Good evening,

I am writing to ask if the following problem can be implemented in Dynare.

Without wasting your time with details on why I am trying to do this,

Just imagine to solve a planner’s problem where the planner maximize his objective function (other than utility) under the constraint of ensuring a given amount of life-time Welfare to the household (the setting is deterministic/perfect foresight).

This will require the sum of discounted utility, to be equal to a given constant ,V,:

[ul]V= sum^{\infty}*{t=0} \beta^{t} U*{t}[/ul]

Now, the infinite forward summation above has a recursive representation of the form:

[ul]W_{t}=U_{t}+beta* W_{t+1}[/ul]

Implementing such a constraint then, would require a condition of the form:

[ul]W_{0}=V[/ul]

This condition is based on an equation which depends on the value of an endogenous variable, W, assessed at a particular point of time (t=0).

My question then is: Is there a way in Dynare to write/implement such a time indexed constraint?

*]PS: in dynare notation it would actually be W_{2}=V since numeration starts from 1, and the first element in the vector is dedicated to the initial steady state