by **kyri82** » Tue Mar 12, 2013 8:06 pm

Hi again,

I am coming back to the estimation of the covariance. I tried to use your advice in assuming a common shock. In particular, I set my exogenous processes as follows:

v1 = rhoI1*v1(-1) + rhoI12*v2(-1) + stdr_ist*(eta1 + PHI*eta3) ;

v2 = rhoI1*v2(-1) + rhoI12*v1(-1) + stdr_ist*(eta2 + PHI*eta3);

Thus, the variance of the "overall" shock is stdr_ist^2 + (stdr_ist^2)*(PHI^2) and the covariance is stdr_ist*PHI (correct??). Then, my shock block writes:

shocks ;

var eta1 = 1;

var eta2 = 1;

var eta3 = 1;

end;

and I do not set anything for the covariance. If I estimate only rhoI1, rhoI12 and stdr_ist (MLE without setting a prior), it converges normally and I get rather logical results:

Improvement on iteration 11 = 0.000000000

improvement < crit termination

Objective function at mode: -169.780830

Objective function at mode: -169.780830

RESULTS FROM MAXIMUM LIKELIHOOD

parameters

Estimate s.d. t-stat

stdr_ist 0.0161 0.0014 11.2415

rhoI1 0.9651 0.0022 438.0741

rhoI12 0.0326 0.0031 10.4305

Note 1: Theta is 2

Note 2: Epsilon is 2

Note 3: Interim period is 0

Total computing time : 0h00m09s

However, I am not sure what Dynare assumes as the covariance between the shocks. Does it indeed assume/impose zero covariance?? Trying to estimate PHI becomes a mess, as it is extremely sensitive to the initial condition. If I set the latter to 0.02, say:

estimated_params ;

stdr_ist , 0.0126 ,,;

rhoI1 , 0.95 , ,;

rhoI12 , 0.0202 , , ;

PHI , 0.02, , ;

end;

estimation(datafile=istshocks1, mode_compute=4) ; %mode_compute=4

it converges and gives me what seem to be logical results.

Improvement on iteration 303 = 0.000000090

improvement < crit termination

Objective function at mode: -171.298880

Objective function at mode: -171.298880

RESULTS FROM MAXIMUM LIKELIHOOD

parameters

Estimate s.d. t-stat

stdr_ist 0.0147 0.0043 3.4273

rhoI1 0.9558 0.0022 441.7531

rhoI12 0.0417 0.0034 12.1793

PHI 0.3894 0.7154 0.5443

Note 1: Theta is 2

Note 2: Epsilon is 2

Note 3: Interim period is 0

Total computing time : 0h00m44s

Nevertheless, even the most minor changes to this initial condition cause trouble. Initial conditions of PHI = 0.019 and 0.0199 (!!) result to the message of no convergence:

POSTERIOR KERNEL OPTIMIZATION PROBLEM!

(minus) the hessian matrix at the "mode" is not positive definite!

=> posterior variance of the estimated parameters are not positive.

You should try to change the initial values of the parameters using

the estimated_params_init block, or use another optimization routine.

Warning: The results below are most likely wrong!

> In dynare_estimation_1 at 643

In dynare_estimation at 62

In BS_CapitalServices3IST1 at 1066

In dynare at 132

Setting PHI = 0.019999 does converge but the estimated parametres are a bit different from the case where the initial condition is 0.02.

My questions are:

1. When I do not set anything for the covariance and I do not ask for the estimation of PHI, does Dynare indeed assume /impose a zero covariance? That is, are the persistence coefficient and the common standard deviation estimated with ML under the restriction of zero covariance?

2. The issues of non-convergence and extreme sensitivity to initial conditions are not normal right? What can it mean? Would you suggest another way to estimate the covariance as well?

Thanks a lot again!!

Kyriacos