This paper shows how particle filtering facilitates likelihood-based inference in dynamic macroeconomic models. The economies can be non-linear and/or non-normal. We describe how to use the output from the particle filter to estimate the structural parameters of the model, those characterizing preferences and technology, and to compare different economies. Both tasks can be implemented from either a classical or a Bayesian perspective. We illustrate the technique by estimating a business cycle model with investment-specific technological change, preference shocks, and stochastic volatility.

We identify structural vector autoregressions using narrative sign restrictions. Narrative sign restrictions constrain the structural shocks and/or the historical decomposition around key historical events, ensuring that they agree with the established narrative account of these episodes. Using models of the oil market and monetary policy, we show that narrative sign restrictions tend to be highly informative. Even a single narrative sign restriction may dramatically sharpen and even change the inference of SVARs originally identified via traditional sign restrictions. Our approach combines the appeal of narrative methods with the popularized usage of traditional sign restrictions. (JEL C32, E52, Q35, Q43)

There has been a call for caution regarding the standard procedure for Bayesian inference in set‐identified structural vector autoregressions on the grounds that the common practice of using a uniform prior over the set of orthogonal matrices induces a non‐uniform prior for individual impulse responses or other quantities of interest. This paper challenges this call by formally showing that when the focus is on joint inference, the uniform prior over the set of orthogonal matrices is not only sufficient but also necessary for inference based on a uniform joint prior distribution over the identified set for the vector of impulse responses. In addition, we show how to conduct inference based on a uniform joint prior distribution for the vector of impulse responses.

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.

We present a novel algorithm called Dynamic Perturbation for solving large-scale macroeconomic models. Our approach involves computing first-order Taylor expansions of the policy functions along the entire equilibrium path. This method applies to a wide range of models and offers significantly higher accuracy than traditional perturbation approaches. Remarkably, even when utilising first-order approximations, our method can effectively handle models with strong nonlinearities and occasionally binding constraints, such as the zero lower bound.

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 study how unexpected changes in uncertainty about fiscal policy affect economic activity. First, we estimate tax and spending processes for the United States with time-varying volatility to uncover evidence of time-varying volatility. Second, we estimate a VAR for the US economy using the time-varying volatility found in the previous step. Third, we feed the tax and spending processes into an otherwise standard New Keynesian model. Both in the VAR and in the model, we find that unexpected changes in fiscal volatility shocks can have a sizable adverse effect on economic activity. An endogenous increase in markups is a key mechanism. (JEL E12, E23, E32, E52, E62)

ABSTRACT 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.

Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic stochastic general equilibrium (DSGE) models; yet no workable rank conditions to ascertain whether an SVAR is globally identified have been established. Moreover, when nonlinear identifying restrictions are used, no efficient algorithms exist for small-sample estimation and inference. This paper makes four contributions towards filling these important gaps in the literature. First, we establish general rank conditions for global identification of both identified and exactly identified models. These rank conditions are sufficient for general identification and are necessary and sufficient for exact identification. Second, we show that these conditions can be easily implemented and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we show that the rank condition for exactly identified models amounts to a straightforward counting exercise. Fourth, we develop efficient algorithms for small-sample estimation and inference, especially for SVARs with nonlinear restrictions.

We show how changes in the volatility of the real interest rate at which small open emerging economies borrow have an important effect on variables like output, consumption, investment, and hours. We start by documenting the strong evidence of time-varying volatility in the real interest rates faced by four emerging economies: Argentina, Brazil, Ecuador, and Venezuela. We estimate a stochastic volatility process for real interest rates. Then, we feed this process in a standard small open economy business cycle model. We find that an increase in real interest rate volatility triggers a fall in output, consumption, investment, hours, and debt. (JEL E13, E20, E32, E43, F32, F43, 011)