Xtlogic failure to converge

[Moritz Kaiser]

Hey y'all,

I am having issues converging a logit fixed effect model, which I want to run in order to conduct a Hausman test. The dependent variable is whether the wage is round or not. The explanatory variables are the wage level (wage) and the price level (cpi_5). The fixed effect is cty_gr which are regions. This is the code that does not converge:

xtset cty_gr
xtlogit round wage cpi_5, fe

In order to work around this issue, I did the following:

logit round wage cpi_5 i.cty_gr
estimates store fe

xtset cty_gr
xtlogit round wage cpi_5, re
estimates store re

hausman fe re

This works, but I was wondering if the two logit fixed effects models are computationally the same and why the first one does not work.

Cheers!

[Carlo Lazzaro]

Moritz:
welcome to this forum.
No, your two codes are not equivalent, as the first one (-logit-), unlike -xtlogit-, ignores the panel structure of your dataset.
I remind myself first that -xtlogit,fe- is a conditional fixed effect estimator, due to the incidental parameter bias ([PDF] The incidental parameter problem since 1948 | Semantic Scholar).

[Joao Santos Silva]

Dear Moritz Kaiser,

In addition to Carlo's helpful reply, please note that the maximum likelihood estimator of a logit model that includes the fixed effects as dummies is only consistent for large T; with T=2 it converges to 2b rather than to b. Also note that it does not make much sense to do a Hausman test in this context. So, my recommendation is that you use xtlogit with the fe option.

Best wishes,

Joao