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help for concindc  Zhuo (Adam) Chen; Centers for Disease Control and Prevention
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Estimating concentration index with grouped and microdata: categorical/actual w
> elfare measure.

concindexi [varlist] [if] [in] [weight] , welfarevar(varname) [
Sigmavar(varname)]

where:

welfarevar is the welfare variable to be used (can be categorical or
continuous but must be ordered. Midpoints are permissible), required.

Sigmavar is the provided standard error of group means. The default is to
estimate the group means with microdata (the correct way to do when
microdata is used) and assume they are zero with grouped data if they are
not provided.

Description

concindc computes the concentration index (CI) for micro data with a
categorical welfare variable or grouped data. See Kakwani, Wagstaff and
van Doorslaer (1997).  Note that although it was originally designed
for microdata with a categorical welfare variable, it can handle
grouped data and microdata with actual (not categorical) welfare
variable. They could be treated as a special case of microdata with
categorical welfare measure:  there is only one observation for each
category. For grouped data, since the program can handle frequency
weight, the group sizes can essentially be treated as frequency
weights. The program also can use standard error of group means of the
health outcome if supplied.  If not, it will be estimated as the
standard deviation of health outcomes.

Formulas

The concentration index is computed as:

C = 2*Sum[f_t*miu_t*R_t]/miu -1

f_t is the population share of the welfare group t the individual belongs
to

miu is the overall mean

R_t his fractional rank in the socioeconomic distribution

miu_t is the group mean

Standard errors of C are obtained by a "covariance" or "formula" method:

Var(C) =  (sum[f_t*(a_t)^2] -(1+C)^2)/n
+ sum(f_t*(sigma_t)^2(2*R_t-1-C))^2/(n*miu^2)

where:

a =  ( 2*R_t- 1 - C)*miu_t/miu + 2 - q_(t-1) - q_t

and:  q_t = sum-(i from 1 to t)-(miu_i*f_i)

is the ordinate of the concentration curve L(p), and q_0 = 0.

and:  sigma_t is the provided or estimated standard error of group means.

Examples
. use "http://chenzhuo.org/Documents/concindc.dta" ( click to run)

. concindc health3w, welf(inc3w)
( click to run)

. concindc health3w , welf(inc3w) sig(stdh3w)
( click to run)

. concindc health3w [aw=wt3w], welf(inc3w) sig(stdh3w)
( click to run)

. concindc health3w [aw=wt3w], welf(inc3w)
( click to run)

The last two commands reproduce the results in the World Bank spread
sheet concentration_index.xls

Saved Results

Concentration index: r(concindex);

Standard error of concentration index: r(stdci);

Author

Zhuo (Adam) Chen, Economist and Preventive Effectiveness Fellow, Centers
for Disease Control and Prevention; Visiting Scholar, The Chicago Center
of Excellence in Health Promotion Economics, The University of Chicago.

Email: zchen1@cdc.gov, chenzhuo@gmail.com

Also see

Online:  help for concindexi, concindexg, ineqdeco, inequal, povdeco,
ineqerr if installed.

Disclaimer
This software was written by Zhuo (Adam) Chen in his private capacity. No
official support or endorsement by the Department of Health and Human
Services, Centers for Disease Control and Prevention is intended, nor
should it be inferred.

I am grateful to Kakoli Roy, PhD, Centers for Disease Control and
Prevention, for comments and help but I take the full responsibility for
any remaining errors.

References

Kakwani, N., Wagstaff A., & van Doorslaer E. 1997.  Socioeconomic
inequalities in health: Measurement, computation, and statisical
inference. Journal of Econometrics 77: 87-103.

Wagstaff et al. Quantitative Techniques for Health Equity Analysis,
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