*************************************************************************************************
*** Example: IV Simulation - 500 reps; n=10; corr(x,u) = 0.5; corr(z,u) = 0; corr (x,z) = 0.8 ***
*************************************************************************************************

clear

* Generating 2 variables with missing values to store estimated values of beta hat from the simulation *
set seed 12345
set obs 500
g data_bxols=.
g data_bxiv=.

* Simulating data based on correlation values and storing estimates of beta hat *
forval i=1/500 {

	preserve
	clear
	set obs 10
	matrix C = (1, 0.8, 0.5 \ 0.8, 1, 0 \ 0.5, 0, 1)
	drawnorm x z u, corr(C)
	g y = 1 + 2*x + u
	reg y x
	local xcoefols =_b[x]
	ivregress 2sls y (x = z)
	local xcoefiv =_b[x]
	restore

	replace data_bxols=`xcoefols' in `i'
	replace data_bxiv=`xcoefiv' in `i'

}

* Summary and histogram of beta hat values *
su data_bxols data_bxiv
hist data_bxols
hist data_bxiv

***************************************************************************************************
*** Example: IV Simulation - 500 reps; n=1000; corr(x,u) = 0.5; corr(z,u) = 0; corr (x,z) = 0.8 ***
***************************************************************************************************

clear

* Generating 2 variables with missing values to store estimated values of beta hat from the simulation *
set seed 12345
set obs 500
g data_bxols=.
g data_bxiv=.

* Simulating data based on correlation values and storing estimates of beta hat *
forval i=1/500 {

	preserve
	clear
	set obs 1000
	matrix C = (1, 0.8, 0.5 \ 0.8, 1, 0 \ 0.5, 0, 1)
	drawnorm x z u, corr(C)
	g y = 1 + 2*x + u
	reg y x
	local xcoefols =_b[x]
	ivregress 2sls y (x = z)
	local xcoefiv =_b[x]
	restore

	replace data_bxols=`xcoefols' in `i'
	replace data_bxiv=`xcoefiv' in `i'

}

* Summary and histogram of beta hat values *
su data_bxols data_bxiv
hist data_bxols
hist data_bxiv

****************************************************************************************************
*** Example: IV Simulation - 500 reps; n=1000; corr(x,u) = 0.5; corr(z,u) = 0; corr (x,z) = 0.01 ***
****************************************************************************************************

clear

* Generating 2 variables with missing values to store estimated values of beta hat from the simulation *
set seed 12345
set obs 500
g data_bxols=.
g data_bxiv=.

* Simulating data based on correlation values and storing estimates of beta hat *
forval i=1/500 {

	preserve
	clear
	set obs 1000
	matrix C = (1, 0.01, 0.5 \ 0.01, 1, 0 \ 0.5, 0, 1)
	drawnorm x z u, corr(C)
	g y = 1 + 2*x + u
	reg y x
	local xcoefols =_b[x]
	ivregress 2sls y (x = z)
	local xcoefiv =_b[x]
	restore

	replace data_bxols=`xcoefols' in `i'
	replace data_bxiv=`xcoefiv' in `i'

}

* Summary and histogram of beta hat values *
su data_bxols data_bxiv
hist data_bxols
hist data_bxiv

**********************
*** Other examples ***
**********************

use "C:\Users\royj\Dropbox\eco5720\Data Sets- STATA\MROZ.DTA", clear

*** OLS ***
drop if lwage==.
reg lwage educ

*** IV using the covariance formula ***
corr lwage fatheduc, cov
g covyz=r(cov_12)
corr fatheduc educ, cov
g covxz=r(cov_12)
g iv1=covyz/covxz
su iv1
di "IV estimate = " r(mean)

*** IV using two stage least squares manually ***
reg educ fatheduc
predict educh
reg lwage educh

*** IV using two stage least squares ***
ivregress 2sls lwage (educ = fatheduc), first