Long run a prior information. Deterministic components. Cointegration

Abstract

In the present chapter we discuss some issues connected to Structural VAR analysis leading to substantial deviations from the analytical apparatus described in the first five chapters of this book. We have in fact so far focused on zero mean stationary series and on the availability of exact linear constraints in order to obtain an identified structure. We remove all these hypotheses in this chapter. Section 6.1 deals with the problems induced by constraints on the long-run considerations. Section 6.2 describes the role of non-zero deterministic components in the VAR and VMA representations. Section 6.3 is devoted to the problems encountered in the analysis of the interactions between non-stationary series, in the light of the concept of cointegration, which is discussed from the viewpoint of its contrast with the concept of “spurious regression”. The main representations of cointegrated systems are briefly described in section 6.3.1, in order to understand fully the different properties of a cointegrating system. Section 6.3.2 deals with the main estimation techniques available to estimate cointegrating relationships, with particular attention being devoted to the maximum likelihood analysis put forward by S. Johansen, since this is the only approach capable of delivering a testing procedure in order to make inference on the number of long-run relationships.