Econometric Methods for Modelling Systems with a Mixture of I(1) and I(0) Variables

This paper considers structural models when both I(1) and I(0) variables are present. The structural shocks associated with either set of variables could be permanent or transitory. We therefore classify the shocks as (P1,P0) and (T1,T0), where P/T distinguishes permanent and transitory, while 1/0 means they are attached to either I(1) or I(0) variables. We first analyse what happens when there are P0 shocks. This is done using a sequence of examples and shows a variety of outcomes that differ from standard results in the cointegration literature. Then conditions are derived upon the nature of the SVAR in the event that T0 (and no P0) shocks are present. Following this a general method that allows for either P0 or T0 shocks is described and related to the literature that treats I(0) variables as cointegrating with themselves. Finally, we turn to an examination of a well-known empirical SVAR where there are P0 shocks. This SVAR is re-formulated so that the extra shock coming from the introduction of an I(0) variable does not affect relative prices in the long-run i.e. it is T0, and it is found that this has major implications for whether there is a price puzzle. It is also shown how to handle long-run parametric restrictions in the presence of P0 shocks when some shocks are identified using sign restrictions.Please see attachment.Please see attachment.