Treat endogenous variable as constant for an equation

General DSGE Modeling
1

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.

2

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?

3

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?

4

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.