RBC Model with Matching Frictions: BK Conditions

Hello Everyone,

As part of a larger project, I am trying to code up a very simple RBC model with matching frictions. I am running into an issue wherein the BK conditions are not satisfied for the model.

Some additional points:

  1. I do get the model to run, when I adjust my matching function (Equation 8, commented out), however, I do believe that the timing on that is wrong.
  2. I have followed the general timing convention for the two state variables E (level of Employment) and K (capital stock).
  3. There don’t seem to be any issues with steady state calculations as the residuals are tiny

I am attaching the mod file and the pdf (where the model equations correspond to the mod file) for your reference. I would really appreciate some help on this

OneSectorLevels_vv.mod (3.2 KB)
RBCModelwithMatching_v.pdf (119.6 KB)

This question comes from the timing of employment(E).

OneSectorLevels.mod (3.1 KB)

Thank you for the response. I understand what you are saying but to me, and your solution does work. I also update equation (5) to E(+1) to ensure consistency with the other equations.

Let me ask a couple of follow up questions:

  1. Doesn’t this suggest that employment (E) is no longer a predetermined variable in the model? Which, based on how I have set up my model doesn’t seem correct.

  2. If I replace the simple wage rule (Equation 11) with the Nash Bargaining one (Equation 12 with E(-1) replace with E), then the model has the same issue – indeterminacy for the BK conditions.

There must be a timing issue in the model. Are you sure your approach to the firm problem is correct? You seem to impose the equilibrium k=K_{-1} before computing the FOC.