Structural VAR (SVAR) Models

Although the estimation of VAR models poses no conceptual difficulties as outlined in the previous chapter, simple OLS estimation equation by equation is sufficient; the individual coefficients are almost impossible to interpret. On the one hand, there are usually many coefficients: A VAR(p) model with n variables, for example, has p × n $$p\times n$$ coefficients per equation and thus p × n 2 $$p\times n^2$$ coefficients in total to interpret, disregarding intercept terms and the ( n + 1 ) n ∕ 2 $$(n+1)n/2$$ parameters of the covariance matrix. On the other hand, there is in general no unambiguous relation between the VAR parameters and the coefficients of a particular (theoretical) model. The last problem is known as the identification problem. To overcome this problem, many techniques have been proposed to give an estimated VAR model an explicit economic interpretation. In this chapter, we will present under the heading of structural vector autoregressive models (SVAR models) the most important techniques. An exhaustive treatment can be found in Kilian and Lütkepohl (Structural vector autoregressive analysis. Cambridge University Press, Cambridge, 2017).