# Expectations dated at t and at t-1

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

example:

y(t) = aE(t)y(t+1)+bE(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.

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

Best,

Michel

hello Michel

[quote=“MichelJuillard”]Yes, that is the way to do it. Then, you use s(t-1) for E(t-1)y(t)

Best,

Michel[/quote]

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 .

Best Regards

catherine

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

regards

Michel

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