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

PostPosted: Sat Apr 26, 2014 8:34 pm
by 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!

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

PostPosted: Fri May 02, 2014 11:48 pm
by 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).

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

PostPosted: Sun May 04, 2014 11:35 pm
by superztt
ahnulxy wrote: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))?

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

PostPosted: Wed May 07, 2014 9:15 am
by 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.