Implementing time-indexed constraint

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:


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

Does that constraint only exist in the first period so that


and thereafter W is unrestricted?

Dear Professor Pfeifer,
Thank you very much for your reply.

Yes that constraint would involve only the variable W at time zero, e.g W_{0} (in Dynare notation at W_{2})

However,notice that, from the way I have defined, W is a recursive process representing the infinite forward summation of discounted life-time utility.
So actually this constraint involves any period in which the simulation is run.

E.g. it basically constraints the planner to ensure a given level of life-time utility. Given this constraint, the planner can then allocate the per-utility as he wants.


If I understand you correctly, you want to have a condition where


where x is an exogenous “indicator” variable that is 1 in period 1 and 0 afterwards.