Robust Minimum Distance Inference in Structural Models

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.