 US 2 a + c + ∆ a − c − ∆ a − c − ∆2 p? = D? = s π? = s (2) AA 2 AA 2 AA 2

To ground the example with industry data, note American Airlines’ 2016 operating costs for the MD80 series were, on average, 9.0 ¢/seat-mi. In contrast, operating costs for the A319 series were

7.7 ¢/seat-mi.7 Hence, let c be 7.7 and ∆ be 1.3. In addition, route-level elasticity has been estimated to be, on average, −2.8 Therefore, we calibrate a by using optimal pricing to back out each market’s elasticity, i.e. equating the Lerner index to the market elasticity, and solving for the value of a that makes the average of these elasticities, weighted by equilibrium sales, equal to −2. We calibrate s, the relative higher demand for American Airlines, by setting the ratio of equilibrium sales equal to the ratio of the carriers’ 2013 domestic sales: 73.4 billion passenger-miles for American Airlines compared to 48.9 for US Airways. Finally, we calibrate k, US Airways’ ﬂeets’ 7 capacity limit should they merge with American Airlines, by dividing US Airways’ pre-merger equilibrium sales over a utilization rate of 70%. This utilization rate is calculated as the ratio of US Airways’ 2013 ‘passenger-miles-per-aircraft-days’ for their A319 aircraft, 364,000, to the 75th percentile value among rivals’ A319 aircraft, 518,000. That is, it is the ratio of how much US Airways used its A319s relative to industry standards. In summary, the model primitives are

c = 7.7 ∆ = 1.3 a = 17 s = 1.75 k = 6.6 (3)

Let us now consider how market outcomes change once the carriers merge. The merger allows American Airlines to tap into US Airways underutilized fleet. In order to accommodate this, we extend firms’ choices to include fleet allocations. Let qUS and qAA be the seat-miles of each carriers’ fleet that is allocated for use. The carriers’ joint problem is:

max DAA(pAA)pAA + DUS(pUS)pUS − cqUS − (c + ∆)qAA (4) pAA,pUS,qAA,qUS≥0

s.t. qAA + qUS ≥ DAA(pAA) + DUS(pUS) ; qUS ≤ k

The problem has two constraints in addition to the non-negativity constraints. The first constraint determines the firm must allocate sufficient aircraft to fulfill demand.9 The second constraint is the capacity limit on US Airways’ fleet. To characterize equilibrium outcomes using FOCs, let λD and λk be the Lagrangian multipliers on these two constraints, let λAA and λUS be the Lagrangian multipliers on the two non-negativity constraints for quantity, and define marginal revenue in terms

∂ ∂ of quantity: µi(p) ≡ ∂ p (Di(p) · p)/ ∂ p Di(p). We ignore the non-negativity constraints on price, as any price above c is better than one below it. Therefore, the equations that deﬁne an equilibrium 8 are:

µAA − λD = 0 −c + λD − λk + λUS = 0 qAAλAA = 0

µUS − λD = 0 −c − ∆ + λD + λAA = 0 qUSλUS = 0 (5)

(k − qUS)λk = 0 (qAA + qUS − DAA − DUS)λD = 0 (λD,λk,λAA,λUS) ≥ 0

It is immediate from these equations that ﬁrms equate marginal revenue across markets: µAA =

λD = µUS. As ﬁrms are free to allocate aggregate production, qAA + qUS, to any market, ﬁrms can always increase sales in one market by reducing sales in the opposite market and transferring the excess production. Thus, sales in one market serve as the opportunity cost of sales in the other market, making it optimal to equate marginal revenue across markets.

In addition, if any of American Airlines’ fleet is used (i.e. if qAA > 0), firms equate marginal revenue of both markets to American Airlines’ marginal cost and US Airways’ fleet is used in its entirety: i.e. if qAA > 0 then λAA = 0, which in turn implies λD = c+∆ and λk = ∆+λUS, the latter a strictly positive value. The intuition is that firms prefer to use the low-cost aircraft first, and once those are fully utilized, tap into the high-cost aircraft. The more interesting finding is that marginal revenue in both markets is set as if marginal cost for both markets are that of the high-cost aircraft. As all low-cost aircraft is utilized first for serving inframarginal consumers, the marginal consumer in both markets is now served with the expensive aircraft. Thus, production rationalization causes prices to rise in the US Airways market and to stay constant in the American Airlines market.

Insert Table 1 around here.

Table 1 summarizes prices, quantities, profits, and consumer welfare with and without production rationalization. As prices are unaltered in the American Airlines market, consumer surplus there is unaffected by the merger. However, production rationalization results in a 6% price increase in the US Airways market, and this price hike depresses consumer welfare in that market by 27%. The firms benefit from the merger, with joint profits increasing 8%, equivalent to 18% of US Airways’ 9 pre-merger profits. The profit increase is limited by US Airways’ excess aircraft prior to the merger, which is not very large: US Airways’ utilization rate was as high as 70% and served less customers than American Airlines. This means the joint firm was able to save ∆ on only 17% of the firms’ pre-merger sales, and a tad more from adjusting price in the US Airways market to account for the joint firm’s new high marginal cost.

Importantly, this example shows how a merger that has no unilateral effects and has substantial, merger-specific, variable cost efficiencies, efficiencies that could be labeled as cognizable efficiencies under the FTC Horizontal Merger Guidelines, can result in substantial consumer welfare loss. This merger scenario would receive little scrutiny from regulators based on current practices as horizontal effects are unlikely –the merging firms do not compete in the same market– and the merger presents significant cognizable efficiencies. In other words, the merging parties could credibly suggest that, by increasing the utilization of US Airways’ efficient fleet, American Airlines could reduce operating costs by 4%,10 and that these savings would likely be passed on to consumers as they are on variable costs. What the analysis ignores is that it is marginal cost that affects pricing decisions, not variable costs. Thus, our key contention is that assessing the benefits of production rationalization on consumers must follow a marginal cost analysis.

The above stylized model illustrates how prices can weakly increase in all relevant markets due to production rationalization. However, it is also possible that production rationalization results in prices decreasing in some markets and increasing in others, or even prices weakly decreasing in all markets. Surely, if US Airways’ fleet had not been constrained, post-merger prices would have decreased on American Airlines’ market and those on US Airways’ market would have remained unchanged, as the joint firm’s marginal cost would be that of US Airways’ fleet.

In the appendix we use a more generalized model to show how, in the presence of diseconomies of scale, production rationalization causes firms to equate marginal revenue across markets, marginal cost across production facilities, and marginal revenue to marginal cost. The key intuition is that if firms could freely move inputs from one market to another, the benefits of selling those inputs in one market would be the opportunity cost of selling them in another, thus making it optimal to 10 equate marginal revenue across markets. In addition, all facilities that rationalize production ought to be operating at the same marginal cost, else it would be optimal to reshuffle production from high marginal cost facilities to low marginal cost ones. In summary, when considering the effects of production rationalization on prices, it is important to consider how reshuffling of production will (weakly) lower marginal costs at high-cost facilities and (weakly) increase marginal cost at low-cost facilities. Hence, prices will (weakly) decrease for consumers previously served from the former and (weakly) increase for consumers previously served from the latter.

3. US Airways - American Airlines merger effect on prices

3.1 A brief on the US Airways - American Airlines merger

US Airways was a major U.S. airline that merged with American Airlines in December of 2013. Initially announced the previous February, the merger allowed American Airlines to emerge from bankruptcy. The Department of Justice issued a complaint against the merger on the grounds that it would facilitate coordinated effects among industry players and reduce competition at select airports (e.g. Washington Reagan, LaGuardia, etc.). However, the DOJ reached a settlement with the merging parties in November of 2013 in which the merging parties would divest landing slots and gates at select airports as a way of decreasing barriers to entry for low cost carriers (cf. United States Disitrict Court for the District of Columbia (2014)). The merging parties ﬁnalized consol- idating operations in April of 2015, when they obtained a Single Operating Certiﬁcate from the FAA.

Prior to the merger, US Airways’ domestic fleet consisted of more fuel efficient aircraft than Amer- ican Airlines’. Specifically, US Airways’ mainline, narrow-body, fleet consisted of 93 Airbus A319s, 75 Airbus A321s, 72 Airbus A320s, and 56 other aircraft, with an average age of 11 years. In contrast, American Airlines’ mainline, narrow-body, fleet consisted of 195 Boeing 737s, 191 McDonnell Douglas MD-80s, and 106 Boeing 757s, with an average age of 14 years. US Air- ways Corp, including US Express, also operated 26 twin-aisle aircraft, 67 regional jets, and 44 11 turbo-props. AMR, including American Eagle, also operated 122 twin-aisle aircraft, 245 regional jets, and 9 turbo-props (cf. US Airways Group, Inc. (2013) and AMR Corporation (2013)). The merging parties viewed the merger as a way of optimizing fleets, calling for the “Right Aircraft in the Right Place at the Right Time [sic]” (AMR Corporation and US Airways Group, Inc (2013)) creating $550M in cost synergies, a 21% increase over the combined firms’ 2013 operating profits (cf. American Airlines Group, Inc (2014)).

The above statements strongly suggest the merging firms wanted to increase utilization of less expensive aircraft and decrease utilization of expensive aircraft. More importantly, it lends credence to our argument that fleet reoptimization could have changed the marginal aircraft for US Airways operations from a low-cost aircraft (e.g. A319) to a high-cost aircraft (e.g. MD80) and that this increase in marginal cost would result in an increase in prices. Our empirical strategy explores this hypothesis. Briefly, we follow a two stage procedure wherein, in the first stage, we show that prices for US Airways did increase because of the merger. Following that, in the second stage, we show that these price increases are related to the marginal cost increases that result due to the merger. A description of data and our measures follows.

3.2 Data

Sources. Our data is obtained from three different sources. First, we use data from the Bureau of Transportation Statistics’ (BTS) Airline Origin and Destination Survey (DB1B database), which contains a 10% sample of all itineraries sold for domestic flights in the US. The data is reported quarterly, and we obtain data from the first quarter of 2010 up to the fourth quarter of 2017. We aggregate up the itineraries to the carrier-route-quarter level and define a route as a unidirectional city pair. As a carrier can serve a route through multiple flight structures (e.g. non-stop flight, one-stop flight connecting at X hub, one-stop flight connecting at Y hub, two-stop flights, etc.), we aggregate only the itineraries that were served with the modal flight structure. We do, however, take total sales regardless of flight structures when calculating shares.11 In addition, we drop observations for which the modal flight structures involved two or more connections. The unit of observation is 12 a carrier-route-quarter triplet: e.g. American Airlines’ offering between Tucson and Miami on the third quarter of 2014. The data contains information on passengers flown, the average price12 paid per passenger, and the flight structure: non-stop or connecting.

Second, we additionally use the Air Carrier Statistics database (T-100 Segment). This data contains, at the monthly level, the number of seats assigned and passengers flown by each carrier’s aircraft class on each (directional) airport pair. An aircraft class is a manufacturer-model pair: e.g. 737-400, 737-800, A320-100/200, etc. We calculate load factors by dividing passengers flown over seats assigned, and calculate the percent of passengers who are flying internationally by differencing passengers reported in the T-100 with those reported in the DB1B (scaled appropriately to account for the 10% sampling) and dividing by the former. The Air Carrier Statistics data is then aggregated to a carrier-route-quarter and merged onto the DB1B data. The DB1B data reports two carriers: an operating carrier, responsible for operating the flight, and a ticketing carrier, responsible for sales of the ticket. The DB1B is aggregated to the carrier-route-quarter level utilizing the ticketing carrier. However, the identity of the modal operating carrier is retained, and it is on this modal carrier that we match the T-100 data. In doing so, we record the modal aircraft class used on each flight leg of each route and the average load factor and percent of passengers who are flying international on those legs. As connecting service has two flight legs, we retain the maximum load- factor across the two legs and average the percentages of international passengers across the two legs.

Lastly, we incorporate cost information using the BTS’ Form 41 - Financial Data, Schedule P.5.2. This data reports, at the quarterly level, domestic operating costs and statistics for each carrier and for each aircraft class. From this data we retain operating costs per hour of airtime, by quarter, carrier, and aircraft class, where operating costs include costs of crews, fuel, maintenance, depreci- ation, and rental equipment. We merge the Schedule P.5.2 cost data with the T-100 data, which has information on air time and on ﬂying distance, and obtain quarterly operating costs per passenger- mile, for each carrier and each aircraft class.

Having obtained quarterly operating costs per passenger-mile, we merge the data onto the T-100 13 dataset and multiply it by travel distance to obtain the average operating cost per person, specific to each flight reported in the T-100. Then, as with the load factor data, we merge this per-person operating cost onto the DB1B data to obtain each carrier’s cost of serving a passenger on each route. For connecting service, we add the operating cost across both flight legs. Thus, our finalized data set has, for each carrier-route-quarter triplet, information on average price and operating cost, total sales, load factors, percent of international passengers, aircraft class, and connecting hub city (when relevant). Importantly, the operating cost measure is the cost of the modal aircraft class assigned to that route, and not necessarily the operating cost of the marginal aircraft.

As the DB1B is an extensive data set with many charter carriers, executive jets, and freight carriers, we retain all observations from American, Alaska, Jet Blue, Continental, Delta, Frontier, Air Tran, Allegiant, Spirit, United, US Airways, Southwest, and Virgin America, and drop observations from any other carrier. Further, we restrict our focus to the largest 10,000 routes. To illustrate the inclusivity of this sample deﬁnition, note that the two smallest routes retained are Iowa City, IA to Fargo, ND and Portland, OR to Tyler, TX. No carrier offers non-stop service on either of these routes, which have an average of 330 quarterly passengers.

We consider a carrier to be active on a route at a certain quarter if the carrier ﬂies at least a thousand passengers or has at least 15% market share in that quarter. 1,000 passengers over a quarter is equivalent to 80 weekly passengers, barely enough to justify a single weekly ﬂight on a regional jet. It is important to note that we do take these offerings into account when calculating market shares.

Route classification. In our analysis, we want to distinguish how the American Airlines / US Airways merger affected prices for US Airways relative to American Airlines. The challenge in conducting this analysis is that in the years that follow the merger, US Airways ceases to exist, and its operations are taken over by American Airlines. To have a yardstick on how prices of the merged firm changed on its US Airways operations, we classify routes according to which of the two merging parties had a more dominant position on that route prior to the merger. Specifically, 14 we use 2013 yearly sales to calculate the Herfindahl index for each route, and the projected change in such index that a merger between US Airways and American Airlines would have implied. Any route in which this projected change is larger than 100 points is classified as a Joint route. For the remaining routes, any route in which US Airways’ share is larger than the average share (i.e. sUS > 1/N) and American Airlines’ share is less than the average share is classified as a US Airways route. Conversely, routes in which American Airlines’ share is larger than the average share and US Airways’ share is smaller than the average share is an American Airlines route. Routes in which neither carrier had shares larger than the average share is classified as a Non-Served route. With this route classification we are able to follow how the merging firms’ prices changed after the merger on routes that were typical US Airways routes (e.g. Phoenix-Vegas), compared to prices on routes that were typical American Airlines routes (e.g. Chicago-Miami).

Measures of price. We use the average price per passenger as our main measure of price, and the log of this price as our main alternative measure. These are also used in other academic papers and allows for straightforward interpretation. We do not use yield, another measure of price that is commonly used in this context, as the merger could have induced yield to increase without having any signiﬁcant effect on price by simply reducing the travel distance of connecting passengers. This can occur by having passengers connect at a different hub (e.g. having a passenger ﬂying from Tucson to San Diego connect in Phoenix instead of Denver). We are able to replicate our results using yield as a measure of price but choose not to pursue this measure to avoid concerns about the impact of network reoptimization on price measures.

US/AA prices. We refer to the merging ﬁrms’ prices as US/AA prices, after the carriers IATA abbreviations. When referring to US/AA prices on US Airways routes, however, we refer solely to US Airways’ prices pre-merger, and American Airlines’ prices post-merger. Although American Airlines’ may have had, on these routes, some sales pre-merger, American Airlines’ prices are excluded. Similarly, when referring to US/AA prices on American Airlines routes, US Airways’ pre-merger prices are excluded. This strategy removes potential noise from sporadic sales when 15 analyzing US/AA prices. For Joint routes, pre-merger prices of both carriers are retained as two separate observations.

Descriptives. There are three key assumptions that underpin our theoretical framework. First, airlines, after a merger, optimize their fleets by reallocating aircraft across routes. Second, prior to the merger, US Airways’ and American Airlines’ ‘marginal’ aircrafts were the A319s and MD80s, respectively. After the merger, the joint firm’s ‘marginal’ aircrafts were MD80s. Third, the merging firm could better utilize the A319 fleet relative to US Airways’ utilization of it, allowing for substi- tution from MD80s to A319s. We now provide descriptive evidence from our data which supports these three assumptions.

Insert Figure 1 around here.

Figure 1 shows the aircraft assignment by American Airlines and US Airways pre merger and that of American Airlines post merger. The bars reflect how many seat-miles were flown by each aircraft class in a given quarter and the grayed area shows the merging period (2014Q1 - 2015Q2). As the figure shows, prior to the merger, American Airlines routes were served primarily with B737s and MD80s, both traditional American Airlines’ aircraft. However, after the merger, these routes were also served with A319s and A321s, two traditional US Airways’ aircraft. Moreover, US Airways’ routes too experienced an increase in American Airlines aircraft, the B737, after the merger. These facts are suggestive that production rationalization, in the form of fleet reoptimization, was taking place.

Insert Figure 2 around here.

Aircrafts’ operating cost, in terms of per seat-mile and per ﬂight-hour, are depicted in Figure 2. Apparent from these ﬁgures is the MD80’s and the A319’s high per-passenger operating cost. In the years following the merger, the operating cost of the MD80 is ~10¢ per seat-mile and that of the A319 is ~0.5¢ less. In comparison, the next highest cost aircraft are the B737, B757, and 16

A320, all of which have similar costs of approximately 7.5¢. The figure also illustrates great temporal variation, both in per-se operating costs as well as in the difference in operating costs across aircraft. To understand from where these cost differences arise, Table 2 shows the aircrafts’ 2016 operating costs, broken down by major cost factors. Not surprisingly, fuel is the primary cost factor and differs significantly across aircraft due to differences in fuel efficiency, aircraft size, and aircraft utilization (e.g. long-haul vs short-haul). Both the A319 and the MD80 have the highest fuel costs; the A319 due to the airplanes’ small size, a typical configuration seats 124 passengers; and the MD80 due to technological inefficiency, it has the highest per-hour operating cost when compared to similarly sized aircraft like the A320 and B737.13 However, the ‘Other’ category also accounts for significant cost variation across aircraft. This category summarizes insurance costs and interchange fees, i.e. the cost of temporarily leasing the aircraft from a third party, among other things. That the MD80 has the highest costs in the ‘Other’ category is indicative that it is the ‘riskiest’ of aircraft and that carriers lease it often, both of which are suggestive that it is indeed used as a marginal aircraft.

Insert Table 2 around here.

In support of our third assumption, namely that US Airways was underutilizing their A319 fleet relative to its potential under the merged firm, Figure 3 depicts the number of days an aircraft is assigned for work, as well as how many passenger-miles such aircraft flew per workday. One can interpret these plots as showing, respectively, the extensive and intensive margins of aircraft utilization. It is clear from the figure that the A319 fleet is used more extensively, both on the extensive and the intensive margin, after the merger. In contrast, the MD80 is used less after the merger, although most of this decreased usage is driven by increased B737 and A321 usage: American Airlines’ fleet renewal project.

Insert Figure 3 around here. 17

3.3 The effect of the merger on prices

3.3.1 US Airways’ prices vs American Airlines’ prices

In this ﬁrst analysis, we explore if the merging ﬁrms’ prices on US Airways routes increased after the merger relative to prices on American Airlines routes.

Insert Figure 4 around here.

Figure 4 shows the price of the merging parties over time, by route type, after controlling for variation due to seasonality and persistent route differences, centered at average values. As is apparent from the ﬁgure, the difference in prices on US Airways routes and prices on American Airlines routes increased after the merger, and prices on Joint routes decreased while those on US Airways routes held steady.

We formalize the above figure using a difference-in-difference estimation. The first difference compares prices before and after the merger. The second difference compares prices across route types: Joint routes, US Airways routes, and American Airlines routes (omitted category). All Non- Served routes are excluded from the estimation sample, as neither carrier was a competitive player on those routes the year prior to the merger and, hence, it is uncertain how they are pricing those routes, neither before nor after the merger. The merging period is also excluded from the sample, as it is unclear to what extent the merging parties were coordinating operations during this time. Additionally, for most specifications, we exclude routes that in 2013 were served with regional jets and turbo-props, e.g. Phoenix-Tucson.14 This focuses the analysis on routes where we expect to see the highest substitutability between A319s and MD80s.

The exact empirical speciﬁcation is

priceirt = α1 ·USr · postt +α2 ·Jointr · postt +α3 ·USr +α4 ·Jointr +α5 · postt +α6 ·xirt +εirt (6)

where priceirt is carrier i’s price, American Airlines’ or US Airways’, on route r in quarter t. 18

USr and Jointr are dummy variables indicating US Airways routes and Joint routes, respectively. postt is a time dummy for all quarters after the merger: 2015Q3 and onward. xirt are a set of controls for costs, demand, and market power. Specifically, we include the following variables which vary separately for each route, carrier, quarter triplet: the operating costs for the modal aircraft used on the route, a dummy for non-stop service, a US Airways fixed effect,15 a dummy for American Airlines’ during their bankruptcy period (2012Q1-2013Q4), load-factor, the percentage of passengers flying international, the incremental travel distance relative to the shortest available option, the incremental travel time relative to the fastest available option, the carrier’s market share at the connecting hub (if relevant) and at endpoint cities, the number of non-stop routes the carrier offers from the connecting hub and from the endpoint cities, and the connecting hub’s and endpoint cities’ share of the carrier’s nationwide enplanements. Additionally, we include controls that vary only at the route-quarter level: the Herfindahl index, the number of carriers, of non-stop carriers, of low-cost carriers (all carriers excluding United , Delta , Continental , and Alaska ), and of potential entrants (carriers with flights at both end-points of a route but no service on the route itself); and the log of population count, employment count, income per capita, GDP in the leisure sector, and employment in the leisure sector. For all variables pertaining to endpoint cities, e.g. population count, we average the values across the two endpoint cities to obtain a single measure per route. Summary statistics of these control variables are given in Table B.1 in the appendix.

In addition to the aforementioned controls, various specifications includes fixed effects for routes, quarters, and the modal aircraft used on the route. We have included such extensive controls so that the estimated effects of the merger on prices, α1, α2, and α5, are most likely driven by unobserved shifts in marginal cost as opposed to other observed factors. Of course, it is also of interest to estimate the effect of the merger on prices overall, irrespective of the mechanism by which prices shifted. Hence, in presenting our results, we also include a subset of specifications with no controls at all. These are indeed the specifications of interest under the assumption that changes in market power and other observed factors are driven by the resulting changes in marginal costs from production rationalization. 19

A positive value on α1 is indicative that prices of the merged firm increased on US Airways routes relative to American Airlines routes following the merger. Table 3 shows the results from these regressions. Depending on the specification, following the merger, average price on US Airways routes increased between $4 and $30 more than what prices on American Airlines routes increased. The results are statistically significant across most specifications, including those with no additional controls and those with the most extensive set of controls. They are also large: a price increase of $28, the estimate from column 3, is equivalent to a 10% increase, twice the 5% SSNIP benchmark used in antitrust to flag a merger as potentially harmful to consumers (cf. U.S. Department of Justice and Federal Trade Commission (2010), section 4.1.2). The specification in the last column uses yield as the dependent variable and there too does the merger appear to induce a 1.3 cent increase in yield, equivalent to a 5% increase, on US Airways’ routes over American Airlines’ routes.

Insert Table 3 around here.

The estimates for Joint routes appear to reflect a positive, but small, price increase following the merger. One would have expected prices to increase on these routes as the merger increased the merging firm’s market power. However, the remedies requested by the DOJ for merger approval should have mitigated, and possibly even negated, this increased market power. The largest price increase estimated, relative to American Airlines’ routes, is of $17, or equivalently, 6.5% (specification VI). Other specifications estimate a price increase of 4% (specification VIII), a negative price change (specification IV and V) or even no statistically meaningful price changes (specifications IX and X). This is suggestive that the DOJ remedies were effective at restricting increases in market power due to the merger.

3.3.2 US Airways’ prices vs rivals’ prices

The above analysis showed that US/AA prices on US Airways routes increased after the merger relative to prices on American Airlines routes. However, such price changes could have resulted 20 from prices decreasing for the American Airlines operations of the joint ﬁrm, as American Airlines was emerging from bankruptcy with renewed cost structures (e.g. new union contracts). They could have also resulted from differential changes on US Airways routes relative to American Airlines routes that were unrelated to the merging ﬁrms’ actions. For example, these are years of growth for international travel and American Airlines’ network was more focused on international travel than US Airways’.

Insert Figure 5 around here.

To explore if prices did in fact increase for the US Airways operations of the joint firm, we compare post-merger changes in prices of the joint firm to those of rival firms, focusing on US Airways routes.

Figure 5 shows the merging firms’ prices over time on US Airways routes. It also shows the average price of rival carriers, segmented by low-cost-carriers and rival legacy carriers, on those same routes. As with Figure 4, we plot the residuals from a regression of price on quarter and route- carrier fixed effects to control for variation from seasonality and long-run differences specific to each route-carrier pair. The figure shows that US/AA prices held steady after the merger while rival firms’ prices were declining.

As before, we formalize the above analysis with a difference-in-difference estimation. However, to adequately compare price shifts relative to rivals’ and to include all information regarding the merging firms’ prices, we use a triple difference analysis (i.e. a DIDID). Specifically, we compare prices before and after the merger, as they differ between the merging parties and their rivals, contrasting the effects across the three route categories: US Airways routes, American Airlines routes, and Joint routes. Our DIDID specification is:

priceirt = β1 ·USAAi ·USr · postt + β2 ·USAAi · Jointr · postt + β3 ·USAAi · postt (7)

+ β4 ·USAAi ·USr + β5 ·USAAi · Jointr + β6 ·USr · postt + β7 · Jointr · postt (8)

+ β8 ·USAAi + β9 ·USr + β10 · Jointr + β11 · postt + β12 · xirt + εirt (9) 21

where priceirt is carrier i’s average price on route r at time t. The dummy variable USAAi equals one whenever the carrier i indexes US Airways or American Airlines. All rival carriers form the omitted category (i.e. control group). As before, we segment the effects according to route type, where USr is equal to one whenever the route is a US Airways route, Jointr is equal to one whenever the route is a Joint route, and the American Airlines routes form the omitted category. Also, as before, we exclude Non-served routes, the merging period, and routes that the merging parties served with regional jets or turbo-props in 2013. xirt are the same control variables as before. Importantly, for a subset of specifications, the control variables include route by quarter fixed effects. These fixed effects capture all price variation that is common across all carriers on the same route and in the same quarter, such as the effects from shifts in market power, entry, and exit, and therefore, all remaining price variation is that of price differences between carriers serving the same route.

A positive value on β1 is indicative that the merging ﬁrms’ prices rose relative to rivals’ more on US

Airways routes than on American Airlines routes. In addition, positive value on β3 is indicative that prices of the merged firm rose relative to rivals on American Airlines routes. The value by which the merging firms’ prices rose relative to rivals’ on Joint routes is computed as the sum of β2 and β3. Notice that under the assumption that rivals react to firms’ price hikes with a measured response, i.e. the reaction is less than one-to-one to the initiating firm’s price hike, the estimated values of β1,

β2 and β3 are lower bounds on the true price increase induced by the merger. The estimated values, shown in Table 4, show the merging firms’ prices rose, relative to rivals’, between $5 to $20 more on US Airways routes than on American Airlines routes, depending on the specification. The estimated values also show the merging firms’ prices rising above rivals’ across all markets, with prices on American Airlines routes rising between $10 and $25 above rivals’ price changes, as given by the ‘USAA × post-merger’ estimates. These increases are statistically significant and economically large: given an average per-passenger price of $250, these price increases are indicative of a 12% price increase on US Airways routes and of a 6% price increase on American Airlines and Joint routes, and even then would only be a lower bound on the true price increase. Importantly, that the merging firms’ price increase over that of rivals’ is largest on US Airways routes is suggestive 22 that fleet reoptimization following the merger is likely to have increased the merging firms’ cost of serving US Airways routes, over and beyond other cost shifts affecting all markets equally (e.g. new union contracts, fuel contracts, financial costs, etc.).

Insert Table 4 around here

3.4 Price-Cost Correlations

As is clear from the past two analysis, prices of US/AA on US Airways routes increased after the merger: they increased relative to the merging firms’ prices on non-US Airways routes and they increased relative to competitors’ prices on US Airways routes. Our model’s conjecture is that marginal costs for US Airways’ operations increased due to the reoptimization of fleets such that the marginal cost of adding an additional flight changed from being that of an A319 to that of an MD80. In order to show that fleet reoptimization leads to changes in price, we examine the relationship between the operating costs of A319s and MD80s with price. Our rationale for this test is that the merging firms’ marginal cost on US Airways routes should have shifted from that of the A319 to that of the MD80. Given the size of American Airlines compared to US Airways, it is very likely that US Airways’ fuel efficient aircraft were not sufficient to replace all of American Airlines’ MD80 fleet while still serving US Airways’ own customers Thus, examining the relationship between operating costs and price pre/post merger could provide insight on whether these price changes reflect marginal cost changes.

In particular, we use cost information to test whether the merging ﬁrms’ prices on US Airways, and US Airways’ pre-merger prices and American Airlines’ post-merger prices on Joint routes, follow the operating costs of the A319 better than they follow the operating costs of the MD80, and how 23 that relationship changed after the merger. Speciﬁcally, we estimate:

A319 MD80 pricert = γA319,pre · crt pret + γMD80,pre · crt · postt (10)

A319 MD80 + γA319,post · crt pret + γMD80,post · crt · postt

pst + γpost · postt + γx · xrt + εrt

A319 MD80 where crt and crt are the merging firms’ average operating costs per passenger for the respective aircraft class, route, and quarter. They are calculated by multiplying the hourly operating cost of the aircraft with the average flight time of the specific route. pret and postt are dummies for the time periods pre- and post- merger. xrt are the same control variables as before. Importantly, these control variables include the operating costs of the modal aircraft flying the route. Hence, a positive

A319 MD80 estimate on either crt or crt is indicative that ﬁrms price each route in accordance with the costs of the marginal aircraft: adding an additional ﬂight requires either adding a marginal aircraft to this route, or reallocating an inframarginal aircraft from another route and adding a marginal aircraft to said route, therefore increase total costs by those of the marginal aircraft.

As done previously, the estimation sample excludes the merger period and routes that the merging parties served with regional jets or turbo-props in 2013. Although the sample includes both US Air- ways and Joint routes, it focuses only on US Airways’ prices in the pre-merger period, i.e. excludes American Airlines prices on Joint routes prior to the merger. It is possible that the inclusion of Joint routes may cause concern, as the post-merger period fuses together ‘would-be US Airways prices’ and American Airlines prices. To mitigate this concern, we also test the above regression limiting the sample to solely US Airways’ routes, therefore capturing exclusively how costs correlate with US Airways prices prior to the merger, and ‘would-be US Airways prices’ after the merger.

Insert Table 5 around here

The results, presented in Table 5, show US Airways’ pre-merger prices followed more closely costs of the A319 (i.e. US Airways’ ‘marginal’ aircraft) than those of the MD80 (i.e. American Airlines’ 24

‘marginal’ aircraft). As shown in Table 5 - Specification (III), a one dollar increase in the per- passenger-cost of operating an A319 is correlated with a statistically significant $3.25 increase in the per-passenger-price. In contrast, a similar increase in the cost of operating an MD80 is associated with a decrease in price of $1.17. Interestingly, after the merger period, the merging firms’ prices are positively correlated with the MD80’s cost and completely uncorrelated, economically, with the costs of the A319. Columns (IV), (V), and (VI) replicates columns (I), (II), and (III) using a log-log specification16 instead of a linear-linear specification and the results are qualitatively the same: pre-merger, a one percent increase in the costs of the A319 is associated with a 0.53 percent increase in price; a pass-through of 53 percent. In summary, prior to the merger, prices on US Air- ways routes tracked closely the costs of the A319 but switched to tracking the costs of the MD80s post-merger in accordance with our propositions.

3.5 Alternate Explanations and Robustness Checks

Route Classification: It is possible that the way we classified our routes could have led to our findings. To ensure that this is not the case, we tested two alternate route classification rules. First, we re-classified routes as being an US Airways route if it is not a Joint route, US Airways had at least 5% market share in 2013, and US Airways’ market share was larger than American Airlines’. Sim- ilarly, a route is classified as an American Airlines route if it was neither a Joint nor a US Airways route and American Airlines had at least 5% market share. Under the previous route classification, we had required US Airways’ and American Airlines’ market shares to be larger than the average market share, as opposed to 5%, to be classified as the respective carrier’s route. This change re-classified many routes from being a Non-Served route to being either a US Airways or an Amer- ican Airlines’ route, therefore changing the estimation sample significantly. It did not, however, change the conclusions from the empirical exercise: prices of the merging firms increased more on routes typically served by US Airways than on routes typically served by American Airlines, and such prices on the former routes increased more than rivals’ prices’ increased on such routes. Secondly, instead of classifying routes as US Airways’ routes (the ‘treated’ group) and American 25

Airlines’ routes (the ‘control’ group), we run a regression of price on the difference in US Airways’ 2013 market share relative to American Airlines’, interpreting this difference as a ‘treatment intensity’. The results from these regressions continue to support the overall message that prices of the merging ﬁrms increased more on routes predominantly served by US Airways than on routes predominantly served by American Airlines. The regression results from these tests are detailed in Appendix Tables B.2 and B.3.

Spurious Correlations: It is possible that our finding between the costs of the different aircraft and prices on US Airways’ routes could be due to some spurious correlations. To negate this possibility and to provide a falsification exercise, we repeat the exact same analysis except that we change the estimation sample to be prices of the merging firms on American Airlines’ routes. According to our theory, if prices are indeed being affected by marginal costs and these costs track that of the MD80, we should expect no changes in the relationship between costs of different aircraft on prices on American Airlines’ routes pre- and post-merger. The results, shown in Tables 5, show exactly that. In particular, we find that on American Airlines’ routes, the merging firms’ prices follow more closely the costs of the MD80, both before and after the merger, than the costs of the A319.

Demand externalities: It is possible that our finding on prices is correlated with the value provided by the jointly merged firm. For example, prices could have increased if the American Airlines’ fre- quent flyer program creates more value for customers than US Airways’ program, and the merged firm adjusted prices to account for such. Similarly, one can think of other value enhancing activities created by the joint firm that can also predict an increase in price. We refute this explanation two ways. First, demand externalities explain increases in price but not the relationship between price and cost. Second, our specifications include a vast set of controls that account for these factors. The estimates on these control variables are economically and statistically significant, indicative that they are indeed appropriately controlling for many such forces.

Cost externalities: It is possible that costs for US Airways could have gone up because of its association with American Airlines. For example, if US Airways’ operations inherited American Airlines’ union contracts and these union contracts increased costs for US Airways operations. 26

Similar to our strategy on demand externalities, we refute this explanation in two ways. First, cost externalities can explain the increases in price but not the relationship between price and operating costs of the A319 and MD80. Second, many regressions include controls for costs of the aircraft used to operate the route, in the form of direct cost estimates as well as aircraft specific fixed effects. Our main findings are not altered by the inclusion of such controls –see, for example, columns 3 and onward in Table 4 and columns 3 and 6 in Table 5.

Aircraft Configuration: It is possible that the jointly merged airlines reconfigured aircraft on US Airways routes, resulting in higher average prices. For example, American could have introduced more first class seats on the routes formerly operated by US Airways routes making them more costly to operate. To rule out this reasoning, we redid our estimations using the median price on the route, as opposed to the average price. We find that our results are consistent with previous findings: cf. columns 7 and 10 of Tables 3 and 4, respectively.

Collinearity issues: It is possible that our regressions are subject to collinearity issues. Hourly operating costs of the MD80 and of the A319 vary over time, but not across routes. As the cost measures included in the price-cost regressions multiply these hourly operating costs by the travel time and these regressions include route fixed effects, most of the variation in these cost measures arise from temporal variation in the hourly operating costs. It is possible the regressions are subject to multi-collinearity issues as there are only ten post-merger quarters and three post-merger variables capturing this temporal variation: MD80 cost x Post-merger, A319 cost x Post-merger, and Post-merger. To address this concern we build four different cost variables, and have non-nested tests dictate which of these four cost variables best fit the pricing data. The first two cost variables

A319 MD80 are simply the cost of the A319 over time and the cost of the MD80 over time: crt , crt . The third cost variable follows the cost of the A319 up to the merger, and that of the MD80 after the merger. The fourth does the opposite:

A319/MD80 A319 MD80 crt = crt (1 − postt ) + crt postt (11)

MD80/A319 MD80 A319 crt = crt (1 − postt ) + crt postt (12) 27

For each one of these variables, and for each of the samples studied, we run the OLS regression:

ν pricert = ην crt + ηpost postt + ηxxrt + εrt (13)

ν where crt is one of the four cost variables and xrt contains the same controls as before.

A319/MD80 Using the regression results, we test whether the model with crt outperforms the other models in terms of ﬁt. Speciﬁcally, we use Vuong (1989)’s likelihood ratio test for non-nested models. As the tests assume log-likelihoods, we assume the error term is distributed normal and

MD80/MD80 calculate the corresponding log-likelihoods. We also test if the model with crt outperforms the other models. Results are presented in Tables 6 and 7.

Insert Table 6 around here

Insert Table 7 around here

As suggested, when fitting prices on US Airways’ routes, the model in which costs are those of the A319 prior to the merger and those of the MD80 after the merger outperforms all other models. It is the model with the highest R-sq and likelihood ratio test confirms that it outperforms all other models. Interestingly, when fitting prices on American Airlines routes, the model in which costs are those of the MD80 both before and after the merger is the one which best fits that data.

4. Discussion

These tests confirm our hypothesis that the merged firms’ prices on US Airways routes increased after the merger, mostly due to the reallocation of aircraft, in which the marginal aircraft for US Airways’ operations became the MD80. The price increases are large, between five and fifteen percent, and consumers are likely to have been affected. A formal estimate of the potential consumer welfare loss needs, at a minimum, a model of demand, and, preferably, a model of supply, so as to include how rivals’ react to the merged firms’ pricing strategies. These models involve complex 28 data processing and, more importantly, strong modeling and identifying assumptions. As welfare calculations are susceptible to such assumptions, we prefer to leave that exercise to future research. That said, the price increases estimated in our paper are considerable – for comparison, the FTC’s SSNIP test flags any price increase of more than five percent as potentially anti competitive.

The purpose of this exercise was to show how production rationalization across merging parties may result in lower average costs for the merging parties but in higher marginal costs for a subset of the merging firms’ production facilities. Many proposed mergers present, to both investors and regulators, production reallocation synergies as one of the key benefits of the merger. We caution both investors and regulators that while such production reallocation can decrease average cost, it can increase marginal cost and this increase in marginal cost may place the merging firm at a disadvantage relative to rivals, resulting in higher prices and lower sales.

Finally, the merger effects proposed here are a subset of cross-market dynamics that have become common as ﬁrms globalize. It is surprising that there is very little research about the beneﬁts and harms that may come to consumers from such cross-market dynamics, including diseconomies of scope (Bulow et al. (1985)), multi-market contact (Bernheim and Whinston (1990), Arie et al. (2017)), and the effects presented here.

5. Conclusion

This paper contains a simple but largely ignored notion: production rationalization decreases marginal costs in high-cost markets and increases it in low-cost markets.. Mergers whose efﬁ- ciencies (a.k.a. synergies) are based on such rationalizations may be beneﬁcial to the merging parties but detrimental to consumers, even if there are no shifts in market power.

The US Airways/American Airlines merger provides a great example of how such rationalization can negatively affect consumers while positively affect the merging parties. As US Airways operated more efﬁcient aircraft than American Airlines prior to their merger, the merger allowed the merging parties to better utilize such efﬁcient aircraft but altered US Airways’ marginal cost from 29

that of a lower-cost aircraft (the A319) to that of a higher-cost one (the MD80). Our empirical analysis shows that this resulted in prices of the merging ﬁrm rising 10% more on US Airways’ routes than on American Airlines’ routes and 12% more than rivals’ prices on US Airways’ routes. Such price hikes are higher than the 5% threshold commonly utilized by the antitrust agencies in determining potentially anti-competitive mergers.

When promoting mergers, ‘synergies’ tend to be highly invoked but much less understood. This paper takes on one such synergy, production reallocation, and illustrates how it affects both firm profits and consumer welfare. The paper pin-points how such synergy could have come about in the US Airways/American Airlines merger and the effect it had on prices. It would be of great value to businessmen and regulators alike to see clear examples of other synergies at play, including increasing economies of scale, know-how diffusion, and information benefits.

Finally, we suggest some caution in interpreting the large welfare losses suggested by our (ex- tremely) simplified model of competition in section 2.1. This is because consumers may have responded to the price increase by switching to more affordable rival carriers and not by leaving the industry as our simplified model suggests. More importantly, American Airlines has initiated a massive fleet renewal project in an effort to retire its MD80 fleet. As American Airlines renews its fleet and its marginal aircraft becomes either a Boeing-737 or an Airbus A319, consistent with our theory, we should expect prices to decrease, potentially to pre-merger levels.

Notes

1Of course, the alternate scenario is also possible wherein the number of fuel efﬁcient aircraft exceeds the number of consumers. This would consequently decrease prices for American customers while retaining prices for US Airways’ customers, making some consumers better off while not affecting others. The example above simply illustrates an extreme event wherein some consumers are negatively affected by production rationalization while others are not beneﬁted by it.

2A predominantly US Airways route is a route that, in the year prior to the merger, US Airways’ 30

share was larger than the average market share of competitors, and for which the expected effect of the merger on the Herﬁndahl index was of less than a 100 point gain.

3See, for example, Heggestad and Rhoades (1978); Evans and Kessides (1994); Gimeno and Woo (1999); Parker and Roller (1997); Jans and Rosenbaum (1997); Fernandez and Marin (1998); Pilloff (1999); Young et al. (2000); Bilotkach (2011); Feinberg (2015); Ciliberto and Williams (2014) for studies on the airline, banking, telecommunication, cement, software, hotel, and cooking oil industries.

4It is incorrect to assume production rationalization is always good for the rationalizing ﬁrms. The ability to rationalize production implies the inability to commit certain cost structures to certain markets. A ﬁrm facing a high cost rival in one market and a low cost rival in another market may prefer to have low cost of supplying the former market and a high cost of supplying the latter market instead of having a medium cost of supplying both markets.

5Firms cannot easily increase ‘output’ by replacing aircraft with a larger aircraft, as factors such as the aircrafts’ range, maintenance base, and crews’ home city are important in determining which aircraft to allocate to each market. In addition, increasing flight distance increases firms’ operating cost per passenger and decreases their value for the flight, therefore providing a poor mechanism to increase ‘output’.

6We assume ﬁrms do not overlap to avoid confounding effects from increased market power with those from production rationalization. It is perfectly feasible, and likely, that US Airways over- lapped with American Airlines on a subset of markets prior to their merger. We also assume monopolist ﬁrms to abstract from rivals’ strategic responses. The intuition and results below do not hinge on either of these two assumptions and the generalized model in the Appendix relaxes the latter, among other things.

7Operating costs per aircraft type were obtained from the Bureau of Transportation Statistics’ Fi- nancial Data (P.5.2 Schedule), from which a cost per hour of ﬂight was calculated. Using the same agency’s T-100 Segment data, we obtained available seat-miles and total ﬂight hours, by aircraft 31

class. Merging these two data sets we obtain each carriers’ operating cost per available seat-mile, by aircraft class. Operating costs are deﬁned as the sum of total costs from ﬂight operations and from direct maintenance.

8Cf. InterVISTAS (2007) and the literature referenced therein.

9We have assumed carriers must allocate sufficient flights to satisfy demand. Alternatively, we could have assumed a rationing rule that would specify which customers get turned away when firms fail to satisfy demand. However, in the absence of strategic rival interaction, the same equilibrium outcomes arise under all rationing rules.

10 pre Cost savings would be calculated as the variable cost savings on the slack capacity (i.e. k − DUS ∆ = pre 2.6), and pre-merger operating expenses would be (c + ∆) · DAA = 63.

11Only 12% of passengers were served with non-modal ﬂight structures.

12We drop observations for which average prices are outrageous –below $25 dollars or above $2,500 dollars.

13The MD80, B737, and A320 seat 143, 147, and 150 passengers, respectively, in a typical 2-cabin conﬁguration.

14To be precise, we exclude routes whose modal aircraft is not in the Airbus’ A319, A320, A321 and A330 families, in Boeing’s 737, 757, and 767 families, not in McDonnell Douglas’s MD80 and MD90 families.

15This fixed effect is separately identified from the route-class fixed effects in that the sample includes two observations for each joint route in the pre-merger period, one for US Airways and one for American Airlines. Therefore, the US Airways fixed effect captures the average price difference US Airways had relative to American Airlines prior to the merger.

16For speciﬁcations that measure price in logs, as opposed to levels, the respective cost measures are also included in logs as opposed to levels, including the operating cost of the modal aircraft used on the route, whenever relevant. 32

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Table 1: Equilibrium prices, quantities, profits, and consumer surplus for the illustrative example Pre-merger Post-Merger Market Price Sales Profits C.S. Price Sales Profits C.S. US 12.3 4.6 21.6 11 13 4.0 8 53.5 AA 13 7.0 28 14 13 7.0 14 Notes: Prices are in cents per seat-mile. C.S. is consumer surplus. Quantity, profits, and consumer surplus are shown per-unit of US Airway’s market size. This is a hypothetical example and no values are representative of actual behavior.

Table 2: Operating costs per seat-mile (cents) and utilization, 2016 Seat-mi Aircraft Class Fuel Wages Maint. Other Total / day A321 (US) 2.08 1.83 1.71 1.00 6.62 780 A320 (US) 2.47 1.88 1.80 0.77 6.92 506 B757 (AA) 2.42 1.86 1.68 1.20 7.16 662 B737 (AA) 2.14 1.94 1.73 1.47 7.28 616 A319 (US) 2.92 2.08 1.73 0.96 7.69 403 MD80 (AA) 3.43 2.06 1.81 1.64 8.94 393 37 * 1.30 Yield * -0.01 -0.17 0.03 * * Log-Price 0.04 0.10 * * 7.99 26.6 Median * * 30.3 17.2 * * -5.86 * Passenger 4.29 7.01 -6.56 per * * 12.1 28.4 Price * * Avg. 9.26 20.2 * * (I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX) (X) 22.7 Table 3: Merging firms’ prices compared across route types × post- 16.0 routes × routes merger (4.51) (1.77) (2.45) (2.10) (1.57) (2.33) (2.50) (0.01) (0.01) (0.17) post-merger (4.81) (1.95) (2.42) (3.63) (2.13) (2.90) (2.59) (0.01) (0.01) (0.21) Joint US Airways’ No. of ObsAdj. R-sqRoute and quarter f.e.Additional control variablesExclude connecting serviceRestrict to largest 200 routesIncl. routes with regional 40,540 jets 40,540Weight obs. 39,063 using sales 7,314 12,753 70,916 0.04 39,063 Y 39,063 39,063 0.79 39,063 Y 0.78 Y 0.80 Y 0.81 Y 0.71 Y Y Y 0.78 Y 0.77 Y Y 0.86 Y 0.91 Y Y Y Y Y Y Y Y Y Standard errors, clustered at the route type and quarter level, shown in parenthesis. (*) statistically different than zero a a 5% confidence level. Notes: The number of observations dropsSee slightly text when for including list the ofas additional control given control variables. by variables the ‘Restricts due merging to firms’ to the joint missing largest sales values 200 in in routes’ 2013. some retains of only these observations control pertaining variables. to the largest routes of each route type, 38 * * 0.18 1.40 Yield -0.73 * * * Y 0.11 -0.05 * * Log-Price 0.08 0.04 * * 14.5 15.8 Median * * 11.2 13.4 * * 15.1 18.9 * * -5.92 -2.59 -1.57 -2.19 -0.01 -0.05 10.7 14.7 * * * 15.5 Passenger * per 7.72 4.96 10.2 * * Price 14.8 14.4 Avg. * * -2.23 -3.76 -4.02 -10.8 17.6 13.5 * * * 5.72 21.2 7.70 * * * (I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX) (X) (XI) (XII) (XIII) (2.88) (0.94) (1.78) (2.09) (3.68) (2.13) (2.74) (3.24) (1.84) (2.00) (0.01) (0.01) (0.20) Table 4: Merging firms’ prices compared to rival firms’ prices post- 15.4 × post- 10.5 routes × routes Joint post-merger 25.5 US Airways × × × Standard errors, clustered at the quarter and carrier level, shown in parenthesis. (*) statistically different than zero a a 5% confidence level. mergermerger (5.79) (1.42) (3.25) (3.38) (5.20) (5.38) (1.24) (3.68) (2.45) (4.01) (2.55) (4.89) (3.90) (2.84) (2.49) (3.12) (3.12) (3.99) (0.01) (2.25) (0.01) (0.30) (2.40) (0.01) (0.01) (0.21) USAA USAA USAA No. of ObsAdj. R-sqRoute, carrier, and quarter f.e.Route by quarter f.e.Route type by carrier byAdditional aircraft control f.e. variablesOnly routes flown non-stop byUS/AA’s US/AA largest 200 routesRestrict to legacy carriersRestrict to Y largest competitor 98,870 onIncl. route 98,870 routes 98,097 served 91,916 with regional 21,779Weight jets observations 37,728 Y using 0.09 78,051 sales 65,735 162,973 Y 91,916 0.76 91,916 91,916 Y 91,916 0.85 Y 0.84 Y Y 0.84 Y 0.85 Y Y Y 0.82 Y Y Y 0.83 Y Y Y 0.79 Y Y Y 0.83 Y 0.85 Y Y Y 0.91 Y Y 0.91 Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Notes: Estimation sample excludes routes which USjets’ Airways and is American flagged. Airlines ‘Restrict service to with legacycompetitor regional carriers’ jets, on retains except route’ observations when restricts only ‘Incl. pertaining the routessales. to sample served Continental, with See to Delta, regional notes two United, in observations and Table per Alaska 3 route-quarter, Airlines. for the ‘Restrict additional merging to information. firms’ largest data and that of their largest rival, as measured by 39

Table 5: Price-Cost analysis: US Airways’ prices regressed on aircrafts’ operating costs US Airways and Joint routes Price per pass Log-Price (I) (II) (III) (IV) (V) (VI) A319 × pre-merger 7.73* 4.03* 3.25* 0.59* 0.56* 0.52* (0.26) (0.39) (0.50) (0.03) (0.04) (0.05) A319 × post-merger -4.10* -2.60* -2.07* -0.09* -0.12* -0.11* (0.46) (0.46) (0.58) (0.02) (0.02) (0.02) MD80 × pre-merger -1.08* -1.59* -1.17* -0.20* -0.19* -0.19* (0.20) (0.24) (0.32) (0.02) (0.02) (0.03) MD80 × post-merger 11.2* 4.55* 3.60* -0.12* 0.03 0.07 (0.47) (0.48) (0.63) (0.04) (0.03) (0.04) No. of Obs 19,078 18,114 18,114 19,078 18,114 18,114 Adj. R-sq 0.67 0.86 0.87 0.06 0.84 0.86

US Airways’ routes only A319 × pre-merger 7.38* 3.79* 3.22* 0.67* 0.56* 0.53* (0.43) (0.55) (0.63) (0.05) (0.06) (0.06) A319 × post-merger -3.76* -2.40* -2.03* -0.13* -0.13* -0.13* (0.73) (0.74) (0.83) (0.03) (0.03) (0.03) MD80 × pre-merger -1.35* -1.27* -0.94 -0.25* -0.20* -0.19* (0.35) (0.39) (0.49) (0.03) (0.04) (0.04) MD80 × post-merger 10.4* 4.56* 3.83* -0.14* -0.00 0.03 (0.64) (0.76) (0.96) (0.06) (0.05) (0.06) No. of Obs 9,403 9,020 9,020 9,403 9,020 9,020 Adj. R-sq 0.60 0.81 0.83 0.02 0.80 0.81

Route f.e. Y Y Y Y Route-carrier-hub-aircraft f.e. Y Y Additional controls Y Y Y Y Notes: Standard errors, clustered at the route level, shown in parenthesis. (*) statistically different than zero a a 5% conﬁdence level. When Joint routes are included, only US Airways’ prices are retained from the pre-merger period. Cost measure constructed by multiplying aircrafts’ hourly operating cost (in thousands of USD) with the routes’ average ﬂight time (in hours). For the log-price regressions, the log of the cost measures are used as the key independent variables. See text for list of ‘additional controls’. 40

Table 6: Price-Cost analysis: most appropriate cost measure Regressions of price per passenger on cost per passenger US Airways’ routes American Airlines’ routes Cost Variable A319 / A319 / MD80 / MD80 / A319 / A319 / MD80 / MD80 / [Pre / Post] MD80 A319 A319 MD80 MD80 A319 A319 MD80 Estimate 2.05* 1.18* 0.40* 0.63* 1.85* 0.39 0.39 1.19* Std. Error (0.32) (0.27) (0.19) (0.20) (0.38) (0.31) (0.26) (0.28) Adj. R-sq 0.9058 0.9053 0.9049 0.9050 0.8215 0.8208 0.8209 0.8213 Log-LH -83,241 –83,446 -83,496 -83,496 -119,413 -119,455 -119,453 -119,424

Regressions of log-price on log-cost Estimate 0.24* 0.08* -0.02 0.03 0.20* 0.01 0.09* 0.21* Std. Error (0.04) (0.03) (0.02) (0.03) (0.04) (0.03) (0.03) (0.03) Adj. R-sq 0.8500 0.8482 0.8478 0.8479 0.7435 0.7422 0.7427 0.7445 Log-LH 8,246 8,199 8,189 8,190 10,545 10,510 10,522 10,577 Notes: Each column is a regression of the merging firms’ prices on a cost measure composed of a certain aircraft’s operating cost in the pre-merger period and a second aircraft’s operating cost in the post-merger period. For US Airways’ routes columns, only prices of US Airways are included from the pre-merger period and estimation sample includes data from US Airways routes as well as Joint routes. Similarly for the American Airlines’ routes columns. Standard errors, clustered at the route level, shown in parenthesis. (*) statistically different than zero a a 5% confidence level. All regressions include route-carrier-hub-aircraft fixed effects as well as the additional control variables used in the regressions of Table 5. 41

Table 7: Price-Cost Analysis: Z-statistics for row model outperforming column model From regressions of price per passenger on costs per passenger US Airways routes American Airlines routes A319 / MD80 / MD80 / A319 / MD80 / MD80 / A319 A319 MD80 A319 A319 MD80 A319 / MD80 4.88 5.25 5.11 A319 / MD80 3.48 3.46 1.50 A319 / A319 3.83 2.83 A319 / A319 -0.66 -2.82 MD80 / A319 -2.56 MD80 / A319 -3.19

From regressions of log-price on log-cost A319 / MD80 / MD80 / A319 / MD80 / MD80 / A319 A319 MD80 A319 A319 MD80 A319 / MD80 7.50 6.17 7.28 A319 / MD80 5.04 3.88 -5.21 A319 / A319 2.38 2.90 A319 / A319 -3.85 -6.44 MD80 / A319 -0.65 MD80 / A319 -7.03 Notes: Z-statistics derived for non-nested likelihood ratio tests displaying if the row model outperforms the column model. A model is a price-cost regression where the merging ﬁrms’ prices are regressed on the operating cost of a given aircraft in the pre-merger period and the operating cost of an alternative aircraft in the post-merger period. Z-statistiscs ought to be compared to a standard normal distribution: e.g. a value larger than 1.64 should be interpreted that the row model outperforms the column model with a conﬁdence of 95%. The test is symmetric: if the Z-statistic for the row model outperforming the column model is z, then the Z-statistic for the column model outperforming the row model is −z. Therefore, only the upper-triangular matrix of results is shown. See notes in Table 6 for additional details. 42 US Airways’ routes American Airlines’ routes * Joint routes

*y-axis scale differs from previous plots

Figure 1: Aircraft assignment by route classiﬁcation 43

Operating costs per passenger Operating costs per hour of ﬂight

Figure 2: Aircraft operating costs 44

Total ﬂeet usage Utilization no. of days aircraft was in use passenger-miles ﬂown per day of use

Figure 3: Aircraft utilization

Figure 4: Average per-passenger prices of AA/US, by route type 45

Figure 5: Average per-passenger prices on US Airways routes, by carrier class

APPENDIX

A. The Effects of Production Rationalization on Market

Outcomes

We characterize production rationalization in the context of two non-overlapping markets, A and B. Two ﬁrms compete in each market, which we label, with slight abuse of notation, as A, −A, B, and −B. Production rationalization, when feasible, occurs only between ﬁrms A and B. Firm chooses

i prices, pi, and demand is given by D (pi, p−i) for i ∈ {A,−A,B,−B}. In addition to choosing prices, i ﬁrms A and B also choose a production input qi, and incur costs C (qi). We assume inputs match to outputs on a one-to-one basis and that ﬁrms are committed to providing all demanded output.

i Therefore, inputs must exceed outputs: qi ≥ D (pi, p−i). Such commitment may be explicitly enforced –e.g. contractual obligations– or implicitly enforced through, for example, repeated game mechanisms (e.g. costly brand building, repeat purchases, etc.). A more general approach would allow for rationing. However, Davidson and Deneckere (1986) have shown equilibrium outcomes can be highly sensitive to the choice of rationing rule. We assume ﬁrms are committed to supplying 46 demanded output to avoid such concerns, which would only distract from the main discussion on production rationalization.

i i Define revenue in the usual way, i.e. R (pi, p−i) = D (pi, p−i) · pi. The non-rationalizing firms, firms −A and −B, choose price to maximize revenue –for simplicity, we omit any costs for these firms. The rationalizing firms choose prices and quantities to maximize revenues minus costs, subject to supplying the demanded output. Therefore, when production rationalization is infeasible, A and B solve:

i i i maxR (pi, p−i) −C (qi) s.t. qi ≥ D (pi, p−i) i ∈ {A,B} (14) pi,qi

We wish to contrast market outcomes from this setting to one in which production rationalization is feasible. We model production rationalization as a contract between ﬁrms A and B in which A offers

B a payment T in exchange for τ input units. Both T and τ can be negative, i.e. A selling input units to B. We assume this contract is agreed on simultaneously with production and price choices, avoiding issues of double marginalization (cf. Dixit (1983)). Therefore, firm A and B choose prices and production amounts that maximize joint profits, and firm A extracts all incremental surplus through the payment T. As we are interested in market outcomes, we simply characterize the joint- optimization problem. In summary, when production rationalization is feasible, A and B jointly solve:

A B A B max R (pA, p−A) + R (pB, p−B) −C (qA) −C (qB) (15) pA,pB,qB,qA A B s.t. qA + qB ≥ D (pA, p−A) + D (pB, p−B)

qA ≥ 0 qB ≥ 0

Consumer surplus is one of the main market outcomes we wish to contrast. As the setting is one

i differentiated Bertrand, let consumer surplus in a given market be S (pi, p−i) for i ∈ {A,B}, and we make the following assumptions on demand, costs, and consumer surplus: 47

Assumption 1. Demand is twice continuously differentiable, strictly downward sloping in own price, weakly upward sloping in rivals’ price, weakly concave, and has increasing differences in prices. In addition, the own effects of a price change on demand dominate the cross effects for both level and slope. Costs are once continuously differentiable, strictly increasing, weakly convex, and non-negative. Consumer surplus is strictly decreasing in both ﬁrms’ prices.

The critical assumption to the conclusions below is that costs are weakly convex, that is, production is characterized by diseconomies of scale. It is because of these diseconomies of scale that rationalizing ﬁrms want to ‘balance’ production across production facilities. Of the remaining assumptions, only the assumptions on the second derivatives of demand are more restrictive than typical market analysis. Concavity is used to prove existence of a pure strategy equilibria, increasing differences to guarantee prices are strategic complements, and the assumption of own price effects dominating cross effects to guarantee a stable equilibria –i.e. that slopes of reactions curves be bounded below one. It is likely that these assumptions can be relaxed for alternatives that preserve existence of equilibria, strategic complementarity, and equilibrium stability.

Before characterizing the equilibria with and without production rationalization, we brieﬂy intro- duce the notion of marginal revenue in terms of quantity, such that statements of the sort ‘marginal revenue equals marginal cost’ can be easily understood.

i ∂ i ∂ i Deﬁnition 1. Firm i’s marginal revenue, denoted µ (pi, p−i), is given by R (pi, p−i)/ D (pi, p−i) ∂ pi ∂ pi

To distinguish between outcomes when production rationalization is feasible to when it is not, denote with star (e.g. x?) equilibrium outcomes from the game in which production rationalization is infeasible, and with ‘hat’ (e.g.x ˆ) those from the game where production rationalization is feasible.

i ∂ i We also denote with subscripts partial derivatives of functions: e.g. D (pi, p−i) ≡ D (pi, p−i) 1 ∂ pi i ∂ 2 i and D (pi, p−i) ≡ D (pi, p−i). The following lemma characterizes these equilibria. 12 ∂ pi∂ p−i

Lemma 1. When production rationalization is infeasible, there exists equilibria in pure strategies 48 and it is characterized by the following equations:

i ? ? i ? ? i ? ? −i ? ? µ (pi , p−i) = C1(qi ) qi = D (pi , p−i) µ (p−i, pi ) = 0 i ∈ {A,B} (16)

When production rationalization is feasible, there exists equilibria in pure strategies, and there exist non-negative constants λ, λA, and λB such that any pure strategy equilibria is characterized by the solution to:

i i −i µ (pî, pˆ−i) = λ C1(qî) = λ + λi λiqî = 0 µ (pî, pˆ−i) = 0 i ∈ {A,B} (17)

A B λ qˆA + qˆB − D (pˆA, pˆ−A) − D (pˆB, pˆ−B) = 0 (18)

Proof. Absent production rationalization, the ﬁrms’ problems are:

i i Firms A and B : maxD (p, p−i) · p −C(q) s.t. q ≥ D (p, p−i) i ∈ {A,B} p,q

−i Firms − A and − B : maxD (p, pi) · p i ∈ {A,B} p

The rationalizing ﬁrms objective function is strictly decreasing in input, q, while the constraint is strictly increasing in it. Thus, at any optimum, the constraint will hold at equality. Therefore, substitute the constraint directly into the objective function and maximize the objective function on price alone. If an equilibrium exists, ﬁrms’ choices must be optimal, and thus the problems’ FOC must hold:

i ? ? i i ? ? i ? ? −i ? ? R1(pi , p−i) −C1 D (pi , p−i) · D1(pi , p−i) = 0 R1 (p−i, pi ) = 0 i ∈{A,B}

i ? ? −i ? ? Divide each of the two equations by D1(pi , p−i) and D1 (p−i, pi ), respectively, to obtain eq. 16. As demand is strictly decreasing in own price, these divisions are always well deﬁned.

To prove existence of equilibria, note that, as demand is downward sloping and concave in own price, and as costs are weakly convex, ﬁrms A and B’s problems are weakly quasi-concave in 49

i (pi,qi) and the constraint, i.e. qi − D (pi, p−i) ≥ 0, is convex. Therefore, the argmax of each of

A and B’s problems are convex, upper-hemicontinous correspondences of p−i. Similarly, firms −A and −B’s problems are strictly quasi-concave, and thus their respective argmax are continuous functions of pi, and therefore convex, upper-hemicontinous correspondences. As all firms’ best- response correspondences are convex and upper-hemicontinuous, and as prices and production choices can be confined to an arbitrarily large compact set, Kakutani’s fixed point theorem applies and there exists an equilibrium to this game.

When production rationalization is feasible, ﬁrms −A and −B’s problems are as before. In contrast, ﬁrms A and B’s joint problem (P) is

A B A B max R (pA, p−A) + R (pB, p−B) −C (qA) −C (qB) pA,pB,qB,qA A B s.t. qA + qB ≥ D (pA, p−A) + D (pB, p−B)

qA ≥ 0 qB ≥ 0

Note the objective function is weakly quasi-concave and the constraints are convex. Therefore, existence of an equilibria follows from the same arguments as for the game absent production rationalization. Eqs. 17 and 18 are obtained by the theory of Lagrange: if there exists a solution to problem (P), then there exists non-negative constants λ, λA, and λB, such that, for any local maximum of (P), the following holds:

i i i R1(pî, pˆ−i) − λD1(pî, pˆ−i) = 0 −C1(qî) + λ + λi = 0 λiqî = 0 i ∈ {A,B}

A B λ qˆA + qˆB − D (pˆA, pˆ−A) − D (pˆB, pˆ−B) = 0

i Divide the ﬁrst equation by D1(pˆi, pˆ−i) to obtain eqs. 17 and 18.

The intuition behind the above proof is the same as in the illustrative airline example given in section 2.1. As production rationalization allows ﬁrms to increase output in one market by decreasing it in the other, marginal revenue in all markets must be equal. That is, sales in one market serve 50 as the opportunity cost of selling in another. Similarly, marginal cost must be the same across any active facility, otherwise ﬁrms could reduce costs by transferring production from a high marginal- cost facility to a low marginal-cost facility.

The next proposition contrasts outcomes from the two games and is the central argument of this section.

Proposition 1. If, without production rationalization, ﬁrm A’s marginal cost is higher than ﬁrm B’s, allowing for production rationalization results in:

? ? 1. production decreasing in market A and increasing in market B (i.e. qˆA ≤ qA and qˆB ≥ qB)

2. prices decreasing and consumer surplus increasing in market A, with strict changes if CA(·)

? ? is strictly convex on any subinterval of [qˆA,qA] and qˆA < qA.

3. prices increasing and consumer surplus decreasing in market B, with strict changes if CB(·)

? ? is strictly convex on any subinterval of [qB,qˆB] and qB < qˆB.

Proof. To simplify notation, we omit the dependency of functions on prices wherever possible, and we denote with ‘star’ and with ‘hat’ functions evaluated at their respective equilibrium values: e.g. i i ?i i ? î î C1 ≡ C1(qi), C1 ≡ C1(qi ) and C1 ≡ C1(qî). We start by noting, and proving, the following facts:

• Firms −A and −B’s best response functions are increasing in rivals’ price. Speciﬁcally, these ﬁrms’ objective functions are supermodular in own price (trivially), and, by assumption 1,

−i −i −i have increasing differences in rivals price: R12(p−i, pi) = p−iD12 + D2 ≥ 0. Therefore, −i ρ−i(pi) ≡ argmaxp R (p, pi) is non-decreasing in pi.

i i i • Revenue is strictly concave in own price. Taking derivatives: R11(pi, p−i) = piD11 +2D1 for i i i i ∈ {A,B,−A,−B}; and since assumption 1 states D1 < 0 and D11 ≤ 0, then R11 < 0.

−i −i • The slope of ρ (p) is bounded below one. Using the implicit function theorem, ρ1 = −i −i −i −i −i −R12/R11 = − p−iD12 + D2 / p−iD11 + 2D1 , and since assumption 1 speciﬁes own 51

price effects are greater than cross price effects, for both level and slope of demand, then

−i −i −i −i −i D12 < D11 and D2 < D1 , and therefore ρ1 < 1.

• Firm A and B’s marginal revenue, evaluated at equilibrium prices, is strictly increasing i i in equilibrium prices. Using derivatives: d µi(p,ρ−i(p)) = ∂ µ + ∂ µ ρ−i. Expand and dp ∂ p ∂ p−i 1 dµ i i i 2 −i i i −i i i i 2 simplify: dp = 2 − D D11/ D1 + ρ1 D2/D1 − ρ1 D D12/ D1 . Bullet point no. 2 −i i i i i above speciﬁes ρ1 < 1, and assumption 1 speciﬁes D2 ≤ D1 and D12 ≤ D11 . There- −i i i −i i i dµi fore ρ1 D2/D1 > −1 and ρ1 D12 < −D11, which in turn implies dp > 0.

• Firm A and B’s demand, evaluated at equilibrium prices, is strictly decreasing in equilibrium

d i −i i i −i −i i i prices. Using derivatives: dp D (p,ρ (p)) = D1 + D2ρ1 , and as ρ1 < 1 and D2 ≤ D1 , d i −i then dp D (p,ρ (p)) < 0.

? With these facts in mind, we start by proving no. 1. By contradiction, supposeq Â > qA. Since Â ?A marginal cost is increasing in output, it must be that C1 ≥ C1 . Importantly,q Â > 0, and therefore A B Â ?A ?A A ?A µˆ = µˆ = C1 . As the FOCs require C1 = µ , then is must be that µˆ ≥ µ . In addition, the ˆB Â ˆB ?A ?A ?B FOCs also require C1 ≥ C1 , and therefore C1 ≥ C1 . By construction, C1 > C1 , and therefore ˆB ?B ? B Â ?B these inequalities imply C1 > C1 , which in turn impliesq ˆB > qB. Finally, as µˆ = C1 and µ = ?B B ?B A ?A C1 , then µˆ > µ . Taken together with µˆ ≥ µ and the last two bullet points above, this ? ˆ i ?i ? impliesp î ≥ pi and D ≤ D for i ∈ {A,B,−A,−B}. In summary, ifq Â > qA, firms A and B’s joint sales are lower with production rationalization than without, but joint input production is higher.

Therefore, the production constraint holds with slack, λ must be zero, and so too must marginal ˆA ˆA ?B ?B cost: i.e. C1 = 0. However, as C1 > C1 , this implies C1 < 0, contradicting that marginal cost cannot be negative.

? A very similar argument can be used to proveq ˆB ≥ qB. To prove the propositions’ statements on ? ? ˆ prices, note that qA > qÂ implies CA ≥ CA, with strict inequality if CA is strictly convex on any ? ? ? ˆ ? ˆ subinterval of [qÂ,qA]. The FOCs imply µA = CA ≥ CA ≥ µÂ, with strict inequality if CA > CA. As ? ? marginal revenue is strictly increasing in equilibrium prices, µA > µÂ iff pA > pÂ. 52

The assertion on consumer surplus follows directly from the assumption that consumer surplus is strictly decreasing in prices and from the fact that ρ−i(p) is strictly increasing in p.

The intuition for the above proof is straightforward: with production rationalization ﬁrms equate marginal cost across active facilties, thus if, absent production rationalization, A’s marginal cost is high, then with production rationalization, ﬁrms reduce production at A’s facility to decrease marginal cost –recall costs are convex. Because marginal cost is lowered in market A, it is optimal to adjust price accordingly in such market. As prices are strategic complements, rival prices follow suit, also decreasing in market A. The total effect is a decrease in prices and an increase in consumer welfare. Due to the same logic, the opposite effects occur in market B, where production is increased with production rationalization, and therefore so too is marginal cost.

As consumers in market A win and consumers in market B lose with production rationalization, the effect of increased production rationalization on consumer welfare is an empirical question. The proposition does not discuss profits directly, as the effect of production rationalization on profits is unclear. It may seem surprising that the rationalizing firms’ joint profits could decrease due to production rationalization, as the firms’ prior price/quantity choices remain feasible. However, profits may decrease because rivals react to the rationalizing firms’ price changes. Specifically, the fall of marginal cost in the high-marginal cost market generates profit for the rationalizing firm, which they increase even further by adjusting (i.e. decreasing) price in that market. Rivals responds to this price decrease by decreasing prices of their own, and in doing so they hurt the rationalizing firms’ profits. The degree by which the rival adjusts price, and the harm that such adjustment causes, are determined by factors other than those which drive the rationalizing firms’ price, and therefore the harm can be large enough to offset any benefits from rationalizing production. Importantly, the rationalizing firm cannot commit to not adjust price, as holding rivals’ prices fixed it is optimal to adjust their own prices.

There are two assumptions that are key to Proposition 1: diseconomies of scale in input production and the lack of free entry despite inputs being transferred freely across markets. The validity of 53 these assumptions will depend on the specific setting under study. Diseconomies of scale in inputs are very common in manufacturing, driven by capacity constraints and/or scarcity –e.g. limestone, used in cement manufacturing, does not travel far and can be scarce depending on quarry reserves. The more relevant assumption is the free transfer of inputs while direct entry is barred: e.g. firm B can sell inputs to firm A but cannot sell directly into market A. Such situation may be common if there are market-specific fixed costs each firm needs to incur to participate in a given market: e.g. store fronts, advertising, distribution channels, branding, etc. In such situations, market A may not be sufficiently large to accommodate firm B as a new entrant, despite firm B having a cost advantage over firm A. It could also be that complementary inputs required to make sales are not available to firms foreign to the market: e.g. an airline may not have access to gates at a specific airport, despite having spare aircraft available to fly into such airport.

The remaining assumptions are not critical to the main conclusions. Specifically, the rationalizing firms could be direct competitors prior to rationalizing production. In such case production rationalization would not only serve to reduce costs, but would also serve as a coordinating device to monopolize their common market. In addition, the transfer of inputs need not be free. Firms would rationalize production as long as the marginal cost differences between the rationalizing firms are larger than the transfer costs of inputs. Finally, inputs need not map one-to-one into outputs; it is sufficient that the function relating input to output be an increasing, weakly convex function.

B. Appendix Tables

Insert Table B.1 around here

Insert Table B.2 around here

Insert Table B.3 around here 54

Table B.1: Summary statistics of control variables Mean Std. Dev Min Max Price ($) 244 79.3 25.9 1,262 Quarterly sales (’000) 10.5 28.0 0.01 486 Market share (%) 35.5 24.1 0.08 100 Op. Cost ($) 151 81.1 10.0 1,329 Non-stop (0/1) 0.20 0.40 0 1 Distance (’000 mi) 1.57 0.80 0.18 5.43 Rel. travel time (%) 9.65 15.5 0 313 Load factor (%) 82.1 6.52 0.73 100 Percent Intl. (%) 10.5 7.04 0.28 63.4 Market share at endpoints (%) 20.6 12.4 0.33 96.9 Destinations at endpoints (#) 29.0 32.9 2 254 Share of carrier’s sales at endpoints (%) 2.13 2.75 0.03 24.1 Rel. travel distance* 8.16 13.9 0 148 Destinations at hub* (#) 100 33.1 2 144 Market share at hub* (%) 55.9 19.8 0.14 100 Share of carrier’s sales at hub* (%) 15.1 6.70 0.19 33.3 Monopoly market** (0/1) 0.10 0.31 0 1 No. of carriers** (#) 2.82 1.50 1 12 No. of LCC** (#) 0.53 0.82 0 6 No. of non-stop carriers** (#) 0.56 1.23 0 9 No. of entrants** (#) 2.04 1.42 0 10

Mean values of key variables, by route type and merging status US routes AA routes Joint routes US/AA Rivals US/AA Rivals US-pre AA-pre AA-post Rivals Price ($) 246 208 268 253 284 246 279 233 Quarterly sales (’000) 7.32 8.93 3.93 5.97 8.98 16.0 27.1 16.5 Market share (%) 57.8 29.4 55.4 33.3 24.5 32.7 50.1 21.2 Op. Cost ($) 134 123 147 142 208 196 161 156 No. of observations 9,404 13,449 15,354 19,911 5,990 6,318 3,689 24,944 Notes: A unit of observation is a route-carrier-quarter triplet, of which there are 99,119 distinct triplets. (*) Statistics for connecting service only; corresponding to 79,233 observations. (**) Statistics for the route- quarter pair; of which there are 35,240 pairs. 55

Table B.2: Merging ﬁrms’ prices compared across route types Alternative route classiﬁcation Avg. price per passenger Log-price (I) (II) (III) (IV) (V) US Airways’ routes ×post- 20.8* 20.0* 8.6* 0.07* 0.02 merger (4.78) (2.21) (3.51) (0.01) (0.01) Joint routes × post-merger 15.6* 11.2* -4.71* 0.04* -0.01 (4.47) (2.24) (1.97) (0.01) (0.01) No. of obs. 65,543 63,496 7,880 63,496 63,496 Adj. R-sq 0.03 0.79 0.82 0.77 0.87

Continuous route classiﬁcation ∆ in ﬁrms’ 2013 shares 22.7* 19.5* 20.6* 0.08* 0.07* × post-merger (10.1) (2.38) (3.38) (0.01) (0.01) No. of obs. 40,540 39,063 7,314 39,063 39,063 Adj. R-sq 0.02 0.77 0.79 0.76 0.86

Route and quarter f.e. Y Y Y Y Additional control variables Y Y Y Y Exclude connecting service Y Weight obs. using sales Y Notes: Under ‘Alternative route classification’, a route is an US Airways route if it is not a Joint route, if US Airways’ 2013 market share was higher than 5% and higher than American Airlines’. Under ‘Continuous route classification’, all US Airways, American Airlines, and Joint routes are included in the estimation and ‘∆ in firms’ 2013 shares’ measures the difference in US Airways’ 2013 market shares to American Airlines’, on all non-Joint routes. Standard errors, clustered at the route type and quarter level, shown in parenthesis. (*) statistically different than zero a a 5% confidence level. See notes in Table 3 for more details. 56

Table B.3: Merging firms’ prices compared across route types; alternative route classification Avg. price per passenger Log-price (I) (II) (III) (IV) (V) US/AA * US Airways’ routes × post- 17.9* 12.5* 4.92 0.03* -0.05* merger (4.78) (2.98) (4.79) (0.01) (0.01) USAA × Joint routes × post- 14.2* -0.90 -6.08* 0.00 -0.03* merger (5.04) (2.23) (3.09) (0.01) (0.01) USAA × post-merger 18.2* 10.3* 11.3* 0.07* 0.10* (0.71) (1.57) (2.80) (0.01) (0.01) No. of Obs 159,813 149,310 23,474 149,310 149,310 Adj. R-sq 0.08 0.84 0.85 0.85 0.92 Route, carrier, and quarter f.e. Y Y Y Y Route by quarter f.e. Y Y Y Y Route type by carrier by aircraft f.e. Y Y Y Y Additional control variables Y Y Y Y Only routes flown non-stop by USAA Y Weight observations using sales Y Notes: A route is an US Airways route if it is not a Joint route, if US Airways’ 2013 market share was higher than 5% and higher than American Airlines’. Standard errors, clustered at the route type and quarter level, shown in parenthesis. (*) statistically different than zero a a 5% confidence level. See notes in Table 4 for more details.