Hello,

I wanted to ask is it possible to have an equilibrium equation of the form

f(E_t(R_t+1)-R_t+1)Q_t S_t + f(E_t(S_t+1)-S_t+1) *(Q_t S_t-N_t)=N_t (non-loglinearized version)

where all variables are endogenous and f is arbitrary function. For example, if f(x)=x^2, I would get variance.

Thank you.

Yes, that is possible, but:

- It is only possible for the conditional variance (the one with E_t), not the unconditional one.
- You need to go to at least second order to preserve the nonlinearity.
- You might need to define auxiliary variables to achieve the desired result (as is done for e.g. Epstein-Zin preferences)