/* Simulations of Dummy Variables - omitted variables
  1. Generate the full range of x for both group0 and group1
  2. Drop some observation from each group and simulate the possible bias
  Created by Jin Man Lee
  Updated 2/17/2015
 */
 
/* Simulation 1 : Positive Bias */
clear
set obs 500
gen group  = rbinomial(1, 0.5)
tab group
gen x = rnormal(10, 2)
gen e = rnormal(0,1)
gen y = 0
replace y = 10 + 0.5*x + e if group == 0
replace y = 5 + 0.5*x + e if group == 1
tw (scatter y x if group == 0 ) (scatter y x if group == 1 )    ///
   (lfit y x if group == 0) (lfit y x if group == 1) (lfit y x)  ,  ///
   legend( lab(1 "Group 0") lab(2 "Group 1")   ///
           lab(3 "Fitted Group 0 ") lab(4 "Fitted Group 1")  ///
		   lab(5 "Fitted all") )
drop if x < 8 & group == 0
drop if x > 12 & group ==  1
tw (scatter y x if group == 0 ) (scatter y x if group == 1 )    ///
   (lfit y x if group == 0) (lfit y x if group == 1) (lfit y x)  ,  ///
   legend( lab(1 "Group 0") lab(2 "Group 1")   ///
           lab(3 "Fitted Group 0 ") lab(4 "Fitted Group 1")  ///
		   lab(5 "Fitted all") )
reg y x
reg y x if group == 0
reg y x if group == 1
reg y i.group##c.x


 /* Simulation 2 : Negative Bias */
clear
set obs 500
gen group  = rbinomial(1, 0.5)
tab group
gen x = rnormal(10, 2)
gen e = rnormal(0,1)
gen y = 0
replace y = 10 + 0.9*x + e if group == 0
replace y = 9 + 0.3*x + e if group == 1
tw (scatter y x if group == 0 ) (scatter y x if group == 1 )    ///
   (lfit y x if group == 0) (lfit y x if group == 1) (lfit y x)  ,  ///
   legend( lab(1 "Group 0") lab(2 "Group 1")   ///
           lab(3 "Fitted Group 0 ") lab(4 "Fitted Group 1")  ///
		   lab(5 "Fitted all") )
	   
drop if x > 11 & group == 0
drop if x < 10 & group ==  1
tw (scatter y x if group == 0 ) (scatter y x if group == 1 )    ///
   (lfit y x if group == 0) (lfit y x if group == 1) (lfit y x)  ,  ///
   legend( lab(1 "Group 0") lab(2 "Group 1")   ///
           lab(3 "Fitted Group 0 ") lab(4 "Fitted Group 1")  ///
		   lab(5 "Fitted all") )
reg y x
reg y x if group == 0
reg y x if group == 1
reg y i.group##c.x