I’d like to ask a clarifying question regarding the stochastic simulation of a medium-sized model.

Let’s say, for the sake of simplicity, that I have an empirical data set. It is made up of a single observation: output. This data is at a monthly frequency and I have filtered it using an HP-filter with smoothing parameter lambda = 129,600. In order to define the percent deviation from the steady-state, I take the log-difference from its HP-filtered trend. I estimated an AR(1) model for the percent deviation and let’s say that the persistence parameter is 0.95.

Now, I’d like to simulate this variable in dynare. In my non-linear model, I have defined output as

y = y-bar*exp(yhat),

where y-bar is steady-state output (normalized to 1), and yhat is a mean-zero, AR(1) process, such as

yhat = phi*yhat(-1) + e_y

so that in steady-state, we get just y = y-bar = 1. The reason I defined output in this way is that if I log-linearize y, I simply get yhat, the AR(1) process. In the parameter section of the .mod file, I have specified that phi is equal to 0.95, just like in the empirical counterpart.

Now, here’s the problem. In my stochastic_simul command, I have specified that I want to simulate the model 100,000 times and drop the first 10,000 before estimating the empirical moments. Additionally, I have added the hp-fllter = 129,600 sub-command, again so that I am comparing apples to apples.

Out of curiosity, and to double-check, I took the simulated series for y and estimated it outside of dynare on a separate statistical package. I repeated the same steps I did with the actual empirical data for output (HP-filtered, then log-differenced), but when I estimated the AR(1) model, I got a coefficient of phi = 0.90.

Did I do something stupid? I’d like to make dynare reproduce a series for y which is statistically a “clone” to the empirical data. Thank you ahead of time. If it helps, I can go ahead and write a .mod file for this; the question above is a simplified version of the actual problem, but a solution to the above would solve the more complex problem for me.