Indirect Inference Based on the Score

The Efficient Method of Moments (EMM) estimator popularized by Gallant and Tauchen (1996) is an indirect inference estimator based on the simulated auxiliary score evaluated at the sample estimate of the auxiliary parameters. We study an alternative estimator that uses the sample auxiliary score evaluated at the simulated binding function which maps the structural parameters of interest to the auxiliary parameters. We show that the alternative estimator has the same asymptotic properties as the EMM estimator but in finite samples behaves more like the distance-based indirect inference estimator of Gourieroux, Monfort and Renault (1993).