Dilution priors for groups of variables in BMA: An application to the recent financial crisis

We apply Bayesian Model Averaging procedures to a dataset on growth to estimate the output gap caused by the recent financial crisis. The special focus of this work lies in group of variables that may simultaneously cause countries to behave differently during episodes of economic recessions. In order to shed light on these variable groups we contribute a new form of dilution prior that compensates for multicollinear variables. To illustrate the effects of such a prior a simulation study is provided. Followingly the method is applied to a global dataset which consists of 150 countries.We use state of the art Bayesian Model Averaging techniques. Since parameter heterogeneity might play an important role in our dataset, a large number of interaction terms are included in the model. To treat these correctly the authors specify a new kind of model prior that accounts for model redundancy, which can be viewed as similar models in the model space. More specifically a dilution prior according to the weak heredity principle is used in the BMA procedure that focuses on similar groups of variables such as financial or trade indicators. Through this procedure models that consist of similar variables from one of these groups get penalized through a shrinkage of their likelihood.The empirical analysis estimates driving factors for the different performance of countries during the recent financial crisis. We find evidence that especially financial indicators such as FDI or openness play an important role in this setting.