Simulation Based Inference in Models with Heterogeneity

In this paper we discuss the usefulness, for models with heterogeneity, of simulation techniques in inference procedures, like maximum likelihood method, generalized moments method or pseudo maximum likelihood methods. These procedures are studied from the point of view of consistency, asymptotic normality, convergence rates and possible asymptotic bias. We carefully distinguish the case where the simulations are different for all the observations from the case where they are identical.