Dear all

I have two questions, one stata question and another econometric question.

First the stata question:

I am performing the following model as suggested by Professor Jeff Wooldridge in another thread which is available here (as well as in chapter 19 of Econometric analysis of cross section and panel data) :

Code:
xtset municipality quarter

xtpoisson preg_rate c.z1##c.z1 c.z2##c.z2  x1 x2 x3 xi, fe vce(robust)
predict yhat

xtivreg2 log_lbw x1 x2 x3 xi   (preg_rate=yhat), fe vce(robust) endog(preg_rate)
where z1 and z2 are my instruments; x1-xi my control variables; preg_rate is the pregnancy rate per municipality (pregnancies per 1000 fertile women) and is treated as a count; and log_lbw is the percentage of low birth weight newborns per municipality [log_lbw=log(1+lbw_rate)]. Both preg_rate and lbw_rate have many zeros (due to small municipalities and the low occurrence of low weight births) and are thus treated as counts, following the methodology proposed by Lindo et al. (2017) which deals with abortion rates.


I would like to ask how could I perform a test of overidentification manually, given that xtivreg2 only detects one instrument (yhat) and thus assumes the model is perfectly identified, when in reality, there are 2 instruments: z1 and z2.

Regarding the econometric question

I would also like to treat the variable lbw_rate as a count in an perform an IV poisson regression. Nevertheless, as Professor Joao Santos Silva mentioned often in this forum and elsewhere, an IV poisson model with fixed effects may suffer from inconsistency caused by the incidental parameters problem associated with fixed efects.

For that reason I employ xtreg with the log transformed variable (also helps to read the results in percentage terms).

My question is whether this is a legitime way to go around the incidental parameters problem of xtivpoisson with fixed effects.

Thank you very much for your time and consideration.





Notes:
xtivreg2 is a userwritten command written by Mark E Schaffer.

I have quarterly data on most 274 municipalities from 2007 to 2014 (unbalanced)
or
I have quarterly data on all 274 municipalities from 2010 to 2014 (balanced)


References:
Cunningham, S., Lindo, J. M., Myers, C. K., & Schlosser, A. (2017). How far is too far? New evidence on abortion clinic closures, access, and abortions. NBER Working Paper, (w23366).
Wooldridge, J. M. (2002). Econometric analysis of cross section and panel data. MIT press. pp: 623-625