Structural VARs and VECMs

Abstract

In Chapters 2 and 6, we have seen that, on the one hand, impulse responses are an important tool to uncover the relations between the variables in a VAR or VECM and, on the other hand, there are some obstacles in their interpretation. In particular, impulse responses are generally not unique and it is often not clear which set of impulse responses actually reflects the ongoings in a given system. Because the different sets of impulses can be computed from the same underlying VAR or VECM, it is clear that nonsample information has to be used to decide on the proper set for a particular given model. In econometric terminology, VARs are reduced form models and structural restrictions are required to identify the relevant innovations and impulse responses. In this chapter, different possible restrictions that have been proposed in the literature will be considered. The resulting models are known as structural VAR (SVAR) models (see, e.g. In the next section, structural restrictions will be discussed for stationary processes. Some of them will also be relevant for VARs with integrated variables. Such variables are explicitly taken into account in VECMs for which structural restrictions will be discussed in Section 9.2. It will be seen that VECMs offer additional possibilities for structural restrictions. The general modelling strategy for both SVARs and SVECMs is to specify and estimate a reduced form model first and then focus on the structural parameters and the resulting structural impulse responses. Estimation of structural VARs and VECMs will be discussed in Section 9.3 and impulse response analysis and forecast error variance decomposition based on such models are considered in Section 9.4. Some extensions of the setup used in this chapter are pointed out in Section 9.5.