We propose a new sequential Efficient Pseudo-Likelihood ( EPL ) estimator for structural economic models with an equality constraint, particularly dynamic discrete choice games of incomplete information. Each iteration in the EPL sequence is consistent and asymptotically efficient, and iterating to convergence improves finite sample performance. For dynamic single-agent models, we show that Aguirregabiria and Mira's (2002, 2007) Nested Pseudo-Likelihood (NPL) estimator arises as a special case of EPL. In dynamic games, EPL maintains its efficiency properties , although NPL does not . And a convenient change of variable in the equilibrium fixed point equation ensures EPL iterationshave the same computational simplicity as NPL iterations . Furthermore, EPL iterations are stable and locally convergent to the finite-sample maximum likelihood estimator at a nearly-quadratic rate for all regular Markov perfect equilibria, including unstable equilibria where NPL encounters convergence problems. Monte Carlo simulations confirm the theoretical results and demonstrate EPL 's good performance in finite samples  .
We propose a new sequential Efficient Pseudo-Likelihood ( k-EPL ) estimator for dynamic discrete choice games of incomplete information. We show that each iteration in the k-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations . Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show k-EPL 's good performance in finite samples in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data .
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EPL
k-EPL
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structural economic models with an equality constraint, particularly
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Each
We show that each
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EPL
k-EPL
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and iterating to convergence improves finite sample performance. For dynamic single-agent models, we show that Aguirregabiria and Mira's (2002, 2007) Nested Pseudo-Likelihood (NPL) estimator arises as a special case of EPL. In dynamic games, EPL maintains its efficiency properties , although NPL does not . And a convenient change of variable in the equilibrium fixed point equation ensures EPL iterationshave the same computational simplicity as NPL iterations
so the first-order asymptotic properties do not vary across iterations
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EPL iterations are stable and locally convergent
we show the sequence achieves higher-order equivalence
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at a nearly-quadratic rate for all
with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any
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equilibria, including unstable equilibria where NPL encounters convergence problems.
equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression.
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confirm
demonstrate
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demonstrate EPL
show k-EPL
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in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data