How do passengers react to airlines’ overbooking strategies? Evidence from the US airlines

Transportation Research Part A 132 (2020) 242–255

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How do passengers react to airlines’ overbooking strategies? Evidence from the US airlines

T

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Hideki Fukuia, , Koki Nagatab a b

Faculty of Law and Letters, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime 790-8577 Japan R.H. Smith School of Business, University of Maryland, College Park, MD 20742 USA

A R T IC LE I N F O

ABS TRA CT

Keywords: Overbooking Denied boarding Bidding system Seat inventory management Control function approach

We examine how passengers react to carriers’ various overbooking strategies by exploiting the fact that in 2011, Delta launched a bidding system that encourages passengers on an overbooked flight to give up their reserved seats voluntarily. To examine whether Delta’s bidding system is effective in increasing (reducing) the number of passengers being voluntarily (involuntarily) bumped, we estimate the changes in the number of denied boardings for Delta and other carriers before and after Delta started its bidding system. To address endogeneity and minimize omitted variable bias, we employ two-step fixed effects Poisson regression models for estimation. The estimation results suggest that Delta’s bidding system seems to work as an effective seat inventory management technique that provides an incentive for potential holdouts to give up their reserved seats voluntarily. As a result, the bidding system is supposed to keep the number of voluntarily bumped passengers from decreasing. Delta’s bidding system seems to effectively keep the number of volunteers relatively constant and, more important, reduce the number of involuntarily bumped passengers.

1. Introduction In this paper, we examine how carriers’ overbooking strategies affect passengers’ reactions to giving up their reserved seats voluntarily or involuntarily in an overbooking situation. Overbooking is a common practice in the airline industry. Indeed, many carriers sell more tickets than available seats to fly with fewer empty seats. However, carriers’ policies vary in terms of their overbooking strategies. One interesting example is Delta’s bidding system, which asks passengers to bid the value of a travel voucher they would accept as compensation for voluntarily giving up their reserved seats when a flight is overbooked. Delta seems to have started this system in 2011. Does this system, which appears to be an efficient method to solicit passengers to give up their reserved seats voluntarily, work as an effective seat inventory management technique in increasing (reducing) the number of passengers being voluntarily (involuntarily) bumped? To examine the effectiveness of Delta’s bidding system, we estimate the changes in the number of passengers voluntarily/involuntarily denied boarding for Delta and other carriers before and after Delta launched its bidding system. Our estimation results suggest that Delta’s bidding system effectively provides an incentive for potential holdouts to give up their reserved seats voluntarily; consequently, the bidding system keeps the number of voluntarily bumped passengers from decreasing and perhaps keeps its load factor as high as possible. The paper is organized as follows. Section 2 provides some background about Delta’s bidding system. A summary of previous

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Corresponding author. E-mail addresses: [email protected] (H. Fukui), [email protected] (K. Nagata).

https://doi.org/10.1016/j.tra.2019.11.001 Received 14 August 2018; Received in revised form 28 September 2019; Accepted 7 November 2019 0965-8564/ © 2019 Elsevier Ltd. All rights reserved.

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studies is also provided in this section. Section 3 describes the estimation model, methods, and the data. The estimation results are reported in Section 4. Section 5 is the conclusion. 2. Background and previous studies 2.1. Background Many carriers intentionally overbook to maximize their aircraft’s capacity utilization, known as load factor, and their revenues. Overbooking is necessary because carriers have allowed their passengers to make reservations and then “no-show” with little or no penalty. According to Belobaba (2009), “In the USA, domestic airline no-show rates average 10–15% of final pre-departure bookings, and can exceed 20% during peak holiday periods. Although there are substantial regional differences, average no-show rates are almost as high throughout the rest of the world…the loss of 10–15% of potential revenues on fully booked flights (which would occur without overbooking) represents a major negative impact on profits.” Consequently, carriers overbook reservations judiciously. Indeed, overbooking is not only one of the oldest revenue management techniques but also one of the most powerful for many carriers1. It is said that carriers usually compute the mean and distribution of the proportion of no-shows and late cancellations for specific markets. Then, they decide on an acceptable percentage of oversold seats and overbook accordingly (Toh and Raven, 2003). For example, according to Klophaus and Pölt (2007), the overbooking module implemented in Lufthansa’s revenue management system balances the risk and associated costs of empty seats and denied boardings and uses constant spoilage costs during the booking period2 (Klophaus and Pölt, 2007; see also Belobaba, 2009; Cook and Billig, 2017). “Factors considered include aircraft capacity, forecasted demand by passenger type, average ticket price by passenger type, forecast cancellation and no-show rates, oversales and spoilage costs, and the likelihood that a turned-away reservation request will choose another flight on the same airline (recapture).” (Barnes, 2012) Usually, carriers do not overbook First Class, moderately overbook Business Class, and aggressively overbook Economy Class. As the factors considered vary across flights, markets and customer segments, overbooking levels also vary across the network, with authorization levels (i.e., the total number of seats to be sold) generally higher in business-oriented routes, where business passengers tend to no-show at higher rates, and lower in leisure-oriented routes, where reservations are more secure (Barnes, 2012). In the United States, when a flight is overbooked, carriers are required first to seek volunteers to give up their reserved seats before using any other boarding priority. According to the Code of Federal Regulations (CFR), a volunteer is “a person who responds to the carrier’s request for volunteers and who willingly accepts the carriers’ offer of compensation, in any amount, in exchange for relinquishing the confirmed reserved space.” If not enough passengers voluntarily give up their reserved seats, the carrier may deny boarding to other passengers in accordance with its boarding priority rules. These passengers who did not give up their seats voluntarily but were denied boarding based on carriers’ boarding priority are considered to have been denied boarding involuntarily regardless whether the passenger accepts the denied boarding compensation (14 CFR 250.2b). Thus, once the number of volunteers is determined, the number of passengers involuntarily denied boarding will be automatically determined. Carriers are required to compensate passengers who show up with tickets but are denied boarding (14 CFR 250.5). The maximum amount of denied boarding compensation (DBC) has been set at $675 or $1350 depending on whether the carrier can offer alternate flight within a predetermined time period since August 25, 2015. Carriers have contrived their overbooking strategies to avoid paying the maximum amount of DBC. In fact, Fig. 1, which is constructed from the US Department of Transportation’s Passengers Denied Confirmed Space Report, shows that since 2008, the industry-wide average number of bumped passengers per 10,000 passengers has decreased for voluntary and involuntary denied boardings. This figure implies that carriers have improved their seat inventory management techniques and thus their aircraft’s capacity utilization. One of the most notable techniques is adopted by Delta: It started a bidding system that asks passengers to bid the value of compensation they would accept for voluntarily giving up their reserved seats around 2011. This system is a kind of blind auction. Delta’s new system … asks passengers to name their price electronically before they arrive at the departure gate if it looks as though there may not be enough seats on a flight. Passengers who check in with Delta online before leaving for the airport or at kiosks 1 Klophaus and Pölt (2007) explain the effectiveness of overbooking as a revenue management technique as follows: “On flights operated by Lufthansa German Airlines 4.9 million passengers did not show up in 2005. This corresponds to 12,500 full Boeing 747 s. To compensate for cancellations and no-shows, most airlines overbook their flights and accept bookings above physical seat capacity. Overbooking allowed Lufthansa to carry more than 570,000 additional passengers. Lufthansa credits the practice of selling more tickets for a flight than there are physical seats for a revenue increase of €105m in 2005 (denied boarding costs already deducted)…” 2 According to Klophaus and Pölt (2007), the overbooking module in the revenue management system (PROS) implemented at Lufthansa works as follows: “Under the assumption of a Gaussian no-show distribution, it calculates the probability of each combination of overbooking level and survivals together with the associated expected denied boarding and spoilage costs and picks the overbooking level where the sum of expected denied boarding and spoilage costs is minimised. There are additional extensions in the PROS overbooking module. It allows piecewise linear denied boarding costs and respects upper limits on the overbooking rate and on the expected number of denied boardings. Furthermore, it respects a service level parameter that specifies the maximum number of expected denied boardings per 10,000 passengers. The PROS overbooking module contains a second overbooking algorithm that maximises revenue instead of MC [minimising costs]. In this case, the calculation of expected revenue per overbooked seat replaces the estimation of spoilage. The algorithm maximises the expected net revenue which is the expected revenue minus expected denied boarding costs.”

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Fig. 1. Industry average number of bumped passengers per 10,000 passengers.

before going through security can type in the dollar amount they would accept from the airline to be bumped from their flight. Delta can then accept the lowest bids, eliminating a lot of the uncertainty early (Esterl, 2011). Fig. 2 shows the numbers of bumped passengers per 10,000 passengers since 2008 for Delta and other carriers. It reveals two notable features: (1) While the number of bumped passengers per 10,000 passengers for other carriers decreased steadily and was around 6 in the first quarter of 2017, (2) the number for Delta has been fluctuating around 10 and shows a slightly increasing trend since 2013. Figs. 3 and 4 also reveal two interesting features. (1) As Fig. 4 shows, Delta decreased its number of involuntarily bumped passengers per 10,000 passengers from 1.8 in the first quarter of 2008 to 0.1 in the first quarter of 2017. But at the same time, as illustrated in Fig. 3, Delta slightly increased its number of voluntarily bumped passengers per 10,000 passengers: Although it was

Fig. 2. Number of bumped passengers per 10,000 passengers. 244

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Fig. 3. Number of voluntarily bumped passengers per 10,000 passengers.

Fig. 4. Number of involuntarily bumped passengers per 10,000 passengers.

about 9.8 in the first quarter of 2008, it reached about 11.5 in the first quarter of 2017; (2) during the same period, both of those numbers for carriers other than Delta declined steadily. These features suggest that (1) carriers other than Delta decreased the overall rate of bumping by decreasing voluntarily and involuntarily bumped passengers whereas (2) Delta appears to have managed to maintain its overall rate of bumping. Indeed, Delta steadily decreased the rate of involuntarily bumped passengers, but at the same time, it increased the rate of voluntarily bumped passengers, especially after 2011, when Delta started its bidding system for voluntarily bumped passengers. In other words, Delta’s bidding system seems to successfully provide an incentive for passengers on an overbooked flight to give up their reserved seats voluntarily instead of holding out to be bumped involuntarily, compared to other carriers’ seat inventory management techniques.

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Fig. 5. Load factor.

The auction solution for airline overbooking was proposed almost 50 years ago by Simon (1968) (See also Vickery, 1972). The mechanism is quite simple. In an overbooking situation, each passenger willing to voluntarily give up his or her reserved seat submits a sealed bid of the minimum amount of compensation he or she will accept. The lowest bidders will be given the amount they bid and be re-accommodated on later flights. Delta utilizes the Internet and mobile technologies to implement the auction scheme under which not only passengers but also Delta seem to be satisfied. Indeed, as Fig. 5 shows, Delta’s average load factor is almost always higher than that of other carriers. Figs. 1–5 provide visual evidence that Delta’s bidding system is an effective seat inventory management technique that keeps its load factor high by providing an incentive for bumped passengers to give up their reserved seats voluntarily. However, other factors such as the average ticket fare and the average number of flights per route could also affect passengers’ reactions. To control for the possible effects of other factors on passengers’ reactions to overbooking, we estimate the changes in the number of bumped passengers for Delta and other carriers by using two-step fixed effects Poisson regression models.

2.2. Previous studies Many studies explored overbooking in the airline industry. However, to our knowledge, few previous studies have explored how carriers’ overbooking strategies affect passengers’ reactions to giving up their reserved seats in an overbooking situation. Indeed, Belobaba (1987), Kimes (1989), McGill and van Ryzin (1999), Rothstein (1971, 1975, 1985), and Smith et al. (1992) only dealt with the history of revenue management in the airline industry and reviewed revenue management research in key areas relating to the airline industry. Alstrup et al. (1986), Amaruchkul and Sae-Lim (2011), Chatwin (1998, 1999), Garrow and Koppelman (2004), Gorin et al. (2006), Karaesmen and van Ryzin (2004), Pulugurtha and Nambisan (2003), Subramanian et al. (1999), and Suzuki (2002, 2006) have dealt with the modeling of seat inventory control for revenue management. Their research focused mainly on the modeling of overbooking that maximizes a given flight’s expected passenger revenue or airline revenue during a certain period. Blanchard (2004) criticized the DBC rule (14 CFR 250.5) that set a statutory cap of $400 for all passengers bumped from flights since 1978 (until 2008), but he did not examine the effects of carriers’ overbooking strategies on passengers’ reactions. Garrow et al. (2011) only provided a qualitative explanation of the impact of the amount of compensation on the number of denied boarding passengers. Lindenmeier and Tscheulin (2008) dealt with customers’ behavioral responses to revenue management practices such as overbooking and showed that the practices had a net negative effect on customer satisfaction. Wangenheim and Bayón (2007) examined how customers behaviorally responded to overbooking experiences, such as downgrading, denied service, or upgrading. They found that customers who experienced the negative consequences of revenue management significantly reduced their number of transactions with the carriers whereas upgraded customers exhibited only weak positive responses. Although these papers dealt with customers’ behavioral responses to overbooking, they did not examine the impact of carriers’ overbooking strategies on passengers’ reactions to giving up their reserved seats in an overbooking situation. Rare exceptions are Simon and Visvabhanathy’s (1977) and Simon’s (1994) research. Simon and Visvabhanathy (1977) argued, based on a questionnaire survey they conducted, that among the passengers on any overbooked flight, a fair portion would accept 246

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small amounts of money or other benefits in exchange for waiting for the next flight. Simon (1994) showed that the rate of involuntary bumping per 10,000 passengers had fallen and that the rate of voluntary bumping had risen greatly since 1978, when the voluntary bumping scheme was introduced along with airline deregulation. Simon (1994) argued that the scheme is a “Pareto improvement” that benefits all parties concerned. Unfortunately, Simon did not have an opportunity to examine the effect of the bidding system adopted by Delta, which is characterized by basically the same mechanism Simon (1994) proposed. To address the lack of empirical research on the subject, we estimate the effect of Delta’s overbooking strategy on passengers’ reactions. 3. Model and data 3.1. Estimation model Our basic estimation model has the following regression formulation of a difference-in-differences model: 4

BPit = α + βDLi +

2017

∑ γt Qt + ∑ t=2

t = 2009

2017

δt Yt +

∑

θt DLi ∙Yt + x it ρ + ci + uit

t = 2009

(1)

The subscripts i and t represent carrier and quarter. The dependent variable, BPit, is each carrier’s quarterly total number of bumped passengers, which includes voluntarily and involuntarily bumped passengers. We use carrier-level quarterly panel data constructed from the US DOT’s Passengers Denied Confirmed Space Report for the period between the first quarter of 2008 and the first quarter of 2017. DLi is the Delta dummy, which is 1 for Delta, 0 otherwise. Qt and Yt are quarter and year dummies. The base categories are the first quarter for Qt and the year 2008 for Yt. DLi·Yt is an interaction term between the Delta dummy and the year dummies intended to capture the changes of the effect of Delta’s seat inventory management strategies on the number of bumped passengers. This is one of the advantages of the regression formulation of the difference-in-difference model: It easily enables us to examine the impact of Delta’s strategies by comparing different periods (Angrist and Pischke, 2008). Delta started its bidding system in 2011. The interaction terms DLi·Yt for the years following 2011 are intended to capture the combined effects of Delta’s bidding system and other seat inventory management techniques. Unfortunately, our main data, the U.S. DOT’s Passengers Denied Confirmed Space Report, is aggregated by carrier and quarter; it does not include any information about airports where denied boarding occurred. Thus, we cannot fully differentiate the effect of Delta’s bidding system from the effect of their other seat inventory management techniques. This is an important limitation of our study. Another important limitation is that our study could not evaluate the cost effectiveness of Delta’s bidding system because Delta does not disclose detailed information about this system, such as actual compensation amounts or airports where denied boarding occurred. Therefore, we cannot examine whether or to what extent Delta’s bidding system contributes to its overall profitability. These limitations should be addressed when non-aggregated, detailed data—including information about when and where denied boarding occurred, route and flight characteristics, actual compensation amounts, etc.—becomes available. 3.2. Control variables and potential endogeneity problem The model includes an array of control variables, xit: (I) carrier’s quarterly total number of passengers (log-transformed), (II) carrier’s quarterly weighted average ticket fare (log-transformed and deflated by CPI-U), (III) carrier’s quarterly average number of domestic and international flights per route, (IV) carrier’s quarterly weighted average load factor on domestic and international routes, and (V) carrier’s quarterly average distance of domestic and international routes. These controls were constructed using the US DOT’s Passengers Denied Confirmed Space Report (regarding (I)), Airline Origin and Destination Survey (DB1B) Market (regarding (II)), and Form 41 Traffic Data, T-100 Domestic/International Segment (all carriers) (regarding III through V). (I) Carrier’s quarterly total number of passengers (log-transformed) (II) Carrier’s quarterly weighted average ticket fare (log-transformed and deflated by CPI-U) All other factors being equal, the greater the number of passengers, the greater the possibility of aircraft/seat inventory mismanagement will be. Thus, the coefficient of the variable that describes a carrier’s quarterly total number of passengers is expected to be positive. In contrast, the variable representing each carrier’s quarterly weighted average ticket fare on domestic routes (logtransformed), which is deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (Source: US Department of Labor (DOL), Consumer Price Index – All Urban Consumers), is expected to have a negative coefficient. Although the maximum amounts are set, the involuntary denied boarding compensation (DBC) can be higher for passengers who paid higher fares. Indeed, the compensation shall be 200% or 400% of the fare to the passenger’s destination or first stopover, with a maximum of $675 or $1350 depending on whether the carrier can offer alternate flight within a predetermined time period (14 CFR 250.5). Therefore, other things being equal, carriers are expected not to aggressively overbook their flights on high-fare routes as opposed to low-fare routes. The ticket fare variable could be endogenous due to possible reverse causality: An increase in the amount of compensation due to the increase of bumped passengers could lead to an increase in ticket price. To deal with this endogeneity problem, we employ a control function approach to address endogeneity (Cameron and Trivedi, 2010; Hilbe, 2011; Wooldridge, 2015a, 2015b). The basic 247

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idea of the control function approach is to derive an additional regressor that controls for the part of the endogenous variable, the average ticket fare variable, pit, that correlates with the error term uit due to reverse causation between the dependent variable, BPit, and the average ticket fare variable, pit. The structural error, uit, could be a function of the first stage error, vit: uit = φvit + ψ, when we have an instrumental variable z, which is unrelated to uit conditional on covariates. ψ is unrelated to vit by definition. Thus, we can correct for endogeneity when we construct estimated residuals, v it̂ , from the fixed effects regression of pit on covariates in the first stage and regress BPit on pit, covariates, and v it̂ in the second stage. The new structural error is independent of the endogenous variable, pit, if we introduce v it̂ in Eq. (1) along with pit. The estimated first stage error, v it̂ , which is an additional regressor in Eq. (1), controls for endogeneity in Eq. (1). This approach is viewed as a variant of the control function approach. An instrumental variable z should have no direct effect on the dependent variable, BPit (each carrier’s quarterly total number of bumped passengers) and should not be correlated with unobserved factors ψ in the equation. At the same time, the instrumental variable z should have the property that changes in z are associated with changes in the endogenous variable, pit (each carrier’s quarterly weighted average ticket fare). As an instrumental variable, we use the fuel price (log-transformed), i.e., the quarterly average US kerosene wholesale/resale price set by refiners (dollars per gallon), which is deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (Source: US Energy Information Administration; US Department of Labor (DOL), Consumer Price Index – All Urban Consumers). The fuel price is unlikely to have a direct effect on the dependent variable, BPit. However, it should have a direct effect on the endogenous variable, pit. Indeed, an increase of fuel price usually forces carriers to raise fares. Thus, a positive sign is expected for the coefficient of the instrumental variable, the fuel price. (III) Carrier’s quarterly average number of domestic and international flights per route The expected signs of the coefficients of variables representing the number of flights per route are negative. The routes with higher flight frequencies could be predominantly business-oriented routes. No-shows are likely to be higher for business passengers than for leisure passengers, which could lead to fewer bumped passengers. (IV) Carrier’s quarterly weighted average load factor on domestic and international routes (V) Carrier’s quarterly average distance of domestic and international routes A higher load factor could lead to a decrease in overbooked flights and bumped passengers. At the same time, an overly aggressive overbooking policy or inaccurate estimates of no-show rates could lead to an increase in overbooked flights and bumped passengers. Then, the signs of the coefficients are indeterminate for the load factor variables. Generally, route distance is not expected to have a direct effect on carriers’ overbooking strategies. Therefore, the signs of the coefficients are also indeterminate for the average route distance variables. 3.3. Estimation method The fixed effect, ci, captures all unobserved time-invariant characteristics of carriers that affect BPit. The error, uit, is the timevarying error, which represents unobserved factors that change over time and affect BPit. It is highly probable that, for example, the variable representing each carrier’s quarterly total number of passengers is correlated with ci, unobserved carrier characteristics. The coefficient estimators will be biased and inconsistent if ci and the explanatory variables are correlated. Thus, we control for the effects of ci by applying the fixed effects model. Especially considering that the above mentioned potential endogeneity and our dependent variable, the number of bumped passengers (BPit), is count data, we use a two-step fixed effects Poisson regression model that controls for unobserved effects and addresses the potential endogeneity problem by applying the above-mentioned control function approach (Cameron and Trivedi, 2010; Hilbe, 2011; Wooldridge, 2015a, 2015b). Although linear regression models are often applied to count variables, they have shortcomings. As the dependent variable, BPit, is equal to or greater than zero, the expected value of BPit conditional on the explanatory variables should be nonnegative. However, coefficients estimated by linear regression models such as ordinary least squares (OLS) could be negative. As a result, the predicted value of BPit could also be negative when linear regression models are applied to our dependent variable, BPit. Thus, regressions were estimated by a fixed effects Poisson regression model, which is appropriate when the dependent variable is a count variable (Cameron and Trivedi, 2010; Hilbe, 2011; Wooldridge, 2010). A central distributional assumption of the Poisson model is the equidispersion, i.e., the equality of the mean and variance of the dependent variable conditional on the explanatory variables. However, this assumption is often violated in real data. Usually the conditional variance exceeds the conditional mean, which is termed as overdispersion; this should be addressed because it “may cause standard errors of the estimates to be deflated or underestimated, i.e., a variable may appear to be a significant predictor when it is in fact not significant.” (Hilbe, 2011) One common way to deal with overdispersion is to use the negative binomial model. However, the negative binomial model can be overdispersed as well. In addition, although we use panel data, it has been discovered that the conditional fixed-effects negative binomial model for count panel data is not a true fixed-effects model because it fails to control for individual fixed effects unless a very specific set of assumptions are met (Allison and Waterman, 2002; Guimarães, 2008; Hilbe, 2011). The negative multinomial model has been suggested as an alternative for the conditional negative binomial, though it produces the same estimators as a conditional Poisson according to Allison and Waterman (2002) and Hilbe (2011). In other words, the negative multinomial model does not provide any additional capability for handling overdispersion than the Poisson model. Thus, 248

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Table 1 Descriptive statistics (2008 Q1–2017 Q1).

Carrier’s quarterly total number of passengers volunteered to give up their seats Carrier’s quarterly total number of passengers denied boarding involuntarily Quarterly average of US kerosene wholesale/resale price by refiners deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (dollars per gallon) (log-transformed) Carrier’s quarterly weighted average ticket fare deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (domestic) (dollars) (log-transformed) Carrier’s quarterly total number of passengers (million) (log-transformed) Carrier’s quarterly average number of domestic flights per route Carrier’s quarterly average number of international flights per route Carrier’s quarterly weighted average load factor (domestic) Carrier's quarterly weighted average load factor (international) Carrier’s quarterly average route distance (domestic) (miles) Carrier’s quarterly average route distance (international) (miles) Observations

Mean

SD

Min

Max

8879.836 902.707 0.0579

8470.0180 928.648 0.319

0 0 −0.700

40939 6167 0.557

4.471

0.243

3.351

4.990

1.887 274.335 130.288 0.799 0.744 760.0194 1823.775 566

0.918 125.168 63.626 0.0436 0.176 615.602 1443.837

−1.477 70.375 0 0.653 0 46 0

3.669 792.174 412.783 0.929 0.901 3801 6806

Notes: Carrier, quarter, and year dummies are omitted for brevity.

Allison and Waterman (2002) suggest applying an unconditional negative binomial regression estimator with dummy variables to represent the fixed effects. However, Hilbe (2011) recommends this form of fixed-effects regression only if there are relatively few panels in the data. According to Hilbe (2011), if there are more than 20 panels, it is preferable to use the conditional fixed effects model because the greater the number of panels, the greater the possible bias in parameter estimates. This is called the incidental parameters problem, first defined by Neyman and Scott (1948). Hilbe (2011) concludes that the negative binomial fixed effects estimator is inconsistent in the presence of a large number of fixed effects, though the nature of this inconsistence is still a matter of debate. Our panel data consists of 21 carriers for the period from 2008 to 2017. Thus, finally, following Hilbe’s (2011) advice and Wooldridge’s argument (Wooldridge, 1999, 2010) that the Poisson assumption is in fact unnecessary for consistent estimation of the conditional mean parameters and the Poisson quasi-maximum likelihood estimator is fully robust to distributional misspecification, we decided to use a fixed-effects Poisson model by applying the control function approach. To correct for the possible underestimation of standard errors due to potential overdispersion, we estimated the standard error using the bootstrap method. 4. Is Delta’s bidding system effective in motivating bumped passengers to give up their reserved seats voluntarily? Table 1 presents descriptive statistics for the unbalanced quarterly panel of 21 carriers for the period from the first quarter of 2008 to the first quarter of 2017 (see Appendix A for the list of carriers that appear in our data set). Table 2 contains the estimation results. As we use the fixed effects model, carrier fixed effects, ci (including Delta dummy), are differenced out of the equation and thus are not reported in Table 2. 4.1. Total number of bumped passengers Column 1 of Table 2, which represents the estimation results from the fixed effects Poisson model, shows that the coefficients of year dummies are all negative except for the 2009 dummy. In addition, the coefficients of year dummies, which increased in their absolute value over the years, are statistically significant except for the 2009 and 2010 dummies. As we use the fixed effects model, carrier fixed effects, ci (including Delta dummy), are differenced out. Therefore, the coefficients of year dummies show the changes over the years in the number of bumped passengers for carriers other than Delta compared to the number of bumped passengers for those carriers in 2008. Likewise, the coefficients of the interaction terms between year dummies and the Delta dummy indicate the changes over the years in the number of bumped passengers for Delta compared to the number of bumped passengers for carriers other than Delta in the current year. The estimation results suggest that carriers other than Delta decreased the overall number of bumped passengers over time. In contrast, the coefficients of the interaction terms between the Delta dummy and year dummies are all positive except for the 2009 dummy. Although the absolute size of the coefficients of the interaction terms fluctuates, it generally increases in its absolute value over the years. Also, the positive coefficients of the interaction terms are statistically significant below the 5% level except for the 2010 and 2013 dummies. These data suggest that Delta generally increased the number of bumped passengers over the years compared to other carriers in the current year. Column 1 of Table 3 presents the results of the test of joint significance of the year dummies and the interaction terms. Only the coefficients for 2012 and 2013 are statistically significant. The results suggest that Delta neither increased nor decreased its number of bumped passengers during the analysis period, except in 2012 and 2013, compared to the number of bumped passengers for carriers other than Delta in 2008. This finding is in line with the suggestion derived from Fig. 2. However, the endogeneity problem is not addressed in the above estimation model. Column 2 of Table 2 presents the results from the two-step fixed effects Poisson model, which deals with the endogeneity of the average fare variable. Even after we address the endogeneity, the overall pattern of the estimation results remains quite similar to the results reported in column 1 of Table 2 except 249

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Table 2 Estimation results. (1) Fixed effects Poisson model

(2) Two-step fixed effects Poisson model

(3) Fixed effects Poisson model

(4) Two-step fixed effects Poisson model

(6) Two-step fixed effects Poisson model

Carrier’s quarterly total number of passengers denied boarding involuntarily

Dependent variable

Carrier’s quarterly total number of bumped passengers

Carrier’s quarterly weighted average ticket fare deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (domestic) (dollars) (log-transformed) Carrier’s quarterly total number of passengers (million) (log-transformed) Carrier’s quarterly average number of domestic flights per route Carrier’s quarterly average number of international flights per route Carrier’s quarterly weighted average load factor (domestic) Carrier's quarterly weighted average load factor (international) Carrier’s quarterly average route distance (domestic) (miles) Carrier’s quarterly average route distance (international) (miles) Y2009

0.167 (0.259)

−1.016 (2.058)

0.0796 (0.241)

−0.795 (2.169)

0.796 (0.545)

−2.978 (2.873)

0.969*** (0.119) −0.00191** (0.000717) −0.0000704 (0.000302) 0.761 (0.776) 0.121 (0.0858) −0.0000261 (0.0000234) 0.00000261 (0.00000916) 0.0501 (0.0667) −0.0615 (0.0766) −0.241* (0.122) −0.383* (0.156) −0.540** (0.180) −0.618*** (0.183) −0.563** (0.195) −0.714*** (0.187) −0.824*** (0.156) −0.0589 (0.0855) 0.116+ (0.0676) 0.240* (0.118) 0.505*** (0.122) 0.265+ (0.146) 0.478*** (0.138) 0.659*** (0.151) 0.672*** (0.146) 0.715*** (0.105) –

0.943*** (0.135) −0.00188** (0.000703) −0.000417 (0.000714) −0.0293 (1.676) 0.263 (0.515) −0.0000262 (0.0000247) 0.00000664 (0.00000773) −0.0257 (0.151) −0.0566 (0.0810) −0.171 (0.111) −0.298* (0.141) −0.443* (0.187) −0.519** (0.178) −0.496** (0.160) −0.739** (0.226) −0.831*** (0.178) −0.127 (0.127) 0.0650 (0.112) 0.199+ (0.109) 0.489*** (0.114) 0.261+ (0.147) 0.548* (0.240) 0.754* (0.303) 0.772** (0.286) 0.802*** (0.243) 1.189 (2.100)

0.962*** (0.134) −0.00194** (0.000694) −0.0000220 (0.000294) 0.840 (0.803) 0.108 (0.0824) −0.0000303 (0.0000228) −0.000000720 (0.00000908) 0.0404 (0.0703) −0.0748 (0.0781) −0.232+ (0.124) −0.409* (0.166) −0.573** (0.191) −0.649*** (0.191) −0.582** (0.197) −0.741*** (0.185) −0.845*** (0.153) −0.0166 (0.0893) 0.256*** (0.0730) 0.367** (0.115) 0.655*** (0.128) 0.399** (0.154) 0.652*** (0.144) 0.838*** (0.149) 0.863*** (0.138) 0.903*** (0.0965) –

0.942*** (0.154) −0.00192** (0.000675) −0.000278 (0.000776) 0.255 (1.727) 0.212 (0.497) −0.0000303 (0.0000233) 0.00000225 (0.00000794) −0.0156 (0.163) −0.0711 (0.0819) −0.180+ (0.108) −0.346* (0.153) −0.502* (0.200) −0.575** (0.183) −0.533*** (0.156) −0.759*** (0.229) −0.850*** (0.178) −0.0666 (0.131) 0.219+ (0.117) 0.337** (0.105) 0.643*** (0.121) 0.396* (0.158) 0.704** (0.252) 0.908** (0.314) 0.937** (0.295) 0.967*** (0.249) 0.879 (2.211)

1.056*** (0.218) −0.00209+ (0.00111) −0.000246 (0.00146) −0.750 (1.475) 0.166 (0.221) 0.0000112 (0.0000550) 0.0000406+ (0.0000217) 0.132+ (0.0752) 0.0818 (0.128) −0.301+ (0.167) −0.115 (0.153) −0.209 (0.162) −0.307+ (0.179) −0.340 (0.242) −0.438 (0.287) −0.620+ (0.341) −0.367*** (0.0733) −1.527*** (0.160) −1.378*** (0.214) −1.087*** (0.168) −0.956*** (0.146) −1.504*** (0.143) −2.089*** (0.230) −2.492*** (0.252) −2.337*** (0.284) –

0.975*** (0.271) −0.00197 (0.00128) −0.00136 (0.00191) −3.246 (2.447) 0.616 (1.097) 0.0000101 (0.0000633) 0.0000539* (0.0000260) −0.111 (0.200) 0.0963 (0.148) −0.0778 (0.240) 0.154 (0.198) 0.0986 (0.234) 0.00665 (0.277) −0.128 (0.306) −0.519 (0.345) −0.646 (0.396) −0.582** (0.184) −1.689*** (0.231) −1.509*** (0.265) −1.136*** (0.209) −0.970*** (0.187) −1.279*** (0.258) −1.787*** (0.311) −2.174*** (0.340) −2.060*** (0.380) 3.789 (2.863)

Y2010 Y2011 Y2012 Y2013 Y2014 Y2015 Y2016 Y2017 Delta*Y2009 (Interaction between Delta dummy and Year 2009 dummy) Delta*Y2010 Delta*Y2011 Delta*Y2012 Delta*Y2013 Delta*Y2014 Delta*Y2015 Delta*Y2016 Delta*Y2017

v it̂ (the fixed effects residuals obtained in the first stage) Endogenous variable Instrumental variable

Carrier’s quarterly total number of passengers who volunteered to give up their reserved seats

(5) Fixed effects Poisson model

(continued on next page)

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Table 2 (continued) (1) Fixed effects Poisson model

Dependent variable

Carrier’s quarterly weighted average ticket fare deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (domestic)

Quarterly average of US kerosene wholesale/resale price by refiners deflated by the quarterly average of monthly CPI-U (1982–84 = 100) (dollars per gallon) (log-transformed)

F-statistic Observations Log likelihood

(2) Two-step fixed effects Poisson model

(3) Fixed effects Poisson model

(4) Two-step fixed effects Poisson model

(6) Two-step fixed effects Poisson model

(5) Fixed effects Poisson model

Carrier’s quarterly total number of bumped passengers

Carrier’s quarterly total number of passengers who volunteered to give up their reserved seats

Carrier’s quarterly total number of passengers denied boarding involuntarily

–

0.04190* (0.0170)

–

0.04190* (0.0170)

–

0.04190* (0.0170)

– 566 −139005.32

2.2e+05

–

2.2e+05

–

2.2e+05

−138935.85

−125711.49

−125677.03

−45961.297

−45896.993

Standard errors in odd columns (1, 3, and 5) are clustered by carrier and those in even columns (2, 4, and 6) are obtained by 1000 bootstrap replications. As we use the fixed effects model, the Delta dummy is differenced out of the equation. Quarter dummies are omitted for brevity. + p < 0.1. * p < 0.05. ** p < 0.01. *** p < 0.001. Table 3 Test of joint significance. (1) Fixed effects Poisson model

(2) Two-step fixed effects Poisson model

(3) Fixed effects Poisson model

(4) Two-step fixed effects Poisson model

Dependent variable

Carrier’s quarterly total number of bumped passengers

Combination of parameters

Coefficient (Standard error)

Carrier’s quarterly total number of passengers who volunteered to give up their reserved seats Coefficient (Standard error)

Y2009 + Delta*Y2009

−0.00881 (0.0424) 0.0542 (0.0374) −0.000978 (0.0439) 0.122* (0.0579) −0.275*** (0.0614) −0.140 (0.0900) 0.0956 (0.0960) −0.0427 (0.0817) −0.110 (0.102)

0.0238 (0.0403) 0.181** (0.0485) 0.135* (0.0533) 0.245*** (0.0664) −0.174* (0.0706) 0.00319 (0.0986) 0.256* (0.106) 0.122 (0.0949) 0.0578 (0.118)

Y2010 + Delta*Y2010 Y2011 + Delta*Y2011 Y2012 + Delta*Y2012 Y2013 + Delta*Y2013 Y2014 + Delta*Y2014 Y2015 + Delta*Y2015 Y2016 + Delta*Y2016 Y2017 + Delta*Y2017

−0.152 (0.233) 0.00837 (0.111) 0.0281 (0.0746) 0.191 (0.126) −0.183 (0.166) 0.0295 (0.293) 0.257 (0.285) 0.0329 (0.156) −0.0296 (0.154)

−0.0822 (0.247) 0.147 (0.123) 0.157+ (0.0820) 0.296* (0.133) −0.1058 (0.174) 0.128 (0.307) 0.375 (0.297) 0.178 (0.165) 0.117 (0.165)

(5) Fixed effects Poisson model

(6) Two-step fixed effects Poisson model

Carrier’s quarterly total number of passengers denied boarding involuntarily Coefficient (Standard error) −0.235* (0.0756) −1.445** (0.107) −1.678*** (0.120) −1.202*** (0.123) −1.165*** (0.139) −1.810*** (0.179) −2.429*** (0.200) −2.930*** (0.191) −2.958*** (0.192)

−0.693* (0.352) −1.593*** (0.195) −1.587*** (0.153) −0.982*** (0.204) −0.872** (0.260) −1.273** (0.422) −1.915*** (0.413) −2.692*** (0.274) −2.706*** (0.287)

+ p < 0.1. * p < 0.05. ** p < 0.01. *** p < 0.001.

for the coefficients of the average ticket fare variable and the 2009 dummy, which changed their signs from positive to negative. This time, the results of the test of joint significance of the year dummies and the interaction terms, which are presented in column 2 of Table 3, show that none of the coefficients of the interaction terms is statistically significant. Again, this finding is in line with the trend shown in Fig. 2, which suggests that Delta does not seem to have proactively tried to decrease the number of bumped 251

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passengers; rather, it has tried to keep the number of bumped passengers relatively constant, perhaps to keep its load factor as high as possible. Regarding control variables, column 2 of Table 2 shows that the coefficient of the average ticket fare variable has an anticipated negative sign but is not statistically significant. The first-step results are shown in column 2 of Table 2. Only the coefficient of interest is reported. The coefficient of the instrument, the fuel price, shows an expected positive sign and is statistically significant. In addition, the first-step F statistics exceed 10. Hence, our instrument could be considered a suitable instrument (Staiger and Stock, 1997). The variable representing each carrier’s quarterly total number of passengers also has an expected positive and statistically significant coefficient. The coefficients of variables representing the number of flights per route have also expected negative signs for domestic and international routes but are statistically significant only for domestic routes. The domestic routes with multiple daily flights could be predominantly business routes. No-shows are likely to be higher for business passengers than for leisure passengers, which could lead to fewer bumped passengers. None of the coefficients of the load factor variable and the route distance variable are statistically significant. One possibility regarding the positive coefficients of the international load factor and route distance variables is that carriers’ aircraft/seat inventory mismanagement (e.g., overly aggressive overbooking policy or inaccurate estimates of no-show rates) resulted in the increase in the number of bumped passengers. 4.2. Number of voluntarily bumped passengers The above estimation results do not shed light on the question of whether Delta’s bidding system successfully provides an incentive for passengers on an overbooked flight to give up their reserved seats voluntarily instead of holding out to be bumped involuntarily. Therefore, in this and the following subsections, we use each carrier’s number of voluntarily and involuntarily bumped passengers as the dependent variable. Column 3 of Table 2 presents the estimation results of the fixed effects Poisson model in which the dependent variable is the number of voluntarily bumped passengers. The overall pattern of estimation results for the control variables is not substantially different from the results reported in column 1 of Table 2. The signs of coefficients are the same except for the coefficient of the variable representing the average distance of international routes, which is not statistically significant. The coefficients of the year dummies and those of the interaction terms between the Delta dummy and the year dummies also show a pattern similar to those presented in column 1 of Table 2. As column 4 of Table 2 shows, even after we control for the average fare variable’s endogeneity, the estimation results are essentially the same. Only the coefficients of the variables representing the average fare and the average distance of international routes changed their signs though neither is statistically significant. Here, the estimation results for the year dummies and the interaction terms suggest that carriers other than Delta decreased the number of voluntarily bumped passengers whereas Delta increased the number of voluntarily bumped passengers over the years, compared to other carriers in the current year. However, the results of the test of joint significance of the year dummies and the interaction terms after controlling for endogeneity, which are presented in column 4 of Table 3, indicate that only the coefficient for the combination of parameters for the year 2012 is statistically significant below the 5% level. Although Figs. 3 and 4 seem to suggest that Delta’s bidding system successfully provides an incentive for passengers on an overbooked flight to refrain from holding out and give up their reserved seats voluntarily in an overbooking situation, the estimation results do not support this suggestion. However, it can be said that Delta’s bidding system does not seem to have a negative impact on passengers who potentially volunteer to give up their seats. Put differently, the bidding system seems to contribute, at least in part, to keeping the number of voluntarily bumped passengers from decreasing. 4.3. Number of involuntarily bumped passengers Last, we use each carrier’s number of involuntarily bumped passengers as the dependent variable to determine whether Delta’s bidding system successfully makes it unattractive for passengers on an overbooked flight to hold out. Column 5 of Table 2 presents the estimation results of the fixed effects Poisson model. Once again, the overall pattern of estimation results for the control variables is essentially the same. Only the coefficients of the variables representing the average load factor and distance on domestic routes changed sign, but neither is statistically significant. Column 5 of Table 2 shows that the coefficients of the year dummies have negative signs except for 2009 and 2010, but none of the coefficients of the year dummies are statistically significant below the 5% level. The estimation results suggest that carriers other than Delta were not successful in decreasing the overall number of involuntarily bumped passengers over time, though they were successful in decreasing the overall number of voluntarily bumped passengers, as suggested in columns 3 and 4 of Table 2. Interestingly, the interaction terms’ coefficients are all negative and statistically significant below the 5% level. As shown in column 6 of Table 2, the sign and significance of the interaction terms remain unchanged even after we address the average fare variable’s endogeneity. The absolute size of the coefficients of the interaction terms decreased from 2010 to 2013, but it increased after 2014. The results of the test of joint significance of the year dummies and the interaction terms, which are presented in column 6 of Table 3, show a similar pattern: The coefficients for the combination of parameters are all negative and statistically significant, and the absolute size of the coefficients decreased from 2010 to 2013 but increased afterward. The estimation results suggest that Delta decreased its total number of involuntarily bumped passengers by about 70% in 2009, compared to the number of involuntarily bumped passengers for carriers other than Delta in 2008. Delta kept decreasing the number of involuntarily bumped passengers 252

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afterward. In 2011, when Delta started its bidding system for voluntarily bumped passengers, its number of involuntarily bumped passengers decreased by about 159% compared to the same number for other carriers in 2008. (In 2008, Delta’s quarterly average number of involuntarily bumped passenger was 2601 whereas the same average number for other carriers was 798. Therefore, it is possible that Delta’s number of involuntarily bumped passengers decreases more than 100% compared to the same number for other carriers in 2008, which is the baseline category for our estimation.) Delta’s number of involuntarily bumped passengers slightly increased in 2012 and 2013, but it decreased again afterward. In 2017, Delta’s number of involuntarily bumped passengers decreased by about 271% compared to the same number for other carriers in 2008. Taken together, the estimation results suggest that carriers other than Delta could not successfully decrease the overall number of involuntarily bumped passengers over time. In contrast, Delta’s bidding system worked effectively in keeping some potential holdouts from being bumped involuntarily. Rather, the bidding system seems to have provided an incentive for potential holdouts to give up their reserved seats voluntarily. Regarding control variables, the positive and statistically significant coefficient of the international route distance variable (presented in column 6 of Table 3) is somewhat puzzling because the result seems to suggest that the longer the international routes, the higher the possibility of aircraft/seat inventory mismanagement. However, this suggestion does not seem valid. A possible explanation of the results can be provided by passengers’ preference for travel time. International routes could be longer than domestic routes. Other factors being equal, passengers would prefer shorter travel times to longer travel times. Passengers on international flights who prefer shorter travel times may be more reluctant to increase their travel time by volunteering to give up their reserved seats compared to passengers on domestic flights of shorter distances. If so, it is not particularly puzzling that the coefficient of the international route distance variable is positive and statistically significant. The result suggests that the longer the international routes, the more passengers hold out, hoping to be bumped involuntarily. 5. Conclusions We examined Delta’s bidding system’s effectiveness in increasing (reducing) the number of passengers being voluntarily (involuntarily) bumped. Our estimation results suggest that (1) Delta’s bidding system seems to work as an effective seat inventory management technique that provides an incentive for potential holdouts to give up their reserved seats voluntarily, and as a result, (2) it keeps Delta’s number of voluntarily bumped passengers from decreasing, thereby keeping Delta’s load factor as high as possible. Our contribution is that we have shown that Delta’s bidding system could be a more effective overbooking management procedure than those of other carriers. Unfortunately, as mentioned above, our main data is aggregated by carrier and quarter. Therefore, we cannot fully differentiate the effect of Delta’s bidding system from the effect of their other seat inventory management techniques. This inability is a major limitation of our study. Another important limitation is that we could not evaluate the cost effectiveness of Delta’s bidding system. Delta does not disclose detailed information about its bidding system, such as actual compensation amounts or airports where denied boarding occurred. Thus, although we could examine whether Delta’s bidding system contributes to keeping its load factor high, we could not examine whether or to what extent their bidding system contributes to increased profitability. As we have shown, Delta’s bidding system seems to provide an incentive for passengers on overbooked flights to voluntarily give up their reserved seats and reduce the number of involuntarily bumped passengers. However, if bumped passengers received much higher compensation than those under the other carriers’ overbooking systems, Delta’s denied boarding cost could be higher than the benefit from increasing its load factor. Therefore, even if Delta’s bidding system is effective in keeping its load factor high, it is not clear whether or to what extent that system is cost effective and profitable compared to other carriers because of the trade-off between the cost of denied boarding associated with aggressive overbooking and the cost of spoilage due to conservative overbooking. These major limitations can be overcome by using non-aggregated, detailed data, which needs to include information about when and where denied boarding occurred, route and flight characteristics (such as distance, departure time, and frequency of flights), actual compensation amounts, and passengers’ show-up rates, boarding rates, and (possibly) go-show rates for each carrier and route. Future research should address these limitations when such detailed data becomes available. Acknowledgements We are grateful to three anonymous reviewers, as well as Tae Oum, Jan Brueckner and seminar participants at the 2018 Air Transport Research Society World Conference for their valuable and helpful comments. Fukui acknowledges financial support from the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (B), 16H03673; Grant-in-Aid for Research Activity Start-up, 17H06916). All remaining errors are the responsibility of the authors.

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Appendix A. List of carriers appeared in the data set (2008 Q1–2017 Q1)

Serial Number

Carrier code

Carrier name

1

9E

Pinnacle Airlines Endeavor Air

2

AA

3

AS

4

B6

5

CO

6

DL

7

EV

8

F9

9

FL

10

HA

11

MQ

12

NK

13

NW

14

OH (1)

15

OO

16

UA

17

US

18

VX

19

WN

20

XE

21

YV

Periods covered by the data set Notes (Source: US DOT’s websitea)

1st Quarter of 2008–2nd Quarter of 2013 3rd Quarter of 2013–4th Quarter of 2013 American Airlines 1st Quarter of 2008–1st Quarter of 2017 Alaska Airlines 1st Quarter of 2008–1st Quarter of 2017 JetBlue Airways 1st Quarter of 2008–1st Quarter of 2017 Continental Air 1st Quarter of 2008–4th Lines Quarter of 2011 Delta Air Lines 1st Quarter of 2008–1st Quarter of 2017 Atlantic Southeast 1st Quarter of 2008–4th Quarter of 2011 ExpressJet 1st Quarter of 2012–1st Airlines Quarter of 2017 Frontier Airlines 1st Quarter of 2008–1st Quarter of 2017 AirTran Airways 2nd Quarter of 2008–4th Quarter of 2014 Hawaiian Airlines 1st Quarter of 2008–1st Quarter of 2017 1st Quarter of 2008–2nd American Eagle Quarter of 2014 Airlines 3rd Quarter of 2014–4th Envoy Air Quarter of 2015 Spirit Air Lines 1st Quarter of 2015–1st Quarter of 2017 Northwest 1st Quarter of 2008–4th Airlines Quarter of 2009 Comair 2nd Quarter of 2008–4th Quarter of 2010 SkyWest Airlines 1st Quarter of 2008–1st Quarter of 2017 United Air Lines 1st Quarter of 2008–1st Quarter of 2017 US Airways 1st Quarter of 2008–2nd Quarter of 2015 Virgin America 1st Quarter of 2012–1st Quarter of 2017 Southwest 1st Quarter of 2008–1st Airlines Quarter of 2017 ExpressJet 2nd Quarter of 2008–4th Airlines Quarter of 2011 Mesa Airlines 1st Quarter of 2008–4th Quarter of 2013

Endeavor operated as Pinnacle prior to August 2013.

American and US Airways began reporting jointly as AA in July 2015 following their 2013 merger announcement.

United and Continental began reporting jointly in January 2012 following their 2010 merger announcement. Delta and Northwest began reporting jointly in January 2010 following their 2008 merger announcement. Atlantic Southeast and ExpressJet began reporting jointly in January 2012.

Southwest and AirTran began reporting jointly in January 2015 following their 2011 merger announcement.

Envoy operated as American Eagle prior to April 2014.

Delta and Northwest began reporting jointly in January 2010 following their 2008 merger announcement.

United and Continental began reporting jointly in January 2012 following their 2010 merger announcement. American and US Airways began reporting jointly as AA in July 2015 following their 2013 merger announcement.

Southwest and AirTran began reporting jointly in January 2015 following their 2011 merger announcement. Atlantic Southeast and ExpressJet began reporting jointly in January 2012.

a US DOT, Database Name: Air Carrier Statistics (Form 41 Traffic) - U.S. Carriers < https://www.transtats.bts.gov/Tables.asp?DB_ID=110&DB_ Name=Air%20Carrier%20Statistics%20%28Form%2041%20Traffic%29-%20%20U.S.%20Carriers&DB_Short_Name=Air%20Carriers > (Accessed on April 20, 2017).

Appendix B. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.tra.2019.11.001.

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