st: Calculating p20/p80 indicator with weights

[<S.Jenkins@lse.ac.uk>]

------------------------------

Date: Mon, 18 Jun 2012 15:35:10 +0200
From: Anke Weber <anke.weber@jrc.ec.europa.eu>
Subject: st: Calculating p20/p80 indicator with weights

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Dear all,

I am using Stata 11, and trying to take into account pweights when 
constructing the p20/p80 inequality measure, i.e. the ratio of the 
average income of the richest 20 percent of the population divided by 
the average income of the bottom 20 percent (using data from the SOEP, 
USS, and EUSILC databases). Would anyone have a suggestion on how to 
account for the sampling weight (of the person) in the data? So far, I 
explored the ineqdeco command, which let's you use aweights but 
unfortunately there is only an p75/p25 or p90/p10 measure. Then, I tried

to use the svy command to calculate separately the 20-percentile and the

80 percentile, using my equivalised income variable (equivincome) but 
this did not work either:

svyset pidp [pweight=a_psnenus_xw]

       pweight: a_psnenus_xw
           VCE: linearized
   Single unit: missing
      Strata 1: <one>
          SU 1: pidp
         FPC 1: <zero>

svy: egen p20= pctile(equivincome), p(20)

egen is not supported by svy with vce(linearized); see help svy 
estimation for a list of
Stata estimation commands that are supported by svy

I would be very happy if some one has an idea of how to calculate the 
p20/p80 indicator with weights!

Many thanks in advance,
Anke
++++++++++++++++++++++++++++++++++++++

There are many solutions. Perhaps the easiest is to use -sumdist- (from
SSC). See also -svylorenz- (SSC). Example below.

. sysuse auto
(1978 Automobile Data)

. sumdist price [w=weight], n(5)
(analytic weights assumed)
 
Distributional summary statistics, 5 quantile groups

------------------------------------------------------------------------
---
Quantile  |
group     |    Quantile  % of median     Share, %      L(p), %
GL(p)
----------+-------------------------------------------------------------
---
        1 |    4181.000       80.574       12.162       12.162
798.896
        2 |    4749.000       91.521       13.632       25.794
1694.304
        3 |    5798.000      111.736       16.461       42.255
2775.571
        4 |    9690.000      186.741       21.242       63.497
4170.884
        5 |                                36.503      100.000
6568.637
------------------------------------------------------------------------
---
Share = quantile group share of total price; 
L(p)=cumulative group share; GL(p)=L(p)*mean(price)

. ret list

scalars:
                r(gl5) =  6568.636904761905
              r(cush5) =  1
                r(sh5) =  .3650305213361488
              r(qrel4) =  1.867411832723068
                 r(q4) =  9690
                r(gl4) =  4170.883950948801
              r(cush4) =  .6349694786638513
                r(sh4) =  .2124204338931906
              r(qrel3) =  1.117363653883215
                 r(q3) =  5798
                r(gl3) =  2775.571249552452
              r(cush3) =  .4225490447706607
                r(sh3) =  .164610561137709
              r(qrel2) =  .9152052418577761
                 r(q2) =  4749
                r(gl2) =  1694.304242749731
              r(cush2) =  .2579384836329517
                r(sh2) =  .1363156666281005
              r(qrel1) =  .8057429177105415
                 r(q1) =  4181
                r(gl1) =  798.8961242391694
              r(cush1) =  .1216228170048512
                r(sh1) =  .1216228170048512
               r(ngps) =  5
                r(p95) =  13594
                r(p90) =  11995
                r(p75) =  7827
                r(p50) =  5189
                r(p25) =  4424
                r(p10) =  3955
                 r(p5) =  3798
             r(median) =  5189
                  r(N) =  74
              r(sum_w) =  223440
               r(mean) =  6568.636904761905

matrices:
       r(relquantiles) :  1 x 4
             r(shares) :  1 x 5
          r(quantiles) :  1 x 4

. di "Ratio of income share of richest 20% to poorest 20% = "
r(sh5)/r(sh1)
Ratio of income share of richest 20% to poorest 20% = 3.0013326

++++++++++++++++++++++++++++++++++++++

NB Anke: please ensure that your email software sends plain text (ASCII)
messages to Statalist.

Stephen
------------------
Professor Stephen P. Jenkins <s.jenkins@lse.ac.uk>
Department of Social Policy and STICERD
London School of Economics and Political Science
Houghton Street, London WC2A 2AE, UK
Tel: +44(0)20 7955 6527
Changing Fortunes: Income Mobility and Poverty Dynamics in Britain, OUP
2011, http://ukcatalogue.oup.com/product/9780199226436.do
Survival Analysis Using Stata:
http://www.iser.essex.ac.uk/survival-analysis
Downloadable papers and software: http://ideas.repec.org/e/pje7.html


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