After reading the paper “Closing Small Open Economy Models” (Stephanie Schmitt-Grohe and Martin Uribe, 2003), I wonder why the portfolio adjustment costs must be the Deviation from steadystate, that is .
Can it be the Deviation from the last period? like .
And does any paper do like that?
Thank for your help.
No, that would not work. The reason we have the portfolio adjustment costs in deviation from the steady state is to induce the model to return to that particular steady state. Otherwise, there would be infinitely many steady states due to a unit root. If you were to specify your model in deviation from the last period, you would not solve the unit root problem.
Also, in terms of the economics, a high level of debt (relative to a benchmark) raises the premium. Your specification just posits that it is the change, rather than the level, that does this.
I see. Thanks professor !