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Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness An empirical model of firm entry with endogenous product-type choices Seim(2006), RAND Journal of Economics Suggestions Wooyong Lee 31 Jan 2013 Introduction Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Before : entry model, identical products In this paper : entry with simultaneous location choice Before or some other papers : complete info game In this paper : incomplete info game (greatly reduces computational burden) Results : video retail industry location data firms differentiate to shield profit from competition more scope for product differentiation → more market power (more entry) Outline Seim(2006) Wooyong Lee 1 Summary of the paper Model Estimation Data and Result 2 Contribution and weakness of the paper Contribution: Endogenized product-quality choice Contribution: Incomplete information on profits Weakness of the paper 3 Suggestions for further research Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Section 1 Summary of the paper Model Setup Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions market m = 1, 2, . . . , M let’s focus on one market m: (script m removed for ease of exposition) location l = 0, 1, . . . , L firm f = 1, 2, . . . , F L+1 decision df = (dfl )L l=0 ∈ {0, 1} Model Setup Seim(2006) Wooyong Lee Summary payoff Πfl = Xl β + ξ + h(Γ.l , n) + εfl Model Estimation Result Contribution and Weakness Product Information Weakness X : observable market characteristics ξ : unobservable market characteristics, known to firms h() : effect of competition on profits; specified later Suggestions Γ.l : interaction between l and 1 through L n = (nl )L l=1 : number of firms at location l εfl : idiosyncratic profitability of firm f at location l Πf 0 normalized to 0 Assumptions Seim(2006) Wooyong Lee Assumption (Independent symmetric private values) Summary ε1 , . . . , εF are private information to the players and are independently and identically distributed draws from the distribution G (·) Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Assumption (Additively separable competitors’ effects) P h(Γ.l , n) = L k=1 γkl nk Assumption (Distance bands) let dkl be the distance between location k and l. γkl = γk 0 l = γb if Db ≤ γkl , γk 0 l < Db+1 , where Db and Db+1 denote cutoffs that define a distance band. Assumptions Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Under distance bands b = 0, 1, . . . , B, with corresponding cutoff points Db and Db+1 where D0 = 0, the resulting payoff function is given by P Πfl = Xl β + ξ + b γb Nbl + εfl γb : competitive effect in distance band b P Nbl = k Ibkl nk : number of firms in distance band b Ibkl := I(dkl ∈ [Db , Db+1 )), I(·) : indicator function nk : number of firms at location k P E := b Nbl : total number of firms in the market Conjectures and equilibrium Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Conjectures and equilibrium Seim(2006) Wooyong Lee Given the expected competitor distribution across market locations, firms calculate its expected profit at each location l : Summary Model Estimation Result E(Πfl ) = Xl β + ξ + Contribution and Weakness P b γb E(Nbl ) + εfl := E(Π̄fl ) + εfl P note that E(Nbl ) = k Ibkl E(nk ) Product Information Weakness Suggestions Structure of the game : 1 firms decide whether or not to enter → E determined 2 Given number of firms E, firms decide locations → solve backward Conjectures and equilibrium Seim(2006) Wooyong Lee Summary Due to the symmetry of rival’s types, firm f ’s perception of firm g ’s location strategy is the same for all competitors. Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Let θ1 = (β, γ). Given ξ, X, E, θ1 , the probability that competitor g chooses location l is given by pgl (ξ, X, E, θ1 ) = P(E(Π̄gl ) + εgl > E(Π̄gk ) + εgk ∀k 6= l, ∀g 6= f ) Expected number of competitors at location k is E(nk ) = (E − 1)pgk P P E(Nbl ) = k Ibkl E(nk ) = k Ibkl (E − 1)pgk + I(b = 0) Conjectures and equilibrium Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Assumption ε are i.i.d. draws from a type 1 extreme-value distribution with scale parameter normalized to one. By this assumption, there exists a closed-form formula for pgl : exp{E(Π̄gl )} pgl = PL k=1 exp{E(Π̄gk )} Since types are symmetric, every firm has the same equilibrium conjecture of its competitors’ location choices : ∗ ∗ L pg := (pgl )L l=1 = pf = p := (pl )l=1 Conjectures and equilibrium Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness A firm’s vector of equilibrium conjectures over all locations l is defined by pl∗ = Suggestions = exp{E(Π̄l (X, p∗ , E, θ1 ))} PL ∗ k=1 exp{E(Π̄k (X, p , E, θ1 ))} P P exp{Xl β + γ0 + (E − 1) b γb j Ibjl pj∗ } PL P P b ∗ k=1 exp{Xk β + γ0 + (E − 1) b γb j Ijk pj } for all l = 1, . . . , L Conjectures and equilibrium Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions let’s analyze E : In equilibrium, each entrant earns nonnegative profits in expectation, while any additional entrant would suffer losses. The probability of entry by a firm into a market involves a comparison of a weighted average of payoffs across locations to the normalized payoff of not entering. Conjectures and equilibrium Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Given the assumption of i.i.d. type 1 extreme-value profitability types, P ∗ exp(ξ) L l=1 exp{E(Π̄l (X, p , E, θ1 ))} P(entry ) = P ∗ 1 + exp(ξ) L l=1 exp{E(Π̄l (X, p , E, θ1 ))} Since the probability of entry is identical across competitors, E = F × P(entry ) Ways to choose F : 50% enter the market, F = 50 Estimation : Econometric Specification Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Assumption The expected number of entrants predicted by the model exactly equals the number of entrants observed in the data. With E being the observed number of entrants, by the entry probability equation, ξ = ln E − ln(F − E) − ln L X exp{E(Π̄l (X, p∗ , E, θ1 ))} l=1 Assumption ξ m are i.i.d. random draws from a Normal distribution with parameter θ2 = (µ, σ) and independent of ε. Likelihood Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Data from market m = 1, . . . , M Each market is treated as an independent F m -player location game dm = (d1m , . . . , dFm ) : vector of actions taken by F m players in market m Suggestions The likelihood function is given by L(θ1 , θ2 ) = M Y m=1 pθ1 (dm |ξ m , Xm , E m )gθ2 (ξ m |Xm , E m , F m ) Estimation Procedure Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness 1 2 3 Suggestions 4 initialize (θ1 , θ2 ) m M given (θ1 , θ2 ), (Xm )M m=1 , F, (E )m=1 , solve equilibrium m conjecture equation for p for each m separately m M calculate ξ m with pm , (θ1 , θ2 ), (Xm )M m=1 , F, (E )m=1 for each m estimate (θ1 , θ2 ) by maximizing likelihood function Estimation Issues Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions initial value : a grid search over the parameter space likelihood maximization : Nelder-Mead optimization algorithm problematic when there are multiple equilibria : appendix proves uniqueness for two distance bands with four locations, simulation evidence suggests further result Data description Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions video retail industry videotapes are standardized; main differentiation by store location isolated markets; no large city nearby, no metropolitan area exclude tourist regions locations by Census tracts Data description Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Data description Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Data description Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions d 0 = 0.5 miles, d 1 = 3 miles Data description Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Estimation Result Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Estimation Result Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Simulation Result Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Simulation Result Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Section 2 Contribution and weakness of the paper Previous Works Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions focused on tradeoff between demand and intensity of competition Early works on product quality differentiation : Hotelling(1929), Lancaster(1966,1979) (competition on characteristic space) Model for Endogenized Product Choice Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Empirically tractable model of competition on characteristic space (tractable for large L) Unisolated market : locations affect each other via distance Empirical Results Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Firms differentiate to shield from competition More scope for product differentiation → more market power(more entry) More disperse population → less gain from differentiation(slightly more entry in total) The two offset each other in video retail industry data Previous Works Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Complete information game → computational burden → Limited number of locations Mazzeo(2002) : entry with product-quality choice, complete information game → uses motel industry data, computation is burdensome with 3 locations Incomplete Information Game Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Introduce private information : idiosyncratic profitability sources: cost, intangible assets, customer service, inventory maintenance etc. As Rust(1994) notes : Bayesian Nash equilibrium conjectures are easy to derive Other works under information asymmetry : Aguirregabiria and Mira(2006), Pakes, Ostrovsky and Berry(2005), Pesendorfer and Schmidt-Dengler(2003) Cost of Assumptions Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Distance band approach : All locations with same distance band have the same impact two at the north one at the north and one at the south ε being i.i.d. type 1 extreme value distribution : idiosyncratic profitability uncorrelated across firms at a location, across location for a firm no spatial correlation Possible Issues Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions When there are multiple equilibria : matching location probabilities to observed location choices is problematic uniqueness for general setting is only verified by simulation Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions Section 3 Suggestions for further research Further research so far Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions entry game with multistore/multiproduct firms (Jia 2008) dynamic entry game timing game (Sweeting 2009) estimation with multiple equilibria (Aguirregabiria 2012 : identical product case) estimation in case of location heterogeneity (Aguirregabiria 2012) Further research so far Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions estimation of demand system by quantity, price data of stores : Wang(2010) effect of other factors on entry decisions: regulation (Gowrisankaran and Krainer 2011), organizational structure (Takechi and Higashida 2012), managerial ability (Goldfarb and Xiao 2011) Suggestions Seim(2006) Wooyong Lee Summary Model Estimation Result Contribution and Weakness Product Information Weakness Suggestions nonlinear effect of additional entrant relaxing distance band assumption investigation of conditions for unique equilibrium