# Investment fixed costs

Dear researchers,
I would like to integrate in a model the possibility of having fixed costs of investment (which would be different from the adjustment costs of investment according to the literature). There would thus be two equations describing investment behaviour. The first one, when investment is not in its stationary state there would be fixed costs (a constant). The second, in the stationary state where investment is equal to the maintenance of the depreciated capital, the fixed cost no longer appears in the investment function. To try to model it I have tagged two different equations by [dynamic] and [static], but Dynare tells me that the static equation, does not correspond to the dynamic equation. Would anyone have a trick to model in Dynare the possibility of having two different equations?
I attached a pdf describing the model, and two .mod files. The first one (fi2.mod) is a classic model that runs properly (without fixed costs), the second one (fi3.mod) tries to take into account the possibility of fixed costs .

I wish you all a happy festive season.
Max.
fix3.mod (1023 Bytes)
fi2.mod (973 Bytes)
fixed_costs.pdf (96.9 KB)

Sorry, but I don’t understand the setup you have in mind. Are we talking about stochastic simulations? Because what you describe sounds like a non-differentiability.
Regarding your error: the dynamic and static model need to be consistent. You cannot use tags to make the static and the dynamic model differ from each other. If you consider the static version of your dynamic model equation, the fixed cost term is still there, while the static model equation does not feature it.

Dear Johannes, I’d like to consider a model of investment with a non-convex adjustment cost. According to Eric Sims’ course (see pdf attached, p.14), when the firm decides to invest it must pay a fixed cost F>0. On the contrary, If it does not invest, the fixed cost is zero. For this reason, I thought that it was possible to tag two different equations for investment. I understand that when I use tags, the static version must be consistent with the dynamic equation, thus the fixed cost must also be present in the steady state. But that is not exactly what I am trying to model.investment_notes_sp12.pdf (263.3 KB)

Non-convex adjustment costs are something that cannot be handled with perturbation techniques. Therefore `stoch_simul` will not work. You may be able to use the extended path method or perfect foresight, but that seems not what you had in mind.

Thank you for your answer. It does not matter if I have to use the perfect foresight solver or the extended path method. As a young and novice researcher, I would like to learn how to solve this kind of problem. Do you have an article to recommend, an example, or a mod file to share that use the extended path method to solve non-convex adjusment costs models? Or something similar?

I am not aware of such an example. The reason is that Dynare most probably does not have the most efficient solution techniques for this type of problem.

Dear Johannes,

Apologies for resurrecting such an old thread but your response above could solve my issue. I have a model where I want to introduce non-convexities in entry costs; I am not looking for a stochastic simulation, perfect foresight is fine. Would the extended path method allow me to solve it?

If you do perfect_foresight, then the standard solver should work as well.