Nonlinear Pricing and Market Concentration in the U.S. Airline Industry
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Nonlinear Pricing and Market Concentration in the U.S.
Airline Industry∗
Manuel A. Hernandez and Steven N. Wiggins†
October 10, 2008
PRELIMINARY VERSION
Abstract
This paper provides new evidence on the impact of market concentration on airlines’
nonlinear pricing strategies. Under a second-degree price discrimination setup, where
firms compete via a collection of quality and price pairs, we derive testable implications
about the effect of market structure on a firm’s relative price schedule. We then test
these predictions using a unique dataset of airline ticket transactions during the fourth
quarter of 2004 that allows us to group fares according to certain characteristics and
restrictions. We find that market concentration differentially impacts various types of
fares. In line with our model predictions, there is a non-negligible decrease in the ratio
or quality premium of high- to low-type fares as we move to less competitive mar-
kets. The ratio of medium- to low-type fares, however, appears to increase with market
concentration. Overall, the observed relative pricing pattern reaffirms the negative cor-
relation between market concentration and price dispersion found in previous studies.
From a welfare perspective, it is interesting to observe that not all travelers are affected
in the same way by a decrease in the level of competition. Business travelers, who
purchase high-price tickets, end up paying relatively lower fares in more concentrated
markets while leisure travelers pay more.
Key Words: Nonlinear Pricing, Price Discrimination, Market Structure, Airline Industry
JEL Code: L11, L93
∗
We thank the valuable comments of Steven Puller, Li Gan, Claudio Piga, Jeff Racine, and participants
of the PERC Applied Microeconomics Student Seminar at Texas A&M University.
†
Department of Economics, Texas A&M University, College Station, TX 77843-4228. Please send any
comments to mhg@tamu.edu or swiggins@tamu.edu.
11 Introduction
It is well established that airlines offer highly dispersed prices. In their seminal paper about
price dispersion, Borenstein and Rose (1994) show that the expected absolute difference in
prices between two passengers on a route is 36% of the airline’s average price. Moreover,
they find that this substantial variation in prices decreases with market concentration. The
negative relationship between price dispersion and market concentration has also been con-
firmed in other related studies (Borenstein, 1989; Stavins, 2001). The observed dispersion
in prices, in turn, may arise both from variation in costs and from discriminatory pricing.
In this paper, we focus on nonlinear pricing, a strategy which has been given less attention
in the literature probably due to data limitations, and examine the impact of market con-
centration on relative prices within a menu of fare options. To the extent that nonlinear
prices enable firms to engage into second-degree price discrimination, our ultimate goal
is to analyze whether market structure conditions affect a carrier’s price discrimination
strategy.1
The airline industry provides an ideal framework to study the effect of market con-
centration on second-degree price discrimination for two main reasons. First, airlines price
discriminate among their customers by offering a range of fares with different characteristics
and restrictions so travelers self-select depending on their individual preferences. On this
point, Puller, Sengupta, and Wiggins (2007) find evidence that theories in which ticket char-
acteristics segment customers and facilitate price discrimination may play a major role in
airline pricing.2 Sengupta and Wiggins (2006) also reveal that ticket characteristics explain
much of the variation in fares. Second, the menu of fare types offered by carriers is similar
across routes with different levels of competition. While some routes are mainly served by
one carrier, other routes are served by several carriers with different market shares. This
allows us to compare a standard set of ticket options across different competitive settings.
Since the pioneer work of Mussa and Rosen (1978) and Maskin and Riley (1984) on
monopolistic nonlinear pricing, there has been a growing theoretical literature extending
this analysis to competitive environments.3 These models assume that firms compete via
a collection of quality and price pairs so consumers self-select which firm to buy from and
1
In order to conclude that nonlinear prices are discriminatory, we must consider costs. Clerides (2004)
argues that despite the controversy on the definition of price discrimination with differentiated products,
any price variation that cannot be explained by cost differences is usually regarded as price discrimination.
We adopt this reasoning in the present study.
2
An alternative theory argues that airline pricing can also be explained in a context of costly capacity,
perishable goods and demand uncertainty. In this setting, airlines may use certain ticket restrictions, such
as advance-purchase requirements, to screen consumers and divert demand from peak periods to off-peak
periods (Gale and Holmes, 1993; Dana, 1998).
3
For a detailed survey on nonlinear pricing and imperfect competition refer to Stole (2007).
2which quality-price pair to accept from an offered menu. But, as pointed out by Busse and
Rysman (2005), most of these general models do not provide a clear prediction regarding
the relationship between nonlinear pricing and market concentration. In this study, we
work with a two-type model, as in Villas-Boas and Schmidt-Mohr (1999) and Liu and
Serfes (2006), that allows us to derive testable predictions about the impact of market
concentration on the relative price schedule.
Using a unique dataset of airline ticket transactions that includes detailed information
on ticket characteristics and restrictions, we are able to group fares into broad categories
according to their cabin and booking class, whether they are refundable or not, and whether
they have specific travel and stay restrictions or not. We then select the lowest quality group
as our base group and analyze if there are any systematic differences between relative fares
across markets with various concentration levels. To the degree that we correctly account for
several cost and route-specific differences, we are able to evaluate whether market structure
conditions do in fact alter a carrier’s price discrimination strategy.
The results obtained indicate that market concentration differentially impacts various
types of fares. In line with our model predictions, there is an important decrease in the ratio
or quality premium of high- to low-type fares as we move to more concentrated markets.
Similar results are obtained under both a two-stage least squares procedure and a partially
linear smooth coefficient model. Medium- to low-type fares, however, increase with less
competition, although this result is not robust to all model specifications. Overall, the
observed relative pricing pattern is consistent with the negative relationship between market
concentration and price dispersion found in previous literature. From a welfare perspective,
it is interesting to observe that not all travelers are affected in the same way by a decrease
in the level of competition. Business travelers, who purchase high-price tickets, end up
paying relatively lower fares in less competitive markets while leisure travelers pay more.
To the best of our knowledge, this is the first study to analyze the impact of market
concentration on relative fares within a menu of ticket options in the U.S. airline indus-
try. Although it is not the main focus of his paper, Borenstein (1989) finds out that
increased market concentration appears to raise a carrier’s low-end prices and decrease its
high-end prices, but he does not explicitly account for ticket-specific factors such as ticket
characteristics (restrictions) and time of purchase. Stavins (2001) uses marginal implicit
prices of ticket restrictions as a proxy for price discrimination and concludes that price
discrimination decreases with concentration, but she only focuses on two restrictions and
on a limited number of routes. The present study is more in line with Busse and Rysman
(2005) who examine the relationship between competition and price-size schedules offered
for display advertising in Yellow Pages. Contrary to our results, they find out that an
additional competitor causes the price of a full page advertisement (high-quality product)
3to fall proportionally more than that of a quarter of a page (low-quality product).
The rest of the paper is organized as follows. The next section provides a brief overview
of the existing literature on nonlinear pricing and market structure, and presents a testable
model. Section 3 describes the data. The empirical strategy we follow to analyze the effect
of market concentration on carriers’ price discrimination strategies is explained in Section
4, together with the estimation results. Section 5 concludes.
2 Theoretical framework
There is a growing theoretical literature on nonlinear pricing that builds on the seminal
work of Mussa and Rosen (1978) and Maskin and Riley (1984). This literature extends
the analysis to settings where several firms compete (Stole, 1995; Villas-Boas and Schmidt-
Mohr, 1999; Armstrong and Vickers, 2001; Rochet and Stole, 2002; Johnson and Myatt,
2003; Liu and Serfes, 2006; and Yang and Ye, 2008).4 These models typically consider
two dimensions of consumer heterogeneity, one vertical and one horizontal. The vertical
dimension captures different marginal valuations of quality while the horizontal dimension
captures brand preferences.5 Firms do not observe consumer preferences and compete by
offering a menu of quality-price (quantity-price) combinations. Based on their preferences,
individuals decide whether to make a purchase and the quality-price pair to buy from
one of the firms. These quality-based models of price discrimination rely on self-selection
constraints where consumers choose the combination that matches their preferences.6
Most of this literature focuses on the efficiency consequences of competition (Stole,
2007). Specifically, on the quality distortions resulting from the range of product varieties
offered under different competitive settings. Similarly, several of these models yield differing
predictions regarding the impact of market structure on a firm’s price schedule. Busse and
Rysman (2005), for example, point out that in Stole’s (1995) model, competition will have a
higher (negative) effect at the bottom of the price schedule since high-valuation consumers
are more brand-loyal and the price reductions necessary to attract them are too high.
Conversely, in Rochet and Stole’s (2002) model, competition will have a higher (negative)
effect at the top of the price schedule since high-valuation consumers can afford more travel
costs and are best able to seek out substitutes.7 More recently, Yang and Ye’s (2008)
4
On this matter, Miravete (2007) indicates that models of nonlinear pricing competition are still on
their infancy relative to the amount of studies dealing with monopolistic nonlinear pricing.
5
To overcome technical difficulties, most models actually rely on one dimension (vertical or horizontal),
perform numerical simulations in case there is not a closed-form solution, or impose further restrictions on
preferences to avoid multidimensional settings (Stole, 2007).
6
Firms maximize profits subject to incentive compatibility and participation constraints.
7
Stole (1995) works with a model of horizontal preference uncertainty with a positive correlation between
4model does not provide a definite prediction about the relationship between competition
and prices over the price schedule. They show that competition has a larger (negative)
effect on the higher end of the quality range, but at the same time it increases the coverage
of individuals with a lower marginal valuation of quality, which in turn end up paying lower
prices.8
In this paper, we focus on a discrete model that allows us to explicitly analyze the
impact of market concentration on relative prices within a standard menu of fare types. As
in Villas-Boas and Schmidt-Mohr (1999) and Liu and Serfes (2006), we work with a two-
type model, described below, that yields closed-form solutions and enable us to perform
comparative statics analysis, while maintaining the number of product types constant.9
Recall that in the airline industry the variety of fare types offered is similar across markets
with different levels of competition.
2.1 A Testable Model10
As in Hotelling’s model, assume that there are two firms located at the end points of a
unit-length interval. Firm 1 is located at the left endpoint and Firm 2 is located at the
right endpoint. Each firm offers two fares of different quality, a low-quality ticket qL at
price pL and a high-quality ticket qH at price pH . We assume that both firms exhibit the
same production technology. To produce a unit of quality q a firm incurs in cost cq (c ≥ 0),
±
and there are fixed costs of producing good of quality q equal to q 2 2.
Consumer preferences, on the other side, differ both in a vertical and a horizontal dimen-
sion. In the airline context, the vertical dimension captures different marginal preferences
over ticket qualities (restrictions) while the horizontal dimension captures preferences over
carriers (or departure times). Firms do not observe these preferences. We assume that
there are two consumer types in the vertical dimension. Specifically, there is a fraction λ
of individuals with a low marginal preference of quality denoted by θL (hereafter low-type
consumers), and a fraction 1 − λ of individuals with a high marginal preference of quality
brand preference and marginal valuation for quality, while Rochet and Stole (2002) work with a model of
horizontal and vertical preference uncertainty where both dimensions are uncorrelated.
8
Yang and Ye (2008) extend Rochet and Stole’s model by relaxing the assumption of full-market coverage.
9
Villas-Boas and Schmidt-Mohr (1999) analyze the effect of horizontal differentiation (competition),
measured through per-unit transportation costs, on loan-granting practices; Liu and Serfes (2006) evaluate
the relationship between the degree of competition, measured through distance between firms, and the Gini
coefficient in the airline market.
10
The model builds on Liu and Serfes (2006). However, we focus on the impact of horizontal differenti-
ation, which measures the degree of competition among firms, on the relative price schedule. Similarly, we
make further assumptions that allow us to solve the model as a two-stage non-cooperative game and look
for a subgame-perfect equilibrium, as in Piga and Poyago-Theotoky (2005).
5denoted by θH (hereafter high-type consumers), where θH > θL .11 Each consumer type is
uniformly distributed over the unit-length interval with a unit mass. The exact location of
an individual in the horizontal dimension is described by the distance d she has to travel to
Firm 1 on the left endpoint. As is standard in this type of models, we assume that trans-
portation costs are quadratic in the distance an individual has to travel to her preferred
firm, and per-unit costs are equal to t. So, the marginal disutility of consuming a good (or
flying in a particular airline or departure time in this case) which is not the consumer’s
preferred good is increasing in the differentiation between the two.12
Overall, a consumer is characterized by an ordered pair (θ, d) where her vertical type
(θ) and horizontal location (d) are independent. Under scenario 1, a type-(θ, d) consumer
who purchases fare (q1 , p1 ) from Firm 1 enjoys utility U (θ, q1 , p1 , d) = v + θq1 − p1 − td2 ,
where v > 0 is the reservation utility obtained from making a purchase. Conversely, if
the same individual purchases fare (q2 , p2 ) from Firm 2, she derives utility U (θ, q2 , p2 , d) =
v + θq2 − p2 − t(1 − d)2 .13 We assume that reservation utility v is sufficiently high so that
the whole market is covered.14
So, Firm i’s, i = 1, 2, decision problem consists in offering fare menu (qiL , piL ) and
(qiH , piH ) that maximizes her profits subject to incentive-compatibility (IC) and participa-
tion constraints, given the other firm’s fare menu. Formally,
2
qiL q2
Max πi = λ[(piL − cqiL )diL ] − + (1 − λ)[(piH − cqiH )diH ] − iH (MAX)
piL ,piH ,qiL ,qiH 2 2
s.t.
θH qiH − piH ≥ θH qiL − piL , (ICH )
θL qiL − piL ≥ θL qiH − piH , (ICL )
qiL , qiH , piL , piH > 0,
where diL and diH are demands for Firm i’s low- and high-quality fares, respectively. It
can be easily shown that Firm 1’s demand functions are given by,
11
Low-type consumers could be regarded as leisure travelers and high-type consumers as business trav-
elers.
12
Alternatively, we could think of transportation costs as being linear. But, given that we normalize the
length of the interval to one and that we (later) assume that there is full-market coverage, the model yields
similar predictions under both linear and quadratic transportation costs.
13
Note that these utility functions imply that firms are only able to sort consumers with respect to their
marginal valuation of quality. Refer to Appendix A for further details about the model.
14
This is equivalent to the full-scale competition case in Villas-Boas and Schmidt-Mohr (1999).
6t + θL (q1L − q2L ) − (p1L − p2L )
d1L = dL = , (1)
2t
t + θH (q1H − q2H ) − (p1H − p2H )
d1H = dH = . (2)
2t
The IC constraints imply that truth telling is a dominant strategy for all customers.
The participation constraint regarding competition for customers with the other firm is
already embedded in the demand functions. The other participation constraint is the usual
individual-rationality constraint (IR), which is assumed to be slack for all consumers (θ, d)
due to the full-market coverage assumption.
If we further assume that the quality of the high-type product is an increasing function
of the quality of the low-type product, i.e. qiH = δqiL , i = 1, 2, where δ > 1, we can solve
this model as a two-stage non-cooperative game and derive a subgame-perfect symmetric
equilibrium where (ICH ) binds and (ICL ) does not.15 In the first stage firms set quality and
in the second stage they compete in prices. The details of the derivations are presented
in Appendix A. As in Villas-Boas and Schmidt-Mohr (1999) and Yang and Ye (2008), we
assume that the degree of horizontal differentiation, captured by transportation cost t,
serves as an index for the level of competition among firms. A decrease in t could then be
regarded as an increase in the intensity of competition.16 We are interested in the effect of
t on the optimal price ratio p∗H /p∗L .
We also extend the model in two directions:17
Extension 1 : Each firm offers three product qualities (high, medium, and low) to three
different consumer types (high, medium and low marginal valuation of quality), each of
them uniformly distributed over the unit-length interval. Per-unit transportation costs
remain equal to t. Considering that we later group tickets into several categories, the
idea is to observe how the price ratio of different product types will vary with the level of
competition.
15
We believe that this further assumption is plausible since first or business class tickets could well be
regarded as an upgraded version of economy class tickets.
16
Recall that the horizontal dimension captures in our case preferences over carriers or departure times.
A lower t implies that passengers will view alternative carriers (flights) as closer substitutes; in the extreme
case of t=0, the horizontal dimension becomes irrelevant and the model will reduce to a perfectly competitive
market. Additionally, more competitive markets usually exhibit a higher flight density and competing firms
schedule their flights at closer departure times between one another (goods are close substitutes), relative to
less competitive markets. In our working sample, the average difference in departure times between flights
in monopolistic routes is 96 minutes, 65 minutes in duopoly routes, and 44 minutes in competitive routes.
17
For more details refer to Appendix A.
7Extension 2 : There are only two product qualities and two consumers types, but we
allow for different per-unit transportation costs between individuals, specifically tH > tL .18
We explicitly assume that high-type consumers are less reluctant to switch carriers than
low-type consumers or it is more costly for them to move away from their preferred carrier
or departure time, similar to Stole (1995).
Figure 1 shows the impact of t on the optimal price ratio derived from our base model.
As can be seen, there is a negative relationship between market concentration and relative
prices or, conversely, there is a positive correlation between market competition and relative
fares. Provided that low-quality fares decrease proportionally more than high-quality fares
with a lower t, it follows that firms will compete more fiercely for low-type consumers with
increased competition.19
Figure 2 presents the effect of t on relative prices when we consider three product
qualities and three consumer types. We observe a decrease in both high- and medium-
quality fares, relative to low-quality fares, as we decrease the intensity of competition.
More interesting, the ratio of high to low-quality fares decreases proportionally more than
the ratio of medium to low-quality fares with an increase in t. Firms still compete more
fiercely for low-type consumers and, to a lower extent, for medium-type individuals.20
Finally, Figure 3 shows how the optimal price schedule will vary with market concentra-
tion when high-type individuals are assumed to face a higher per-unit transportation cost
than low-type individuals (tH > tL ). In this case, variations in the level of competition are
measured through changes in tL and tH . As shown in the figure, there is also a negative
relationship between market concentration and relative fares but this inverse relationship
is more pronounced with changes in the level of competition for low types, which are also
more reluctant to switch firms.21
In sum, under a standard second-degree price discrimination framework we would expect
market concentration to have a negative impact on the ratio of high- to low-quality fares,
and, to a lower extent, on the ratio of medium- to low-type fares. This seems reasonable
18
As in Liu and Serfes (2006).
19
The fact that absolute fares decrease with a lower t is consistent with the lower market power enjoyed
by each firm. The high-quality fare, in turn, must always leave a higher net surplus (information rent)
to high-type consumers because they can always buy the low-type product. With increased competition,
firms would worry less about providing additional informational rents to high-type consumers because these
individuals would enjoy a higher net surplus anyway due to a lower t.
20
It is straightforward to deduce that firms will worry less about high- than medium-type consumers
because the former would anyway enjoy higher informational rents with increased competition.
21
Although not reported, absolute fares decrease with either a decrease in tL or tH . This is explained
by the incentive compatibility constraints that restrict consumers to select the fare type designed for them.
So a decrease in tL , for example, will not only decrease pL , but also pH (in a lower extent), to prevent
high-type consumers from buying low-quality fares.
8in the airline, considering also that low-type individuals are generally less brand-loyal and
more price sensitive than high-type travelers. These predictions are also in line with the
positive relationship between market competition and price dispersion found in previous
empirical studies about airline pricing.22
We now proceed to describe our dataset and empirically examine the relationship be-
tween market concentration and relative fares within a standard menu of fare types in the
U.S. airline industry. Our goal is to test our model predictions and analyze whether market
structure conditions affect a carrier’s pricing discrimination strategy.
3 Data
The main data source of this paper is a census of airline tickets purchased between June
and December 2004 for travel in the fourth quarter of the same year. The dataset was
provided by one major Computer Reservation System (CRS) vendor, and includes tickets
purchased directly from airlines, including their websites, and through travel agents and
several online travel sites. Overall, the data represents around thirty percent of all domestic
ticket transactions in the U.S. in the corresponding quarter. For each ticket sold or itinerary,
we have information on the fare paid, origin and destination, segments (or coupons) involved
in the itinerary, carrier and flight number, cabin and booking class, and dates of purchase,
departure and return.
As in Borenstein (1989) and Borenstein and Rose (1994), we define a route as a pair
of airports regardless of direction, where one airport is the origin of the itinerary and the
other one is the destination. We drop all itineraries other than one-way and roundtrips,
and restrict the analysis to direct or nonstop itineraries. We also exclude tickets that in-
volve travel with different airlines (e.g. interline tickets). Prices are measured as roundtrip
fares, so in the case of one-way tickets the fare is doubled. To avoid holiday peaks, we
drop transactions involving travel on Thanksgiving, Christmas and New Year.23 The data
includes tickets for flights operated by AirTran, Alaska, American, America West, Conti-
22
It is worth to mention that Borenstein (1985) and Holmes (1989) also uncover the possibility of a
positive relationship between price dispersion and competition under a monopolistic competition setup.
This will occur in a context where firms primarily sort their customers based on the strength of their
brand preferences, so there will be more competition between firms for consumers who are less brand-
loyal (probably low-type individuals in our model). Similarly, Gale (1993) developed a simple two-period
model of airline price discrimination, where the product is initially homogenous and becomes horizontally
differentiated just prior to departure, and finds that price dispersion will also increase with competition. In
this case there will be more competition between firms for consumers who are less time-sensitive (probably
low-type individuals in our model).
23
We exclude travel on the Wednesday prior to Thanksgiving until the following Sunday. We also exclude
all travel beginning on December 22nd through the end of year.
9nental, Delta, Frontier, Hawaiian, Midwest, Northwest, Spirit, Sun Country, ATA, United,
and US Airways.24
Due to confidentiality reasons, the major CRS vendor did not provide information on
ticket restrictions. Consequently, the transaction dataset was then merged to historical data
from a travel agent’s CRS, containing a large subset of ticket fares, and their restrictions,
offered for travel in the last quarter of 2004.25 For each fare listed on this second dataset,
we have information on origin and destination, carrier, booking class, departure date from
origin, advance purchase requirements, refundability, travel restrictions, and maximum or
minimum stay restrictions. The matching procedure followed is fully described in Puller,
Sengupta and Wiggins (2007). Basically, an itinerary from the transaction dataset was
matched to a posted fare from the travel agent’s dataset based on route, carrier, prices
falling within a two percent range of one another, and the itinerary satisfying advance pur-
chase requirements, travel and stay restrictions according to the date of purchase, departure
and return.
In the present study, we restrict the analysis to matched itineraries where we observe at
least one thousand observations per route and one hundred observations per route-carrier.
This results in 878,169 tickets across 246 routes with different levels of competition. The
whole list of routes is reported in Table 1 Since our matched sample represents only 33% of
the total transactions observed in the routes analyzed, we proceed to examine if there are
any systematic differences in the fare distribution of matched itineraries versus unmatched
ones. In Figure 4, we plot kernel density estimates of fares for both groups. Although our
matching procedure appears to match a lower rate of tickets within the lower end of the
fare distribution, it is clear that we are able to match tickets over a wide range of prices.
The resulting dataset allow us to group fares based on certain relevant characteristics
and restrictions. Specifically, we group tickets into five broad categories according to their
cabin and booking class, refundability, and specific travel and/or stay restrictions. Group
F fares include first class tickets. Group 1 fares correspond to refundable business and full
coach tickets and Group 2 to refundable coach tickets. Group 3 fares include nonrefundable
tickets without any travel or stay restriction, while Group 4 include nonrefundable tickets
with travel and/or stay restrictions. Under the plausible assumption that a higher number
of restrictions results in a lower ticket quality, Group F is our highest quality group while
Group 4 is our lowest quality group. This grouping procedure matches our theoretical
24
With the exception of Southwest, our dataset includes tickets from all of the main carriers operating
in the U.S. domestic market during the period of study. We are not able to include Southwest tickets in the
analysis since we only have limited data for them.
25
The travel agent’s dataset is incomplete because some of the posted fares in the system are usually
deleted after a certain period of time, although not in a systematic way.
10framework where we assume that carriers offer fares of different quality for consumers to
self-select.
Our dataset of matched ticket transactions was finally complemented with carrier’s
market shares on each route and market structure measures, as well as several controls
commonly used in the literature to analyze airline pricing.26 Appendix B provides a full
description of all the variables used in the analysis. In the case of market structure variables,
we include both a continuous measure, the Herfindahl-Hirschman Index or HHI, and three
categorical variables, monopoly, duopoly and competitive, defined according to Borenstein
and Rose (1994).27 Other carrier and market controls used include hubs, slot-controlled
airports, presence of Southwest and other low cost carriers, distance, total number of flights,
per capita income, tourism index and temperature difference.
Table 3 presents descriptive statistics of our final dataset. Roundtrip fares range from
62 dollars for a trip Las Vegas (LAS) – Los Angeles (LAX) in American to 4,806 dollars
for a trip San Francisco (SFO) – New York-Kennedy (JFK) in United. The average fare
paid is 457 dollars or 31.3 cents per mile. As expected, the proportion of tickets sold is
negatively correlated with fare quality. The fraction of tickets in Group F through 4 is 5%,
7%, 12%, 28%, and 47%, respectively. Around 61% of the tickets are bought less than two
weeks prior to departure, and 25% in the last 3 days. The average flight load factor when
a ticket is purchased is 44%. Additionally, more than eight of every ten itineraries involve
travel to/from a hub of the operating carrier, three of every four itineraries are a roundtrip
travel, and two of every three tickets involve travel during peak times.28
The distribution of tickets by route concentration, reported in Table 4, indicates that
40% of the itineraries in our sample correspond to competitive routes, 48% to duopoly
routes, and 12% to monopoly routes. This uneven distribution is mainly explained by the
fact that 18% of the routes included in the study are monopoly markets, while duopoly
routes represent 48% of the total routes and competitive routes represent the remaining
34%.29 Besides, competitive markets exhibit a higher flight density.30 If we segment the
sample by flying distance, we observe a similar distribution of routes (and tickets) by market
concentration among most groups. Only in routes involving travel distances between 1,000
26
Table 2 details the sources of information consulted to construct these other variables.
27
We use number of nonstop passengers on a route to calculate carriers’ market shares and market
structure measures, instead of number of flights used by Borenstein and Rose (1994). As indicated by
Stavins (2001), using either the number of passengers or the number of flights on a route as a basis for
market concentration calculations appear to yield similar results.
28
Peak time is defined as Monday through Friday between 7-10am and 3-7pm.
29
In Borenstein and Rose (1994), 12% of the 521 routes analyzed are monopoly markets, 41% are duopoly
markets, and 46% are competitive markets. Their period of analysis is the second quarter of 1986.
30
In the markets analyzed, the average number of daily takeoffs in monopoly, duopoly, and competitive
routes is 15, 24, and 33, respectively.
11and 1,499 miles the fraction of monopoly routes (and tickets) is above 18%. On average,
we have a reasonable number of tickets per route across markets with different levels of
concentration and flying distance.
4 Empirical Estimation
Under the theoretical framework described previously, we would expect the ratio of high- to
low-quality fares to decrease with market concentration, particularly fares on the higher end
of the quality range. To the extent that nonlinear prices enable firms to engage into second-
degree price discrimination, our ultimate goal is to examine whether market structure
conditions affect a carrier’s price discrimination strategy. This involves isolating the effect
of competitive interactions on relative fares from cost and market-specific effects.31
Figure 5 shows a strong correlation between our ticket grouping and fares, as expected.
The average fare per mile across tickets in Group F through 4 is 96, 83, 42, 26, and 17 cents,
respectively. This positive correlation between quality and price, which is recurrent across
itineraries involving different travel distances, perfectly fits in our theoretical setup where
we assume that carriers offer different quality-price combinations for consumers to self-
select.32 We now proceed to analyze if there are any systematic price differences between
these five fare types across markets with various concentration levels. We conveniently
select Group 4, the lowest quality group, as our base group so we can examine the impact
of market concentration on relative prices on a pairwise basis.
A first look at the data indicates that market concentration differentially impacts rel-
ative fares within a menu of fare types (see Figure 6). As we move to more concentrated
markets, the average fare per mile of Group F or first class tickets decreases relative to
Group 4 tickets. In competitive routes, the ratio of Group F to Group 4 fares is close to 5.9
while in monopolistic routes the ratio is less than 4.6. Group 1 relative fares also decrease
with market concentration, but to a lower extent. The fare ratio decreases in this case
from 4.5 to 3.9. On the contrary, the ratio of Group 2 to Group 4 fares shows a moderate
increase as we move to less competitive markets, from 2 in competitive markets to 2.7 in
monopoly markets, while Group 3 relative fares do not seem to vary with market structure
conditions (the ratio fluctuates around 1.5). More interesting, this relative pricing pattern
31
We do not worry about any cost issues in our model because, as is standard in these type of models,
firms are assumed to face a constant marginal cost. As we discuss later, marginal costs in the airline industry
are better defined as the sum of a marginal cost of production plus a shadow cost of capacity (Dana, 1998).
The latter may vary at the ticket, flight, carrier and market level.
32
Although not reported, this five-type fare structure together with dummy variables for time of purchase
and one-way travel and carrier fixed effects, explain on average around 76% of fare variation in each of the
routes analyzed. Details are available upon request.
12generally holds under alternative market structure definitions (see Figure 7).33
The non-negligible decrease in the ratio of high- to low-type fares with market concen-
tration, particularly the ratio of Group F to Group 4 fares, matches our model predictions
derived in Section II. In our model, as we move to less competitive markets, the lower price
ratio results from the fact that low-type fares increase proportionally more than high-type
fares. In our data, however, Group F and Group 1 absolute fares actually decrease with
market concentration.34 The observed relative pricing pattern is also in line with previous
studies that find a negative effect of market concentration on price dispersion (Borenstein,
1989; Borenstein and Rose, 1994; and Stavins, 2001). Provided that these studies do not
include first class tickets, it is interesting to still observe a negative correlation between
market concentration and price dispersion after allowing for a broader range of ticket qual-
ities.
A closer look at the data also suggests that market structure conditions affect a carrier’s
nonlinear pricing strategy, especially on the higher end of the quality range. Figures 8 and
9 show United Airlines’ (UA) average relative prices, by fare type and day of purchase,
for two of her main short-distance and long-distance routes in our sample. Among short-
distance routes, Washington-Dulles (IAD) – Boston (BOS) is a competitive market and
San Francisco (SFO) – San Diego (SAN) a monopoly market. Among long-distance routes,
Los Angeles (LAX) – Philadelphia (PHL) is a competitive route and San Francisco (SFO)
– Washington-Dulles (IAD) a monopoly route. With a few exceptions, the ratio of Group
F and Group 1 to Group 4 fares is lower in the selected monopoly routes than in the
competitive ones, independent of the time of purchase.35
The next step involves examining whether carriers do in fact modify their price discrim-
ination strategy when they face less competition. Since we cannot conclude that nonlinear
33
These alternative definitions include the level of HHI and Verlinda’s (2005) market structure categories.
In the former case, routes are divided into three groups: HHI less than or equal to 0.5, HHI between 0.5 and
0.8, and HHI greater than 0.8. In the latter case, a route is considered a monopoly if a carrier transports
at least 50% of nonstop passengers and the share of the second major carrier is less than one ninth of the
share of the first carrier; a route is considered a duopoly if two carriers cumulatively transport at least 50%
of nonstop passengers and the share of the third major carrier is less than one ninth of the share of the
second carrier; all other routes are considered competitive.
34
As previously mentioned, Borenstein (1989) also finds out that high-end prices decrease in more con-
centrated routes while low-end prices increase. His period of analysis is the third quarter of 1987. The
relative increase of Group 2 fares with market concentration, which our model fails to predict, together with
the relative decrease of high-type fares, suggests that airlines might be following a complementary strategy
to induce travelers to purchase tickets of higher quality. We leave this discussion to the end, although it is
beyond the scope of the present study.
35
Note that Group F and Group 1 relative fares actually overlap with Group 2 relative fares in the
observed monopoly markets, while in the competitive markets they are quite different.
13prices are discriminatory without considering costs, ideally we would like to compare the
price-cost ratio of different ticket qualities under different competitive settings. However,
marginal costs are not observed directly. Moreover, marginal costs in the airline industry
are better described as the sum of a marginal cost of production, incurred only on the
tickets (seats) that are sold, plus a shadow cost of capacity, incurred whether or not the
ticket (seat) is sold (Dana, 1998). While the ratio of marginal cost of production across fare
types may be neutral to market structure, like the cost of meals and service provided, the
expected (and unexpected) shadow cost of capacity ratio may not be neutral.36 Specifically,
the shadow cost of capacity will depend on several factors at the ticket, flight, carrier, and
route level. Similarly, carriers may face a different relative demand for fare types across
markets which, in turn, could affect their price discrimination strategy. In Figures 8 and 9,
for example, part of the difference in relative prices across routes may be due to differences
in the fraction of business and leisure travelers.
Consequently, we cannot assume that the marginal cost ratio and the relative demand
for different fare types are invariant to the level of competition, as in Busse and Rysman
(2005) in their study on Yellow Pages advertising. The task is then to isolate the impact of
competitive interactions on relative fares from other factors that may explain fare variations
across markets. We attempt to do so by including in the analysis several controls at the
ticket, flight, carrier and market level. The idea is to account for possible differences in
(shadow) costs across fares, as well as differences in market characteristics (like population
attributes) across routes.
4.1 Model Specification
In practice, we estimate two reduced-form models of log airfare on group dummies for fare
types, market concentration, carrier’s market share, and a set of controls. Our key variables
are the dummy variables for fare groups that measure the quality premium of the different
fare types over Group 4 fares, our base group. In the second equation, we interact these
group dummies with our market structure measures to examine how these premiums will
vary with market concentration. The log-linear fare equations are then given by,
36
For example, assume that there is an excess demand for high-quality tickets from business travelers
during peak periods. If, at the same time, competitive routes exhibit a higher flight density during peak
periods than monopoly routes, then we would expect the shadow cost of high- to low-quality fares to vary
as we move to more competitive markets. The direction of the change is, however, uncertain. As pointed
out by Borenstein and Rose (1994), an increase in the number of flights is likely to lower the shadow cost
of capacity for flights facing excess demand buy may raise the demand uncertainty for any given flight.
143
X
ln pijkt = β0 + βf 1 qfi + β2 mktstructurek + β3 mktsharejk (3)
f =F
+Xijkt λ + α1j + κ1k + εijkt
3
X 3
X
ln pijkt = δ0 + δf 1 qfi + δ2 mktstructurek + δf 3 (qfi × mktstructurek ) (4)
f =F f =F
+ δ4 mktsharejk + Xijkt γ + α2j + κ2k + υijkt
where pijkt is the price per mile of ticket i charged by carrier j on route k at time t, qfi is a
dummy variable for Group f fare, f = F, .., 3, mktstructurek is the route’s market structure
(measured through HHI or categorical variables for monopoly and duopoly), mktsharejk is
the carrier’s market share on route, and Xijkt is a vector of ticket, flight, carrier and route
controls. We specify the error terms to have a carrier effect α1j (α2j ), a route effect κ1k
(κ2k ) common to all carriers on a route, and a white noise error εijkt (υijkt ) specific to each
observation.
The ticket-specific factors include dummy variables for time of purchase (0-3 days, 4-6
days, 7-13 days, and 14-21 days) and one-way tickets. At the flight level, we control for the
average load factor at purchase of the itinerary’s flight segments and whether the itinerary
involves departure and/or return during peak time. At the carrier level, we control if either
endpoint of the route is a primary or secondary hub for the operating carrier. The market-
specific factors include a dummy variable to indicate the presence of a slot-controlled airport
at either endpoints, categorical variables to indicate if Southwest or other low-cost carriers
have more than five percent of the market share on the route, log of distance, log of total
number of flights on the route, log of average per capita income at the endpoints, fraction of
accommodation to personal income at destination city of itinerary (tourism index), and log
of absolute temperature difference between endpoints.37 All of these variables are intended
to account for factors, other than market structure, that may explain fare variations across
markets, specifically cost and market-specific factors. For example, one-way travel, a higher
load factor at purchase or traveling during peak time presumably increases the shadow
cost of a ticket. Slot-controlled airports are also supposed to raise the cost of serving a
market. Following Borenstein (1989) and Bornstein and Rose (1994), the tourism index
is intended to measure the proportion of leisure travelers on each destination city. As
37
Slot-controlled airports include Washington-National (DCA), New York-Kennedy (JFK), and New
York-La Guardia (LGA). The five percent threshold to account for the presence of Southwest or other
low-cost carriers on a route follows Lee and Luengo-Prado (2005).
15in Brueckner, Dyer, and Spiller (1992) and Stavins (2001), a larger absolute temperature
difference between the origin and destination might also indicate a higher proportion of
leisure travelers on the route. It is also widely accepted that the presence of Southwest or
other major low-cost carriers induces significant price reductions on the route.
Our parameters of interest are βf 1 in equation (3) and, in particular, δf 1 and δf 3 in
equation (4). We expect coefficients βf 1 and δf 1 to have a positive effect on prices since
they approximate the quality premium of different fare types with respect to our base
group (Group 4). The sign of δf 3 indicates how these premiums will vary with market
concentration. Naturally, any cost differences across fare types that we are not able to
account for may also be embedded in these premiums. To the extent that these differences
are basically differences in the marginal cost of production, which are typically neutral
to market structure, any variation on the premium across different competitive settings
will indicate whether carriers do in fact vary their nonlinear pricing strategy with market
concentration. The advantage of working at the ticket level is that we can more accurately
account for the shadow cost of fares.
4.2 Estimation Results
The estimation results of equation (3), following a two-stage least squares (2SLS) approach,
are reported in Table 5.38 We treat carrier effects as fixed and route effects as random,
and we address the potential endogeneity of market share and HHI using the instruments
proposed by Borenstein (1989) and Borenstein and Rose (1994).39 The carrier’s market
share is instrumented using its geometric mean of enplanements at the two endpoint air-
ports of the route, divided by the sum of all carriers’ geometric mean of enplanements at
the endpoints. The instrument for HHI is the square of the fitted value of market share
(obtained from its first-stage regression) plus the rescaled sum of the square of all other
carriers’ share. We also instrument log of total number of flights on a route with the log
average population at the two endpoints. In Model 1 we measure market concentration
using HHI while in Model 2 we use categorical variables for market type (the competitive
category is our base group).
As expected, the quality premium, over Group 4 tickets, decreases across Groups F
through 3. Under Model 1, Group F, 1, 2 and 3 fares are 170%, 108%, 41% and 27% higher
than Group 4 fares, other things constant. Under Model 2, these premiums are 170%,
105%, 39%, and 31%, respectively. Similarly, most of the estimated parameters of the
control variables result significant and have the expected sign under both models. Tickets
38
For matters of comparison, we also report the ordinary least squares (OLS) results. In both cases, the
standard errors are clustered on origin city.
39
We do not use instruments for market type dummies.
16bought closer to departure time are more expensive than those bought several days ahead.
Travelers who purchase 0-6 days in advance end up paying, on average, 15% to 18% more
than those who purchase over 21 days in advance. One-way tickets are 14% more expensive
than half the price of roundtrip fares. With respect to flight controls, a one standard
deviation increase in the load factor at purchase (0.29) is associated with a 4% increase
in fares. Tickets that involve travel during peak periods are around 2% more expensive
than those during off-peak periods. Similar to Borenstein (1989), airport dominance leads
to higher prices. Fares on routes where the operating carrier has a hub at either endpoint
are 38-41% higher than fares on routes that do not involve a hub for the carrier. However,
route dominance (market share) does not result significant. With respect to route controls,
fares are 17-19% higher on itineraries where one of the endpoints is a slot-controlled airport.
In routes where low-cost carriers, other than Southwest, collectively have five percent or
more of market share, prices are 10-11% lower than in other routes, while in routes where
Southwest has five percent or more of market share, prices are 34-35% lower. Besides, the
larger the distance traveled the lower the fare per mile paid. A 10% increase in distance
decreases the fare per mile by almost 10%. A higher flight frequency also decreases fares
while a higher per capita income has the inverse effect. Finally, a one standard deviation
increase in the tourism index (0.03), indicating a larger presence of leisure travelers, results
in a 4% decrease in fares. The absolute temperature difference between route endpoints
does not result significant.
Table 6 presents the estimation results for equation (4), where we allow quality premi-
ums to vary with market concentration. Note that the estimated coefficients of the control
variables are very similar to those under equation (3). As in our preliminary analysis, there
is a non-negligible decrease in the premium of Group F fares, over Group 4 tickets, as we
move to highly concentrated markets under both specifications. In the first model, the
estimated premium decreases from 176% at the 10th percentile of HHI (0.34) to 159% at
the 90th percentile of HHI (0.89). In the second model, this premium decreases from 173%
in competitive markets to 129% in monopoly markets. Group 1 premium only shows a
significant decrease with market concentration under the second specification, particularly
from competitive to duopoly markets (from 119% to 93%). Group 2 premium exhibits, in
turn, a moderate increase from competitive to monopoly routes, from 36% to 60%. Group
3 premium does not seem to vary across different competitive settings. All of these results
are summarized in Table 7. Overall, after controlling for several costs- and market-specific
factors, we still observe differences in relative fares (quality premiums) across routes with
different levels of competition, especially on the higher end of the quality range. This
suggests that market structure conditions do in fact affect carriers’ price discrimination
strategy, at least for some airlines, as we discuss next.
17We performed separate estimations for each major carrier to examine whether this
nonlinear pricing pattern is recurrent across major airlines (refer to Table 7).40 In most
cases, we find a significant quality premium of the different fare types over Group 4 tickets.
However, the decrease in the premium of Group F and Group 1 fares as we move to less
competitive markets is only significant for United and Delta. In the case of the former,
Group F and Group 1 premiums decrease from 189% and 172%, respectively, in competitive
markets to 127% and 94% in monopoly markets. In the case of the latter, the corresponding
premiums decrease from 176% and 158% to 112% and 98%. Group 2 premiums of both
airlines show, at the same, a moderate increase with market concentration (from 33% to
77% in United and from 43% to 74% in Delta). American also exhibits a significant decrease
in the premium of Group F fares, from 145% to 123%, but Group 1 premium increases from
74% to 141%. Northwest, on the contrary, shows an increase in the premium of all high-
quality fares with market concentration, while Continental and US Airways do not seem to
vary their premiums with market structure.
4.3 Testing for endogeneity of group dummies
In light of our results, we now turn to examine whether the key variables in the analysis, i.e.
dummy variables for fare groups, are exogenous, as we have previously assumed. According
to the revenue management literature, quantity or inventory control is a natural tactic in
the airline industry to maximize the revenue of each flight.41 It may be the case that
different ticket types sold at different points in time, partly result from optimal quantity
adjustments that we do not account for in our estimations and which also affect prices. If
so, dummy variables for fare types would be endogenous and the estimates reported above
would be biased.
Following Wooldridge (2008), we carried out a regression-based procedure to test the
null hypothesis that the set of group dummies is exogenous in equation (3), while allowing
another set of explanatory variables to be endogenous. Recall that in our estimations
we treat market share, HHI and log of total flights on route as endogenous. The first
step involves regressing each dummy variable for fare type on all included and excluded
exogenous variables used to estimate equation (3) plus dummy variables for aircraft size.
We believe that aircraft size is a valid instrument for group dummies since the possible
number of fare types offered by airlines are partly determined by aircraft size, while prices
are better determined by seat availability at the time of purchase, i.e. load factor at
40
Main carriers include American (AA), United (UA), Delta (DL), Continental (CO), US Airways (US),
and Northwest (NW).
41
For a general discussion on this practice, commonly referred to as yield management in the airline
industry, see Talluri and Van Ryzin (2005).
18purchase. The second step consists in adding the reduced-form residuals of the first step
as additional regressors in the log fare per mile equation specified in equation (3). This
augmented equation is estimated by 2SLS where we still instrument for market share, HHI,
and log of total flights, but group dummies and their reduced-form residuals act as their
own instruments. We finally perform a heteroskedastic-robust test to evaluate whether
the coefficients of the reduced-form residuals in the augmented equation are statistically
different from zero.
Although not reported, the reduced-form regressions from the first step confirm that the
dummy variables for fare types are partially correlated with aircraft size dummies.42 Table
9 summarizes the test results for the second step. It is easily seen that we cannot reject
the null hypothesis that the set of group dummies is exogenous under both specifications
of equation (3).
4.4 Alternative Estimation
To check the robustness of our results, we also performed a partially linear smooth coefficient
regression which allows us to model the quality premiums in equation (3) as a function of
HHI. That is,
3
X
ln pijkt = g0 (HHIk ) + gf 1 (HHIk )qfi + Xijt φ + αj + κk + νijkt (5)
f =F
where g0 (·) and gf 1 (·), f = F, .., 3, are unspecified smooth functions of HHI, and Xijt are a
subset of controls from equation (3).43 We use least-square cross validation and a second-
order Gaussian kernel function to estimate the bandwidth of HHI.44 The advantage of this
model is that it does not impose any functional form on the relationship between market
concentration and quality premiums. Due to the computational burden of this method,
we work with a 1% random sample of the dataset (8,709 observations), maintaining the
proportion of tickets by route, carrier and fare type.
Figure 10 shows how the quality premiums of the different fare types, over Group 4 fares,
vary with less competition. Consistent with our previous results, we observe that Group F
premium declines in highly concentrated markets. The premium is around 170% at a HHI
42
Provided that we allow for additional endogenous explanatory variables in our estimations, it is impos-
sible to perform a Cragg-Donald weak identification test. These results at least confirm that aircraft size
dummies are potential instruments for group dummies.
43
Due to multicollinearity in the estimation process, we only include certain controls at the ticket, flight
and carrier level. We treat both carrier and route effects as random.
44
For further details on this estimation method refer to Li and Racine (2007).
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