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.
Reconciling Narrative Monetary Policy Disturbances with Structural VAR Model Shocks?
Structural VAR studies disagree with narrative accounts about the history of monetary policy disturbances. We investigate whether employing the narrative monetary shocks as a proxy variable in a VAR model aligns both shock series. We find that it does not.
Monetary Policy in a World Where Money (Also) Matters
IWH Discussion Papers,
While the long-run relation between money and inflation as predicted by the quantity theory is well established, empirical studies of the short-run adjustment process have been inconclusive at best. The literature regarding the validity of the quantity theory within a given economy is mixed. Previous research has found support for quantity theory within a given economy by combining the P-Star, the structural VAR and the monetary aggregation literature. However, these models lack precise modelling of the short-run dynamics by ignoring interest rates as the main policy instrument. Contrarily, most New Keynesian approaches, while excellently modeling the short-run dynamics transmitted through interest rates, ignore the role of money and thus the potential mid-and long-run effects of monetary policy. We propose a parsimonious and fairly unrestrictive econometric model that allows a detailed look into the dynamics of a monetary policy shock by accounting for changes in economic equilibria, such as potential output and money demand, in a framework that allows for both monetarist and New Keynesian transmission mechanisms, while also considering the Barnett critique. While we confirm most New Keynesian findings concerning the short-run dynamics, we also find strong evidence for a substantial role of the quantity of money for price movements.