Can government spending shock capture net export information

Dear Johannes,
Thank you for your helpful guidance last time, I am grateful.
I apply a closed economy model to an economy where GDP data contains net exports (exports constitute a nonnegligible proportion of GDP), I cannot apply an open economy model, because my focus is not on exports but on other aspects of the model, and adding exports will only complicates our model and we need to save degrees of freedom for estimating other parameters.
the resource constraint for allocation is as follows:
where Y is output, C is consumption, I is investment, G is government spending.
we assume government spending/gdp ratio G/Y follows an exogenous process
I am wondering that can innovations to G/Y capture noise in net exports?
Thank you very much and look forward to hearing from you.
Best regards,


and the thread in Open vs closed economy