We propose an approach for Bayesian inference in time-varying structural vector autoregressions (SVARs) identified with sign restrictions. The linchpin of our approach is a class of rotation-invariant time-varying SVARs in which the prior and posterior densities of any sequence of structural parameters belonging to the class are invariant to orthogonal transformations of the sequence. Our methodology is new to the literature. In contrast to existing algorithms for inference based on sign restrictions, our algorithm is the first to draw from a uniform distribution over the sequences of orthogonal matrices given the reduced-form parameters. We illustrate our procedure for inference by analyzing the role played by monetary policy during the latest inflation surge.

A long tradition in macro-finance studies the dynamics of aggregate stock returns and dividends using vector autoregressions, imposing the restrictions implied by the Campbell-Shiller (CS) identity to sharpen inference. We develop Bayesian methods that encode a priori skepticism about return predictability while imposing the restrictions. We highlight that persistence in dividend growth induces “dividend momentum,” a previously overlooked channel for return predictability. By combining Bayesian shrinkage and the CS restrictions, we obtain more plausible degrees of return predictability, superior out-of-sample forecasts, and Sharpe ratios, which cannot be obtained by using either shrinkage or the CS restrictions on their own.

We examine optimal capital requirements in a quantitative general equilibrium model with banks exposed to nondiversifiable borrower default risk. Contrary to standard models of bank default risk, our framework captures the limited upside, but significant downside risk of loan portfolio returns. This helps to reproduce the frequency and severity of twin defaults : simultaneously high firm and bank defaults. Hence, the optimal bank capital requirement, which trades off a lower frequency of twin defaults against restricting credit provision, is higher than under default risk models which underestimate the impact of borrower default on bank solvency.