Pricing and Market Concentration in Oligopoly Markets 1

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1 Pricing and Market Concentration in Oligopoly Markets 1 (Preliminary. Comments welcome) Vishal Singh Ting Zhu March 8, 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.

2 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

3 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 industries 1. 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

4 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 it 2. 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. STAPLES, INC. and OFFICE DE- POT, INC. Defendants. Case No. 1:97CV The table reported can be found at: 2

5 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

6 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

7 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 Model 2.1 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 p m = Z m θ + f (N m, δ) + ε p m, (1) where p m are the observed prices in market m, Z m are all exogenous market characteristics that affect prices except the market structure variables. The function f (N m, δ) represents the impact of the underlying market structure on prices. In empirical applications, the 5

8 market structure variables are typically captured using measures such as concentration ratio or Herfindahl Index. Finally, ε p m are market specific unobservables that influence prices. In context of the current paper, our dependent variable p m would be the price of a particular car-type (e.g. economy) at each airport location, and the exogenous variables Z m 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 ε p m are correlated with explanatory variables in the regression. Of particular concern in (1) are the variables that capture the competitive structure,f (N m, 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

9 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: π N mk = π N m (X m ; β) + ε mk, This profit function has two components: π m (X m ; β) captures the expected payoffs as a function of exogenous demand and cost shifters 4, X m, and the number of competitors (N) in the market, while ε mk 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., ε mk = ε m, the equilibrium assumption implies that the probability of observing n active firms in a market is P (N m = n) = Pr ( πm n 0 and πm n+1 < 0 ) (2) = Pr ( ) π m n ε m < π m n+1 ) = F ( π m) n F, ( π n+1 m 4 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

10 where F (.) is the cdf of ε m. Finally, if a firm does not enter a market, its payoff in that market is normalized to zero. Therefore P (N m = 0) = Pr ( π 1 m < 0 ) = 1 F ( π 1 m). 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 π mk (N) = X m β + α 1 N α n + ε mk (3) n=2 where ε mk = ηu m0 + σu mk, α n 0 for n = 2,..., N. where, X m represents the observed market characteristics and α 1 N n=2 α n 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 u m0 represents characteristics of the market that are observed by the firms, but not econometrician,and u mk are firm specific unobservables. Thus, this model allows for heterogeneity across firms. u mk and u m0 are assumed to distributed i.i.d. standard normal across firms and markets. For identification, we impose the traditional constraint that the variance of ε mk equal one, via the restriction σ = 1 η 2, where η is the correlation of the unobservable ε mk in a given market. Firm k will enter market m given that there are N 1 players in the markets if π mk (N) > 0. Assuming that profits are declining in rivals entry, and the ranking of profitability (which is determined by the ranking of u mk 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 N m = max (n : # {k : π mk (n, ε mk ) 0}), (4) n 8

11 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, Pr (N m = 0) = xmβ α1 xmβ α1... xmβ α 1 df (ε m1, ε m2,...ε mk ). (5) 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, K K Pr (N m = 1) = Pr (ε m B mi ) Pr (ε m (B mi B mj )) (6) i=1 i=1 j i K + Pr (ε m ((B mi B mj B ml ))) +... i=1 j i l i,j + ( 1) K+1 Pr (ε m (B m1 B m2... B mk )) where B mi is defined as the region of ε m that satisfies the conditions of firm i being a monopoly in the market: B mi = { ε m : π mi (1) > 0 and π m( i) (2) < 0 }. The expression of the probability of the a market being monopoly is complicated because B mi and B mj 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 (N m = 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, x m ) from the model: ν m =N m E(N α, β, x m ). (7) 9

12 By construction, ν m is mean independent of the exogenous data when evaluated at the true parameter values: E [ν m x m, 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, x m ), we use simulation technique. Given S draws for the underlying random variables ε m and guesses of α and β, we can construct the equilibrium number of firms ˆN (ε s, α, β, x m ). The estimate of E(N α, β, x m ) is simply E(N α, β, x m ) = 1 S S s=1 ˆN (ε s, α, β, x m ). (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 follows 5 : ( εm ε p m ) (( 0 BV N 0 ) ( 1 ρ, ρ σ 2 )). (10) where ε p m given ε m 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 ε p m given ε m is also normal with mean equal to E [ε p m ε m ] = ρε m. 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

13 The expectation of ε p m varies under different market structure. Given the observed number of firms N m, we can represent the error term in price regression as follows ε p m N m = ρe [ε m N m ] + v p m, (11) where v p m now is the pure idiosyncratic error term effecting prices. Under BR s specification of a firm s entry payoff, an expression of E [ε m N m ] can be obtained as follows: E [ε m N m ] = = π Nm+1 m π Nm m φ ( π Nm m Φ ( π Nm m φ (ε) ε dε (12) Φ ( π m Nm ) Φ ( π m Nm+1 ) ) ) φ N ( π m+1 m ) Φ ( π m Nm+1 ). In the empirical application, we insert the estimates of E [ε m N m ] form the first stage entry model in the price regression where the covariance between ε m and ε p m, 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 ε p m is only correlated with the market level unobservables, the price regression can be specified as ln P m = Z m θ + f (N m, δ p ) + E [ε p m u m0 : N = N m ] + vm p (13) where vm p = ε p m E [ε p m u m0 : N = N m ]. Note however, that with this specification there is no close form solution for E [ε p m u m0 : N = N m ] 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 ε m 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 Traffic # of firms Unobservable ε m Price A L 1 0 p A B H 1 1 p B C H 2 0 p C 11

14 Here Market B has high traffic but only one firm enters this market due to unobserved negative shocks (ε m = 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 δ true and θ true represent the competition and traffic parameters in the price regression. When the correlation is positive, both δ true and θ true are underestimated as δ and θ are from the regression without considering the impact of ε m, while the opposite is true for ρ < 0. True Parameter Biased Values Estimates ρ > 0 ρ < 0 Competition Effect δ true = p B p C δ = p B p C δ true > δ δ true < δ Sensitivity to Traffic θ true = p B p A H L θ = p B p A H L θ true > θ θ true < θ 3 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

15 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

16 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

17 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: πm N = V N (X m, α, β) S (Y m, γ) F N (W m, λ) + ε m (14) = π m N + ε m, where πm N is a firm s latent profit of entering market m when there are N firms in the market. This profit function has three components: V N (X m, α, β) is the variable profit from serving a representative consumer, S (Y m, γ) is a function that captures the size of the market, and F N (W m, λ) represent the fixed cost of entry. (α, β, γ, λ) are the parameters to be estimated. Finally, ε m summarizes the unobserved characteristics and is assumed to be independent normally distributed across markets. In BR (1991), the market size S (Y m, 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 V N (X m, α, β) is modeled as a function of N (the number of competitors in the market) and X m that represent the exogenous demand and cost shifter that 15

18 impact variable profits: N V N (X m, θ) = α 1 + X m β α n, α n 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 N F N (W m, λ) = W m λ W + λ 1 + λ n, λ n 0 for n = 2,...N. (16) n=2 where in our empirical application W m 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 α 1 + X m β and λ 1 + W m λ W 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

19 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: where ( ) ˆα, ˆβ, ˆλ S N = F N (W m, ˆλ ) V N (X m, ˆα, ˆβ ), are parameter estimates from the model and W m and X m are factors that influence firms fixed cost and variable profit respectively. The per firm break even market size, s N is simply 1 N S 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 only 6. 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

20 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 Mid- West. 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

21 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 compared to 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