Transport Policy 125 (2022) 218–230 Contents lists available at ScienceDirect Transport Policy journal homepage: www.elsevier.com/locate/tranpol Market heterogeneity and the relationship between competition and price dispersion: Evidence from the U.S. airline market Charles Howell a, b, *, Emili Grifell-Tatjé c a Department of Business, Universitat Autònoma de Barcelona, Spain b University of Nebraska Omaha, United States c Department of Business, Universitat Autònoma de Barcelona, Spain A R T I C L E I N F O A B S T R A C T JEL classification: Previous studies agree that competition influences price dispersion, however there is disagreement on the di­ D24 rection of the effect. To explain this contradiction in findings we include a measure not typically considered in D40 competitive analysis, the level of market heterogeneity. We find that the response of price dispersion to changes D43 in competition is conditioned by differentiation. When products in a market are homogenous, increasing L93 competition reduces price dispersion, while in a market with heterogeneous products, the same increase in Keywords: competition increases price dispersion. We include an output attribute index as a control for market heteroge­ Price discrimination Product differentiation neity and test our method on 73,981 observations of airfare data from 2002 through 2016. The implication of our Pricing findings for policymakers is that the traditional measures of market concentration do not determine the level of Airline industry competition alone. Decisions on allowing or disallowing mergers should consider market heterogeneity, not just Output attribute index concentration. The results of this work contribute toward extending knowledge on the effect of competition on Firm heterogeneity price dispersion and introduce a method of measuring market differentiation. 1. Introduction inverse-U-shaped relationship between competition and price disper­ sion, with dispersion initially growing as a concentrated market be­ The relationship between market structure and price dispersion has comes competitive, but then declining at higher levels of competition. interested economists since merchants first posted prices. Textbook Understanding why these conclusions differ can significantly impact theory argues that as a market becomes competitive dispersion will how policies and regulations are formed. To contribute to this under­ evaporate as all prices converge on marginal cost. However, this is not standing, we consider the qualitative characteristics associated with the reflected in real-world markets where persistent price dispersion can be product. Based on these characteristics—which Ray and Mukherjee observed in markets of all structures. The relationship between market (1996) refer to as “output attributes”—we introduce a new measure of structure and price dispersion has been documented in markets for market heterogeneity grounded in index number theory. products such as groceries (Kaplan et al., 2016; Eden 2018), retail gas­ In this paper, we identify the cost premium driven by a higher level oline (Lach and Moraga-González, 2017; Shepard, 1991), auto insurance of output attributes and use this premium to measure market differen­ (Dahlby and West, 1986), and U.S. domestic airline fares (Borenstein tiation. Price dispersion arising from cost differences is not considered and Rose, 1994; Gerardi and Shapiro, 2009; Dai et al. 2014). Despite this discrimination, so this premium is removed from the fare price creating depth of study, the relationship between market structure and dispersion a more homogenous product. Remaining price dispersion is measured remains unclear. The lack of clarity is particularly obvious in relation to and analyzed. This study answers three research questions. First, how U.S. domestic airline fares, where the three articles cited come to widely much price dispersion is driven by cost differences resulting from a wide differing conclusions. range of output attributes? Second, how does the level of competition In one of the first studies on market structure and dispersion of affect price dispersion after accounting for output attribute cost-driven airline fares, Borenstein and Rose (1994) find that price dispersion in­ price dispersion? Third, are the direction and magnitude of competi­ creases with competition. This finding is contradicted by Gerardi and tion’s effect on price dispersion dependent on the level of output attri­ Shapiro (2009), who argue the textbook model and find that competi­ bute differentiation in the market? tion strictly reduces price dispersion. Dai et al. (2014) find an The U.S. domestic airline market is ideal for empirically testing the * Corresponding author. E-mail address: cbhowell@unomaha.edu (C. Howell). https://doi.org/10.1016/j.tranpol.2022.06.001 Received 28 February 2021; Received in revised form 10 May 2022; Accepted 5 June 2022 Available online 9 June 2022 0967-070X/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by- nc-nd/4.0/). C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 relationship between market structure and price dispersion. Airlines can discrimination in differentiated product markets, showing that market sort passengers by product valuation using ticket characteristics such as power is not a requirement for discrimination. The model was formal­ advance-purchase discounts, round trip, or refundability. There is also ized by Holmes (1989), who demonstrated that firm-level elasticity of heterogeneity between airlines in output attributes such as on-time demand can be decomposed into two components, industry elasticity performance, departure frequency, or load factor. Additionally, the U. and cross-price elasticity. Industry elasticity is based on consumer S. market is dynamic and includes routes with a wide range of carriers valuation of the basic product whereas cross-price elasticity is based on and competitive levels. the price of a substitute. The distinction between these two forms is We find that by including the measure of market heterogeneity we important for our analysis because they result in a different amount of can explain the contradictions in previous results. In short, we find that price dispersion, a distinction we expand on later in this section. in markets where the product is more homogenous, the textbook effect Cost-driven price variances are not considered price discrimination, of a reduction in price dispersion is associated with increases in nor dispersion, and distinguishing between the two makes empirical competition. While in more heterogeneous markets, an increase in work difficult. Shepard (1991) works around this difficulty by exploiting competition leads to an increase of dispersion. These results form the a situation where firms have similar production costs but differ in their basis for policy recommendations. They show that introducing a mea­ ability to price discriminate. Shepard compares price differentials be­ sure of market heterogeneity as a complement to the Herfin­ tween full-service and self-service gasoline, at stations that offer both dahl–Hirschman Index (HHI) of market concentration is imperative products, with the price differentials between full-service and when regulators examine potential mergers. For example, in the current self-service gasoline at stations that offer only one or the other. Results business press there is speculation on “mergers of equals” like Spirit and show that the differential is greater in multi-product stations. Frontier Airlines, or JetBlue and Alaska Airlines. As we show in this The product of the airline industry, a seat on a flight, is perishable in paper, market concentration alone is not sufficient to understand the nature and has uncertain demand. Considering these characteristics, impact of these potential mergers. In addition, when policy is based on Dana (1999) models a system where the firm must establish prices and the findings of applied economics, it is important to understand and quantities (inventory of seats) prior to knowing what demand will be. resolve contradictions. In a recent article on trends in air transportation Equilibrium in the model is found by establishing multiple price points policy, Button (2019) notes that there is a lack of replication in air with a limited number of seats available at each point. Dana’s model transport work which can lead to credibility issues. To that end, in this shows that as competition increases, the average price level falls and the paper we show how these contradictions can be resolved without degree of price dispersion increases. Also looking at the airline industry, invalidating previous work. Stavins (2001) studies dispersion due to price discrimination. Using the We make two major contributions in this paper. First, we introduce a marginal implicit price of ticket restrictions in interaction with market general method of measuring market heterogeneity. This method can be concentration, Stavins examines restrictions used to separate consumers applied in any empirical research that controls for levels of market by valuation of convenience and flexibility. The model shows that the power. Second, our results from the applied section contribute to the marginal effect of restrictions is less on concentrated routes, or in other research line on understanding the relationship between market struc­ words, the same ticket restriction yields a greater discount on a more ture, competition, and price dispersion. The paper is structured as fol­ competitive route. lows. In section 2 we provide a motivational discussion and background As shown in the section, there are multiple theoretical explanations on price dispersion and market structure. In section 3 we introduce a for observed price dispersion. In this paper, we focus mainly on price measure of differentiation based on output attributes and apply it to fare discrimination and cost differences, expanding on price discrimination prices. In section 4 we outline the data and variable construction and in in the next section and on cost differences in section 3. section 5 present the results. Finally, we cover conclusions, policy rec­ ommendations, and ideas for further research in section 6. 2.2. Market structure and price dispersion 2. Background Borenstein (1985) builds on a generalized price discrimination model introduced by Salop (1979) by developing a characteristic space 2.1. Price dispersion model of monopolistic competition. In this model, brand characteristics and consumer preferences differ on one dimension and are represented The study of price dispersion has a long history because its existence as equidistant points on a unit-circumference circle. Through reserva­ runs counter to the textbook model of most market forms. Standard tion price, the model allows for two forms of price discrimination, theory allows for price dispersion in a monopoly market where firms can sorting consumers by preferred brand or by basic utility. The first form is sort consumers and price discriminate, but under perfect competition, termed “monopoly-type discrimination” because only one brand can all firms accept a single market price. Between the polar cases, most provide a positive consumer surplus. Under this form of discrimination, oligopoly models allow for little to no dispersion in price, and in models the firm sorts consumers based on industry elasticity and basic valuation of monopolistic competition, price dispersion is driven by product cost of the brand; high-valuation consumers are charged a higher price while differences. Theoretical explanations for price dispersion include costly low-valuation consumers receive a discount. Under the second form, information search, uncertain demand, price discrimination, and cost “competitive-type discrimination”, multiple firms can provide consumer differences. surplus. Here it is more effective for the firm to segment by cross-price In one of the earliest studies, Stigler (1961, p. 214) focuses on the elasticity, providing a discount to customers on the verge of switching role of information and search stating, “Price dispersion is a manifes­ brands. The model shows that price dispersion is greater under tation—and, indeed, it is the measure—of ignorance in the market.” competitive-type discrimination than under monopoly-type discrimi­ Stigler shows that cost of search, changing supply and demand condi­ nation. Applying this model to price dispersion in airline fares, Boren­ tions, and the difficulty of updating prices generate the observed price stein and Rose (1994) find that competitive-type discrimination dispersion. In the same vein of information and search, Stahl’s (1989) dominates and that price dispersion increases as airline markets become model of temporal price dispersion shows that sales and intentional more competitive. price fluctuations allow retailers to generate price dispersion by capi­ In contrast, Gerardi and Shapiro (2009) find that increasing talizing on uninformed consumers. competition strictly reduces price dispersion in airline fares. Citing The second common source of dispersion is price discrimination, traditional microeconomic theory, they argue that as competitors enter which results from exploiting differences in consumers’ willingness to the market, incumbents will find it difficult to price discriminate. Using pay. Borenstein (1985) introduced a model of third-degree price panel data, they analyze the effect of competition on price dispersion in 219 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 U.S. airfares between 1993 and 2006 and find that competition has a Are the direction and magnitude of the effect of competition on price negative effect on price dispersion. dispersion dependent on the level of output attribute differentiation in In another panel data study of airfares, Dai et al. (2014) find that the the market? We believe that answers to these three research questions effect of competition on price dispersion has a non-monotonic inver­ will contribute to understanding the relationship between price se-U-shaped relationship. They point to two opposing effects, first a dispersion and market structure and may be able to explain contradic­ direct price effect which increases dispersion as a highly concentrated tions found by previous work.1. market becomes more competitive, and then an indirect “quality” effect that leads to reduced dispersion as less concentrated markets become 3.1. A cost approach even more competitive. The three studies noted above have all been of the U.S. domestic When production of a scalar output has associated qualitative output market; however, this question has been looked at in other markets as attributes, Ray and Mukherjee (1996) note that these attributes affect well. In a study of the market connecting the U.K. and Ireland, Gaggero the maximum output quantity producible from a given input bundle, or and Piga (2011) find a negative relationship between competition and in the dual problem, the minimum cost achievable.2 Ignoring these price dispersion. In their work, they also discuss monopoly-type and output attributes when measuring and comparing the cost of production competitive-type price discrimination, finding evidence of processes can result in underestimating or overestimating costs. Begin­ monopoly-type. Obermeyer, Evangelinos, and Püschel (2013) move the ning with standard notation, we denote output as y ∈ R+ , the vector of empirical setting for this same question to the European airline market. output attributes as q ∈ Rm n + , the vector of inputs as x ∈ R+ , the vector of Their results support the argument for a non-monotonic relationship, input prices as w ∈ Rn+ and the vector of output prices as p ∈ Ri+ . Note with the effect of further competition depending on the current degree of that one output can be associated with multiple prices. The production concentration. possibility set that defines the output and associated output attributes This paper considers a variable of market structure that is not typi­ possible for a given set of inputs is noted as cally included in this type of analysis: differentiation and the degree of firm heterogeneity in the market. By adding this variable, we contribute T = {(x, y, q) : x can produce y with output attributes q}. (1) to understanding the relationship between market structure, competi­ Given technology set T, we now define the set of inputs x required for tion, and price dispersion. every output quantity y with the level of output attributes q as L(y, q) = {x : (x,y,q) ∈ T}. Technology set T defines all the possible input vectors 3. Methodology that can produce a specific output at a given output attribute level. With the addition of input prices w, we move from input quantities to pro­ In this section, we show how the presence of a wide or narrow range duction cost and can define the least expensive bundle of inputs required of output attributes can alter the response of price dispersion to a change to generate a specified quantity of output and level of output attributes. in competition. In homogenous markets where firms have similar levels For an output quantity y, output attribute vector q and input prices w, of output attributes, monopoly-type discrimination dominates, while in the firm allocates the inputs to generate the required quantity of output heterogeneous markets that exhibit differentiation, competitive-type at a minimum cost, defined as discrimination is stronger. For example, imagine that the Seattle–Salt { } Lake City (SEA–SLC) route is served by Delta and Alaska Airlines, and c(w, y, q) = min wT x : x ∈ L(y, q) (2) assume that they have similar output attributes. With little to differen­ Including the transpose of the input price vector “T,” we express the tiate between brands, consumers are sorted on reservation price as minimum cost as wT x(q), where wT x(q) = c(w, y, q). As defined in (2), under monopoly-type discrimination. Compare this with a second route, more inputs x would be required to create either a greater quantity of y Philadelphia to Raleigh-Durham (PHL–RDU) served by American Air­ at the same level q or an equal quantity of y with a greater output lines and Frontier. On this route, if we assume market heterogeneity attribute level q. Comparing one output quantity y at two output attri­ based on differing output attributes, then the possibility of competitive- bute levels q and q0, where q ≥ q0 , we would find that x(q) ≥ x(q0 ) and type discrimination exists. To control for this difference by route, we wT x(q) ≥ wT x(q0 ). introduce an output attribute index that allows us to categorize markets From (2) we derive the minimum cost of providing output quantity y, as heterogeneous or homogenous, and we compare price dispersion on with output attributes q and input prices w. However, the cost between these two types of routes. The comparison lets us explore our first periods for a single firm, or between individual firms in a single period, research question: How much price dispersion is driven by cost differ­ can vary greatly based on the scale of operations. For this reason, we ences resulting from a wide range of output attributes? move to a unit or average cost function to better understand the effect of Moving to a dynamic analysis, and our second research question, we changes in output attributes. The move to a unit or average cost function look at changes in the level of competition and examine the effect on is also useful when applying cost changes to unit prices. With output price dispersion after controlling for differences in output attribute defined as y, we can find a unit or average cost function ac(w, y, q) as levels. Returning to the SEA–SLC route, assume there is an increase in competition coming from a third airline that provides attributes similar c(w, y, q) ac(w, y, q) = . (3) to the incumbents, JetBlue for example. The model would predict a y decrease in price dispersion following the increase in competition. However, if instead the change in competition on the SEA–SLC route comes from an airline with lower output attributes, Frontier for 1 example, the opportunity for competitive-type discrimination is created An alternative approach would be to control for the number of full-service allowing customers to be sorted by output attribute preference. The carriers (FSCs) and low-cost carriers (LCCs) in the market. The drawbacks would be that there is no distinction between carriers in each group, less model would now predict an increase in price dispersion following the distinction between markets, and that the approach would not allow for change increase in competition, as hypothesized by Borenstein and Rose (1994). over time as carriers adjust their product offerings. Comparing the effect of competition on routes that vary by output 2 An alternative approach was introduced by Spady and Friedlaender (1978). attribute index sheds light on the second question: How does the level of In their hedonic cost-function approach, an effective output is calculated such competition affect price dispersion after controlling for output attribute that C = C(ψ (y, q), w) where ψ (y, q) is a vector of functions that defines an cost-driven price dispersion? effective output and where ψ i = ψ i (y, qi1 , …, qi1 ). We adopted the Ray and Comparing routes that vary in competition and in the level of Mukherjee (1996) approach in this paper because it more easily adapts to product differentiation also lets us answer our third research question: multiple outputs. 220 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 Since our interest lies in capturing the cost premium of providing a with (4), ac(wh , yh , qh ) ≥ ac(wh , yh , q0 ) as well as c(wh , yh , qh ) ≥ c(wh , yh , greater level of output attributes, we measure cost differences between q0 ), thus Q(wh , yh , qh , q0 ) ≤ 1. An index value of 1 signifies that the different attribute levels for the same firm and period. Extending (3), we cost of firm h reflects the lowest level of attributes, while a value of 0.5 define ac(wh , yh , qh ) h = 1, …, k as the average minimum cost given w, would indicate that firm h has a unit cost that is double that of providing y, and output attribute level q, which defines the attribute level the lowest level of attributes.5 In section 4, we discuss moving this currently provided by firm h in a specific market. Similarly, ac(wh , yh , measure to the market level to measure market heterogeneity. Note that q0 ) h = 1, …, k is the minimum cost for the same output quantity and the output attribute index Q(w, y, q, q0 ) is bounded between 0 and 1 price level, but with the lowest level of output attributes in the market with the same result ranking as the HHI and the Gini coefficient have. q0 , where q0 = {q01 ,…,q0m } and q0j = Min {q0jh , h = 1,..,k}, j = 1,..,m.19 3.2. Output attribute index 3.3. Implementing the output attribute index In the literature, changes in average cost are thought to come from a In this section we outline implementing both a parametric and non- limited number of sources. Capturing the change from the price of in­ parametric approach to estimate and construct the empirical production puts, Konüs (1939) defines a theoretical input price index as a scalar frontier needed to estimate minimum cost c(wh , yh , qh ). function that compares input price vectors w0 and w1 for a given output y in the context of a cost function.3 Building on the Konüs approach, 3.3.1. A non-parametric approach Grifell-Tatjé and Lovell (2015) discuss the drivers of unit cost change. The non-parametric data envelopment analysis (DEA) method was They show that a difference in average cost can come from only two introduced by Charnes et al. (1978) and moved to the economic context sources, a change in the price of inputs or a change in productivity. In by Färe et al. (1985).6 Non-parametric models estimate the frontier this paper, we extend these concepts by introducing an output attribute using the minimum extrapolation method and require minimal as­ index which collects the impact on the unit cost of changes between the sumptions of the functional form of production. With our focus on level of output attributes q and q0 as finding the minimum cost for a given level of output and output attri­ butes, we use a cost minimization model with variable returns to scale. Q(wh , yh , qh , q0 ) = ac(wh , yh , q0 ) ; h = 1, .., k The minimum cost is found by solving the DEA linear programming ac(wh , yh , qh ) (4) problem for one observation h with output quantity yh and output 0 c(wh , yh , q ) attribute level q. = ; h = 1, .., k. c(wh , yh , qh ) ∑ k ∑ k ∑ k The index of output attribute differentiation defined in the first row c(wh , yh , q) = minwTh x s.t. λl xli ≤ x i = 1,…,n; λl yl ≥ yh ; λl qlj ≥ q j holds output quantities and input prices equal, allowing measurement of l=1 l=1 l=1 the impact on unit cost of a change in the output attributes from q to q0. ∑ k = 1,…,m; λl = 1; λl ≥ 0. Remember that q0 has been defined in the previous section 3.1 as the l=1 vector with the lowest level of output attributes. The second row, after (5) simplifying by dropping y, shows that the impact on the total minimum The minimum cost is solved for twice, first with q taking the value of cost of a change in the output attributes from q to q0is equal to the unit observed qh to find c(wh ,yh ,qh ) and then as q0 to find c(wh , yh , q0 ). The cost result from the first row. These results show that the output attri­ applied part of the paper follows the non-parametric approach. bute index can be calculated on either minimum unit cost or minimum cost, meaning the model can be easily applied to the case of multiple 3.3.2. A parametric approach outputs as well.4. Recalling that qh represents the observed level of output attributes The cost function and Q(wh , yh , qh , q0 ) in (4) can also be estimated for a firm in a market and that q0 represents the lowest level of observed by a parametric method, where the model is defined a priori and re­ quires assumptions on the functional form of production. The form most attributes in the market, then for all cases where qh ≥ q0 and consistent common in airline cost functions is the translog (Christensen et al., 1973). Regarding the estimation method of airline cost functions, pre­ 3 vious literature includes the application of both deterministic para­ A Konüs (1939) price index is in the literature considered a theoretical index in contrast with the alternative classification as an empirical index. As a metric frontiers (Gillen et al., 1990; Johnston and Ozment, 2013) and theoretical index, a Konüs price index is defined directly from the underlying stochastic parametric frontiers (Ahn and Sickles, 2000; Assaf, 2009). A production technology, and it inherits the desirable properties from it. Conse­ deterministic linear programing approach for the estimation of para­ quently, because the underlying production technology is unobserved, a Konüs metric functions is also possible (Aigner and Chu, 1968). We define C as price index is also unobserved, and must be estimated. Empirical index the total cost per firm at time t, w as the price of inputs, y as output, and q numbers, like the well-known Laspayres, Paasche, Fisher, or as output attributes, and include a time trend variable (t) to account for Edgeworth-Marshall, are constructed from observable market transactions and the panel nature of our data. Assuming the standard restrictions to can therefore be calculated directly. Their calculation depends on both prices and quantities and, because this information is not fully observable in the case of output attributes, the empirical index numbers are not a suitable alternative in this study. Balk (2018) provides a comprehensive introduction to empirical index numbers. The original formulation of a Konüs price index is K(w0 , w1 , y) = c(w1 , y)/c(w0 , y), in which c(w1 , y) and c(w0 , y) are cost frontiers without output attributes. The Konüs price index converts a comparison of two input price vectors w0 and w1 to a ratio of two scalars. K(w0 , w1 , y)⋛1 and it shows if 5 the cost of producing y is more expensive, equally expensive, or less expensive The output attribute index can be formulated in the form of difference with input prices of w1 than w0 . Grifell-Tatjé and Lovell (2015, Ch 5) provide a instead of ratio. The formulation is based on the first row of (4) and is given discussion of the Konüs price index, and the implicit input quantity index and by.ac(wh , yh , qh ) − ac(wh , yh , q0 ) ≥ 0. 6 its decomposition. The output attribute index defined in (4) is similar to a See Liu et al. (2013) for a general survey of DEA or Schefczyk (1993) for a theoretical Konüs price index. detailed discussion of this technique applied to airlines. 4 In addition to multiple outputs, this method could be applied to a revenue function to capture differentiation by input attribute. 221 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 ensure input price linear homogeneity and symmetric cross effects,7 the time period t, and define Sjt (p(q0 )) as dispersion of adjusted prices. The translog cost function to be estimated is method of measuring price dispersion will be defined in the next section. Hereafter we note price dispersion as Sjt ( ⋅), to signify either Sjt (p(q)) or ∑ n ∑ n ∑ n ∑ l ln Cht = αi ln wiht + 12/ αij ln wiht ln wjht + αiy ln yiht Sjt (p(q0 )). i=1 i=1 j=1 i=1 Following the structure of previous literature, we define Sjt ( ⋅) as ∑ l ∑ l n ∑ ∑ l dependent variables and competition (Com) as the independent variable. +12 αijy ln yiht ln yjht + αijwy ln wiht ln yjht We also include dummy variable χ jt as a control for the presence of a / i=1 j=1 i=1 j=1 ∑ m bankrupt carrier in the market.8 Market fixed effects are represented as + αkq ln qkht + αt t + εht . υj and we include a full set of quarterly time dummies as γt to control for k=1 exogenous demand and cost effects. Residuals are captured by. εjt . Given the log nature of the translog cost function, the value Q(wh , yh , Because we are measuring product-level price dispersion rather than qh , q0 ) in (4) can be directly calculated after parameters α̂ = {̂ αi , ̂ α ij , ̂ α iy , brand-level dispersion,9 we add a control variable for the carriers pre­ α α ijwy , ̂ ̂ ijy , ̂ α t } are estimated. Recalling (4) as Q(wh , yh , qh , q0 ) = α kq , ̂ sent in the market. Firms differ in their pricing strategies and vary in c(wh , yh , q0 )/c(wh , yh , qh ), we have their amounts of price discrimination. When measuring brand-level ( ) [ ( ) ] dispersion, firm strategy would be captured in the fixed effects, but in Q wh , yh , qh , q0 = exp ln c wh , yh , q0 − ln c(wh , yh , qh ) the case of product-level dispersion it must be accounted for. To control [ ] for firm strategy, we add a dummy variable for each of the carriers ∑ m ∑ m represented in our study as δht . The following panel regression is then = exp α qk ln q0kt − ̂ α qk ln qkht . ̂ (6) estimated as a baseline, k=1 k=1 Sjt ( ⋅ ) = β1 Comjt + θ χ jt + δht + γt + υj + εjt , (8) Using expression (6), we find the cost premium of providing a higher level of attributes. It is worth mentioning that the form of the previous which measures the effect of competition on price dispersion over time expression is linked to the specification of a translog function. However, as coefficient β1 , but does not account for the level of market hetero­ the specification of other functional forms may have associated a geneity. different formulation of expression (6), an aspect that is open to future To account for the level of market heterogeneity, we add Qjt to the research. A drawback of any parametric approach is that the functional estimation as the value of the output attribute index, expression (4), for form must be defined prior to estimation. Because the interaction of output attributes, output, and inputs is not well-defined, in the applied market j in time period t. In the previous section, we defined Q(wh , yh , part of this paper we use the non-parametric DEA approach defined in qh , q0 ) as a firm-level output attribute index; moving this measure to the Section 3.3.1. market level is discussed in subsection 4.5. The addition of this variable is unique to the literature and contributes to understanding the rela­ tionship between market structure, competition, and price dispersion. 3.4. Estimating market price dispersion and the effect of competition The following panel regression addresses our first two research ques­ tions and is estimated with the same control variables as are used in (8): Using expression (5), we find the cost premium of providing a higher level of attributes and remove it from price, allowing us to measure the Sjt ( ⋅ ) = β1 Comjt + β2 Qjt + θχ jt + δht + γt + υj + εjt . (9) amount of price dispersion resulting from differentiation by output at­ Our third research question focuses on the effect of the interaction tributes. Beginning with observed prices by market and quarter, ph (qh ) between competition and product differentiation on price dispersion. represents a vector of observed prices for firm h in a specific market and Specifically, when the market is homogenous (low differentiation) the quarter. Noting the definition of the output attribute index from (4), we effect of an increase in competition is thought to reduce price dispersion, use the formula below to generate the vector ph (q0 ) that equalizes prices but when the market is heterogeneous (high differentiation) the effect of for differences in output attributes between firms and removes any cost increasing competition is an increase in price dispersion. To capture this premium for differentiation by output attribute: effect, we add the interaction of Com and Qjt to equation (9) and estimate ( ) ( ) ph q0 = ph (qh )⋅Q wh , yh , qh , q0 i = 1, .., l; h = 1, .., k. (7) the following panel regression with the same control variables as are used in (8): An alternative way of explaining formula (7) is that the unit margin, ph (qh ) Sjt ( ⋅ ) = β1 Comjt + β2 Qjt + β3 (Com⋅Q)jt + θχ jt + δht + γt + υj + εjt . defined here as αh = ac(wh , yh , qh ) , can be applied to the minimum unit (10) cost with the lowest level of attributes to find an adjusted price ph (q0 ) = αh ⋅ac(wh , yh , q0 ). To address potential problems of endogeneity with the competition We now move the analysis from the firm to the market level, and the focus to changes in price dispersion over time. With p(q) as the vector of all observed prices in a market and p(q0 ) as the vector of all adjusted prices, we define Sjt (p(q)) as the observed price dispersion in market j at 8 As noted by Ciliberto and Schenone (2012), during a bankruptcy, airlines lower route-specific prices, and increase them after emerging from bankruptcy. 7 To impose homogeneity of degree one input prices, we divide totalm cost C 9 The terms “product-level price dispersion” and “brand-level price disper­ ∑ and all input prices w by one of the input prices. We also require that αk = sion” are often referred to as “inter-firm price dispersion” and “intra-firm price m m m k=1 1, ∑ αkj = ∑ αjk = ∑ αky = 0. We apply Shephard’s lemma to obtain the dispersion.” In this paper we focus more on product-level, or inter-firm, price k=1 k=1 k=1 dispersion. The output attributes we use in this paper are experienced by all m share of input k in total cost: Sk = ∂ln C/∂ lnwk = αk + ∑ αjk ln wjht + consumers equally and allow firms to differentiate their products. For example, k=1 all passengers, first class and coach, experience the same arrival time. The m ∑ question of how the presence of output attributes affects intra-firm price αky ln yht ; k = 1, …, m, where Sk = wk xc /C it follows that Sk = 1. k=1 dispersion would be a promising area for future research. 222 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 variables in formulas (8–10), we adopt the instrumental variable this data set we build a panel of quarterly on-time performance measures approach.10 In the empirical section, instrumented variables are denoted for each carrier for each of the sixty quarters analyzed. A flight is by a hat. considered on-time if it arrives within 15 min of its scheduled arrived time. Average on-time arrival performance over the period was 80.6%, 4. Data with a minimum of 11.5%, a maximum of 100%, and a standard devi­ ation of 8.3%. Flight frequency is sourced from the T-100 Domestic In this section we provide a discussion of the sources and construc­ Segment table, collected as part of Form 41. We calculate it as the tion of the data used in the applied portion of this study. All data are average number of daily flights provided by the carrier.14 On the pre­ provided by the Bureau of Transportation Statistics (BTS), 11 an inde­ viously mentioned SFO–SLC market route, in Q4 2016, United Airlines pendent statistical agency within the U.S. Department of Transportation. averaged 0.86 flights per day, Alaska Airlines 1.02, and Delta Airlines Our unit of analysis is a non-stop, coach-class flight between two city 2.37. pairs. Non-stop refers to a flight with no intermediate stops between city Load factor, the proportion of aircraft seats with revenue-paying pairs. The market is defined by a set of city pairs which we term a route. passengers, is also sourced from the T-100 Domestic Segment table. For example, three airlines service the route San Francisco (SFO) to Salt Because passengers prefer a lower load factor, the output attribute is Lake City (SLC) with non-stop flights: Delta, Alaska Airlines, and United measured as (1 – load factor) to be consistent with other output attri­ Airlines. We measure the price dispersion of all carriers on the route, in butes. Average load factor during the period under observation was 73% this example, the prices of Delta, Alaska, and United. We combine ob­ with a standard deviation of twelve percentage points. We measure the servations in cities with close-by airports that are easily substitutable. output attributes of on-time performance and load factor at the carrier For example, O’Hare (ORD) and Midway (MDW) are both located in the level and flight frequency at the carrier-route level. An extended Chicago metropolitan area, so observations for these airports are treated description of output, on-time performance, frequency, load factors, and as a single location; therefore, flights from San Francisco to O’Hare routes by carrier can be found in Table 1. Output is presented as average (SFO–ORD) or Midway (SFO–MDW) constitute a single route.12. passenger miles per quarter and route, and we can see significant Table 1 4.1. Flight operations, output quantities, and output attributes Statistics of output, output attributes, and routes – average route. Carrier Passenger On-Time Flight Load Routes Flight operations data used to generate our best-practice production Miles Arrival Frequency Factor frontier and to derive minimum costs are sourced from BTS Form 41. y (millions) q1 (%) q2 (#) q3 (%) (#) Traffic data are reported monthly and financial data are collected quarterly and include statistics on traffic, capacity, cost, income, and AirTran 31 79 2.7 24 119 Airways Co. balance sheet accounts. Alaska Airlines 56 83 2.5 21 87 To measure output, a number of airline studies have used measures Inc. of output generated, such as ton miles available or seat miles available America West 65 81 3.2 23 83 (Assaf, 2011; Arjomandi and Seufert, 2014; Lee and Worthington, Airlines Inc. American 105 79 4.3 19 208 2014), while others have focused on the revenue-generating measures of Airlines Inc. revenue passenger miles (RPM) or revenue ton miles (Färe et al., 2007; ATA Airlines 64 78 2.1 26 35 Wang et al., 2014). With our focus on passenger ticket prices, we have Continental Air 86 79 3.3 19 120 chosen to use RPM, calculated as the number of paying passengers Lines Inc. multiplied by the miles traveled, as our measure of output (y).13. Delta Air Lines 79 82 3.6 18 260 Inc. Three variables were chosen for output attribute vector q: i) on-time Envoy Air 10 78 3.8 29 169 arrival performance, ii) flight frequency, and iii) load factor. Numerous ExpressJet 10 78 2.6 25 209 previous studies (see Borenstein, 1989; Douglas and Miller, 1974; Airlines Inc. Ippolito, 1981; Suzuki, 2000; Gayle and Yimga, 2018) have identified Frontier Airlines 35 78 2.2 15 68 Inc. these attributes as important in differentiating air carriers. We source Hawaiian 90 93 4.0 13 23 on-time arrival data from the BTS On-Time Performance database. From Airlines Inc. JetBlue Airways 65 77 2.9 17 97 Mesa Airlines 7 81 1.8 21 154 10 Higher price dispersion can make a market attractive to prospective en­ Inc. Northwest 52 79 3.0 20 197 trants. This attraction can create reverse causation and positive bias in the least- Airlines Inc. squares estimates of β. Although, a Hausman endogeneity test did not indicate PSA Airlines 4 70 1.8 30 92 this bias, we have chosen to follow the previous literature in using instrumental Inc. variables to keep our results consistent. Endogeneity can also arise from SkyWest 9 82 2.4 21 336 omitted variables, a problem also solved by the instrumental approach. We used Airlines Inc. market-level variables of distance between end points, arithmetic and geo­ Southwest 43 82 3.5 24 455 metric mean of endpoint populations, total enplaned passengers, and two var­ Airlines Co. iables introduced by Borenstein and Rose (1994). We also used the Hausman Spirit Air Lines 31 73 1.2 15 147 United Air Lines 95 80 3.4 17 197 test to check for endogeneity in our Q variable and found no evidence of Inc. endogeneity. 11 US Airways Inc. 61 81 3.5 20 160 https://www.transtats.bts.gov/homepage.asp (Accessed February 15, Virgin America 95 81 3.1 18 27 2022.). 12 The following close-by airports are combined in the results: DFW (Dal­ las–Fort Worth) and DAL (Love Field); LGA (LaGuardia), EWR (Newark) and JFK (J. F. Kennedy); AZA (Phoenix–Mesa Gateway) and PHX (Phoenix Sky 14 Harbor); TPA (Tampa) and PIE (St. Pete–Clearwater); DCA (Reagan) and IAD As carriers can enter or exit a market during a quarter, we find the average (Washington Dulles); ORD (O’Hare) and (MDW) Midway. number of daily flights for each month the carrier was active in the market, 13 By using only passenger miles, we are ignoring freight and mail as an then find the average for the quarter based only on the months they were active. output; however, because passenger revenue is typically 98% of total revenue For example, if Delta entered a market in March, its flight frequency for that for this group of carriers, the impact of freight and mail is negligible. quarter would be based only on the number of daily flights performed in March. 223 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 variation in values. coach-class itineraries for flights within the U.S. We include both one-way and round-trip tickets, but define ticket price as a one-way fare, 4.2. Inputs thus round-trip tickets are included as half of the full fare. Itineraries costing less than $10 are excluded to eliminate frequent flyer tickets, We use the standard airline inputs of fuel, labor, flight capital, and promotional tickets, or non-revenue passengers. We also exclude fares purchased materials and services (see Oum et al., 2005; Färe et al., 2007; that the BTS has flagged as questionable. Wu et al., 2013; Wang et al., 2014). These form our input quantity vector Following previous work, we use the Gini coefficient as our primary x and input price vector w. Fuel data are sourced from Form 41 schedule measure of dispersion S( ⋅) for estimations (8–10), and this Gini coeffi­ P-12(a) and are measured as total gallons of fuel consumed. The price is cient takes a value between 0 and 1.18 Our calculation for the Gini co­ calculated as a ratio of total cost to gallons of usage. Regarding labor, we efficient of fares follows the formula established by Borenstein and Rose use the number of full-time equivalents (FTE) as the measure of labor. (1994) and Gerardi and Shapiro (2009).19 Because the Gini coefficient is Total salary and benefits divided by the number of FTE provides the labor bounded between zero and one, we follow Gerardi and Shapiro and use price. For flight capital, we follow a process similar to that of Färe et al. the log-odds ratio given by S( ⋅) = ln[Gini /(1 − Gini)], which provides (2007) and define capital as the total number of seats available based on an unbounded statistic. To further understand how competition affects the number of planes in service and the seat configuration used by the price and dispersion, we also look at the 10th percentile price (P10), the carrier. The cost of capital comes from two sources, leasing rates and 90th percentile price (P90), and the spread between these two prices capital depreciation, and the price is calculated as the ratio of the total (P90–P10). The fifteen-year period between 2002 and 2016 provides 73, cost of capital to quantity. The final input is purchased materials and 981 separate quarterly route observations with 20 individual carriers services, which is calculated as total operating expenses less the cost of all and 2079 routes represented. At 0.23, the overall Gini measure is in line other identified inputs. The result is deflated by the Bureau of Labor with the measure in previous studies.20. Statistics (BLS) producer price index (PPI) of air transportation support activities to obtain quantities, and the price is set equal to the index 4.5. Differentiation value.15 Table 2 provides a quarterly average of inputs by carrier and the average route. As with outputs, we can observe a significant amount of As defined in (4), the output attribute index Q(wh , yh , qh , q0 ) mea­ variation. sures the impact on the unit cost of a change between output attribute level qh and q0. However, for the purpose of (8–10), we need a measure 4.3. Competition and market structure at the market level to indicate the degree of differentiation by output attribute in the market. Forsund and Hjalmarsson (1979) demonstrated Following previous works, we use two proxy measures for competi­ that it was possible to create a firm representative of an industry based tion, the HHI and the number of carriers on a route. The HHI, a measure on the arithmetic average of all firm inputs, outputs, and output attri­ of market concentration, varies from 0.0 to 1.0 and is calculated as the butes qh . The value for q0 is already at the market level and does not sum of the squares of market shares of all firms in the market.16 Our need to be averaged. A similar approach was used by Yu et al. (2018) in definition of a market as non-stop flights between two city pairs is their study of ferry transportation. Following these examples, we create relatively narrow, which is reflected in the average HHI score of 0.76 a representative carrier for each route and quarter and calculate a over the period of analysis.17 This value is in line with the 0.79 HHI market output attribute index defined as Q(w, y, q, q0 ) where w, y, and reported by Dai et al. (2014) and the 0.72 to 0.78 noted by Gerardi and q are the average of all carriers in the market. The interpretation of Q(w, Shapiro (2009). To facilitate comparison of the HHI value and the y, q, q0 ) at the market level is the same as for the case of firm h provided number of carriers, we follow Gerardi and Shapiro (2009) and use the after expression (4). Over the period observed, the average value for negative of the log of the HHI, noted in our estimation as the instru­ Q(w, y, q, q0 ) was 0.95 with a standard deviation of 0.09. For the mented variable − ln HERF. ̂ purpose of our estimation, we want a value that increases with differ­ entiation to match the value of − ln HERF ̂ which increases with 4.4. Ticket data competition, so we use the inverse value noted as Q(w, y, q, q0 )− 1 . We analyze coach-class tickets over the fifteen-year period of the first 5. Results quarter 2002 to the fourth quarter 2016. Ticket price data come from the Airline Origin and Destination Survey (DB1B), a 10% quarterly sample 5.1. Descriptive results collected by the BTS that is reported by all U.S. carriers that have at least 1% of the total scheduled-service domestic passenger revenue. The Results for observed and adjusted fare and price dispersion values are reporting group changed over the period of observation, ranging from presented in Table 3. To provide detail and context, we have separated ten to eighteen firms as carriers entered and exited the group. the results by degree of market concentration. Following Borenstein and Following previous airline literature (see Borenstein and Rose, 1994; Rose (1994), we are grouping together markets where one carrier has a Gerardi and Shapiro, 2009; Dai et al., 2014), we include non-stop, 18 The Gini coefficient is a value between 0 and 1 and is equal to twice the expected absolute difference as a proportion of the mean price between any two randomly drawn ticket prices. For example, a Gini coefficient of 0.20 would 15 https://www.bls.gov/data/Series PPI industry group data for air trans­ indicate an expected absolute price difference of 40% of the mean fare for any portation support activities, not seasonally adjusted. two randomly drawn (∑tickets. ) [ ( 19 ∑ PAXj )] k GINI = 1 − 2 x farei x total PAX PAXi Revenues x total PAX x 1 − i total PAX 16 ∑ i=1,N j=1,i HHI = s2h where s is the share of firm h in the market and k is the number h=1 of firms. here N is the number of different fare-level tickets reported by a carrier on a 17 The U.S. Department of Justice guidelines for horizontal mergers consider specific route, farei is the fare for the ith ticket, and PAXi is the number of an HHI below 0.15 as indicating a non-concentrated market, between 0.15 and passengers. traveling at that fare. 20 0.25 moderate concentration, and above 0.25 high concentration. https: Borenstein and Rose (1994), using Q2 1986 data, calculated a Gini of 0.18, //www.justice.gov/atr/horizontal-merger-guidelines-08192010 (Accessed Gerardi and Shapiro (2009) calculated 0.22 for the 1993–2006 period, and Dai February 9, 2022.). et al. (2014) calculated 0.23 for the 1993–2008 period. 224 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 Table 2 Statistics of input quantity and input prices (route average). Fuel (x1) Labor (x2) Flight Capital (x3) Other Material (x4) Carrier Gal (000’s) Price ($) FTE (#) Price ($) Seats (#) Price ($) Quantity Price ($) AirTran Airways Co. 661 2.00 62 15.69 29 17.51 9 141.51 Alaska Airlines Inc. 1,037 2.02 113 22.96 47 14.51 22 143.73 America West Airlines Inc. 1,222 1.05 133 14.32 56 18.15 24 123.41 American Airlines Inc. 2,162 1.88 254 21.49 96 11.64 49 143.73 ATA Airlines 1,160 1.43 138 14.29 55 22.64 28 131.10 Continental Air Lines Inc. 1,566 1.68 203 20.10 72 16.65 60 135.55 Delta Air Lines Inc. 1,496 2.00 175 24.02 69 11.94 52 143.73 Envoy Air 352 1.85 55 12.31 17 13.80 6 137.50 ExpressJet Airlines Inc. 222 1.46 28 16.45 14 17.95 4 141.12 Frontier Airlines Inc. 770 2.38 76 16.80 30 21.69 13 153.56 Hawaiian Airlines Inc. 1,424 2.13 134 23.22 73 19.04 29 151.11 JetBlue Airways 1,236 2.19 112 20.89 50 13.03 17 149.31 Mesa Airlines Inc. 155 2.64 16 10.99 10 26.82 3 150.74 Northwest Airlines Inc. 1,242 1.52 131 23.21 58 9.89 31 131.46 SkyWest Airlines Inc. 126 2.50 28 14.89 11 23.93 2 149.31 Southwest Airlines Co. 834 1.79 85 24.96 40 10.34 11 143.73 Spirit Air Lines 431 1.66 30 22.22 21 21.15 6 167.44 Trans World Airlines 1,461 0.90 198 15.98 65 23.17 26 114.18 United Air Lines Inc. 1,720 1.90 237 20.65 77 11.89 63 143.73 US Airways Inc. 1,196 1.92 156 18.83 60 15.59 43 140.57 Virgin America 1,553 2.23 94 27.05 66 28.23 28 164.01 Table 3 Statistics by market structure and output attribute index (average weighted by number of passengers). Market Output Attribute Index Avg Fare per Mile ($) Avg Gini Count of Structure Range Avg Observed Adjusted Observed Adjusted Markets Monopoly 1.00–1.01 1.00 0.29 0.28 0.249 0.249 18,794 1.01–1.05 1.02 0.37 0.36 0.246 0.246 15,747 1.05–1.10 1.07 0.42 0.39 0.234 0.234 7,314 1.10–1.15 1.12 0.42 0.37 0.225 0.225 3,407 1.15 + 1.38 0.40 0.30 0.189 0.189 8,526 Average 1.07 0.34 0.32 0.238 0.238 53,788 Duopoly 1.00–1.01 1.00 0.24 0.24 0.245 0.246 5,659 1.01–1.05 1.03 0.23 0.22 0.254 0.257 4,672 1.05–1.10 1.07 0.26 0.24 0.253 0.257 2,138 1.10–1.15 1.12 0.30 0.26 0.245 0.253 916 1.15 + 1.27 0.35 0.26 0.224 0.239 1,423 Average 1.05 0.25 0.24 0.247 0.250 14,808 Competitive 1.00–1.01 1.00 0.17 0.17 0.250 0.250 2,698 1.01–1.05 1.03 0.17 0.16 0.262 0.265 1,576 1.05–1.10 1.07 0.22 0.20 0.277 0.281 610 1.10–1.15 1.12 0.28 0.24 0.274 0.281 217 1.15 + 1.30 0.43 0.32 0.255 0.269 284 Average 1.04 0.19 0.18 0.257 0.260 5,385 All Market 1.00–1.01 1.00 0.24 0.24 0.248 0.248 27,151 Structures 1.01–1.05 1.03 0.27 0.26 0.253 0.254 21,995 1.05–1.10 1.07 0.31 0.29 0.251 0.254 10,062 1.10–1.15 1.12 0.35 0.30 0.242 0.247 4,540 1.15 + 1.34 0.39 0.29 0.209 0.215 10,233 Overall Average 1.06 0.28 0.26 0.245 0.247 73,981 90% or greater share as Monopoly, markets where the top two carriers slack in consumers’ ability to discern differences, we define a market as combined have a 90% or greater share as Duopoly, and then all other homogenous when minimum unit costs at attribute levels q and q0 are markets as Competitive. These groupings are not intended to infer specific equal or no more than 1% different.21 In other words, the value of market characteristics, but simply to group together markets of similar Q(w, y, q, q0 )− 1 is between 1.00 and 1.01. The next four groupings are concentration. Results are further categorized into five levels of market considered heterogeneous: markets with Q(w, y, q, q0 )− 1 values be­ differentiation using the value of Q(w, y, q, q0 )− 1 . The first grouping tween 1.01 and 1.05, then those with values between 1.05 and 1.10, contains markets we would consider homogenous. To allow for some those with values between 1.10 and 1.15, and finally those with a value 21 For context, a 1% difference in unit costs adds roughly $1.00 to the total cost per passenger on a flight of average length. 225 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 greater than 1.15. The higher the value of Q(w, y, q, q0 )− 1 the greater while Table 6 presents the same measure of competition but with the the level of market heterogeneity. (P90–P10) as the measure of dispersion.24 In Table 5 baseline estimation We observe a sharp difference in per mile fares between the three (8), we see that effect of competition on price dispersion, measured as − market structures. In the Competitive group average fares are $0.19 per ln HERF, ̂ is negative and significant, echoing Gerardi and Shapiro mile. Fares rise by 32% to an average fare of $0.25 in the Duopoly group, (2009). These findings are reinforced in Table 6 where we see that an and then increase by another 35% to an average of $0.34 per mile in the increase in competition reduces the (P90) price by more than the (P10) Monopoly group. Fares that have been adjusted to remove the costs of a price, resulting in a narrower spread and a reduction in dispersion. We higher level of attributes are lower but retain a similar difference be­ also see in the second column of Table 5 that the effect of competition on tween concentration levels. We can also observe that generally per mile price dispersion, after removing the cost of product differentiation, is fares increase as market heterogeneity increases. stronger than the coefficient on observed price. This result would be The level of price dispersion, given by the average Gini coefficient in expected because adjusted prices reflect a market that is more homog­ the third column, also varies by levels of market concentration and enous in terms of output attributes. For brevity’s sake, we do not report differentiation. The table shows a first glimpse of the relationship be­ adjusted values in Table 6, but results mirror those of Table 5.25 tween market concentration and level of differentiation, which is one of Results for estimation (9), which bridges (8) and (10), are inter­ the objects of this study that the econometrical analysis in the next esting, but not very informative. We see that the significantly negative section will help to clarify. The values for the adjusted Gini coefficient effect of competition on price dispersion is strengthened over (8) once show an overall increase, which highlights a shortcoming of the adjusted the level of differentiation is accounted for. Although the negative co­ Gini as a measure of dispersion for our use. As a measure of dispersion, efficient on Q(w, y, q, q0 )− 1 was unexpected, in fact our model did not the Gini measures dispersion across the whole range of fares and can be make predictions on what happens within a market when the level of sensitive to changes in the middle. There are often common fare points differentiation changes. used by all carriers in a market. For example, multiple carriers may offer Turning to formula (10), we now address the question of the inter­ a $145 advance-purchase fare. Our method of adjustment may move one action effect of competition on price dispersion in homogenous and or all carriers off that point, creating more dispersion. To better un­ heterogeneous markets. As can be seen in both Table 5 and 6, the derstand the data, we have added a second measure of dispersion that is interaction effect is significant and positive. To verify the validity of the more focused on the tails of the dispersion, the 10th (P10) and 90th interactive term, we performed a Wald test on the results of estimations (P90) percentile price per mile and the spread between them. We define (9) and (10) and found that in addition to being significant, it adds to the the spread (P90–P10) as simply the 90th percentile price per mile less model. With an F value of 52.21, we reject the null hypothesis that the 10th percentile price per mile. An increase in the spread value in­ model (9) is as good as (10). A similar test was run based on both dicates a wider dispersion. measures of competition and both measures of dispersion. All showed Our first research question compares the levels of dispersion in the same validity of the interactive measure. markets with a wide and narrow range of attributes. To explore this Understanding the question of interaction requires a more detailed question, we perform a comparison of means and outline the results in level of information that is provided by the rewriting of expression (10), Table 4. Using the definition of homogenous as a value of and the specification of different levels of market differentiation in Q(w, y, q, q0 )− 1 between 1 and 1.01 and heterogeneous as values greater concordance with Table 3. To simplify interpretation, we provide than 1.01, we calculate weighted means of dispersion on the Gini co­ Table 7 as the resulting coefficient on competition at various levels of efficient and the (P90–P10) spread. Our test establishes the null hy­ Q(w, y, q, q0 )− 1 . Table 7 can be interpreted as reducing formula (10) to pothesis that the mean dispersion in a homogenous market is greater the formula below, and then finding (β1 +β3 Q) at various levels of Q: than or equal to the mean dispersion in a heterogeneous market. We ( ) reject the null hypothesis and accept the alternative that dispersion is Sjt ( ⋅ ) = β1 + β3 Qjt Comjt + β2 Qjt + θχ jt + δht + γ t + υj + εjt . (11) greater in heterogeneous markets in every case except the Gini measure Results in Table 7 show that considering interactive effects, the effect in the Monopoly structure.22. of competition on dispersion is negative in homogenous markets, but We also looked at the dispersion of prices that had been adjusted in turns positive when the market becomes more differentiated in terms of concordance with (7) by removing the cost of providing a higher level of output attributes. This result can be seen in the Gini measure and in the attributes, and found mixed results. In terms of the Gini measure, we see relative changes of the (P10) and (P90) coefficients and the resulting an increase in dispersion, but the (P90–P10) spread shows a reduction in (P90–P10) spread. In both measures, the effect of competition on dispersion. These results may be explained by the existence of common dispersion changes sign at a Q(w, y, q, q0 )− 1 value of about 1.10. As fare points noted earlier.23. noted in our discussion of the Borenstein (1985) model in section 2.1, dispersion reduction in homogenous markets is driven from 5.2. Fixed-effects panel estimation results monopoly-type discrimination when firms compete based on market elasticity. While in the more heterogeneous markets, the increase in Table 5 contains estimation results using the HHI as the measure of dispersion arises from competitive-type discrimination and more competition and the Gini log-odds ratio as the measure of dispersion, cross-price elasticity competition. Estimations from Table 5, 6, and 7 are reproduced in Table 8, 9 and 10 with the log of the number of carriers in the market (ln N)̂ as the 22 One possible explanation for this is that in the more highly concentrated measure of competition. Here we see in Table 8 that the effect of Monopoly markets carriers providing a higher level of output attributes do not competition has almost no effect on price dispersion and the coefficient offer price reductions and engage in limited price discrimination. This expla­ is not significant. In fact, it is not until we add the interactive effects of nation is supported by Table 4, where that same group has a per mile fare formula (10) and allow for differences by level of differentiation that the significantly higher than any other group’s per mile fare. This difference also may explain the 0.410 measure for the (P90–P10) spread in this group, many higher price tickets, and only a few lower-priced tickets. 23 24 On prices that have been adjusted, the Gini value for all market structures In tests of instrument validity, we found all instruments were significant, together is 0.248 for homogenous markets and 0.246 for heterogeneous mar­ and with an F-test value of 6962, we can reject that they are weak instruments. 25 kets. For the (P90–P10) spreads, these values are 0.259 and 0.304. As in Table 5, the reduction in dispersion is greater on the adjusted prices. The (P90–P10) spread is − 0.511 on observed prices and − 0.546 on adjusted prices. 226 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 Table 4 Independent samples weighted unequal variances T-test. Mean Observed Gini Coefficient Mean Observed (P90–P10) Spread Monopoly Duopoly Competitive Monopoly Duopoly Competitive Homogenous 0.249 0.245 0.250 0.316 0.260 0.182 Heterogeneous 0.229 0.248 0.266 0.410 0.286 0.250 P-Value 1.00 0.00 0.00 0.00 0.00 0.00 Reject H0 No Yes Yes Yes Yes Yes Table 5 Panel Estimates Dep Var: Gini log-odds ratio (Observed or Adjusted Prices). Estimation Formula: Observed Adjusted Observed Observed (8) (8) (9) (10) − ln HERF ̂ − 0.164** − 0.253*** − 0.222*** − 2.380*** (0.068) (0.068) (0.069) (0.338) Q(w, y, q, q0 ) − 1 − 0.208*** − 0.286*** (0.009) (0.015) Interaction Variables ̂ ⋅Q(w, y, q, q0 ) − − ln HERF 1 2.234*** (0.067) Observations 73,981 73,981 73,981 73,981 Notes: All regressions include quarter and carrier dummies, and a dummy variable indicating whether any carrier in the market was currently in bankruptcy. Standard errors are in parentheses. * Significant at the 10 percent level, ** Significant at the 5 percent level, *** Significant at the 1 percent level. coefficient becomes significant. Results from Table 9, using the (P10) unchanged, though not as statistically strong. The loss in statistical and (P90) to measure dispersion, closely mirror those of Table 6 in terms significance is largely because a significant number of routes are served of sign, coefficient value, and significance. In Table 9, the effect of by a single carrier. When differentiation by output attribute is measured competition is significant and negative even before controlling for dif­ at the route level, these single-carrier routes show no differentiation, ferentiation. Finally, Table 10 reports the effective coefficient based on masking the true level of heterogeneity in service levels. interactive effects at various levels of Q(w, y, q, q0 )− 1 . Under this In addition to testing the robustness of the output attribute index, we measure of competition, we see the effect of competition on the Gini check for robustness in our regression results from formula (10). Our coefficient, and the (P90–P10) changes sign when Q(w, y, q, q0 )− 1 presented results are based on a static fixed-effects panel within the values are greater than 1.15. estimator. Because there is a fair amount of persistence in the measure Table 7 5.3. Robustness checks Coefficient (β1 + β3 Q) on Com ( − ln HERF) ̂ at Different Output Attribute Index Levels Dependent Variable: Gini log-odds ratio, 10th Percentile Price or 90th In this section we test the robustness of the output attribute index Percentile Price. Q(w, y, q, q0 ) we introduced. As discussed in section 4, the values for Output Attribute Index − ln HERF − ln HERF the output attributes of on-time arrival and load factor are measured at ̂ ̂ the carrier level, whereas the value for flight frequency is measured at Range Avg Gini (P10) (P90) (P90–P10) the route level. An alternative would be to measure all output attributes 1.00–1.01 1.00 − 0.146 − 0.600 − 1.053 − 0.453 at the route level. The logic being that although the information is less 1.01–1.05 1.03 − 0.079 − 0.445 − 0.750 − 0.305 accessible at the route level, it is the route-level output attribute that 1.05–1.10 1.07 0.010 − 0.238 − 0.346 − 0.108 directly affects consumers. To test for robustness, we replicate the 1.10–1.15 1.12 0.122 0.021 0.159 0.139 1.15 + 1.34 0.614 1.158 2.382 1.223 method with this alternative measure and find that results are essentially Table 6 panel estimates dep var: Log of 10th or 90th percentile observed price. Estimation Formula: Log(P10) Log(P90) Log(P10) Log(P90) Log(P10) Log(P90) (8) (8) (9) (9) (10) (10) − ln HERF ̂ − 1.044*** − 1.555*** − 1.076*** − 1.603*** − 5.772*** − 11.155*** (0.060) (0.059) (0.061) (0.061) (0.064) (0.103) Q(w, y, q, q0 ) − 1 − 0.096*** − 0.224*** − 0.257*** − 0.562*** (0.009) (0.009) (0.018) (0.022) Interaction Variables − ln HERF ̂ ⋅Q(w, y, q, q0 ) − 1 5.172*** 10.102*** (0.366) (0.443) Observations 73,981 73,981 73,981 73,981 73,981 73,981 Notes: All regressions include quarter and carrier dummies, and a dummy variable indicating whether an carrier in the market was currently in bankruptcy. Standard errors are in parentheses. * Significant at the 10 percent level, ** Significant at the 5 percent level, *** Significant at the 1 percent level. 227 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 Table 8 replicate the estimation with instrumented competition, the effect is Panel Estimates Dep Var: Gini log-odds ratio (Observed or Adjusted Prices). stronger at − 0.015. These results might indicate that there are indirect Estimation Formula: Observed Adjusted Observed Observed effects of competition on dispersion through Q. A simple way to test for these results is suggested by Judd and Kenny (1981). They suggest (8) (8) (9) (10) comparing the result coefficient between a model that includes the ln N ̂ 0.007 − 0.072 − 0.020 − 1.041*** mediator and one that does not, subtracting one from the other. We have (0.074) (0.074) (0.073) (0.186) found these values already as equations (8) and (9). Using the results Q(w, y, q, q )0 − 1 − 0.194*** − 0.260*** from Table 5, we find that the indirect effect of competition on disper­ (0.008) (0.013) sion, through Q, is 0.031 compared with the direct effect of − 0.222.26. Interaction Variables ̂ ⋅ Q(w, y, q, q0 ) − ln N 1 0.893*** (0.144) 5.4. Reconciliation with previous studies Observations 73,981 73,981 73,981 73,981 In this section, we reconcile our results with those of previous studies Notes: All regressions include quarter and carrier dummies, and a dummy var­ and explore how our findings can help explain some of the contradic­ iable indicating whether any carrier in the market was currently in bankruptcy. tions between those studies. Like previous researchers, we perform a Standard errors are in parentheses. panel analysis of the effect of competition on price dispersion using * Significant at the 10 percent level, ** Significant at the 5 percent level, *** fixed-effects estimation to control for time-invariant market-specific Significant at the 1 percent level. factors. However, we introduce a measure of market differentiation and Table 9 Panel estimates dep var: Log of 10th or 90th percentile observed price. Estimation Formula: Log(P10) Log(P90) Log(P10) Log(P90) Log(P10) Log(P90) (8) (8) (9) (9) (10) (10) ln N ̂ − 0.985*** − 1.269*** − 0.991*** − 1.293*** − 2.959*** − 5.241*** (0.056) (0.051) (0.056) (0.051) (0.185) (0.187) Q(w, y, q, q0 ) − 1 − 0.029*** − 0.124*** − 0.187*** − 0.419*** (0.008) (0.007) (0.013) (0.013) Interaction Variables ( ) ln N ̂ ⋅Q w, y, q, q0 − 1 2.137*** 3.983*** (0.144) (0.146) Observations 73,981 73,981 73,981 73,981 73,981 73,981 Notes: All regressions include quarter and carrier dummies, and a dummy variable indicating whether any carrier in the market was currently in bankruptcy. Standard errors are in parentheses. * Significant at the 10 percent level, ** Significant at the 5 percent level, *** Significant at the 1 percent level. for dispersion in any given market, we first test our results with the its interaction with competition, showing that the effect of competition addition of a lag of the dependent variable. As might be expected, the on price dispersion differs depending on whether the market is ho­ lagged variable is highly significant both statistically and economically. mogenous or heterogeneous based on output attributes. However, our main results for competition, differentiation, and the Our results from estimation formula (8) are in line with those of interaction are robust to the addition of this lag. Gerardi and Shapiro (2009). The difference is our extension of the model We test further and use dynamic panel data methods to account for to include the level of market heterogeneity in formula (9) and the the possibility of correlation between the transformed lagged variable interaction effect in formula (10). Our extension refines their work, and the transformed error term. We test several specifications, including because of our finding that the effect of competition can differ based on the Arellano and Bond (1991) difference generalized- the degree of differentiation. However, in a sample where markets are method-of-moments (GMM) estimator, the Blundell and Bond (1998) predominantly more homogenous, the result would indicate a negative system GMM estimator, and the Arellano and Bover (1995) system GMM relationship, just as Gerardi and Shapiro (2009) found. with forward orthogonal deviations from Roodman (2003). This last Dai et al. (2014) find an inverse-U-shaped relationship, with price specification, which differences observations by subtracting the mean of dispersion increasing as a highly concentrated market initially becomes future observations, fits our data well. Because airlines can enter or exit more competitive, but decreasing when a less concentrated market be­ a market easily, or switch between direct and connecting service, our comes even more competitive. They do not control for the level of dif­ panel has many gaps. The forward orthogonal deviation method retains ferentiation. What we find does not contradict their results but can observations that would have been lost through first differences. Though provide further insight into what is happening in the market. When a the absolute value of coefficients varies somewhat between the methods, monopoly market first receives a second carrier, there is a move from again our main results for competition, differentiation, and the inter­ highly concentrated to more competitive. Concurrent with that change action hold up. there is a probability of an increase in differentiation and therefore an As a further check for robustness, we test for the existence of indirect increase in dispersion. For markets that are already less concentrated, effects of competition on dispersion through our measure of heteroge­ differentiation is more likely to have peaked and competition increases neity Q. A concern would be that heterogeneity has no effect on its own, but only through mediation of competition. As a first step in this check, we run a simple regression with competition predicting heterogeneity Q. 26 We find that the relationship is statistically significant at the 5% level We also tested the presence of an LCC as a method of measuring market heterogeneity. In neither estimation (9) nor (10) was the measure significant, but has a small effect, with a coefficient of 0.005, on competition. If we nor was the model fit as good as that of the base model. 228 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 Table 10 both for observed price dispersion and for price dispersion after removing cost differences due to product differentiation. Second, we ⌢ Coefficient (β1 + β3 Q) on Com ( ln N) at Different Output Attribute Index Levels Dependent Variable: Gini log-odds ratio, 10th Percentile Price or 90th Percentile find that if we control for the level of product differentiation, competi­ Price. tion has a strictly negative effect on price dispersion. Finally, using a Output Attribute Index ln N ̂ ⌢ fixed-effects panel estimation with interactions, we find that the direc­ ln ln N tion and magnitude of the effect of competition on price dispersion is Range Avg Gini (P10) (P90) (P90–P10) dependent on the level of product differentiation in the market. We also 1.00–1.01 1.00 − 0.148 − 0.822 − 1.258 − 0.436 find that at higher levels of differentiation, an increase in competition 1.01–1.05 1.03 − 0.121 − 0.758 − 1.139 − 0.381 can increase price dispersion. 1.05–1.10 1.07 0.085 0.672 − 0.979 0.307 − − − Whereas homogeneity is an absolute, heterogeneity is gradable and 1.10–1.15 1.12 − 0.041 − 0.566 0.780 − 0.214 1.15 + 1.34 0.156 − 0.095 0.096 0.192 has levels. We see that the switch from price dispersion decreasing to increasing as competition grows occurs only at a certain level of dif­ are likely to come in the form of battles between carriers serving the ferentiation. This finding might imply that although these results can be same niche. We see this effect in the descriptive data of Table 3 in the generalized to other industries, the point at which the affect occurs may column Avg Gini Observed. In the competitive structure, as markets be different. We also reconcile our study’s findings with findings in become more differentiated, dispersion increases from 0.250 to 0.277, previous research and helps to explain the contradictory results. but then begins decreasing, dropping to 0.255 at the highest levels of Our findings provide regulators information to consider when heterogeneity. A similar effect is seen in the duopoly structure.27. reviewing potential mergers. Typically, regulators focus on the HHI and Reconciling our findings with those of Borenstein and Rose (1994), how the merger will affect market concentration. However, as we have we look to two particular points, the difference in econometric methods shown, the market HHI alone is not enough when trying to understand and the lack of a variable controlling for differentiation. Gerardi and changes related to pricing. Regulators should also consider the level of Shapiro (2009) provide a full discussion on the differences between the differentiation provided by the firms and how a merger might affect cross-section method and the fixed-effects panel method used by Bor­ differentiation in the markets they are part of. A merger or horizontal enstein and Rose (1994). In short, they show that the cross-section alliance between two carriers with similar attributes can result in a method would bias the coefficient on competition. They also note greater increase in fare price, and in price dispersion, than the increases several time-invariant factors that could cause this bias. We would argue that would result from a merger between two carriers with quite that the level of differentiation in the market is one of the most impor­ different attributes. A further consideration for policymakers is that tant of these. To test this theory, we run a cross-section estimation on our market concentration alone does not determine the level of competition. data set and find a positive relationship between competition and A market with two carriers of similar attributes will be more competitive than one where the carriers have quite different attributes, since market dispersion. However, once we add Q(w, y, q, q0 )− 1 to the estimation, power is not determined by market concentration alone. either on its own or as an interaction variable, the sign on competition Between April 2008 and November 2013, the U.S. Department of turns negative.28. Justice approved four separate airline mergers. In a review of this de­ cision, Gifford and Kudrle (2017) conclude that a contributing factor to 6. Conclusions this decision was the belief by the U.S. Justice Department that potential entry and competition by a low-cost carrier (LCC) would restrain any In this study we have introduced an output attribute index which price increases. As measured by price dispersion, we find that belief to collects the cost impact of various changes in levels of output attributes. be flawed. Some evidence can be seen in the strong growth in airline Our new method allows us to measure the amount of product differen­ profitability following these mergers.29 Had our findings here been tiation that is due to output attributes. Markets with a wide range of considered, perhaps some of these mergers would not have been output attributes are categorized as heterogeneous markets, whereas approved. those with a narrow range of output attributes are classified as ho­ From a strategic perspective, these results can provide carriers some mogenous markets. direction when choosing routes to enter or exit. Entering a route where Returning to our research questions, we can now draw conclusions. the current competitors are similar to the potential entrant would be less First, price dispersion is greater in heterogeneous markets. This is true attractive, unless the potential entrant could adjust its product offering. On the other side, entering a route where the current carriers are dis­ 27 similar will allow the entrant greater latitude to price discriminate and To validate our findings, we have adjusted formula (10) to allow for the generate higher fares. nonmonotonic effect found by Dai et al. (2014). We replaced the measure − Our study has focused on the effects on price dispersion. Further ̂ ith HHI and HHI2 and introduced interactions of Q(w, y, q, q0 )− 1 ith the ln HERF research using our techniques could analyze the effect on average prices HHI terms. Without the interaction, we found a coefficient of 0.283 on HHI and and price deciles to further understand how changes in competition − 0.211 on HHI2, compared with the 0.536 and − 0.344 found by Dai et al. (2014) on a different time period. Adding the interaction term we find a sig­ affect markets, conditioned on the level of differentiation. This analyt­ nificant result of − 0.195 on the interaction with HHI and − 0.148 with HHI2. ical method could also be applied to other economic models to under­ Recalling that the HHI is a measure of concentration (higher values indicate less stand how explicitly controlling for the level of differentiation by output competition), this validation supports our conclusion that at higher levels of attribute affects model outcomes. Some possible examples may be pro­ differentiation, an increase in competition can add to dispersion, while in the ductivity analysis, a hedonic price equation, or other models where more homogenous markets, competition reduces price dispersion. market power plays a significant role. 28 As an additional step to ensure the validity of our findings, we followed the same methodology as Borenstein and Rose used (1994) and ran a series of Author statement cross-sectional regressions on each quarter in our sample. Using this method, we found a median coefficient of 0.144 on competition, compared to their Charles Howell: Conceptualization, Methodology, Formal Analysis, 0.323. We then added the interaction measure − ln HERF⋅Q(w, ̂ y, q, q0 )− 1 to the cross-sectional regressions and found the median coefficient on competition to Data Curation, Writing – Original Draft. Emili Grifell-Tatjé: Writing – be − 2.517, similar to our results in Table 5. With this method, the median value Review & Editing, Supervision, Conceptualization and Methodology. of the coefficient on the interaction variable is 0.264. These values differ from our findings using panel data, but the direction, signs, and conclusion would be 29 the same. U.S. domestic airline profitability rose from 1.05 in 2008 to 1.20 by 2016. 229 C. Howell and E. Grifell-Tatjé Transport Policy 125 (2022) 218–230 Acknowledgements Färe, R., Grosskopf, S., Lovell, C.A.K., 1985. The Measurement of Efficiency of Production. Springer Netherlands, Dordrecht. https://doi.org/10.1007/978-94-015- 7721-2. We would like to thank the German Aviation Research Society and Färe, R., Grosskopf, S., Sickles, R.C., 2007. Productivity? Of US airlines after the European Aviation Conference for awarding this work the 2018 deregulation. J. Transport Econ. Pol. 41 (1), 93–112. European Aviation Economics and Management Prize. We are also Forsund, F.R., Hjalmarsson, L., 1979. Generalised farrell measures of efficiency: an application to milk processing in Swedish dairy plants. Econ. J. 89 (354), 294–315. grateful to the Generalitat de Catalunya project 2017SGR-1036 and the https://doi.org/10.2307/2231603. Spanish Ministerio de Economía, Industria y Competitividad, project Gaggero, A.A., Piga, C.A., 2011. Airline market power and intertemporal price PID2020-114460GB-C31, for their generous financial support of this dispersion. J. Ind. Econ. 59 (4), 552–577. https://doi.org/10.1111/j.1467- 6451.2011.00467.x. research. Charles Howell would also like to thank the Generalitat de Gayle, P.G., Yimga, J.O., 2018. How much do consumers really value air travel on-time Catalunya for their generous early-stage research staff grant. We would performance, and to what extent are airlines motivated to improve their on-time like to give a special thanks to Lluis Bru, Josep Ll. Raymond and the two performance? Econ. Transp. 14, 31–41. https://doi.org/10.1016/j. ecotra.2018.01.003. anonymous reviewers, who provided invaluable input and the audience Gerardi, K.S., Shapiro, A.H., 2009. Does competition reduce price dispersion? New at the OR60 Annual Conference 2018 (Lancaster), the XXXIII Jornadas evidence from the airline industry. J. Polit. Econ. 117 (1), 1–37. https://doi.org/ de Economía Industrial 2018 (Barcelona) and the 15th Aviation Student 10.1086/597328. Gifford, D.J., Kudrle, R.T., 2017. U.S. Airlines and antitrust: the struggle for defensible Research Workshop 2018 (Bremen). Please address correspondence to policy towards a unique industry. Indiana Law Rev. 50 (2), 539. https://doi.org/ Charles Howell, College of Business Administration, 300 Mammel Hall, 10.18060/4806.1146. 6708 Pine Street, Omaha NE 68182 - Email: cbhowell@unomaha.edu. Gillen, D.W., Oum, H., Tretheway, M.W., 1990. Airline cost structure and policy implications: a multi-product approach for Canadian airlines. J. Transport Econ. Pol. 9–34. Appendix A. Supplementary data Grifell-Tatjé, E., Lovell, C.A.K., 2015. Productivity Accounting, the Economics of Business Performance. Cambridge University Press, New York. https://doi.org/ Supplementary data to this article can be found online at https://doi. 10.1017/CBO9781139021418. Holmes, T.J., 1989. The effects of third-degree price discrimination in oligopoly. Am. org/10.1016/j.tranpol.2022.06.001. Econ. Rev. 79 (1), 244–250. Ippolito, R.A., 1981. Estimating airline demand with quality of service variables. References J. Transport Econ. Pol. 15 (1), 7–15. https://doi.org/10.2307/20052594. Johnston, A., Ozment, J., 2013. Economies of scale in the US airline industry. Transport. Res. Part E Logist. Transp. Rev. 51, 95–108. https://doi.org/10.1016/j. Ahn, S.C., Sickles, R.C., 2000. Estimation of long-run inefficiency levels: a dynamic tre.2012.09.002. frontier approach. Econom. Rev. 19 (4), 461–492. https://doi.org/10.1080/ Kaplan, G., Menzio, G., Rudanko, L., Trachter, N., 2016. Relative Price Dispersion: 07474930008800482. Evidence and Theory. National Bureau of Economic Research Working. https://doi. Aigner, D.J., Chu, S.F., 1968. On estimating the industry production function. Am. Econ. org/10.3386/w21931. Paper Series No. 21931, 1–72. Rev. 58 (4), 826–839. Konüs, A.A., 1939. The problem of the true index of the cost of living. Econometrica 7 Arellano, M., Bond, S., 1991. Some tests of specification for panel data: Monte Carlo (1), 10–29. https://doi.org/10.2307/1906997. evidence and an application to employment equations. Rev. Econ. Stud. 58 (2), Lach, S., Moraga-González, J.L., 2017. Asymmetric price effects of competition. J. Ind. 277–297. https://doi.org/10.2307/2297968. Econ. 65 (4), 767–803. https://doi.org/10.1111/joie.12158. Arellano, M., Bover, O., 1995. Another look at the instrumental variable estimation of Lee, B.L., Worthington, A.C., 2014. Technical efficiency of mainstream airlines and low- error-components models. J. Econom. 68 (1), 29–51. https://doi.org/10.1016/0304- cost carriers: new evidence using bootstrap data envelopment analysis truncated 4076(94)01642-D. regression. J. Air Transport. Manag. 38, 15–20. https://doi.org/10.1016/j. Arjomandi, A., Seufert, J.H., 2014. An evaluation of the world’s major airlines’ technical jairtraman.2013.12.013. and environmental performance. Econ. Modell. 41, 133–144. https://doi.org/ Liu, J.S., Lu, L.Y., Lu, W.M., Lin, B.J., 2013. A survey of DEA applications. Omega Int J 10.1016/j.econmod.2014.05.002. Manage S. 41 (5), 893–902. https://doi.org/10.1016/j.omega.2012.11.004. Assaf, A., 2009. Are U.S. airlines really in crisis? Tourism Manag. 30 (6), 916–921. Obermeyer, A., Evangelinos, C., Püschel, R., 2013. Price dispersion and competition in https://doi.org/10.1016/j.tourman.2008.11.006. European airline markets. J. Air Transport. Manag. 26, 31–34. https://doi.org/ Assaf, A., 2011. A fresh look at the productivity and efficiency changes of UK airlines. 10.1016/j.jairtraman.2012.08.014. Appl. Econ. 43 (17), 2165–2175. https://doi.org/10.1080/00036840903085071. Oum, T.H., Fu, X., Yu, C., 2005. New evidences on airline efficiency and yields: a Balk, B.M., 2018. Empirical productivity indices and indicators. In: Grifell-Tatjé, E., comparative analysis of major North American air carriers and its implications. Lovell, C.A.K., Sickles, R. (Eds.), The Oxford Handbook of Productivity Analysis. Transport Pol. 12 (2), 153–164. https://doi.org/10.1016/J.TRANPOL.2005.01.002. Oxford University Press, New York, pp. 77–120. Ray, S.C., Mukherjee, K., 1996. Decomposition of the Fisher ideal index of productivity: a Blundell, R., Bond, S., 1998. Initial conditions and moment restrictions in dynamic panel non-parametric dual analysis of US airlines data. Econ. J. 106 (43), 1659–1678. data models. J. Econom. 87 (1), 115–143. https://doi.org/10.1016/S0304-4076(98) https://doi.org/10.2307/2235206. 00009-8. Roodman, D., 2003. XTABOND2: Stata Module to Extend Xtabond Dynamic Panel Data Borenstein, S., 1985. Price discrimination in free-entry markets. Rand J. Econ. 16 (3), Estimator. 380–397. https://doi.org/10.2307/2555565. Salop, S., 1979. Monopolistic competition with outside goods. Bell J. Econ. 10 (1), Borenstein, S., 1989. Hubs and high fares: dominance and market power in the U.S. 141–156. https://doi.org/10.2307/3003323. Airline industry. Rand J. Econ. 20 (3), 344–365. https://doi.org/10.2307/2555575. Schefczyk, M., 1993. Operational performance of airlines: an extension of traditional Borenstein, S., Rose, N.L., 1994. Competition and price dispersion in the U.S. Airline measurement paradigms. Strat. Manag. J. 14 (4), 301–317. https://doi.org/ industry. J. Polit. Econ. 102 (4), 653–683. https://doi.org/10.1086/261950. 10.1002/smj.4250140406. Button, K., 2019. Applied economics and understanding trends in air transportation Shepard, A., 1991. Price discrimination and retail configuration. J. Polit. Econ. 99 (1), policy. Transport Pol. 80, 78–85. https://doi.org/10.1016/j.tranpol.2019.04.022. 30–53. https://doi.org/10.1086/261739. Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision Spady, R.H., Friedlaender, A.F., 1978. Hedonic cost functions for the regulated trucking making units. Eur. J. Oper. Res. 10 (2), 429–444. https://doi.org/10.1016/0377- industry. Bell J. Econ. 9 (1), 159–179. https://doi.org/10.2307/3003618. 2217(78)90138-8. Stahl II, D.O., 1989. Oligopolistic pricing with sequential consumer search. Am. Econ. Christensen, L.R., Jorgenson, D.W., Lau, L.J., 1973. Transcendental logarithmic Rev. 79 (4), 700–712. production frontiers. Rev. Econ. Stat. 55 (1), 28–45. https://doi.org/10.2307/ Stavins, J., 2001. Price discrimination in the airline market: the effect of market 1927992. concentration. Rev. Econ. Stat. 83 (1), 200–202. https://doi.org/10.2307/2646703. Ciliberto, F., Schenone, C., 2012. Bankruptcy and product-market competition: evidence Stigler, G.J., 1961. The economics of information. J. Polit. Econ. 69 (3), 213–225. from the airline industry. Int. J. Ind. Organ. 30 (6), 564–577. https://doi.org/ https://doi.org/10.2307/1829263. 10.1016/j.ijindorg.2012.06.004. Suzuki, Y., 2000. The relationship between on-time performance and airline market Dahlby, B., West, D.S., 1986. Price dispersion in an automobile insurance market. share: a new approach. Transport. Res. Part E Logist. Transp. Rev. 36 (2), 139–154. J. Polit. Econ. 94 (2), 418–438. https://doi.org/10.1086/261380. https://doi.org/10.1016/S1366-5545(99)00026-5. Dai, M., Liu, Q., Serfes, K., 2014. Is the effect of competition on price dispersion Wang, K., Fan, X., Fu, X., Zhou, Y., 2014. Benchmarking the performance of Chinese nonmonotonic? Evidence from the U.S. Airline industry. Rev. Econ. Stat. 96 (1), airlines: an investigation of productivity, yield and cost competitiveness. J. Air 161–170. https://doi.org/10.1162/REST_a_00362. Transport. Manag. 38, 3–14. https://doi.org/10.1016/j.jairtraman.2013.12.012. Dana, J.D., 1999. Equilibrium price dispersion under demand uncertainty: the roles of Wu, Y., He, C., Cao, X., 2013. The impact of environmental variables on the efficiency of costly capacity and market structure. Rand J. Econ. 30 (4), 632–660. https://doi. Chinese and other non-Chinese airlines. J. Air Transport. Manag. 29, 35–38. https:// org/10.2307/2556068. doi.org/10.1016/j.jairtraman.2013.02.004. Douglas, G.W., Miller, J.C., 1974. Quality competition, industry Eeuilibrium, and Yu, M.M., Chen, L.H., Hsiao, B., 2018. A performance-based subsidy allocation of ferry efficiency in the price-constrained airline market. Am. Econ. Rev. 64 (4), 657–669. transportation: a data envelopment approach. Transport Pol. 68, 13–19. https://doi. Eden, B., 2018. Price dispersion and demand uncertainty: evidence from U.S. Scanner org/10.1016/j.tranpol.2018.04.004. data. Int. Econ. Rev. 59 (3), 1035–1075. https://doi.org/10.1111/iere.12296. 230