Expectations dated at t and at t-1

[pburriel]

Does Dynare solve non-linear rational expectations models with expectations dated at t and at t-1?

example:

y(t) = a*E(t)y(t+1)+b*E(t-1)y(t)+c*x(t)+e(t)

Where y is the endogenous variable, x is exogenous, e is an error term and E(t-j)y(t+i) is the expectation based on the information at t-j of the variable y(t+i).


If so, how should I enter the term E(t-1)y(t)? Can I do it through a change of variable like

s(t)=E(t)y(t+1)


Thanks.

[MichelJuillard]

Yes, that is the way to do it. Then, you use s(t-1) for E(t-1)y(t)

Best,

Michel

[Catherine]

hello Michel

Yes, that is the way to do it. Then, you use s(t-1) for E(t-1)y(t)

Best,

Michel

Does Dynare solve non-linear expectations models with the variable for the current period that have been set in the past.



y(t)=summation E(t-j)x(t) (y , x are endogenous variables)
j=0: infinity


I can't expresse and simplify the above equation because of the variable for the current period that have been set in the past .

please~ help me.

Best Regards

catherine

[MichelJuillard]

This requires some a longer explanation. I'm traveling at the moment and will answer in about 10 days

regards

Michel

[admin]

Does Dynare solve non-linear expectations models with the variable for the current period that have been set in the past.



y(t)=summation E(t-j)x(t) (y , x are endogenous variables)
j=0: infinity


I can't expresse and simplify the above equation because of the variable for the current period that have been set in the past .

Sorry, for the delay in answering. In fact, Dynare can't handle exactly that infinite sum over expectation set at an infinity of dates in the past. The only way I know of attacking the problem is to truncate the summation and express each term separately:
E(t-1)x(t)+E(t-2)x(t)+...+E(t-k)x(t)
if we only take into consideration the expectations formed over the k previous periods.

You can always check whether taking k+1 periods change a lot the results

Kind regards

Michel