I am stuck with an indeterminacy problem in a canonical SOE model. To simplify the model, I introduce the foreign economy by ad-hoc processes. International risk sharing with perfect capital mobility implies that
c_t = y^*_t + q_t \tag{1}
where
q_t
is the real exchange rate. This, with the Euler equation, directly translate into the UIP, but introducing UIP, instead of the equatio above, yields indeterminacy. I get rid of inteterminacy whenever I exclude UIP and include the equation above. What would be driving the indeterminacy (or determinacy) then. Are these two equations mathematically not equivalent? Thanks in advance.
It seems that above in (1) you are omitting to divide q by sigma as in your model. Furthermore this equivalence requires sigma to be the same in the two economies which is not the case in your model (0.3 and 0.7)
Thank you. I made a typo there by omitting to divide by sigma. However, it is still correct in the .mod file except the fact that foreign sigma equals 0.7 invalidates equation (1). Nonetheless, since the foreign block is exogenous, I doubt that would actually cause problem. In any case, the problem still persists. I have an explanation for this. Equation (1) makes the Net Foreign Asset level of the home country at the steady state determinant, whereas with UIP, it is indeterminant. (1) implies UIP but not vice versa. Hence, it would be incorrect to argue that (1) and UIP are equivalent.