In SOE models, there is international risk sharing in the international market. A common form is shown below where consumption depends on the consumption in the rest of the world and the real exchange rate.
However, this equation does not appear in the model’s solution (written in DYNARE). Why is there the need to mention it in the paper as it does not appear to be used in DYNARE?
Let me ask though, what risk is being shared here, intuitively. I know in some macro models (not DSGE), households share risk so that individual consumption varies only with aggregate income (not idiosyncratic income), helping to mitigate the effect of wide volatilities in one’s income on his/her consumption. So in the equations above, I guess if consumption varies with c^*_t and s_t, the household is mitigating some kind of risk. But intuitively I cannot see what risk it is.