RDP 2013-06: Estimating and Identifying Empirical BVAR-DSGE Models for Small Open Economies 5. Conclusions

BVAR-DSGE models represent a compromise between theoretically coherent DSGE models and more empirically orientated VAR models. The method of Del Negro and Schorfheide (2004) uses a DSGE model to generate a prior for the parameters of a BVAR, but does not accommodate the block exogeneity restriction typically imposed in models of small open economies. Consequently the small economy ceases to be small, in the sense that its shocks can have an impact on the large economy. This paper describes an alternative method of estimating and identifying an empirical BVAR model, where a DSGE model is used as a source of prior information, that is suitable for small open economies.

Like Del Negro and Schorfheide (2004), the method developed in this paper involves estimating a reduced-form BVAR and then identifying it. However, this paper uses a prior that allows some variables to be excluded from some equations. In this way, lags of the small economy variables can be excluded from the large economy equations. Alternative approaches may well exist. One possible alternative might be to place a prior directly on the contemporaneous matrix, perhaps using some combination of the methods of Waggoner and Zha (2003) and Park (2011). I leave exploring these possibilities for future research.

One of the main findings of Justiniano and Preston (2010a) is that in an estimated small open economy model of Canada, little role is found for US shocks in explaining fluctuations in Canadian variables at various forecast horizons. I apply the method outlined in this paper to the Justiniano and Preston (2010a) model using US and Australian data. I show that a similarly small role for foreign shocks is suggested by the DSGE model for Australia, but the empirical BVAR-DSGE model that imposes block exogeneity restrictions finds a larger role. However, the contribution of foreign shocks to fluctuations in some variables, such as the terms of trade, is still much smaller than one would expect intuitively, and some of the impulse responses to foreign shocks are surprising, possibly reflecting the possibility that for Australia the United States is no longer a good proxy for the world economy for the latter part of the sample. Ultimately, while the empirical BVAR-DSGE model allows a greater role for the data, the DSGE model still has considerable influence, both in informing the prior and identifying the model, and consequently a better DSGE model should result in a better empirical BVAR-DSGE model.