# Treat endogenous variable as constant for an equation

I am looking for a way to model that the expected value of variable A depends on today’s value of variable B forever.

To make more clear what I have in mind:

• one-worker firm decides to enter in period t with idiosyncratic productivity z_t

• idiosyncratic productivity remains at z_t for the whole life of the firm i.e. until separation and death (probability of separation each period is \delta)

Therefore, the expected discounted value of a firm entering with z_t and wage w is:

J = z_t - w + \beta *(1-\delta) *Jfuture;

Jfuture = z_t - w(+1) + \beta *(1-\delta) *Jfuture(+1);


In my model, z_t can change over time but I want Jfuture, Jfuture(+1), Jfuture(+2),… to abstract from any expected changes in z_t(+1), z_t(+2)….
z_t should simply be treated as a constant in the computation of Jfuture.

My firm concept is more complex than the simplified outline above which prevents me from reformulating the equation above (using e.g. the formula for a sum to infinity of a geometric series).

I couldn’t find an answer to this question, neither in the manual nor in previous forum posts.
I’d be greatful for any idea or workaround that helps me to achieve what I outlined above.

Is this a perfect foresight exercise? Or a stationary stochastic simulation? Put differently, can you define a constant z_parameter that you can use in the recursive definition?

It is a stationary stochastic simulation.
z_t doesn’t follow an exogenous shock process but is endogenously determined (basically pinned down by a free-entry condition).

Therefore, I guess the constant z_parameter would have to be “updated” every period in simulations / for obtaining IRFs.
I guess updating a parameter within stationary stochastic simulations goes agains how Dynare treats parameters?

But wouldn’t that imply that the equilibrium is not stationary anymore? You would need to keep track of the full history of realized z_t over time.