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st: using "tobexog" with panel data


From   Michael Mulcahy <mulcahy_uconn@yahoo.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: using "tobexog" with panel data
Date   Sat, 25 Feb 2012 05:46:38 -0800 (PST)

Hi,
Is there a way to adjust Prof. Baum's tobexog (Baum et al. 2003) 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 


* Baum, C.F., Schaffer, M.E., and Stillman, S. 2003. Instrumental Variables and GMM: Estimation and Testing. The Stata Journal, Vol. 3, No. 1, pp. 1-31.  Working paper version: Boston College Department of Economics Working Paper No 545. http://ideas.repec.org/p/boc/bocoec/545.html

*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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