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Advances in Using Vector Autoregressions to Estimate Structural Magnitudes

Christiane Baumeister, James D. Hamilton
Econometric Theory, Nr. 3, 2024
Abstract

This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.

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Tracking Weekly State-Level Economic Conditions

Christiane Baumeister, Danilo Leiva-León, Eric Sims
Review of Economics and Statistics, Nr. 2, 2024
Abstract

This paper develops a novel dataset of weekly economic conditions indices for the 50 U.S. states going back to 1987 based on mixed-frequency dynamic factor models with weekly, monthly, and quarterly variables that cover multiple dimensions of state economies. We find considerable cross-state heterogeneity in the length, depth, and timing of business cycles. We illustrate the usefulness of these state-level indices for quantifying the main contributors to the economic collapse caused by the COVID-19 pandemic and for evaluating the effectiveness of the Paycheck Protection Program. We also propose an aggregate indicator that gauges the overall weakness of the U.S. economy.

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Energy Markets and Global Economic Conditions

Christiane Baumeister, Dimitris Korobilis, Thomas K. Lee
Review of Economics and Statistics, Nr. 4, 2022
Abstract
We evaluate alternative indicators of global economic activity and other market funda-mentals in terms of their usefulness for forecasting real oil prices and global petroleum consumption. World industrial production is one of the most useful indicators. However, by combining measures from several different sources we can do even better. Our analysis results in a new index of global economic conditions and measures for assessing future energy demand and oil price pressures. We illustrate their usefulness for quantifying the main factors behind the severe contraction of the global economy and the price risks faced by shale oil producers in early 2020.
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Structural Vector Autoregressions with Imperfect Identifying Information

Christiane Baumeister, James D. Hamilton
American Economic Association Papers and Proceedings, May 2022
Abstract
The problem of identification is often the core challenge of empirical economic research. The traditional approach to identification is to bring in additional information in the form of identifying assumptions, such as restrictions that certain magnitudes have to be zero. In this paper, we suggest that what are usually thought of as identifying assumptions should more generally be described as information that the analyst had about the economic structure before seeing the data. Such information is most naturally represented as a Bayesian prior distribution over certain features of the economic structure.
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A Comparison of Monthly Global Indicators for Forecasting Growth

Christiane Baumeister, Pierre Guérin
International Journal of Forecasting, Nr. 3, 2021
Abstract
This paper evaluates the predictive content of a set of alternative monthly indicators of global economic activity for nowcasting and forecasting quarterly world real GDP growth using mixed-frequency models. It shows that a recently proposed indicator that covers multiple dimensions of the global economy consistently produces substantial improvements in forecasting accuracy, while other monthly measures have more mixed success. Specifically, the best-performing model yields impressive gains with MSPE reductions of up to 34% at short horizons and up to 13% at long horizons relative to an autoregressive benchmark. The global economic conditions indicator also contains valuable information for assessing the current and future state of the economy for a set of individual countries and groups of countries. This indicator is used to track the evolution of the nowcasts for the U.S., the OECD area, and the world economy during the COVID-19 pandemic and the main factors that drive the nowcasts are quantified.
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Drawing Conclusions from Structural Vector Autoregressions Identified on the Basis of Sign Restrictions

Christiane Baumeister, James D. Hamilton
Journal of International Money and Finance, December 2020
Abstract
This paper discusses the problems associated with using information about the signs of certain magnitudes as a basis for drawing structural conclusions in vector autoregressions. We also review available tools to solve these problems. For illustration we use Dahlhaus and Vasishtha’s (2019) study of the effects of a U.S. monetary contraction on capital flows to emerging markets. We explain why sign restrictions alone are not enough to allow us to answer the question and suggest alternative approaches that could be used.
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Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks

Christiane Baumeister, James D. Hamilton
American Economic Review, Nr. 5, 2019
Abstract
Traditional approaches to structural vector autoregressions (VARs) can be viewed as special cases of Bayesian inference arising from very strong prior beliefs. These methods can be generalized with a less restrictive formulation that incorporates uncertainty about the identifying assumptions themselves. We use this approach to revisit the importance of shocks to oil supply and demand. Supply disruptions turn out to be a bigger factor in historical oil price movements and inventory accumulation a smaller factor than implied by earlier estimates. Supply shocks lead to a reduction in global economic activity after a significant lag, whereas shocks to oil demand do not.
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Inference in Structural Vector Autoregressions when the Identifying Assumptions are not Fully Believed: Re-evaluating the Role of Monetary Policy in Economic Fluctuations

Christiane Baumeister, James D. Hamilton
Journal of Monetary Economics, 2018
Abstract
Point estimates and error bands for SVARs that are set identified are only justified if the researcher is persuaded that some parameter values are a priori more plausible than others. When such prior information exists, traditional approaches can be generalized to allow for doubts about the identifying assumptions. We use information about both structural coefficients and impacts of shocks and propose a new asymmetric t-distribution for incorporating information about signs in a nondogmatic way. We apply these methods to a three-variable macroeconomic model and conclude that monetary policy shocks are not the major driver of output, inflation, or interest rates.
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Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information

Christiane Baumeister, James D. Hamilton
Econometrica, Nr. 5, 2015
Abstract
This paper makes the following original contributions to the literature. (i) We develop a simpler analytical characterization and numerical algorithm for Bayesian inference in structural vector autoregressions (VARs) that can be used for models that are overidentified, just‐identified, or underidentified. (ii) We analyze the asymptotic properties of Bayesian inference and show that in the underidentified case, the asymptotic posterior distribution of contemporaneous coefficients in an n‐variable VAR is confined to the set of values that orthogonalize the population variance–covariance matrix of ordinary least squares residuals, with the height of the posterior proportional to the height of the prior at any point within that set. For example, in a bivariate VAR for supply and demand identified solely by sign restrictions, if the population correlation between the VAR residuals is positive, then even if one has available an infinite sample of data, any inference about the demand elasticity is coming exclusively from the prior distribution. (iii) We provide analytical characterizations of the informative prior distributions for impulse‐response functions that are implicit in the traditional sign‐restriction approach to VARs, and we note, as a special case of result (ii), that the influence of these priors does not vanish asymptotically. (iv) We illustrate how Bayesian inference with informative priors can be both a strict generalization and an unambiguous improvement over frequentist inference in just‐identified models. (v) We propose that researchers need to explicitly acknowledge and defend the role of prior beliefs in influencing structural conclusions and we illustrate how this could be done using a simple model of the U.S. labor market.
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