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st: question about insturmental variables and probit/logits


From   "Ed Levitas" <levitas@uwm.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: question about insturmental variables and probit/logits
Date   Mon, 3 Oct 2011 10:22:55 -0500

Hello Stata listers,

A similar question to this has been asked before.  Previous responses have suggested the use of QVF, GLLAMM, and similar programs.

However, I don't think my data will allow me to follow these procedures.  Simply, I have a dichotomous outcome, and an endogenous regressor.  I also have two hierarchical levels (firms, and project development characteristics/year).  For simplicity, assume one exogenous regressor and the endogenous regressor:

DV = BExog(it) + BEndog(itk)

where 
DV = 1 if firm i's kth project advances to a new stage of development by the end of year t, and zero otherwise
Exog(it) = is a firm level exogenous regressor measured at the end of year t, and pertains to firm i.
Endog(ikt) = is a project level endogenous regressor measured at the end of year t, pertaining to firm i's project k.

Is the following an efficient way to estimate unbiased coefficients given my 2 levels of analysis?

(note that I put arithmetic operators in for clarity but I do recognize that this is improper syntax for STATA)
1) XTREG Endog(itk) = BInst(itk) + BExog(it)  (Where BInst is suitable instrument; ie highly correlated to Endog and highly uncorrelated to Exog )

2) PREDICT yhat

3) BOOTSTRAP: XTLOGIT DV = BExog(it) +  Byhat(itk), pa cluster(firm)  

Is this effective, or does it create additional biases?

Thank you in advance for any suggestions/criticisms you have,

Ed


 
****************************************
Edward Levitas, PhD
Associate Professor
Sheldon B. Lubar School of Business
University of Wisconsin-Milwaukee
3202 N. Maryland Ave.
Milwaukee, WI  53211
ph: (414) 229-6825
fx: (414) 229-6957
http://www4.uwm.edu/business/faculty/busfaculty/levitas.cfm




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