RDP 2013-06: Estimating and Identifying Empirical BVAR-DSGE Models for Small Open Economies 1. Introduction

DSGE models provide an internally and theoretically consistent description of the macroeconomy. They give clear economic interpretations of the shocks affecting the economy. This interpretability, however, comes at a cost; a reduced-form VAR, for example, generally provides a better fit of the data. The aim of this paper is to develop a model in which the shocks can still be interpreted but the fit with the data may be improved.

The approach in this paper is to use an estimated DSGE model as a source of prior information about the parameters of a VAR. This effectively relaxes some of the relationships in the DSGE model, which, while theoretically well founded, may not hold in the data. One reason for this lack of fit is that all models are necessarily simplifications of reality. For example, many small open economy models include an uncovered interest parity condition, which can be derived from an arbitrage condition between foreign- and domestic-currency denominated risk-free bonds. Despite these theoretical underpinnings, uncovered interest parity has been widely found to be at odds with the data. In small open economy models other common simplifications include the assumptions that all imports are consumption goods, labour is the only input to production and financial markets operate largely without frictions. All of these assumptions can be relaxed, and whether they are of quantitative importance depends on the question to be answered.

Bayesian methods are a way of integrating prior information into parameter estimates. A Bayesian VAR (BVAR) that uses priors from an estimated DSGE model will therefore represent a compromise between the theoretically coherent DSGE and a VAR that may fit the data better. Another interpretation of this hybrid model is that the parameters of an unrestricted VAR are being pulled towards those of the DSGE model.

The DSGE model is a potentially useful way of formulating a prior for a VAR. The parameters in the DSGE model have straightforward economic interpretations.

For example, the intertemporal elasticity of substitution captures the willingness of an individual to trade off consumption today for future consumption. DSGE models are frequently estimated using Bayesian methods. One way to form a prior about the intertemporal elasticity of substitution is to look at microeconomic data, such as surveys of household consumption behaviour. However, the mapping from microeconomic to macroeconomic estimates may not be straightforward, and often priors are based on previous similar macroeconomic studies. In contrast, while priors for reduced-form VARs do exist (most notably the Minnesota prior for forecasting; see, for example, Doan, Litterman and Sims (1984)), it is more difficult to form a prior over the coefficient on, say, the second lag on a particular variable in the VAR, as it has no clear economic interpretation. The method proposed in this paper is a way of utilising information from the DSGE model, whose parameters are relatively easy to place priors over, in forming priors for a VAR.

Several studies have previously examined eliciting priors for a BVAR from general equilibrium models. The focus of Ingram and Whiteman (1994) was on forecasting using the resulting reduced-form BVAR. Of particular interest is Del Negro and Schorfheide (2004), who also estimate a reduced-form BVAR with DSGE model-based priors, and then use information from the DSGE model to identify it, a strategy I follow. This method has previously been applied to small open economies, for example by Hodge, Robinson and Stuart (2008) and Lees, Matheson and Smith (2011), for Australia and New Zealand respectively.

While the DSGE prior in these papers is based on a small open economy model, the Del Negro and Schorfheide (2004) approach does not allow for small open economy restrictions on the BVAR estimates. Hodge et al (2008) and Lees et al (2011) deal with this problem implicitly by estimating small BVARs of only five variables that do not include foreign output, interest rates or inflation, although these are included in the DSGE prior.^[1] This, however, is somewhat unsatisfactory because it is necessary to include foreign variables to adequately capture the dynamics of small economies; see, for example, Dungey and Pagan (2000, 2009). However, by including foreign variables but not imposing restrictions that limit the ability of the small open economy to affect the large economy may result in unrealistically large effects. The estimation approach presented here to circumvent this problem draws on DeJong, Ingram and Whiteman (1993). Filippeli, Harrison and Theodoridis (2011) independently developed a similar estimation methodology, but did not take small open economy considerations into account.

This paper is structured as follows. Section 2 describes the methodology used to estimate the empirical BVAR-DSGE model, and Section 3 discusses its identification. Section 4 provides an empirical example, by estimating an empirical BVAR-DSGE model for Australia where the Justiniano and Preston (2010a) model is used as a prior. This empirical BVAR-DSGE model estimates a larger role for the foreign shocks in the small economy's business cycle than the DSGE model. Finally, the conclusions of this paper are presented in Section 5.

Footnote

These VARs include domestic output growth, inflation, interest rates and growth in the real exchange rate and the terms of trade. [1]