The Effect of Mergers in the U.S. Airline Industry on
Consumer Welfare: An Empirical Analysis on the
U.S. Airways/American Airlines Merger
University of Amsterdam
Amsterdam School of Economics
Faculty of Economics and Business
Name: Dianne van der Hoek Student number: 10553584
Contact: dianne.vanderhoek@student.uva.nl
Date of Completion: July 14, 2018, Amsterdam
Course: Master Thesis Economics Track: Markets and Regulation Supervisor: Dr. A.M. Onderstal
2 Statement of originality
This document is written by student Dianne van der Hoek who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
3 Table of Contents
Abstract………...………..4
1. Introduction………..5
2. Literature Review………...6
2.1 Merger Analyzation Methods………....………...6
2.1.1. Stock-Market-Method……...………..………...7
2.1.2. Regression Analyses with DiD estimator………...…....10
2.2 Empirical Research on Mergers in the U.S. Airline Industry………..10
3. The US Airways/American Airlines merger ..………15
4. Methodology………..………..………...15
4.1 Hypotheses………..16
4.2 First Approach – Stock-Market-Method………..………...17
4.2.1 Regressions…………..………...………...17
4.2.2 Data……….………...17
4.2.3 Variables………...…….18
4.2.4 Assumptions………...19
4.3 Second Approach – Regression Analyses with DiD estimator………...20
4.3.1. Regressions……….21 4.3.2. Data………...22 4.3.3. Explained Variables………....23 4.3.4. Control Variables………24 4.3.5. Assumptions………26 5. Regression Results...………....………..29
5.1 Results First Approach: Stock-Market-Method………...29
5.1.1. Overview Stock Price changes……….30
5.1.2. Regression Results Stock-Market-Method………..31
5.2 Results Second Approach: Regression Analyses with DiD estimator………..32
5.2.1. DiD estimator Results Second Approach: pricing equation……….32
5.2.2. DiD estimator Results Second Approach: frequency equation………....34
5.2.3. DiD estimator Results Second Approach: difference between TSLS and OLS…..35
5.3 Robustness Check…..……….………36
6. Conclusion & Discussion……….…..38
7. References……….….41
8. Appendix………....44
8.1 First Approach Assumption Results...………...………..44
4 Abstract
This master thesis is an original study to focus on the consequences mergers have on consumer welfare in the U.S. airline industry. Using a sample of twelve routes within the United States of America, the effects on the U.S. domestic market are analysed. Data of these routes are collected on the average airfares, flight frequencies, average number of passengers on a flight, distance of the route, presence of a high-speed train, population and GDP of the cities of arrival, stock prices of the three largest competitor firms, and index rates of the New York Stock Exchange. All of these variables are conducted over a time period of nine years, to see if this merger was consumer enhancing or deteriorating. Two analyses are performed to check for reliable outcomes and to check if these two analyses are valid in predicting post data on ex-ante data. First, an event study called the stock-market-method is performed. Results of this analysis show a significant decrease in the value of the stocks of the competitor firms after the merger. Second, two regression analyses with inclusion of a differences-in-differences estimator are performed. In this approach, it is assumed that changes in airfares and flight frequency will reflect consumer welfare the most accurate. The results on airfares, as well as the results on flight frequencies did not have significant outcomes. However, airfares increased after the merger whereas flight frequencies decreased after the merger.
5 1. Introduction
Since deregulation of the U.S. airline industry in 1978, mergers in this industry are increasingly common (Hüschelrath & Müller, 2011). Numbers found in the database of Airlines for America show thirty-nine mergers in the U.S. between 1978 and 2016. However, under deregulation, authorities no longer consider the profitability of competitor airlines. So, even if the merger reduces the number of competitors in a market, the authorities will not disapprove the merger as long as new competitors are free to enter this market and the merger does not create barriers to entry (Morrison and Winston, 2007). Furthermore, others found evidence that the number of actual competitors in this market significantly influences the price level on a route (Morrison & Winston, 2007; Borenstein, 1989). According to these findings, approvals from mergers by the authorities do not necessarily implicate a positive outcome for consumer welfare.
This study focusses on two models to provide an answer on the main question if these models are, ex-post, a reliable approximation of the effects ex-ante. The two models used in this study are an event study, the stock-market-method, introduced by Duso et al (2003), and two regression analyses with inclusion of a differences-in-differences estimator. These models are conducted on the particular merger between US airways and American Airlines, due to the fact that after the merger this airline, nowadays known under the name American Airlines Group (AAG), has been the leading firm in the U.S. domestic market up until this day onwards (Statistica, 2018)1.
Despite the widespread interest in this methodology about ex-ante versus ex-post policy evaluations, there has not been much research on this comparison. One motivation for a comparison like this is that forecasts of post-merger outcomes are offered and it is very useful to know how accurate these forecasts are. An ideal environment for this ex-ante versus ex-post analysis is offered by the U.S. airline industry for several reasons. First, a broad set of data on prices and quantities is publicly available of this industry. Second, with at least nine mergers occurring during a time span of two years, a wave of consolidation occurred during a short period of time (Liang, 2013). Third, with almost every proposed merger in the airline industry receiving regulatory approval, antitrust enforcement was quite lax. Therefore, observation of merger effects are made possible which otherwise might have been prevented. From previous research, it shows that ex-ante versus ex-post models are usually underpredicting the effects of mergers (Björnerstedt & Verboven, 2016; Peters, 2003). Furthermore , the effect of a merger in
1 According to Statistica (3 May, 2018), American Airlines Group is in terms of domestic market shares the
leading firm with 18.3%, followed by competitors Southwest Airlines, Delta Airlines, United Airlines, and JetBlue Airways with respectively, 18.2%, 16.8%, 14.9%, and 5.5%.
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the U.S. airline industry on consumer welfare is analysed for which no overall conclusion can be met, according to previous research. This study provides an answer to the main question, which states: Is the event study of the stock-market-method and the method of regression analyses an accurate approximation to analyse the effects of a merger ex-post, on ex-ante data? The sub question states: Is this particular merger between US Airways and American Airlines consumer enhancing or are, after deregulation, mergers approved by authorities which are not beneficial for consumers at all? An answer to the sub question is provided by answering two questions: (i) What effect did the merger have on prices? And (ii) What effect did the merger have on flight frequencies? In this study, consumer welfare is equivalent to consumer surplus and is stated as the surplus that exists because prices are lower than the consumers’ willingness to pay (Belleflame & Peitz, 2015). Due to this study, an overall answer on the effect of mergers in the airline industry might be performed. Although, from previous research it seems that every merger has its own outcome and no overall conclusion can be based on the results of one particular merger.
The paper is organised as follows. In Section 2, a review of previous empirical analyses of mergers in the U.S. airline industry is provided as well as a thorough explanation of two merger analyses. Section 3 discusses the insights of the U.S. airline industry and the course of events concerning the merger of US Airways and American Airlines. In Section 4, two models for assessing the effects of the merger are constructed and data used in the empirical analyses is described. In Section 5, the regression results are explained. The last section, section 6, concludes, followed up by a discussion.
2. Literature Review
This section provides a thorough explanation of two merger analyzation methods. The stock-market-method and the regression analyses, including advantages and disadvantages of these methods, are discussed in paragraphs 2.1.1 and 2.1.2 respectively. Hereafter, previous research on mergers in the U.S. airline industry and their effect on consumer welfare is explained in paragraph 2.2.
2.1 Merger analyzation Methods
The unilateral effects of mergers, and how to measure these, are manifold investigated. This because, in general, competition authorities are required to evaluate whether a horizontal merger is presumable to raise concerns with respect to coordinated and non-coordinated effects. Meaning, whether the merger might increase the probability of collusion in the market and,
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respectively, whether the merger might increase the market power of the merging firms (Filistrucchi et al, 2012). To address the issue of assessment of these effects, competition authorities have devised multiple methods. Among which are the stock-market-method and regression analyses, both with inclusion of a difference-in-differences (DiD) estimator.
2.1.1. Stock-Market-Method
To illustrate the theoretical substantiation of this method, the effects of a merger are analysed on the basis of the following simple example in which the model contains n firms in the market prior to the merger. Marginal costs are identical for all firms and the merger involves m firms,
in which the merged firm has lower marginal costs. The inverse demand function is 𝑝(𝑄) = 1 − 𝑄, where p reflects the price and Q is the total quantity supplied by n firms.2 Profit
maximization is the main goal of each firm i, which is provided by the following function: 𝜋𝑖 = (𝑝 − 𝑐𝑖)𝑞𝑖. In which, 𝜋𝑖 reflects firm i’s profit, qi and ci reflects the quantity sold by firm
i and, respectively, the marginal costs of firm i, and p reflects the price. After solving for the first order conditions in the pre-merger symmetric case, the following equilibrium price and quantities can be found:
𝑝∗ =𝑛𝑐+1
𝑛+1 and 𝑞
∗ = 1−𝑐 𝑛+1
This leads to an equilibrium profit and consumer surplus of: 𝜋∗ = 1−𝑐 (𝑛+1)2 and 𝐶𝑆 = 𝑛2 2 ( 1−𝑐 𝑛+1) 2 =1 2(1 − 𝑝 ∗)2
From these equations, it shows that an increase in prices, increases producer surplus and reduces consumer surplus (Belleflamme & Peitz, 2015).
Achieving efficiencies through marginal cost savings is one of the main potential outcomes of a merger. In the case where no efficiency gains arise, there are now n-1 firms in the market which would imply the market structure changes. However, this is still a case of a symmetric equilibrium with the following equations for price and quantity:
𝑝 =𝑛𝑐−𝑐+1 𝑛 and 𝑞 = 1−𝑐 𝑛 . 2 Note that 𝑄 = ∑ 𝑞 𝑖 𝑛 𝑖=1 and 0 < c < 1
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This implies that the profits and consumer surplus equation is now transformed to:
𝜋 = (1−𝑐 2 ) 2 and (𝑛−1) 2 2 ( 1−𝑐 𝑛 ) 2 =1 2(1 − 𝑝) 2.
Comparting the pre- and post-merger situation, it shows that post-merger prices and quantities are higher than pre-merger prices and quantities. So, in the case of no efficiency gains in the post-merger period, producer surplus increases due to a price increase and consumer surplus decreases. In the case with efficiency gains in the post-merger period, prices are lower, competitors’ profits are lower, and consumer surplus is higher compared to the no efficiency gains situation. These effects tend to be more visible as the level of efficiency increases.
Duso et al (2003) conducted a research that investigates the determinants of European merger control decisions. The authors analysed the relation between consumer surplus, total welfare, and profit and used the theoretical result that the effects of a merger on consumer surplus are directly linked to the effects on the competitor firms of the merged firm. They considered a sample of 164 merger control decisions in the EU and registered the reaction of the stock market price of competitor firms to the merging firms to evaluate the anti-competitive consequences of these mergers. Competitors’ profits were estimated on the hand of the market reaction around the date of announcement. A merger is said to be pro-competitive if it increases consumer welfare, and anti-competitive if it decreases consumer welfare. A merger is classified as procompetitive whenever the impact of the merger on competitor firms stock prices is negative. Meaning, when investors would like for the merger to take place because it will have a positive effect on their returns, the investors will invest more in the newly merged firms and less in the competitor firms. Conversely, a merger is classified to be anti-competitive whenever competitor firms benefit and their stock prices increase. Duso et al (2003) evaluated whether systematic errors were made by the European Commission (EC) in their decisions to block pro-competitive mergers. According to them, the stock market serves as an accurate tool to predict whether a proposed merger is pro- or anti-competitive.
Duso et al (2003) introduced a graph to clear out these results. This graph shows that the change in competitors’ profits moves in the opposite direction as the change in consumer surplus: as the efficiency level increases, competitors’ profits decreases while consumer surplus increases. Differently stated, consumers will be benefitted if the merger hurts competitor firms, and vice versa. The welfare level does increase as well as the level of efficiency increases, since efficiency tends to increase aggregate profits and hereby increasing consumer surplus as well
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as total welfare. Another important feature of this figure is the element that mergers are not attractive if they do not achieve at least some level of efficiency. In the model, a critical level of efficiency is notable in which prices remain unchanged so that this value ensures that the merger does not affect consumers.
This approach, to analyse the competitive effects of mergers through the use of stock market data has multiple advantages. First, stock market data avoid a potential censoring problem since data on stock market prices are available at any time, whether the merger is approved for or not. The competition authorities, in some cases, have to base their judgement on insufficient data which is no problem in this method (Duso et al, 2003). Second, stock market data are relatively easy to obtain, compared to the alternative of estimation of structural demand parameters to get measures of consumer surplus. Third, the stock market is an independent assessment of the anti-competitive effects of mergers. It is not carried out by insiders and therefore can be viewed as exogenous to the decision. This due to the fact that the stock market is uncontrollable and has no incentive to manipulate effects. Thus, the source of information of the stock market is independent (Brady & Feinberg, 2000). Finally, since stock market data changes day to day, this data is more suitable for dynamic analysis compared to using accounting data while studying anti-competitive effects. The use of annual accounting data would require an explicit dynamic specification of which the structure may not be easily tested (Duso et al, 2003).
However, this method contains some limitations as well. First, this method mainly focuses on unilateral, or non-coordinated, effects of proposed mergers without considering coordinated effects, while competition authorities are aimed to analyse coordinated effects as well (Duso et al, 2003). Second, so called “in play” effects may be induced due to the merger announcement, such that it increases the likelihood of competitors to be involved in subsequent mergers themselves. In this predisposition, an increase in stock prices of competitor firms may not be a reliable indicator for anti-competitiveness of the merger (Fridolfsson & Stennek, 2000). Third, the official announcement date of a merger can be pointed out but in reality some rumours about an upcoming merger already spread and investors speculate on this. Here fore, some effects on the stock prices of competitor firms already have taken place before the date of announcement. This makes it more difficult to draw valid conclusions by using this method (Duso et al, 2003). Finally, this method cannot be applied to vertical mergers but instead only to horizontal mergers due to the fact that vertical mergers do not necessarily take place among competitors in the same industry. However, this last limitation does not apply to this study since it concerns horizontal mergers in the airline industry.
10 2.1.2. Regression Analyses with DiD estimator
To measure the impact of mergers on pricing and other market equilibrium outcomes, the DiD estimator is quite often used. The reason for this is that a much more flexible framework is offered by direct before and after comparisons of prices than do other methods. The DiD estimator analyses changes in the relevant variable in a treatment group in comparison to a control group that is unaffected by the change, in which the control group should be as similar as possible to the treatment group, both in terms of supply and demand shocks. This method is conducted by, for example, Kim and Signal (1993) whom used a DiD estimator to examine if price changes are associated with mergers in the airline industry. Despite the widespread application of this estimator to measure the effects of mergers, there do exist multiple shortcomings to this method. One of the most striking criticism is that the DiD estimator can present false positives (Bertrand et al., 2004). The authors applied the DiD estimator and showed how the DiD estimator reports significant positive effects in 45 percent of the cases, even though no real change in the market was present. This result shows that in serially correlated data a bias is introduced, so that the standard errors are inconsistent in OLS regressions. A second criticism is raised by Simpson and Schmidt (2008), who showed that even though the control group has the same supply and demand shocks as the treatment group, if the two groups embody these shocks evidently, the DiD estimator might be biased due to the fact that the two groups include this difference in the embodiment of supply or demand shocks. Finally, the third criticism derives from the possible endogeneity in the change in the market. Whenever the DiD estimator analyses a change which is not exogenous, the estimator will be biased and inconsistent. In the case of mergers, it seems evident that the decision concerning the functioning of firms in the market is not an exogenous one, and much less so is their pricing decision (Jiménez and Perdiguero, 2018).
2.2 Empirical Research on Mergers in the U.S. Airline Industry
In previous research concerning the reliability of models which forecast ex-post evaluations based on ex-ante data, Peters (2003) found that such simulation models can forecast a large component of the price change ex-post, but it cannot be expected to account for all of it since the model slightly underestimates the forecasts. This result is confirmed by the study of Björnerstedt and Verboven (2006).
Peters (2003) analysed post-merger prices of six airlines by using merger simulations, and compared these forecasts with actual post-merger prices. In this study, the dataset is quarterly based and consists of total passengers, city-pairs, airports, airport-pairs, and airlines.
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To measure the merger effect on prices, the relative price change is defined as the difference between an average percentage price change and the actual percentage price change. Peters (2003) included a control group to include other firms which also merged during this period, as did Borenstein (1990) and Kim and Signal (1993). Peters (2003) conducted a merger simulation consisting of demand estimation using pre-merger data; pre-merger marginal costs; and forecasting post-merger prices. In this study, Peters (2003) indicated the pre-merger period as the first four quarters of 1985. The merger announcement took place in January 1986. The post-merger period is indicated by the first four quarters after the merged firms’ operations were fully integrated. His results show that linear forecasting based on the relationship between market structure and price can yield results which aim close to the predictions from merger simulation. However, these forecasts do not completely fit. This incompletion is again caused by changes in marginal costs, which are desired to be predicted at first. Peters (2003) found results on the effect of mergers on flight frequencies as well, which show there is a strong tendency to reduce flight frequencies post-merger in segments where both carriers operated pre-merger. The findings by Peters (2003) are supported by the study of Björnerstedt and Verboven (2006), who used merger simulation to forecast ex-post evaluations on ex-ante data on a merger between two large firms in the Swedish painkiller market. This merger is unique in the sense that the two firms had no other competitors in the market. First, an ex-post analysis is conducted of the merger effects. Hereafter, a regression is performed where the dependent variable is represented by the average price level, and a DiD estimator is included to compare pre- and post-merger data. Results show the models underpredict the merging firms’ price increase. Both firms raised their prices by exactly the same percentage. However, the model predicts much larger price increases. Thereby, the model predicts little response of the outsider firms, which in reality is not the case. Outsider firms raised their price by a large percentage after the merger as well. An explanation for these deviations in the results of the model is a plausible increase in marginal costs post-merger and the possibility of partial collusion.
In previously executed research, contradictory results of the effects of mergers on consumer welfare are found. Kim and Signal (1993) as well as Morrison and Winston (2007) found that mergers are associated with higher airfares. On the other hand, Brueckner et al (1992) and Lichtenberg and Kim (1989) contended that airfares were lowered due to mergers. Some other studies, for example Borenstein (1990), could not reach significant results.
Kim & Signal (1993) used data on 11,629 sample routes worldwide, obtained from 14 airline mergers. The data is collected on a quarterly basis and includes airfares on the particular routes, numbers of passengers and carriers, distance, concentration, market shares of different
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airlines, and fare per mile. For each route in the sample, a control group is constructed. The control group consists of all routes on which, during the period of analysis, neither one of the merging firms operated and on which the distance falls within 7.5 percent of that of the sample routes. To identify changes in airfares as a result of the mergers, the fare change of a sample route is compared with the fare change in the control group. In other words, they used a difference-in-differences estimator. Their results show an increase in airfares on routes served by the merging firms while the control group showed this was not the case at routes unaffected by the merger. Mergers may lead to more efficiency in operations, but the impact of efficiency gains on airfares is more than offset by increased market power.
Morrison & Winston (2007) investigated the effects on consumer welfare for six mergers approved during two years in the 1990s. They collected data on frequency, travel time, the change in airfares, and cities on routes served by merging firms, and performed a two-stage least squares regression (TSLS-regression). Regression results of this study show three out of six mergers reduced consumer welfare, whereas three improved it. However, when taking a closer look at the welfare improving mergers, it shows that the benefits from increased frequent-flyer programs are critical. If frequent-frequent-flyer benefits and their costs from higher fares were eliminated, the mergers would actually lower annual welfare. Frequent-flyer programs can induce higher barriers to entry due to encouraged brand loyalty. So, elimination of frequent-flyer programs could lead to more competition and lower fares. It seems in this study, a bias is created due to addition of the frequent-flyer program, whereas Kim & Signal (1993) only used data on economy-class tickets.
Brueckner et al (1992) found contradictory results compared to Kim and Signal (1993) and provides an analysis which links airfares to the structure of airline hub-and-spoke systems. The empirical model of their analysis provides results that show that the Northwest-Republic and TWA-Ozark mergers have reduced fares in the markets served by the hubs at Minneapolis and St. Louis, respectively. They used data on the fare paid by the typical passenger who uses a hub airport. This is the connecting passenger; whose round trip consists of four flight segments since it requires a change of plane at the hub. The variables included are airline itinerary, which contains a route flown by a given carrier, with the direction of travel specified, the number of passengers observed on the itinerary at the given fare, a dollar fare, the distance of the trip, and the fare class. The dataset contains of 6,054 observations in total. An OLS-regression and TSLS-regression on these variables is performed, using fares as dependent variable. Their results show that in reducing airline costs, networks play an important role. These findings are in line with the findings of Brueckner and Spiller (1992), whom carried out different tests by
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investigating the relation between spoke traffic densities and fares. They find that both the marginal cost of carrying an extra passenger and fares are reduced by higher density. Also, the study of Brueckner et al (1992) highlights the role of networks on hub concentration. Their findings show that a merger leading to a concentrated hub also generates an efficiency gain by creating a larger network. These efficiency gains are passed on to passengers in the form of lower fares. More generally, this analysis suggests that in a merger, consumers in markets not directly affected by the merger may benefit due to the complementarity effect through which prices fall. This principle may be relevant for merger analysis in other industries.
Another study with corresponding results to those of Brueckner et al (1992) is the study of Lichtenberg and Kim (1989), whom analysed the effect of mergers on prices, productivity, costs, and capacity utilization in the U.S. airline industry during the period 1970-1984, using panel data. In the sample period, five mergers occurred and are investigated. Their objective was to compare the performance of airlines involved in a merger with that of airlines not involved in a merger both before and after the merger occurred. After this, the difference between the before and after comparisons is calculated. In their study, they used six variables: the implicit price of output, a binary variable to indicate a merger, and four input variables among which fuel, labour, ground property and equipment, and flight equipment. To measure the effect of mergers on these airline performance variables, an OLS regression with time fixed effects and airline fixed effects is performed. They use the implicit price of airline services as independent variable, since it is, according to them, the closest measure to consumer welfare. Their results show 6.0 percent higher estimates of the mean output of airlines involved in a merger compared to that of airlines not involved in a merger in the four years prior to the merger, and 5.1 percent lower in the four years post-merger. This indicates a change of -11 percent in pre- to post-merger difference. Results also show that these mergers were associated with reductions in unit costs. The average annual rate of unit cost growth is a statistically significant 1.1 percentage points lower for carriers involved in a merger than that of carriers not involved in a merger. Almost 86 percent of this cost reduction appears to have been passed on to consumers. However, Lichtenberg & Kim (1989) do not expect their parameters estimates to be unbiased estimates of the effects of all proposed mergers. For this reason, it is not clear whether U.S. airline mergers have had similar effects to those estimated in this study.
Another study, performed by Borenstein (1990), again showed different results compared to the previous four. In this study, an analysis on the same two mergers as in Brueckner et al (1992) is performed, the Trans World Airlines’ (TWA) merger with Ozark Airlines. Borenstein (1990) analysed the effects of these two mergers that resulted in airport
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dominance and may have created substantial market power, whereas Brueckner et al (1992) focused on the change in airfares due to these mergers in hub-and-spoke networks. Borenstein (1990) performed a before and after comparison of the prices charged by the merging firms, to test the acquisition of market power. Data from the third quarter of the years 1985 till 1987 were collected on the eight largest domestic carriers on routes that include their major hub airport relative to the industry average prices charged on routes of the same distance. The major hub of Northwest is Minneapolis and respectively St. Louis for TWA-Ozark. Results show that the two mergers accounted for the largest hub airport price increases during this event window. Minneapolis and St. Louis were two of the least expensive hubs to travel to, or from, in 1985. However, by 1987 these two airports were about as expensive as the other major dominated hubs. The analysis performed to get to these results weights the number of passenger miles that the carriers provided on each route. According to Borenstein (1990), this result does support one or both hypotheses about the advantages of a dominant airline at an airport: first, airport dominance reduces the threat from potential competition, and second, airport dominance allows use of marketing devices that increase the attractiveness of a carrier. Concluding, Borenstein (1990) found in his research concerning the Northwest-Republic merger a significant increase in airfares, but no evident proof regarding a significant change in airfares on routes affected by the TWA-Ozark merger that occurred in the same year.
Agreed upon by almost all economists, the joint effect of a merger cannot a priori be determined due to the fact that mergers in the airline industry have twofold effects that will influence airfares in opposite directions (Lichtenberg & Kim, 1989, Kim & Singal, 1993). Therefore, the two opposing effects need to be decomposed in order to understand what the potential effects of a merger are. On the one hand, mergers reduce competition, especially at hub airports where barriers to entry are possible to exist and concentration is high, which will increase the market power of the dominant airline and raise the price-cost margin. This drives up airfares. On the other hand, airfares might be reduced by mergers by lowering unit costs due to economies of scale and improved productivity and by attaining efficiency gains. However, the overall effect of a merger on airfares is unknown and there exist no agreement among economists about this effect (Rubinfeld et all, 2013).
15 3. The US Airways/American Airlines Merger
This section enlightens the details of AAG as a firm before, times, and after the merger between US Airways and American Airlines in facts and figures.
Over the past two decades, the U.S. airline industry has undergone tremendous changes: since 2000, all five legacy carriers in the U.S. have declared bankruptcy. In fact, there were no bankruptcies declared at all during the period 1982-1989. The first of five was United Airlines, which filed bankruptcy in December 2002, followed up by US Airways in September 2004, and Northwest and Delta Airlines a year later on in September 2005. Only much later, on November 29, 2011, American Airlines filed for bankruptcy (Liang, 2013). After the file for bankruptcy, all of these airlines were successfully involved in a merger with another airline.
American Airlines nowadays is the largest carrier in the U.S. and the second-largest carrier in the world, based on revenue seat miles. American Airlines carries out approximately 3,400 flights between 250 destinations every day. The top three competitors of American Airlines are Southwest Airlines Company, Delta Air Lines, and United Continental Holdings, whom together dominate the U.S. domestic airline market. At the end of 2017, the market shares of these firms sum up to 63.5%.3
Due to the fact that this merger would lead to the largest airline in the domestic market, antitrust concerns were raised this would hinder competition and lead to higher fares. Therefore, the merger was blocked by the Department of Justice (DoJ). Eventually, US Airways and American Airlines reached a settlement with the DoJ, clearing their way in becoming the largest airline in the world. However, this agreement stated that the merged firm had to give up airport terminal gates, take-off and landing slots, and ground facilities at the main hubs Boston, Chicago, Dallas, Miami, Los Angeles, New York La Guardia, and Washington, to low-cost carriers. The DoJ demanded this in order to enhance system-wide competitive airfares for consumers.
4. Methodology
To provide an answer to the main- and sub question, two analyses on this merger are performed. First, an event study on stock prices of competitor firms and the overall index is performed. Second, a regression analysis with a DiD estimator is conducted, to collect results of the effect of the merger and multiple control variables on the price of airfares and flight frequency. In this section, the stated hypotheses are discussed first in section 4.1. Thereafter, the
3 American Airlines makes up 22.8%, Southwest Airlines 21.5%, and Delta Air Lines 21% based on Revenue
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method is discussed in section 4.2, with inclusion of a thorough explanation of the method itself, the used regression function, the data, the variables, and the assumptions. In section 4.3, the second analysis is thoroughly explained including the used regression models, data, explained variables, control variables, and assumptions.
4.1 Hypotheses
To provide an answer to the main question, Is the event study of the stock-market-method an accurate approximation to analyse the effects of a merger ex-post, on ex-ante data?, the null hypothesis is stated as follows:
H0A: An ex-ante evaluation, based on an event study, is an accurate approximator on ex-post
results, based on a DiD. Meaning, signs of both predictors are equal.
This hypothesis is based on the findings of Duso et al (2007) and implies that the merger decreases stock prices of competitor firms, which means the merger is welfare enhancing.
To provide an answer to the sub question, which states: Is this particular merger between US Airways and American Airlines consumer enhancing or are, after deregulation, mergers approved by authorities which are not beneficial for consumers at all?, two other questions are answered: (i) What effect did the merger have on prices? And (ii) What effect did the merger have on flight frequencies?. For this, two null hypothesis, H0B and H0C, are
constructed which are based on previous research. This previous research feeds the expectation the merger will result in a reduction in the intensity of competition on the routes flown. Due to the fact carriers mainly compete in terms of airfares and flight frequencies, the merger would be expected to lead to an increase in airfares and to a decrease in flight frequencies on the routes affected (Borenstein, 1990; Kim & Signal, 1993; Morisson, 2007; Peters, 2003). In the case of flight frequencies, carriers have a strong tendency to reduce the frequency of flights post-merger in segments where both carriers operated pre-merger. This is expected for the reason that direct competition in that segment is reduced due to the merger and here fore the incentive to maintain high levels of capacity is reduced as well (Peters, 2003). The hypotheses are stated as follows:
H0B: the merger effects have a tendency to increase airfares.
17 4.2 First Approach – Stock-Market Analysis
Duso et al (2007) performed an analysis on a sample of 164 mergers and collected evidence on whether the stock market anticipated that these mergers were anti-competitive or pro-competitive. They have proven that in case of a merger, when profits of competitors decrease, consumer welfare increases.
Therefore, in this thesis, an analysis is performed on the change in stock prices of the three largest competitor firms of American Airlines: Southwest Airlines, Delta Airlines, and United Continental Holdings. With the use of data on these firms and the overall index, the New York Stock Exchange, there is checked for a jump in data at the date of announcement of the merger. To see whether this jump is indeed caused by the presence of the merger, a DiD estimator is constructed.
4.2.1. Regressions
To support the analysis of Duso et al (2007), a DiD estimation is performed of the following form:
𝑙𝑜𝑔 𝐾𝑖𝑡
𝐶𝑜𝑚𝑝𝐹𝑖𝑟𝑚
𝐾𝑖𝑡𝐼𝑛𝑑𝑒𝑥 = 𝛼 + 𝛾𝐷𝑡>𝑇+ 𝜀𝑖𝑡
This regression shows the relative percentage change in stock prices for the three competitor firms against the overall index rates. Due to implementation of the DiD estimator a before and after analysis is conducted, where T is the date of announcement of the merger and γ represents the DiD estimator. A positive value of γ indicates stock prices of the competitor firms have increased after the merger, whereas a negative value indicates stock prices have decreased after the merger.
The data used here concerns unbalanced panel data. Due to implementation of the DiD-estimator, there is no need to include fixed effects (Stock & Watson, 2012).
4.2.2. Data
Data for this analysis is collected from Yahoo!Finance, from the three largest competitors of American Airlines: Southwest Airlines, Delta Airlines, and United Continental Holdings, and the overall index. All three competitor firms are registered on the New York Stock Exchange (NYSE) (Statistica, 2018).
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Data is collected from February 1, 2013 up until February 27, 2013, the month the merger was announced. Since the date of announcement is February 14, 2013, the announcement date of the merger falls in the middle of this event window, which provides a properly before-and-after analysis. There is chosen for the date of announcement instead of the implementation date due to the fact that investors anticipate on rumours and on the announcement itself, which all occur in advance of the actual merger. A second reason is, by using the stock market reactions on the day of announcement, the impact of a merger on competitors’ stock prices is identified even if the merger is blocked. Therefore, previous research almost always uses the date of announcement as reference point (Kim & Signal, 1993; Duso et al, 2007; Bilotkach & Pai, 2014; Peters, 2003).
4.2.3. Variables Stock prices Competitor Firms
The explanatory variable in this analysis is the stock price of the competitor firms, relative to the overall Index rate. Where, 𝐾𝑖𝑡𝐶𝑜𝑚𝑝𝐹𝑖𝑟𝑚, indicates the stock price of competitor firm i at time t. Stock prices are noted in US dollars.
Index
The stock price of the competitor firms is divided by the index of the NYSE. Where, 𝐾𝑖𝑡𝐼𝑛𝑑𝑒𝑥, indicates the price index of the NYSE at time t. Of course, the index level of the NYSE does not differ per firm but remains the same, no matter which firm is analysed. But due to the fact it concerns panel data, the same values are analysed multiple times for the different competitor firms, indicated with i.
Binary Time Variable
The first, and only, variable of interest concerns a binary time variable, which takes on the value of one for the date of announcement and the dates thereafter, and zero otherwise. The coefficient of this variable is the DiD estimator. If the sign of this coefficient is negative, the merger let to a reduction in stock prices of the competitor firms. Indicating the merger was actually welfare enhancing. On the contrary, if the sign of this coefficient is positive, the merger let to an increase in stock prices of the competitor firm and was welfare deteriorating.
19 4.2.4. Assumptions
In this section, the assumptions of stationarity, homoskedasticity, autocorrelation, and no perfect multicollinearity are accounted for and should be met in these regressions to accomplish valid results. Thereby, the assumptions for use of a DiD estimator should be met also.
First, a test on stationarity is performed on all variables. Data is stationary if its probability distribution does not change over time, so it assumes that the future will be like the past. Otherwise, the variable is said to be non-stationary. In this study, panel data from one month is used. If there are changes over time, data from the past is not reliable for predicting the future. If the time series do not change over time, which means a constant mean and variance, and if there is autocorrelation over time, the data is called stationary (Stock & Watson, 2012). To test for stationarity, a Dicky-Fuller test is conducted. The panel data used in this study concerns unbalanced panel data, hence the fisher variant is used. Every variable is tested for stationarity, except for the dummy variables since they do not have a relation with time. Results are shown in Appendix A.1 through A.3. The variable for the NYSE Index is stationary with 1% significance. However, results on the variable stock prices of competitor firms show non-stationarity on the 10% significance level. Because a maximum significance level of 5% is usual, a difference of this variable is created. The results of a stationarity test on the first-difference of this variable are shown in appendix A.3, and show stationarity at the 1% significance level.
Second, a test for homoskedasticity is performed. According to Stock and Watson (2012), the error term is homoskedastic if the variance of the conditional distribution of ui given
by Xi is constant for i = 1,…,n and in particular does not depend on Xi. If this is not the case,
the error term is called heteroskedastic. To test for homoskedasticity, a likelihood-ratio test is conducted. Results are shown in appendix B. The results show a p-value of 0.000, which indicate that the null hypotheses which states heteroskedasticity is not rejected. For this reason, robust standard errors are used in the final regression analysis.
Third, to check if heteroskedastic and autocorrelated (HAC) standard errors should be used, there is tested for autocorrelation with the use of a Wooldridge test. Results are shown in appendix C, where the p-value of 0.3939 results in no rejection of the null hypothesis which states no autocorrelation. So, the variables are not autocorrelated and there is no need to use HAC standard errors. The use of robust standard errors will satisfy in this analysis, although it does not harm to use HAC standard errors even if there is no autocorrelation.
Fourth, the assumption of no perfect multicollinearity is tested. Perfect multicollinearity reflects an exact linear relation between the regressors of the model and usually reflects a
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mistake in the model. The k+1 first order conditions are not independent and as a result it is impossible to retrieve k+1 estimates. Here fore, no perfect multicollinearity is highly preferred in the research data. To test for this, a VIF test is used. There is perfect multicollinearity if the value of the VIF test is equal or above ten. The results are shown in appendix D and show for both variables a VIF value of exactly 1.0. Meaning, there is no perfect multicollinearity between the variables.
In this analysis, it concerns a differences-in-differences estimator with a single regressor. Therefore, all least squares assumptions apply to DiD and are tested for, starting with a test on the first least squares assumption which states the conditional distribution of the error term, given the independent variables, has a mean of zero. In this study, observational data is used in which the variables are not randomly assigned. Instead, there is assumed that the variables are as if randomly assigned which means E(ui|Xi)=0 (Stock & Watson, 2012). The
second least squares assumption states that all variables are independently and identically distributed. This is accounted for by testing for heteroskedasticity and autocorrelation. In case of heteroskedasticity, conditional on the regressor, the variance of the error changes over the observations. Which is the case in this study and implies variables are not identically distributed. In case of autocorrelation the errors are correlated with each other but not with the regressors. In this case, variables are not independently distributed. According to Appendix B and C there is heteroskedasticity, but no autocorrelation. This problem is accounted for by the use of robust standard errors. The third least squares assumption states large outliers are unlikely. A scatterplot in Appendix E show no large outliers in the data of the stock-market-method.
After all these assumptions are met, the regression with DiD estimator is performed. Results of this analysis are discussed in section 5.1 and are shown in table 4.
4.3 Second Approach – Regression Analysis with DiD estimator
The second approach conducted to provide an answer to the sub question is implementation of a DiD estimator with additional regressors. The use of a DiD estimator is to examine the effects of the merger on airfares and flight frequencies through a before and after analysis. Since the consideration of flight frequencies is less common than that of airfares in the literature, the analysis of both variables allows for obtaining a complete overview of the impact of the merger on consumer welfare.
The use of a DiD estimator is used by studying the differential effect of a treatment, in this case the merger, on a treatment group versus a control group. The estimator calculates the
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effect of the merger on the outcome variable by comparing the average change over time in the outcome variable for the treatment group, compared to the average change over time in the outcome variable for the control group (Stock & Watson, 2012).
The treatment group will contain the market in which firms merge, whereas the control group will contain the market in which firms do not merge. Due to implementation of a DiD estimator, again there is no need to include fixed effects. The DiD estimator can be defined as the difference in the average result in the treatment group before and after the merger minus the difference in the average results in the control group before and after the merger (Stock & Watson, 2012).
4.3.1. Regressions
To analyse the effect of the merger on airfares and flight frequencies, the DiD estimator is used. The empirical approach is defined by the following expression:
𝑌𝑖𝑡 = 𝛽0+ 𝛽1𝑃𝐴𝑀𝑖𝑡+ 𝛽2𝑅𝐴𝑀𝑖𝑡 + 𝛽3(𝑃𝐴𝑀𝑖𝑡 ∗ 𝑅𝐴𝑀𝑖𝑡) + 𝛽𝑋𝑖𝑡+ 𝜀𝑖𝑡
The endogenous dependent variable Yit is the weighted average airfare, adjusted for inflation
in 2017 dollars, from 2009 till 2017, on route i at time t, and alternatively the number of quarterly flights offered on route i at time t.4
The variable PAM is a binary variable which indicates the period after the merger. Here fore, it takes on the value of one for all routes in the periods after the merger and zero for all routes in the periods prior to the merger. Due to implementation of this binary variable, the change in prices and frequencies after the merger on all routes will be reflected.
The variable RAM is a binary variable which indicates the routes affected by the merger. Here fore, the variable is equal to one if it concerns routes where US Airways or American Airlines have been offering services, and zero otherwise. This binary variable reflects the impact on routes which are affected by the merger in relation to those that are unaffected by the merger.
By construction, the interaction variable PAM*RAM is a binary variable as well, which takes on the value of one only for those routes affected by the merger, only in the periods after the merger. The coefficient of this variable is the DiD estimator. If the coefficient is positive and significant, the merger led to an increase in prices and, respectively flight frequencies. On
4 Note: These airfares include only the price paid at the time of the ticket purchase and do not include other fees
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the contrary, if this coefficient has a negative and significant sign, the merger led to a decrease in prices and flight frequencies.
Finally, a set of control variables (X) is introduced that might affect airfares or flight frequencies. Since one of the first researches by Borenstein (1989), multiple studies have estimated pricing equations that include explanatory variables related to competition, demand, and other route characteristics to estimate the effect of a merger on consumer welfare. However, less attention has been paid to the estimation of flight frequency equations. Nevertheless, in general, the variables for this equation are similar to those used in pricing equations (Bilotkach & Pai, 2014). Hence, the following regression equations are estimated:
Pricing equation: 𝑃𝑅𝑖𝑡 = 𝛽0+ 𝛽1𝑃𝐴𝑀𝑖𝑡+ 𝛽2𝑅𝐴𝑀𝑖𝑡+ 𝛽3(𝑃𝐴𝑀 ∗ 𝑅𝐴𝑀)𝑖𝑡+ 𝛽4𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖 + 𝛽5𝐷𝑒𝑚𝑎𝑛𝑑𝑖𝑡 + 𝛽6𝐻𝑆𝑇𝑖𝑡+ 𝛽7𝐿𝑜𝑛𝑔𝑖+ 𝛽8𝐷𝑆1𝑡+ 𝛽9𝐷𝑆2𝑡+ 𝛽10𝐷𝑆3𝑡+ 𝜀𝑖𝑡 Frequency equation: 𝐹𝑅𝑖𝑡 = 𝛽0+ 𝛽1𝑃𝐴𝑀𝑖𝑡+ 𝛽2𝑅𝐴𝑀𝑖𝑡+ 𝛽3(𝑃𝐴𝑀 ∗ 𝑅𝐴𝑀)𝑖𝑡+ 𝛽4𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑖 + 𝛽5𝐷𝑒𝑚𝑎𝑛𝑑𝑖𝑡 + 𝛽6𝐻𝑆𝑇𝑖𝑡+ 𝛽7𝐿𝑜𝑛𝑔𝑖+ 𝛽8𝐷𝑆1𝑡+ 𝛽9𝐷𝑆2𝑡+ 𝛽10𝐷𝑆3𝑡+ 𝜀𝑖𝑡 4.3.2 Data
Data is collected on a quarterly basis from the T-100 Domestic Segment Database of the Research and Innovative Technology Administration, Bureau of Transportation Statistics (RITA BTS). From this data base, domestic economy-class airfares are obtained, as well as number of carriers and passengers by route, frequency of flights, distance of flights, and the fact if there is a substitute of a high-speed train on that route. All first-class tickets, business-class tickets, and other tickets that involve more than one connecting point on any directional trip are excluded from the sample.5
American Airlines (AA) and US Airways began reporting jointly as AA in July 2015 following their 2013 merger announcement (BST, 2018). The data set will provide data of the first quarter of 2009 up until the fourth quarter of 2017. Since the merger was announced at
5 Thus, only direct flights and economy-class tickets are included and there is no distinction between direct
flights and single-connection flights for the reason that these flights could represent different markets, as a passenger is required to wait for a connecting flight.
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February 14, 2013 and realized by December 9, 2013, the date of announcement of the merger as well as the implementation date falls in the middle of this event window. Taking the research by Peters (2003) as an example, the period prior to the merger is indicated as the twelve quarters pre-dating the February 2013 announcement. The period post-merger is indicated by the first ten quarters after the merged firms’ operations were fully integrated. Seasonal fixed effects are included in the regression to rule out seasonal fluctuations as the summer period in which demand for plane tickets tend to increase drastically.
The airline industry is made up of hub-and-spoke (HUB) networks, which are complex interconnected systems. The HUB network refers to airline carriers using central airports as hub locations to connect passengers to their final destination. The HUB network system provides an increased number of flight frequency and destinations (Shy, 1996, 2001; Brueckner, 2004). In this study, data of multiple routes served by one of the merged firms, served by none of the merged firms, and served by either one of them pre as well as post-merger are collected. In this way, analysis of the data will be more accurate. The chosen routes for this study are all connected with main HUBs of American Airlines, which include routes departing from or arriving at Charlotte, Chicago O’Hare, Dallas, Miami, Philadelphia, Phoenix, and Washington DC (Kirby, 2013). Furthermore, there occurs no differentiation in this study between Full Service Airlines (FSA) and Low-Cost Carriers (LCC) due to the fact that American Airlines concerns a FSA and will only be compared with other FSA’s on the same routes. To be included in the sample, a route has to be flown by at least 1,200 passengers per year.6 All sample routes meet these criteria.
4.3.3 Explained Variables
Explained variables, or regressands, are those variables which value depends on the values of explanatory variables. The explained variables represent the output or outcome whose variation is being studied (Stock & Watson, 2013). In this analysis, two explained variables are used which both indicate consumer welfare:
6 Note that 1,000 passengers per year is equivalent to 250 passengers per quarter. Since the data base contains
only 10 percent of the raw data, 25 observations will be provided by 250 passengers. This is the minimum amount of observations required to draw reasonable statistical inferences about the data. Borenstein (1990) uses respectively 1,000 passengers and Kim & Singal (1993) use 1,200 passengers.
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• Price (PR) = weighted average airfare on route i at time t.
The airfare tends to be an accurate measure for consumer welfare since an increase in airfares reduces consumer surplus. Following previous research of Lichtenberg and Kim (1989), Kim and Signal (1993), and Morrison and Winston (2007), in this study the average airfare on a particular route in a particular quarter in US dollars is used.
• Flight Frequency (FR) = the number of quarterly flights offered on route i at time t. On the supply side, frequency of traffic implies economies of scale. Here fore, an increase in the supply of air services tends to reduce airfares (Liang, 2013). A conventional measure of the frequency of traffic is the number of flights on a route. In this study, the number of flights on a particular route in a particular quarter is used.
4.3.4. Control variables
Control variables are those variables which are held constant throughout the course of investigation in order to test the relative relationship of the explained and explanatory variables, but which strongly influences experimental results. The control variables itself are not of primary interest to the experiment (Stock & Watson, 2013). This analysis uses in both regressions seven different control variables, which are all explained in this section:
Period after the Merger
The binary variable, PAM, indicating the period after the merger, which takes on the value of one for all routes in the periods after the merger and zero for all routes in the periods prior to the merger. Due to implementation of this binary variable, the change in prices and frequencies after the merger on all routes is reflected.
Routes affected by the Merger
The merger variable, RAM, which indicates routes affected by the merger, contains a binary variable which is equal to one if it concerns routes where US Airways or American Airlines have been offering services, and zero otherwise.
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Distance
Number of miles separating the airports of origin and destination on a particular route.
Airfares are expected to increase as the distance of routes increase due to increases in variable costs (Kim & Signal, 1993; Morrison & Winston, 2007). The coefficient of the distance variable is expected to be positive but lower than one in the pricing equation. This indicates that the increase in costs is less than proportional to the increase in the number of miles flown. By contrast, the relationship between frequency and route length is expected to be negative. On routes with a greater distance, carriers may prefer to reduce flight frequency and use larger airplanes whose efficiency increases with distance.
Demand
On the one hand, more passengers cause demand to increase which tend to drive up airfares. On the other hand, more passengers tend to lower the airfares due to economies of scales (Morrison & Winston, 2007). Therefore, the expected sign of the coefficient of demand is ambiguous in the pricing equation. The expected sign of the demand variable in the frequency equation is positive, since supply must adjust to the levels of demand, this should be the variable with the strongest influence on the frequency decisions of airlines. In this model, the total number of passengers carried by airlines on a particular route is used.
In order to correct for a possible bias in the estimated coefficient of this variable, an instrumental variable procedure is applied for. The mean population and GDP per capita of the endpoints of the routes are used as instruments (Statista, 2018).
High-speed train
It concerns a binary variable which takes on the value of one on routes where high-speed-trains are a substitute of air transport, and zero otherwise (Fagada & Perdiguero, 2014).
The coefficient of this variable is expected to be negative in the pricing equation, since high-speed trains can force airlines to reduce fares. The expected effect on the frequency equation is less clear given the fact that if airlines wish to compete with high-speed trains, they are required to maintain high frequencies.
Long
According to Morrison and Winston (2007), long distance routes differ from short distance routes in their quality. Aside from the difference in variable costs due to a longer distance, airfares tend to be higher as a consequence of a higher service level.
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Here fore, the coefficient on this variable in the pricing equation is expected to be positive as prices tend to increase. The coefficient of this variable in the flight frequency equation is ambiguous. Longer distance might, again, give airlines a preference to reduce flight frequency and use larger airplanes.
In this study, a binary variable is used for this variable to capture this difference between short- and long-distance routes. The binary variable takes on the value of one if the particular route is equally or greater than 500 miles, and zero otherwise.
Seasonal Dummies
Three binary variables for the first, second, and third quarter of each year are implemented to rule out seasonal fluctuations as the summer period, where demand for plane tickets tends to be higher compared to other seasons.
Only three binary variables are taken into account to prevent for miscalculations due to the so called dummy variable trap. Which means, if there is an intercept in the regression and if all binary variables are included as regressors, then the regression will fail because of perfect multicollinearity (Stock & Watson, 2012).
4.3.5. Assumptions
In this approach, as well as in the first approach, the assumptions of stationarity, heteroskedasticity, autocorrelation, and no perfect multicollinearity should be met. However, first, correlation between all regressors and the regressands is measured.
The correlation coefficient is an important measure to capture the strength between the different variables used in a study. Results are shown in Appendix E. These results show a perfect correlation between the control variable demand and the dependent variable flight frequency, which is exactly 1.0000. This might also indicate endogeneity of the demand variable. To prevent for a possible bias in the coefficient of this estimator, two instrumental variables are used which are the mean population of the cities of destinations and the GDP of the cities of destination, in the same event window as the other variables. The regression coefficients are now said to be overidentified, since the number of instruments is higher than the number of endogenous variables, respectively two against one. This is a necessity since both instruments need to be valid instruments to produce meaningful results.
First, a test on the relevance of the instruments is performed. Due to the fact that it is not possible to check this with flight frequency as dependent variable, since these two variables are perfectly correlated, the regression with airfares as dependent variable is used. First, the
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two-stage-least-squares regression with the two instruments is performed (Appendix F.1), where after the variable demand is tested to see if this variable is indeed endogenous. Appendix F.2 shows that the Durbin chi-squared as well as the Wu-Hausman F-statistic show very low p-values of 0.0000, which means that the null hypothesis indicating that this variable is exogenous is rejected, and it was correct to treat this variable as an endogenous variable. Hereafter, the first stage regression statistics are reported in Appendix F.3, which reflects the relation between the instruments and the endogenous variable and thus indicates if it concerns relevant instruments. The partial R-squared, which measures the correlation between the endogenous variable and the instruments after the effect of the other regressors is partialed out, is a relevant approximation. The partial R-squared take on the value of 0.7254, which is reliably high. A second interesting value is the F-statistic, which is 49.7998. This is much higher than any of the critical values shown in the table, so the null hypothesis that the instruments are weak is rejected. At last, a test for overidentification is performed. The results in Appendix F.4 shows a p-value of this test higher than 0.05, which suggests that these instruments are valid. So, the estimators are unbiased and consistent, and this model is correctly specified.
Second, a test on exogeneity of the instruments is performed with use of the Hansen’s J-statistic. Results of this test are shown in Appendix F.5, where the p-value of the J-statistic is 0.1468. Concluding, the null hypothesis that the instruments are exogenous is not rejected. This indicates that this model uses valid instruments, both relevant and exogenous.
Hereafter, the other three assumptions are analysed. First, a test on stationarity of the data is performed. In this analysis, unbalanced panel data from 2009 until 2017 is used. Here fore, the Dicky-Fuller test with the fisher variant is conducted. As in the first approach, every variable is tested for stationarity, except for the dummy variables since they do not have a relation with time. The results of this test are shown in appendix G. The variables airfares, frequency, and demand are all stationary. However, the variable distance is not stationary, since the inverse normal Z-statistic is larger than 0.05. For this reason, the null-hypothesis cannot be rejected. One way to account for this non-stationarity, is to take the first lagged value of this variable (appendix G.4, G.5). Therefore, the first difference of the distance variable is conducted where after this variable shows stationarity as well.
Second, the assumption of homoskedasticity is tested. As in the first approach, a likelihood-ratio test is conducted. The results are shown in appendix H. This test requires that both hetero-and homoskedastic panels have to be estimated with generalised least squares regressions. The null hypothesis of the likelihood-ratio test is that the panel is homoskedastic. For the first regression equation which has airfares as a dependent variable, a chi2 of 464.65
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and a p-value of 0.0000 is found. This result does reject the null hypothesis at the 1% level, hence the panel is heteroskedastic. The second equation, which has flight frequency as the dependent variable, has a chi2 of 455.09 and a p-value of 0.0000. This result again does reject the null hypothesis at the 1% level, hence the panel is again heteroskedastic. From these results can be concluded that all panels are heteroskedastic. Here fore, regular standard errors cannot be used and robust standard errors are used in this study, which allow for serial correlation (Stock & Watson, 2012).
Hereafter, an autocorrelation test is performed to test the independence of the values of the error term. It is necessary to prevent for autocorrelation to get reliable results. Because it concerns panel data, the Woolridge test for autocorrelation is a good fit. The results show a p-value lower than 0.05 for both regressions, which indicates no independence between the p-values of the error term (Appendix I). Here fore, it is necessary to use HAC standard errors, which is a form of clustered standard errors, to preserve valid results.
The fourth assumption is the assumption of no perfect multicollinearity. Again, there is no perfect multicollinearity as long as the values of the VIF test are equal of below ten. The results are shown in Appendix J. All values are below five, so it can be concluded that there is no perfect multicollinearity.
Again, as in the first analysis, this analysis includes a differences-in-differences estimator. In this analysis, DiD estimator with multiple regressors. All least squares assumptions are again tested for. As in the first analysis, the first least squares assumption which states the conditional distribution of the error term, given the independent variables, has a mean of zero, cannot easily by tested because observational data is used in which the variables are not randomly assigned. Instead, there is assumed that the variables are as if randomly assigned which means E(ui|Xi)=0 (Stock & Watson, 2012). The results for testing the second least
squares assumption are equal to the results in the first analysis. Appendix I and J show heteroskedasticity and no autocorrelation. Therefore, the variables are again independently but not identically distributed. This error is accounted for by the use of robust standard errors. The third least squares assumption, which states large outliers are unlikely, is confirmed in Appendix L.1 through L.3. Three scatterplots on airfares, flight frequency, and demand are viewed in a graph over time which show no large outliers in the data. Furthermore, DiD requires in addition a parallel trend assumption. This assumption is the most critical assumption of the four to ensure internal validity of DiD models. According to this assumption, it is required that the difference between the control and treatment group is constant over time in the absence of treatment. No statistical test exist for this assumption, however, visual inspection satisfies.
