Approximate Maximum Likelihood for Complex Structural Models

TL;DR

This paper introduces a new simulation-based estimation method that balances efficiency and robustness for complex structural models with intractable likelihoods, offering near-maximum likelihood performance while maintaining simplicity.

Contribution

A novel approach using constrained approximation to structural models that achieves near-efficiency of maximum likelihood without sacrificing parsimony or robustness.

Findings

The new method delivers estimators nearly as efficient as maximum likelihood.

It maintains model parsimony and robustness against misspecification.

Applicable in scenarios where maximum likelihood is infeasible.

Abstract

Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments, Gallant and Tauchen (1996), promises efficiency, the price to pay for this efficiency is a loss of parsimony and thereby a potential lack of robustness to model misspecification. This stands in contrast to simpler I-I estimation strategies, which are known to display less sensitivity to model misspecification precisely due to their focus on specific elements of the underlying structural model. In this research, we propose a new simulation-based approach that maintains the parsimony of I-I estimation, which is often critical in empirical applications, but can also deliver estimators that are nearly as efficient as maximum likelihood. This new approach is based on using a constrained approximation to the structural model, which ensures identification and can deliver estimators that are nearly efficient. We demonstrate this approach through several examples, and show that this approach can deliver estimators that are nearly as efficient as maximum likelihood, when feasible, but can be employed in many situations where maximum likelihood is infeasible.