Indirect inference with a non-smooth criterion function

Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function is discontinuous and does not permit the use of derivative-based optimisation routines. Using a change of variables technique, we propose a novel simulation algorithm that alleviates the discontinuities inherent in such indirect inference criterion functions, and permits the application of derivative-based optimisation routines to estimate the unknown model parameters. Unlike competing approaches, this approach does not rely on kernel smoothing or bandwidth parameters. Several Monte Carlo examples that have featured in the literature on indirect inference with discontinuous outcomes illustrate the approach, and demonstrate the superior performance of this approach over existing alternatives.
Comment: This paper is a revision of arXiv:1708.02365 and supersedes the earlier arXiv paper "Derivative-Based Optimization with a Non-Smooth Simulated Criterion"