** FLS 6183 & FLP 0468
** Lab 2:  Omitted Variable Bias	
* Data: 13/09/2018

clear

* Part a. No correlation between X and Z

* We will create a data set with 500 observations. We are establishing that X has a mean of 7 and a standard deviation of 8.  
* We are estiablishing at Y with mean 100 and standard deviation of 20.  We are also establishing that Z has a mean of 20 and a standard deviation of 2.
* In addition, we will stipulate that the correlation between X and Z is 0, that the correlation between X and Y = 0.7 and the correlation between Y and Z = 0.3.
* x, y and z are randomly drawn from a normal distribution. Please note in the matrix C below the order is (y, x, z) in each colunm and row.


matrix m = (100,7,20)
matrix sd = (20,8,2)
matrix C = (1, 0.7, 0.3 \ 0.7, 1, 0 \ 0.3, 0, 1)
drawnorm y x z, n(500) means (m) sds(sd) corr(C) seed(12345)

summarize
corr y x z

regress y x
estimates store m1
 
regress y x z 
estimates store m2
esttab m1 m2, se 
esttab m1 m2, ci 

* Part b. Correlation between X and Z =0.75

* We will create a data set with 500 observations. We are establishing that X has a mean of 7 and a standard deviation of 8.  
* We are estiablishing at Y with mean 100 and standard deviation of 20.  We are also establishing that Z has a mean of 20 and a standard deviation of 2.
* In addition, we will stipulate that the correlation between X and Z is 0.75, that the correlation between X and Y = 0.7 and the correlation between Y and Z = 0.3.
* x, y and z are randomly drawn from a normal distribution.

clear 

matrix m = (100,7,20)
matrix sd = (20,8,2)
matrix C = (1, 0.7, 0.3 \ 0.7, 1, 0.75 \ 0.3, 0.75, 1)
drawnorm y x z, n(500) means (m) sds(sd) corr(C) seed(12345)


summarize
corr y x z

regress y x
estimates store m3
regress y x z
estimates store m4
esttab m2 m4, se 

esttab m3 m4, se 
esttab m3 m4, ci
 
 * Part C. Analysis with Dummy Variable
 
generate random = runiform()
kdensity random
sum random, detail
gen d=1 if random <=0.5
replace d=0 if random >0.5