  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.
