This paper develops estimation and inference tools for the structural parameter in the dynamic game with a high-dimensional state space under the assumption that the data are generated by a single Markov perfect equilibrium. The equilibrium assumption implies that the expected value function evaluated at the equilibrium strategy profile is not smaller than the expected value function evaluated at a feasible suboptimal alternative. The target identified set is defined as the set of parameters obeying this inequality restriction. I estimate the expected value function in the two-stage procedure. At the first stage, I estimate the  law of motion of the state variable and the equilibrium policy function using modern machine learning methods. At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator . The proposed estimator of the identified set converges at the root-N rate to the true identified set and can be used to construct its confidence regions .
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a high-dimensional state space into the dynamic model of imperfect competition. In the first stage, I estimate the state variable's law of motion and the equilibrium policy function using machine learning tools. In the second stage, I plug the first-stage estimates into a moment inequality and solve for the structural parameter. The moment function is presented as the sum of two components, where the first one expresses the equilibrium assumption and the second one is a bias correction term that makes the sum insensitive (i.e., orthogonal) to first-stage bias . The proposed estimator uniformly converges at the root-N rate and I use it to construct confidence regions. The results developed here can be used to incorporate high-dimensional state space into classic dynamic discrete choice models, for example, those considered in Rust (1987), Bajari et al. (2007), and Scott (2013) .
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This paper develops estimation and inference tools for the structural parameter in the dynamic game with
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates
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under the assumption that the data are generated by a single Markov perfect equilibrium. The equilibrium assumption implies that the expected value function evaluated at the equilibrium strategy profile is not smaller than the expected value function evaluated at a feasible suboptimal alternative. The target identified set is defined as the set of parameters obeying this inequality restriction. I estimate the expected value function in the two-stage procedure. At the
into the dynamic model of imperfect competition. In the
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state variable's
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of the state variable
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modern machine learning methods. At
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construct the estimator of the expected value function
plug the first-stage estimates into a moment inequality and solve for the structural parameter. The moment function is presented
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the naive plug-in estimator expected value function of ? and the
two components, where the first one expresses the equilibrium assumption and the second one is a
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which removes the bias of the naive estimator
that makes the sum insensitive (i.e., orthogonal) to first-stage bias
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of the identified set
uniformly
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to the true identified set and can be used to construct its confidence regions
and I use it to construct confidence regions. The results developed here can be used to incorporate high-dimensional state space into classic dynamic discrete choice models, for example, those considered in Rust (1987), Bajari et al. (2007), and Scott (2013)