Test overidentification when instrumenting xtivreg2 with predicted values of xtpoisson

[Antonio Melo]

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) :

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

[Jeff Wooldridge]

By construction, you are generating one instrument for one endogenous variable, so in the estimation there are no overidentifying restrictions. One thing you can do is include, say, z1 and z2 separately in the second-step estimation and test their coefficients. If the IVs are valid, no function of them should be significant.

The question about lbw_rate is more difficult. If you leave it as a count, you can apply a method described by Frank Windmeijer, 2002, Economics Letters. Unfortunately, I don't know if it's been coded in Stata. It might be possible to do it with Stata's gmm command.

[Joao Santos Silva]

Dear Antonio Melo,

Further to Jeff Wooldridge's useful advice, you can also do the IV estimation using as instruments yhat and the Zs, in which case you can perform the over-id test. That was the approach used in (see the first 2 lines of page 291):

Windmeijer, Frank and Santos Silva, J.M.C. (1997), Estimation of Count Data Models with Endogenous regressors; An Application to Demand for Health Care, Journal of Applied Econometrics, 12(3), pp. 281-294.

Of course, in that case we were dealing with a binary variable, but the principle is the same.

Best wishes,

Joao

[Antonio Melo]

Dear Professors

I would like to thank you for your help. It made things much more clear to me.

Thank you very much, once again.

Best,
António