Log-linearization of CMR (2014)

General DSGE Modeling Replication Attempts
1

Hi,

I am currently trying to transform the model of CMR (2014) so that I can compare it to the Smets and Wouters (2007) Model which is in log-differences. As the CMR model is non-linear I tried to

  1. Use the loglinear option which is not possible as there are zero and negative steady-state values.
  2. I tried to transform every variable with the exp()-substitution but unfortunately it didn’t work out. The file in which I tried doing it is attached as US_CMR14_rep.mod.
  3. And I tried to append the logs of the variables which I want to observe as auxiliary variables to the model but then I get an issue with the steady-state file as I don’t know how to add the additional variables there. I attached the file it as well.

Now I am hoping that someone is able to help me and give me an insight what I am doing wrong.

Thanks a lot!

Model file:
US_CMR14_rep.mod (84.0 KB)
Steady-State File:
US_CMR14_rep_steadystate.m (24.2 KB)
Original CMR File:
financial_copy.mod (82.1 KB)

2

Option 3 should be straightforward. You can usually copy the exact definition of the auxiliary variables from the model block to the end of the steady state file.

4

Thank you very much for your fast reply!

I managed to add the auxiliary variables to my mod file and the steady state file:
gdp_log = log (c) + log (i) + log (g);
c_log = log(c);
i_log = log (i);
pi_log = log (pi);
h_log = log (h);
wtilde_log = log (wtilde);

However, I think that the variables are in levels and therefore if I want to have the percentage deviations from steady state I need to subtract the log of the steady-states of the variables as well, am I right? Like that:

gdp_log = (log (c)-log(steady_state(c))) + (log (i)-log(steady_state(i))) + (log (g)-log(steady_state(g)));
c_log = log(c)-log(steady_state(c));
i_log = log (i)-log(steady_state(i))
pi_log = log (pi)-log(steady_state(pi));
h_log = log (h)-log(steady_state(h));
wtilde_log = log (wtilde)-log(steady_state(wtilde));

US_CMR14_rep.mod (85.3 KB)
US_CMR14_rep_steadystate.m (24.4 KB)

Thanks!

5

Yes, that would be the correct way to get percentage deviations from steady state.

6

Okay thank you!

How exactly would I have to implement this? Because when I just change the equations in the mod file and in the steady-state file, I run into this error:

Index exceeds the number of array elements. Index must not exceed 0.

Error in US_CMR14_rep_static (line 34)
pitilde__ = y(26)^params(18)*y(24)^(1-params(18));

Error in resid (line 85)
z = feval([M_.fname ‘_static’],…

Error in US_CMR14_rep (line 2208)
resid;

Error in dynare (line 235)
evalin(‘base’,fname) ;

Do I have to specify the steady states of the variables as a parameter or what am I missing here?

Thank you!

US_CMR14_rep.mod (85.6 KB)
US_CMR14_rep_steadystate.m (24.7 KB)

7

Please upgrade to Dynare 6.1 and use
US_CMR14_rep_steadystate.m (24.7 KB)
US_CMR14_rep.mod (85.6 KB)