Tao Zha

What Does Monetary Policy Do

This paper uses a single time frame and data set to present and analyze the results that have emerged from the recent empirical literature on the effects of monetary policy. It uses statistical methods that allow the analysis of larger models than appear previously in this literature. Monetary policy actions are shown to be largely systematic responses to the state of the economy. Consequently, there is more uncertainty about the effects of monetary policy than might be thought on the basis of simple graphical or narrative approaches to assessing the evidence. JEL Classifications: E3, E4, E5  1996 by THE BROOKINGS INSTITUTION. This document may be freely reproduced for educational and research purposes provided that i) this copyright notice is included with each copy, ii) no changes are made in the document, and iii) copies are not sold, but retained for individual use or distributed free. 1 Indiana University, Yale University, and Federal Reserve Bank of Atlanta, respectively. A draft of this paper is available by ftp from ftp://ftp.econ.yale.edu/pub/sims/bpea or by http from http://ezinfo.ucs.indiana.edu/~eleeper/home.htm. The authors would like to acknowledge what they have learned about the implementation of monetary policy from conversations with Lois Berthaume, Will Roberds, and Mary Rosenbaum of the Atlanta Fed, Charles Steindel of the New York Fed, Marvin Goodfriend of the Richmond Fed, and Sheila Tschinkel. David Petersen of the Atlanta Fed helped both in locating data and in discussions of the operation of the money markets.

Error bands for impulse responses

We examine the theory and behavior in practice of Bayesian and bootstrap methods for generating error bands on impulse responses in dynamic linear models. The Bayesian intervals have a firmer theoretical foundation in small samples, are easier to compute, and are about as good in small samples by classical criteria as are the best bootstrap intervals. Bootstrap intervals based directly on the simulated small-sample distribution of an estimator, without bias correction, perform very badly. We show that a method that has been used to extend to the overidentified case standard algorithms for Bayesian intervals in reduced form models is incorrect, and we show how to obtain correct Bayesian intervals for this case.

Bayesian Methods for Dynamic Multivariate Models

If dynamic multivariate models are to be used to guide decisionmaking, it is important that probability assessments of forecasts or policy projections be provided. When identified Bayesian vector autoregression (VAR) models are presented with error bands in the existing literature, both conceptual and numerical problems have not been dealt with in an internally consistent way. In this paper, the authors develop methods to introduce prior information in both reduced-form and structural VAR models without introducing substantial new computational burdens. Their approach makes it feasible to use a single, large dynamic framework (for example, twenty-variable models) for tasks of policy projections. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Identifying monetary policy in a small open economy under flexible exchange rates

Previous empirical study on the effects of monetary policy shocks in small open economies has produced exchange rate responses that are inconsistent with existing open economy macroeconomic theory. We argue that a careful identification of monetary policy in an explicit open economy setting is required. Using Canada as a case study, we specify and estimate a vector-autoregressive model that focuses on the identification of contemporaneous monetary policy, and we obtain tightly estimated results overall. The resulting dynamic responses to the identified monetary policy shock as well as to a foreign shock are consistent with traditional open economy analyses and highlight the importance of the exchange rate as a transmission mechanism.

DOES MONETARY POLICY GENERATE RECESSIONS

The issue of uncovering the effects of monetary policy is far short of resolution. In the identified VAR literature, restrictions have been imposed to identify the effects of unpredictable monetary policy disturbances. We offer critical views on the unreasonable assumptions in the existing work and argue for careful economic argument about identifying assumptions. We display a structural stochastic equilibrium model in which our VAR identification would produce correct results while drawing attention to the serious lack of time series fit in most of the DSGE literature.

Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference

Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference.

Conditional Forecasts in Dynamic Multivariate Models

In the existing literature, conditional forecasts in the vector autoregressive (VAR) framework have not been commonly presented with probability distributions or error bands. This paper develops Bayesian methods for computing such distributions or bands. It broadens the class of conditional forecasts to which the methods can be applied. The methods work for both structural and reduced-form VAR models and, in contrast to common practices, account for the parameter uncertainty in small samples. Empirical examples under the flat prior and under the reference prior of Sims and Zha (1998) are provided to show the use of these methods.

Block recursion and structural vector autoregressions

In applications of structural VAR modeling, finite-sample properties may be difficult to obtain when certain identifying restrictions are imposed on lagged relationships. As a result, even though imposing some lagged restrictions makes economic sense, lagged relationships are often left unrestricted to make statistical inference more convenient. This paper develops block Monte Carlo methods to obtain both maximum likelihood estimates and exact Bayesian inference when certain types of restrictions are imposed on the lag structure. These methods are applied to two examples to illustrate the importance of imposing restrictions on lagged relationships.

Sources of Macroeconomic Fluctuations: A Regime-switching DSGE Approach

We examine the sources of macroeconomic economic fluctuations by estimating a variety of medium-scale DSGE models within a unified framework that incorporates regime switching both in shock variances and in the inflation target. Our general framework includes a number of different model features studied in the literature. We propose an efficient methodology for estimating regime-switching DSGE models. The model that best fits the U.S. time-series data is the one with synchronized shifts in shock variances across two regimes and the fit does not rely on strong nominal rigidities. We find little evidence of changes in the inflation target. We identify three types of shocks that account for most of macroeconomic fluctuations: shocks to total factor productivity, wage markup, and the capital depreciation rate.

Understanding Markov-switching rational expectations models

We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models and we develop an algorithm to check these conditions in practice. We use three examples, based on the new-Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov-switching with forward looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.