Robust Minimum Distance Inference in Structural Models

TL;DR

This paper introduces a robust minimum distance inference method for structural models that remains valid even when some parameters are not fully identified, providing reliable hypothesis testing and application to monetary policy analysis.

Contribution

It develops an identification-robust inference procedure with chi-squared asymptotic distribution that does not require knowledge of the level of under-identification.

Findings

The method is applicable to both fixed and structural parameters.

It maintains correct size under partial identification.

Monte Carlo simulations show good finite sample performance.

Abstract

This paper proposes minimum distance inference for a structural parameter of interest, which is robust to the lack of identification of other structural nuisance parameters. Some choices of the weighting matrix lead to asymptotic chi-squared distributions with degrees of freedom that can be consistently estimated from the data, even under partial identification. In any case, knowledge of the level of under-identification is not required. We study the power of our robust test. Several examples show the wide applicability of the procedure and a Monte Carlo investigates its finite sample performance. Our identification-robust inference method can be applied to make inferences on both calibrated (fixed) parameters and any other structural parameter of interest. We illustrate the method's usefulness by applying it to a structural model on the non-neutrality of monetary policy, as in \cite{nakamura2018high}, where we empirically evaluate the validity of the calibrated parameters and we carry out robust inference on the slope of the Phillips curve and the information effect.