Simulation-based inference. A survey with special reference to panel data models

In this article we study the recent developments of inference methods based on simulations. In particular, we discuss the Simulated Generalized Method of Moments, the Simulated Maximum Likelihood Method, and the Simulated Pseudo Maximum Likelihood Methods. The asymptotic properties of the estimators are described when the number of observations n goes to infinity, and we distinguish the case where the number H of simulations per observation is fixed from the case where this number also goes to infinity. In the former case, the possible asymptotic bias is evaluated and, in the latter case, we carefully examine the consequences of the assumptions on the relative divergence rates of n and H. We also show how these methods apply to various contexts, in particular to the case of panel data models.