How should Observables be set in the steady_statemodel_block?

Estimation
1

Dear All,

I believe not to have fully understood how to set observables in the steady_state_model block.
After adding observables, the model steady_state block provides residuals different from zero.
(dynare_estimation_init:: The steady state at the initial parameters cannot be computed.)

I am trying to estimate the Ascari, Castelnuovo and Rossi 2010 paper on NK with trend inflation starting from the code kindly provided on Prof. Pfeifer’s website: https://github.com/JohannesPfeifer/DSGE_mod/tree/master/Ascari_Sbordone_2014

The idea is to use 3 observables (GDP deflator, real GDP, fed-fund-rate).

I have transformed the series following the paper “A Guide to Specifying Observation Equations for the Estimation of DSGE Models”:
In general:

  1. log the data.
  2. take first difference - for the GDP, I use the cycle extracted with HP filter although I know it is not advised.
  3. I get a stationary time series with mean zero.

Model:
The dynare code is written in exp form.
At this point all the variables are interpreted in logs and have non-zero steady state - y_ss.
So, my observables should be specified in the model block as:
y_obs = y - y_ss (as in listing number 7 of the paper)

Is this reasoning, correct?

Then, I have added the observables to the steady_state_model block in the following way:
Pi_bar = (1+trend_inflation/100)^(1/4); %set Pi_bar to reflect quarterly inflation
pi=Pi_bar;
i=1/betaPi_bar-1;
i_bar=i;
y=(p_star^(1+(epsilonalpha)/(1-alpha))(epsilon/((epsilon-1)(1-alpha))((1-betathetaPi_bar^((epsilon-1)(1-var_rho)))/(1-betathetaPi_bar^(epsilon*(1-var_rho)/(1-alpha))))d_ns^phi_par)^(-1))
^(((phi_par+1)/(1-alpha)-(1-sigma))^(-1));
Y_bar=y;
…

Pi_obs=Pi_bar;
y_obs=Y_bar;
i_obs=1/beta*Pi_bar -1;
end;

I attach my files below.

In general, what is the logic to be followed in this step?

I am new to this subject and any comment, reference or advise would be of great help.

Many thanks in advance!

estim_asc.zip (7.4 KB)

2
  1. For GDP the data treatment should work. But once you have y_obs = y - y_ss, the steady state of y_obs is obviously 0.
  2. The problem is inflation and the interest rate. With trend inflation, you are interested in the means, so having mean 0 data is bad. Do not take out the mean for Pi and i.
  3. The second problem relates to gross vs. net rates. Having
    Pi_bar =(1+trend_inflation/100)^(1/4)
    indicates a quarterly gross inflation rate. Thus, the data needs to be a quarterly gross rate as well.The corresponding data would be the the log-difference of the quarterly GDP deflator.
  4. In contrast, i=1/betaPi_bar-1 is a quarterly net interest rate. This needs to be considered.