Bayesian Analysis of Weak Form Reduced Rank Structure in VEC Models

The concept of cointegration that enables the proper statistical analysis of long-run comovements between unit root processes has been of great interest to numerous economic investigators since it was introduced. However, investigation of short-run comovement between economic time series seems equally important, especially for economic decision-makers. The concept of common features and based on it the idea of two additional reduced rank structure forms in a VEC model (the strong and the weak one) may be of some help. The strong form reduced rank structure (SF) takes place when at least one linear combination of the first differences of the variables exists, which is white noise. However, when this assumption seems too strong, the weaker case can be considered. The weak form appears when the linear combination of first differences adjusted for long-run efects exists, which is white noise. The main focus of this paper is a Bayesian analysis of the VEC models involving the weak form of reduced rank restrictions. After the introduction and discussion of the said Bayesian model, the presented methods will be illustrated by an empirical investigation of the price - wage spiral in the Polish economy.