Imposing equilibrium restrictions in the estimation of dynamic discrete games
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- Dynamic discrete game
- Nested pseudo-likelihood
- Fixed point algorithms
- Convergence
- Convergence selection bias
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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.