ECO 2901 EMPIRICAL INDUSTRIAL ORGANIZATION

Transcription

1 ECO 2901 EMPIRICAL INDUSTRIAL ORGANIZATION Lecture 7 & 8: Models of Competition in Prices & Quantities Victor Aguirregabiria (University of Toronto) Toronto. Winter 2018 Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

2 Introduction Introduction Main source of strategic interactions between firms comes from firms price and quantity decisions. Models of competition where firms choose prices or quantities are at the core of IO. Main motives to estimate these models: 1. Complete supply / demand equilibrium model: counterfactuals such as mergers, taxes/subsidies; trade liberalization; etc. 2. of firms marginal costs 3. Identification/estimation of the Nature of Competition: firms beliefs about the strategies or response of their rivals. 4. Help to deal with measurement problems in the estimation of PF: De Loecker (2011); Orr (2017). Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

3 Introduction Equilibrium model of demand & supply The answer to many economy questions in IO require the consideration of and equilibrium model of demand and supply. E.g., effects of competition on consumer welfare and profits; effects of a new policy; mergers; etc. A common approach to answer these questions is: (a) estimate demand and supply parameters; (b) construct counterfactual versions of the models that can be used to measure the causal effect of interest, and obtain the counterfactual equilibrium. E.g., Counterfactuals: (a) model without the policy change; (b) model with an hypothetical merger. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

4 of firms costs Introduction In many applications, researches do not have direct information on firms costs. A common approach to estimate firms costs is based on the specification and estimation of a model of competition, e.g., Cournot, Bertrand, Stackelberg, Monopolistic Competition, Collusion,... The model predicts that for every firm i, MR i = MC i, where the concept of MR i depends on the assumed model of competition. Based on a estimation of demand, we can construct estimates of MR. Then, the FOC implies estimates of MC. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

5 Introduction of firms costs (2) We use this sample of realized MCs to estimate the marginal cost function, and in particular how the marginal cost depends on: - output of different products (economies of scale / scope); - capacity; - historical cumulative output (i.e., learning by doing); - geographic distance between the firm s production plants (i.e., economies of density) -... Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

6 Introduction Estimating the "Nature of competition" The estimation of MCs is typically based on an assumption about competition: about the nature of competition in an industry. Nature of competition: how firms compete with each other: - is the product homogeneous or differentiated? - do firms compete in prices or in quantities? - what does a firm believe about strategy/response of other firms? - is there collusion between some or all the firms? Example: Nash-Cournot competition. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

7 Introduction Estimating the "Nature of competition" (2) Assumptions on "beliefs" and "no collusion / collusion" may be diffi cult to justify. They have important implications on our estimates of firms costs, on our interpretation of competition, and on our predictions using the model. We would like to learn from our data about the nature of competition. This is the purpose of the conjectural variation approach. This approach tries to estimate simultaneously firms costs and a set of parameters (i.e., conjectural variation parameters) that represent firms believes and that describe the nature of competition in the industry. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

8 Outline Outline 1. Introduction 2. Empirical Cournot models 2.1. Model and 2.2. Detecting collusion using estimates of PF 3. Empirical Bertrand models of product differentiation 3.1. Model and 3.2. Detecting collusion using estimates of PF 4. Conjectural variation approach 4.1. Homogeneous product industry 4.2. Differentiated product industry Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

9 Main References Outline Bresnahan, T. (1982): The Oligopoly Solution Concept is Identified, Economics Letters, 10, Bresnahan, T. (1987): Competition and Collusion in the American Automobile Market: The 1955 Price War, Journal of Industrial Economics, 35, Corts, K. (1999): Conduct Parameters and the Measurement of Market Power, Journal of Econometrics 88 (2), Genesove, D. and W. P. Mullin (1998): Testing static oligopoly models: Conduct and cost in the sugar industry, The Rand Journal of Economics 29 (2), Nevo, A. (2001): Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, 69 (2), Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

10 Cournot: Empirical Cournot models Model Model Homogenous product such as sugar. N firms active in the industry. The variable profit of firm i is ( ) Π i = p Q; X D, ε D q i C (q i ; Z i, ω i ) Firm i believes Q i q i = 0. The optimal response q i : MR i = MC (q i ; Z i, ω i ) where MR i p ( Q; X D, ε D ) + p(q;x D,ε D ) Q q i. These conditions characterize the equilibrium output of each firm as a function of the exogenous variables (X D, ε D, Z i, ω i : i = 1, 2,...N). Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

11 Cournot: Empirical Cournot models The researcher has data from M markets: { } Data = q im, Z im, Xm D : i = 1,..., N m ; m = 1,..., M Suppose that the demand function has been estimated in a fist step, such that there is a consistent estimate p(.) of the demand function, and an estimated residual ε D m of the error term in each firm-market. The researcher can construct consistent estimates of marginal revenues as: ( ( MR im = p Q m ; Xm D, ε ) D m + p Q m ; Xm D, ε ) D m q im Q Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

12 Empirical Cournot models Cournot: (2) We can also write the estimated MR as: MR im = p m [ 1 1 η D m q im Q m ] where η D m is the estimate of the elasticity of demand at market m. The marginal revenue of a Cournot firm depends on: - Market price (positively) - The market elasticity of demand (positively) - The firm s market share (negatively) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

13 Empirical Cournot models Cournot: (3) Consider a power specification of a firm s variable cost function: C (q i ; Z i, ω i ) = 1 γ + 1 qγ+1 i exp{z i α + ω i } such that MC (q i ; Z i, ω i ) = q γ i exp{z i α + ω i }. The econometric model is: ) ln ( MR im = γ ln (q im ) + Z im α + ω im We are interested in the estimation of the parameters α and γ. γ measures the degree of diseconomies of scale (γ > 0) or economies of scale (γ < 0). Firms relative effi ciency, Z im α + ω im, and of its sources Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

14 Empirical Cournot models Cournot: (4) The model implies that E (ln (q im ) ω im ) < 0, so OLS will provide a (downward) bias estimate of γ. Under assumption E (Z jm ω im ) = 0 for any (i, j), a natural approach to estimate this model is using GMM based on moment conditions that use the characteristics of other firms as an instrument for output. ([ ] Z [ ) E im ln ( MR j =i Z im γ ln (q im ) Z im α] ) = 0 jm Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

15 Empirical Cournot models Cournot: (5) An alternative specification: ω im = ω m (1) + ω (2) im, where the market fixed effect ω m (1) may be correlated with the observable exogenous variables Z, e.g., more profitable markets may attract firms with different variables Z (more effi cient firms). In this model, the moment conditions shows be constructed for the equation in deviations with respect to the market means, i.e., ( [ ] [ ]) Z E im ) ln ( MR j =i Z im γ ln (q im ) Z im α = 0 jm Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

16 Detecting collusion Empirical Cournot models Homogeneous product industry. The researcher has estimated the PF using data on firms inputs and output. Function MC (q i ; Z i, ω i ) is already estimated. Demand is also estimated. Suppose all the firms are colluding. Then, for every i: MR Collusion m [ where MRm Collusion = p m 1 1 η D m ]. = MC im Hypothesis 1: Cournot. [ It implies ] MRim Cournot MC im = 0, where MRim Cournot p m 1 1 q im η D Q m m Hypothesis 2: Collusion. [ It] implies MRm Collusion MC im = 0, where MRm Collusion p m 1 1 η D m Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

17 Empirical Cournot models Detecting collusion [2] These two hypothesis are non-nested. We can use Vuong (1989) non-nested test to choose between these models. [This is the approach in Gasmi, Laffont, and Vuong (JEMS, 1992) to test collusion in soft-drinks industry]. Let y (1) im Define: ln(mrcournot im /MC im ) and y (2) im ln(mrcollusion m /MC im ). where S j = (MN) 1 i,m [ Z = S 1 S 2 MN S12 y (j) im [ S 12 = (MN) 1 i,m y (1) im y (2) im ] 2, and Under the null that model 1 [Cournot] is correct, Z is (asymp) standard normal. ] 2. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

18 Empirical Bertrand models of product differentiation Bertrand: Model Model Differentiated product. N firms, each firm sells 1 product. The variable profit of firm i is Π i = p i q i (p, X, ξ) C (q i (p, X, ξ); X i, ω i ) Firm i believes p i p i = 0. The optimal response p i : q i + p i q i (p, X, ξ) p i = MC (q i ; X i, ω i ) q i (p, X, ξ) p i That can be written as MR i = MC i ] 1 MR i p i [1 η D i (p, X, ξ) where η D i (p, X, ξ) is the demand elasticity. = MC (q i ; X i, ω i ) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

19 Empirical Bertrand models of product differentiation Bertrand: Model (2) Model The F.O.C. can be also written as: p i = MC i + m i (p, X, ξ) where m i (p, X, ξ) is the equilibrium price-cost margin for firm i, that is equal to: p i m i (p, X, ξ) = η D i (p, X, ξ) Note that the (actual) equilibrium price cost margin can be calculated given the demand, without knowing the cost parameters. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

20 Empirical Bertrand models of product differentiation Bertrand: The researcher has data from J products (alternatively, there may be also M markets): Data = {p i, X i : i = 1,..., J} Suppose that the demand function has been estimated in a fist step, such that there is a consistent estimate q i (.) of the demand system, and estimated residuals ξ i of the unobserved product characteristics in demand. The researcher can construct consistent estimates of marginal revenues as: ] 1 MR i = p i [1 η D i (p, X, ξ) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

21 Empirical Bertrand models of product differentiation Bertrand: (2) Consider a power specification of a firm s variable cost function: C i = 1 γ + 1 qγ+1 i exp{x i α + ω i } such that MC i = q γ i exp{x i α + ω i }. The econometric model is: ) ln ( MR i = γ ln (q i ) + X i α + ω i We are interested in the estimation of the parameters α and γ. γ measures the degree of scale diseconomies (γ < 0) or economies (γ > 0). Firms relative effi ciency, X i α + ω i, and of its sources. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

22 Empirical Bertrand models of product differentiation Bertrand: (3) The model implies that E (ln (q i ) ω i ) = 0, so OLS will provide (downward) bias estimates of γ. Under assumption E (X j ω i ) = 0 for any (i, j), a natural approach to estimate this model is using GMM based on moment conditions that use the characteristics of other firms as an instrument for output. ([ ] X [ ) E i ln ( MR j =i X i γ ln (q i ) X i α] ) = 0 j Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

23 Empirical Bertrand models of product differentiation Bertrand: Multiproduct Firms There are F firms indexed by f. Each firm produces a set of differentiated products, J f. The variable profit of firm f is: Π f = j J f [p j MC j ] q j (p, X, ξ) where here, for simplicity, we assume that marginal costs are constant (CRS). The firm believes that p f = 0. But it takes into account the p f substitution (cannibalization) effects between the products that it sells: i.e., reducing the price of its own product j reduces the demand of its other products k = j. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

24 Empirical Bertrand models of product differentiation Bertrand: Multiproduct Firms. F.O.C. The F.O.C. for firm f product j: [ s j + (p j MC j ) s ] j p j + + (p k MC k ) s k = 0 p k J f ; k =j j The second term captures the cannibalization effects between the own products that the firm internalizes when it decides its optimal prices. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

25 Empirical Bertrand models of product differentiation Multiproduct as source of market power We can write F.O.C. for firm f product j as: p j MC j = + [ ] 1 sj s j p j [ ] [ ] 1 sj p j (p k MC k ) s k p k J f ; k =j j With substitutes, the second term is positive. Selling multiple products contribute to increase the price-cost margin of each of the products. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

26 Empirical Bertrand models of product differentiation Multiproduct as source of market power [2] As an example, consider the standard logit model of demand. We have s j p j = α s j (1 s j ) and s k p j = α s j s k, such that: p j MC j = [ ] 1 α(1 s j ) + 1 α(1 s j ) (p k MC k ) α s k k J f ; k =j Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

27 Empirical Bertrand models of product differentiation Bertrand: Multiproduct Firms. Equilibrium We can write these F.O.C. as follows: [p f MC f ] s f p j = s j where [p f MC f ] is the vector of price-cost margins for firm f, and s f is the vector of partial derivatives. p j And the vector of firm f best response prices is: [ ] 1 sf p f = MC f + p f s f If we know demand and MCs, we can use this system of equations to compute equilibrium prices. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

28 Empirical Bertrand models of product differentiation Bertrand: Multiproduct Firms. Model implies that: [ ] 1 sf MC f = p f p f s f We can construct the vector of marginal revenues as [ ] 1 sf p f p f s f. Then, we can estimate the structure of the marginal costs: e.g., ) ln ( MR j = γ ln (q j ) + X j α + ω j Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

29 Nevo (2001) on Cereals Nevo (2001) Ready-to-Eat (RTE) cereal market: highly concentrated; many apparently similar products, and yet price-cost margins (PCM) are high. What are the sources of market power? Product differentiation? Multi-product firms? Collusion? Nevo: (1) estimates a demand system of differentiated products for this industry; (2) recovers PCMs and compare them to rough/aggregate estimates of PCM at the industry level; (3) based on this comparison, tests Bertrand vs (full) Collusion [and rejects collusion]; (4) Under Bertrand, compares estimated PCMs with the counterfactual with single-product firms. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

30 Nevo (2001): Data Nevo (2001) A market is a city-quarter. IRI data on market shares and prices. 65 cities x 20 quarters [Q188-Q492] x 25 brands [total share is 43-62%]. Most of the price variation is cross-brand (88.4%), the remainder is mostly cross-city, and a small amount is cross-quarter. Relatively poor brand characteristics so model includes brand fixed effects. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

31 Nevo (2001) Nevo (2001): Identification of demand Specification of unobserved demand ξ jmt : controls for ξ (1) jm ξ jmt = ξ (1) jm + ξ(2) t + ξ (3) jmt and ξ(2) t using fixed effects. Instrument for p jmt : average prices in other local markets in the same region as market m (R m ): p j( m)t = 1 R m p jm m R m ; m =m t Assumption: After controlling for brand-city fixed effects, all the correlation between prices at different locations comes from correlation in costs, and not from spatial correlation in demand shocks. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

32 Nevo (2001) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

33 Nevo (2001) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

34 Nevo (2001) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

35 Nevo (2001) Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

36 Conjectural variation approach Conjectural variation: Model Homogeneous product industry We first consider the CV model in an homogeneous product industry. The variable profit of firm i is ( ) Π i = p Q; X D, ε D q i C (q i ; Z i, ω i ) Suppose that firm i believes that Q i = θ i, where θ i is a parameter q i that represents the believes of firm i. The "perceived" MR of firm i is: ( ) MR i = p Q; X D, ε D + p ( Q; X D, ε D ) [1 + θ i ] q i Q If we treat these beliefs θ i as exogenous, we can define an equilibrium where q i is a function of the exogenous variables (X D, ε D, θ i,z i, ω i : i = 1, 2,...N). Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

37 Conjectural variation approach Homogeneous product industry Conjectural variation: Model (2) F.O.C: where MR i = P + p Q [1 + θ i ] q i. MR i = MC (q i ; Z i, ω i ) The value of the parameters {θ i } are related to the "nature of competition", i.e., Cournot, Perfect Competition, Bertrand, Stackelberg, or Cartel (Monopoly). PC / Bertrand no diff: θ i = 1; MR i = P Cournot: θ i = 0; MR i = P + p Q q i Cartel n < N firms: θ i = n 1; MR i = P + p Q n q i Cartel all firms: θ i = N 1; MR i = P + p Q N q i Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

38 CV: Conjectural variation approach The researcher has data from M markets: { } Data = q im, Z im, Xm D : i = 1,..., N m ; m = 1,..., M It may not be panel data (firms are different in each market). Suppose that the demand function has been estimated in a fist step, such that there is a consistent estimate p(.) of the demand function, and an estimated residual ε D m of the error term in each market. The researcher can construct estimates: ( δ m = p Q m ; Xm D, ε ) D m Q Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

39 Conjectural variation approach CV: (2) Consider the variable cost function: C i = 1 γ + 1 qγ+1 i such that MC i = q γ i [α 0 + Z i α 1 ] + ω i. [α 0 + Z i α 1 ] + ω i The econometric model is: ] P m (1 + θ im ) [ δ m q im = q γ im [α 0 + Z im α 1 ] + ω im We are interested in the estimation of the parameters α s, γ, and θ im. We need to impose some restrictions on θ im. The most common restriction is θ im = θ at every observation (i, m). Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

40 Conjectural variation approach CV: (3) [P m δ m q im ] ] = θ [ δ m q im + α 0 q γ im + α [ 1 Zim q γ ] im + ωim We have an additional identification problem. Firm s output q im is regressor associated both to the CV parameter θ and to the parameters in the MC. To make the discussion simpler consider: ] ] [P m δ m q im = θ [ δ m q im + α 0 q im + α 1 [Z im q im ] + ω im Victor Aguirregabiria () Empirical IO Toronto. Winter / 41

41 Conjectural variation approach CV: (4) [P m δ m q im ] ] = θ [ δ m q im + α 0 q im + α 1 [Z im q im ] + ω im To identify the parameters in the model we need not only instruments for q im, but we also need the following type of exclusion restrictions: 1. The slope of the inverse demand curve δ m cannot be constant (no linear demand) and it should depend on exogenous variables; 2. The exogenous variables affecting δ m should not be collinear with Z im or with {Z jm : j = i}. Example: Genesove and Mullin (RAND, 1988), seasonality in the demand of sugar that does not affect production costs. Victor Aguirregabiria () Empirical IO Toronto. Winter / 41