So first this question asks "how I would discriminate between model(1) and model(2)".
It appears that both models are non-nested so I would come up with a hybrid model consisting of Xt,Zt and Qt regressors. I know I need to test for Zt=0 and Qt=0 but I'm not sure if I need to test for Xt=0. My logic tells me no as the point is to compare model(1) and model(2), since they both contain Xt as regressor this won't tell me if model(1) is better than model(2) and vice-versa. But someone please correct me if I'm wrong.
For the second part where: Given the available information, would it be desirable for you to come up with a third and dominant model?
First a third model would be desirable only if model(1) and model(2) are not "good" or we would want a better model. But from the way the question is formulated it cannot be the second one, so I believe I should test each individual models to see if they are "good".
For this part the only thing I can think about is doing the following for each equation: t-test(Individual Significance Test) F-test(Joint Significance Test)
Apart from these two tests there aren't really any other information that can be used to tests the models.
So if model(1) and model(2) fail any of these tests then a third and dominant model would be desirable. Is my understanding correct?