Variance Decomposition Analysis

While impulse response functions trace the effects of a shock to one endogenous variable on other variables in the VAR, variance decomposition breaks down the variance of the forecast error into components that can be attributed to each of the endogenous variables. Specifically, it provides a breakdown of the variance of the n-step ahead forecast errors of variable i which is accounted for by the innovations in variable j in the VAR. As in the case of the orthogonalized impulse response functions, the orthogonalized forecast error variance decompositions are also not invariant to the ordering of the variables in the VAR. Thus, we use the generalized variance decomposition which considers the proportion of the n-step ahead forecast errors of x_t which is explained by conditioning on the non-orthogonalized shocks but explicitly allows for the contemporaneous correlation between these shocks and the shocks to the other equations in the system.

As opposed to the orthogonalized decompositions, the generalized error variance decompositions can add up to more or less than 100% depending on the strength of the covariance between the different errors.