Inequality index

[fereshte yousefzade]

Hello
How can I calculate the income deciles using STATA?
For example, Palma's ratio

[Stephen Jenkins]

There are 9 deciles that divide an ordered income distribution into 10 decile groups. The Palma ratio measure of inequality is equal to the share of total income held by richest 10% divided by the share of total income held by the poorest 40%. (Please follow FAQ advice and provide relevant literature references or explain more fuller what is required. This is a multidisciplinary list.)

You could use sumdist available from SSC. (I think you may have been told about this before.)

Observe the following:

sysuse auto, clear
sumdist mpg, ngp(10)
return list
di "Palma ratio = "  r(sh10) / (r(sh1) + r(sh2) + r(sh3) + r(sh4))
di "Palma ratio = "  r(sh10) / r(cush4)

which yields

. sysuse auto, clear
(1978 Automobile Data)

. sumdist mpg, ngp(10)
 
Distributional summary statistics, 10 quantile groups

---------------------------------------------------------------------------
Quantile  |
group     |    Quantile  % of median     Share, %      L(p), %        GL(p)
----------+----------------------------------------------------------------
        1 |      14.000       70.000        6.853        6.853        1.459
        2 |      17.000       85.000       10.279       17.132        3.649
        3 |      18.000       90.000       10.279       27.411        5.838
        4 |      19.000       95.000        9.645       37.056        7.892
        5 |      20.000      100.000        3.807       40.863        8.703
        6 |      22.000      110.000       13.642       54.505       11.608
        7 |      24.000      120.000       10.470       64.975       13.838
        8 |      25.000      125.000        7.931       72.906       15.527
        9 |      29.000      145.000       12.119       85.025       18.108
       10 |                                14.975      100.000       21.297
---------------------------------------------------------------------------
Share = quantile group share of total mpg; 
L(p)=cumulative group share; GL(p)=L(p)*mean(mpg)

. return list

scalars:
               r(gl10) =  21.29729729729729
             r(cush10) =  .9999999999999998
               r(sh10) =  .149746192893401
              r(qrel9) =  1.45
                 r(q9) =  29
                r(gl9) =  18.10810810810811
              r(cush9) =  .8502538071065988
                r(sh9) =  .1211928934010152
              r(qrel8) =  1.25
                 r(q8) =  25
                r(gl8) =  15.52702702702702
              r(cush8) =  .7290609137055836
                r(sh8) =  .0793147208121827
              r(qrel7) =  1.2
                 r(q7) =  24
                r(gl7) =  13.83783783783784
              r(cush7) =  .6497461928934009
                r(sh7) =  .1046954314720812
              r(qrel6) =  1.1
                 r(q6) =  22
                r(gl6) =  11.60810810810811
              r(cush6) =  .5450507614213197
                r(sh6) =  .1364213197969543
              r(qrel5) =  1
                 r(q5) =  20
                r(gl5) =  8.7027027027027
              r(cush5) =  .4086294416243654
                r(sh5) =  .0380710659898477
              r(qrel4) =  .95
                 r(q4) =  19
                r(gl4) =  7.891891891891891
              r(cush4) =  .3705583756345177
                r(sh4) =  .0964467005076142
              r(qrel3) =  .9
                 r(q3) =  18
                r(gl3) =  5.837837837837837
              r(cush3) =  .2741116751269035
                r(sh3) =  .1027918781725888
              r(qrel2) =  .85
                 r(q2) =  17
                r(gl2) =  3.648648648648649
              r(cush2) =  .1713197969543147
                r(sh2) =  .1027918781725888
              r(qrel1) =  .7
                 r(q1) =  14
                r(gl1) =  1.45945945945946
              r(cush1) =  .0685279187817259
                r(sh1) =  .0685279187817259
               r(ngps) =  10
                r(p95) =  34
                r(p90) =  29
                r(p75) =  25
                r(p50) =  20
                r(p25) =  18
                r(p10) =  14
                 r(p5) =  14
             r(median) =  20
                  r(N) =  74
              r(sum_w) =  74
               r(mean) =  21.2972972972973

matrices:
       r(relquantiles) :  1 x 9
             r(shares) :  1 x 10
          r(quantiles) :  1 x 9

. di "Palma ratio = "  r(sh10) / (r(sh1) + r(sh2) + r(sh3) + r(sh4))
Palma ratio = .40410959

. di "Palma ratio = "  r(sh10) / r(cush4)
Palma ratio = .40410959