Simulation-based estimation with many auxiliary statistics applied to long-run dynamic analysis

Abstract

The existing asymptotic theory for estimators obtained by simulated minimum distance does not cover situations in which the number of components of the auxiliary statistics (or number of matched “moments”) is large — typically larger than the sample size. We establish the consistency of the simulated minimum distance estimator in this situation and derive its asymptotic distribution.

Our estimator is easy to implement and allows us to exploit all the informational content of a large number of auxiliary statistics without having to, (i) know these functions explicitly, or (ii) choose a priori which functions are the most informative. As a result, we are able to exploit, among other things, long-run information. We illustrate the implementation of the proposed method through Monte-Carlo simulation experiments based on small- and medium-scale New Keynesian models. These examples highlight how to conveniently exploit valuable information from matching a large number of impulse responses including at long-run horizons.