Dynamic Discrete Choice Structural Models in Empirical IO

Transcription

1 Dynamic Discrete Choice Structural Models in Empirical IO Lecture 3: Dynamic Games wh : Identification, Estimation, and Applications Victor Aguirregabiria (Universy of Toronto) Carlos III, Madrid June 28, 2017 Carlos III, Madrid June 28, /

2 Outline Outline [1] Introduction, Motivation, and Examples [2] Model: Basic Assumptions [3] Identification (a) Test of equilibrium beliefs (b) Full identification of the model [4] Estimation [5] Empirical applications (a) Entry in unexplored markets (b) Bidding behavior after deregulation Carlos III, Madrid June 28, /

3 Introduction, Motivation, and Examples Dynamic games of oligopoly competion Dynamic games of oligopoly competion Firms compete not only in prices or quanties but also in other dimensions such as market entry, capacy, qualy, advertising, R&D and innovation, or product design. This type of competion at the extensive margin is typically modelled using discrete choice games. Most of these choices involve sunk costs and are partly irreversible: dynamic decisions. During the last decade, there have been important developments in the estimation and solution of dynamic games and an increasing of empirical applications. Carlos III, Madrid June 28, /

4 Introduction, Motivation, and Examples Examples of Empirical Applications Examples of Empirical Applications Land use regulation (entry cost) and entry-ex and competion in the hotel industry: Suzuki (IER; 2013); Subsidies to entry in small markets for the dentist industry: Dunne et al. (RAND, 2013); Environmental regulation and entry-ex and capacy choice in cement industry: Ryan (ECMA, 2012); Demand uncertainty and firm investment in the concrete industry: Collard-Wexler (ECMA, 2013); Time-to-build, uncertainty, and dynamic competion in the shipping industry: Kalouptsidi (AER, 2014); Carlos III, Madrid June 28, /

5 Introduction, Motivation, and Examples Examples of Empirical Applications Examples of Empirical Applications [2] Fees for musical performance rights and the choice of format (product design) of radio stations: Sweeting (ECMA, 2013); Hub-and-spoke networks, route entry-ex and competion in the airline industry: Aguirregabiria and Ho (JoE, 2012); Competion in R&D and product innovation between Intel and AMD: Goettler and Gordon (JPE, 2011); Product innovation of incumbents and new entrants in the hard drive industry: Igami (JPE, 2017); Cannibalization and preemption strategies in the Canadian fast-food industry: Igami and Yang (QE, 2016) Carlos III, Madrid June 28, /

6 Introduction, Motivation, and Examples Examples of Empirical Applications Examples of Empirical Applications [3] Release date of a movie: Einav (EI, 2010). Dynamic price competion: Kano (IHIO, 2013); Ellickson, Misra, and Nair (JMR, 2012). Endogenous mergers: Jeziorski (RAND, 2014). Exploation of a common natural resource (fishing): Huang and Smh (AER, 2014). Carlos III, Madrid June 28, /

7 Introduction, Motivation, and Examples Out-of-equilibrium beliefs Equilibrium beliefs: a common assumption In games, the best response of a player depends on her beliefs about the behavior of her opponents. The most common assumption is that players beliefs about other players actions are in equilibrium, i.e., they are unbiased expectations of the actual behavior of other players. Dynamic games: Markov Perfect Equilibrium (MPE). Maskin & Tirole (1988); Ericson & Pakes (1995). There are good reasons to impose assumption of equilibrium beliefs: (a) This assumption has identification power. (b) Counterfactual analysis: model predicts how beliefs change endogenously. Carlos III, Madrid June 28, /

8 Introduction, Motivation, and Examples Sources of out-of-equilibrium beliefs Out-of-equilibrium beliefs Sometimes, the assumption of equilibrium beliefs can be unrealistic. There are different sources of bias in players beliefs: (a) Bounded rationaly: Limed capacy to process information / compute; (b) Asymmetric information about other players permanent characteristics (learning); (c) Strategic uncertainty: Wh multiple equilibria, players can have different beliefs about the selected equilibrium. Some players believe that they are playing equilibrium A, other players believe they are playing equilibrium B,... Carlos III, Madrid June 28, /

9 Introduction, Motivation, and Examples Out-of-equilibrium beliefs Strategic Uncertainty and oligopoly competion In the context of games of oligopoly competion, Strategic Uncertainty seems particularly plausible, especially when firms are competing in new markets, or after substantial regulatory changes. Dynamic games are typically characterized by multiple equilibria, and some equilibria are better for some firms, i.e., firms do not have incentives to coordinate their beliefs. Firms are very secretive about their own strategies and face significant uncertainty about the strategies of their competors. Implications for the evaluation of a new policy. Carlos III, Madrid June 28, /

10 Introduction, Motivation, and Examples Out-of-equilibrium beliefs Empirical applications of games wh biased beliefs In experimental economics, researchers have used data from games played in laboratory experiments to study whether players have biased beliefs and whether these beliefs converge over time to an equilibriums, e.g.,van Huyck et al. (AER, 90); Camerer & Ho (ECMA, 99); Heinemann et al. (REStud, 09). The empirical lerature using field data is more recent: Goldfarb & Xiao (AER, 2011); Aguirregabiria and Magesan (2015); Doraszelski, Lewis, & Pakes (NBER wp, 2016); Asker, Fershtman, Jeon, & Pakes (NBER wp, 2016); Jeon (2016) Carlos III, Madrid June 28, /

11 Model: Basic Assumptions Dynamic Game Two players i and j. Dynamic game over T periods. Every period t, each player takes an action Y {0, 1}. One-period payoff function is: Π = π i (Y, Y jt, X t ) + ε (Y ) X t is a vector of common knowledge state variables wh transion f (X t+1 Y, Y jt, X t ). Payoff functions π i (.) and π j (.) are nonparametrically specified. ε = {ε (0),ε (1)} is private info of player i and unobservable to researcher. It is i.i.d. over time and players wh CDF Λ. Carlos III, Madrid June 28, /

12 Model: Basic Assumptions Example: Dynamic game of market entry-ex The average prof of an inactive firm, π (0, Y, X t ) + ε (0), is normalized to zero. The prof of an active firm is π (1, Y, X t ) + ε (1) where: ( ) π (1, Y jt, X t ) = H t θ M i θ D i Y jt θ FC i0 θ FC i1 Z 1{Y 1 = 0} H t ( θ M i θ D i j =i Y jt ) is the variable prof of firm i. H t represents market size (e.g., market population) and is an exogenous state variable. θ M i and θ D i are parameters. θ FC i0 + θ FC i1 Z is the fixed cost of firm i, where θ FC i0 and θ FC i1 are parameters, and Z is an exogenous firm-specific characteristic. 1{Y 1 = 0} θ EC i is the entry cost. In this model, X t = (H t, Z, Z jt, Y i,t 1, Y jt 1 ). Carlos III, Madrid June 28, /

13 Model: Basic Assumptions Markov Perfect Equilibrium The concept of Markov Perfect Equilibrium (MPE) can be described as a combination of. ASSUMPTION 1: Players strategy functions depend only on payoff relevant state variables: X t and ε. ASSUMPTION 2: Players have beliefs about the behavior of other players and about their own behavior in the future. Given these beliefs, they maximize expected intertemporal payoffs. ASSUMPTION 3: Players have rational expectations on their own behavior in the future. ASSUMPTION EQUIL: Players have rational expectations about other players behavior now and in the future. Carlos III, Madrid June 28, /

14 Relaxing MPE Model: Basic Assumptions Following the concept of Rationalizabily: We maintain Assumptions 1 to 3; We relax Assumption EQUIL of "equilibrium beliefs". Carlos III, Madrid June 28, /

15 Model: Basic Assumptions Strategies, Choice Probabilies, and Beliefs Let σ (X t, ε ) be the strategy function for player i at period t. P (X t ) Pr(σ (X t, ε ) = 1 X t ) is the choice probabily of player i. Player i s beliefs at period t about the behavior (choice probabily) of player j at period t + s is B (t) i,t+s (X t+s ). Equilibrium (unbiased) beliefs: B (t) i,t+s (x) = P j,t+s (x) at any t, s 0, and x. Carlos III, Madrid June 28, /

16 Model: Basic Assumptions Best Response Functions { Given his beliefs at period t, B (t) i = B (t) i,t+s }, (X) : X X, s 0 a player best response is the solution of a single-agent Dynamic Programming problem wh some specific expected payoffs and expected transion probabilies. This DP problem has expected payoffs: π B(t) i,t+s (Y i,t+s, X t+s ) B (t) i,t+s (X t+s ) π i (Y i,t+s, 1, X t+s ) +(1 B (t) i,t+s (X t+s )) π i (Y, 0, X t+s ) Carlos III, Madrid June 28, /

17 Model: Basic Assumptions Best Response Functions (2) The expected transion of the state variables: f B(t) i,t+s (X t+s+1 Y i,t+s, X t+s ) B (t) i,t+s (X t+s ) f (X t+s+1 Y i,t+s, 1, X t+s ) +(1 B (t) i,t+s (X t+s )) f (X t+s+1 Y i,t+s, 0, X t+s ) Carlos III, Madrid June 28, /

18 Model: Basic Assumptions Best Response Functions (3) { } { } Given π B(t) i,t+s and f B(t) i,t+s the DP problem can be represented using the Bellman equation: { V B(t) (X t, ε ) = max π B(t) Y i,t+s (Y, X t ) + ε (Y ) +β V B(t) i,t+1 (X t+1, ε +1 )dλ(ε +1 ) f B(t) (X t+1 Y, Carlos III, Madrid June 28, /

19 Model: Basic Assumptions Best Response Functions (3) The best response function for player i is: { } {Y = 1} ε (0) ε (1) π B(t) (x t ) + ṽ B(t) (x t ) π B(t) ṽ B(t) values. (x) π B(t) (x) v B(t) (1, x) π B(t) (0, x). (1, x) v B(t) (0, x), i.e., difference of continuation The best response probabily function is: ( ) P (x t ) = Λ π B(t) (x t ) + ṽ B(t) (x t ) Carlos III, Madrid June 28, /

20 Data Identification We have a random sample of M markets, indexed by m, where we observe {Y imt, Y jmt, X mt : t = 1, 2,..., T data } for every market m = 1, 2,..., M. T data is small and M is large. Model can include time-invariant common-knowledge market characteristics ω m which are unobservable to the researcher. Nonparametric fine mixture structure of ω m. Carlos III, Madrid June 28, /

21 Identification question Identification Given this model and data, is possible to fully identify all the structural functions of the model, i.e., players payoff functions π i (y i, y j, x) and players belief functions B (t) i,t+s (x)? Is possible to test for the null hypothesis that players beliefs are in equilibrium? Before we address these questions for this model, is helpful to review the identification of the model when we impose the restriction of equilibrium beliefs (MPE). Carlos III, Madrid June 28, /

22 Identification Identification wh equilibrium beliefs (1) ASSUMPTION EQUIL: Beliefs are in equilibrium (unbiased): B (t) i,t+s (x) = P j,t+s (x) at any t, s 0, and x. ASSUMPTION ID-1. Players play the same equilibrium in markets wh the same x variables, i.e., P imt (x) = P (x) for any market m. Under condion ID-1, we can use our sample of markets to estimate consistently CCPs P (x) for every player, t, and value x. Hotz-Miller inversion: Define q (x) Λ 1 (P (x)) where Λ 1 is the inverse of the CDF Λ. This distribution is assumed known to the researcher (this condion can be relaxed) such that q (x) is identified. Carlos III, Madrid June 28, /

23 Identification Identification wh equilibrium beliefs (2) The model implies: q (x) = π B(t) (x t ) + ṽ B(t) (x t ) = B (t) (x) + ( 1 B (t) And wh equilibrium beliefs: [ π i (1, x) + c B(t) (1, x) ) [ ] (x) π i (0, x) + c B(t) (0, x) q (x) = P jt (x) [ π i (1, x) + c (1, x)] + (1 P jt (x)) [ π i (0, x) + c (0, x)] ] Carlos III, Madrid June 28, /

24 Identification Identification wh equilibrium beliefs (3) Bajari et al. (2010) provide condions for the nonparametric identification of dynamic games under MPE. In addion to Assumption ID-1, and Equilibrium beliefs, there is an important exclusion restriction. ASSUMPTION ID-2 (Exclusion Restriction): X t = (S, S jt, W t ) such that S enters in the payoff function of player i but not in the payoff of the other player. π (Y, Y jt, S, S jt, W t ) = π (Y, Y jt, S, W t ) Carlos III, Madrid June 28, /

25 Identification Examples of exclusion restrictions The exclusion restriction in Assumption ID-2 appears naturally in many dynamic games of oligopoly competion. Entry-ex game: Lagged incumbent status of the competor: Y j,t 1. Game of investment in capal, capacy, qualy, etc. The competor s capal stock at previous period, K j,t 1. Carlos III, Madrid June 28, /

26 Identification Identification results wh equilibrium beliefs Under ID-1 & Equil. Beliefs: Beliefs are identified (from behavior of other players) but payoffs are NOT identified. Under ID-1 & ID-2 & Equil. Beliefs: Beliefs and payoffs are identified. Carlos III, Madrid June 28, /

27 Identification Identification when beliefs are out-of-equilibrium We maintain Assumptions ID-1 & ID-2, and relax Assump. EQUIL. Model implies: q (x) = B (t) (x) = ( 1 B (t) [ ] π i (1, x) + c B(t) (1, x) ) [ ] (x) π i (0, x) + c B(t) (0, x) ASSUMPTION ID-3: The probabily distribution over states tomorrow X t+1 is independent of S t condional on the vector W t and the choices Y t : f (X t+1 Y t, X t ) = f (X t+1 Y t, W t ). Carlos III, Madrid June 28, /

28 Identification Examples of models that satisfy Assumption ID-3 Market entry-ex: In this case, S jt = Y j,t 1. It is clear that Y jt contains all the information about S jt+1. More generally, multinomial dynamic games where Y jt can be capal, capacy, qualy, product design, etc, and S jt = Y j,t 1. Dynamic games of multi-armed band decisions. Carlos III, Madrid June 28, /

29 Identification Identification when beliefs are out-of-equilibrium Under ID-1 to ID-3 & Unrestricted Beliefs: Null hypothesis of Equilibrium Beliefs is testable. Under ID-1 to ID-3 & beliefs are restricted at two points in support(s): Payoffs and contemporaneous beliefs are fully identified. Carlos III, Madrid June 28, /

30 Identification Test of Equilibrium Beliefs Test of Equilibrium Beliefs Model under assumptions ID-2 & ID-3 (I om W): [ ] q (s i, s j ) = B (t) (s i, s j ) π i (1, s i ) + c B(t) (1) = π i depends on s i but not on s j. ( ) [ ] 1 B (t) (s i, s j ) π i (0, s i ) + c B(t) (0) The continuation values c B(t) do not depend on eher s i or s j. Carlos III, Madrid June 28, /

31 Identification Test of Equilibrium Beliefs (2) Test of Equilibrium Beliefs Given three values of S j, say sj a, sb j, and sc j, we have that the function q (.) identifies the following function of contemporaneous beliefs: q (s i, sj c ) q (s i, sj a) q (s i, sj b) q (s i, sj a) = B (t) (s i, sj c ) B(t) (s i, sj a) B (t) (s i, sj b) B(t) (s i, sj a) The behavior of player i identifies a function of his beliefs. Under null hypothesis equilibrium beliefs, B (t) (x) = P jt (x) such that: ( q (s i, sj c ) q (s i, sj a) ) ( Pjt (s i, sj c q (s i, sj b) q (s i, sj a) ) P jt(s i, sj a) ) P jt (s i, sj b) P jt(s i, sj a) = 0 Carlos III, Madrid June 28, /

32 Identification Test of Equilibrium Beliefs Test of Equilibrium Beliefs (3) We can test the null hypothesis of equilibrium beliefs using a Likelihood Ratio Test in a nonparametric multinomial model for the CCPs P i and P j. The log-likelihood function of this multinomial model is: l (P i, P j ) = y imt ln P (x mt ) + (1 y imt ) ln [1 P (x mt )] m,t + y jmt ln P jt (x mt ) + (1 y jmt ) ln [1 P jt (x mt )] m,t Test statistic: [ ) )] LR = 2 l ( P u i, P u j l ( P c i, P c j Carlos III, Madrid June 28, /

33 Identification Test of Equilibrium Beliefs (4) Test of Equilibrium Beliefs ) The unconstrained MLE ( P u i, P u j is just the frequency estimator of CCPs. ) And the constrained MLE ( P c i, P c j is the estimator subject to the equlibrium constraints: Λ 1 (P (s i, s (c) j = 0 Λ 1 (P (s i, s (b) j )) Λ 1 (P (s i, s (a) ( j )) Pjt (s i, sj c )) Λ 1 (P (s i, s (a) ) P jt(s j )) P jt (s i, sj b) P jt(s Carlos III, Madrid June 28, /

34 Estimation Identification Estimation Suppose that the null hypothesis is rejected. It is possible to use the estimated beliefs B(t) (s i, sj c ) B(t) (s i, sj a) B (t) and estimated actual behavior of the other player, P jt (s i, s c j ) P jt(s i, s a j ) (s i, s b j ) B(t) (s i, s a j ) P jt (s i, sj b) P jt(s i, sj a to study different hypotheses/models of ), learning. Carlos III, Madrid June 28, /

35 Estimation (2) Identification Estimation Alternatively, we can keep our agnostic approach about the structure of beliefs but impose the restriction that these beliefs are unbiased at two values of S j, i.e., for s a j and s b j we have B (t) (s i, s a j ) = P jt(s i, s a j ) and B (t) (s i, s b j ) = P jt(s i, s b j ). Then, for any other value of S j is identified. Given the identification of beliefs, the estimation of the payoff function proceeds in a very similar way as in the estimation of single-agent dynamic structural model. Carlos III, Madrid June 28, /

36 Identification Estimation How two choose points where to impose unbiased beliefs? (a) Applying the test of equilibrium beliefs. (b) Testing for the monotonicy of beliefs and using this restriction. (c) Minimization of the player s beliefs bias. (d) Most vised states. Carlos III, Madrid June 28, /

37 Monte Carlo Experiments Monte Carlo Experiments Main purposes of these experiments: [1] To evaluate the power the power of the test. [2] To assess the price, in terms of precision of our estimates, of relaxing the assumption of equilibrium beliefs? [3] Evaluate the bias induced by imposing the assumption of equilibrium beliefs when this assumption does not hold in the DGP. Carlos III, Madrid June 28, /

38 Monte Carlo Experiments Monte Carlo Experiments: Model Dynamic game of market entry and ex. π 1mt (1, Y 2mt, X mt ) = α 1 δ 1 Y 2mt + Y 1mt 1 θ EC 1 π 2mt (1, Y 2mt, X mt ) = α 2 δ 2 Y 1mt θ S S 2m + Y 2mt 1 θ EC 2 S 2m has a discrete uniform distribution wh support { 2, 1, 0, 1, 2}. Carlos III, Madrid June 28, /

39 Monte Carlo Experiments Monte Carlo Experiments: Design Table 3 Summary of DGPs in the Monte Carlo Experiments For all the experiments: α = 2.4; δ = 3.0; θ EC = 0.5; β = 0.95 S 2m Uniform { 2, 1, 0, +1, +2} M = 2, 000; T = 5; MC rep = 10, 000 Experiment 1U: θ S = 0.5; Unbiased beliefs Experiment 1B: θ S = 0.5; Biased beliefs Experiment 2U: θ S = 1.0; Unbiased beliefs Experiment 2B: θ S = 1.0; Biased beliefs Carlos III, Madrid June 28, /

40 Monte Carlo Experiments MCs: Cost of Relaxing Equil Beliefs Monte Carlo Experiment 1U Estimation WITH equil. rest. Estimation WITHOUT equil. rest. Parameter Bias Std Bias Std (True value) (%) (%) (%) (%) Payoffs α (2.4) (4.13) (9.20) (5.88) (15.42) δ (3.0) (3.35) (7.83) (4.83) (12.54) θ EC (0.5) (0.42) (13.30) (15.20) (22.35) Carlos III, Madrid June 28, /

41 Monte Carlo Experiments MCs: Benefs of Relaxing Equil Beliefs Monte Carlo Experiment 1B Estimation WITH equil. rest. Estimation WITHOUT equil. rest. Parameter Bias Std Bias Std (True value) (%) (%) (%) (%) Payoffs α (2.4) (13.88) (11.11) (0.34) (11.79) δ (3.0) (9.93) (9.15) (5.14) (10.24) θ EC (0.5) (65.55) (15.56) (2.68) (29.63) Carlos III, Madrid June 28, /

42 Empirical Application: BK & MD EMPIRICAL APPLICATION Dynamic game of store location by McDonalds (MD) and Burger King (BK) using data for Uned Kingdom during the period Panel of 422 local markets (districts) and six years, Information on the number of stores of McDonalds (MD) and Burger King (BK) in Uned Kingdom. Information on local market characteristics such as population, densy, income per capa, age distribution, average rent, local retail taxes, and distance to the headquarters of each firm in UK. Carlos III, Madrid June 28, /

43 Empirical Application: BK & MD Table 1 Descriptive Statistics for the Evolution of the Number of Stores Data: 422 markets, 2 firms, 5 years = 4,220 observations Burger King McDonalds # Markets # Markets # of stores # of stores stores per mark Carlos III, Madrid June 28, /

44 Model Empirical Application: BK & MD K imt {0, 1,..., K } number of stores of firm i in market m at period t 1. Y imt {0, 1} decision of firm i to open a new store. Y imt + K imt = # stores of firm i at period t. Firm i s total prof function is equal to: Π imt = VP imt EC imt FC imt Carlos III, Madrid June 28, /

45 Model (2) Empirical Application: BK & MD Variable prof function: VP imt = (W m γ) (Y imt + K imt ) [ θ VP 0i + θ VP can,i (K imt + Y imt ) com,i (K jmt + Y jmt ) +θ VP ] Entry cost: EC imt = 1{Y imt > 0} [ ] θ EC 0i + θ EC K,i 1{K imt > 0} + θ EC S,i S imt + ε Fixed cost: FC imt = 1{(K imt + Y imt ) > 0} [ θ FC 0i + θ FC lin,i (K imt + Y imt ) +θ FC qua,i (K imt + Y imt ) 2 ] Carlos III, Madrid June 28, /

46 Empirical Application: BK & MD Tests of Unbiased Beliefs Data: 422 markets, 5 years = 2,110 observations BK: D (p-value) ( ) MD: D (p-value) ( ) We can reject hypothesis that BK beliefs are unbiased (p-value ). Restriction is more clearly rejected for large values of the state variable (distance to chain network) S MD. Carlos III, Madrid June 28, /

47 Empirical Application: BK & MD Where to impose unbiased beliefs? We propose three different creria: [1] Minimize distance B i P j [2] Test for monotonicy of beliefs: if not rejected, impose unbiased beliefs in extreme values of S j. [3] Most vised values of S j. In this empirical application, the three creria have the same implication: impose unbiased beliefs at the lowest values for the distance S j. Carlos III, Madrid June 28, /

48 Empirical Application: BK & MD Var Profs: Estimation of Dynamic Game Data: 422 markets, 2 firms, 5 years = 4,220 observations β = 0.95 (not estimated) Equilibrium Beliefs Biased Beliefs BK MD BK MD θ VP (0.1265) (0.2284) (0.2515) (0.4278) θ VP can cannibalization (0.0576) (0.0304) (0.1014) (0.0710) θ VP com competion (0.0226) (0.0272) (0.0540) (0.0570) Log-Likelihood Carlos III, Madrid June 28, /

49 Empirical Application: BK & MD Estimation of Dynamic Game Data: 422 markets, 2 firms, 5 years = 4,220 observations β = 0.95 (not estimated) Equilibrium Beliefs Biased Beliefs BK MD BK MD Fixed Costs: θ FC 0 fixed (0.0220) (0.0265) (0.0478) (0.0489) θ FC lin linear (0.0259) (0.0181) (0.06) (0.0291) θ FC qua quadratic (0.0061) (0.0163) (0.0186) (0.0198) Carlos III, Madrid June 28, /

50 Empirical Application: BK & MD Estimation of Dynamic Game Data: 422 markets, 2 firms, 5 years = 4,220 observations β = 0.95 (not estimated) Equilibrium Beliefs Biased Beliefs BK MD BK MD Entry Cost: θ EC 0 fixed (0.0709) (0.0679) (0.1282) (0.0989) θ EC K (K) (0.043) (0.0395) (0.096) (0.0628) θ EC S (S) (0.0368) (0.0340) (0.0541) (0.0654) Carlos III, Madrid June 28, /

51 Other empirical applications Other empirical applications Goldfarb & Xiao (AER, 2011): Entry in US local telephone markets after the 1996 Telecommunications Act of Level-K rationalizabily. Find that more experienced, better-educated managers can predict better competor behavior. Doraszelski, Lewis, & Pakes (NBER wp, 2016): Dynamic price competion in a new electricy market in UK. Evidence of substantial strategic uncertainty but also convergence over time. Tests of different models of learning (fictious play, adaptive learning). Asker, Fershtman, Jeon, & Pakes (NBER wp, 2016): Dynamic bidding. Persistent asymmetric information as the source of biased beliefs and learning. Experience Based Equilibrium (EBE). Jeon (2016): Dynamic game of capacy investment in the shipping industry. Source of biased beliefs is Knightian uncertainty about the evolution of demand. Evidence of biased beliefs and slow learning. Carlos III, Madrid June 28, /

52 Conclusions Summary and Conclusions Strategic uncertainty can be important for competion in oligopoly markets. Under these condions, the assumption of equilibrium beliefs can be too restrictive and can bias our estimates and policy evaluations. There are reasonable condions under which this restriction is testable. If rejected, is also possible to identify the model under weaker condions that unbiased beliefs everywhere. It will be interesting to see more empirical applications on evaluation of policy changes, deregulations, mergers, that take into account the possibily of temporary biased beliefs. Use of estimated contemporaneous beliefs to understand how firms learn over time about other firms strategies. Carlos III, Madrid June 28, 2017 /