Non-linear gmm

[Francesca Salvati]

Hello,
I am estimating a system of non-linear equations using the "gmm" command in Stata. After a bunch of iterations the objective function value starts appearing with the message "backed up". What is the meaning of "backed up" and what is this kind of issue associated with? After some iterations, the code ends up converging but displays unreasonably large standard errors. Thank you for your help.

[Daniel Schaefer]

The message "backed up" means that the iterator tried to move in a certain direction in the space defined by the maximum likelihood function of your model parameters, but had to take a step back. The iterator is looking for a maximum and will take steps that have a higher probability of leading closer to a maximum. If that step leads to a region of that space with a lower predicted likelihood, then the iterator will "back up" to the previous iteration, then take another step in a different direction. The "backed up" message is only really a problem if it appears on the last iteration, because that might indicate the iterator has not converged on a maximum.

Edit: This is documented in the pdf entry for maximize.

help maximize

Then click view full pdf entry. Or just look here under remarks and examples.

[Francesca Salvati]

Thank you, I am aware of the maximize file but I wasn't entirely sure if the message appearing in some iterations but not others would be problematic. Based on your very helpful explanation, I suppose that if the message keeps appearing alongside the same value for the objective function over many many iterations, it means that it can't really find a better region, meaning that wherever it is stuck might be a potential maximum?

[Daniel Schaefer]

it means that it can't really find a better region, meaning that wherever it is stuck might be a potential maximum?

It depends. It could have found a relatively flat region, suggesting there is no meaningful local maximum - though you are more likely to see a "not concave" message in that case. Or there could be a steep gradient, but only in one direction, and the iterator took many wrong turns before finding the correct direction. If the iterator backed up on the last iteration, then it could have found an analytically perfect local maximum, but it is much more likely that there is a gradient leading to a maximum in a direction that the iterator cannot find.

[Francesca Salvati]

Thank you, this is extremely helpful!

[Yongsheng Wang]

Hello, I would like to ask how to do a nonlinear gmm regression using the "gmm" command

[Daniel Schaefer]

That's a question you would be better answering by taking a class or reading a textbook.