Method of Simulated Moments with antithetic sampling in the presence of endogeneity
This post illustrates a use of the Method of Simulated Moments (MSM) to tackle the problem of endogeneity . It is also shown how the efficiency of the resulting estimator can be improved using Monte-Carlo variance reduction. The original work was conducted together with P. Bertazzoni and V. Kazakova . Background The Method of Simulated Moments (McFadden, 1989), or MSM, is a variant of the Generalized Method of Moments (GMM). Rather than computation, however, it uses simulation in the moment conditions. This is especially useful when the likelihood is computationally intractable, for instance in models with missing, incomplete, or noisy data, or those with complicated dynamic formulations. The general idea is to match properties of observed data to those of data simulated under known conditions. The model is estimated by varying simulation parameters until the difference between selected moments of the empirical and the simulated sample is minimal. Consider a set of moment conditions ...