Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference

2024-04-17

AI Summary

This paper addresses the challenge of identifying specific structural shocks in structural vector autoregressive (SVAR) models using heteroskedasticity alone—without conventional sign or exclusion restrictions. Within a Bayesian framework, we propose a non-centered stochastic volatility approach that dispenses with such auxiliary constraints. Theoretically, we derive necessary and sufficient conditions for partial and global identification of structural parameters. Methodologically, we develop a heteroskedasticity-based statistical identification diagnostic and introduce a shrinkage prior centered at homoskedasticity, ensuring identification is fully data-driven. Empirically, applying the method to a U.S. fiscal structural model, we achieve partial identification of structural shocks without imposing additional identifying restrictions, thereby substantially enhancing estimation robustness and economic interpretability.

Technology Category

• Machine Learning: Structured Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We consider structural vector autoregressions identified through stochastic volatility. Our focus is on whether a particular structural shock is identified by heteroskedasticity without the need to impose any sign or exclusion restrictions. Three contributions emerge from our exercise: (i) a set of conditions under which the matrix containing structural parameters is partially or globally unique; (ii) a statistical procedure to assess the validity of the conditions mentioned above; and (iii) a shrinkage prior distribution for conditional variances centred on a hypothesis of homoskedasticity. Such a prior ensures that the evidence for identifying a structural shock comes only from the data and is not favoured by the prior. We illustrate our new methods using a U.S. fiscal structural model.

Problem

• Analyzing partial identification in structural VARs with stochastic volatility
• Comparing non-centred versus centred parameterizations for shock identification
• Evaluating fiscal tax shock identification using Bayesian estimation methods

Innovation

• Non-centred stochastic volatility parameterization for structural VARs
• Improved structural parameter precision via Monte Carlo experiments
• Enhanced shock identification consistency in fiscal applications