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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,