Projection Inference for set-identified SVARs
This paper addresses inference challenges for structural vector autoregressive (SVAR) models under set identification. We propose a projection-based inferential method that simultaneously delivers asymptotic frequentist coverage and robust Bayesian credibility: the Wald ellipsoid for reduced-form parameters is projected onto the structural parameter space to construct joint confidence regions. We establish, for the first time in general stationary SVARs, that this projection method achieves asymptotic 1−α frequentist coverage and robust Bayesian credibility. Moreover, we introduce a posterior-calibrated radius adjustment algorithm that ensures exact robust credibility of 1−α while guaranteeing precise 1−α coverage over the identification set. Theoretically, our work unifies dual guarantees—frequentist and robust Bayesian—within a coherent framework; computationally, it remains efficient and implementable. Empirically, we replicate the Baumeister–Hamilton (2015) labor supply–demand model, demonstrating the method’s tightness and robustness.