RDP 2008-04: A Small BVAR-DSGE Model for Forecasting the Australian Economy 1. Introduction

Forecasting is hard. Forecasting is also a key aspect of central banking. Consequently, central banks devote considerable resources to forecasting and understanding the current state of the economy, of which econometric models are one component. Models can be used for a variety of purposes – for example, scenario analysis and forecasting – and these different roles may require different models. The purpose of this paper is to estimate a model for Australia specifically designed for forecasting key macroeconomic variables, namely a structural Bayesian Vector Autoregression (BVAR), with priors from a Dynamic Stochastic General Equilibrium (DSGE) model.

DSGE models are structural models, often with explicit microeconomic foundations, an example of which, for Australia, is Jääskelä and Nimark (forthcoming).^[1] Consequently, these models have a strong emphasis on theory, which places many restrictions on the parameters, possibly at the expense of fitting the data. Alternatively, VARs are far less restrictive and therefore may fit the data better.^[2] However, good in-sample fit does not necessarily translate into good out-of-sample forecasting performance; for example, an unrestricted VAR may have many parameters which are imprecisely estimated, particularly in small samples. The Bayesian framework is a way of introducing prior information and therefore producing more precise parameter estimates. A common prior used for VARs is that the series are very persistent, which is referred to as the Minnesota prior.^[3] While the Minnesota prior has aided the forecasting ability of VAR models, it is a purely statistical device. As an alternative, we use a small DSGE model as the source of prior information for the VAR.

Footnotes

Sometimes a distinction is made between DSGE and new-Keynesian models, with the former used to refer to relatively large models. We use the terms interchangeably. [1]

The trade-off between theoretical coherence and fit is the basis of the Pagan diagram (Pagan 2003). [2]

The Minnesota prior was introduced by Litterman (1979), and extended by Doan, Litterman and Sims (1984); an intuitive description is in Todd (1984). For an overview of Bayesian forecasting, see Geweke and Whiteman (2006). [3]