Projection Inference for set-identified SVARs

2025-04-18

AI Summary

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.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study the properties of projection inference for set-identified Structural Vector Autoregressions. A nominal $1-alpha$ projection region collects the structural parameters that are compatible with a $1-alpha$ Wald ellipsoid for the model's reduced-form parameters (autoregressive coefficients and the covariance matrix of residuals). We show that projection inference can be applied to a general class of stationary models, is computationally feasible, and -- as the sample size grows large -- it produces regions for the structural parameters and their identified set with both frequentist coverage and emph{robust} Bayesian credibility of at least $1-alpha$. A drawback of the projection approach is that both coverage and robust credibility may be strictly above their nominal level. Following the work of cite{Kaido_Molinari_Stoye:2014}, we `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 identified set with probability $1-alpha$. %eliminating the excess of robust Bayesian credibility also eliminates excessive frequentist coverage. We illustrate the main results of the paper using the demand/supply-model for the U.S. labor market in Baumeister_Hamilton(2015)

Problem

• Evaluates projection inference for set-identified SVARs
• Ensures frequentist coverage and robust Bayesian credibility
• Calibrates Wald ellipsoid to eliminate excessive credibility

Innovation

• Projection inference for set-identified SVARs
• Calibrated Wald ellipsoid ensures exact credibility
• Applicable to stationary models with robust coverage