# Log linearization problem

If I directly perform logarithmic linearization on the model, the steady states of the linearized variables will all become 0; however, the coefficients in some equations will contain the steady-state values of the original nonlinear model variables. Can I directly calibrate these variable steady-state values? This way, I wouldn’t need to solve for the steady state explicitly. Nevertheless, there should still be certain rules that the calibrated steady states must satisfy, right?

Yes, see

The impulse response graphs of my model are opposite to what I anticipated, and I’ve searched for a long time but couldn’t locate the problem. Therefore, I’m interested in studying the impact of the model’s microstructure and parameters. What methods do you typically use to investigate such issues, and how would the impulse responses be expected to change?

The usual step is to start with the simplest model you can come up with and work from there. Debugging big models is a mess.

I apologize for the inconvenience. I have already reduced the model to a simple, standard medium-scale DSGE, but I find that the model is highly sensitive to parameters. I am unsure about which parameters to adjust and often encounter issues with the Blanchard-Kahn (BK) conditions (although I can use deterministic simulation to avoid this error). Is there any other method to obtain IRFs that are more in line with expected signs? Can estimation be used to assist with my calibration? Is it possible to estimate a model that does not meet the BK conditions?

It is not possible to estimate a model, with Dynare, that does not satisfy BK conditions (ideally over all the prior space). Maybe you can use the `sensitivy` command to identify where is the problem (if you cannot reduce further the model). I am not sure to understand how deterministic simulation can help (if you have local indeterminacy or unstable solutions).

Best,
Stéphane

This logic strikes me as odd. If your model were truly a

model, you would not experience the issues you are describing. There must still be a fundamental issue.

How can I use the `sensitivity` command to help me identify issues? Are there any examples? It seems to me that the `sensitivity` command is more like a command used after estimation. Using deterministic simulation with linear approximation does not require satisfying the Blanchard-Kahn conditions.

Indeed, it is quite strange. My model is copied from a textbook, with parameters that are very similar. I may need to investigate further.

True… If you have indeterminacy, you will find a solution with a perfect foresight solver, but the solution is not unique.

Examples for the `sensitivity` (formerly ``dynare_sensitivity) command are available in the tests folder. Options are described in the reference manual. Also:

Best,
Stéphane.

I used the `irf_calibration` command to test my parameter sensitivity, but MATLAB produced the following results.

0.0% of the prior support gives unique saddle-path solution.
0.0% of the prior support gives explosive dynamics.

For 100.0% of the prior support dynare could not find a solution.

``````For 100.0% The steadystate routine has thrown an exception (inconsistent deep parameters).
``````

All parameter values in the specified ranges are not acceptable!

Sensitivity computations stopped: no parameter set provided a unique solution

And my code for `irf_calibration` as follow:
varobs c i k y A;
estimated_params;
delta ,uniform_pdf,0,0.1;
gamma , inv_gamma_pdf,1,0.25;
thetaw, beta_pdf,0.75,0.025,0,1;
thetap, beta_pdf,0.75,0.025,0,1;
alpham, beta_pdf,0.33,0.025,0,1;
chiu1,inv_gamma_pdf,0.03,0.25;
chiu2,inv_gamma_pdf,0.01,0.25;
end;
estimated_params_init(use_calibration);
end;
irf_calibration;
y(1:4),eps_a,+;
end;
dynare_sensitivity(Nsam =200000);
When adjusting parameters manually, I indeed obtained positive IRFs for y. I am wondering if, when using this command, it is not feasible to first provide the steady state and then calibrate the parameters?

I made some modifications to my mod file, placing parameter assignments within the `steady_state` block, and obtained the following image. However, I noticed that the results seem to differ from those on YouTube… There is a lack of information available on GSA, making it difficult for me to locate the steady state.
untitled.fig (21.0 KB)

You need to provide the mod-file.

test.mod (6.2 KB)
This is my mod

You need to provide a steady state conditional on the parameter values. The graphs are degenerate because you are overwriting the sampled draws.

Some large models or models that need to match actual data often cannot represent the steady state as a combination of parameters. Is it possible to use linearization of the model, where all steady-state variables become zero, and then the GSA toolbox can be used for analysis directly? I am not very familiar with the specific implementation process of the GSA toolbox, so I am unsure about the specific requirements for it to successfully analyze a model, although I have read Marco Ratto’s paper.

The problem is that generally, linearization still requires the computation of steady state values. Only rarely does it help, e.g. if for some reason you only need observed variable ratios while there are no cross-restrictions implied by the parameters.

Dear Professor, where can I find more example mod files for conducting GSA analysis? I find that there are too few examples available. Are there any mod files used by Macro Matto in his presentations that I could refer to?

There are some examples at tests/gsa · master · Dynare / dynare · GitLab
The summer school material is for example at
Dynare Summer School 2021 · Wiki · Dynare / dynare · GitLab