Ramsey policy is not optimal

[cesk]

Dear all,

I am working on a project on optimal monetary policy in a search-and-match model in the presence of a cash-intensive informal sector which gives the possibility of evading taxes.

After I ran the command ramsey_policy, I noticed that the response of the economy to exogenous shocks (TFP and public expenditure) is not optimal at all. In fact, the alleged optimal policy is largely beated by a simple taylor rule. Maybe there are problems with my model, but I also replicated the paper by Faia (2008), "Optimal monetary policy rules with labor market frictions" and the responses of some variable under the ramsey_policy command are quite different than those presented in her paper (and I know she is doing Ramsey in a timeless perspective).

Have you already found similar problems when using the ramsey_policy command?

Best,
Claudio.

[jpfeifer]

Please provide me with the problematic examples.

[cesk]

Dear Johannes,

thank you for the quick reply. I attach the mod files of my model (one just computes IRFs with a Taylor rule, the other under the optimal policy) and the mod file of the Faia model. For the latter, the IRFs of a TFP shock differ with respect to those displayed at pag 1617 of the article published in the JEDC. In particular, unemployment goes down whereas in her paper it increases in the first periods after the shock under the optimal policy.

I also attach a short pdf file with a description of my model, it could help to better understand the dynamics of the economy.

Best regards,
Claudio

[jpfeifer]

Dear Claudio,
thanks a lot. I will have a look at the issue, but it might take some time.

[cesk]

Ok no problem! I just hope I raised a useful issue.

Best,
Claudio

[jpfeifer]

Dear Claudio,
I started working on the Faia mod-file, but face some problems.
1. Is there a reason you work with Nash bargaining (eq. 23) instead of the version with real wage rigidity (24), which is what Faia presumably used?
2. It seems you failed to distinguish between y_i being before costs and y being after subtracting costs. Put differently, the y in (26) is different from the one in (6) after imposing symmetry.
3. Do I see it correctly that LOM for z below equation (6) is inconsistent with equation (6), because i) there is an exp() missing on the shock and ii) z would have mean 0, which cannot be?

[cesk]

Dear Johannes,

thank you for replying to this post.

1) You are right, it is my oversight. I did not consider real wage rigidity, but now I added it and the results (especially the behavior of unemployment) do not change qualitatively;

2) I am pretty sure that the aggregate resource constraint is correct. If you substitute (27) into (26) and use the definition of y - equation (6) - you should obtain equation 13 in the mod file and aggregation is trivial given Rotemberg pricing;

3) Yes, it is a weird way of defining the exogenous process for TFP. I think one correct way to define it is given by equations (16) and (17) in the mod file.