st: using "tobexog" with panel data

[Michael Mulcahy <mulcahy_uconn@yahoo.com>]

Hi,
Is there a way to adjust Prof. Baum's tobexog test for application in a (strongly balanced) panel count data context (cities = 596, T=12, total N=7152) ? 


* I'm investigating the impact of a dichotomous city-level policy innovation "treatment" on a dependent count variable. 

* I suspect endogeneity of the policy innovation (adopted by subset of U.S. cities in my sample in different years). 
* It's possible that there's simultaneous causality between the policy and the dependent variable. 

* My model includes a 1-yr lagged dependent variable, and, following Wooldridge (2005), the initial value of the dependent variable and within-subj means of the time-varying regressors, and 11 year-dummies. 

* The organizations generating the counted events (the dependent variable) are also involved in the process of advocating the policy innovation, so the effect of the policy "treatment" on the dependent variable may precede adoption of the policy. To test for this, I'm implementing Laporte and Windmeijer's (2005) approach to time-varying binary treatment effects (all pre-policy year =0, adoption-year and all post-adoption years ==1, plus year dummies to measure possible effects in 5-year period encompassing adoption - 2-pre, 2-post, and year of adoption). 

* For the tobexog test, I just test for endogeniety of the year-of-adoption indicator. 


*So the structural panel model looks like this:
count(it) = count(i,t-1) 
count(i,t=1) time-constiv(i) time-varyingiv(it) mean-time-varyingiv(i) 
year-dummies step-policydummy(it) time-varying-policydummy(it)

*The tobexog model looks like this:
tobexog count(it) count(i,t-1) 
count(i,t=1) time-constiv(i) time-varyingiv(it) mean-time-varyingiv(i) year-dummies
(policy-adoptionyeardummy(it) = instrument(it)) ll[(0)] ul[(121)] aweights (using fweights produces same report)

*This test is positive for endogeneity of the year-of-adoption indicator.

*Can I accept this result as evidence of endogeneity of the policy treatment, even though the test is not explicitly designed for the panel context? If not, can anyone suggest a modification appropriate for the panel context? 



Thank you for your consideration!

Mike 

*Laporte and Windmeijer 2005. "Estimation of panel data models with binary indicators when treatment effects are not constant over time." Economics Letters 88: 389-396.

*Wooldridge 2005. "A Simple 
Solution to the Initial Conditions Problem in Dynamic, Nonlinear Panel 
Data Models with Unobserved Heterogeneity" Journal of Applied 
Econometrics 20: 39-54.

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