Making an endogenous variable exogenous

[Yad]

Hi again,

I have a small open economy model with two sectors, exportable and importable sectors, and terms of trade shocks. one of the equations in my model is this:
x = p(y-a). x is export, p is the price of exportable good, y is the production of exportable good in the domestic economy and a is domestic absorption of the exportable good. so that the difference between the production and absorption of exportable good is exported. Here, export (x) is an endogenous variable.

I am interested in imposing an export demand shock to the model. If i just let x follow an AR(1) process then that means that I have an extra equation in the model and Dynare tells me that the number of equations exceed the number of endogenous variables. so no solution

Can anyone think of how i can impose a shock to x here?
I was thinking to add an exogenous component to the left hand side of the equation. i.e. z + x = p(y-a), and then let z follow an AR(1) process, meaning that export would be composed of an endogenous part (x) and an exogenous part (z). does that make any economic sense? anyone know any paper which has done a similar thing.

Would be grateful to your help.

Cheers,
Yad

[jpfeifer]

I am not familiar with your setup. But it seems that it is inconsistent with what you desire. Your small open economy has no pricing power and does not affect world markets. As such, it can export any amount it wants to the world markets. The more usual version would be a semi-small open economy with pricing power where deman for the domestic good is explicitly modeled. See for example Adolfson et al (2007): Bayesian estimation of an open economy DSGE model with incomplete pass-through