Pricing and Market Concentration in Oligopoly
Markets1
(Preliminary. Comments welcome)
Vishal Singh
Ting Zhu
March 8, 2006
1 The
authors are Assistant Professor of Marketing and Doctoral Student in Marketing respectively at Tepper School of Business, Carnegie Mellon University. They can be reached at
vsingh@andrew.cmu.edu (Singh) and tzhu@andrew.cmu.edu (Zhu) for comments and suggestions. The authors are listed in alphabetical order and contributed equally.
Abstract
We study the relationship between prices and market concentration in the Auto Rental
Industry. We develop an original database that includes the number of auto rental operating firms at every commercial airport in the country. The data is particularly interesting
as we observe a large variation in market structure ranging from over 100 monopoly and
duopoly markets to several airports with more than nine firms. In addition we collect
daily rental prices in each market that are regressed against the market structure variables and other control factors. Unlike most previous studies we explicitly account for
endogeneity of market structure in the price regressions. In particular, we estimate a
static entry model for predicting the equilibrium number of firms in the first stage. The
parameters from the entry model are then used to derive terms that are inserted in the
price equation to correct for endogeneity of competitive parameters. Our results show
that ignoring this endogeneity severely biases the market structure parameters. The
prices in concentrated markets (monopoly/duopoly) are found to be approximately 30%
higher compared to competitive markets with seven or eight firms. Policy implications
of our model and results are discussed.
Keywords: Price, Market Concentration, Entry Models, Auto Rental
1
Introduction
A long stream of literature in economics and marketing strategy examines the relationship between competitive characteristics of a market and profitability. In the structureconduct-performance paradigm of industrial organization, this literature relies on a crosssectional data across industries to document the impact of market concentration on profitability. A general finding in this literature is that higher market shares and seller
concentration are associated with higher profitability (see for example, Buzzell et. al
1987, Schmalensee 1989). However, the profit-concentration studies have been criticized
on several grounds. First, these studies are plagued by measurement problems as accounting profits are in general poor indicators of economic profits. Second, the cross-sectional
data from different industries used in these studies is problematic due to large differences
in demand and supply conditions across industries. Finally, these studies are subject to
the “efficiency” critique offered by Demsetz (1973) who argued that positive correlation
between profits and market concentration could be due to the competitive superiority of
a few firms.
Over the past several decades, the profit-concentration studies have been replaced by
a stream of research that examines the relationship between market structure and prices,
rather than profits. An advantage of using prices as opposed to profits is that they are
easier to obtain and are not subject to accounting conventions. Weiss (1989) provides
a collection of large number of price-concentration studies and argues that since prices
are determined in the market, they are not subject to superiority criticism like profits.
Furthermore, majority of the price-concentration studies use data across local markets
within an industry rather than across industries1 . These studies include a wide range of
industries such as Grocery (Cotterill 1986), Banking (Calem and Carlino 1991), Airlines
(Borenstein and Rose 1994), Hospitals (Keeler, Melnick and Zwanziger 1999), Driving
lessons (Asplund and Sandin 1999), Cable television (Emmons and Prager 1997), Movie
theaters (Davis 2005) and so on.
A general finding in this literature is that high concentration is associated with significantly higher prices (Weiss 1989, see also various studies cited in a recent survey by Newmark (2004)). However, as pointed out by both Bresnahan (1989) and Schmalensee (1989)
1
Now, virtually all structural empirical work in economics and marketing is industry-specific. These
studies incorporate more industry- and firm-specific details to provide a deeper understanding on the
underlying economic primitives of demand, cost, and competitive behavior. See for example recent
surveys by Kadiyali et al. (2001), Dube et al. (2004), Reiss and Wolak (2004), and Chintagunta et al.
(2004).
1
in their chapters in the Handbook of Industrial Organization, the price-concentration regressions such as those used in the literature suffer from serious endogeneity issues. In
particular, there might be unobserved demand and cost shocks in a market that not only
influence prices but also the underlying market structure. For instance, a market with
unobserved high costs are likely to have higher prices, but these markets are also likely
to attract fewer entrants. Evans, Froeb and Werden (1993) formally address this issue
and propose a combination of fixed effects and instrumental variable procedures that are
applicable when one has access to panel data. They study the price-concentration in the
airline industry and find that the effect of concentration on price is severely biased using
OLS procedures.
Recent structural work in marketing (see Chintagunta et al. (2006) and the accompanying comments) has pointed out the endogeneity problems associated with short term
marketing activities such as pricing and promotions, while taking the underlying competitive structure in the industry as exogenous. However, the endogeneity of market structure
is a serious problem in the price-concentration studies such as those mentioned above.
The bias in the parameters capturing the competitive interactions can also have important policy implications. As Whinston (2003) points out, price-concentration studies are
one of the most commonly used econometric technique employed by FTC in analyzing
horizontal mergers. Similarly, Baker and Rubinfeld (1999) note that “reduced form price
equations are the workhorse empirical methods for antitrust litigation...”.
The following example from a highly litigated case on the merger between Staples and
Office Depot underscores the importance of considering market structure as endogenous
when analyzing relationship between price and number of firms in the market. Table
1 reports one of the important evidence used by FTC to challenge the merger between
the two firms and eventually decline it2 . The table shows the advertised prices of five
products at Office Depot from two markets: Orlando, FL and Leesburg, FL. Office Depot
is a monopolist in the Leesburg market, while Orlando market is an Oligopoly with three
office supply firms (Office Max and Staples being the other two). It is quite evident
that the prices in monopoly market are significantly higher. However, a fundamental
question that must be addressed is whether higher prices in Leesburg are driven by lack
of competition alone. In particular, one needs to consider the underlying demand and
cost conditions that result in a monopoly in one market but allow several firms to enter
2
FEDERAL TRADE COMMISSION, Plaintiff, vs.
POT, INC. Defendants.
Case No.
1:97CV00701.
http://www.ftc.gov/os/1997/04/pubbrief.htm
2
STAPLES, INC. and OFFICE DEThe table reported can be found at:
in another. Positive correlation between price and market concentration could result
if, for example, there are unobserved high costs in Leesburg that not only results in
higher prices but also attract fewer entrants. Similarly demand conditions may vary
systematically across markets (for example the population of Orlando is ten times that
in Leesburg) such that certain markets are only able to sustain small number of firms.
In this paper we study the relationship between price and number of firms in the auto
rental industry. We develop an original data set that includes the number of car rental
firms at every commercial airport in the United States. The data is quite unique in that
we observe a wide cross-section of market structures ranging from several monopoly and
duopoly markets to many airports with more than nine firms. For each of these markets
we collect an extensive set of variables that capture the demand and cost conditions.
These variables include both airport specific factors (e.g. airline passenger traffic) as well
as local demographics in the city where the airport is located (e.g. income, retail wages).
In addition we have collected data on daily rental prices from every firm and for each car
type (economy, full size, etc.). Thus our data set consists of approximately 450 markets
(airports) for which we observe the number of firms serving each market and the prices
they charge.
Our primary objective in this paper is to test how the prices change with the number
of competitors in the market. However, in doing so we take into account the endogeneity
of market structure. Since we observe only a cross-section of markets, we cannot use the
approach used in Evans et. al (1993) that requires a panel data structure. Instead, we use
a two-stage estimation procedure to address the endogeneity of market structure. In the
first stage, we estimate an equilibrium model of entry that predicts the number of competing firms in a market. In particular, we follow the literature advanced by Bresnahan
and Reiss (1987, 1990, 1991) and Berry (1992) that endogenizes the competitive structure
characteristics such as number of firms and degree of concentration in the market. The
key insight underlying the research is that we can infer features of latent profit functions
by observing entry decisions of firms as they will enter if they expect positive profits,
but not otherwise. Since market entry decisions are discrete, the model suggests using
a discrete choice framework to draw inferences about the factors that impact a firm’s
actions. The approach parallels the standard single-agent discrete choice models where
the researcher makes inferences about unobserved latent utility based on the inequality
restrictions. However, in the case of entry games, payoffs and resulting behavior reflect
the interaction of decisions of multiple individual agents. Thus, estimation is based on an
oligopolistic equilibrium concept rather than on an individual utility maximization. In
3
the empirical application, the parameter estimates from this first stage entry model are
used to derive correction terms that are inserted in the price equation to correct for the
correlation between the price errors and the market structure variables. The procedure
is similar to the two-step estimation used widely in labor econometrics (Heckman 1976,
1979)3 .
Our application in this paper is to the auto rental industry, which offers several
advantages over the industries considered in previous applications. As discussed in the
data section below, the industry is interesting as we observe a wide range of market
structures ranging from 68 monopoly markets to over 50 competitive markets with more
than nine firms. In addition, most previous price-concentration applications suffer from
problems related to market definition and price measurement, which is less of a concern
in the auto rental industry. Consider, for example, the Grocery industry studied in
Cotterill (1986) where market definition and trading areas are quite difficult to define.
The problem in this industry is magnified due to the fact that product assortments tend
to overlap across a wide range of retail formats. For example, supermarkets, discount
stores, dollar stores, price clubs, and supercenters all tend to have significant overlap
in product assortment which makes the industry definition itself difficult. In addition,
grocery retailers are multi-product firms carrying thousands of products which makes the
collection and comparison of prices for all products very difficult, if not impossible. The
common approach to deal with the problem is to create some aggregate price indexes
or rely on the prices from a handful of products. For example, Manuszak and Moul
(2006) revisit the Office Depot and Staples merger case and use data from five products.
They use a similar approach to correct for endogeneity of market structure in the price
regression as that described in this paper.
The auto rental industry analyzed in this paper overcomes the problems associated
with market definition and price measurement to a large extent. The market in this
industry is reasonably well defined since the primary clientele for auto rentals at the
airport locations are the passengers flying into the airport (according to firms Annual
Reports). While airport locations would be competing with outlets in downtowns or
other city locations that we do not consider, the problem is less severe compared to
market definitions in previous studies. Similarly the price information is reasonably easy
to collect and compare across firms and markets as (at least at the outlet level) these are
single product firms with car rental being the primary business. Finally, the product is
3
See also various examples in Maddala (1983.) Recent applications in context of market concentration
include Mazzeo (2002) and Zhu et al. (2005).
4
fairly homogenous in that the quality of a particular car-type tends to be similar across
firms, although these firms may differ in terms of service quality.
Results from the first-stage model show that many demand and cost factors such as
airport traffic, wages, and local demographics are important determinants in firm’s entry
decisions. In addition, parameters of the latent payoff functions show that profits are
higher in holiday markets as well as markets with headquarters for large firms, while
markets with better infrastructure of public transportation have lower profits. Entry of
additional competitors in the market significantly reduces profits, although the impact
is higher for the first few entrants. For pricing, several of the demand and cost control
variables, service quality (in-terminal counters), and product quality (car size) are found
to be significant. In terms of the primary focus of the paper, we find that concentrated
markets (those with fewer than three firms) have prices that are approximately 30-35%
higher than competitive markets (with more than seven firms). More importantly, we
find that ignoring this endogeneity of market structure in the price regressions severely
biases the competition parameters. In particular, the competitive interaction parameters
are double in magnitude once we insert the correction terms in the price equation. The
magnitude of bias is similar to those reported in Evans, Foreb and Werden (1993) who
find OLS parameters to be biased in the magnitude of 150 to 250 percent.
The rest of the paper is structured as follows. In the next section we describe the
price regression, first-stage entry model, and the correction procedure. Data from the
auto rental market is discussed in Section 3 and we present the results in Section 4 where
we also provide robustness checks and discuss the implications of our findings. Section 5
concludes.
2
2.1
Model
Price and Market Concentration
Consider a typical price-concentration regression model where the relationship between
the prices, exogenous market characteristics, and the market structure variables can be
specified as follows:
ln pm = Zm θ + f (Nm , δ) + εpm ,
(1)
where pm are the observed prices in market m, Zm are all exogenous market characteristics
that affect prices except the market structure variables. The function f (Nm , δ) represents
the impact of the underlying market structure on prices. In empirical applications, the
5
market structure variables are typically captured using measures such as concentration
ratio or Herfindahl Index. Finally, εpm are market specific unobservables that influence
prices.
In context of the current paper, our dependent variable pm would be the price of a
particular car-type (e.g. economy) at each airport location, and the exogenous variables
Zm would include demand and cost conditions at the airports such as number of passengers flying into the airport, local demographics, and other controls such as firm and
car-size fixed effects. Since we do not observe market shares in our data, we can not
use concentration ratio or Herfindahl Index. Instead the competitive structure in our
application is captured by including the total number of car rental firms offering services
at the airport. In the empirical application, we also run models using a flexible dummy
specification for Monopoly, Duopoly, etc. markets.
The price equation in (1) represents a typical model used in the price-concentration
literature (see for example various studies in Weiss 1989). As is well known, ordinary
least squares estimator applied to such a model is inconsistent if the unobservable εpm are
correlated with explanatory variables in the regression. Of particular concern in (1) are
the variables that capture the competitive structure,f (Nm , δ) , since there are likely to
be unobservable demand and cost conditions in a market that not only influence prices,
but also the number of the firms that operate in the market. For instance, markets with
unusually high costs are likely to have higher prices, but these markets are also likely
to attract fewer entrants. Similarly, unobserved positive or negative demand shocks can
influence a firm’s pricing as well as decision to operate in the market.
A possible solution to this econometric problem is to use instrumental variable techniques. For example, one could look for variables that impact the long-term entry decisions of the firms, but do not impact the short-term prices. However, such instruments
are, in general, difficult to find. Instead, we use a two-stage estimation procedure to
address the endogeneity of market structure. In the first stage, we estimate an equilibrium model of entry that predicts the number of competing firms in a market. In the
second stage, estimates from the entry model are used to derive correction terms that are
inserted in the price equation to alleviate the correlation between the price errors and
the market structure variables.
2.2
Endogenous Entry Decisions
To model the number of car rental companies operating at an airport, we follow the
literature on multi-agent discrete games, which provides an empirical approach to analyze
6
game theoretic models where agents make discrete choices such as entry and exit (see
Reiss 1996 for a survey). The approach is advanced by Bresnahan and Reiss (BR)
(1990, 1991). The authors develop econometric models to investigate how the number
of firms varies across markets due to various demand and cost factors. The approach
endogenizes the competitive structure in the market by implicitly analyzing the first
stage of a two stage game in which firms first decide whether or not to enter followed by
price or quantity competition. The key insight underlying the research is that we can
infer features of latent profits by observing entry decisions of firms as they will enter if
they expect positive profits, but will not enter otherwise.
Unlike the structural models of supply and demand that provide marginal conditions,
discrete decisions imply threshold conditions for players’ unobserved profits. Econometrically, this feature of the model suggests using a discrete choice framework to draw
inferences about the factors that impact a firm’s actions. However, unlike the singleagent discrete choice models that have been used extensively in the marketing literature
to model consumer choice, in the case of a discrete game, payoffs and resulting behavior
reflect the interaction of decisions of multiple agents. Thus, estimation is based on an
oligopolistic equilibrium concept rather than on an individual utility maximization.
Assume that firm k’s latent profits in market m with N entrants ( including itself)
can be specified as follows:
N
N
πmk
= π̄m
(Xm ; β) + εmk ,
This profit function has two components: π̄m (Xm ; β) captures the expected payoffs as
a function of exogenous demand and cost shifters4 , Xm , and the number of competitors
(N ) in the market, while εmk summarizes the unobserved characteristics. To identify
the parameters of the model, an equilibrium assumption is imposed that all active firms
expect non-negative profits while additional entrant would find entry into the market
as unprofitable. In BR’s framework where all firms are symmetric, i.e., εmk = εm , the
equilibrium assumption implies that the probability of observing n active firms in a
market is
n
n+1
P (Nm = n) = Pr πm
≥ 0 and πm
<0
n
n+1
≤ εm < −π̄m
= Pr −π̄m
n
n+1
= F (π̄m
) − F π̄m
,
4
(2)
Although exclusion restrictions are not required for identification due to the non-linear functional
form, our empirical application includes several variables in the entry model that are not included in
the price regression. For example, variables such as previous years annual airport traffic and population
growth rate of previous years are likely to impact firm’s entry decisions but not short-term pricing.
7
where F (.) is the cdf of εm . Finally, if a firm does not enter a market, its payoff in that
market is normalized to zero. Therefore
1
P (Nm = 0) = Pr πm
<0
1
.
= 1 − F π̄m
While restrictive, the model above generates close form solutions for the probability
of each market configuration. In the empirical application, we also estimate a variant
of the model proposed by Berry (1992), which allows for between firm heterogeneity by
introducing firm specific unobservables. Following Berry (1992), we define firm k’s profit
when there are N players at market m as
πmk (N ) = Xm β + α1 −
N
X
αn + εmk
(3)
n=2
where εmk = ηum0 + σumk ,
αn ≥ 0 for n = 2, ..., N.
where, Xm represents the observed market characteristics and α1 −
PN
n=2
αn captures
how a firm’s profit decreases as more competitors enter the market. Note that is a
more flexible specification for capturing the competition effect compared to ln(N ) used
in Berry (1992). The term um0 represents characteristics of the market that are observed
by the firms, but not econometrician,and umk are firm specific unobservables. Thus, this
model allows for heterogeneity across firms. umk and um0 are assumed to distributed i.i.d.
standard normal across firms and markets. For identification, we impose the traditional
p
constraint that the variance of εmk equal one, via the restriction σ = 1 − η 2 , where η
is the correlation of the unobservable εmk in a given market.
Firm k will enter market m given that there are N − 1 players in the markets if
πmk (N ) > 0. Assuming that profits are declining in rivals’ entry, and the ranking of
profitability (which is determined by the ranking of umk in our application) does not
change with the set of entering firms, a Nash equilibrium exits in each market. However,
the uniqueness of the equilibrium is not guaranteed since the identities of the entering
firm are different in different equilibrium. This multiplicity of equilibria where certain
values of the underlying latent payoffs could simultaneously be consistent with more than
one equilibrium outcome is a common problem in multi-agent discrete games. For the
current setup, Berry(1992) proves that although the identities of entering firms are not
unique across equilibria, the number of firms which is defined as
Nm = max (n : # {k : πmk (n, εmk ) ≥ 0}) ,
n
8
(4)
is uniquely determined. Hence we can base an estimation strategy on this unique number
of firms.
An additional complication with this framework is the complex inequalities that the
model yields for a certain outcome to be an equilibrium. In terms of the stochastic
structure of the model, these inequalities translate into complex regions of integration
for the model’s unobservables. For example, with K potential entrants in the market,
the equilibrium number of firms in the market could be 0, 1, 2, ..., K, K+1 possible mutually exclusive outcomes in total. Since the number of entering firms (N ) is uniquely
determined from the model, the probability of each outcome is well defined. For example,
Z −xm β−α1 Z −xm β−α1 Z −xm β−α1
dF (εm1 , εm2 , ...εmK ) .
(5)
...
Pr (Nm = 0) =
−∞
−∞
−∞
As we can see, the calculation of the probability involves high-dimensional integration
with large number of players in the market. In addition, the regions of ε space that
leads to an N firm equilibrium is hard to describe. The fundamental problem arises from
the large number of possible combination of entering firms, which leads to summation of
different integration region. For example,
Pr (Nm = 1) =
K
X
Pr (εm ∈ Bmi ) −
i=1
+
K X
X
Pr (εm ∈ (Bmi ∩ Bmj ))
(6)
i=1 j6=i
K X
X
X
Pr (εm ∈ ((Bmi ∩ Bmj ∩ Bml ))) + ...
i=1 j6=i l6=i,j
+ (−1)K+1 Pr (εm ∈ (Bm1 ∩ Bm2 ∩ ... ∩ BmK ))
where Bmi is defined as the region of εm that satisfies the conditions of firm i being a
monopoly in the market:
Bmi = εm : πmi (1) > 0 and πm(−i) (2) < 0 .
The expression of the probability of the a market being monopoly is complicated because Bmi and Bmj overlap on the region where both firms would make a profit as a
monopolist but neither would make a profit in a duopoly. This is the set that yields
multiple equilibrium. The expression for Pr (Nm = n) becomes far more complicated as
n increases.
Berry (1992) proposes simulation methods to solve the problem and defines a prediction error as the difference between the observed number of firms and the expected
number of firms E(N |α, β, xm ) from the model:
νm =N
˙ m − E(N |α, β, xm ).
9
(7)
By construction, νm is mean independent of the exogenous data when evaluated at the
true parameter values:
E [νm |xm , α = α∗ , β = β ∗ ] = 0.
(8)
Given the condition, either nonlinear regression or GMM can be used to estimate the
model. In order to get the E(N |α, β, xm ), we use simulation technique. Given S draws
for the underlying random variables εm and guesses of α and β, we can construct the
equilibrium number of firms N̂ (εs , α, β, xm ). The estimate of E(N |α, β, xm ) is simply
E(N |α, β, xm ) =
S
1X
N̂ (εs , α, β, xm ) .
S s=1
(9)
In our application, we use “frequency estimator” discussed above to construct the predicted number of entrants for each market, and use nonlinear regression technique to
estimate the parameters that minimize the distance between the predicted the number
of firms and the observed number of firms in the data.
2.3
Correcting for Endogenous Market Structure in the Price
Equation
Having estimated the parameters from the latent payoff functions, we derive correction
terms that will be inserted in the price regression to correct for the potential correlation
between the price errors and the market structure variables. The procedure is similar
to the selection correction used frequently in labor econometrics (Heckman 1976, 1979).
More formally, we specify the correlation of the error terms for the prices and the entry
payoffs as follows5 :
εm
εpm
˜BV N
0
0
1 ρ
,
.
ρ σ2
(10)
where εpm given εm represent the error terms from the price and entry model and ρ is
the covariance between the two. With normally distributed error terms, the conditional
distribution of εpm given εm is also normal with mean equal to
E [εpm |εm ] = ρεm .
5
Although Hechman’s two stage approach was proposed in the context of a parametric model with
normal distribution, the method can be extended to non-normal errors. With exclusion restrictions for
model identification, a more flexible polynomial approximation can be used for the second stage error
correction.
10
The expectation of εpm varies under different market structure. Given the observed number of firms Nm , we can represent the error term in price regression as follows
p
εpm |Nm = ρE [εm |Nm ] + vm
,
(11)
p
now is the pure idiosyncratic error term effecting prices.
where vm
Under BR’s specification of a firm’s entry payoff, an expression of E [εm |Nm ] can be
obtained as follows:
Z
E [εm |Nm ] =
=
Nm +1
−π̄m
ε
Nm
−π̄m
Nm
φ π̄m
Nm )
Φ (π̄m
φ (ε)
Nm ) − Φ (π̄ Nm +1 )
Φ (π̄m
m
Nm +1
− φ π̄m
.
Nm +1 )
− Φ (π̄m
dε
(12)
In the empirical application, we insert the estimates of E [εm |Nm ] form the first stage
entry model in the price regression where the covariance between εm and εpm , ρ, becomes
an additional parameter to be estimated.
A similar error correction term can be obtained from the entry model that allows for
firm heterogeneity to be used in the price regression. In particular, assuming that εpm is
only correlated with the market level unobservables, the price regression can be specified
as
p
ln Pm = Zm θ + f (Nm , δp ) + E [εpm |um0 : N = Nm ] + vm
(13)
p
= εpm − E [εpm |um0 : N = Nm ] . Note however, that with this specification there
where vm
is no close form solution for E [εpm |um0 : N = Nm ] so we rely on simulation techniques.
To illustrate how the competitive interaction parameters may be biased by ignoring
the endogeneity of market structure consider the following simple example. Suppose our
sample consists of three airport markets for which we observe the number of car rental
firms and corresponding prices. For simplicity, assume that the only observed market
condition in our data is airport traffic which is either High(H) or Low(L). In addition,
there are market specific unobservables εm that impact firm’s entry decision and are
assumed to take one of the two values: 0 or − 1. Suppose the observed prices, market
structure, traffic, and unobservables from the three markets are as follows:
Market
A
B
C
Traffic
# of firms
Unobservable εm
L
H
H
1
1
2
0
−1
0
11
Price
pA
pB
pC
Here Market B has high traffic but only one firm enters this market due to unobserved negative shocks (εm = −1). These negative shocks could be related to cost factors
(e.g. high wages) or demand factors (e.g. good public transportation) both of which
are likely to deter entry. At the same time, these negative shocks could influence firm’s
pricing decisions. Note however, the impact of these unobservables will be different on
market structure and prices depending on whether cost or demand factors dominate. For
example, negative demand shocks result in lower entry and lower prices, while high costs
would result in lower probability of firm entry but higher prices. Figure 1 illustrates
the bias depending on the direction of correlation which is also summarized in the Table
below. The correlation between the unobserved factors influencing prices and entry is
represented by ρ, while δtrue and θtrue represent the competition and traffic parameters
in the price regression. When the correlation is positive, both δtrue and θtrue are underestimated as δ and θ are from the regression without considering the impact of εm , while
the opposite is true for ρ < 0.
3
True Parameter Biased
Values
Estimates
ρ>0
ρ<0
Competition Effect
δtrue = pB 0 − pC
δtrue > δ
δtrue < δ
Sensitivity to Traffic
θtrue =
θtrue > θ
θtrue < θ
p0B −pA
H−L
δ = pB − pC
θ=
pB −pA
H−L
Data Description
Our application in this paper is to the auto rental industry. The car rental business
began as early as 1918, with small operators providing car rentals to individuals in local
markets. Currently, the industry is fairly consolidated with eight major firms along
with a host of regional operators who conduct their operations through combination
of company-owned and licensee operated locations. Most of these firms have locations
in local markets as well commercial airports. The local city locations typically target
individuals who need a vehicle for special occasions, insurance replacements, and repairs,
while the airport locations are primarily geared towards business and leisure travelers.
With the deregulation in the airline industry, the number of airport locations has grown
dramatically over years and now account for a significant proportion of revenues for
most companies. For instance, Hertz generates 90% of its revenues from its airport
12
locations in the US (2003 Annual Report). In this study we focus on the airport car
rental locations for which we develop an original database that consists of three major
pieces of information: (1) List of all domestic commercial airports and exogenous variables
describing each airport, (2) Number and identities of all car rental companies operating
at those airports, (3) Rental price for each car type (economy to full size).
Given the three pieces of information, the auto rental industry seems quite suitable
for the purpose of the study for several reasons. First, our data is quite complete in
that we have been able to collect information on number of firms and prices for every
commercial airport in the country. Second, our focus on only airport locations makes
the market definition reasonably clean as these locations tend to target customers flying
into the airport. While to a certain extent the airport locations would be competing
with outlets in downtowns or other city locations that we do not consider, the market
definition is significantly cleaner than previous applications, for example, in retailing or
banking industries. Finally, the price information in this industry is also reasonably easy
to collect and compare across firms and markets as these are single product firms with
car rental being the primary business. However, we should point out that these firms
also generate revenues by providing ancillary products and services such as supplemental
equipment (child seats, ski racks, cellular phones, navigation systems), insurance, and
gasoline payment options, for which we do not have any information. Nevertheless, the
problem is not as severe as with multi-product operations such as supermarkets and
hospitals.
Our data collection strategy relies on a variety of sources. First, we use the list of
commercial airports provided by the Federal Aviation Administration (FAA). This list
consists of the airport codes, full names, and addresses (city, state, and Zip codes) for
all commercial airports in the country including Alaska and Hawaii. For each of these
airports we use the aviation data provided by the Bureau of Transportation Statistics
to collect information on the air traffic variables. These include measures on the total
number of passengers as well as information on number of major airlines flying into the
airport. Finally, the airport addresses were used to collect information on various demand
and cost factors using data from the Census and the Bureau of Labor Statistics (BLS).
The full list of variables describing each airport is provided in Table 2. The first
set includes the standard variables capturing the demand (e.g. population, income) and
cost (rent, wages) conditions in a market. The next three variables capture the airline
traffic flow at the airports. The variable “Traffic 2004” is the total number of passengers
flying into the airport in the year 2004, while “Major Airline” and “Destination” are the
13
number of major airlines serving the airport and the total number of direct destinations
that are connected through the airport. Since the primary clientele for car rentals at
the airport locations tend to be passengers flying into the airport we expect these airline
traffic variables to play a major role in determining the number of car rental firms that
operate. The variable “Number of HQ” is the number of large corporations that have
their head quarters located in the market while the variable “Pub Ratio” is the percentage
of population in the market that uses public transportation to work. This variable serves
as the proxy for public transportation infrastructure in a market that can be thought as
a substitute for renting cars. Finally, Holiday represents holiday airports such as Miami,
Las Vegas, and Atlantic City.
Our next major piece of data includes the number and identities of all car rental
companies that are observed to operate at each airport. We collected this information
from Orbitz and Expedia websites as well as information from individual firms. In Table
3 we report the observed market structure in this industry along with a distribution of
airport traffic for each market structure. We use a total of 458 airports in the analysis
and exclude airports from Alaska and an additional 9 markets with missing variables. As
can been seen from Table 3, we observe a wide range of market structure in this industry
ranging from over 130 airports with either a monopoly or duopoly to over a hundred very
competitive markets with eight or more firms. We can also observe that the number of
firms increase with demand, as measured by the airport traffic. In the empirical section
below, we will use the airport traffic to compute the entry thresholds, i.e., the minimum
demand required for an additional firm to enter the market.
The last piece of information in our database is the car daily rental prices at all the
airports. We collected this information for rental period starting on Monday, March 21,
2005 at 10 a.m and returning the car on Tuesday, March 22 at 10 a.m. This information
was collected exactly one week in advance on Monday, March 14, 2005 for all the markets.
We collected the price information on five popular car types: Economy, Compact, Midsize, Standard, and Full-size and excluded special vehicles such as minivans and SUVs as
these tend to be available in only a few markets. In Figure 2 we display the distribution
of prices for each car type in concentrated (less than three firms) and competitive (seven
plus) markets. Two patterns are apparent from the distribution of prices shown in
Figure 2: the prices increase by car size from economy to full-size, and prices tend to fall
with competition. However, there seems to be wide dispersion in prices within market
structure suggesting the need for other control variables. We discuss these issues further
in the results section below.
14
4
Results
We now present the results from the model and data discussed above. We first provide
estimates from the first stage entry model, followed by price regressions and discuss the
implications of the bias when treating market structure variables as exogenous.
4.1
First Stage Entry Estimates
We rely on the variables outlined in the data section above to capture the factors impacting firm’s entry decisions. Obviously, profits and entry costs at any airport location
depend on a large number of factors including agreements between car rental firms and
airport authorities through negotiations and/or bidding processes. These agreements
provide for concession payments based upon a specified percentage of revenue generated
at the airport, subject to a minimum annual fee, and often include fixed rent for terminal
counters or other leased properties and facilities. Unfortunately, we do not observe many
of these factors and rely primarily on observed market characteristics.
We estimate two alternate models to describe the factors impacting firm’s entry decisions. In addition to the variant of Berry (1992) described in the model sections, we also
estimate a model proposed by BR (1991) who specify a simple yet flexible profit function
that governs firm behavior in a symmetric equilibrium. In BR’s framework, that authors
assume that a representative firms’ profits can be specified as follows:
N
πm
= VN (Xm , α, β) S (Ym , γ) − FN (Wm , λ) + εm
(14)
N
= π̄m
+ εm ,
N
is a firm’s latent profit of entering market m when there are N firms in the
where πm
market. This profit function has three components: VN (Xm , α, β) is the variable profit
from serving a representative consumer, S (Ym , γ) is a function that captures the size
of the market, and FN (Wm , λ) represent the fixed cost of entry. (α, β, γ, λ) are the
parameters to be estimated. Finally, εm summarizes the unobserved characteristics and
is assumed to be independent normally distributed across markets.
In BR (1991), the market size S (Ym , γ) is captured using the population in the market
or some function to include population in neighboring markets. Since our application is
to car rental companies operating at the airports, our empirical application also includes
measures on airport traffic such as the total number of passengers flying into the airport.
The variable profit VN (Xm , α, β) is modeled as a function of N (the number of competitors in the market) and Xm that represent the exogenous demand and cost shifter that
15
impact variable profits:
VN (Xm , θ) = α1 + Xm β −
N
X
αn ,
αn ≥ 0 for n = 2, ..., N.
(15)
n=2
Note that under this specification, the variable profits decrease as more firms enter
the market. The exogenous factors influencing variable profits include variables such as
income and wages in the market. Finally, the fixed costs are expressed as
FN (Wm , λ) = Wm λW + λ1 +
N
X
λn , λn ≥ 0 for n = 2, ...N.
(16)
n=2
where in our empirical application Wm includes a measure of real estate prices and
regional dummies that capture any systematic differences in fixed costs across airports
in different regions. Under the model specification above, the variable profits and fixed
costs for a monopolist are α1 + Xm β and λ1 + Wm λW respectively.
The left panel of Table 4 presents the parameter estimates based on the model as
outlined above. Most of the parameter estimates seem reasonable and in the correct
direction. The profitability of a market is increasing in the number of headquarters of
large companies, suggesting that the presence of headquarters captures attractiveness of
market conditions beyond those captured by local demographic characteristics. Retail
wages and the convenience of public transportation have negative impact, which is intuitive as good public transportation infrastructure can be thought of as a substitute
for renting cars. The positive coefficient for Holiday dummy suggests that profitability
is significantly higher in holiday markets. Estimates of the competition effects indicate
that the number of rivals in the market is an important determinant of profitability, as
entry by additional competitors reduces profits significantly except when the market is
already competitive (entry by the eighth firm is found to be insignificant). In relative
terms, magnitude of the impact is found to be higher with entry of the second and the
third player.
To capture market size, we use information annual airport traffic, population in the
market that the airport is located and population growth rate in the market. For model
identification, the coefficient of airport traffic is normalized to one. The local population
has a small but statistically significant impact on demand, whereas population growth
rate is found to be insignificant. For capturing the fixed costs of entry we use real estate
prices in the market and regional dummies that capture any systematic differences in
fixed costs across airports in different parts of the country. Fixed costs are increasing
16
with real estate cost, and given the same market characteristics, are lowest in airports in
South. Fixed costs are also found to be increasing with entry of additional competitors.
The right panel of Table 4 shows the results form entry model discussed in the model
section. The results are more or less consistent with those presented above. Airport
traffic and population have a positive impact on profits while the profits go down with
higher retail wages and real estate prices. In addition, profits are higher in holiday
markets as well as markets with headquarters for large firms, while markets with better
infrastructure of public transportation have lower profits. Looking at the competitive
effects we find that additional entrant lower profits and the impact is highest with the
second entrant.
The parameter estimates can be used to derive entry thresholds, defined by BR(1991)
as the minimum market size required to support a given number of firms. The entry
thresholds for a market with N firms is calculated as follows:
SN =
FN Wm , λ̂
,
VN Xm , α̂, β̂
where α̂, β̂, λ̂ are parameter estimates from the model and Wm and Xm are factors
that influence firms’ fixed cost and variable profit respectively. The per firm break even
market size, sN is simply
1
S .
N N
The ratio of these thresholds can provide insights on the
toughness of competition with additional entry. For example, if the breakeven thresholds
increase disproportionately with additional firms it can be interpreted as evidence of
price-cost margins declining with entry since with constant margins, a market would only
need to double to support another firm. With declining margins, the per firm break even
market sizes will increase with entry of additional firms. We plot the entry thresholds for
our data in Figure 3. To make the interpretation easier, the numbers are calculated for
each market configuration by ignoring the negligible influence of population i.e., market
size is a function of airport traffic only6 . Figure 3 presents the estimated entry thresholds
where we observe that the ratio of entry thresholds is greater than 1 and that the entry
by second and third firm increases the intensity of competition substantially.
4.2
Price Regressions
The first-stage entry estimates, while interesting on their own, mainly serve as a tool for
correcting potential endogeneity in the price regression. Our primary objective in the
6
All other covariates are set at their sample means.
17
paper is to study the relationship between prices and market structure. Our data includes
the prices offered by every firm for five car types: Economy, Compact, Mid, Standard
and Full size. In what follows we pool the data across all firms and car types and regress
log of prices against firm and car type fixed effects, other market specific covariates, and
market structure variables. To capture the competitive structure in a market we use two
specification: (1) Total number of firms, (2) An indicator variable for monopoly, duopoly,
and so on.
The results from the regression are reported in Table 5. The unit of analysis in these
regression is each firm-size and the observations are weighted to avoid overemphasizing
markets with large number of firms. In particular, each observation receives as weight
of inverse of the total number of firms in the market. We use seven market specific
covariates: log(Airport Traffic), PopulationD (population density in the market), Retail
Wages, Pub Ratio (% of population that uses public transportation to work), Num HQ
(number of Head Quarters for major firms in the market), Poverty (measure of income)
and an indicator variable for holiday destinations. Note that the airport traffic in the
price regression is the total number of passengers flying into the airport in the month of
March 2005, the month our price data is collected, and not the annual airport traffic in
2004 as used in the first-stage model.
The left panel in Table 5 shows the results from the models that ignore the endogeneity of market structure variables. The first specification uses the total number of firms
in the market to capture the competitive structure while the second uses a more flexible
indicator variable specification to capture the nonlinearities in the relationship between
price and number of firms in the market. The control variables generally have the expected sign with the exception of Num HQ. Prices tend to be higher in markets with
larger traffic, higher population density, higher retail wages, and holiday destinations,
while markets with lower income levels and better public transportation infrastructure
tend to have lower prices. The variable In-Terminal is an indicator variable that takes a
value 1 if the car is offered inside the airport terminal. The parameter estimate shows
that the prices are approximately 10% higher for such convenience. In terms of car-type,
the parameters are of expected sign with economy cars approximately 13% cheaper and
full-size cars 12% more expensive compared to mid-size. Finally, the regional indicator
variables suggest that prices are highest in airports on the East cost and cheapest in MidWest. Turning to the more interesting parameters capturing the competitive structure,
results from the first column indicate that adding an equivalent of one additional firm
at the airport reduces the price by approximately 2.3%. Column 2 uses a more flexible
18
specification and shows that monopoly markets have prices that are approximately 16%
higher compared to highly competitive markets with eight firms.
The right panel in Table 5 shows the regression results after inserting the term that
corrects for endogeneity of market structure. The last row in columns 3 & 4 shows the
estimated parameter that represents the correlation between the unobservables that affect
the prices and the payoff functions underlying firm’s entry decisions. The parameter
is similar in magnitude in both columns and is precisely estimated. The estimate is
positive suggesting the unobserved factors affect both observed prices and probability
of firm entry in same fashion. Recall from our discussion in Section 2.3 that a positive
coefficient will result in underestimating the competition parameters. Comparing the
control variables across the models that correct for this endogeneity and the models in
columns 1 & 2, we find that the parameters for some of the market specific variables
change somewhat while there is virtually no change in the In-Terminal or car-type fixed
effects. The biggest change however is in the parameters of primary interest, i.e. those
capturing the competitive interactions. In particular, looking the # of firms parameter
in Model 3 we find that the impact of an additional entrant in the market is almost twice
that suggested by Model 1. A similar picture appears when using a dummy variable
specification. For instance, the monopoly prices are found to be 38% higher compared
to the base of eight firm oligopoly versus 16% as suggested by Model 2.
In Table 6 we present the results that use Berry’s (1992) entry model to derive the
correction terms. The results are quite similar to those presented in Table 5. The parameter estimates for the control variables have the same sign and are similar in magnitude
to those reported in the right hand panel of Table 5 (estimates after correction). More
importantly, parameter representing the correlation between the unobservables that affect the prices and the payoff functions is found to positive suggesting the unobserved
factors affect both observed prices and probability of firm entry in same fashion. The
competitive interaction parameters after correction are remarkable similar under the two
specification of the firm entry model. For instance, when the competition is measured by
the total number of firms, the coefficient is -0.041 compared to -0.043 in Table 5. Similarly, the competitive parameters are significantly larger when using a dummy variable
specification compared to estimates without correction, and are similar in magnitude
under both specification for the underlying entry model.
Overall, our results show a significant bias in the competitive interaction parameters
from the models that treats the market structure variables as exogenous. Results are
similar to those reported by Evans, Foreb and Werden (1993) who find bias in the OLS
19
parameters in the magnitude of 150 to 250 percent. The magnitude of bias in OLS
regressions can be quite important since, as discussed in the introduction, such price
regressions are often used by FTC to predict price and welfare effects of mergers. Our
results show that price implications for such mergers can be severely biased. For example,
according to the regression estimates, a merger that changes a duopoly market to a
monopoly would result in prices that are approximately 5% higher compared to negligible
1% as predicted by the model without correction.
In closing we should also point out that the two-stage estimation procedure outlined in
the paper can also be useful in making predictions due to changes in exogenous variables.
Consider for instance change in prices due to a exogenous change in airport traffic.
According to the price regressions, the coefficient of traffic is positive indicating that an
increase in demand will result in higher prices. However, it is important to understand
source of increase in traffic: whether it is short term demand shock or a long term change
of market condition. If it is a short term event, e.g., a sports competition that attracts
a lot of travellers to the airport, then we expect prices go up due to higher demand.
However, if the higher traffic is driven by a long term factor, such as a new resort,
then the answer becomes subtle. In particular, according the parameter estimates from
the entry model, a permanent increase in traffic (which is an important determinant of
number of firms) may induce additional competitors to enter the market leading to lower
prices.
5
Conclusion
A long stream of literature in economics and marketing strategy examines the relationship between market structure and outcomes such as prices, revenues, and profits. In
the structure-conduct-performance paradigm of industrial organization, this literature
relies on cross-sectional data across industries or local markets within an industry to
document the impact of market concentration on these outcome variables. However, the
price-concentration regressions such as those used in the literature suffer from serious
endogeneity issues since there are likely to be unobserved demand and cost shocks in a
market that not only influence prices but also the underlying market structure. In this
paper we investigate the relationship between price and number of firms in the auto rental
industry. We develop an original data set that includes the number of car rental firms
at every commercial airport in the United States. For each of these markets we collect
an extensive set of variables that capture the demand and cost conditions. In addition
20
we collect data on daily rental prices from every firm and for each car type. Using this
data, we test how the prices change with the number of competitors in the market.
Our modeling approach takes into account the endogeneity of market structure in the
price regression by using a two-stage estimation procedure to address the endogeneity of
market structure. In the first stage, we estimate an equilibrium model of entry that predicts the number of competing firms in a market. The parameter estimates from the first
stage entry model are then used to derive correction terms that are inserted in the price
equation to correct for the correlation between the price errors and the market structure variables. We find that concentrated markets (those with fewer than three firms)
have prices that are approximately 30-35% higher than competitive markets (with more
than seven firms). More importantly, we find that ignoring the endogeneity of market
structure in the price regressions severely underestimates the competition parameters,
and the competitive interaction parameters are double in magnitude once we insert the
correction terms in the price regression.
There are of course several caveats to our analysis and directions for future research.
Foremost, the validity of correction in the price regressions depends on the correct specification of the first-stage entry model. In this paper we used the models proposed by
BR and Berry (1992) and found similar results. Depending on the specific application,
models used in Mazzeo (2001) for discrete heterogeneity, Seim (2005) for firm location
and Zhu et al. (2005) that allow for firm identities can be considered. All these papers
analyze the underlying market structure variables by have limited or no information on
price, quantity, and costs. In the marketing literature, recent structural work has examined issues such as brand value creation and competitive advantage (Besanko et al. 1998),
product line competition (Kadiyali et al. 1999, Draganska and Jain 2005), channel power
(Kadiyali et al. 2000), retailer pricing (Sudhir 2001, Chintagunta 2002), and price discrimination (Besanko et al. 2003, Chintagunta et al. 2003, Khan and Jain 2004). These
papers use variants of the methods proposed in Berry, Levinsohn, and Pakes (1995) and
Nevo (2001) and have detailed information (primarily from scanner data) on price and
quantity (and sometimes costs). However, they treat the market structure variables as
exogenous. With availability of long panel datasets with sufficient variation in number of
competitors, it would be interesting to combine these two steam of literatures in future
work.
21
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25
Table 1: Comparison of Office Depot’s Advertised Prices
Cover Page of January 1997 Local Sunday Paper Supplement
Orlando, Fl. Leesburg, Fl.
Percent
(3 firms) (Depot only)
Difference
Copy Paper
$17.99
$24.99
39%
Envelopes
$2.79
$4.79
72%
Binders
$1.72
$2.99
74%
$1.95
$4.17
114%
File Folders
Uniball Pens
$5.75
$7.49
30%
Table 2: Summary Statistics
Variables
Population
Pop Change Rate
Poverty Ratio
Housing Value
Retail Wage
Traffic 2004
Major Airline
Destination
Number of HQ
Pub Ratio
Holiday
Mean
Std Dev
412269.97
0.14
0.13
79350
21800.54
1267136.46
2.37
43.73
6.69
0.02
0.09
966758.39
0.16
0.05
49777
3211.57
3633197.91
3.12
53.50
19.53
0.05
0.29
26
Table 3: Market Structure and Airport Traffic
Market Strucutre
N
5th Ptcl
25th Pctl
No Firms
Monopoly
Duopoly
Oligopoly-3
Oligopoly-4
Oligopoly-5
Oligopoly-6
Oligopoly-7
Oligopoly-8
Oligopoly-9+
19
68
66
49
33
33
49
37
53
51
393
1,198
1,707
2,548
6,202
3,052
35,837
60,929
254,404
359,594
797
2,250
3,946
17,896
24,113
44,563
142,183
171,211
555,223
2,556,379
27
Median
Mean
75th Pctl
95th Pctl
2,128
2,637
2,859
9,879
4,376
6,401
7,336
16,248
7,137
16,927
15,031
60,954
24,986
38,656
43,857
120,715
42,826
60,582
74,987
142,379
89,618
146,821
222,200
468,020
222,797
731,332
387,507
2,033,441
301,726
702,145
650,208
1,236,778
1,235,494 2,747,626 3,898,859 10,030,133
4,315,597 7,619,785 10,999,813 23,575,604
Table 4: Parameter Estimates from Entry Model
Without Heterogeneity
With Heterogeneity
Variable
Estimate Std. Error
Variable
Parameter Est Std. Err
Variable Profit
Number of HQ
Holiday
Retail wage
Poverty
Pub Ratio
α1
α2
α3
α4
α5
α6
α7
α8
Market Size
Population Growth
Population(in 10,000)
Traffic(in 10,000)
Fixed Cost
Housing Unit Value
Mid-west
South
West
λ1
λ2
λ3
λ4
λ5
λ6
λ7
λ8
Log Likelihood
0.041
0.081
-0.040
0.008
-0.037
21.319
13.848
4.905
0.922
0.682
0.349
0.390
0.014
0.179
0.080
-0.481
-0.202
0.252
0.412
0.274
0.288
0.094
0.181
0.079
0.565
0.020
Num of HQ
0.027
Holiday
0.009
Retail wage
0.018
Poverty
0.008
Pub Ratio
0.378
Traffic
0.833 Population Growth
Population
1.230
0.348 Housing Unit Value
0.195
Mid-west
0.116
South
0.067
West
η
0.013
a1
a2
0.009
a3
a4
0.008
na
a5
a6
0.067
a7
0.184
a8
0.183
0.178
0.276
0.207
0.144
0.108
0.090
0.079
0.091
0.116
-601.715
Objective function
0.009
0.018
1
28
0.2284
1.2362
-0.1462
-0.0344
-0.3812
2.1047
0.0866
0.1579
-0.2315
-0.1133
0.5156
0.3335
0.5364
1.4303
2.3348
0.2161
0.7506
0.3825
1.9938
1.0235
0.3055
732.19
0.0538
0.2162
0.0756
0.0539
0.1101
0.1189
0.0633
0.0336
0.0957
0.1015
0.1025
0.1027
0.0907
0.085
0.0947
0.1562
0.1741
0.1577
0.2759
0.3583
0.5592
29
-0.0236
na
na
na
na
na
na
na
na
N OF FIRMS
Monopoly
Duopoly
Oligopoly-3
Oligopoly-4
Oligopoly-5
Oligopoly-6
Oligopoly-7
Error Correction
Variable
Intercept
Log(March Traffic)
Population
Retail Wage
Pub Ratio
Num of HQ
Poverty
Holiday
In-Terminal
Economy
Compact
Standard
Full Size
Midwest
South
west
na
0.0024
na
na
na
na
na
na
na
na
na
0.1479
0.1316
0.1293
0.1041
0.0973
0.0371
-0.0155
na
na
0.0183
0.0171
0.0148
0.0152
0.0143
0.0117
0.0120
0.0313
-0.0430
na
na
na
na
na
na
na
0.0050
0.0039
na
na
na
na
na
na
na
0.0352
na
0.3249
0.2758
0.2399
0.1993
0.1868
0.1011
0.0228
Table 5: Estimation Results from Price Regression
Estimates Without Correction
Estimates With Correction
MODEL 1
MODEL 2
MODEL 3
MODEL
Parameter Est Std. Err Parameter Est Std. Err Parameter Est Std. Err Parameter Est
3.7778
0.0203
3.5996
0.0330
3.7156
0.0225
3.3334
0.0316
0.0026
0.0310
0.0026
0.0485
0.0037
0.0507
0.5063
0.0759
0.4874
0.0778
0.5727
0.0764
0.5627
0.7597
0.4850
0.7792
0.4846
0.8309
0.4839
0.9102
-0.0450
0.0081
-0.0443
0.0081
-0.0547
0.0082
-0.0537
-0.1180
0.0303
-0.1241
0.0303
-0.1020
0.0303
-0.1100
-0.0058
0.0036
-0.0048
0.0036
-0.0046
0.0036
-0.0040
0.1164
0.0141
0.1255
0.0144
0.1110
0.0141
0.1163
0.0961
0.0089
0.0946
0.0090
0.0969
0.0089
0.0970
-0.1383
0.0088
-0.1386
0.0088
-0.1381
0.0088
-0.1382
-0.0957
0.0085
-0.0960
0.0085
-0.0961
0.0085
-0.0962
0.0858
0.0088
0.0856
0.0088
0.0861
0.0088
0.0860
0.1171
0.0084
0.1171
0.0084
0.1171
0.0084
0.1171
-0.0784
0.0097
-0.0786
0.0097
-0.0825
0.0097
-0.0863
-0.0412
0.0095
-0.0408
0.0095
-0.0372
0.0095
-0.0358
-0.0283
0.0095
-0.0300
0.0095
-0.0314
0.0095
-0.0335
0.0055
na
0.0332
0.0283
0.0228
0.0213
0.0200
0.0154
0.0134
4
Std. Err
0.0531
0.0041
0.0785
0.4837
0.0082
0.0303
0.0036
0.0144
0.0090
0.0088
0.0085
0.0088
0.0084
0.0098
0.0095
0.0095
Table 6: Parameter Estimates from Price Regression (Berry)
With Correction Using Berry’s (1992) Entry Model
Variable
Parameter Est Std. Err
Parameter Est Std. Err
Intercept
Log(March Traffic)
PopulationD
Retail Wages
Pub Ratio
Num of HQ
Poverty Ratio
Holiday
3.6577
0.0542
0.5122
0.9551
-0.0570
-0.0823
-0.0060
0.1292
0.0253
0.0038
0.0757
0.4845
0.0082
0.0344
0.0036
0.0141
3.2595
0.0583
0.5591
0.9943
-0.0617
-0.0851
-0.0052
0.1381
0.0511
0.0041
0.0780
0.4838
0.0083
0.0346
0.0036
0.0144
In-Terminal
Economy
Compact
Standard
Full Size
0.1013
-0.1370
-0.0954
0.0864
0.1171
0.0089
0.0088
0.0085
0.0088
0.0084
0.0984
-0.1377
-0.0960
0.0861
0.1171
0.0090
0.0088
0.0085
0.0088
0.0084
Midwest
South
West
-0.0843
-0.0335
-0.0286
0.0097
0.0095
0.0095
-0.0873
-0.0333
-0.0299
0.0097
0.0095
0.0095
N OF FIRMS
Monopoly
Duopoly
Oligopoly-3
Oligopoly-4
Oligopoly-5
Oligopoly-6
Oligopoly-7
-0.0410
na
na
na
na
na
na
na
0.0032
na
na
na
na
na
na
na
na
0.3054
0.2846
0.2635
0.2239
0.1950
0.1123
0.0450
na
0.0257
0.0245
0.0213
0.0205
0.0182
0.0145
0.0139
Error Correction
0.0597
0.0075
0.0712
0.0082
30
Price
B’
N = 1, ε m = 0
ρ >0
B
N = 1, ε m = −1
δ
A
N = 2, ε m = 0
C
N = 1, ε m = 0
L
H
Traffic
Price
N = 1, ε m = −1
B
ρ <0
δ
N = 1, ε m = 0
B’
A
N = 2, ε m = 0
C
N = 1, ε m = 0
L
H
Figure 1: Illustration of Estimation Bias
31
Traffic
Price Distribution of Economy−Sized Cars in Concentrated Markets Price Distribution of Economy−Sized Cars in Competitive Markets
30
90
80
25
70
60
Frequency
Frequency
20
15
10
50
40
30
20
5
10
0
0
20
40
60
80
100
120
0
0
20
40
60
80
100
120
Price(Mean=51.99 Std=15.62)
Price(Mean=47.05 Std=14.39)
Price Distribution of Compact−Sized Cars in Concentrated Markets Price Distribution of Compact−Sized Cars in Competitive Markets
60
90
80
50
70
60
Frequency
Frequency
40
30
20
50
40
30
20
10
10
0
0
20
40
60
80
100
120
0
0
Price(Mean=53.56 Std=14.19)
Price Distribution of Mid−Sized Cars in Concentrated Markets
20
40
60
80
100
120
Price(Mean=49.16 Std=14.73)
Price Distribution of Mid−Sized Cars in Competitive Markets
50
90
45
80
40
70
35
Frequency
Frequency
60
30
25
20
50
40
30
15
20
10
10
5
0
0
20
40
60
80
100
120
0
0
20
40
60
80
100
120
Price(Mean=57.62 Std=14.27)
Price(Mean=55.37 Std=15.76)
Price Distribution of Standard−Sized Cars in Concentrated Markets Price Distribution of Standard−Sized Cars in Competitive Markets
35
80
70
30
60
25
Frequency
Frequency
50
20
15
40
30
10
20
5
0
10
0
20
40
60
80
100
120
0
0
Price(Mean=61.65 Std=15.82)
Price Distribution of Full−Sized Cars in Concentrated Markets
20
40
60
80
100
120
Price(Mean=60.37 Std=15.91)
Price Distribution of Full−Sized Cars in Competitive Markets
50
80
45
70
40
60
50
30
Frequency
Frequency
35
25
20
40
30
15
20
10
10
5
0
0
20
40
60
80
Price(Mean=63.78 Std=14.42)
100
120
0
0
20
40
60
80
Price(Mean=60.86 Std=16.08)
32
Figure 2: Distribution of Auto Rental Prices
100
120
9
1028044
8
710436
7
244978
Number of Firms
6
137153
5
74527
4
36516
3
8879
2
1181
1
0
3
10
4
5
10
10
6
10
Traffic (log scale)
Figure 3: Entry Thresholds based on the Parameter Estimates of Entry Model
33