I specfied the exports as a function of the foreign GDP. This should capture the exogenous shock of foreign GDP on home exports, and this variable only appears in exports equation. I write it as following:
Yx = exp(Ystar)*((pd/s)^(tau));
The shock of this foreign GDP is written as following:
Ystar = rho_Ystar*Ystar(1)+ e_Ystar;
with rho_Ystar=0.9595106 and sigma_Ystar=0.0120537
The thing is, I find it odd that a positive foreign gdp shock with the specification above has a negative effect on exports. It also has a negative effect on domestic output. how to fix that? any thing other specification to consider ?
Thank you for all the help, and to everyone has helped!
I would need to see the codes. You are saying that a positive shock to e_Ystar decreases Yx?
I figured the problem. It’s the value of tau, which represent the elasticity of demand for home exports. I have few questions:

If I set the value of tau less than 1, the model cant find the steady states and produces non zero residuals of the static equations. However, if I set the value of tau larger than 1 then I get a solutions and impulse responses. if I set it around 3, I get positive effect of Ystar on Yx. How can I explain this? is it normal to have small open economy demand elasticity of exports larger than 1?

Can any one cite a source to get the calibrated parameters values for open economies in the literature?
Thank you so much for all the help!!
Here’s probably the most relevant paper to read: cid.econ.ucdavis.edu/Papers/pdf/w20063.pdf.
As a general note, a lot of models contain parameters that really aren’t robust to a wider range. When people are writing down models, they are a lot more ad hoc and casual than in an ideal world!