use file.dta, clear            //Select data for PERIOD==0

gen y=dep_var                  //(GP/SPECIALIST/HOSPITAL/EMERGEN)
gen x=score_income

global X "YOUNG OLDER SRHCAT MCS2 CRONICA2 CRONICA3 CRONICA4 ACCIDENT"
global Z "x  _INIVELEST_2 _INIVELEST_3 _INIVELEST_456 _INIVELEST_78 INSURANCE _ITAMAMUN_2 _ITAMAMUN_3 _ITAMAMUN_4 _ILABSTATUS_2 _ILABSTATUS_3 _ILABSTATUS_456 PROV2 PROV3 PROV4 PROV5 PROV6 PROV7 PROV8" 


quietly regress y $X $Z	 
drop if e(sample)~=1			


* CONCENTRATION INDEX PERIOD==0

egen m_y0 = mean(y)		

sort x, stable
gen rj=(_n-1)/_N
gen r=rj+0.5/_N				
quietly sum r 
sca var_r = r(Var)			

egen rank = rank(x), unique		
tsset rank
newey y r, lag(1)
nlcom 2*var_r*(_b[r]/(_b[_cons]+0.5*_b[r]))/(1-m_y0)		
mat coef=r(b)
mat var=r(V)
sca CI0=coef[1,1]			
sca se0=sqrt(var[1,1])
sca t0=CI0/se0
display "CI Periodo 0", CI0, "Std Err", se0 


* DECOMPOSITION OF INEQUALITY IN UTILISATION 	***********
* CONTRIBUTIONS OF NEED FACTORS PERIOD=0

qui dprobit y $X $Z 
mat dfdx=e(dfdx)

sca need0=0
foreach x of global X {
	qui {
 	    mat b0_`x' = dfdx[1,`=colnumb(dfdx,"`x'")']      	/* partial effect of x */
		sca b0_`x' = b0_`x'[1,1]		    		/* beta coeff. of x  */
		corr r `x', c
		sca cov0_`x' = r(cov_12)				/* covariance b/w x and expenditure rank */
		sum `x' 
		sca m0_`x' = r(mean)				/* mean of x */
		sca elas0_`x' = (b0_`x'*m0_`x')/m_y0		/* elasticity of y with respect to x */
		sca CI0_`x' = 2*cov0_`x'/m0_`x'			/* concentration index for x in relation to expenditure */  
		sca con0_`x' = elas0_`x'*CI0_`x'			/* contribution of x to CI for y in relation to household expenditure */
		sca prcnt0_`x' = con0_`x'/CI0			/* percentage of CI for y accounted for by x */
		sca need0=need0+con0_`x'				/* contribution of all need factors */
	}
	di "`x' elast:", elas0_`x', "`x' c_i:", CI0_`x', "`x' cont:", con0_`x', "`x' percont:", prcnt0_`x'
}


* CONTRIBUTIONS OF NON-NEED FACTORS PERIOD=0

sca nonneed0=0
foreach x of global Z {
	qui {
 		mat b0N_`x' = dfdx[1,`=colnumb(dfdx,"`x'")']	
        sca b0N_`x' = b0N_`x'[1,1]				/* beta coeff. of x  */ 		
		corr r `x', c
		sca cov0N_`x' = r(cov_12)				/* covariance b/w x and expenditure rank */
		sum `x' 
		sca m0N_`x' = r(mean)				/* mean of x */
		sca elas0N_`x' = (b0N_`x'*m0N_`x')/m_y0		/* elasticity of y with respect to x */
		sca CI0N_`x' = 2*cov0N_`x'/m0N_`x'			/* concentration index for x in relation to expenditure */  
		sca con0N_`x' = elas0N_`x'*CI0N_`x'			/* contribution of x to CI for y in relation to household expenditure */
		sca prcnt0N_`x' = con0N_`x'/CI0			/* percentage of CI for y accounted for by x */
		sca nonneed0=nonneed0+con0N_`x'
	}
	di "`x' elast:", elas0N_`x', "`x' ci:", CI0N_`x', "`x' cont:", con0N_`x', "`x' percont:", prcnt0N_`x'
}

di "Inequality due to need factors P0:", need0 
di "Inequality due to non-need factors P0:", nonneed0
sca HI0 = CI0 - need0
di "Horizontal Inequity Index P0:", HI0
di "CI",  CI0 


* CONCENTRATION INDEX PERIOD==1

use file.dta, clear            //Select data for PERIOD==1

gen y=dep_var                  //(GP/SPECIALIST/HOSPITAL/EMERGEN)
gen x=score_income

quietly regress y $X $Z	
drop if e(sample)~=1

egen m_y1 = mean(y)	

sort x, stable 
gen rj1=(_n-1)/_N
gen r1=rj1+0.5/_N				
quietly sum r1 
sca var_r1 = r(Var)			

egen rank1 = rank(x), unique		
tsset rank1
newey y r1, lag(1)
nlcom 2*var_r1*(_b[r1]/(_b[_cons]+0.5*_b[r1]))/(1-m_y1)			
mat coef=r(b)
mat var=r(V)
sca CI1=coef[1,1]			
sca se1=sqrt(var[1,1])
sca t1=CI1/se1

display "CI Periodo 1", CI1, "Std Err", se1 



* DECOMPOSITION PERIOD 1	
* CONTRIBUTIONS OF NEED FACTORS PERIOD=1

quietly dprobit y $X $Z	
mat dfdx=e(dfdx)

sca need1=0
foreach x of global X {
	qui {
		mat b1_`x' = dfdx[1,`=colnumb(dfdx,"`x'")']	
		sca b1_`x' = b1_`x'[1,1]				/* beta coeff. of x  */
		corr r1 `x', c
		sca cov1_`x' = r(cov_12)				/* covariance b/w x and expenditure rank */
		sum `x' 
		sca m1_`x' = r(mean)				/* mean of x */
		sca elas1_`x' = (b1_`x'*m1_`x')/m_y1		/* elasticity of y with respect to x */
		sca CI1_`x' = 2*cov1_`x'/m1_`x'			/* concentration index for x in relation to expenditure */  
		sca con1_`x' = elas1_`x'*CI1_`x'			/* contribution of x to CI for y in relation to household expenditure */
		sca prcnt1_`x' = con1_`x'/CI1			/* percentage of CI for y accounted for by x */
		sca need1=need1+con1_`x'				/* contribution of all need factors */
	}
	di "`x' elast:", elas1_`x', "`x' cind:", CI1_`x', "`x' con:", con1_`x', "`x' percon:", prcnt1_`x'
}






* CONTRIBUTIONS OF NON-NEED FACTORS PERIOD=1

sca nonneed1=0
foreach x of global Z {
	qui {
 		mat b1N_`x' = dfdx[1,`=colnumb(dfdx,"`x'")']	
        sca b1N_`x' = b1N_`x'[1,1]				/* beta coeff. of x  */ 		
		corr r1 `x', c
		sca cov1N_`x' = r(cov_12)				/* covariance b/w x and expenditure rank */
		sum `x' 
		sca m1N_`x' = r(mean)				/* mean of x */
		sca elas1N_`x' = (b1N_`x'*m1N_`x')/m_y1		/* elasticity of y with respect to x */
		sca CI1N_`x' = 2*cov1N_`x'/m1N_`x'			/* concentration index for x in relation to expenditure */  
		sca con1N_`x' = elas1N_`x'*CI1N_`x'			/* contribution of x to CI for y in relation to household expenditure */
		sca prcnt1N_`x' = con1N_`x'/CI1			/* percentage of CI for y accounted for by x */
		sca nonneed1=nonneed1+con1N_`x'
	}
	di "`x' elast:", elas1N_`x', "`x' cind:", CI1N_`x', "`x' cont:", con1N_`x', "`x' percon:", prcnt1N_`x'
}

di "Inequality due to need factors P1:", need1 
di "Inequality due to non-need factors P1:", nonneed1
sca HI1 = CI1 - need1
di "Horizontal Inequity Index P1:", HI1
di "CI1",  CI1 



***DECOMPOSITION OF CHANGE - NEED
 
foreach x of global X {
	qui {
		sca ChCoefN_`x'=elas1_`x'*(CI1_`x'-CI0_`x')
		sca ChElasN_`x'=CI0_`x'*(elas1_`x'-elas0_`x')
		sca ChangeN_`x'=ChCoefN_`x'+ChElasN_`x'
		}
	di "`x' ccoef:", ChCoefN_`x', "`x' celast:", ChElasN_`x'
}


***DECOMPOSITION OF CHANGE - NONNEED


foreach x of global Z {
	qui {
		sca ChCoefNoN_`x'=elas1N_`x'*(CI1N_`x'-CI0N_`x')
		sca ChElasNoN_`x'=CI0N_`x'*(elas1N_`x'-elas0N_`x')
		sca ChangeNoN_`x'=ChCoefNoN_`x'+ChElasNoN_`x'
		}
	di "`x' ccoef:", ChCoefNoN_`x',"`x' celastic:", ChElasNoN_`x'
	
	
}