Abstract
In this paper, we develop a new model of a static game of incomplete information with a large number of players. The model has two key distinguishing features. First, the strategies are subject to threshold effects, and can be interpreted as dependent censored random variables. Second, in contrast to most of the existing literature, our inferential theory relies on a large number of players, rather than a large number of independent repetitions of the same game. We establish existence and uniqueness of the pure strategy equilibrium, and prove that the censored equilibrium strategies satisfy a near-epoch dependence property. We then show that the normal maximum likelihood and least squares estimators of this censored model are consistent and asymptotically normal. Our model can be useful in a wide variety of settings, including investment, R&D, labor supply, and social interaction applications.
Highlights
Identification and estimation of strategic interaction models have recently received a great deal of attention in econometrics, owing to the growing interest and application of stochastic games in various fields including industrial organization, labor, political and international economics
The number of players is assumed to Econometrics 2015, 3 be fixed, and the asymptotic inferential theory relies on a large number of independent repetitions of the same game in different markets or in a single market at different points of time
To develop the asymptotic theory, we instead assume that the number of players grows unboundedly, and the players reside on an exogenously given lattice so that the vector of their choices and characteristics can be viewed as a dependent random field, which can be handled by the limit theorems for near-epoch dependent (NED) random fields established by Jenish and Prucha [5]
Summary
Identification and estimation of strategic interaction models have recently received a great deal of attention in econometrics, owing to the growing interest and application of stochastic games in various fields including industrial organization, labor, political and international economics. To develop the asymptotic theory, we instead assume that the number of players grows unboundedly, and the players reside on an exogenously given lattice so that the vector of their choices and characteristics can be viewed as a dependent random field, which can be handled by the limit theorems for near-epoch dependent (NED) random fields established by Jenish and Prucha [5] We derive this model explicitly in two game-theoretical applications: (i) R&D investment by firms under strategic complementarities; and (ii) labor supply decision by women under peer effects. The R&D expenditure could be viewed as a censored decision variable whose optimal values below a certain threshold are unobserved This type of model in the single-firm setup is analyzed by Gonzalez and Jaumandreu [15]. The latter is consistent with the Schumpeterian argument that economies of scales make R&D more attractive to large firms than to small firms
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