Working Paper: CEPR ID: DP14007
Authors: Victor Aguirregabiria; Mathieu Marcoux
Abstract: Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions -- MPEC, NFXP, NPL, and variations -- have different merits and limitations. MPEC guarantees local convergence, but requires the computation of high-dimensional Jacobians. The NPL algorithm avoids the computation of these matrices, but -- in games -- may fail to converge to the consistent NPL estimator. We study the asymptotic properties of the NPL algorithm treating the iterative procedure as performed in finite samples. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the computation of Jacobian matrices. We present simulation evidence illustrating our theoretical results and the good properties of the spectral algorithm.
Keywords: Dynamic Discrete Games; Convergence; Selection Bias; Nested Pseudo Likelihood; Spectral Algorithms
JEL Codes: C13; C57; C61; C73
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| convergence of the NPL algorithm (C45) | stability of the stochastic mapping (C62) |
| stability of the stochastic mapping (C62) | convergence of the NPL algorithm (C45) |
| convergence of the NPL algorithm (C45) | selection bias in the estimator (C51) |
| failure to converge of the NPL algorithm (C62) | selection bias in the estimator (C51) |
| stochastic nature of the sample NPL mapping (C59) | lack of convergence of the NPL algorithm (C62) |
| lack of convergence of the NPL algorithm (C62) | attenuation bias in the estimation of competition effects (L11) |
| convergence of the NPL algorithm (C45) | properties of the sample NPL mapping (C45) |
| properties of the sample NPL mapping (C45) | biases in the estimated structural parameters (C51) |