Standard NK model with CES prod. fund. => questionable IRFs


The IRFs of my model do not seem to make sense, or I am simply not understanding them.

The model contains:
]CES production function/:m]
]Calvo pricing with inflation indexation/:m]
]Consumption habit formation/:m]
]Capital adjustment cost/:m]
]Taylor rule/:m][/ul]

I wrote it down in log-linearised form and simulate based on calibrated values from (Unalmis et al. 2012 - this is a stripped down version of their model).
Unalmis_log_reduc.mod (2.63 KB)

My concern is about the IRFs:
]monetary policy shock leads to comovement of interest rate, output and inflation. Shouldn’t inflation/output and interest rate move in opposite direction? Furthermore, investment increases!?/:m]
]marginal costs and return on capital move erratically following a TFP shock (e_ay)/:m][/ul]

My understanding is that this is not how such a model should behave and the second point tells me that there might be a timing issue. Capital is timed correctly if I am not mistaken.

Any hint as to why this model behaves in such a strange way is much appreciated.

Thanks a lot in advance,


That is hard to tell without knowing the model in detail. At first sight, everything looks ok.

Due to general equilibrium effects, the nominal interest rate can go any way. You only know that the real interest rate must increase after a positive shock to the policy rate:

That is actually the case. The “erratic” behavior is actually not that erratic, it simply shows there is not much persistence. If you increase the persistence of the shocks and the interest smoothing, things look more “normal”. What stays is that reactions in the first period are quite differently from the rest. I cannot judge whether this is expected or due to e.g. a timing problem.

thanks a lot Johannes for your quick reply.

indeed, further fine tuning of the shocks led to more ‘normal’ looking behaviour.

the question about the model was just one part of a bigger question, which is about model estimation.

first I wanted to check whether the base model makes sense, of which I am now convinced. the extension (commodity in production and storage) seems to be fine as well, in my point of view.

this leaves the data and the prior.

about the data:
attached you can find the time series I try to estimate the model on (log deviations from HP one sided trend).
model_filtered_ts_post.pdf (6.12 KB)
to give you some background. the extended model is supposed to model the aluminium demand from the u.s. economy and competitive storage.

do you see any issue with the data per se? too large deviations, for the aluminium part (first two graphs)?

I find that my model has difficulties in capturing the influence of the demand side on the aluminium market.

maybe this is normal, but I am not sure, thats why I am asking for advice. what would your intuition be?

many thanks


Dear Thore,
the biggest issue I see is that in very small samples like the one you use, the one-sided HP-filter can deviate quite far from being mean 0. If you look at s_lme_obs, it seems to have a strong trend and have a negative mean. The opposite applies to r_obs. I am not sure your model can capture this.

I agree, my model does not capture the interaction between the commodity market and the real economy.

would you suggest using the 2 sided HP filter then?

find attached the time series when using the 2 sided HP:
HP_filtered_2s_post.pdf (6.19 KB)

I guess the problem runs deeper than just data treatment. If your model is not able to

then more filtering clearly is not the solution. If the model does not fit the data, you should change the model, not the data (unless there is a good reason for processing the data differently)