Dear Listers,
I'm trying to estimate a model using a cross-section dataset: y_ij =
f(x_ij,u_j,e_ij), where y_ij is a binary, x_ij are regressors at the
firm-level (firm i in sector j), u_j is unobservable sector-specific
effects and e_ij are unobservable firm-specific effects. One way to
capture as mush as u_j in the model is to add separate dummies into
the model. But I have around 100 sectors and adding about 100 dummies
doesn't seem to be a good choice. Moreover, I've heard that dummies
can't be added to logistic specifications as they can in OLS models.
Q1: Theoretically, I'm not sure if one can't add dummies to a logistic
regression as she does in an OLS.
Another recommended approach is to put constraints on the
log-likelihood function in order to sweep out the u_j. One way
suggested by Chamberlain (1980) is to condition the log-likelihood
function on Sigma(y_ij).
Q2: Is there any advantages for tis approach compared to adding
separate dummies into the model?
Q3: Do you any better, similar approach for this purpose?
I have been recommended to use Stata -xtlogit- FE with constraints to
run the second approach.
Q4: I couldn't figure it out why -xtlogit- and not -logit- as I'm not
using a panel but a cross-section
Q5: How can I define and use the constraint suggested by Chamberlain?
Can you probably post me the code, as I tried many formulations on my
own but neither actually worked out.
Thank you so much for your time and support.
Good luck all,
Fardad
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