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st: Uncorrelated observations


From   "vmz@vol.net.mt" <vmz@vol.net.mt>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Uncorrelated observations
Date   Tue, 20 Oct 2009 20:47:01 +0100

Dear Statalisters,
I am going over Microeconometrics Using Stata by A.Colin Cameron & Pravin
K.Trivedi ,and I have been trying hard to understand what is meant by
the 3rd assumption,on page 81,
E(UiUj | Xi , Xj) = 0 ,i~=j,(conditionally uncorrelated observations) .I
have generated the following data to get some insight on the purpose of
this assumption,but I am getting nowhere.I have written the following
two programs trying to shed some light,but i am not pleased with the
output.

*First program :
version 9
drop _all
set obs 30000
set seed 1267655
gen Xi = invnorm(uniform())*10+100
 qui summ Xi
gen Ui = Xi-r(mean)
keep in 1/15000
drop Xi
gen n = _n
sort n
save Ui,replace
drop _all
set obs 30000
set seed 1267655
gen Xj = invnorm(uniform())*10+100
 qui summ Xj
gen Uj = Xj-r(mean)
keep in 15001/30000
drop Xj
gen n = _n
sort n
save Uj,replace
use Ui,clear
merge n using Uj
drop _merge
drop n
gen UiUj = Ui*Uj
summ
* Note that this demonstrates the first assumption,that E(Ui | Xi)= 0
(exogeneity of regressors) is demonstrated)
* since (.023252 -.0232521)/2 = 0 ,which is the expected values of the
full 30000 observations.
* The expected value of the 15000 pairs of observations,is -.1155355
,which is way off from zero.


*Second Program
version 9
drop _all
set obs 30000
set seed 1267655
gen Xi = invnorm(uniform())*10+100
gen Xj = Xi[_n-1]
qui summ Xi
replace Xi = Xi-r(mean)
rename Xi Ui
qui summ Xj
replace Xj = Xj-r(mean)
rename Xj Uj
summ
gen UiUj = Ui*Uj
summ

* Again,the mean (expected value) of Ui is zero ,but that of Ui*Uj is
1795954.
* This is making me think that there is something basic that I am not
following.
* Can anyone help me with this.I thank you before hand.Victor M.Zammit

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