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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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Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information
Christiane Baumeister, James D. Hamilton
Econometrica,
No. 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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The Quantity Theory Revisited: A New Structural Approach
Makram El-Shagi, Sebastian Giesen
Abstract
While the long run relation between money and inflation is well established, empirical evidence on the adjustment to the long run equilibrium is very heterogeneous. In this paper we show, that the development of US consumer price inflation between 1960Q1 and 2005Q4 is strongly driven by money overhang. To this end, we use a multivariate state space framework that substantially expands the traditional vector error correction approach. This approach allows us to estimate the persistent components of velocity and GDP. A sign restriction approach is subsequently used to identify the structural shocks to the signal equations of the state space model, that explain money growth, inflation and GDP growth. We also account for the possibility that measurement error exhibited by simple-sum monetary aggregates causes the consequences of monetary shocks to be improperly identified by using a Divisia monetary aggregate. Our findings suggest that when the money is measured using a reputable index number, the quantity theory holds for the United States.
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