Calculating elasticities, concentration index and contribution of residuals in a decomposition analysis

[jacob kazungu]

Hello members,

I am doing a decomposition of the concentration index in stata to determine the % contribution of my predictor variables to the existing inequalities in health insurance coverage. I have been able to calculate elasticities, concentration indices and contribution of all of my predictor variables but I can't do the same for the residuals.

I undestand that the sum of the % contributions (for the predictor variables+ the residuals) should be 100%, and the concentration index of the residuals=overall concentration index - sum of concentration indices of the predictor variables.

Using the above formula (if it is true) I can get the above estimates. But is there a command in stata that one can run to get all the three estimates without using the addition and subtraction as above?

Below is my code for the whole decomposition.

conindex insured [aw=weight], rank(v191) bounded limits(0 1) wagstaff
sca CI = r(CI)

global X ragecat employment gender hheadsex residence maritalstatus ///
media hholdsize education ses

qui glm insured $X [aw=weight], family(binomial) link(logit)

qui margins , dydx(*) post
mat coeff = e(b)
sum insured [aw=weight]
sca m_y=r(mean)

foreach x of varlist $X {
qui{
mat b_`x' = coeff[1,"`x'"]
sca b_`x' = b_`x'[1,1]

qui sum `x'
gen double scaled_`x' = `x'/r(max)
conindex scaled_`x' [aw=weight], rank(v191) bounded limits(0 1) wagstaff

sca CI_`x' = r(CI)
sum `x' [aw=weight]

sca elas_`x' = (b_`x' * r(mean))/m_y

sca con_`x' = elas_`x' * CI_`x'
sca prcnt_`x' = con_`x'/CI
}

di "`x' elasticity:", elas_`x'
di "`x' concentration index:", CI_`x'
di "`x' contribution:", con_`x'
di "`x' percentage contribution:", prcnt_`x'

}

[Sumon Khan]

Hi Jacob, I am also trying to do decomposition analysis but have failed several time. Hope you will able to complete your analysis. Can you please help me to soleve the following:
In decomposition analysis, how can I get
 Coefficient
 Mean
 Elasticity
 Absolute contribution
 Percentage contribution to Concentration index

I lookforward to your reply.

[barun singh]

Hello members,

I am doing a decomposition of the concentration index in stata to determine the % contribution of my predictor variables to the existing inequalities in health insurance coverage. I have been able to calculate elasticities, concentration indices and contribution of all of my predictor variables but I can't do the same for the residuals.

I undestand that the sum of the % contributions (for the predictor variables+ the residuals) should be 100%, and the concentration index of the residuals=overall concentration index - sum of concentration indices of the predictor variables.

Using the above formula (if it is true) I can get the above estimates. But is there a command in stata that one can run to get all the three estimates without using the addition and subtraction as above?

Below is my code for the whole decomposition.

conindex insured [aw=weight], rank(v191) bounded limits(0 1) wagstaff
sca CI = r(CI)

global X ragecat employment gender hheadsex residence maritalstatus ///
media hholdsize education ses

qui glm insured $X [aw=weight], family(binomial) link(logit)

qui margins , dydx(*) post
mat coeff = e(b)
sum insured [aw=weight]
sca m_y=r(mean)

foreach x of varlist $X {
qui{
mat b_`x' = coeff[1,"`x'"]
sca b_`x' = b_`x'[1,1]

qui sum `x'
gen double scaled_`x' = `x'/r(max)
conindex scaled_`x' [aw=weight], rank(v191) bounded limits(0 1) wagstaff

sca CI_`x' = r(CI)
sum `x' [aw=weight]

sca elas_`x' = (b_`x' * r(mean))/m_y

sca con_`x' = elas_`x' * CI_`x'
sca prcnt_`x' = con_`x'/CI
}

di "`x' elasticity:", elas_`x'
di "`x' concentration index:", CI_`x'
di "`x' contribution:", con_`x'
di "`x' percentage contribution:", prcnt_`x'

}

did you find the solution to calculate residual ?