Choosing between Order-of-Entry Assumptions in Empirical Entry Models: Evidence from Competition between Burger King and McDonald s Restaurant Outlets

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1 Choosing between Order-o-Entry Assumptions in Empirical Entry odels: Evidence rom Competition between urger King and cdonald s Restaurant Outlets Philip G. Gayle* and Zijun Luo** September 2, 2013 Forthcoming in Journal o Industrial Economics Abstract We demonstrate how a non-nested statistical test developed by Vuong (1989) can be used to assess the suitability o alternate order-o-entry assumptions used or identiication purposes in empirical entry models. As an example, we estimate an entry model o cdonald s and urger King restaurant outlets in United States. The data set ocuses on relatively small isolated markets. For these markets, the non-nested tests suggest that order-o-entry assumptions that give urger King outlets a irst-mover advantage are statistically preerred. Last, a onte Carlo experiment provides encouraging results suggesting that the Vuong-type test yields reliable results within the entry model ramework. Keywords: Empirical Entry odel; Non-nested Statistical Test; Competition in Fast Food JEL Classiication codes: L13; L66; C1; C25 We thank the editor, John Asker, and two anonymous reerees or very helpul comments that signiicantly improved the quality o this paper. We thank Daru Zhang or her dedicated work in data collection and Zhuojie Huang or his specialty in GIS. The authors beneited rom discussions with Linchun Chen, Kim P. Huynh, Felicia Ionescu, and Dean Scrimgeour. This paper was presented at the 2012 International Industrial Organization Conerence in Washington, D.C., arch 16, 2012, and in South China Normal University, Guangzhou, China. We thank ark anuszak, ark Roberts, Rodrigo oita, Hiau Looi Kee, Javier Elizalde, rian Adams, Zhiqiang Dong, Yuan Liu, Jie Wang, Zhong Wang, and conerence participants or their helpul comments. All remaining errors are ours. * Kansas State University, Department o Economics, 320 Waters Hall, anhattan, KS 66506; Voice: (785) ; Fax:(785) ; gaylep@ksu.edu; Corresponding author. ** Colgate University, Department o Economics, 13 Oak Drive, Hamilton, NY 13346; Voice: (315) ; zluo@colgate.edu.

2 1 1. Introduction Static econometric entry models with heterogeneous irms oten pose estimation challenges due to the presence o multiple Nash equilibria. One way researchers have dealt with these challenges is to invoke one o many alternate equilibrium selection assumptions to render identiication and estimation easible. While econometrically convenient, such equilibrium selection assumptions are not always easy to justiy. However, at a minimum it may provide more comort to readers o this type o research i researchers provide statistical evidence that discriminate among alternative equilibrium selection assumptions. As such, the main contribution o this paper is to show how Vuong-type non-nested tests [see Vuong (1989)] can be used to choose between alternate equilibrium selection assumptions that are commonly made when using static entry models. To illustrate the implementation o non-nested tests, we use data on the presence o urger King and cdonald s restaurant outlets in a cross-section o local markets in the United States. We also use the opportunity to provide inerence on competition between urger King and cdonald s restaurant outlets in the United States, which is another contribution o our paper. Static entry models can be divided into two categories: (i) entry models o complete inormation; and (ii) entry models o incomplete inormation. The complete inormation assumption in entry models implies that all parts o each irm s proit unction are common knowledge to rival irms. In contrast, an incomplete inormation assumption implies that part o each irm s proit unction is private inormation or the irm. ultiple Nash equilibria in the entry game can occur irrespective o whether complete or incomplete inormation is assumed or

3 2 the proit unctions o irms. 1 However, in this paper we ocus on static entry games o complete inormation. 2 Researchers have used various methods to deal with the challenges posed by multiple Nash equilibria in static entry models o complete inormation. For example, resnahan and Reiss (1991) proposed that the model be restricted to predict the total number o entering irms but not irm identities. However, a caveat with this approach is that the researcher will not be able to make use o inormation that captures the heterogeneity o irms. erry (1992), azzeo (2002), Tamer (2003), Einav (2010), and Cleeren et al. (2010), among others, 3 provide an alternative method to obtain unique equilibrium while still allowing or irm heterogeneity. In particular, these papers exploit the act that a unique equilibrium o the entry model can be obtained by assuming that irms enter the relevant market sequentially. Since irst-movers preempt other players in an entry game, an order-o-entry assumption essentially is an equilibrium selection assumption when multiple equilibria dier based on the identity o irms that ultimately enter. It must be noted however, that while the sequential entry assumption may be used to obtain a unique equilibrium o the entry model, the order-o-entry assumption does not urther imply that price and output determination ollow this assumed order. An alternative estimation strategy that can handle situations o multiple equilibria, and does not require invoking an order-o-entry assumption, is the bounds-type approach outlined in Ciliberto and Tamer (2009). However, the bounds-type estimation approach has its own challenges. For example, parameters might only be set identiied rather than point identiied 1 In a dynamic entry/exit game setting, Doraszelski and Satterthwaite (2010) argue that an equilibrium might not exist when irms are not allowed to choose mixed entry/exit strategies in an entry/exit game o complete inormation. The authors urther show that, instead o allowing mixed strategies, an incomplete inormation assumption is an alternate way to guarantee that an equilibrium exists in the entry/exit game. 2 For examples o entry models o incomplete inormation, see Seim (2006), Einav (2010) and Yang (2012). 3 See erry and Reiss (2007) or an excellent review o this literature.

4 3 when using the bounds-type estimation approach, but invoking an order-o-entry assumption approach makes it possible to point identiy parameters. So some researchers may still opt to go the route o invoking an order-o-entry assumption to estimate parameters o the entry model. Our paper illustrates to these researchers one way to ormally test competing order-o-entry assumptions i their preerred estimation strategy is to invoke an order-o-entry assumption. First, we use the empirical entry model ramework developed by Cleeren et al. (2010) to identiy a unique equilibrium in a multi-player, multi-equilibrium, entry game. This ramework easily allows or estimation o the entry model under alternate order-o-entry assumptions. We then ocus on statistical selection o the most appropriate order-o-entry assumption or the entry model. The basic ramework or the non-nested maximum likelihood statistical selection test is developed by Vuong (1989), but we implement it in the context o long-run strategic entry decisions o irms, while Gasmi, Laont, and Vuong (1992) implement it to distinguish between dierent assumptions about the nature o short-run product market competition between irms. Across the types o markets in the cdonald s-urger King data set we use, we ind that order-o-entry assumptions that give urger King outlets irst-mover advantage are statistically avored. Furthermore, there is evidence that order-o-entry assumptions matter or the resulting parameter estimates o the type o entry model we consider, which can prove crucial in settings where policy conclusions need to be drawn based on estimated parameters. In the data section we discuss the characteristics o markets present in our data set. We also run a small-scale onte Carlo experiment to assess the power o the test in distinguishing between alternate ordero-entry assumptions. The experiment reveals that the test gives correct results in 77 out o 100 simulations.

5 4 Since our econometric analysis is applied to data on urger King and cdonald s restaurant outlets in United States, it is instructive to briely review previous work on the astood industry. ost papers in this literature conclude that there is signiicant dierence between cdonald s and urger King s response to various market characteristics and thereore these two chains are not considered perectly substitutable. Some researchers such as Laontaine (1995) and Kalnins and Laontaine (2004) ocus on the ranchising eature o the industry. They identiy dierent actors that aect ranchisee and ranchisor s decision-making. Graddy (1997) ocuses on price discrimination within the ast-ood industry, while Stewart and Davis (2005) are more generally concern about price dispersion o dierent ast-ood chains. Kalnins (2003) applies spatial econometrics to hamburger price data to assess the degree o substitutability o products and locations o spatially dispersed ranchised chains. Thomadsen (2005) uses spatial econometric models to analyze how ownership structure and market geographic characteristics jointly inluence the pricing decision o cdonald s and urger King restaurant outlets and ound that cdonald s outlets give a statistically signiicant higher utility to consumers than do urger King outlets. Thomadsen (2007) examines the optimal product positioning decision o cdonald s and urger King restaurant outlets and inds that the equilibrium depends crucially on market size. Standard models o entry, which include the type o entry model we use in this paper, capture the competitive eects o entry, i.e. reduction in proits due to additional entry, but not the eects o learning. Toivanen and Waterson (2005) constructed an entry model designed to capture the eects o learning. Speciically, they design their entry model to identiy a positive spillover eect between competitors when there is at least one store o the competing irm already present in the market. The authors estimate their model using panel data on the

6 5 presences o cdonald s and urger King restaurant outlets in local markets in the United Kingdom (U.K.). They ind that existing rival presence in a market increases the probability o entry by increasing expected market size. This result suggests that a potential entrant can learn about the proitability o a market by observing the existing rival s perormance. Yang (2012) uses the same dataset as Toivanen and Waterson (2005) and urther explored the learning aspects o irms entry strategy, but in contrast, Yang (2012) uses a ramework in which irms have incomplete inormation about each other s proitability. The positive spillover eect result persists even under incomplete inormation. Importantly, Yang (2012) distinguishes between hidden inormation on cost or demand. He inds that signiicant positive spillover eects or both restaurant chains can only be ound in the hidden cost speciication, while a learning eect is signiicant and positive or urger King under all speciications. The rest o the paper is organized as ollows: Section 2 outlines the econometric model as well as the non-nested test procedure used or selecting the appropriate order-o-entry assumption. In Section 3 we discuss our data and descriptive statistics. Section 4 presents estimation results rom our model as well as results o the non-nested test. The last section concludes. 2. The odel Let the numbers o cdonald s ( or AC) and urger King ( or K) restaurant outlets in a market be denoted by N and N, respectively. Proit or an outlet o chain type (, ) = is given by a latent variable Π such that ( N, N ) π ( N, N ) Π = ε, (1)

7 6 π is the deterministic part, and where ( N, N ) ε is the part that is unobservable to researchers but observed by all irms (complete inormation assumption) and thereore we assume this part o proit is random. We assume that outlets o the same brand/chain are homogeneous. 4 Three standard assumptions are employed here or the deterministic part o restaurant outlets proit: ASSUPTION 1 π ( N + 1, N ) < π ( N, N ) ( N, N + 1) π ( N, N ) π < ASSUPTION 2 π π ( N, N + 1 ) π ( N, N ) ( N + 1, N ) π ( N, N ) ASSUPTION 3 π ( N + 1, N 1 ) < π ( N, N ) ( N 1, N + 1) π ( N, N ) π <. Assumptions 1 and 2 are derived rom the act that restaurant outlets within any particular market, either o the same chain or not, compete with each other and thus a new entrant lowers the proitability o existing outlets o either chain. Assumption 3 states that the negative proit impact due to the new entry o within chain restaurant outlet is greater than the negative proit impact due to entry o a dierent type chain outlet. In other words, intra-chain competition is more intensive than inter-chain competition. As mathematically shown and proven in Cleeren et 4 See Thomadsen (2005) or a discussion o the justiication o this homogenous assumption.

8 7 al. (2010), 5 each o these three assumptions is needed to derive a generalized probability expression (see equation (3) below) that deals with all the possible cases in which multiple Nash equilibrium might arise. In other words, together, these three assumptions are necessary to ensure a well deined probability space on which to build the likelihood unction. With these assumptions, an observed market structure (, ) n n is a Nash equilibrium i π π ( n + 1, n ) < ε π ( n, n ) ( n, n + 1) < ε π ( n, n ). (2) Conditions in (2) will admit multiple Nash equilibria without additional structure on the entry game. Furthermore, these conditions will yield a unique Nash i we assume that outlets enter according to a certain sequence. In addition, Cleeren et al. (2010) argue that when looking at a market structure with totally n competing irms, only the number o players o each type during these irst n moves matters, and their exact order o entry is otherwise irrelevant (p.462). Let n be the number o cdonald s outlets during the irst n moves in the assumed sequence o entry, the probability o observing market structure (, ) Nash Equilibrium (SPNE) is given by: n n as a Subgame Perect ( =, = ) P N n N n = π ( ) π ( ) n, n n, n π ( n + 1, n ) π ( n, n + 1) ( ) (, ) ( ) π n + 1, n 1 π n, n ( ) φ (, ) π ( n + 1, n) π( n + 1, n ) ( ) φ u u du du I n n u u du du ( ) π n, n π n 1, n+ 1 ( ) φ (, ) I n n u u du du π ( n, n+ 1 ) π( n, n+ 1 ) (3) where I( x ) is an indicator unction that takes the value 1 i x > 0, and 0 otherwise. φ ( ) denotes the standardized bivariate normal density unction speciied as: 5 In Cleeren et al. (2010), see Assumptions 1, 2A and 2 on page 460, Claims 1, 2 and 3 and the discussion o these claims on page 461, as well as the ormal proo o these claims in the Appendix.

9 8 φ 1 1 u + u 2ρu u, = exp 2πσ σ 1 ρ ( u u ) u u ρ, (4) where ρ is a parameter that measures the correlation o shocks across chain-type proits with 1< ρ < 1. When ρ 0 with endogenous variables (, ), equations (3) and (4) together yield a bivariate ordered probit model n n. However, i we impose the restriction ρ = 0, then shocks to chain-type proits are assumed independent and the model reduces to two separate ordered probit models - one or each chain-type. Suppose in a market there are two cdonald s outlets and two urger King outlets. I the assumed sequence o entry or up to 6 outlets is given either by,, or, based on equation (3) the probability o observing market structure (, ) ( 2, 2) n n = is given by the same expression, ( ) ( ) π n, n π n, n (, ) φ (, ) P N n N n u u du du = = =. π ( n + 1, n) π( n, n+ 1 ) This is because or all three o these assumed entry sequences, there are exactly two cdonald s outlets in the irst 4 = n + n entries, i.e. n ~ = 2, which implies that indicator unction I ( ) in ~ ~ = equation (3) yields the ollowing: I( n n ) = I( n n ) = I( 2 2) 0 However, or those. 6 ( ) ( ) same assumed sequences o entry, the probability o observing market structure is computed using a dierent expression in each case., = n n 1,1 Considering market structure (, ) = ( 1,1) n and assumed order-o-entry, n there is only 1 cdonald s outlet in the irst 2 = n + n entries, which implies, n ~ = 1 and the indicator unction I ( ) in equation (3) yields the ollowing: 6 Since our exposition draws heavily rom Cleeren et al. (2010), the reader is reerred to that paper or additional examples and discussion.

10 ( ) ( ) ( ) I n n = I n n = I 1 1 = 0. Thereore, assuming entry sequence, the appropriate probability expression or the (, ) = ( 1,1) equation (3) is: ( ) n market structure that is implied by n ( ) π n, n π n, n (, ) φ (, ) P N n N n u u du du = = =. π ( n + 1, n) π( n, n+ 1 ) Considering market structure (, ) = ( 1,1) n and assumed order-o-entry, n there are 2 cdonald s outlets in the irst 2 entries, which implies n ~ = 2 ; I ( n ~ n ) = I( 2 1) = 1; and I( n n ~ ) = I( 1 2) = 0, the appropriate probability expression or the (, ) = ( 1,1) is implied by equation (3) is: ( =, = ) P N n N n = π ( ) π ( ) n, n n, n π ( n + 1, n ) π ( n, n + 1) π ( + ) π ( ) π ( ) n 1, n 1 n, n π ( ) n + 1, n n + 1, n (, ) (, ) φ u u du du φ u u du du Last, considering market structure (, ) = ( 1,1) n. Thereore, assuming entry sequence n market structure that n n and assumed order-o-entry, there is 0 cdonald s outlet in the irst 2 entries, which implies, n ~ = 0 ; I ~ = ~ = ( n n ) = I( 0 1) 0; and I( n n ) = I( 1 0) 1, the appropriate probability expression or the (, ) = ( 1,1) is implied by equation (3) is: ( =, = ) P N n N n = π ( ) π ( ) n, n n, n π ( n + 1, n ) π ( n, n + 1) π ( ) π ( + ) n, n n 1, n 1 π ( n, n + 1 ) π ( n, n + 1) (, ) φ u u du du (, ) φ u u du du. Thereore, assuming entry sequence n market structure that n 9

11 10 Once the probability expression or each market structure is constructed, we can easily compile these market structure probabilities to construct a well-deined log likelihood unction: T n max, n max t t t t t D t, t [ P( N = n, N = n )] N N, LL = log (5) t = 1 t t n = 0, n = 0 where superscript t indexes markets and D, is a zero-one indicator variable that equals one t t t N N i N = n and t t N = n but zero otherwise. Note that the log likelihood unction in equation t t (5) is a unction o the correlation parameter, ρ, via equations (3) and (4). Additional parameters will be introduced once the proit unction is speciied. Speciication o Proit Function speciied as: For any given market with market structure (, ) (, ) N 1 N π N N = β X + δ + γ, i, j i= 1 j= 1 N N, the deterministic part o proit is, (6) where X is a vector o market-speciic characteristics including population and other sociodemographic variables, while β is the associated chain-speciic vector o parameters that capture how the proit o a restaurant outlet o a given chain-type is aected by a marginal change in the relevant market-speciic characteristic. δ measures the marginal proit eect due to entry o same chain-type restaurant outlets (intra-chain competition), while γ measures the marginal proit eect due to entry o dierent chain-type restaurant outlets (inter-chain competition). β, δ, and γ are chain-speciic parameters to be estimated.

12 11 Note that we assume π = 0 when N = 0. Thus there are only N 1 intra-chain marginal competitive eect parameters starting rom the second same chain-type restaurant outlet in the particular market. Also, rom Assumptions 1-3, we must have, δ < 0 ; γ < 0; δ < γ ; δ, i< δ, i + 1; γ, i γ, i+ 1 In our estimation, we impose these restrictions. <, (, ) =. Given the unctional orm speciication o the proit unction in equation (6) and the log likelihood equation in equation (5), we estimate the parameters o the model via aximum Likelihood, that is, we estimate the parameters by solving the ollowing optimization problem: 7 β, δ, γ, ρ ( X ; β, δ, γ, ρ ) ax LL. (7) Non-nested Test Procedure The non-nested test procedure we use in this paper is an application o tests developed by Vuong (1989). Gasmi, Laont, and Vuong (1992) also applied the non-nested test procedures in a dierent setting. For each pair o assumed order-o-entry model speciications ( p, q) likelihood ratio statistic is: T p q, (8) t= 1( t t ) LR LL LL S S, the where T is the total number o observations in the sample, while p LL t and q LL t are the optimal values at observation t taken by the log likelihood unctions or order-o-entry model speciications S p and S q respectively. Vuong (1989) argues that the likelihood ratio statistic in equation (8) can be normalized by its variance: 7 We numerically optimize the log likelihood unction over the parameter space using the minsearch algorithm in the ATLA computer sotware.

13 12 T 2 p q T p q ( LL ) ( ) 2 t LL t T LLt LL t, (9) ω T t= 1 t= 1 = so that the ollowing non-nested test statistic: NNT = T, (10) ω 0.5 LR is asymptotically distributed standard normal under the null hypothesis o equal it. 8 A one-tale statistical test at the 5% signiicance level or the standard normal distribution has critical values ± I 1.64 < NNT < 1.64 we conclude the data are unable to discriminate between the two order-o-entry models, and thereore the null hypothesis cannot be rejected. I NNT < 1.64, we conclude that order-o-entry speciication S q better explains the data compared to speciication explains the data compared to speciication S q. S p, but i NNT > 1.64, we conclude that speciication S p better One o the very important eatures o this type o non-nested normalized likelihood ratio test is that, as noted by Gasmi, Laont, and Vuong (1992), it can be used to test between two dierent models even though one or both o them are mis-speciied. In other words, without committing to declare a true model, the test allows the researcher to conclude which, i any, o the two models being compared better its the data. 3. Data We obtained our dataset via the Internet in the spring o For store location inormation, we rely on cdonald s and urger King online restaurant locator on their homepage. We collect market structure data or the 48 contiguous states o the United States. 8 The equations used here or the LR statistic; the variance o the LR statistic; and the non-nested test statistic, correspond to equations (3.1), (4.2) and (5.6) on pages 312, 314 and 318 respectively in Vuong (1989).

14 13 Local markets are delineated at the city level. Socio-demographic characteristic data o each city are obtained rom the U.S. Census ureau Census 2000 Summary File 3. Google ap is used to ensure each city in our sample can reasonably be treated as a single local market. A single local market is deined as an isolated city that is more than 10 miles away rom the closest neighboring city. It is well known in the literature that static entry models o the type we consider in this paper are better suited or data with a cross-section o individually isolated markets. Figure 1: Geographical Distribution o arkets In our data, we have included 2,506 isolated city areas. Figure 1 shows a geographical distribution o the cities/markets in our sample throughout the 48 contiguous states o the United States, where each market is designated with a black dot on the map. These cities each have at least one cdonald s (AC) or urger King (K) restaurant outlet, but neither restaurant chain

15 14 has more than 3 outlets. The total number o cdonald s restaurants in our sample is 3083, while the total number o urger King restaurants is The observed numbers o occurrences o each market structure in the data are reported in Table 1, while Table 2 presents deinitions and simple descriptive statistics o all socio-demographic variables that we use in the analysis. arket Structure: N, N ( ) Table 1: Observed arket Conigurations Number o arkets Percent o Total (%) (1, 0) (2, 0) (3, 0) (0, 1) (1, 1) (2, 1) (3, 1) (0, 2) (1, 2) (2, 2) (3, 2) (0, 3) 0 0 (1, 3) (2, 3) (3, 3) Total Static entry models better it industries that can reasonably be described as being in a long-run equilibrium state. According to the U.S. Securities and Exchange Commission (SEC) 9 y year-end o 2011, cdonald s and urger King have and 7204 outlets, respectively, in the United States. Thus our sample has 21.9% o all cdonald s outlets and 27.8% o all urger King outlets in the U.S.

16 15 ilings o cdonald s and urger King, cdonald s outlets in the United States has gone rom to between 2002 and 2012, an increase o less than 5% in 10 years, while urger King outlets in the U.S. and Canada has gone rom 7534 to 7476, a decrease o less than 1% in 6 years. 10 These numbers show that there are minimal changes in cdonald s and urger King restaurant outlets over this 10-year period, and thereore it is reasonable to argue that during this period the industry in North America is approximately in a long-run equilibrium state. Table 2: Deinition and Descriptive Statistics or Variables used in our Analysis Name Deinition ean in ax S. D. Pop Population (in 1K) PCI Per Capita Income (in 1K$) White Percentage o Pop that is white (%) ale Percentage o Pop that is male (%) Family a Percentage o households reported as amily (%) A Percentage o population that has achelor s degree or above (%) a From the deinition o U.S. Census ureau, A amily includes a householder and one or more other people living in the same household who are related to the householder by birth, marriage, or adoption Thus, the number o amily households is equal to the number o amilies. See documentation or Census 2000 Summary File 3 or detail. Inormation in Table 1 provides some support or the three assumptions outlined in the model section o the paper. One challenge to those assumptions is the idea that restaurant outlets already present in a market can positively inluence subsequent entry, an eect Toivanen and Waterson (2005) reer to as a positive spillover eect, which they ound when analyzing the expansions o cdonald s and urger King outlets in the United Kingdom. I there are strong 10 The SEC iling documents are available only back to 2006 or urger King when it irst went IPO in that year. In addition, rom 2006 to 2012, urger King s K10 annual reports only provide numbers o outlets or U.S. and Canada combined.

17 16 positive spillover eects in our U.S. data set, we should expect the vast majority o markets to contain both cdonald s and urger King outlets, and the correlation between outlets o both chain-types being in a given market should be high. However, only 60.14% o the markets in our sample contain both cdonald s and urger King outlets. oreover, the correlation between the presence o both in a given market is only These characteristics o our data are appropriate or the model ramework we use. Judging rom the standard deviations o the variables in Table 2, one can see that sociodemographic variations across our sample cities are not trivial. Not surprisingly, consistent with population density, Figure 1 shows that more markets are concentrated in the eastern and western regions o the United States compared to the central region. We ollow azzeo (2002) and transorm socio-demographic variables in the ollowing manner: x T = ln xt xt, T t= 1 * 1 t where T is the total number o observations o the ull sample (2506 in our paper). This transormation implies that when the untransormed variable takes on a value equal to its mean, the associated transormed variable will take on a value o zero. These transormations should not aect the qualitative impact o variables since each variable s ordinal property is preserved. So or example, the transormed population variable still remains a valid index o market size. As discussed in azzeo (2002) and conirmed by our own experience, the advantage o such a transormation o the variables helps with making estimation o the nonlinear entry model easier. 11 Ater putting inormation in Table 1 into a 2506-by-2 matrix, we calculate the correlation o the two columns to obtain the correlation o

18 17 In Table 3, we present three reduced-orm regression speciications in which number o cdonald s restaurant outlets, number o urger King restaurant outlets, and the total number o cdonald s and urger King restaurant outlets are dependent variables respectively. Table 3 demonstrates that the number o restaurant outlets is positively related to population, and negatively related to percentage o households reported as amily. The variable Highway is a zero-one dummy variable that equals to 1 when a city/market is within 6 miles o driving distance to an interstate highway. Not surprisingly, locations close to inter-state highways attract both restaurants. Table 3: Reduced-orm Regressions Variables AC K AC+K Constant 1.447** 1.171** 2.618** (0.226) (0.207) (0.315) Pop ** ** ** (0.0023) (0.0018) (0.0036) PCI (0.0041) (0.0039) (0.0059) White ** * (0.0963) (0.0904) (0.135) ale (0.414) (0.360) (0.563) Family ** ** ** (0.180) (0.173) (0.257) A (0.207) (0.193) (0.299) Highway 0.141** 0.174** 0.315** (0.0255) (0.0230) (0.0362) Observations 2,506 2,506 2,506 R-squared Notes: The reduced-orm regressions are estimated using Ordinary Least Squares (OLS). We have included state dummies. Robust standard errors are in parentheses. ** indicates statistical signiicance at the 1% level; * indicates statistical signiicance at the 5% level. 4. Results Recall that in our sample, there are maximum 3 cdonald s and 3 urger King restaurant outlets in any given market. Thus there could be up to 20 dierent possible entry

19 18 orders or these 6 restaurants. We begin by ocusing on the ollowing our order-o-entry speciications: (1) cdonald s outlets move irst: (2) urger King outlets move irst: (3) Alternate moves starting with : (4) Alternate moves starting with : In Table 4, we report proit unction parameter estimates or both chain-type irms under each o the our distinct assumed entry orders. Several results can be drawn rom these parameter estimates. First, among the socio-demographic variables we consider, the most robust determinants o entry are the size o population in a particular market (Pop), the percentage o amily households (Family), and i city is within six miles o driving distance to an interstate highway (Highway). These results are consistent with those rom the reduced-orm regressions reported in Table 3. A location that is within six miles o the nearest interstate highway, which has a relatively large population and a small proportion o amily households, appears to be most conducive or ast ood entry. oth large local population and a nearby highway imply a larger market size. The positive signs rom these two variables are consistent with previous literature. On the other hand, amily households are more likely to cook on their own or go to a iner dining restaurant, which is suggested by the negative sign on the Family variable. Second, intra-chain competitive eects ( δ 1 and δ 2 ) are strong and statistically signiicant, while inter-chain competitive eects ( γ 1, γ 2 and γ 3 ) seem to be relatively weak. There could be several actors that contribute to these competitive eects results, one o which may be that dierentiation across the chains are suiciently strong and brand-loyal customers comprise a signiicant segment o the market. It is also possible that the weak inter-chain

20 19 competitive eects result could in part be due to some market characteristics that we the researchers cannot observe, and thereore cannot ully control or in the models. 12 Table 4: Estimation Results or the Static Entry odel AC K AC K AC K AC K Constant ** ** ** ** ** ** ** ** (0.0581) (0.1085) (0.0675) (0.0793) (0.0730) (0.1153) (0.0644) (0.0742) Pop ** ** ** ** ** ** ** ** (0.0210) (0.0266) (0.0209) (0.0250) (0.0207) (0.0247) (0.0201) (0.0231) PCI (0.0861) (0.0955) (0.0749) (0.0821) (0.0862) (0.0961) (0.0748) (0.0843) White * * (0.0594) (0.0599) (0.0536) (0.0527) (0.0600) (0.0585) (0.0543) (0.0534) ale (0.3034) (0.3266) (0.2840) (0.3105) (0.2981) (0.3163) (0.2847) (0.3109) Family ** ** ** ** ** ** ** ** (0.1223) (0.1301) (0.1083) (0.1171) (0.1189) (0.1273) (0.1122) (0.1163) A (0.0441) (0.0461) (0.0381) (0.0400) (0.0451) (0.0461) (0.0386) (0.0397) Highway ** ** ** ** ** ** ** ** (0.0321) (0.0336) (0.0290) (0.0301) (0.0318) (0.0329) (0.0299) (0.0318) ** ** ** ** ** ** ** ** δ 1 (0.0666) (0.0703) (0.0730) (0.0528) (0.0790) (0.0684) (0.0695) (0.0521) ** ** ** ** ** ** ** ** δ 2 (0.0326) (0.0748) (0.0354) (0.0742) (0.0554) (0.0750) (0.0345) (0.0697) ** * ** γ 1 (0.0044) (0.0986) (0.0508) (0.0783) (0.0368) (0.1166) (0.0499) (0.0737) γ 2 (0.1019) (0.1230) (0.0546) (0.0640) (0.0713) (0.1006) (0.0546) (0.0825) γ ** * ** ** ** ( ) (0.1160) (0.1299) (0.0670) ( ) (0.1129) (0.1355) (0.0885) ** ** ** ** ρ (0.0123) (0.0027) (0.0092) (0.0032) Log likelihood Notes: odels are estimated using aximum Likelihood. Standard errors are in parentheses. ** indicates statistical signiicance at the 1% level; * indicates statistical signiicance at the 5% level. 12 We thank an anonymous reeree or suggesting this possibility.

21 20 Despite the relatively small values or most inter-chain competitive eects, two results stand out. First, the negative and statistically signiicant values o γ 3 in K proit unctions suggest that the presence o a third AC outlet has a distinctively negative impact on the proit o K outlets. Second, when the assumed entry order is either K moves irst or alternate moves that begin with K, i.e. either or, the presence o the irst K outlet has a distinctively negative impact on the proit o AC outlets ( γ 1 in AC proit unction). While the magnitudes o coeicients on population are consistent across order-o-entry speciications in Table 4, the magnitudes o other coeicients that are statistically signiicant vary across order-o-entry speciications. Interestingly, coeicients o Family and Highway are the largest or both chains under the entry order assumption, ollowed by, then, with the smallest. Such result shows that dierent entry order assumptions imply dierent types o response to changes in socio-demographic variables. oth the magnitudes and statistical signiicance o intra and inter-chain competitive eects parameters vary across order-o-entry speciications. For example, the entry o a second cdonald s outlet reduces the proit o the existing cdonald s outlet by a larger amount under entry order ( δ 1 = ) compared to ( δ 1 = ). So there is evidence that order-o-entry assumptions matter or the resulting parameter estimates, which can prove crucial in settings where policy conclusions need to be drawn based on estimated parameters. Overall, the intra and inter-chain competitive eects parameters seem more sensitive across order-o-entry assumptions compared to the sensitivity o parameters associated with the

22 21 demographic variables. This result makes sense since the order-o-entry assumptions directly relate to strategic interactions between the restaurant outlets. Last, the unobserved portion o the proit unction o cdonald s and urger King are highly cross-correlated as indicated by the estimates o ρ. Note that the estimates o ρ are close to 1, but statistically dierent rom 1. As mentioned beore, the non-nested likelihood ratio test can be used to test competing model speciications even i the models are mis-speciied. The results o the test are reported in Table 5. The non-nested test statistics show that entry orders and are statistically indistinguishable at conventional levels o statistical signiicance, but each o these entry orders is statistically preerable to and. In addition, is statistically preerred to. In summary, among the our entry orders considered thus ar, entry orders that give urger King outlets irst-mover advantage seem to be statistically preerable across the sample o markets in our data set. Table 5: Results o Non-nested Test p q ,8405 To urther investigate whether the irst-mover advantage o urger King outlets persists across a comprehensive set o alternate entry order assumptions, we estimate the entry model under each o the possible order-o-entry assumptions and test them against each other. 13 There 13 We thank anonymous reerees or pointing out the importance o estimating and testing all entry orders, as well as the onte Carlo experiment below.

23 22 are a total o 20 entry orders when at most 3 AC and 3 K outlets are present in a given market. We report the results o these non-nested tests in Table A-1 in Appendix A. 14 A positive number in Table A-1 suggests that the entry order assumption in the row is either statistically indistinguishable rom the column entry order or statistically dominates the column entry order, while a negative number suggests that the column entry order is either statistically indistinguishable rom the row entry order or statistically dominates the row entry order. An examination o the row that has the entry order reveals that is never dominated by any o the 19 alternate entry orders, and it strictly dominates 11 o the 19 alternate entry orders. In addition, is statistically dominated by ; ; ; ; ; ; ; ; ; ; and, each o which gives urger King outlets better irstmover advantage than the entry order. In general, the results in Table A-1 suggest that entry orders that give urger King outlets a irst-mover advantage are most oten statistically preerable. As a cautionary note, the reader is reminded that our sample o markets exclude major metropolitan areas, as well as markets that cannot reasonably be considered as isolated. Thereore, we cannot say whether our indings extend to all markets in the United States. We can only claim that our results suggest urger King outlets have a irst-mover advantage over cdonald s outlets in relatively small isolated markets. Last, we use a small-scale onte Carlo experiment to assess the power o the Vuong (1989) test within the context that we use it in this paper. Details on how we construct and 14 In the interest o space, we do not report the regression estimates o the entry model under the 20 dierent ordero-entry assumptions. However, we are happy to provide these estimates upon request.

24 23 implement the experiment are provided in Appendix. The ollowing discussion only provides a big picture description o the experiment and its results. We irst generate 100 data sets, each containing 1000 markets. Similar to our real data set, we allow a maximum o three outlets o each type in each market o a simulated data set. Each simulated data set consists o simulated variables that capture market characteristics. In each simulated data set we use: (i) the simulated market characteristic variables; (ii) parameterized outlet proit unctions; and (iii) a speciic order-o-entry assumption, to generate the equilibrium number o outlets o each type that will be present in each simulated market. Thereore, the advantage we have with each simulated data set relative to the real cdonald s- urger King data set is that, we actually know the true order-o-entry that generate the equilibrium market structure in each simulated data set. Each simulated data set is generated assuming the entry order is. For each simulated data set we econometrically estimate the entry model under, the true order-o-entry, as well as under, and then apply the non-nested test to see which o the two order-o-entry assumptions is statistically avored by the test. Given that there are 100 simulated data sets, this process produces 100 non-nested test statistic values. Figure 2 graphically illustrates the results o the non-nested tests.

25 24 Non-nested Test Statistic Value 7 Figure 2: Plot o Computed Non-nested Test Statistic Values rom onte Carlo Experiment Test Events Ranked ased on Computed Value o Test Statistic 5% Conidence band 5% Conidence band Non-nested Test Statistic Value The vertical axis in Figure 2 measures the computed value o the non-nested test statistic or each o the 100 test events. On the horizontal axis we rank test events by their computed test statistic value. A positive test statistic value that is greater that 1.64 (one-tale cuto value at the 5% level o signiicance) suggests that the order-o-entry assumption is statistically preerred to the order-o-entry assumption. Alternatively, a negative test statistic value that is less that suggests that the order-o-entry assumption is statistically preerred to the order-o-entry assumption. Among the 100 test events the results are clear that, at the 5% level o signiicance, is never statistically preerred to, but is statistically preerred to in 77 test events. Thereore, at a 5% level o statistical signiicance, the test reveals the correct order-o-entry entry assumption 77% o the time. A similar result is

26 25 obtained when is the order-o-entry used to generate simulation data sets, and tested against the order-o-entry assumption Conclusion In research that uses static empirical entry models o complete inormation, it is oten convenient to assume that players enter sequentially, which makes it necessary to speciy a suitable order o entry. In this paper, we show how a Vuong-type non-nested test can be used to statistically assess the suitability o entry order assumptions. As an example, we estimate and test alternate order-o-entry assumptions in our entry model on cdonald s and urger King restaurant outlets. The data set we use ocuses on relatively small isolated markets in the United States. In these markets, the results suggest that the more suitable assumption or the entry model is that urger King outlets have a irst-mover advantage over cdonald s. Furthermore, there is evidence that order-o-entry assumptions matter or the resulting parameter estimates o the type o entry model we consider, which can prove crucial in settings where policy conclusions need to be drawn based on estimated parameters. We also conducted a small-scale onte Carlo experiment to assess the reliability o the Vuong-type statistical test to reveal the most suitable order-o-entry assumption. Results rom the experiment are encouraging, suggesting that at a 5% level o signiicance the test reveals the true order-o-entry 77% o the time. The estimated entry model also provides some interesting results on the ast ood burger industry. We ind that, among the socio-demographic variables we consider, the most robust determinants o entry o either cdonald s or urger King restaurant outlets are: (1) the size o 15 When testing against at the 5% level o statistical signiicance, 76 out o 100 test events reveal that dominates, while the remaining 24 test events suggest these two order-o-entry assumptions are statistically indistinguishable.

27 26 population in a particular market; (2) the percentage o amily households; and (3) i the city is within six miles o driving distance to an interstate highway. We also ind that intra-chain competitive eects are strong and signiicant, while most inter-chain competitive eects seem to be relatively weak. There could be several actors that contribute to these competitive eects results, one o which may be that dierentiation across the chains are suiciently strong and brand-loyal customers comprise a signiicant segment o the market. Future research may want to explore the robustness o these indings in other sample markets.

28 27 Appendix A: Comprehensive Set o Non-nested Test Results Table A-1 Comprehensive Set o Non-nested Test Results q p

29 28 Table A-1 Comprehensive Set o Non-nested Test Results (cont.) q p

30 29 Appendix : Procedure o the onte Carlo experiment In an eort to assess the reliability o the non-nested test in our context, we have implemented a small-scale onte Carlo experiment. The ollowing discussion describes the procedure we use. Simulated arket Characteristic Variables Our sample consists o 100 dierent simulated data sets. In each simulated data set there are 1000 markets. Each simulated data set contain three independent variables that measure market characteristics, and the values taken by these independent variables vary across the 1000 markets and across the 100 data sets. A uniorm probability distribution is used to generate the values o our simulated independent variables. The minimum and maximum values taken by the three simulated independent variables respectively correspond to variables Pop, PCI and ale in our real cdonald s-urger King sample markets. The simulated market characteristic variables are denoted: Pop_sim; CPI_sim; and ale_sim. Unobserved Part o Proit Random Draws Similar to our real cdonald s-urger King data set, we assume there are two types o competing outlets, denoted and respectively, which can populate a simulated market. Each outlet has a proit unction o the orm speciied in equations (1) and (6), i.e. (, ) N 1 N or (, ) Π N N = β X + δ + γ ε, i, j i= 1 j= 1 =, where ε is the unobserved part o the proit unction. Just as we did in our entry model, we continue to assume that the unobserved

31 30 parts o outlet proit (, ) ε ε are distributed bivariate standard normal across outlets, with crosscorrelation parameter ρ. For each data set, we draw the unobserved part o outlets proit rom a bivariate normal distribution with 0.6. ρ =, which yields a 1000-by-2 matrix o unobserved proit draws ( ε, ε ) Each row o this matrix corresponds to a market in a simulated data set. Each simulated data set has a dierent 1000-by-2 matrix o unobserved proit draws. Creating a Complete Simulated Data Set Given the simulated market characteristic variables ( Ones, Pop_sim, CPI_sim, ale_sim), the unobserved proit draws ( ε, ε ) X = assumed proit unction parameters in Table -1 ( β, δ, i, γ, i), and the, we can use outlet proit unctions to compute the equilibrium number o outlets o each type ( N, N) that will be present in each simulated market under a speciic order-o-entry assumption. In particular, let the simulated proit or outlet be denoted by ( N, N ) ( X,,, ) Π = π β δ γ ε. Since outlets must have non-negative proits in equilibrium, we essentially solve or the vector o integer values ( N, N ) such that Π ( ) N N ( N, N), 0. To obtain a unique solution vector, we impose the order-o-entry assumption. This speciic order-o-entry assumption is imposed in all 100 simulated data sets that we create. In the end each simulated data set has data on market characteristic variables, as well as number o outlets o each type in each market. arket structure conigurations and their associated requencies in a typical simulated data set are reported in Table -2.

32 31 Table -1 Assumed Parameters AC K Constant Pop_sim CPI_sim ale_sim δ δ γ γ γ ρ 0.6 Table -2 A Typical Simulated Data Set kt. Str. 0, 0 1, 0 2, 0 3, 0 0, 1 1, 1 2, 1 3, 1 0, 2 1, 2 2, 2 3, 2 0, 3 1, 3 2, 3 3, 3 Obs Econometric Estimation and Non-nested Test Once we have all 100 simulated data sets established, we econometrically estimate the entry model on each data set under each o two distinct order-o-entry assumptions, where one o the two order-o-entry assumptions is the true one used or generating the simulated data. In our experiment, the two distinct order-o-entry assumptions used or estimating the entry model are: (i) ; and (ii). As previously stated, the simulated data are generated under the order-o-entry assumption. Once the entry model is econometrically estimated under each o the two order-o-entry assumptions or a given simulated data set, we then compute the non-nested test statistic according to equations (8), (9) and (10) in the paper. Since there are 100 simulated data sets, this process produces 100 computed non-nested test statistics. The number o cases in which the computed value o the non-nested test statistic suggests that is the statistically