Corner Solutions: Computation of Standard Errors


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


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.

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!

**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)

Thank you again in advance!