Simulation-Based Method of Moments and Efficiency

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Abstract
The method of moments is based on a relation Eθ0(h(Xt, θ)) = 0, from which an estimator of θ is deduced. In many econometric models, the moment restrictions can not be evaluated numerically due to, for instance, the presence of a latent variable. Monte Carlo simulations method make possible the evaluation of the generalized method of moments (GMM) criterion. This is the basis for the simulated method of moments. Another approach involves defining an auxiliary model and finding the value of the parameters that minimizes a criterion based either on the pseudoscore (efficient method of moments) or the difference between the pseudotrue value and the quasi-maximum likelihood estimator (indirect inference). If the auxiliary model is sufficiently rich to encompass the true model, then these two methods deliver an estimator that is asymptotically as efficient as the maximum likelihood estimator.