Heaviside function on Gen. Eq. model

Hello guys, in this post I’m attaching the equations of a model I’m developing.

As you see, the RHS of the ‘Demand Capital’ equation has a portion multiplied by a heaviside function (takes the value of 1 if the endogenous variable ‘n’ was less than 0 in the previous period, 1 otherwise).

The rationale is the following: I want to negatively shock the exogenous variable ‘q’ in order to, by the ‘Balance Sheet’ equation, activate the Heaviside function in the ‘Demand Capital’ and check the implications on the dynamics of the variables of the model.
In this case ‘q’ is exogenous, but it could be endogenous through an AR1 process.

Nonetheless, I still don’t understand the implications that the nature of these equations have over the methodologies that I potentially could use.

Does the model would fit for a deterministics, stochastic or extended path framework?
Would even fit in a equilibrium framework or it would have to be nonequilibrium?
Would aproximating the Heaviside function help to get rid of the kink at 0?

Addressing these kind of questions would help to understand better what approach should I follow.

Your opinions would serve me greatly, I hope I was clear enough.
equations.pdf (110 KB)

It would still be equilibrium as agents are optimizing and markets clear (subject to the friction you add). The problem you intoduce is the non-differentiability due to the indicator. This implies that derivative based solution techniques like perturbation will not work.

Determinstic solvers can better cope with this problem. That is why determinstic models are often used. Global solution techniques can also often handle non-differentiabilities like this.