Priors from General Equilibrium Models for VARs

Article excerpt

Abstract: This paper uses a simple New-Keynesian dynamic stochastic general equilibrium model as a prior for a vector autoregression, shows that the resulting model is competitive with standard benchmarks in terms of forecasting, and can be used for policy analysis.

JEL classification: C11, C32, C53

Key words: Bayesian analysis, DSGE models, forecasting, vector autoregressions

1 Introduction

Dynamic stochastic general equilibrium (DSGE) models are popular nowadays in macroeconomics. They are taught in virtually every economics Ph.D. program, and represent a predominant share of publications in the field. Yet, when it comes to policy making, these models are scarcely used--at least from a quantitative point of view. The main quantitative workhorse for policy making at the Federal Reserve System is FRB-US, a macro-econometric model built in the Cowles foundation tradition--a style of macroeconomics that is no longer taught in many Ph.D. programs. (1) In their decision process, Fed policy makers rely heavily on forecasting. They want to know the expected path of inflation in the next few quarters, and by how much a 50 basis point increase in the federal funds rate would affect that path. FRB-US offers answers to these questions--answers that many macroeconomists would regard with suspicion given both the Lucas' (1976) critique and the fact that in general the restrictions imposed by Cowles foundation models are at odds with dynamic general equilibrium macroeconomics (Sims, 1980). General equilibrium models on the other hand have a hard time providing alternative answers. The fact that these models are perceived to do badly in terms of forecasting, as they are scarcely parameterized, is perhaps one of the reasons why they are not at the forefront of policy making.

While progress is being made in the development of DSGE models that deliver acceptable forecasts, e.g., Smets and Wouters (2003), this paper proposes an approach that combines a stylized general equilibrium model with a vector autoregression (VAR) to obtain a specification that both forecasts well and is usable for policy analysis. Specifically, the approach involves using prior information coming from a DSGE model in the estimation of a vector autoregression. Loosely speaking, this prior can be thought of as the result of the following exercise: (i) simulate time series data from the DSGE model, (ii) fit a VAR to these data. In practice we replace the sample moments of the simulated data by population moments computed from the DSGE model solution. Since the DSGE model depends on unknown structural parameters, we use a hierarchical prior in our analysis by placing a distribution on the DSGE model parameters. A tightness parameter controls the weight of the DSGE model prior relative to the weight of the actual sample. Markov-Chain Monte Carlo methods are used to generate draws from the joint posterior distribution of the VAR and DSGE model parameters.

The paper shows that the approach makes even a fairly stylized New Keynesian DSGE model competitive with standard benchmarks in terms of forecasting real output growth, inflation, and the nominal interest rate--the three variables that are of most interest to policy makers. (2) Up to this point our procedure borrows from the work of DeJong, Ingram, and Whiteman (1993), and Ingram and Whiteman (1994), who are the first to use priors from DSGE models for VARs. Ingram and Whiteman showed that prior information from the bare-bones stochastic growth model of King, Plosser, and Rebelo (1988) is helpful in forecasting real economic activity, such as output, consumption, investment, and hours worked.

In addition to documenting the forecasting performance of a trivariate VAR with a prior derived from a monetary DSGE model, this paper makes two contributions that significantly extend the earlier work. First, we show formally how posterior inference for the VAR parameters can be translated into posterior inference for DSGE model parameters. …


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