This paper considers structural models with both I(1) and I(0) variables. The structural shocks associated with either set of variables could be permanent or transitory. We classify the shocks as (P1,P0) and (T1,T0), where P/T distinguishes permanent/transitory, while 1/0 means they are attached to structural equations with either I(1) or I(0) variables as their ‘dependent’ variable. We show that P0 shocks can affect cointegration analysis and provide a formula to compute the permanent component if they are present. Finally, we reformulate a well‐known empirical structural vector autoregression showing the impact of P0 shocks when there are just long‐run parametric and sign restrictions. Copyright © 2015 John Wiley & Sons, Ltd.