Variance in equilibrium equations


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:

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