Has the “Golden Rule” Lost its Aura? Revisiting Multimarket
Contact under Asymmetric Pricing in the U.S. Domestic Airline
Industry
(COMPLETED RESEARCH)
Ramnath K. Chellappa
Raymond Sin
V. Sambamurthy
[ram@bus.emory.edu]
[rsin@ust.hk]
[sambamurthy@bus.msu.edu]
Goizueta Business School,
School of Business and
Eli Broad Graduate School of
Emory University
Management
Management
1300 Clifton Road
Hong Kong University of
Michigan State University
Atlanta GA 30322
Science & Technology, Hong
East Lansing, MI 48824
Kong
Abstract
Extant research suggests that tacit collusion or the “golden rule” of refraining from
aggressive pricing in jointly contested markets is an integral feature of the US airline
industry. Our research revisits this past wisdom in the presence of airlines that pursue
a distinctly different pricing strategy. Amongst airlines, Southwest and JetBlue largely
practice an Everyday Low Price (EDLP) price-format which can be best characterized
as a portfolio-level pricing strategy while most others engage in some form of temporal
fare promotions. In a first study using both posted and transacted airline prices, we
examine the impact of asymmetric pricing strategies on the understanding of
multimarket contact (MMC). By first ignoring these differences in pricing strategy, we
1
are able to replicate extant results, i.e. the golden rule appears to be followed
throughout this sector even in today and for purely online tickets. We then separately
identify multimarket contact of a focal firm with like and asymmetric firms and develop
both carrier-route and route-level measures of MMC.
Our results confirm that the
impact of MMC on prices is rendered insignificant (or less significant) when accounting
for the presence of this alternative pricing strategy.
Subsequently we differentiate
between MMC with similar carriers and those with EDLP carriers. Our findings show
that while tacit collusion appears to take place when MMC occurs between non-EDLP
carriers, MMC with EDLP carriers actually lowers prices in the marketplace. Further,
it also appears that EDLP airlines avoid MMC with each other. Our findings argue
that any tacit collusion from mutual forbearance is a possibility only when both firms in
contact are likely to employ price changes; when there is asymmetry in the pricing
rationale there is no scope for tacit collusion. We conclude with a call to include such
asymmetries in pricing mechanisms for other industry contexts as well in newer gametheoretic formulations of MMC.
1. Introduction
While general economic theories on pricing and competition suggest that firms may
compete on the basis of price (Bertrand), quantity (Cournot) quality (vertical
differentiation), or consumers’ preferences (horizontal differentiation), a different stream
of literature emerges and points out that a different dynamic exists in the competition
among firms that compete in more than one market.
For example, Burger King
2
competes with McDonalds in Austin as well as in Houston. This type of competition is
known as “multimarket competition”. Extant research in this area suggests that rational
firms will not undercut multimarket competitors in a given market as they will foresee a
response from their competitors in other markets leading to mutual forbearance, a form
of tacit collusion, and higher prices. Such behavior is purportedly observed in a number
of industry contexts, such as the cell phone, software, and airline industries (Evans and
Kessides 1994; Busse 2000; Chellappa et al. 2010). The airline industry, in particular,
has received revived interest among academic researchers due to innovations in
information technology (IT). Advancements in IT and the ubiquity of the Internet have
enabled airlines to not only execute sophisticated pricing algorithms, but the lowered
menu costs have also allowed airlines to run promotions and push them to consumers
through their own websites or online travel agents.
Extant research suggests that tacit collusion or the “golden rule” of refraining
from aggressive pricing in jointly contested markets is an integral feature of the US
airline industry. Our research revisits this past wisdom in the presence of airlines that
pursue a distinctly different pricing strategy. Amongst airlines, Southwest and JetBlue
largely practice an Everyday Low Price (EDLP) format which can be best characterized
as a portfolio-level pricing strategy while most others engage in some form of temporal
fare promotions. In a first study using both posted and transacted airline prices, we
examine the impact of asymmetric pricing strategies on the understanding of
multimarket contact (MMC). By first ignoring these differences in pricing strategy, we
are able to replicate extant results, i.e. the golden rule appears to be followed
3
throughout this sector even today and in electronic markets. We then separately
identify multimarket contact of a focal firm with like and asymmetric firms and develop
both carrier-route and route-level measures of MMC.
Our results confirm that the
impact of MMC on prices is rendered insignificant (or less significant) when accounting
for the presence of this alternative pricing strategy.
Subsequently we analyze MMC
with similar non-EDLP carriers and those with EDLP carriers. Our findings show that
while tacit collusion appears to take place when MMC occurs between non-EDLP
carriers, MMC with EDLP carriers actually lowers prices in the marketplace. Further,
it also appears that EDLP airlines avoid MMC with each other. Our findings argue
that any tacit collusion from mutual forbearance is a possibility only when both firms in
contact are likely to employ price changes; when there is asymmetry in the pricing
rationale there is no scope for tacit collusion. We conclude with a call to include such
asymmetries in pricing mechanisms for other industry contexts as well in newer gametheoretic formulations of MMC.
2. Data and Method
In this section, we first discuss the nature of our data and explain the econometric
model employed in this study. We then discuss the operationalization of various
multimarket contact measures and conclude with a discussion of the variables used in
our econometric analysis.
4
2.1 Data
Our data is collected from two primary sources. First, we obtained prices and detail
descriptions of airline tickets from online travel agents and individual airlines’ websites.
This raw data on offered tickets was gathered using web-based spiders that we
developed using Curl, and later processed by a parser that we wrote in Perl and other
database scripting languages. In addition to the set of all major U.S. carriers and online
travel agents, a list of the top 500 U.S. domestic routes – which account for over 86% of
all domestic passenger enplanements in the U.S. – was provided as input to the spiders.
The spiders were sent out on a daily basis in the third quarter of 2004 to collect price
and other attribute information for tickets requiring one- to four-week advance
purchases, including weekday as well as weekend departures and returns. Our agents
operated in parallel and submitted identical reservation requests to all online travel
agents and airlines’ websites simultaneously in order to minimize price variations that
may arise from the timing of ticket requests.
We restrict our attention to only coach class, non-refundable, roundtrip tickets.
Further, to control for any price difference that may be attributed to differences in
flight duration or the number of connections on any given route, we consider flights that
have at most one stop between an origin and a destination.
As a result, 46,854
observations – approximately 4.15% of the full sample – have been eliminated.
Our
final data set includes 1,083,515 unique tickets and final prices, including taxes and fees,
offered by fourteen network carriers.
5
Second, we constructed a comparable dataset on purchased tickets using the
Origin and Destination Survey (DB1B) for the corresponding routes and carriers in the
same quarter of 2004. DB1B is a 10% sample of all airline tickets sold by reporting
carriers, including origin, destination and other itinerary details of passengers
transported.
After restricting our attention to only coach class, non-refundable
roundtrip tickets with at most one stop on each way, the resulting number of
observations for purchased tickets is 142,595.
Further, we used the Air Carrier
Statistics (Form 41 Traffic and 298C Summary Data) provided by the U.S. Bureau of
Transportation Statistics to assemble data on airlines’ operational details, as well as
information on the respective markets (e.g. origin-destination distance, hub information,
etc.).
We also collected information on market share and the number of competing
airlines in each origin-destination pair from DB1B in the second and third quarters of
2004.
We then merged this dataset that contains detailed information on airlines and
markets with the pricing data on offered tickets (collected online) and purchase tickets
(based on DB1B), respectively. This yielded a complete profile of all relevant variables
at the ticket level, allowing us to control for various market- and airline-specific factors
in our examination of the effects of multimarket contact on airline pricing.
We
subsequently created two subsets of data, one that consists of only observations from
HILO airlines while the other consists of only observations from EDLP airlines, from the
full sample to perform additional analyses that complement our main investigation.
6
Table 1 summarizes the operationalization of variables included in this study; and
Tables 2 and 3 report descriptive statistics for our data.
2.2 Model
Our baseline model is a replication of the model employed by Evans and Kessides (1994),
and is of the following form:
ln pricekm
m
km
Xkm
~ N 0,
~ N 0,
Zm
k
m
km
(1)
where pricekm is the average fare charged by airline k on route m, Xkm are variables that
vary by the airline’s identity within a given route, and Zm are route characteristics. The
three-part error structure consists of a carrier effect
k
, a route effect
m
that is
common to all carriers on an observed route, and a white-noise error that is specific to
the observation at the carrier-route level
km
.
Consistent with extant empirical
studies on airline pricing where the dependent variable is at the carrier-route level (e.g.
Borenstein (1989), Borenstein and Rose (1994), Hayes and Ross (1998)), Chellappa et al.
(2011)), and a Hausman test on random-effects specification, we treat the airline effects
as fixed while the route effects as random.
The variables that we include in the X vector are: directkm , the percentage of
tickets offered by airline k on route m that are direct flights; hubkm , a variable that
indicates if at least one endpoint airport on the observed route is a hub for airline k;
7
and RTsharekm , the market share of airline k on route m.
We include the following
variables in the Z vector: ln distancem , the natural logarithm of distance (in miles)
between the origin and destination airports on the observed route; ln distancem
square of ln distancem
2
, the
to capture the non-linear effects of distance on prices due to
economies of scale from fuel efficiency on long-distance flights; RTherfm , the Herfindahl
index for route m; and EDLPmktm , a variable that indicates if at least one of the airlines
that operate in the observed market is an EDLP carrier.
Finally, our measure of
multimarket contact is included in either the X vector or the Z vector, depending on the
unit of measurement.
We estimate our model using both the measures proposed by
Evans and Kessides (1994) – MMCEKm , a route level measure included in the Z vector –
and by Baum and Korn (1996) – MMCBKkm , a carrier-route level measure included in
the X vector – respectively. We compute the additional measure at the carrier-route
level in order to explore the implications of multimarket contact at the same level as the
dependent variable. This approach is not only consistent with that in extant literature
that studies multimarket contact in various contexts (Feinberg 1985; Pilloff 1999;
Coccorese and Pellecchia 2009; Chellappa, Sambamurthy et al. 2010), but is also
recommended by Gimeno and Jeong (2001) based on an extensive review of existing
research on multimarket competition. In particular, Gimeno and Jeong observe that
while the multimarket construct can be operationalized at different levels of analysis
(e.g. markets, firms-in-markts, dyadic pairs of firms), it is necessary to “align analyses
8
with the level of dependent variables” (p. 363).
The operationalization of the
multimarket contact measures employed in this study is presented in the Appendix.
3. Results
Table 4 is a replication of Evans and Kessides’s (1994) model using prices of both
offered tickets (spider data) and purchased tickets (DB1B data).
The signs of the
coefficient estimates of the variables are largely consistent with those reported in Evans
and Kessides; the only exceptions are the estimates of the Herfindahl index for
purchased tickets, which are negative as opposed to positive. A negative sign suggests
that prices increase with intensity of competition, which may be attributed to tacit
collusion posited in the theory of multimarket contact.
Notice that the coefficient estimates for the multimarket contact variables are
positive and significant.
The results are robust for both types of tickets, and for
multimarket contact measured at both the route level MMCEKm and the carrier-route
level MMCBKkm .
In sum, when we employ the same set of variables that are
considered in Evans and Kessides, the conclusion that we draw on the effects of
multimarket contact on firm’s pricing are largely consistent with those reported in prior
literature.
Table 5 presents the coefficient estimates of a modified model, which includes the
EDLP market identifier, on the same sets of data. We can make two key observations
from the results: First, the EDLPmktm indicator variable is negative and highly
significant; this suggests that prices of tickets in markets where EDLP carriers operate
are lower than those in other markets. Second, both multimarket contact measures for
9
offered tickets become insignificant once EDLPmktm is introduced. For purchased tickets,
even though the coefficients for MMCEKm and MMCBKkm remain positive and significant,
the magnitudes of these coefficients are approximately 40% smaller compared to those
reported in Table 4. These two results indicate that airlines’ pricing behaviors vary
significantly with markets characterized by different competitive environments, which
are largely defined by the presence of EDLP airlines.
Do these results imply that the traditional understanding of the relationship
between multimarket contact and pricing is no longer applicable? Or do they simply
point towards the possibility that multimarket contact can have different implications
on how firms set prices depending on the type of competitors with whom they engage in
multimarket contact? In the subsequent analysis, we aim to shed light on this issue by
decomposing the multimarket contact measure into separate components according to
the types of competitors that an airline come into contact with.
Table 6 presents the coefficient estimates of the model that incorporates two
decomposed MMC measures defined at each level, and focuses only on HILO
observations.
The decomposition is based on the type of firms with whom that an
airline engages in multimarket contact. At the route level, MMCEKm is broken down
into eMMCEKm , which calculates only the contacts between HILO airlines and EDLP
airlines; and hMMCEKm , which calculates only the contacts among HILO airlines.
Likewise, MMCBKkm is broken down into eMMCBKkm and hMMCEKm accordingly.
As
with the previous models, we conduct the analysis using both offered tickets and
purchased tickets.
10
Two very interesting observations emerge from this model: First, the coefficient
estimates for both eMMCEKm and eMMCBKkm are negative and significant; and the result
is robust with respect to both offered tickets and purchased tickets. This suggests that,
other things being constant, when a HILO airline engages in multimarket contact with
an EDLP carrier, it actually lowers its prices as opposed to charging higher prices that
implies tacit collusion.
In fact, extant research suggests that EDLP is a deliberate
pricing strategy that is not reactive to competitors’ pricing (Sin et al. 2009); further, the
presence of EDLP firms in a market changes not only the overall distribution of prices
at the market level but also the distributions of prices of individual competing firms
(Chellappa, Sin et al. 2011). In other words, while a HILO carrier may ideally want to
engage in tacit collusion with EDLP airlines, it really has no choice but to lower its own
price to battle with this type of competitors.
Second, with the exception of offered
tickets, hMMCEKm and hMMCBKkm are both positive and significant. This suggests that
a HILO airline charges higher prices when engaged in multimarket contacts with other
airlines that employ similar pricing strategies. The second result is highly consistent
with findings reported by existing literature.
3.1 Discussion and conclusions
A main goal of this research is to examine the impact of multimarket contact on prices.
Whilst there is much research in the airline industry on this subject, two fundamental
factors that can potentially influence prices – presence of EDLP airlines and the shift
towards electronic markets, have not been accounted for.
11
From our analysis, we can conclude that if the presence of asymmetric pricing strategies
is ignored, then we shall observe that the results are similar to that of extant research
even for online prices, i.e., multimarket contact will lead to higher online prices.
However, the moment we identify the differences in airlines’ pricing strategies in this
assessment, we see fundamentally different results.
We observe that when network
airlines meet EDLP carriers, the prices are reduced.
Essentially our research
underscores the tension between firms’ ability to practice their adopted pricing strategy
and the dictates of the market.
12
Appendix:
Table 1: Description of Variables
Factor
Variable
Related Literature Explanation
Ticket
Direct flights
(Evans and
The percentage of tickets offered by airline k on route m that
Kessides 1994)
are direct flights.
Characteristic
Directkm
(Borenstein 1989;
Borenstein 1991;
An indicator variable equals to 1 if at least one of the endpoint
Berry et al. 1997;
airports on a given route is a hub for the observed airline; 0
Hayes and Ross
otherwise.
Hub
hubkm
Airline
1998)
Characteristics
(Borenstein 1989;
Market Share
RTsharekm
Borenstein and
The observed carrier’s share of passengers on the observed
Rose 1994; Evans
route.
and Kessides
13
1994; Baum and
Korn 1996)
(Borenstein 1989;
Evans and
Kessides 1994;
Market distance
Non-stop distance (in miles) between the origin and the
Berry, Carnall et
destination airports on the observed route.
distancem
al. 1997; Hayes
Market
and Ross 1998;
Characteristics
Stavins 2001)
(Borenstein 1989;
Borenstein and
Herfindahl Index
Rose 1994; Evans
Herfindahl index for all passengers on the observed route.
RTherfm
and Kessides
1994)
14
Average Route
(Evans and
Route level measure of multimarket contact, based on Evans
Kessides 1994)
and Kessides (1994).
(Baum and Korn
Carrier-route level measure of multimarket contact, based on
1996)
Baum and Korn (1996).
(Chellappa, Sin et
An indicator variable equals to 1 if at least one EDLP airline
al. 2011)
(Southwest or JetBlue) operates in the market; 0 otherwise.
Contact
Multimarket
MMCEKm
Contact
Multimarket
Measures
Contact
MMCBKkm
EDLP market
Price-format
EDLPmktm
15
Table 2: Descriptive Statistics on Offered Tickets (N=2,064)
MEAN STD Min
pricekm
distancem
Max
Correlation Matrix
377.28 139.93 101.13 1200.79 1.00
1173.58 629.32 148.00 2586.00 0.34 1.00
directkm
0.22
0.34
0.00
1.00 -0.20 -0.34 1.00
hubkm
0.34
0.47
0.00
1.00 -0.03 -0.15 0.65 1.00
RTsharekm
0.23
0.29
0.01
1.00 -0.14 -0.15 0.71 0.60 1.00
RTherfm
0.49
0.20
0.00
1.00 -0.14 -0.47 0.13 0.11 0.05 1.00
MMCEKm
130.94 50.04
0.00 268.00 0.17 -0.30 0.10 0.06 -0.03 0.08 1.00
MMCBKkm
0.56
0.17
0.00
0.98 0.09 -0.16 0.07 -0.04 -0.05 0.03 0.73 1.00
EDLPmktm
0.19
0.39
0.00
1.00 -0.29 0.02 0.00 0.01 0.08 0.09 -0.53 -0.48 1.00
Table 3: Descriptive Statistics on Purchased Tickets (N=2,057)
MEAN STD
pricekm
distancem
Min
Max
Correlation Matrix
315.82 99.23 64.00 956.00 1.00
1173.05 627.97 148.00 2586.00 0.35 1.00
directkm
0.30
0.39
0.00
1.00 0.05 -0.30 1.00
hubkm
0.34
0.47
0.00
1.00 0.20 -0.15 0.61 1.00
RTsharekm
0.23
0.29
0.01
1.00 0.17 -0.15 0.74 0.60 1.00
RTherfm
0.49
0.20
0.00
1.00 -0.20 -0.47 0.11 0.11 0.05 1.00
16
MMCEKm
130.85 49.96
0.00 286.00 0.18 -0.29 0.05 0.06 -0.03 0.08 1.00
MMCBKkm
0.56
0.17
0.00
0.98 0.14 -0.16 0.04 -0.03 -0.05 0.03 0.73 1.00
EDLPmktm
0.19
0.39
0.00
1.00 -0.32 0.02 0.03 0.01 0.09 0.09 -0.53 -0.48 1.00
Table 4: Estimates of model, omitting the EDLP market identifier
Independent
Route Level MMC
Carrier-Route Level MMC
variables
Offered
Purchased
Purchased tickets
Offered tickets
tickets
tickets
-1.7698*
2.5660***
-2.0884**
2.5834***
(1.0470)
(0.7805)
(1.0530)
(0.7861)
1.9393***
0.5891**
2.0802***
0.6089**
(0.3207)
(0.2383)
(0.3217)
(0.2402)
-0.1224***
-0.0257
-0.1343***
-0.0285
(0.0243)
(0.0180)
(0.0243)
(0.0181)
0.0151
0.0742***
0.0221
0.0825***
(0.0247)
(0.0204)
(0.0247)
(0.0204)
0.0159
0.0378**
0.0176
0.0393***
(0.0136)
(0.0150)
(0.0136)
(0.0151)
0.0588
0.3773***
0.0439
0.3567***
(0.0385)
(0.0382)
(0.0385)
(0.0382)
-0.0004
-0.1349**
-0.0682
-0.1681***
(0.0734)
(0.0547)
(0.0717)
(0.0544)
INTERCEPT
ln distancem
ln distancem
2
directkm
hubkm
RTsharekm
RTherfm
17
0.0010***
0.0014***
(0.0002)
(0.0002)
--
--
--
--
0.1463***
0.3255***
(0.0510)
(0.0461)
MMCEKm
MMCBKkm
EDLPmktm
N
-2LL
--
--
--
--
2064
2057
2064
2057
-418.9
-426.7
-416.5
-417.3
Table 5: Estimates of model, including the EDLP market identifier
Independent
Route Level MMC
Carrier-Route Level MMC
variables
Offered
Purchased
Purchased tickets
Offered tickets
tickets
tickets
-1.4154
2.7967***
-1.4602
2.8861***
(1.0111)
(0.7563)
(1.0128)
(0.7597)
1.8698***
0.5458**
1.8928***
0.5310**
(0.3093)
(0.2307)
(0.3093)
(0.2320)
-0.1171***
-0.0224
-0.1190***
-0.0219
(0.0234)
(0.0174)
(0.0234)
(0.0175)
0.0126
0.0744***
0.0137
0.0789***
(0.0246)
(0.0203)
(0.0245)
(0.0203)
0.0190
0.0416***
0.0195
0.0426***
(0.0135)
(0.0149)
(0.0135)
(0.0149)
INTERCEPT
ln distancem
ln distancem
2
directkm
hubkm
18
0.0453
0.3539***
0.0423
0.3408***
(0.0384)
(0.0381)
(0.0382)
(0.0379)
0.0542
-0.0995*
0.0448
-0.1073**
(0.0712)
(0.0532)
(0.0703)
(0.0531)
0.0002
0.0009***
(0.0002)
(0.0002)
--
--
--
--
0.0193
0.1978***
(0.0529)
(0.0486)
RTsharekm
RTherfm
MMCEKm
MMCBKkm
-0.2382***
-0.1638***
-0.2485***
-0.1852***
(0.0358)
(0.0269)
(0.0328)
(0.0253)
2064
2057
2064
2057
-456.9
-457.2
-467.1
-463.9
EDLPmktm
N
-2LL
Table 6: Estimates of model with decomposed MMC measures (HILO observations only).
Independent
Route Level MMC
Carrier-Route Level MMC
variables
Offered
Purchased
Purchased tickets
Offered tickets
tickets
tickets
-0.6865
3.8925***
-0.0716
4.3154***
(1.1308)
(0.8657)
(1.1382)
(0.8672)
INTERCEPT
19
1.6648***
0.2570
1.4512***
0.1236
(0.3435)
(0.2620)
(0.3458)
(0.2629)
-0.1037***
-0.0035
-0.0875***
0.0062
(0.0259)
(0.0197)
(0.0260)
(0.0197)
0.0855***
0.0507**
0.0821***
0.0513**
(0.0276)
(0.0220)
(0.0275)
(0.0220)
0.0116
0.0368**
0.0098
0.0360**
(0.0138)
(0.0156)
(0.0138)
(0.0156)
0.0074
0.4414***
0.0213
0.4468***
(0.0425)
(0.0424)
(0.0423)
(0.0422)
0.1772**
-0.0433
0.1759**
-0.0466
(0.0774)
(0.0586)
(0.0770)
(0.0583)
-0.0065***
-0.0051***
(0.0013)
(0.0010)
--
--
-0.0001
0.0005***
(0.0002)
(0.0002)
--
--
--
--
-0.1638***
-0.1749***
(0.0428)
(0.0350)
0.0869*
0.1439***
(0.0446)
(0.0406)
ln distancem
ln distancem
2
directkm
hubkm
RTsharekm
RTherfm
eMMCEKm
hMMCEKm
eMMCBKkm
--
--
hMMCBKkm
N
-2LL
1940
1933
1940
1933
-446.1
-362.8
-460.3
-387.0
20
21
Multimarket Contact Measures
1. Average Route Contact (Evans and Kessides, 1994):
1
MMCEKm
fm fm 1 / 2
Dkm D jm
where akj
akj Dkm D jm
k
j k 1
m
k,j indicate the identity of two firms. Hence
akj calculates the total number of
akj Dkm Djm is
contacts between k and j across all markets. The numerator,
k
j k 1
the total number of cross-market contacts between pairs of firms that are active
in market m. In the denominator, fm is the number of firms that are active in
market m. fm fm
1 / 2 is the number of firm pairs in market
m.
2. Firm-in-market Level Multimarket Contact (Baum and Korn, 1996):
Dkm
D jm
j k m
MMCBKkm
Dkm
N mmc
j s.t.
Dkm
Djm
1
m
m
where m denotes the observed (focal) market in a set of potential markets M,
Dkm
Djm
is an indicator variable set equal to 1 if firm k (j) is active in market
m and to 0 otherwise.
Dkm
The numerator
Djm
counts the total number of contacts
j k m
between firm k and firm j across all markets, in which both firms meet at least
once outside the focal market. For firms that firm k encounters only in the
Dkm
observed market,
Djm
equals 1, hence their contacts with firm k will
m
be excluded from the calculation of MMCBKkm .
22
Dkm denotes the total number of markets in which firm
In the denominator,
k
m
operates.
This is a proxy measure of “firm size”. N mmc denotes the number of
firms that are active in market m which also contact firm k in markets outside
the focal market. In other words, MMCBKkm is a relative measure of multimarket
contact, which is scaled by the size of firm k and the number of competitors; it
measures the relative importance of market m to firm k, taking into account the
potential influence that firm i’s competitors may have on its cross-market
performance.
Instrumental Variable Approach
It is reasonable to expect that an airline’s share of passenger on a route RTshare ,
as well as the Herfindahl index constructed from this variable RTherf , to be
endogenous to the price that it charges; a Hausman specification test rejects
exogeneity for RTshare and RTherf . We resolve this issue by using instrumental
variable and the two-stage least square approach. Following Borenstein (1989)
and Borenstein and Rose (1994), we use the geometric share of enplanements of
an observed carrier at the endpoints of a given route as the instrument for its
market share, and later use it to construct the instrument for RTherf .
The
geometric enplanement share of the observed airline i on a given route is defined
as follows:
23
ENPi1 ENPi 2
GENPSH i
(2)
ENPj 1 ENPj 2
j
where j indexes all airlines; ENPj 1 and ENPj 2 are airline j ’s average daily passenger
enplanements at the two endpoint airports on the observed route during the
second quarter of 2004.
In other words, GENPSHi is defined as the observed
carrier’s geometric mean of passenger enplanements at the endpoints of a route
divided by the sum of the geometric mean of each carrier’s enplanements at the
endpoint airports across all carriers on the observed route.
We construct the instrument for RTherf using the square of the fitted value
RTshare from the first-stage regression, plus a rescaled sum of squares of the
shares of all other carriers:
IRTherf
2
RTsharei
RTherf
1
RTsharei2
RTshare
2
2
1
RTshare i
(3)
where i indexes the observed airline. The rationale behind the second term in
IRTherf
is that the concentration of traffic on a route that is not served by the
observed airline is exogenous to the price of the observed airline; for example,
Delta’s price on the Boston–LaGuardia Airport route does not affect the division
of passengers between American and United. The rescaling ensures that the part
in a Herfindahl index that is calculated for passengers who do not travel on the
observed carrier remains unchanged.
We then use IRTherf as the excluded
exogenous variable in the first-stage regression of RTherf that generates RTherf .
24
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