How should Observables be set in the steady_statemodel_block?

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:

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.

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

i_obs=1/beta*Pi_bar -1;

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! (7.4 KB)

  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.