Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks
American Economic Review,
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.
Inference in Structural Vector Autoregressions when the Identifying Assumptions are not Fully Believed: Re-evaluating the Role of Monetary Policy in Economic Fluctuations
Journal of Monetary Economics,
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.
Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information
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.