Theoretical x empirical moments

Stochastic simulations
1

Hello,

I want to compare theoretical moments to moments from the real data. And I don’t understand a few things.

If I use stoch_simul after the estimation command, dynare takes posterior means of parameters, std devs of shocks and run a simulated time series based on periods=integer, right? The output gives moments of these series. If I am right, these series are not filtered, thus I can’t compare them to the moments from the real data. I know that there is an option hp_filter in the stoch_simul, but I am not sure as for the first differences. What is the right procedure to compare moments from data and from the simulation if my data are transformed prior to the estimation in a way that:

  • output is GDP in log differences; demeaned (y_obs)
  • inflation is constructed as log differences of HICP, demeaned (pi_obs)
  • interest rate is demeaned (ir_obs)

and measurement equations in the model are as follows:

y_obs = y-y(-1);
pi_obs = p;
ir_obs = i;

Thanks a lot!

Martin

2

If the model objects and the data transformation perfectly match, then you can directly compare the moments. For example, output in the model and the data is first differenced.