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Working Paper
Specification Choices in Quantile Regression for Empirical Macroeconomics
Quantile regression has become widely used in empirical macroeconomics, in particular for estimating and forecasting tail risks to macroeconomic indicators. In this paper we examine various choices in the specification of quantile regressions for macro applications, for example, choices related to how and to what extent to include shrinkage, and whether to apply shrinkage in a classical or Bayesian framework. We focus on forecasting accuracy, using for evaluation both quantile scores and quantile-weighted continuous ranked probability scores at a range of quantiles spanning from the left to ...
Working Paper
Endogenous Uncertainty
We show that macroeconomic uncertainty can be considered as exogenous when assessing its effects on the U.S. economy. Instead, financial uncertainty can at least in part arise as an endogenous response to some macroeconomic developments, and overlooking this channel leads to distortions in the estimated effects of financial uncertainty shocks on the economy. We obtain these empirical findings with an econometric model that simultaneously allows for contemporaneous effects of both uncertainty shocks on economic variables and of economic shocks on uncertainty. While the traditional econometric ...
Working Paper
Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and ...
Working Paper
Addressing COVID-19 Outliers in BVARs with Stochastic Volatility
Incoming data in 2020 posed sizable challenges for the use of VARs in economic analysis: Enormous movements in a number of series have had strong effects on parameters and forecasts constructed with standard VAR methods. We propose the use of VAR models with time-varying volatility that include a treatment of the COVID extremes as outlier observations. Typical VARs with time-varying volatility assume changes in uncertainty to be highly persistent. Instead, we adopt an outlier-adjusted stochastic volatility (SV) model for VAR residuals that combines transitory and persistent changes in ...
Working Paper
Measuring Uncertainty and Its Effects in the COVID-19 Era
We measure the effects of the COVID-19 outbreak on uncertainty, and we assess the consequences of the uncertainty for key economic variables. We use a large, heteroskedastic vector autoregression (VAR) in which the error volatilities share two common factors, interpreted as macro and financial uncertainty. Macro and financial uncertainty are allowed to contemporaneously affect the macroeconomy and financial conditions, with changes in the common component of the volatilities providing contemporaneous identifying information on uncertainty. The model includes additional latent volatility ...
Working Paper
Real-time nowcasting with a Bayesian mixed frequency model with stochastic volatility
This paper develops a method for producing current-quarter forecasts of GDP growth with a (possibly large) range of available within-the-quarter monthly observations of economic indicators, such as employment and industrial production, and financial indicators, such as stock prices and interest rates. In light of existing evidence of time variation in the variances of shocks to GDP, we consider versions of the model with both constant variances and stochastic volatility. We also evaluate models with either constant or time-varying regression coefficients. We use Bayesian methods to estimate ...
Working Paper
No-Arbitrage Priors, Drifting Volatilities, and the Term Structure of Interest Rates
We derive a Bayesian prior from a no-arbitrage affine term structure model and use it to estimate the coefficients of a vector autoregression of a panel of government bond yields, specifying a common time-varying volatility for the disturbances. Results based on US data show that this method improves the precision of both point and density forecasts of the term structure of government bond yields, compared to a fully fledged term structure model with time-varying volatility and to a no-change random walk forecast. Further analysis reveals that the approach might work better than an exact term ...
Working Paper
Macroeconomic Forecasting in a Multi-country Context
In this paper we propose a hierarchical shrinkage approach for multi-country VAR models. In implementation, we consider three different scale mixtures of Normals priors — specifically, Horseshoe, Normal- Gamma, and Normal-Gamma-Gamma priors. We provide new theoretical results for the Normal-Gamma prior. Empirically, we use a quarterly data set for the G7 economies to examine how model specifications and prior choices affect the forecasting performance for GDP growth, inflation, and a short-term interest rate. We find that hierarchical shrinkage, particularly as implemented with the ...
Working Paper
Empirical simultaneous prediction regions for path-forecasts
This paper investigates the problem of constructing prediction regions for forecast trajectories 1 to H periods into the future - a path forecast. We take the more general view that the null model is only approximative and in some cases it may be altogether unavailable. As a consequence, one cannot derive the usual analytic expressions nor resample from the null model as is usually done when bootstrap methods are used. The paper derives methods to construct approximate rectangular regions for simultaneous probability coverage which correct for serial correlation. The techniques appear to work ...
Working Paper
Large Vector Autoregressions with Stochastic Volatility and Flexible Priors
Recent research has shown that a reliable vector autoregressive model (VAR) for forecasting and structural analysis of macroeconomic data requires a large set of variables and modeling time variation in their volatilities. Yet, there are no papers jointly allowing for stochastic volatilities and large datasets, due to computational complexity. Moreover, homoskedastic VAR models for large datasets so far restrict substantially the allowed prior distributions on the parameters. In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time varying ...