Hello everybody,
I have been estimating my model, and no matter how much I modify the data, I always obtain some autoregressive coefficient very close to 1. So what I did was truncate the Beta distribution to 0.99 so that it did not exceed this value.
Review the eigenvalues of the model, and none have an exact value of 1.
I tried with the linear model, nonlinear model, the onesided hpfilter, among other things, and I still get high persistence. So what is this problem due to?
In the last estimation, I used a nonlinear model, and as observation equations, I used the first differences of the several time series. I demeaned the data, and I used the DickeyFuller test to ensure they did not have unit roots and no series has this problem.
For this last estimate, I obtained three parameters (\rho^C, \rho^L, \rho^P) corresponding to the coefficient of an autoregressive process at the top of the distribution, that is, 0.99.
Checking in the forum, I saw that it could be due to errors in the specifications of the observation equations.
To make sure this is not the problem, what I did with most of the series was the following:

I divided the time series by the population aged 16 and over.

I adjusted the resulting series in (1) for seasonality.

I got the base 10 logarithms of the resulting series in (2) and multiplied by 100.

Finally, I subtracted the mean of the process from each observation, to obtain series of zero mean.

The specification of the observation equation (for example of consumption) is as follows:
C_{obs} = 100\times log(C_{t}/C_{t1})
If all these steps were correct, what could be wrong with my model?
I attach the necessary files
Database.mat (8.7 KB)
Estimation2_mh_mode.mat (20.8 KB)
Estimation3.log (12.0 KB)
Estimation3.mod (24.1 KB)
Estimation3_mode.mat (20.7 KB)