** FLS 6183 & FLP 0468
** Lab 3:  Omitted Variable Bias	
* Data: 13/09/2018

clear

* Question 1

* 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

* Let's save the stats we will need to compare if diff is stat diff to implement Clogg, Petkova and Haritou (1995) 
scalar b = _b[x]
scalar vb = _se[x]^2
scalar ve = e(rmse)^2
 
regress y x z 
estimates store m2
esttab m1 m2, se 

* Let's save the stats we will need to compare if diff is stat diff and calculate t test as proposed by  Clogg, Petkova and Haritou (1995) 

scalar d = scalar(b)-_b[x]
scalar se = sqrt(_se[x]^2-scalar(vb)*e(rmse)^2/scalar(ve))
di scalar(d)
di scalar(se)
di scalar(d)/scalar(se)

* suest 
hausman m1 m2, alleqs 


* 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

coefplot m3 m4,  drop(_cons z) xline(0) 


* Question #2 

* Case 1

clear

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)

* Solution proposed by Pedro Castro, Jose Octavio, Vinicius and Sergio 

* Gerar 10 grupos a partir dos decis de z
xtile groups = z, nq(10)

gen group1 = 0
replace group1 = 1 if groups == 1
gen group2 = 0
replace group2 = 1 if groups == 2
gen group3 = 0
replace group3 = 1 if groups == 3
gen group4 = 0
replace group4 = 1 if groups == 4
gen group5 = 0
replace group5 = 1 if groups == 5
gen group6 = 0
replace group6 = 1 if groups == 6
gen group7 = 0
replace group7 = 1 if groups == 7
gen group8 = 0
replace group8 = 1 if groups == 8
gen group9 = 0
replace group9 = 1 if groups == 9
gen group10 = 0
replace group10 = 1 if groups == 10

* Gerar variável aleatória para sortear subamostra 
generate subsample = runiform()
replace subsample = 0 if subsample <=0.5
replace subsample = 1 if subsample >0.5

regress y x group2 group3 group4 group5 group6 group7 group8 group9 group10 if subsample == 0
estimates store m5

esttab m1 m2 m5, ci 

* Case 2 

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)

* Gerar 10 grupos a partir dos decis de z
xtile groups = z, nq(10)

gen group1 = 0
replace group1 = 1 if groups == 1
gen group2 = 0
replace group2 = 1 if groups == 2
gen group3 = 0
replace group3 = 1 if groups == 3
gen group4 = 0
replace group4 = 1 if groups == 4
gen group5 = 0
replace group5 = 1 if groups == 5
gen group6 = 0
replace group6 = 1 if groups == 6
gen group7 = 0
replace group7 = 1 if groups == 7
gen group8 = 0
replace group8 = 1 if groups == 8
gen group9 = 0
replace group9 = 1 if groups == 9
gen group10 = 0
replace group10 = 1 if groups == 10

* Gerar variável aleatória para sortear subamostra 
generate subsample = runiform()
replace subsample = 0 if subsample <=0.5
replace subsample = 1 if subsample >0.5

regress y x group2 group3 group4 group5 group6 group7 group8 group9 group10 if subsample == 0
estimates store m6

esttab m3 m4 m6, ci 

* Question 3 

* Case 1
clear

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)

* Criar os grupos
xtile groups = z, nq(3)

gen group1 = 0
replace group1 = 1 if groups == 1
gen group2 = 0
replace group2 = 1 if groups == 2
gen group3 = 0
replace group3 = 1 if groups == 3

regress y x group2 group3
estimates store m7
regress y x z group2 group3
estimates store m8

esttab m1 m2 m5 m7 m8, ci 

* Case 2 

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)

* Criar os grupos
xtile groups = z, nq(3)

gen group1 = 0
replace group1 = 1 if groups == 1
gen group2 = 0
replace group2 = 1 if groups == 2
gen group3 = 0
replace group3 = 1 if groups == 3

regress y x group2 group3
estimates store m9
regress y x z group2 group3
estimates store m10 

esttab m3 m4 m6 m9 m10, ci