Hi, I am just a new user. I am confused about the future operator.
When typing in x(+1)y(+1), I wonder whether it means the product of the expectation or the expectation of the product, as shown in the title.
Or, how do we let dynare tell them apart?
Have you ever have some FOCs which has parts like E(x_t+1) E(y_t+1)?
Most time we have something like this: E(x_t+1*y_t+1).
[quote=“ahnulxy”]Have you ever have some FOCs which has parts like E(x_t+1) E(y_t+1)?
Most time we have something like this: E(x_t+1*y_t+1).[/quote]
In the Calvo pricing case, there is something like E(sum of (x_leads* y_leads))/E(sum of (x_leads)). So I wonder, if I type in sum of x_leads* y_leads/sum of x_leads, is it treated as E(sum of x_leads* y_leads)/E(sum of x_leads) or E(sum of x_leads* y_leads/sum of (x_leads))?
That is not correct. In the Calvo case, you get E_t( something )=0. What you wrote down seems to be a wrong or at least strange transformation. Using the FOC in the form E_t( something )=0 avoids this issue. Dynare by default treats everyting as E(x_t+1*y_t+1).
If you really want to get E(x_t+1) E(y_t+1) you have to use auxiliary variables as in the Epstein-Zin case. See e.g. [Expected value of a power).