Simulated asymptotic least squares theory

Abstract

We develop in this paper a general econometric methodology referred to as the Simulated Asymptotic Least Squares (SALS). It is shown that this approach provides a unifying theory for 'approximation-based' or simulation-based inference methods and nests the Simulated Nonlinear Least Squares (SSNLS), the Simulated Pseudo Maximum Likelihood (SPML), the Simulated Method of Moments (SMM) in both parametric and semiparametric settings, the Indirect Inference (II) and the Efficient Method of Moments (EMM). We produce a new notion of Efficiency Bounds in Direction and provide a general study of the efficiency in the SALS framework. In the particular case of the II and the EMM methods and when the instrumental model is of a GMM type, we characterise a new weighting matrix for a more efficient estimation about the structural parameters of interest ?0. This new weighting matrix does no longer correspond, in the general case, to the classical one as characterised by Hansen (1982). Generalized global specification tests extending the previous existing ones are also proposed