Indirect Inference with a Non-Smooth Criterion Function

TL;DR

This paper introduces a novel simulation algorithm for indirect inference with discontinuous endogenous variables, enabling the use of derivative-based optimization without relying on kernel smoothing or bandwidth parameters.

Contribution

It proposes a change of variables technique that reduces discontinuities in the criterion function, improving estimation efficiency in models with discontinuous outcomes.

Findings

Algorithm outperforms existing methods in Monte Carlo simulations.

No need for kernel smoothing or bandwidth tuning.

Demonstrates superior accuracy and convergence.

Abstract

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.