Time Varying Structural Vector Autoregressions and Monetary Policy

One or two of you may be interested in this paper.  The introduction is in the continuation frame:

Primiceri, Giorgio E., "Time Varying Structural Vector Autoregressions and Monetary Policy". Review of Economic Studies, Vol. 72, No. 3, pp. 821-852, July 2005 (SSRN link, July 2004 version on author website) Abstract: Monetary policy and the private sector behaviour of the U.S. economy are modelled as a time varying structural vector autoregression, where the sources of time variation are both the coefficients and the variance covariance matrix of the innovations. The paper develops a new, simple modelling strategy for the law of motion of the variance covariance matrix and proposes an efficient Markov chain Monte Carlo algorithm for the model likelihood/posterior numerical evaluation. The main empirical conclusions are: (1) both systematic and non-systematic monetary policy have changed during the last 40 years - in particular, systematic responses of the interest rate to inflation and unemployment exhibit a trend toward a more aggressive behaviour, despite remarkable oscillations; (2) this has had a negligible effect on the rest of the economy. The role played by exogenous non-policy shocks seems more important than interest rate policy in explaining the high inflation and unemployment episodes in recent U.S. economic history.

1 Introduction (This is from the July 2004 version)  

There is strong evidence that US unemployment and inflation were higher and more volatile in the period between 1965 and 1980 than in the last twenty years. The literature has considered two main classes of explanations for this difference in performance. The first class of explanations (see, for instance, Blanchard and Simon, 2001, Stock and Watson, 2002, Sims and Zha, 2004) focuses on the heteroskedasticity of the exogenous shocks, which have been much more volatile in the 70s and early 80s than in the rest of the sample. The second class of explanations emphasizes the changes in the transmission mechanism, i.e. the way macroeconomic variables respond to shocks. Particular attention has been given to monetary policy. If monetary policy varies over time, this has a potential direct effect on the propagation mechanism of the innovations. Furthermore, if agents are rational and forward-looking, policy changes will be incorporated in the private sector’s forecasts, inducing additional modifications in the transmission mechanism.

Many authors (among others Boivin and Giannoni, 2003, Clarida, Galí and Gertler, 2000, Cogley and Sargent, 2001 and 2003, Judd and Rudebusch, 1998, Lubik and Schorfheide, 2004) have argued that US monetary policy was less active against inflationary pressures under the Fed chairmanship of Arthur Burns than under Paul Volcker and Alan Greenspan. However, this view is controversial. Other studies have in fact found either little evidence of changes in the systematic part of monetary policy (Bernanke and Mihov, 1998, Hanson, 2003, Leeper and Zha, 2002) or no evidence of unidirectional drifts in policy toward a more active behavior (Sims, 1999 and 2001a).  

This paper investigates the potential causes of the poor economic performance of the 70s and early 80s and to what extent monetary policy played an important role in these high unemployment and inflation episodes. The objective here is to provide a flexible framework for the estimation and interpretation of time variation in the systematic and non-systematic part of monetary policy and their effect on the rest of the economy. Two are the main characteristics required for an econometric framework able to address the issue: 1) time varying parameters in order to measure policy changes and implied shifts in the private sector behavior; 2) a multiple equation model of the economy in order to understand how changes in policy have affected the rest of the economy. For this purpose, this paper estimates a time varying structural vector autoregression (VAR), where the time variation derives both from the coefficients and the variance covariance matrix of the model’s innovations. Notice that any reasonable attempt to model changes in policy, structure and their interaction must include time variation of the variance covariance matrix of the innovations. This reflects both time variation of the simultaneous relations among the variables of the model and heteroskedasticity of the innovations. This is done by developing a simple multivariate stochastic volatility modeling strategy for the law of motion of the variance covariance matrix. The estimation of this model with drifting coefficients and multivariate stochastic volatility requires numerical methods. An efficient Markov chain Monte Carlo algorithm is proposed for the numerical evaluation of the posterior of the parameters of interest.  

The methodology developed in the paper is used to estimate a small model of the US economy, delivering many empirical conclusions. First of all, there is evidence of changes both in nonsystematic and systematic monetary policy during the last forty years. The relative importance of non-systematic policy was significantly higher in the first part of the sample, suggesting that a Taylor-type rule is much less representative of the US monetary policy in the 60s and 70s than in the last fifteen years. Furthermore, private sector responses to non-systematic policy (monetary policy shocks) appear linear in the amplitude of non-systematic policy actions. Turning to the systematic part of policy, there is some evidence of higher interest rate responses to inflation and unemployment in the Greenspan period. However, a counterfactual simulation exercise suggests these changes did not play an important role in the high inflation and unemployment episodes in recent US economic history. In fact, the high volatility of the exogenous non-policy shocks seems to explain a larger fraction of the outbursts of inflation and unemployment of the 70s and early 80s.  

From the methodological perspective, this paper is related to the fairly well developed literature on modeling and estimating time variation in multivariate linear structures. Canova (1993), Sims (1993), Stock and Watson (1996) and Cogley and Sargent (2001) model and estimate VARs with drifting coefficients. On the other hand, multivariate stochastic volatility models are discussed by Harvey, Ruiz and Shephard (1994), Jacquier, Polson and Rossi (1995), Kim, Shephard and Chib (1998), Chib, Nardari and Shephard (2002). However, these studies impose some restrictions on the evolution over time of the elements of the variance covariance matrix. Typical restrictions are either the assumption that the covariances do not evolve independently of the variances or a factor structure for the covariance matrix. Following this line of research, Cogley (2003) and Cogley and Sargent (2003) use time varying variances in the context of VARs with drifting coefficients. However, in their model the simultaneous relations among variables are time invariant. As it will be made clear in the next section, their analysis is limited to reduced form models, usable almost only for data description and forecasting. Boivin (2001) considers the opposite case of time varying simultaneous relations, but neglects the potential heteroskedasticity of the innovations. Ciccarelli and Rebucci (2003) extend the framework of Boivin (2001) allowing for t-distributed errors, which account for non-persistent changes in the scale of the variances over time. Uhlig (1997) introduces unrestricted multivariate stochastic volatility in the context of VARs, but his model assumes that the VAR coefficients are constant. Here instead, both the coefficients and the entire variance covariance matrix of the shocks are allowed to vary over time. This is crucial if the objective is distinguishing between changes in the typical size of the exogenous innovations and changes in the transmission mechanism.  

There is also a more recent literature that models time variation in linear structures with discrete breaks, meant to capture a finite number of switching regimes (see, for instance, Hamilton, 1989, Kim and Nelson, 1999, Sims, 1999 and 2001a and Sims and Zha, 2004). Discrete breaks models may well describe some of the rapid shifts in policy. However they seem less suitable to capture changes in private sector behavior, where aggregation among agents usually plays the role of smoothing most of the changes. Furthermore, even in a structural VAR, the private sector equations can be considered as reduced form relations with respect to a possible underlying behavioral model, where policy and private sector behavior are not easily distinguishable. If policy responds also to expectational future variables (instead of only to current and past ones), then also the policy equation in the VAR will be a mixture of policy and private sector behavior, determining smoother changes of the coefficients. Finally, the existence of any type of learning dynamics by private agents or the monetary authorities definitely favors a model with smooth and continuous drifting coefficients over a model with discrete breaks.  

From the perspective of the empirical application, this paper is related to a large literature that analyzes changes in the conduct of monetary policy and their effect on the rest of the economy. Most of the existing academic work has emphasized the role of monetary policy in the poor economic performance of the 70s (among others, see Judd and Rudebusch, 1998, Clarida, Galí and Gertler, 2000, Boivin, 2001, Cogley and Sargent, 2001 and 2003, Lubik and Schorfheide, 2004, Boivin and Giannoni, 2003, Favero and Rovelli, 2003). This paper contrasts the most popular view and stresses the role of heteroskedastic non-policy innovations. In this respect, the conclusions are more similar to Bernanke and Mihov (1998) and Sims and Zha (2004)...