Kalman Filter in Dynare vs MATLAB

Estimation ML/Bayesian estimation
1

Hello,

I am having problem in replicating Dynare estimation results in MATLAB.
I have the same solution matrices both in Dynare and MATLAB as well as observation equations and related var-covar matrices.
In dynare estimation, I use mode_compute=4 and lik_init=1 and everything works well. However, in MATLAB, Kalman filter produces very different log-likelihood with same parameter values and csminwel in MATLAB produces very different posterior modes.
I couldn’t find any argument why Kalman filter should produce different results using the same arguments. Maybe someone can help me?
Thank you.

Burak

2

Dear Burak,

I am not familiar with Kalman filter routines in Matlab and I do not think we ever compared the results. Could you please post files for replicating the issue?

Best,
Stéphane.

3

Actually, I compared the likelihood and modes with various Kalman filter implementations in Matlab and was able to obtain the same results. So there must be something wrong with your approach.

4

Dear Stéphane and Johannes,

Thank you very much for your replies.

Stéphane,
I attached the files. If you run Comparison.m file, you will see the comparison of solution matrices and loglikelihood values. The mod files are in Dynare_Files folder. For MATLAB, files are in Mfiles folder and model_solution.m solves the model, sysmat.m defines measurement equation and kalman.m implements the Kalman filter. I also plot the likelihood values of each period and there is clear downward trend over time.

Johannes,
In other models, I managed to obtain similar (but not exact) results in Dynare and MATLAB but this time the differences are dramatic. May I kindly ask, if you could share one of your implementations in MATLAB, if possible? Because I follow the approach of Herbst and Schorfheide from their book and I was thinking the differences are derived from the initialization of the filter since I have exactly the same matrices in transition and measurement equations. I would be more than appreciated for your help.

Thank you once more time for your replies.

Burak

ModelBurak.zip (3.0 MB)

5

Did you take into account that your mod-file uses ´presample=4` to initialize the Kalman filter recursions?

6

Kalman-Filter recursions start from the first data point in MATLAB.
I use ‘presample=4’ in MATLAB only when I am computing the sum of log-likelihood and I drop the first 4 values of the log-likelihood values and sum up the remaining log-likelihood values.
I thought this is what Dynare does when presample option is used.

7

Ok. I found the reason. Dynare detrends the data first and then initiates Kalman Filter. So, there is no constant in the observation equation in Dynare.
But in MATLAB, I put trend values as constant in the measurement equation. So, I guess and I don’t know why, the prediction becomes erroneous over time because of the constant term in the measurement equation.

And I realized, Dynare initiates Kalman filter at period ‘presample+1’. Then I do not understand what the difference is between first_obs and presample options.

8
  1. From what I can see in the description of your kalman.m, it does not allow a constant in the state transition equation. So not demeaning the data will cause problems.
  2. presample starts the Kalman recursion at observation 1 and updates the respective matrices. But when computing the joint likelihood, the sum over the values for the respective observations only starts at presample+1. In contrast, with first_obs you start both the recursion and the sum at time first_obs. Put differently, presample allows you to already move from the initialization with the unconditional mean and variance to the steady state Kalman filter values.
9

  1. The variables in the model are detrended and log-linearized around steady-state and that’s why there is no constant in the transition equation in “kalman.m”

  2. Yes, I agree. I missed the starting point in “kalman_filter.m” of Dynare.

And Prof. Johannes, thank you for your help and time.

Best,

Burak