Estimating Market Power in Differentiated Product Markets

Transcription

1 Estimating Market Power in Differentiated Product Markets Metin Cakir Purdue University December 6, 2010 Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

2 Outline Outline Estimating structural market equilibrium models Supply side: Review of Cournot and Bertrand competition Demand side: Homogeneous vs. differentiated product markets Review of classical demand system models Random utility models: Discrete choice modeling An empirical application to ready to eat cereal industry Nevo, 2001 Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

3 Quantity Setting Firms Cournot Model: Max q i π i = P(Q)q i c(q i ) Supply Side Cournot Competition where Q is aggregate quantity and q i is quantity produced by firm i. The FOC is: π i q i where = P + q i P(Q) q i c (q i ) = 0 P(Q) q i P(Q) q i P(Q) q i = P(Q) Q Q q i = P(Q) Q = P(Q) } Q {{ } P (Q) ( qi q i + q j ( q i ) 1 + q ) j q } {{ i } θ C Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

4 Quantity Setting Firms Supply Side Cournot Competition At the optimum P = MC P (Q)θ C q i where P (Q) is the slope of inverse demand, θ C = Q q i = 1 + q j q i is the conjectural variation (not elasticity). θ C = 1 Cournot-Nash. ( q j q i = 0) θ C = 0 Perfect Comp. ( q j q i = 1) θ C = N Cartel (Symmetry) ( q j q i = 1) Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

5 Price Setting Firms Supply Side Bertrand Competition Bertrand Model: Bertrand competition refers to a model of oligopoly in which two or more firms compete by simultaneously setting prices. A price setting game can be formalized as: Players: n 2 players (firms), i,..., n Actions: Each firm simultaneously sets price p i P i = [0, ] Payoffs: π i (p i, p i ) = p i D(p i, p i ) C i (D(p i, p i )) Under assumption of profit maximization A Bertrand Nash equilibrium is a vector of prices (pi, p i ) such that for each player i, Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

6 Supply Side Bertrand Competition Price Setting Firms Bertrand equilibrium with differentiated products is simply the solution to the system of first-order conditions implied by each firms profit-maximizing pricing decision. Let output of each firm denoted as: Firm i s profit maximization problem is given as: Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

7 Supply Side Bertrand Competition Price Setting Firms P i = MC q i / dq i dp i where dq i dp i dq i dp i = q i p i p i p i + q i p j p j p i = q i p i + q i p j θ B θ B = 0 Bertrand-Nash. (p i = MC q i / q i p i ) θ B = Perfect Comp. p i = MC θ B = 1 Cartel (Symmetry) (p i = MC q i /( q i p i + q i p j )) Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

8 Demand Side Homogeneous Product Markets NEIO models are typical examples of structural market equilibrium models for homogeneous product markets. Empirical applications use macro (aggregate) data Demand side: Typically a single product demand curve is estimated Supply side: A model of Cournot competition is employed Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

9 Demand Side Differentiated Product Markets Could refer to vertical or horizontal differentiation Empirical applications use brand and/or individual level data Demand side: Requires a demand system estimation of competing brands Supply side: A model of Bertrand competition is employed Wide range of applicability of these models in IO and Marketing: Analysis of competition Market power Price discrimination Advertisement Merger analysis Analysis of consumer behavior Sensitivity to price Valuation of product attributes Brand loyalty Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

10 Demand Side Demand system models: The dimensionality problem Suppose we have observations of the same 50 brands of ice cream from 50 cities, 2500 data points. We also have data on 4 product and 6 consumer characteristics. We seek to estimate bulk ice cream demand elasticity. We can take a classical demand system approach, i.e. AIDS model. This would require: Estimating a total of 2500 own and cross price elasticities, using 2500 data points Even with symmetry, homogeneity and adding up restrictions estimation would be impractical Instead we can work in product characteristics space rather than product space (discrete choice models): Redefine consumer s utility as a function of product characteristics Redefine consumer s problem as a probability of buying a particular product rather than how much to buy Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

11 Demand Side Random Utility Models, RUM Random Utility Models RUMs describe the relation of explanatory variables to the outcome of a choice, without reference to exactly how the choice is made. Agent i, i = 1,..., n is assumed to make a choice among j = 1, 2,..., J possible alternatives. Agent i chooses the alternative that provides the greatest utility, U ij > U ik j k Researcher observes the choice and its attributes, x ij, but not the utility Therefore, the utility is assumed to be represented additively as the sum of a partially observable part, V ij, and an unobservable part, ɛ ij, such that Usually we ll assume V ij = x ij β Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

12 Demand Side Random Utility Models, RUM Random Utility Models Let f(ɛ i ) denote the joint density of random vector ɛ i = (ɛ i1,..., ɛ ij ). The probability that agent i chooses alternative j is: This cumulative distribution is the probability of each random term ɛ ik ɛ ij is below observed quantity V ij V ik. Since the joint density of random errors is f(ɛ i ), we can rewrite as: where I is indicator function equal to 1 if the term in parentheses is true. The model collapses to logit if f(ɛ i ) is i.i.d. extreme value The model collapses to probit if f(ɛ i ) is multivariate normal Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

13 Demand Side Multinomial Logit Multinomial Logit Logit model is derived by assuming error terms follow a Type I extreme value distribution. Specifically, assume that the errors are independent across i and j with a density function: f(ɛ ij ) = exp( ɛ ij )exp( e ɛ ij)), and the cumulative function F(ɛ ij ) = exp( e ɛ ij)) By this assumption the logit probability of individual i choosing alternative j is Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

14 Demand Side Multinomial Logit Estimation Likelihood function: L(β) = n J i=1 j=1 (P ij) Y ij where Y ij =1 if person i selects j and zero otherwise. The loglikelihood is: L(β) = n J i=1 j=1 Y ij(x ij β log[ J j=1 exp(x ijβ)]) where V ij = x ij β. The score is L β (β) = i j (Y ij P ij )x ij ) Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

15 Demand Side Multinomial Logit Independence of Irrelevant Alternatives, IIA MNL model is subject to IIA problem. Take 2 alternatives k and l P ik P il = [exp(v ik )/ j l=1 exp(v il][exp(v il )/ j l=1 exp(v il] 1 That is, the ratio of probabilities are unaffected from any other outside alternatives. Because they cancel at the ratio. This imposes restrictions on substitution patterns Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

16 Demand Side Multinomial Logit Independence of Irrelevant Alternatives, IIA The reason for IIA problem is i.i.d errors not the logit itself The problem is that consumer characteristics are independent of the observed product The solution to this problem can be interacting consumer characteristics with product characteristics Nested Logit Mixed Logit Multinomial Probit Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

17 Empirical Application Nevo, 2001, Econometrica RTE industry is a classic example of a concentrated differentiated-products industry: high concentration high price-cost margins large advertising to sales ratio aggressive introduction of new products The paper analyzes price competition by estimating the true economic price-cost margins (PCM) and distinguishing between three sources: firm s ability to differentiate its brands from those of its competitors portfolio effect (ability to charge more by producing imperfect substitutes) price collusion Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

18 Empirical Application Nevo, 2001, Econometrica The steps of estimation are: estimate the demand function (random coefficient logit model) as a function of observed product characteristics, unobserved product characteristics, and unknown parameters Compute PCM implied by three industry structures by using demand elasticities single product firms multi-brand oligopolistic firms multi-brand monopolistic firm Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

19 Empirical Application Supply side Empirical Framework: Supply Side Suppose there are F firms, each of which produces some subset, Γ j, of the j = 1,..., J different brands. define Ω = 1 if f : (r, j) Γ f, Ω = 0 otherwise. then Ω jr = Ω S jr where S jr = s r (p) p j s(p) Ω(p mc) = 0 Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

20 Empirical Application Supply side Empirical Framework: Supply Side Notice the resemblance to the simple Bertrand Model θ B = 0 Bertrand-Nash. (P i = MC q i / q i P i ) θ B = Perfect Comp. P i = MC θ B = 1 Cartel (Symmetry) (P i = MC q i /( q i P i + q i P j )) Ownership matrix allows to estimate different market structures. If none of the products are within the same subset it is single-product Bertrand-Nash If some of the products are within the same subset it is multi-product Bertrand-Nash If all of the products are within the same subset it is collusion Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

21 Empirical Application Demand side Empirical Framework: Demand Side Multinomial Logit: The estimation of the demand curves using random coefficient logit model is not an easy task. To better understand the procedure we first focus on estimation via multinomial logit. Let the utility of consumer i from choosing alternative j in town t is given by the equation: where i = 1,..., N, j = 1,..., 50, t = 1,..., 50 p jt observed price of product j in town t, x jt is 4 dimensional observed product characteristics, ξ jt is the unobserved product characteristics, ɛ ijt is mean zero error term Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

22 Empirical Application Demand side Empirical Framework: Demand Side Multinomial Logit: Since the coefficients are the same for all consumers we can obtain an aggregate utility function Assuming ɛ jt is i.i.d extreme value, the market share of product j is given by Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

23 Empirical Application Demand side Empirical Framework: Demand Side Multinomial Logit: Elasticities of Demand s jt = e x jt β αp jt +ξ jt ex kt β αp kt +ξ kt We seek to obtain s jt p kt. Let G j = e x jt β αp jt +ξ jt s jt = s jt p kt = If k j then G j G k G j p kt G k s jt 0 p kt = G k ( s jt p kt = α ( ) ( ) G + j (1+ Gk 50 1 G k ) 2 p kt ( + G j ( G k ) ) G j ( G k ) 2 ) ( G k ( G k ) ( αg k ) ) so that Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

24 Empirical Application Demand side Empirical Framework: Demand Side Multinomial Logit: Elasticities of Demand s jt p kt ( = α G j ( G k ) ) ( G k ( G k ) ) Products with higher shares are close substitutes regardless of content similarly it can be shown that if If k = j then Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

25 Empirical Application Demand side Empirical Framework: Demand Side Random Coefficient Logit u ijt = x j β i α i p jt + ξ j + ξ jt + ɛ ijt individual heterogeneity is captured as deviations from mean value: α i = α + ΠD i + Σv i β i = β + ΠD i + Σv i v i N(0, I K+1 ) Note that coefficients are functions of demographic variables and unobserved component v i Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

26 Empirical Application Demand side Empirical Framework: Demand Side Random Coefficient Logit Let θ = (θ 1, θ 2 ) where θ 1 = (α, β) and θ 2 = (vec(π), vec(σ)) then the utility can be rewritten as deviations from mean u ijt = δ jt (x j, p jt, ξ j, ξ jt ; θ 1 ) + µ ijt (x j, p jt, v i, D i ; θ 2 ) + ɛ ijt δ jt = x j β i α i p jt + ξ j + ξ jt Component of utility from alternative j that is same across all consumers µ ijt = [p jt, x j ] (ΠD i + Σv i ) component of utility from alternative j that is individual specific Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

27 Empirical Application Demand side Empirical Framework: Demand Side Random Coefficient Logit: Market Shares Under the assumption of Type I extreme value for ɛ ijt the market share s ijt is given by: s ijt = ν D e δ jt +µ ijt eδ jt +µ ijt s jt (x, p t, δ t ; θ 2 ) = [ ν] D dp (D, v, ɛ) = dp (v)dp (D) e δ jt +µ ijt eδ jt +µ ijt Integral can be evaluated by simulation to obtain shares. It adds up the market shares of different types of consumers based on distribution of types. Nevo (2000a): A Practitioner s Guide to estimation of Random Coefficients Logit Models of Demand, Journal of Economics and Management Strategy, 9, Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28

28 Empirical Application Demand side Empirical Framework: Demand Side Random Coefficient Logit: Elasticities of Demand Own price elasticity, j = k, η jkt = p jt s jt ν D α is ijt (1 s ijt )dp (v)dp (D) Cross price elasticity, j k, η jkt = p kt s jt ν D α is ijt s ikt dp (v)dp (D) Metin Cakir (Purdue) Market Equilibrium Models December 6, / 28