Econometric Issues When Modeling with a Mixture of I(1) and I(0) Variables

Abstract

This paper considers structural models when both I(1) and I(0) variables are present. It is necessary to extend the traditional classification of shocks into permanent and transitory and we do this by introducing a mixed shock. The extra shocks coming from introducing I(0) variables into a system are then classified as either mixed or transitory. Conditions are derived upon the nature of the Structural VAR in the event that these extra shocks are transitory. In many instances this might be the most reasonable identification. But there do exist applications where the shocks are mixed. We analyze what happens when there are mixed shocks, finding that it changes a number of ideas that have become established from the co-integration literature. An example where there is a mixed shock is Peersman’s (2005) model where the structural shock in the interest rate, an I(0) variable, has a permanent effect on two of the I(1) variables. We look at the results he establishes and investigate a number of scenarios involving either treating the shock as transitory or allowing it to be mixed, as well as allowing it to have some extra zero long-run effects to what Peersman considered. Finally, the paper looks at how one applies sign restrictions to an SVAR which features mixed shocks, illustrating this with Peersman’s model. One needs to exercise considerable care in how one does this.