High persistence in estimates

Estimation ML/Bayesian estimation
1

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, non-linear model, the one-sided hp-filter, among other things, and I still get high persistence. So what is this problem due to?

In the last estimation, I used a non-linear model, and as observation equations, I used the first differences of the several time series. I demeaned the data, and I used the Dickey-Fuller 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:

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

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

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

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

  5. The specification of the observation equation (for example of consumption) is as follows:
    C_{obs} = 100\times log(C_{t}/C_{t-1})

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)

2
  1. You must use the natural logarithm, not the base 10 one.
  2. Have you tried to compare the means and standard deviations of the model simulated with what you consider a sensible calibration to the moments from the data you are feeding in? That might give you a clue why a unit root is favored by the data.
3

I was doing this exercise that you recommended, and apparently, the public debt is the problem, in particular the parameter associated with this relationship:

\frac{1 + i^*_{t}}{1 + i_{ss}} = (\frac{D_{t}}{D_{ss}})^{\kappa}\times \exp(\epsilon_{t})

Which, following the SGU 2003 model, takes very small values ​​(0.0001). However, this doesn’t work with my data, so I moved the mean of the distribution closer to 0.01. With this at least one of them is no longer 0.99 but 0.983

I appreciate your comment. However, I have another doubt, the values ​​of the AR (1) of the other two coefficients that were obtained in the calculation of the mode have a value of 0.00 in the posterior mode, however in the posterior mean they were approximately 0.985, is this still a problem?

4
  1. Why don’t you try to estimate that parameter?
  2. Is there a theoretical justification for that particular equation? SGU (2003) was about technical tricks to get the model stationary.
  3. If the mode and the mean differ so much, there is usually a convergence issue. Have you had a look at the trace plots?