According to Lütkepohl (1982) and Triacca (1998), the bi-variate model specification may have consequences in terms of the loss of information which can distort the direction of causality between variables because of the potential variable bias. To overcome this problem, some authors include additional variables, however, robust methods should be used to address the lack of statistical motivation in selecting the control variables to be considered in the causal analysis. For this reason, one of the purposes of this paper is to apply a robust Bayesian probabilistic model to identify the most relevant variables to be considered in the causal relationship between the public debt and economic growth.
Our contribution to the extant literature is to propose an alternative methodology to test the causality between economic growth and public debt based on a multivariate framework in which we include variables with the highest posterior probability of inclusion in the model using the World Bank database. Simultaneously this method considers the presence of several structural breaks which can be approximated by smooth breaks in the Flexible Fourier Form (FFF-VAR). One advantage of the Flexible Fourier Form is that this method can mimic the nature of breaks without knowing the number of break dates, the location, or the magnitude.