Time varying VARs with inequality restrictions

In many applications involving time-varying parameter VARs, it is desirable to restrict the VAR coe¢ cients at each point in time to be non-explosive. This is an example of a problem where inequality restrictions are imposed on states in a state space model. In this paper, we describe how existing MCMC algorithms for imposing such inequality restrictions can work poorly (or not at all) and suggest alternative algorithms which exhibit better performance. Furthermore, previous algorithms involve an approximation relating to a key integrating constant. Our algorithms are exact, not involving this approximation. In an application involving a commonly-used U.S. data set, we show how this approximation can be a poor one and present evidence that the algorithms proposed in this paper work well.