Projection Inference for set-identified SVARs

We study the properties of the classical \emph{projection} method to conduct simultaneous inference about the coefficients of the structural impulse-response function and their identified set in Structural Vector Autoregressions. We show that -- as the sample size grows large -- projection inference produces regions for the structural parameters and their identified set with both frequentist coverage and robust Bayesian credibility of at least $1-\alpha$. We then calibrate the radius of the Wald ellipsoid to guarantee that -- for a given posterior on the reduced-form parameters -- the robust Bayesian credibility of the projection method is exactly $1-\alpha$. If the bounds of the identified set are differentiable, our calibrated projection also covers the product of the identified sets for each structural parameter of interest with probability $1-\alpha$. We illustrate the main results of the paper using a demand/supply-model of the U.S.~labor market.