Implementing Variable Capacity Utilization with OccBin

Occbin
1

Hi all,

I am trying to implement variable capacity utilization in a two-sector “putty-clay” firm investment model in Dynare. Given a tax on capital in one of the sectors, the profit-maximizing firm might not want to utilize all available capital when faced with a sudden productivity or tax shock. Theoretically, we have complementarity between the capacity constraint and its shadow multiplier, where the latter appears in the inter-temporal firm investment decision. The relevant FOCs, including the complementarity condition, are:

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I am relatively new to Dynare, but my understanding is that the go-to way of modeling complementarity is with the OccBin toolkit. The resulting simulations seem fine, except that some of the variables turn negative for certain periods. I assume the negative variables indicate some inconsistency, and my questions are:

  1. Is it possible to specify some of the variables as positive only?
  2. Does the use of OccBin in the attached .mod file correctly represent the pen-and-paper complementarity above?

Mod file:
v2.mod (3.8 KB)

Thanks!

2

At first sight the mod-file looks OK. But keep in mind that OccBin uses a piecewise linear solution. You cannot restrict an arbitrary linear function to not go below 0. That’s approximation error you may have to live with. If you don’t need stochastics, you could try a perfect foresight solution with lmmcp. That would preserve nonlinearities.

3

Ah, that makes sense! Thanks for the clarification.