Corner Solutions: Computation of Standard Errors

[John Baum]

Hi,

my question is concerned with ML estimation in Dynare: how the standard errors are computed if a corner solution of a parameter exists?

Regards

[jpfeifer]

Hi, could you be more precise please. What do you mean with corner solution? And standard errors for which object? If you mean for the parameters at the maximum likelihood point: it uses the inverse of the hessian to compute them. For a true corner solution, this is of course not a valid way and usually fails with a warning because the Hessian at the corner is not positive definite.

[John Baum]

Thank you very much for the quick response. So far I understood how the standard errors are computed.

For clarification: by 'corner solution' I mean that the estimated parameter value hits the lower or upper bound. In particular in my case chi (see table below) is the habit formation parameter which is bounded between 0 and 1. The result by Maximum Likelihood shows that chi hits the boundary point of 1 but no warning message (which indicates that the hessian is not-positive definit) is associated with this result!

RESULTS FROM MAXIMUM LIKELIHOOD
parameters
Estimate s.d. t-stat

alpha 0.1537 0.1036 1.4836
kappa 0.0238 0.0128 1.8541
chi 1.0000 0.1037 9.6462
sigma 0.0100 0.0101 0.9854
phi_pi 1.0000 0.7255 1.3783
phi_x 0.8810 0.3620 2.4341
rho_rd 0.8406 0.0612 13.7416
standard deviation of shocks
Estimate s.d. t-stat
epsv 0.6505 0.0719 9.0469
epsx 0.2715 0.0217 12.5101
epsr 0.4824 0.0380 12.6787
Total computing time : 0h00m20s

My question now is: Is the result for chi and the corresponding value of the standard deviation reliable or not? Please have also a look on the mod-file:

Baum_ML.mod

(944 Bytes) Downloaded 49 times

Thank you again in advance!