ABCs (and Ds) of Understanding VARs
The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state space system for a vector of observables. An associated state space system (A, ^ B,C, ^D) determines a vector autoregression for those same observables. We present a simple condition for checking when these two state space systems match up and when they do not when there are equal numbers of economic and VAR shocks. We illustrate our condition with a permanent income example.