How to differentiate E(x_t+1) E(y_t+1) and E(x_t+1 * y_t+1)

[superztt]

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?

Thanks!

[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).

[superztt]

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).

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))?

[jpfeifer]

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. http://www.dynare.org/phpBB3/viewtopic.php?f=1&t=3417.