ECO 2901 EMPIRICAL INDUSTRIAL ORGANIZATION

Transcription

1 ECO 2901 EMPIRICAL INDUSTRIAL ORGANIZATION Lecture 1: Introduction to the Course Victor Aguirregabiria (University of Toronto) Toronto. Winter 2016 Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

2 Organization of the Course Organization of the Course Class Meetings: Fridays, 9:00-11:00am; room GE minutes break at 10am Offi ce hours: Tuesdays and Thursdays 3:00-4:00pm Evaluation: Problem Set (50%); Final Exam (50%) I expect that you: (1) attend every class meeting; (2) read the papers/material before each lecture; (3) participate in class; (4) go through class notes and understand them; (5) do the problem set on time; (6) prepare for the final exam. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

3 Organization of the Course A General Description of this Course This courses deals with models, methods, and empirical applications in Industrial Organization (IO). IO deals with the behavior and competition of firms in markets. In Empirical IO, we use data (i.e., prices, quantities) and models to understand the factors that determine consumer and firm behavior in markets. This course emphasizes the need to combine data, models, and econometric techniques to understand how markets operate. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

4 Topics Organization of the Course 1. Introduction to Empirical IO 2. Estimation of Production Functions 3. Demand Estimation 4. Static Models of Cournot and Bertrand Competition 5. Empirical Models of Market Entry 6. Dynamic Structural Models of IO 7. Single-Agent Models of Firm Behavior 8. Structural Models of Dynamic Demand 9. Dynamic Games of Oligopoly Competition Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

5 Lecture 1: Introduction to Empirical IO: Outline Lecture 1: Introduction to Empirical IO: Outline 1. Some Basic Ideas in IO 2. Data in Empirical IO 3. Specification of a Structural Model in EIO 4. Equilibrium and Comparative Statics 5. Identification and Estimation 6. Extension and the Rest of the Course Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

6 Some Basic Ideas in IO Some Basic Ideas in IO (1) IO studies the behavior of firms in markets, their strategic interactions, and the implications on profits and consumer welfare. Some examples of type of firm decisions that we study in IO are: - Price and Quantity choice; - Investment in capacity, inventories, physical capital,...; - R&D, patents; - Advertising; - Geographic location of plants and stores; - Product design; - Entry in new markets; - Adoption of new technologies; - Vertical relationships; Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

7 "New" Empirical IO "New" Empirical IO Emphasizes the need to: [1] Study competition separately for each industry. Industries are very heterogeneous in their exogenous characteristics. There is not a common relationship between market power and concentration across industries. [2] Use micro-level data of individual firms, products, and markets, on prices, quantities, number of firms, and exogenous characteristics affecting demand or costs. [3] Estimate structural models of consumer and firm behavior. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

8 Specification of a Structural Model in Empirical IO Specification of a Structural Model in EIO (1) To study competition in an industry, EIO researchers propose and estimate structural models of demand and supply. What is an structural model in empirical IO? Models of consumer and firm behavior where consumers are utility maximizers and firms are profit maximizers. The parameters are structural in the sense that they describe consumer preferences, production technology, and institutional constraints. Under the principle of revealed preference, these parameters are estimated using micro data on consumers and firms choices and outcomes. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

9 Specification of a Structural Model in Empirical IO Specification: Typical Structure of IO Models 1. Model of consumer behavior (Demand) - Product differentiation? 2. Model for firms costs - Economies of scale; Economies of scope? Entry costs? Investment costs? 3. Equilibrium model of static competition - Price (Bertrand), Quantity (Cournot). 4. Equilibrium model of market Entry-Exit 5. Equilibrium model of dynamic competition - Investment, advertising, quality, product characteristics, stores, etc. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

10 Specification of a Structural Model in Empirical IO Specification: Example Example based on Ryan (Econometrica, 2012). We start with an empirical question. US cement industry. Evaluation of the effects in this industry of the 1990 Amendments to the Air Clean Act. The new law restricts the amount of emissions a cement plant can make. It requires the adoption of a "new" technology that implies lower marginal costs but larger fixed costs than the "old" technology. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

11 Specification of a Structural Model in Empirical IO Specification: Key Characteristics of the Industry The model here, though simple, incorporates some important features of the cement industry. 1. Homogeneous product. (We abstract from spatial differentiation). 2. Substantial fixed costs from operating a plant (cement furnace). 3. Variable costs increase in a convex way when output approaches full capacity. 4. Capacity investment is an important strategic variable. 5. Industry is very local (due to high transportation costs per dollar value). It can be characterized as a set of many "isolated" local markets. 6. Oligopolist industry. Small number of firms at a local market. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

12 Specification of a Structural Model in Empirical IO Specification: Data The specification of the model depends importantly on the data that is available for the researcher. M local markets (e.g., towns) observed over T consecutive quarters. We index markets by m and quarters by t. For every market-quarter observation, the dataset contains information on: the number of plants operating in the market (N mt ), aggregate amount of output produced by all the plants (Q mt ), market price (P mt ), and some exogenous market characteristics, population, average income, etc (X mt ). Data = { P mt, Q mt, N mt, X mt : m = 1, 2,..., M; t = 1, 2,..., T } Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

13 Specification of a Structural Model in Empirical IO Specification: Structure of the model Our model of oligopoly competition has four main components: (a) demand equation; (b) cost function; (c) model of Cournot competition; (d) model of market entry. An important aspect in the construction of an econometric model is the specification of unobservables. In general, the richer the specification of unobservables in a model, the more robust the empirical findings. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

14 Specification of a Structural Model in Empirical IO Specification: Demand Equation Demand is linear in prices and in parameters. ( ) Q mt = Smt β 0 + β X X D mt β 1 P mt + ε D mt β 0 and β 1 0 are parameters. S mt represents true demand size. S mt S mt exp{ε S mt} ε S mt and ε D mt are random variables with zero mean. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

15 Specification of a Structural Model in Empirical IO Specification: Demand Equation (2) For some of our derivations it is convenient to represent demand using the inverse demand curve: P mt = A mt B mt Q mt where A mt β 0 + β X X mt + ε D mt β 1 B mt 1 β 1 S mt Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

16 Specification of a Structural Model in Empirical IO Specification: Cost Function Every firm, either an incumbent or a potential entrant, has the same cost function: C (q imt ) = VC mt (q) + FC mt The Variable Cost is quadratic: VC mt (q) = ( γ MC 1 + γ MC X XMC mt with γ MC 1, γ MC X, and γmc 2 0 are parameters. The marginal cost is: where MC mt γ MC 1 + γ MC X The Fixed Cost is: MC mt (q) = MC mt + γ MC 2 q XMC mt + ε MC mt FC mt = γ FC 1 + γ FC X + ε MC ) γ MC mt q q2 is the exogenous MC. XFC mt Victor Aguirregabiria () Empirical IO Toronto. Winter / 40 mt + ε FC

17 Specification of a Structural Model in Empirical IO Specification: Cournot Competition Suppose that there are N mt plants active in local market m at quarter. We assume that firms active in a local market compete with each other ala Cournot. The profit function of a firm is: Π mt (q, Q) = P mt (q + Q) q VC mt (q) FC mt This best response output is characterized by the following condition of optimality: P mt + P mt(q + Q) q q = MC mt (q) An given our specification of demand and costs, this condition implies: A mt MC mt q mt (N) = B mt (N + 1) + γ MC 2 Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

18 Specification of a Structural Model in Empirical IO Specification: Cournot Competition (2) The equilibrium price-cost margin is, ( ) P mt AVC mt = B mt + γ MC 2 /2 q mt (N) And the Cournot equilibrium profit of an active firm (with N firms in the market) is: Πmt(N) = ( B mt + γ MC 2 /2 ) ( ) 2 A mt MC mt B mt (N + 1) + γ MC FC mt 2 This Cournot equilibrium profit function is continuous and strictly decreasing in the number of active firms, N. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

19 Specification of a Structural Model in Empirical IO Specification: Model of Market Entry The equilibrium entry condition establishes that every active firm and every potential entrant is maximizing profits. Active firms should be making non-negative profits: Π mt(n mt ) 0. Potential entrants are not leaving positive profits on the table: Π mt(n mt + 1) < 0. There is a unique value of N that satisfies the equilibrium conditions Π mt(n) 0 and Π mt(n + 1) < 0. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

20 Specification of a Structural Model in Empirical IO Specification: Model of Market Entry (2) Let Nmt be the real number that (uniquely) solves the condition Πmt(N) = 0. ) Nmt (1 + γmc 2 + ( ) 1 + γ A mt MC 2 /2B mt MC mt B mt FC mt B mt The equilibrium number of firms is the largest integer that is smaller than N mt: N mt = int(n mt) The entry equilibrium condition, Π mt(n mt) = 0, is equivalent to: (q mt ) 2 = ( N mt ) 2 FC mt int(nmt) B mt + γ MC 2 /2 Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

21 Specification of a Structural Model in Empirical IO Structural Equations The model can be described as a system of three equations with three endogenous variables, N, P, and q Q/N, Demand equation: P = A B N q Cournot Equilibrium Condition: q = Entry Equilibrium Condition: q 2 = A MC B (N + 1) + γ MC 2 FC B + γ MC 2 /2 where A, B, MC, γ MC 2, and FC are exogenously given. This system of equations is denoted as the structural equations of the model. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

22 Equilibrium: Existence and uniqueness Reduced Form Equations This is a system of simultaneous equations. The solution to this system of equations determines the value (or values) of the endogenous variables {N, P, q} for given values of the exogenous variables X and ε (ε D, ε S, ε MC, ε FC ), and the structural parameters θ {β s, γ MC s, γ FC s}. N = f N (X, ε, θ) q = f q (X, ε, θ) P = f P (X, ε, θ) This system of equations is denoted as the reduced form equations of the model. The model has well-defined reduced form functions/equations if for every value of (X, ε, θ) an equilibrium exists and it is unique. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

23 Equilibrium: Existence and uniqueness Equilibrium Existence and Uniqueness Given the assumptions of our model, we have that for every value of (X, ε, θ) an equilibrium exists and it is unique. Entry equilibrium condition determines q, FC q = B + γ MC 2 /2 Plugging q into Cournot eq. condition, we get: ) N = (1 + γmc 2 + ( A MC ) 1 + γ MC 2 /2B B FC B And plugging these expressions for N and q in the demand equation we obtain the equilibrium price: FC P = MC + (γ MC 2 + B) B + γ MC 2 /2 Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

24 Identification and Estimation Identification The researcher wants to use data and this model to estimate the vector of structural parameters θ {β s, γ MC s, γ FC s}. Econometric model (without ε S mt): ( P mt 1 ) q mt β 1 S mt Q mt S mt = β X X D mt β 1 P mt + ε D mt = γ MC X X MC mt + γ MC 2 q mt + ε MC mt qmt 2 + β S 1 γ MC 2 q mt = γ FC X mt XFC mt + ε FC mt Assumption 1: Mean independence between exogenous observables and unobservables: E (ε mt X mt ) = 0 Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

25 Identification (2) Identification and Estimation We say the parameters of the model are identify if there is a feasible estimator of θ that is consistent in a statistical or econometric sense. A standard approach to prove identification consists in using the moment restrictions implied by the model to show that we can uniquely determine the value of θ as a function of moments that include only observable variables. For instance, in a classical linear regression model Y = X β + ε under the assumptions E(X ε) = 0 and E(X X ) is non-singular, we have that β = E(XX ) 1 E(XY ) such that this expression shows that the vector of parameters β is identified using data of Y and X. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

26 Identification and Estimation Endogeneity In our model, the mean independence assumption E(ε mt X mt ) = 0 is not suffi cient to identify the mode. The three structural equations include endogenous regressors. From the reduced form (equilibrium conditions of the model), we know that P mt, q mt, and N mt depend on the unobservables ε mt such that: E(ε mt P mt ) = 0 ; E(ε mt q mt ) = 0 ; E(ε mt N mt ) = 0 Therefore, OLS estimation of any of the structural equations, for instance demand Q mt S mt = β X X D mt β 1 P mt + ε D mt generates inconsistent estimates. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

27 Endogeneity (2) Identification and Estimation Under the mean independence assumption E(ε mt X mt ) = 0 we can estimate consistently "reduced form parameters". However, without further restrictions, the parameters that we can identify from the reduce form equations are not suffi cient to separately identify the structural parameters in demand, variable costs, and fixed costs. For instance, in the reduce form equation for N mt we have: ) N mt (1 + γmc 2 + ( ) A mt MC mt B mt 1 + γ MC 2 /2B mt FC mt B mt Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

28 Identification and Estimation Some identification approaches in empirical IO To identify the model we need more information, either in the form of data or/and additional restrictions in the model. Some identification approaches used in EIO include: 1. Randomized experiments 2. Exclusion restrictions (Instrumental Variables) 3. "Natural experiments" as exclusion restrictions 4. Restrictions on covariance-structure of unobservables 4a. Arellano-Bond instruments 4b. Hausman-Nevo instruments 4c. Zero-covariance between unobservables 5. Partial identification (bounds) Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

29 Identification and Estimation Randomized experiments The implementation of a randomized experiment is an ideal situation for the identification of an econometric model. However, the careful design of a useful randomized experiment is not a trivial problem. The structural model is a useful tool in the design of the randomized experiment. Suppose that we want to estimate first the demand equation. We need to design an experiment that generates sample variation in price that is not perfectly correlated with X mt it is independent of the unobserved demand shock ε D mt. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

30 Identification and Estimation Randomized experiments (2) Suppose that experiment consists in a firm subsidy per unit of output produced and sold in the market, τ mt τ mt is determined as random draw from some distribution. We need also to assume that the implementation of the experiment does not introduce any change in the behavior of consumers. Under these conditions, we have that E(τ mt ε D mt) = 0; no perfect collinearity between τ mt and X mt ; and E(τ mt P mt ) = 0. These conditions imply that we can use τ mt as an instrument for the P mt in the demand equation, to identify all the parameters in the demand. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

31 Identification and Estimation Randomized experiments (3) Possible issues. Agents behavior may change if they know that they are the subjects of an experiment. Firms may change the way they compete during the time that experiment is implemented. For instance, they may decide to agree not to change their levels of output such that the subsidy will not be pass-through to the price and they will keep the subsidy as a pure transfer. Most importantly, if some consumers are aware of the existence of this experiment, and given the temporary nature of the experiment, they may decide to buy cement for inventory. In that case, the experiment will affect the demand and the estimates of the demand parameters based on this randomized experiment will be biased. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

32 Identification and Estimation Exclusion restrictions (Instrumental Variables) In econometrics, the most common approach to deal with endogeneity problems is using instrumental variables. In a system of simultaneous equation, we can get instrumental variables if we impose exclusion restrictions: some exogenous variables do not enter into some structural equations. For instance, if X MC or/and X FC includes variables which are not in X D, then we can use these variables in (X MC,X FC ) as instruments for P mt in the estimation of the demand. For instance, the price of limestone and coal could be exclusion restrictions in our application. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

33 Identification and Estimation "Natural experiments" as exclusion restrictions Consider an unexpected natural shock at period t that affected the production cost of firms in a specific region. Let I mt be the indicator of the event market affected by the natural experiment. I mt = 1{t t } E m E m is the binary indicator of the event "market m belongs to the region affected by the natural event". The key identification assumption to use I mt as an instrument for price is that the natural event did not affect demand such that E(I mt ε D mt) = 0. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

34 Identification and Estimation "Natural experiments" (2) Assumption E(I mt ε D mt) = 0 is typically implausible. Though the natural event is completely exogenous and unexpected, it may have occurred in markets that have relatively high (or low) levels of demand, or during a period of high (or low) demand. For this reason, most applications using identification from natural experiments assume a particular structure of unobservables. ε D mt = ω D m + δ D t + u D mt, The researcher can control for ω D m using market dummies, and for δ t using time dummies. The identification assumption is that E(I mt u D mt) = 0. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

35 Identification and Estimation Restrictions on covariance-structure of unobservables Suppose that: ε D mt = ω D m + δ D t + u D mt, ε MC mt = ω MC m + δ MC t + umt MC This structure together with restrictions on the serial or/and the spatial correlation of the shocks umt D or umt MC, can be exploited to obtain exclusion restrictions and instrumental variables estimators. We distinguish two cases depending on whether the restrictions are on the serial correlation of the shock (i.e., Arellano-Bond Instruments), or on the spatial correlation (i.e., Hausman-Nevo Instruments). Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

36 Identification and Estimation Arellano-Bond instruments Consider the demand equation in first differences: ( ) Qmt = β X X D mt β 1 P mt + δ D t + umt D S mt Suppose that the shock u D mt is not serially correlated over time such that u D mt is correlated with u D mt 1 but not with ud mt 2,... Arellano-Bond instruments. Under this condition, the lagged endogenous variables {P mt 2, Q mt 2, N mt 2 } are not correlated with the error u D mt, and they are potential instruments to estimate demand parameters. In our example, given that the model does not incorporate dynamics in demand or supply, the key identification assumption is that shocks umt MC in the marginal cost are more time persistent that demand shocks umt. D Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

37 Identification and Estimation Hausman-Nevo instruments Suppose that we can classify the M local markets in R regions. Local markets in the same region may share similar supply of inputs in the production of cement and similar production costs. Suppose that the demand shock u D mt is not spatially correlated, such that local markets in the same region have independent demand shocks. Under these assumptions, the average price in region R (excluding market m): 1 P ( m)t = P M R m 1 m =m,m t R can be used as an instrument to estimate demand parameters. The key identification assumption is that the MC has spatial correlation that is not present in demand shocks u D mt. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

38 Identification and Estimation Zero-covariance between unobservables In simultaneous equations models, an assumption of zero covariance between the unobservables of two structural equations provides a moment condition that can be used to identified structural parameters. For instance, consider the restrictions: E(ε FC mt ε D mt) = 0 and E(ε FC mt ε MC mt ) = 0. These conditions imply two additional moment restrictions that together with the E(X mt ε mt ) = 0 can identify all the parameters of the model. Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

39 Identification and Estimation Zero-covariance restrictions: Example Suppose that the unobserved demand, ε D mt, and the unobserved fixed cost, ε FC mt, are not correlated. ( ) 1 2 Qmt Under this assumption, the model implies that is not correlated with ε D mt. Therefore, we can use 1 S mt ( Qmt N mt S mt N mt ) 2 as an instrument of P mt in the estimation of the demand. That is, we have two moment conditions two estimate two parameters: ( ) Qmt E β S 0 + β 1 P mt = 0 mt E ( 1 S mt ( Qmt N mt ) 2 [ ] ) Qmt β S 0 + β 1 P mt = 0 mt Victor Aguirregabiria () Empirical IO Toronto. Winter / 40

40 Extensions Identification and Estimation The previous model is quite restrictive in different economic and econometric aspects. Some possible extensions: 1 Heterogeneity in firm costs. 2 Product differentiation (vertical or/and horizontal). 3 Forward-looking behavior: dynamic entry and exit decisions. 4 Endogenous costs: a firm s investment can reduce its MC. 5 Endogenous product quality: a firm s investment can improve the quality of its product. 6 Product portfolio: e.g.,store locations. 7 Mergers. 8 Collusive behavior Victor Aguirregabiria () Empirical IO Toronto. Winter / 40