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st: Interesting Results - But Am I Right?


From   Sachin Chintawar <schint1@tigers.lsu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interesting Results - But Am I Right?
Date   Fri, 24 Apr 2009 15:00:42 -0600

Dear Statalist Users
I have been playing around with endogenous variable models and the
hypothsis that 'An increase in instruments tend to increase the bias
of our estimates'. While this was shown to be true by A. Buse 'The
Bias of Instrumental Variable Estimators' in Econometrica (1992). My
simulation results showed the contrary (A simple variation was that
this was a probit model - Thanks to Mr. Martin for the million
questions while I was coding it). The program until now is given
below. Under the conditions specified I see that as I increase the
instuments (from z1 to z4) the bias in the 'beta' value actually
decreases. My question is
1. Am I specifying everything in the model right?
2. Why this difference in results from another paper?
---------------------------------------------------Start
Example-----------------------------------------------------------------------------
global numobs 500             // sample size N
global numsims "50"         // number of simulations
set seed 123456789

capture program drop endoprob

program endoprob // , rclass
version 10.1
drop _all
set obs $numobs
   generate u = rnormal()
   generate mu = rnormal()
   //generate x = rnormal()
   generate z1 = rnormal()   // 4 Instruements
   generate z2 = rnormal()
   generate z3 = rnormal()
   generate z4 = rnormal()
   // Also be written *drawnorm u mu x1 z1 z2 z3 z4
   generate a = 0.5*u
   generate x = z1 + a
   regress x  z1   // endogenous regressor with four instruments

   predict px

   generate y = 0.5 + px + mu + u>4    //Reduced Form Equation
   ivprobit y (x= z1)
   predict py
end
simulate _b _se y py , ///
   reps($numsims): endoprob

mean x* y*
--------------------------------------------------------------End
Example------------------------------------------------------------------
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