Hausmann Test with logit, omitted regression output with fixed effects

[Jana Schue]

Dear Forum,

I have a problem regarding random and fixed effects with the Hausmann test in a logit regression.

I have as independent variable a binary variable reflecting industries (1 for dirty, 0 for clean). As dependent variable I also have a binary variable (purpose). The command is as follows:

xtlogit purpose dirty_l2 cf_l2 growth_l2 capexi_l2 adexi_l2 sl_l2 fs_l2 om_l2, fe
estimates store FE
xtlogit purpose dirty_l2 cf_l2 growth_l2 capexi_l2 adexi_l2 sl_l2 fs_l2 om_l2, re
estimates store RE
hausman FE RE

The Hausmann test shows me a significant result and that means that I should use fixed effects.

The problem is that the regression with fixed effects is omitted. I guess it is because the independent variable is industry related:

purpose | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
dirty_l2 | 0 (omitted)
cf_l2 | .03374 .0515483 0.65 0.513 -.0672928 .1347729
growth_l2 | 1.032585 .8782802 1.18 0.240 -.6888127 2.753983
capexi_l2 | .4081369 6.973933 0.06 0.953 -13.26052 14.07679
adexi_l2 | 11.63989 9.286588 1.25 0.210 -6.561483 29.84127
sl_l2 | -.0486311 .1810182 -0.27 0.788 -.4034202 .3061579
fs_l2 | .4090683 .4382702 0.93 0.351 -.4499255 1.268062
om_l2 | -.2673203 1.438415 -0.19 0.853 -3.086561 2.551921


For my work, I am now wondering whether I should simply leave out the Hausman test and use random effects, or whether the results of the Hausman test are important and the regression then outputs nothing. I would be very happy about an assessment and / or literature!

Thank you,
Jana

[Andrew Musau]

I am now wondering whether I should simply leave out the Hausman test and use random effects, or whether the results of the Hausman test are important and the regression then outputs nothing.

Essentially, you will be fitting noise if you proceed with random effects knowing that it is not consistent. Search the forum for mentions of correlated random effects that will allow you to get estimates on the time-invariant variables while giving you FE estimates on the time-varying variables. On literature references, find your favorite econometrics textbook. The discussion on random effects vs. fixed effects is covered in virtually all mainstream textbooks.

[Carlo Lazzaro]

Jana:
If you go -re- when (conditional) -fe- is the way to go, -re- is an inconsistent estimator. Therefore your coefficients are unreliable.
That said, what strikes me is that no coefficient seems to reach statistical significance in the regression table (please use CODE delimiters. Thanks) you shared. Even though I'm not a p-value fan, this sounds strange. Hence, I'd double-check your model specification before being worried about the (conditional) -fe- vs -re- strategy.

[Jeff Wooldridge]

Is this true panel data? Or are you doing “fixed effects” using industry FEs with firm level data? I’m wondering if dirty_I2 varies across time.

I maybe can recommend the correlated random effects probit, which will allow you to keep dirty_I2 while being similar in spirit to FE. Plus it doesn’t rule out serial correlation.

[Jana Schue]

Thank you very much for your answers, that was really helpful!