Identification-robust inference with simulation-based pseudo-matching

We develop a general simulation-based inference procedure for partially specified models. Our procedure is based on matching auxiliary statistics to simulated counterparts where nuisance parameters are calibrated neither assuming identification of parameters of interest nor a one-to-one binding function. The conditions underlying the asymptotic validity of our (pseudo-)simulators in conjunction with appropriate bootstraps are characterized beyond the strict and exact calibration of the parameters of the simulator. Our procedure is illustrated through impulse-response (IR) matching in a simulation study of a stylized dynamic stochastic equilibrium model, and two empirical applications on the New Keynesian Phillips curve and on the Industrial Production index. In addition to usual Wald-type statistics that combine structural or reduced form IRs, we analyze local projections IRs through a factor-analytic measure of distance which eschews the need to define a weighting matrix.