Some Practical Issues in Maximum Simulated Likelihood

In this paper, I explore ways of recapturing the efficiency property for estimators that rely on simulation. In particular, I show that this can be achieved by exploiting two-step maximum stimulated likelihood (SL) estimation methods that are familiar from classical applications. I also construct a diagnostic test for adequacy of number of simulations employed to guarantee negligible bias for the MSL and provide some evidence on the computational requirements of the Geweke-Hajivassiliou-Keane (GHK) simulator as a function of (a) the dimension of the problem and (b) the number of simulations employed in a vectorized context. I outline how one can derive a similar approach for checking the adequacy of the number of Gibbs resamplings in simulation estimation methods the employ this technique. This chapter also shows how to suitably introduce simulation into classical hypothesis testing methods and provide test statistics (simulated Wald, Lagrange Multiplier, and Likelihood Ratio Tests) that are free of influential simulation noise. Finally, I explain how simulation-variance-reduction techniques, notably antithetics, can improve substantially the practical performance of the GHK simulator and present extensive Monte-Carlo evidence confirming this.