Unobserved heterogeneity in dynamic games: Cannibalization and preemptive entry of hamburger chains in Canada

Igami, Mitsuru; Yang, Nathan Article Unobserved heterogeneity in dynamic games: Cannibalization and preemptive entry of hamburger chains in Canada Quantitative Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Igami, Mitsuru; Yang, Nathan (2016) : Unobserved heterogeneity in dynamic games: Cannibalization and preemptive entry of hamburger chains in Canada, Quantitative Economics, ISSN 1759-7331, The Econometric Society, New Haven, CT, Vol. 7, Iss. 2, pp. 483-521, https://doi.org/10.3982/QE478 This Version is available at: https://hdl.handle.net/10419/150415 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ Quantitative Economics 7 (2016), 483–521 1759-7331/20160483 Unobserved heterogeneity in dynamic games: Cannibalization and preemptive entry of hamburger chains in Canada Mitsuru Igami Department of Economics, Yale University Nathan Yang Desautels Faculty of Management, McGill University We develop a dynamic entry model of multi-store oligopoly with heterogeneous markets, and estimate it using data on hamburger chains in Canada (1970–2005). Because more lucrative markets attract more entry, firms appear to favor the presence of more rivals. Thus unobserved heterogeneity across geographical markets creates an endogeneity problem and poses a methodological challenge in the estimation of dynamic games, which we address by combining the procedures proposed by Kasahara and Shimotsu (2009), Arcidiacono and Miller (2011), and Bajari, Benkard, and Levin (2007). The results suggest that the omission of unobserved market heterogeneity attenuates the estimates of competition, and the trade-off between cannibalization and preemption is an important factor behind the evolution of market structure. Keywords. Dynamic oligopoly, entry and exit, entry deterrence, market structure, preemption, unobserved heterogeneity. JEL classification. L13, L81. 1. Introduction We develop a dynamic entry model of multi-store oligopoly with heterogeneous markets, and estimate it using data on hamburger chains in Canada (1970–2005). The possibility of unobserved heterogeneity across markets is a common cause of concern in many empirical settings, and introduces a particularly severe endogeneity problem in the context of entry and market structure as it leads to biased estimates of competition. Our data feature puzzling patterns in which firms appear to favor the presence of Mitsuru Igami: [email protected] Nathan Yang: [email protected] We thank the editor, four anonymous referees, Victor Aguirregabiria, Peter Arcidiacono, John Asker, Steven Berry, Ron Borkovsky, Andrew Ching, Ulrich Doraszelski, Florian Ederer, Liran Einav, Amit Gandhi, Ronald Goettler, Philip Haile, Kenneth Hendricks, Johannes Hörner, Thomas Holmes, Hiroyuki Kasahara, Kei Kawai, Myongjin Kim, John Lazarev, Robin Lee, Mitsukuni Nishida, Ariel Pakes, Mar Reguant, Qiaowei Shen, Minjae Song, Alan Sorensen, K. Sudhir, Junichi Suzuki, Kosuke Uetake, Yasutora Watanabe, and Li Yang, as well as the seminar participants at the 11th Annual IO Day at NYU Stern in 2013, the 2013 Econometric Society NASM, the 2013 IO Conference at the University of Tokyo, Arizona, Carnegie–Mellon/Pittsburgh, McGill Desautels, Oklahoma, Rochester Simon, Toronto Rotman, Wisconsin–Madison, and Yale for suggestions. We thank the staff at the Toronto Reference Library for their patient data-collection support. Copyright ©2016 Mitsuru Igami and Nathan Yang. Licensed under the Creative Commons Attribution- NonCommercial License 3.0. Available at http://www.qeconomics.org. DOI: 10.3982/QE478 484 Igami and Yang Quantitative Economics 7 (2016) more rivals, presumably because (unobservably) more lucrative markets attract more entry. Indeed, our preliminary regressions suggest models without unobserved market heterogeneity generate attenuated estimates of competition. The static entry literature such as Berry (1992) has already demonstrated the severity of the endogeneity problem and solved it by a simulation estimator that assumes an order of entry, but addressing this problem in the estimation of a dynamic oligopoly model poses a methodological challenge. Standard two-step approaches such as Bajari, Benkard, and Levin (2007) require nonparametric estimation of equilibrium strategies in the first stage. With unobserved market heterogeneity, these strategies become conditional on unobserved market types and difficult to estimate. A quick solution to this problem is to impose some parametric restrictions on the conditional choice probabilities (CCPs) to ameliorate the data requirement, and either incorporate market fixed effects or estimate CCPs by market (e.g., Suzuki (2013)). In the presence of dynamic strategic interactions among multi-store firms, however, equilibrium entry strategies could be nonmonotonic in a complicated manner, so parametric restrictions would be inconsistent with the equilibrium play of the game. More specifically, researchers have studied entry and exit at the firm level in both static and dynamic frameworks (e.g., Bresnahan and Reiss (1991), Berry (1992), Mazzeo (2002), Seim (2006), Ciliberto and Tamer (2009), Ryan (2012), and Collard-Wexler (2013)), but many industries are populated by firms with multiple outlets or products,1so entry and exit occur at the outlet/product level at least as often as at the firm level. The incentives for such firms are more complicated than for single-store firms. The entry of new outlets harms the profitability of the existing ones (i.e., cannibalization), but the threat of rivals’ entry gives rise to preemption motives.2This strategic trade-off may dictate multi-store firms’ entry decisions and influence the evolution of market structure over time. For these reasons, we build on recent methodological advances to systematically incorporate such unobserved heterogeneity in our estimation procedure, in three steps. First, we identify the (minimum) number of market types required to rationalize the state transition patterns across markets by using Kasahara and Shimotsu’s (2009)approach. Second, we estimate the firms’ entry/exit strategies that are conditional on market types by using Arcidiacono and Miller’s (2011) method. Third, we use the estimated strategies and forward simulations to estimate the firms’ profit functions and sunk costs of entry following Bajari, Benkard, and Levin’s (2007) second-stage procedure. We believe the combination of these three techniques represents a useful empirical tool to measure competition accurately in the presence of endogeneity problems and strategic dynamics. 1We refer to such enterprises as multi-outlet, multi-product, or chain-store firms interchangeably. 2Earlier theoretical work on the cannibalization–preemption trade-off includes Schmalensee (1978), Eaton and Lipsey (1979), and Judd (1985). They took a motive in the U.S. Federal Trade Commission’s complaint in 1972 against the four largest manufacturers of ready-to-eat breakfast cereal, which charged that “brand proliferation” (i.e., the frequent introduction of new product varieties) resulted in high barriers to entry. Thus the underlying theme of this paper applies to a broader context of competition outside retail services. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 485 Three findings emerge from our structural analysis. First, unobserved heterogeneity across geographical markets significantly affects the firms’ profits and introduces attenuation biases in the estimates of competition if not properly accounted for (i.e., the estimated negative impact of other shops’ presence on a shop’s profit becomes smaller in a model without heterogeneous markets). Second, shops of the same chains compete more intensely with each other than with shops of different chains, which implies that cannibalization is one of the most important considerations for the firms’ entry decisions. Third, preemption motives are at least as important as cannibalization in shaping the evolution of market structure. Our counterfactual simulations suggest that without such motives, McDonald’s would enter markets less aggressively. Thus an accurate measurement of competition requires a model with multi-store ownership, dynamic strategic interactions, and unobserved market heterogeneity. We have chosen to study hamburger shops, an archetypical chain business, for three reasons. First, they represent one of the simplest cases of multi-store oligopoly. The provision of homogeneous services is one of the main purposes of retail chains. This institutional feature limits the scope of product differentiation among outlets and, hence, helps us identify the trade-off between cannibalization and preemption in its purest form. Second, hamburger shops compete within relatively small geographical markets. Thomadsen’s (2005) estimates suggest only shops within approximately 05miles compete as close substitutes, even in car-obsessed California. Nevertheless, multiple shops of the same chain often compete even within such narrowly defined markets, which provides us with enough data to investigate cannibalization as well as unobserved heterogeneity across geographical markets. Third, store opening/closure is the main strategic dimension of hamburger chains’ competitive dynamics, and our interviews suggest cannibalization and preemption are among the most important considerations of their store-development officers.3Thus hamburger chains provide us with a clean, feasible, and relevant context for the study of dynamic strategic interactions with unobserved market heterogeneity. The rest of the paper is organized as follows. The remainder of this section summarizes the related literature and this paper’s contributions. Section 2lays out our model. Section 3explains the institutional features of the industry and presents descriptive statistics of our data set as well as preliminary regressions. Section 4shows our estimation approach and results. Section 5analyzes the effects of cannibalization and preemption on entry by conducting counterfactual simulations. Section 6con- cludes. The appendices are included and the Supplements, available in files on the journal website, http://qeconomics.org/supp/478/supplement.pdf and http://qeconomics. org/supp/478/code_and_data.zip, feature sensitivity analysis and other institutional considerations. 1.1 Related literature This paper builds on three strands of literature, namely, market entry, preemption games, and structural estimation of dynamic oligopoly. 3Based on our interviews (in person and by phone) with the store-development officers of various hamburger chains in Canada, conducted on multiple occasions between October 22, 2009 and July 18, 2011. 486 Igami and Yang Quantitative Economics 7 (2016) First, among many papers that study entry, Arcidiacono, Bayer, Blevins, and Ellickson (2015) is the most closely related work in terms of modeling, because they also consider entry dynamics of oligopolistic chain stores. Whereas their main objective is to propose and illustrate the use of a continuous-time framework, we focus on addressing unobserved market heterogeneity and assessing the implications of cannibalization and preemption on market structure. Likewise, Holmes (2011) studies cannibalization from the perspective of Walmart’s single-agent problem, whereas oligopolistic interactions including preemption motives are the main feature of our study. In terms of substantive interests, Toivanen and Waterson (2005) analyze the entry patterns of McDonald’s and Burger King in the United Kingdom, using a static model without unobserved market characteristics, and find a “positive effect” of rival presence on expected profits. By contrast, this paper explicitly controls for both dynamics and unobserved market heterogeneity, and assesses the extent to which these factors could bias the estimates of competition. Second, many theoretical papers have studied preemption games, including Fudenberg and Tirole (1985), Riordan (1992), Quint and Einav (2005), and Argenziano and Schmidt-Dengler (2012). Few empirical papers structurally estimate such models, but Schmidt-Dengler (2006)andIgami(forthcoming) do so in the specific context of technology adoption. By contrast, this paper aims to quantify the effect of preemption motives in a more general context of entry and market structure, and assesses their implications for the measurement of competition. Third, our empirical approach relies on the combination of three recent advances in the estimation of dynamic games (Bajari, Benkard, and Levin (2007), Kasahara and Shimotsu (2009), and Arcidiacono and Miller (2011)). The purpose is to incorporate unobserved market heterogeneity in the CCP-based estimation of dynamic oligopoly, including the procedure to determine the number of market types, which is typically assumed apriori. 4Our results indicate the presence of significant heterogeneity across markets, and highlight the importance of its inclusion for accurate measurement of competition. Given these literature contexts, this paper aims to make contributions by combining the recently developed methods to address the major endogeneity problem concerning entry and market structure, and showing that incorporating dynamic strategic interactions and unobserved market heterogeneity significantly alters one’s conclusion about competition, which is fundamental to an analysis of any market. 2. Model This section presents our model. The purpose of this research is to assess and address the endogeneity problem caused by unobserved market heterogeneity. We investigate this issue in the context of a dynamic entry game among multi-store firms in which cannibalization and preemption could play potentially important roles. 4A typical specification is a nonparametric finite mixture with two or three points of support. Aguirregabiria and Mira (2007) considered a parametric finite-mixture specification for unobserved market heterogeneity with only one unknown scale parameter but with 21 unobserved market types. They also detected an attenuation bias in the estimates of competition effects when unobserved heterogeneity is ignored, thereby foreshadowing our findings. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 487 The setting is as follows. Time is discrete with an infinite horizon, t=12∞. Geographical markets m=12M are independent of each other5and, hence, the following exposition focuses on a particular market mwithout loss of generality. A finite number of firms, indexed by i=12I, operate finite numbers of outlets (nimt = 012). The firms’ entry/exit decisions in a given period, aimt ∈{10−1}, will change their numbers of outlets in the subsequent period. Market structure is a collection of nimt across firms, nmt ≡{nimt}I i=1. Besides market structure, the demand shifter zmt and market type μm∈{12K}also affect the firms’ period profits. The timeline is as follows. •In each period, in each geographical market, each firm observes the industry state smt ≡(nmtzmt),markettypeμm, and the independent and identically distributed (i.i.d.) private cost shocks εimt(aimt)associated with the discrete choices of entry/exit. These shocks represent the firms’ idiosyncratic conditions in terms of real estate information, corporate finance, and other managerial or organizational climate for storedevelopment activities. •Each firm forms expectations over the evolution in the future of its rivals’ decisions a−imt ≡{ajmt}j=iand the industry state smt . •Based on the current state and these expectations, each firm decides on aimt and earns period profit as a function of the current state and its decision, Πi(aimtsmtμm;ψi)=nimtπi(smtμm;αiθi)−Ci(aimt;κi)+εimt(aimt) (1) where πiis the average profit per outlet (parameterized by αiand θi, and specified in the estimation section) and Ciis the sunk cost of entry/exit that equals κ+if aimt =1,0 if aimt =0,andκ−if aimt =−1. The letter ψdenotes a vector of all parameters, (α θκ). •Finally, each firm implements its entry/exit decision and the endogenous state evolves according to nimt+1=nimt +aimt. The demand shifter evolves exogenously according to some first-order Markov process, f(zmt+1|zmt). Each firm maximizes the present value of its future profits with discount factor β∈ (01). The following Bellman equation characterizes its dynamic programming problem, Vi(smtεimtμmσ;ψ) =max σi(smtεimt μm)Πi(smtεimtμmσ;ψ) (2) +βEVi(smt+1εimt+1μmσ;ψ)|smtμmσ where σis a Markov-strategy profile that maps (smt εimtμm)−→ aimt ∈{10−1}for each firm. After the i.i.d. private cost shocks, εimt, are integrated out, a Markov-perfect equilibrium (MPE) is σthat satisfies Vi(smμmσ;ψ) ≥Vi(smμm˜σiσ−i;ψ) ∀˜σi= σi(3) for all firms, when the firms correctly perceive the transition probabilities of s. 5See Appendix Cfor the validity of this assumption in the hamburger chain industry. 488 Igami and Yang Quantitative Economics 7 (2016) 2.1 Definitions of cannibalization and preemption Cannibalization means competition within a firm. In the context of chain stores, multiple stores of the same chain may compete with each other within a single geographical market. The effect of cannibalization on profits will manifest itself in αi,whichistheparameter that governs the relationship between a store’s profit and the presence of other shops. See Sections 4.3 and 5.1 for the specification and operationalization regarding how we measure cannibalization and its effects. The underlying mechanism for preemption also resides in αi, because preemptive motives cannot exist unless the presence of rival shops affects the profit of a shop, but preemption is more difficult to measure than cannibalization. We propose measuring the effect of preemptive motives based on the difference in the timing of a firm’s store opening when its rivals condition their store-opening actions on the presence of the focal firm’s shops and when they do not. In the former case, the focal firm has preemptive motives because its rivals may give up entry once it opens a sufficient number of stores to saturate the market. In the latter case, it cannot influence the rivals’ future actions and, hence, will lose preemptive motives for early entry.6 To complete this definition, we further specify the counterfactual behavior of rivals (when they do not condition on the focal firm) as the conditional distribution of rival shops with the number of the focal firm’s shops integrated out. That is, the focal firm competes against the same number of rival shops on average, but their entry/exit actions completely ignore the presence or absence of the focal firm’s shops. We have chosen this specification because it does not alter the effective market size for the focal firm and obviates the need to impose ad hoc beliefs on rivals in the counterfactual. See Section 5.2 and Appendix Bfor further details and the empirical analysis. 2.2 Identification Bajari, Chernozhukov, Hong, and Nekipelov (2009) discuss conditions for nonparametric identification of a dynamic discrete game, with a generic period payoff function Πi(aia−is) +εi(ai), and stress the need for firm-specific payoff shifters to achieve identification. Our model (and data) does not seem to contain such variables and might appear underidentified at a first glance. However, the physical characteristic of storedevelopment investment leads to a natural exclusion restriction based on time lags, namely that the rival chains’ actions (store opening/closure) merely alter the state in the next period and do not enter the firm’s current payoff, and hence Πi(aia−is) = 6Tirole (1988, Section 8.6.2) proposes measuring the effect of preemptive motives by the difference in the timing of a monopolist incumbent chain’s opening of its second shop in the presence and absence of a potential entrant, based on a stylized timing game between two firms, with an exclusive focus on the opening of the second shop in the market. This measure is useful given the specific context and focus of his model. However, this notion of preemption becomes elusive in a more general setting with multiple chains, each of which may operate multiple outlets in the same market, because the incumbent–entrant distinction becomes blurred and an analyst cannot justify an exclusive focus on the second shop. To guide our subsequent analysis with a more empirically relevant concept, we therefore propose an alternative measure of preemptive motives. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 489 Πi(ais)in our empirical context (see equation (1)). Thus our payoff functions are identified, with I×2equations (Iplayers and two choices) and I×2free parameters rather than I×2×3I−1in their model (see their Sections 2.1 and 3.5). 3. Industry and data This section explains the industry context and our data set from the hamburger chains in Canada (1970–2005). Anecdotal evidence (Sections 3.1 and 3.2)aswellasourpreliminary regressions (Section 3.3) suggest cannibalization and preemptive motives are major economic forces behind the firms’ entry decisions. These regressions will also highlight the importance of incorporating unobserved heterogeneity across geographical markets to correctly infer the degree of competition. 3.1 Why hamburger chains Hamburger shops have represented an archetypical chain-store business since the 1950’s in the United States and the 1970’s in Canada, and are therefore an obvious industry for a study of multi-store oligopoly dynamics. Moreover, hamburger chains offer a clean, feasible, and relevant setting to analyze cannibalization and preemption. First, hamburger chains are among the simplest forms of multi-product (outlet) firms in oligopolistic competition, because the purpose of the franchised restaurant business is to provide homogeneous goods and services. Their efforts to produce identical products have been so successful that The Economist magazine routinely uses the prices of Big Macs across countries to analyze foreign-exchange rates (i.e., the Big Mac index), based on the premise of purchasing-power parity.7Furthermore, the services and the dining experience are also supposed to be homogenized across outlets. These features limit the scope of differentiation among outlets of the same chain, and hence simplify our task of identifying cannibalization and preemption. Second, hamburger shops compete in relatively small geographical markets and therefore provide us with sufficient cross-sectional variation for econometric purposes. Thomadsen’s (2005) estimates suggest that even in California, where most consumers drive (and hence are willing to travel long distances), only shops within approximately 05miles compete as close substitutes in a statistically significant manner. Defined at this microscopic level, sufficient geographical markets exist for the use of a two-step estimation approach. Third, entry and exit (i.e., opening and closing of outlets) are the most important strategic decisions for any hamburger chain, and qualitative evidence suggests cannibalization and preemption are their main consideration along with the demographic characteristics of the area. Notwithstanding the extremely local nature of markets, multiple outlets of the same chain frequently compete against each other even within such narrowly defined geographical markets, making cannibalization a real concern. Thus cannibalization and preemption are highly relevant economic forces in the evolution of market structure in this industry. 7See, for example, “The Big Mac index: Bunfight,” The Economist, February 2, 2013. 490 Igami and Yang Quantitative Economics 7 (2016) 3.2 Data Our original data source—archived phone directories—contains the universe of hamburger shops in Canada between 1970 and 2005, with their opening and closing years, as well as locations.8We supplement it with the market characteristics from the Canadian Census.9We have chosen to focus on the sample of 400 geographical markets from seven major cities (Toronto, Montreal, Vancouver, Calgary, Edmonton, Winnipeg, and Ottawa), which covers the majority of the total Canadian population.10 We define a geographical market based on a cluster of shops that existed at any point in time between 1970 and 2005 and were located within a 05-mile radius of each other (see Section A.1 for a sensitivity analysis with alternative market definitions). After identifying all such clusters, we make two adjustments. First, we omit downtowns, which typically contain a continuum of areas that are densely populated by shops, because we believe the nature of competition can be radically different in such places. Second, we use Google Maps to manually assess the location characteristics of each of the remaining clusters and refine market definition (e.g., by splitting a cluster into two when it contains a highway or a wide river running through it). These procedures leave 400 clusters in the data, with potential undersampling of central business districts. Nevertheless, the final sample still represents the majority of all shops in the seven cities, and is suitable for the analysis of cannibalization and preemption. The average number of hamburger shops grew from less than 05during the 1970’s to approximately 18in the early 2000’s. The five chains operating in Canada are A&W, Burger King, Harvey’s, McDonald’s, and Wendy’s. Except for Harvey’s, which is headquartered in Toronto, all other chains are based in the United States and hence do not have “home-towns” in Canada. McDonald’s is the largest chain by the number of outlets, and A&W is second, although Harvey’s is the second largest in Toronto, its hometown. The other two have considerably less presence in Canada (Table 1). We assume geographical markets are independent of each other, and abstract from supply-chain considerations across markets, based on the empirical evidence in Appendix C. Likewise, we abstract from the contractual details of each shop’s operation, based on the empirical evidence in Appendix D. Table 2shows that the total number of shops across the five chains rarely exceeds three in any market-year observation, which is consistent with our interviews with the store-development officers of various chains. They repetitively mentioned three as the magic number of shops that would saturate a typical market. This observation appears to corroborate the relevance of our market definition to the actual strategic planning of store openings at these chains. 8See Yang (2014) for more details on data. 9Census tracts do not necessarily coincide with our geographical markets (defined in the following paragraph), and hence we match them based on their overlaps in terms of zip code. 10We suspect smaller cities may potentially represent qualitatively different empirical settings, the inclusion of which might confound our estimates. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 497 atively few markets demonstrate high probabilities of belonging to the high-type category, which seems to broadly agree with the skewed distribution of market fixed-effect estimates from our preliminary regressions (Figure 1(left)).16 The correlation coefficient between ˆ qmHigh and the market fixed effect is 029,which indicates some nonnegligible updating actually took place in the Arcidiacono–Miller algorithm, so that the final outcome is not totally dictated by the initialization procedure. At the same time, this mildly positive correlation would appear to suggest both the static and the dynamic approaches are shedding light on some genuine market heterogeneity in the data. Figure 2summarizes [ˆ pij (s μ)], the market type-specific CCPs of entry, for a select demographic state (with both z1and z2in their highest levels, respectively). Three graphs on the left-hand side show McDonald’s entry probabilities in high-, middle-, and low-type markets, respectively, and the other three graphs on the right-hand side correspond to those of the other four chains. Three patterns emerge. First, market types matter. Firms enter higher-type markets more frequently, which is the reason we estimate a model with unobserved market types in the first place. Second, McDonald’s enters more frequently than its rivals, by a factor of approximately 4. This difference mirrors our earlier observation that McDonald’s operates almost one-half of all shops in the data, with the remainder split between the four other chains (Table 1). Third, a higher number of same-chain shops, Ni, reduces the chance of further entry in most cases, highlighting the importance of cannibalization concerns, whereas the impact of the number of rivalchain shops, Nj, is nuanced and highly nonmonotonic. For example, McDonald’s is most likely to open a new shop in high- and middle-type markets when three and two rivalchain shops already exist, respectively, which is consistent with the statements of the store-development officers of these firms that three shops saturate a typical geographical market.17 This nonmonotonic relationship between entry probability and Njwould appear to caution against the use of more restrictive specifications to estimate CCPs, especially when an analyst suspects the presence of dynamic strategic interactions. The exit CCPs in Figure 3exhibit such nonmonotonicities as well.18 16This comparison is intended only for qualitative assessment purposes. These two measures of the distribution of market heterogeneity are not directly comparable, because [ˆ qmμ]aretypeprobabilitiesfrom the fully dynamic model, whereas the fixed-effect estimates stem from the static regressions for descriptive purposes. Also note that although we label three types as high, middle, and low, there does not necessarily exist an obvious rank order of types in either Kasahara and Shimotsu’s (2009) or Arcidiacono and Miller’s (2011) approaches, and hence some markets may belong to both “high” and “low” with positive probabilities but not “middle.” For further interpretations of this finding, see the discussion of our main results in Table 4. 17Based on our interviews (in person and by phone) with the store-development officers of various hamburger chains in Canada, conducted on multiple occasions between October 22, 2009 and July 18, 2011. 18The exit strategies in low-type markets feature counterintuitive patterns in which the CCPs are the highest when (NiN−i)=(20)and (30). Because firms rarely operate multiple shops in low-type markets in the first place (see negligible entry CCPs in Figure 2), these cells represent low-probability events. Thus we suspect our exit CCP estimates for low-type markets might be picking up some unusual data patterns such as a chain’s massive entry efforts in a “wrong” location that were promptly scaled back (e.g., in an unpopular shopping mall). 498 Igami and Yang Quantitative Economics 7 (2016) Figure 2. Arcidiacono–Miller estimates of entry probabilities by market type. Note:Eachgraph represents the CCP estimates of entry when the market’s demography features the highest levels of population (z1) and income (z2). The other 15 demographic states entail their own CCP estimates, but the three qualitative patterns (see text) are similar, and hence we omit them from the display to avoid redundant graphs. In summary, our estimates of the equilibrium strategies corroborate our view that both market types and firm heterogeneity matter, and that cannibalization and preemption could be the key determinants of entry behaviors. We will use these CCP estimates to recover the underlying profit and cost functions in what follows. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 499 Figure 3. Arcidiacono–Miller estimates of exit probabilities by market type. Note:Eachgraph represents the CCP estimates of exit when the market’s demography features the highest levels of population (z1) and income (z2). The other 15 demographic states entail their own CCP estimates, but their qualitative patterns are similar, and hence we omit them from the display to avoid redundant graphs. 4.4 Profit function and sunk cost Having nonparametrically recovered the equilibrium strategies from the data, we can proceed to estimate the firms’ profits and sunk costs by using Hotz et al.’s (1994)and Bajari, Benkard, and Levin’s (2007) forward-simulation approach. Intuitively, the underlying idea is to find the values of the parameter vector ψthat would best rationalize the 500 Igami and Yang Quantitative Economics 7 (2016) observed equilibrium strategies, ˆσ(μ), in the sense that ˆσi(μ) delivers higher expected payoffs Vi(sμ ˆσ;ψ) than any other Vi(s μ ˜σiˆσ−i;ψ) based on deviating strategies ˜σi: revealed preference. Bajari, Benkard, and Levin (2007) propose to use the estimated MPE strategy profile, ˆσ, and its perturbed versions, (˜σiˆσ−i), to compute these expected payoffs by simulating the sequences of period profits into the distant future, and by constructing the expected values, Vi(s μ ˆσ;ψ) =E∞  τ=t βtΠ(sτετμ;ψ)stμ ˆσ(13) =1 NS  ns ∞  τ=t βτΠiτ(ns;μ ˆσψ) where the expectation is over the evolution of states and ns =12NS is the index of simulations. Likewise, we can compute the expected payoffs from some strategies that deviate from the MPE strategy, denoted by ˜σi, by perturbing the choice probabilities in ˆσiby ∼N(0σ2 ). The MPE assumption in equation (3) requires the following distance metric to be nonnegative, gnp (s μ;ψ) ≡Vi(sμ ˆσ;ψ) −Visμ ˜σi(np) ˆσ−i;ψ≥0(14) where np is the index of perturbed strategies. We generate each “perturbed” strategy, ˜σi(np) by adding a random draw to the estimated choice probability ˆσiin each bin of thediscretizedstatespace.WecomputeVi(s μ ˜σi(np) ˆσ−i;ψ) from NP such deviations, denote each distance metric by gnp , and construct the objective function W(ψ)=1 NP  np mingnp (s μ;ψ)02(15) which we subsequently minimize to obtain our estimates, ˆ ψ. Our empirical implementation proceeds based on the specifications β=09,NS = 1000,NP =1000,σ=002,andεit(ait)∼EV1i.i.d., and under the standard normalization to set ˆκ−=0.19 We follow the standard empirical models of entry and market structure (e.g., Seim (2006)) and specify the average period profit per outlet as πimt =πsmtμm;αiθi=αi 1(μm)+αi 2nimt +αi 3n−imt +θi 1z1mt +θi 2z2mt(16) where α1,α2,andα3represent the base profit, competition with same-chain outlets, and competition with rival-chain outlets, respectively.20 The z’s and θ’s denote demand 19We should carefully interpret ˆα1,ˆκ+, and ˆκ−because they are not identical to the primitives of the model (α1κ+κ−)and are not separately identified from each other. Under our normalization, ˆκ−=0, Aguirregabiria and Suzuki (2014)show ˆα1=α1+(1−β)κ−and ˆκ+=κ+−κ−.Thatis,theestimatefor the fixed component of profit also incorporates the opportunity cost of operation (i.e., of postponing exit), and the gross entry-cost estimate actually represents the net cost of entry and exit. See also Supplement Section O.4. 20See Supplement Section O.1 for the estimates based on a more flexible functional form. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 501 Table 4. Second-stage estimates by the number of market types. Chain: McDonald’s Others Number of Types (K): One Two Three Four One Two Three Four (1) (2) (3) (4) (5) (6) (7) (8) Base profit (α1)1036 8456 4272 4242 1670 2087 3109 3081 (0053)(0002)(0560)(0358)(0089)(0003)(0358)(0358) Type-2 market – −1982 −0594 −0537 –−1144 −0754 −0751 (–) (0003)(0099)(0120)(–) (0002)(0120)(0120) Type-3 market – – −3801 −3962 ––−1377 −1514 (–) (–) (0830)(0158)(–) (–) (0158)(0275) Type-4 market – – – −4227 –––−1519 (–) (–) (–) (0275)(–) (–) (–) (0158) Own competition (α2)−0109 −0105 −0356 −0301 −0974 −1324 −2000 −1970 (0023)(0003)(0043)(0375)(0086)(0003)(0375)(0375) Rival competition (α3)−0220 −0133 −0237 −0227 −0172 −0119 −0241 −0263 (0010)(0003)(0010)(0012)(0025)(0002)(0012)(0012) Population (θ1)−0015 0034 0004 −0010 −0050 −0071 −0088 −0080 (0009)(0003)(0010)(0025)(0017)(0003)(0025)(0025) Average income (θ2)0001 0011 −0030 −0015 −0080 −0059 −0171 −0128 (0011)(0003)(0023)(0041)(0022)(0003)(0041)(0041) Net entry sunk cost (κ)9904 72432 33976 34434 10555 11223 13114 13395 (0269)(0001)(4932)(0419)(0262)(0003)(0420)(0419) Note: Exit cost is normalized to zero, and hence we should interpret κas the net sunk cost. Standard errors are from bootstrapping across markets. The value of the objective function at our preferred estimate (columns 3 and 7 together) is W(ˆ ψ) =297499. shifters and their impacts on profits. In terms of firm heterogeneity, we will focus on the distinction between McDonald’s and the other four chains, for the same reasons we explained in Section 4.2. In addition, we impose a simplifying assumption that the presence of rival-chain shops affects a store’s profit symmetrically (i.e., αij 3=αi 3∀j= i,where αij 3represents the effect of chain j’s shop on chain i’s shop), so that n−imt =j=injmt becomes a sufficient statistic for rival-chain competition. Conceptually, nothing prevents us from constructing another layer of the structural model (with richer patterns of crossbrand substitution) underlying this store-level period profit function (16), but the data constraint limits the extent to which we can plausibly identify such additional structures (see Section 4.2 for details). Columns 3 and 7 of Table 4show the estimates of the profit functions and sunk costs based on our preferred model with ˆ K=3, and contain three findings. First, the estimates for ˆα1(μ) suggest that market types matter and they affect the chains differently.21 By contrast, columns 1 and 5 show the results without market types (i.e., K=1), which seem to feature somewhat attenuated parameter estimates. Second, substantial 21The market type-specific intercepts for McDonald’s and its rivals are (42723109),(36782355), and (04711732)in high-, middle-, and low-type markets, respectively, which means low-type markets are relatively more profitable for non-McDonald’s chains. This asymmetry seems to explain our earlier finding in Figure 1(right) that some markets exhibit positive probabilities of belonging to high and low types but not middle. That is, such cases represent markets in which non-McDonald’s chains are more active than in 502 Igami and Yang Quantitative Economics 7 (2016) heterogeneity exists between McDonald’s and the other four chains. McDonald’s has to incur higher sunk costs on average ( ˆκmcd >ˆκother), but it also earns higher profits (ˆαmcd 1>ˆαother 1) with the exception of low-type markets. This finding appears consistent with the industry common knowledge that McDonald’s invests heavily in many aspects of the hamburger restaurant business, including kitchen equipment, employee training, and store development (Love (1995)). Third, a shop’s profit decreases with the presence of other shops (i.e., ˆα2<0and ˆα3<0). This competitive effect is stronger among shops of the same chain than of rival chains (i.e., ˆα2<ˆα3<0), making cannibalization one of the most important determinants of profits. We should also note that ˆαmcd 3and ˆαother 3 are almost identical and reside within the standard error of each other, which leads us to doubt that a more detailed account of cross-brand substitution patterns would alter our findings materially. Finally, the two demographic variables do not appear to affect profits in a systematic manner. We suspect the sparsity of entry/exit data might be limiting the extent to which we can estimate their effects precisely (see Section A.2 for further details). What happens if we misspecify the extent of unobserved heterogeneity across markets? Our baseline analysis uses Kasahara and Shimotsu’s (2009) method to determine the number of unobserved market types ( ˆ K=3), but previous research has typically imposedsomeadhocK’s. In a similar manner, we could (wrongly) assume K=2or 4and investigate the consequences of such misspecification. Columns2,4,6,and8ofTable4show that both the two- and four-type models lead to qualitatively similar parameter estimates, with three noteworthy patterns. First, the type-specific intercepts, ˆα1(μ)’s, suggest the two-type model collapses the middle and low types (in our baseline, three-type model) into a single type (type 2), with the new intercepts lying between those of the two types, whereas the four-type model introduces a redundant type (type 4) that appears statistically indistinguishable from type 3. Second, the competition parameters, ˆα2and ˆα3, seem attenuated in the two-type model, which is a result reminiscent of the preliminary regression without market dummies (column 1 of Table 3) as well as the structural estimates without market types (columns 1 and 5 of Table 4). Moreover, their relative magnitudes are reversed for McDonald’s (i.e., ˆαmcd 3<ˆαmcd 2), which appears counterintuitive. Third, the four-type results closely resemble our three-type baseline. These comparisons suggest that two types are not sufficient to capture the underlying heterogeneity across markets, whereas the inclusion of the fourth type is redundant. Figure 4plots the evolution of the number of shops to assess the fit of the estimated model with ˆ K=3. The model-generated MPE is based on a particular configuration of Pakes and McGuire’s (1994) algorithm and is not guaranteed to be unique, so the sole purpose of this exercise is to show that an MPE with a similar trajectory of ntexists. See Supplement Section O.3 for further discussions. other markets relative to McDonald’s, which could be an indication of consumers’ taste heterogeneity as an underlying mechanism behind market heterogeneity. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 503 Figure 4. The average number of McDonald’s per market. Note: The model path shows the mean number of shops across 1000 simulations (in each of the 400 markets) based on the model-generated MPE strategies. 4.5 Identifying assumptions Before proceeding to the counterfactual simulations, this subsection will discuss three important assumptions that, if not satisfied, can be potential sources of biases. First, we assume the unobserved market types are time-invariant. To the extent that the observed characteristics (i.e., population and income) capture important changes at the market level, this assumption is not restrictive. However, if some unobserved factors (e.g., traffic patterns and ethnic composition) had drastically altered the latent demand for hamburgers in some neighborhoods in the middle of the sample period, the restaurant chains might have responded by entry/exit at the time of changes in types. Thus this assumption may not always be valid and can be a potential source of biases. Arcidiacono and Miller’s (2011) approach allows time-varying market types in principle, but we have chosen to assume constant market types for three reasons. The first reason is conceptual and relates to our first step of analysis. We intend to keep our model consistent across the three steps of our empirical analysis. Specifically, we identify the (minimum) number of market types in our first step based on Kasahara and Shimotsu’s (2009) approach, which assumes time-invariant types. The second reason is more practical and relates to our second step of analysis. Entry and exit entail large sunk costs and hence are infrequent events even for the large fast-food chains. By allowing entry/exit strategies to vary by three market types and two firm types (i.e., McDonald’s vs. the other four), we are already demanding a lot from the relatively sparse data in our estimation task. The third reason is that we expect the biases to be minor because the Arcidiacono-Miller approach (as we currently implement it) estimates the probabilities that each market belongs to the three types, qmμ (see equation (9)). Even if markets in reality had spent different lengths of time in multiple types, ˆ qmμ would adjust accordingly to reflect different degrees to which market mbelonged to type μ. Thus, although 504 Igami and Yang Quantitative Economics 7 (2016) the severity of potential biases is theoretically unknown, we have conceptual as well as practical reasons to prefer our current assumption of time-invariant market types. The second important assumption is stationarity. We assume both the consumers’ preferences and the restaurant chains’ technologies remain constant in the fast-food hamburger business during our sample period (1970–2005) in Canada’s seven major cities. In reality, tastes may change and important innovations could have occurred, but we doubt Canadians took decades to acquire their true tastes for fast-food hamburgers or that new technologies (e.g., new kitchen equipment, toys and playgrounds for kids, new methods of location hunting, or novel management practices) revolutionized the core production process.22 Third, we assume the firms play the same equilibrium, conditional on market types. Geographical markets may vary by their demographic features and the realized configuration of shops but share the same MPE as long as they belong to the same market type. In other words, we allow three different equilibrium plays of the game parameterized by the unobserved profitability of the market, αi 1(μm), in equation (16). Had the data manifested any obvious symptom of more equilibria, the Kasahara–Shimotsu approach would have indicated more than three types to rationalize it. Our alternative estimate with four market types suggests the fourth type is redundant. Although we can consider additional types/equilibria at the conceptual level, they will not be observationally distinguishable. Thus we do not expect our equilibrium assumption to be a source of biases. 5. Effects of cannibalization and preemptive motives The strategic trade-off between cannibalization and preemption makes the analysis of chain stores complicated and intriguing. In this section, we assess the implications of cannibalization and preemption on market structure by comparing the entry patterns in the estimated model with those under hypothetical settings in which cannibalization and preemptive motives are muted. 5.1 Less cannibalization How does cannibalization affect market structure dynamics? Cannibalization appears to be a real concern for chain stores, according to our interviews with their storedevelopment officers, as well as our structural estimates of the firms’ profit functions. These parameter estimates convey the relative importance of each factor in an abstract measure (i.e., normalized profit functions based on εimt ∼EV1and κ−=0), but ideally we would like to obtain a more direct measure of the cannibalization effect to illustrate its implications on competition. For these reasons, this subsection examines the evolution of market structure when shops that belong to the same chains do not cannibalize as much as in the baseline 22Our preliminary regressions exhibit a mild time trend but negligible changes in coefficient estimates with or without time trend/dummies, and hence we expect any manifestation of nonstationarity to be a minor source of biases. See Section A.2 for details. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 505 Figure 5. Counterfactual number of McDonald’s. Note: The model and counterfactual paths show the mean number of shops across 1000 simulations (in each of the 400 markets) based on the model and counterfactual strategies, respectively. model. Specifically, we solve an alternative model in which ˜α2=ˆα3for each firm; that is, same-brand shops will no longer be particularly close substitutes as in the baseline estimates. Figure 5(dark solid line) suggests that without strong cannibalization, the firms would open shops more aggressively. The average number of McDonald’s would surpass 05by 1984, which is 5 years earlier than the baseline, and the level of ˜ nmcd 2005 would be higher by 105%. Thus cannibalization appears to be an important force that slows the chain stores’ entry process. The profit-function estimates in Table 4already foreshadowed this pattern, so the result is not particularly surprising by itself. Nevertheless, we believe constructing the counterfactual history of market structure is valuable because it suggests the extent to which competition estimates based on simple models could be biased. As we explained in the discussion of fit (Section 4.4), a model-generated MPE is not necessarily unique, and hence this particular counterfactual exercise should be interpreted only as an attempt to construct one (out of many possible versions of) dynamic implication of the estimated model. That said, we paid attention to the computational details of the MPE, so that both the baseline and counterfactual trajectories are generated from exactly the same coding configuration with respect to the initial conditions and other details of numerical search for optimal strategies. Although detailed analysis of product differentiation is beyond the scope of this paper, one practical implication of this finding is that chain-store operators might have incentives to “diversify” brands to keep growing profitably. A “diversified chain store” might sound contradictory, because uniformity characterizes a chain operation. However, this defining characteristic does not preclude a retailer from operating multiple 506 Igami and Yang Quantitative Economics 7 (2016) chains (brands) of stores. The prevalence of multi-brand operation in practice seems to corroborate this view.23 5.2 When McDonald’s cannot affect its rivals Despite theorists’ attention to preemption games and antitrust practitioners’ interest in entry deterrence for over three decades,24 little empirical work exists on the subject. Besanko et al. (2010) attribute this lack of evidence to the anticompetitive nature of entry deterrence. Because such strategies might violate antitrust statutes, firms would be reluctant to report them especially when they are effective. Another reason is the fact that suitable empirical methodologies to analyze dynamic strategic interactions have been developed only recently. Moreover, preemption is not necessarily an action or outcome, but an underlying motivation for taking particular actions in expectation of favorable outcomes in the future, which is why we frequently use the phrase “preemptive motives” instead of “preemption” in this paper. Thus the construction of a no-preemption counterfactual requires attention to the firms’ expectations as well as actions. How would McDonald’s entry strategy change in the absence of preemptive motives? We design the no-preemption environment specifically from McDonald’s perspective, by making its four rivals nonstrategic players (with respect to McDonald’s) who appear and disappear irrespective of nmcd mt , simply according to the conditional distribution of the number of their shops in the data. This distribution is conditional on the demographic variables but integrates out the number of McDonald’s. That is, we shut down McDonald’s preemptive motives by forcing its rivals to behave as if McDonald’s actual entry did not matter, so that McDonald’s actions can no longer affect its rivals. When the presence or absence of its stores does not change the rivals’ subsequent entry/exit decisions, McDonald’s will lose preemptive motives and its optimal entry strategy will differ from the baseline model. We intend to measure this difference as the manifestation of (the lack of) preemptive motives in entry decisions. Operationally, this counterfactual setting amounts to drawing the number of four rival chains’ shops, n−mcd mt , from its empirical distribution conditional on the demographics (but with the number of McDonald’s, nmcd mt , integrated out). From the perspective of McDonald’s, its rivals become part of nature, and n−mcd mt evolves exogenously just like zmt. Thus McDonald’s solves what has effectively become a single-agent dynamic programming problem. McDonald’s cannot influence its rivals, but the latter’s presence will still hurt the former’s profits, so this exercise isolates McDonald’s preemptive motives 23Yum! Brands would be an example of multi-chain operation in the fast-food industry. The company owns KFC, Pizza Hut, and Taco Bell, among others. Likewise, Darden Restaurants is the world’s largest fullservice restaurant company, with more than 2000 outlets, operating a horizontally diversified set of casualdining chains including Olive Garden, Long Horn Steakhouse, Red Lobster, Bahama Breeze, Seasons 52, Eddie V’s Prime Seafood, The Capital Grille, and Yard House. In a broader set of retail sectors, we can find more vertically differentiated portfolios, such as various lines of hotel brands owned by Hilton Worldwide, which range between luxury, full-service, and select-service categories. Supermarket operators have also relied on multiple store formats, from supercenters to convenience stores (e.g., Carrefour Express, Tesco Express, and Walmart Express). 24See the introductory section for the theoretical literature and its competition-policy background. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 513 Table 10. Preliminary regressions (ordered probit) with traffic lights in Toronto. Dep. Var.: Decision to Enter/Exit (1) (2) (3) (4) Own-store presence (γ1)−12598∗∗∗ −11173∗∗∗ −12230∗∗∗ −12771∗∗∗ (01010)(00983)(01015)(01028) Rival-store presence (γ2)−04130∗∗∗ −02730∗∗∗ −03637∗∗∗ −04183∗∗∗ (00635)(00566)(00605)(00637) Population (thousand, λ1)00510∗∗∗ ––00379∗∗∗ (00090)(–) (–) (00116) Traffic lights (count) – 00558∗∗∗ 00418∗∗∗ 00194∗ (–) (00074)(00082)(00106) Income (thousand C$,λ2)00189∗∗∗ –00223∗∗∗ 00182∗∗∗ (00046)(–) (00044)(00047) Market dummies Yes Yes Yes Yes Firm dummies Yes Yes Yes Yes Number of observations 13,825 13,825 13,825 13,825 Pseudo R20.1606 0.1444 0.1569 0.1624 Note: Standard errors are given in parentheses. The symbols ***, **, and * indicate significance at the 1%,5%,and10% levels, respectively. Appendix B: No-preemption counterfactuals This appendix reports alternative no-preemption counterfactual simulations. B.1 No threat of entry As we discussed in Section 2.1, our design of the no-preemption counterfactual differs from Tirole’s (1988) operationalization, because the latter is appropriate only for a stylized case in which the identities of an incumbent monopolist and a potential entrant are clear and the analytical focus is exclusively on the timing of the second shop’s opening. Both of these conditions appear too restrictive in our empirical setting. Nevertheless, we can implement a Tirolean counterfactual by simply eliminating all rivals. Figure 6compares the Tirolean counterfactual and our preferred counterfactual, both of which are designed to simulate an environment without preemptive motives, but the outcomes differ. The Tirolean counterfactual features more aggressive entry of McDonald’s than in our baseline counterfactual, because by eliminating all potential competitors in the future, the former setting enlarges the expected effective sizes of markets for McDonald’s. By contrast, our preferred counterfactual lets in the rivals in a manner that is comparable to the actual entry patterns in the data (and therefore allows McDonald’s to be preempted), and hence the residual demand for McDonald’s remains the same as in the data on average. B.2 Pre-commitment One might wonder why we focus exclusively on McDonald’s in the setting in which its rivals are not best responding to its new strategy. Why not shut down all firms’ preemp- 514 Igami and Yang Quantitative Economics 7 (2016) Figure 6. No-preemption counterfactual without threat of entry. Note: The counterfactual paths show the mean number of McDonald’s shops across 1000 simulations (in each of the 400 markets). tive motives by studying some alternative equilibrium? The reason is twofold. First, preemptive motives exist as long as firms engage in dynamic strategic interactions. In other words, we cannot completely isolate preemptive motives when firms’ entry decisions are best responses to each other, which is why we analyze how a particular firm (McDonald’s) changes its best response when its rivals stop responding to it. Second, open-loop Nash equilibrium is a common alternative to MPE (e.g., Dockner, Jorgensen, Van Long, and Sorger (2001)) and is often used to shut down some aspects of dynamic strategic interactions. However, it does not necessarily shut down preemptive motives and can actually strengthen them, as we demonstrate in what follows. An open-loop Nash equilibrium does not require subgame perfection or optimal state-contingent plans. The literature typically implements it by considering firms’ pre-commitment to time-contingent action plans (e.g., Chicu (2012)), thereby shutting down state-by-state reactions among firms. However, we should note that firms are still best responding to each other at time zero in terms of their time-contingent plans. If a firm knows the other firms are planning to enter at certain points in the future, it would consider entering earlier than them, and the rivals are formulating their time-contingent plans likewise. Thus pre-commitment does not imply the absence of preemptive motives, because firms are still strategically choosing their timing of entry. Figure 7shows that pre-commitment actually seems to strengthen preemptive motives. The open-loop equilibrium features disproportionately high entry rates in the first few years, followed by a long period of unchanged market structure. This counterfactual timing pattern is consistent with the absence of reactive motives, but inconsistent with the absence of preemptive motives, and hence we prefer our analysis in the previous subsection as a study of preemptive motives. Potentially, multiple open-loop Nash equilibria may exist, and we did encounter a few slightly different open-loop Nash strategies. However, the timing pattern of ntre- Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 515 Figure 7. Pre-commitment reinforces preemptive motives. Note: The counterfactual paths show the mean number of McDonald’s shops across 1000 simulations (in each of the 400 markets). mains unchanged. That is, regardless of the computational details, optimal entry strategies with pre-commitment seem to entail relatively high entry probabilities in the first few years, and practically zero entry afterward. Appendix C: Absence of supply-chain considerations We assume geographical markets are independent from each other. This assumption would be problematic if economies of density existed as in Holmes’ (2011) study of Walmart, in which he showed a systematic geographical pattern of Walmart’s entry that radiates from the headquarters.27 We investigate this possibility from three directions as follows. First, Figure 8(left) plots the distance between the headquarters and each new McDonald’s shop in Toronto by opening year. If McDonald’s preferred a tight network of stores for logistics purposes, the graph would exhibit an upward trend over time, but it does not. Instead, we find a slightly downward trend with low statistical significance, and the adjusted R2is 00073. Second, Figure 8(right) plots the distance between each new shop and its nearest existing shop of the same chain. If McDonald’s preferred a tight network based on its shops’ distance from distribution centers, this graph should demonstrate clustering patterns around certain logistically optimal distances. In fact, new shops are located anywhere between 0 and 10 miles from the nearest existing shops, with a slightly decreasing trend over time (statistically significant at the 1% level) and the adjusted R2of 01645.Thus cannibalization concerns appear to dominate hypothesized economies of density. Third, we interviewed a store-development officer at McDonald’s specifically on this topic, who explicitly stated, “Decisions made by [the] Real Estate [department] do not 27Nishida (2015) also found economies of density in the context of convenience stores in Japan. 516 Igami and Yang Quantitative Economics 7 (2016) Figure 8. Locations of new McDonald’s in Toronto. Note: The headquarters of McDonald’s in Toronto is located at McDonald’s Place, M3C 3L4. We calculate the driving distance from each shop using Google Maps. These graphs focus on McDonald’s in Toronto for the purpose of illustration, but we find a similar (lack of) geographical pattern in the other six cities, as well as for the other four chains. take into consideration any supply chain efficiencies,” including potential efficiencies in terms of labor and supervision of restaurants. This description of the internal decision process (i.e., stated preference) is consistent with the two data patterns in the above (i.e., revealed preference). Thus economies of density do not appear to be a primary consideration for the hamburger business, in which highly localized competition dominates other factors.28 Based on this empirical evidence, we believe our model is useful for capturing important aspects of entry and competition in the hamburger chain industry. Appendix D: Profits from franchised and company-operated restaurants Our data do not contain comprehensive information on the contractual details of the five hamburger chains between 1970 and 2005, and hence our model abstracts from the distinction between franchised and company-operated outlets. This omission could be problematic if these two contractual formats affect the firms’ overall profits in a significantly different manner. For this reason, we have chosen to investigate their potentially different profit implications, using publicly available information from annual reports. Table 11 shows selected items from the income statements and other operation details of McDonald’s in the middle of our sample period, with an emphasis on how sales, operating profits, and the number of restaurants compare between franchised and 28In our view, McDonald’s and other hamburger chains concentrate their efforts on microlevel location hunting and the sophistication of cooking processes, whereas Walmart and other supercenters seem to compete primarily in the efficiency of purchasing and distribution logistics on a relatively larger geographical scale. In other words, hamburger restaurants and supercenters embody different technologies and operate under different geographical constraints. Quantitative Economics 7 (2016) Unobserved heterogeneity in dynamic games 517 Table 11. Franchised versus company-operated outlets at McDonald’s. Year 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 Share of franchised operations (%) Number of restaurants 69 72 74 74 76 76 77 78 78 77 Sales 70 71 72 72 73 74 75 75 74 73 Operating profits for company 64 64 64 64 64 65 65 65 63 63 Systemwide operating results Number of restaurants 24,447 22,008 20,519 19,084 17,668 15,969 14,160 12,651 11,788 11,282 Franchised 16,795 15,949 15,086 14,197 13,374 12,186 10,944 9,918 9,237 8,735 Company operated 7,652 6,059 5,433 4,887 4,294 3,783 3,216 2,733 2,551 2,547 Sales ($mn) 34,930 33,342 31,225 28,999 27,540 25,986 22,939 20,913 19,577 17,867 Franchised 24,463 23,830 22,330 20,863 19,969 19,123 17,146 15,756 14,474 12,959 Company operated 10,467 9,512 8,895 8,136 7,571 6,863 5,793 5,157 5,103 4,908 Average sales ($mn) 14151515161616171716 Franchised 15151515151616161615 Company operated 14161617181 818192019 Consolidated income statement Operating profits* ($mn) 4,721 4,692 4,482 4,145 3,954 3,731 3,241 2,863 2,659 2,359 Franchised 3,004 3,009 2,848 2,658 2,546 2,416 2,093 1,871 1,682 1,481 Company operated 1,717 1,683 1,634 1,486 1,408 1,315 1,148 992 977 879 Note: “Operating profits” excludes selling, general, and administrative expenses, as well as other operating costs that cannot be attributed to either franchised or company-operated restaurants. Source: McDonald’s Corporation Annual Report. 518 Igami and Yang Quantitative Economics 7 (2016) company-operated outlets. For example, in year 2000, the restaurants operated by franchisees accounted for 70% of sales, 64% of operating profits for the company,and69% of the total outlet count. These numbers fluctuate over the years but seem to be well aligned with each other overall, with one exception. Note that the franchised outlets’ contribution to the company’s operating profit (63%–65%) is consistently below their shares of sales and the number of outlets (69%– 78%), which implies that the franchisees take approximately one-tenth of profits for themselves. This pattern reflects the profit-sharing arrangement between the franchisees and the company, and presumably constitutes an important part of the incentive scheme. Consequently, the possibility remains that the company faces somewhat different expected profits from opening new shops, depending on whether the existing and new shops are operated by franchisees or the company, which could potentially bias our results. At the same time, we should also consider the magnitude of this profitability difference, which, at approximately 10%, is not negligible but probably does not completely alter the firm’s entry decisions either. Our profit function estimates seem to imply the effects of market types and competition could often dominate the subtle difference in contractual arrangements. Moreover, anecdotal evidence suggests that even though franchised outlets contribute relatively smaller profits on average, the companies are not particularly enthusiastic about cannibalizing them, because franchise agreements are an active area of litigation, and one of the most common types of disputes concerns competition with same-chain outlets. 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