PROBIT with fixed effects

[Piku Sarkhel]

Hi,

I am attempting to estimate a PROBIT model for water connection where the dependent variable is 1=if piped water connection and 0 if not. To account for region specific variation I have included district (geographical unit of administrative area ) fixed effects by using i.DIstrict as well as added the cluster option with cluster(District). Is this the right thing to do to account for fixed effects . I raise this question because I read somewhere in this forum that fixed effects are incompatible with non-linear estimation. Please help!!

[Joseph Coveney]

Yeah, I read that, too. But I think that they also said that if you've got at least 50 or 60 observations per cluster (district, in your case), then you might be okay. If I recall correctly, I think they said something to the effect that you ought to have enough observations per cluster to feel confident that you could run probit separately on each cluster.

Short of that, I'm not so sure that just appending a cluster(district) option to a probit . . . i.district model will fix up the incidental parameters problem.

[Piku Sarkhel]

Hi Joseph,

Thanks for the reply. But in my cases there are 60 odd districts (its a nationally representative survey data containing close to 50k households) so running separate probit would be cumbersome.

[daniel klein]

Why not changing to a logit, where the fixed-effects can be conditioned out of the likelihood? Any specific reason to stick with the probit specification?

Best
Daniel

[Piku Sarkhel]

Hi Daniel,

no reason except that PROBIT uses standardized normal making inference easier to comprehend. Could you help me out with "conditioning out the fixed effects" in cross section data ?

BEST

PS

[daniel klein]

See

help xtlogit
help clogit

Best
Daniel

[Joseph Coveney]

. . . in my cases there are 60 odd districts (its a nationally representative survey data containing close to 50k households) so running separate probit would be cumbersome.

You misunderstood. No one is asking you to run a separate probit on each of the clusters. It was that the criterion for deciding whether a fixed effects probit would not suffer from unacceptable bias (actually lack of statistical consistency), is that you have enough observations per cluster that you could run separate probit regressions for each of the 60 odd districts and get legitimate results. On the basis of that, if you have 50 000 households distributed roughly equally among the sixty districts, then you're probably okay with the fixed-effects probit regression.