> Date: Sat, 19 May 2007 21:49:57 +0900 (JST)
> From: <[email protected]>
> Subject: st: 95% cofidence intervals of the Gini coefficient
>
> Dear Friends
>
> I am a user of STATA9.
>
> I calculate the Gini coefficient using -ineqdeco- and -inequdec0-.I understood the
> difference between -ineqdeco- and inequdec0-.
> My question is how to compute 95% confidence interval from the data set including
> values zero in weighted data. I have already used -ineqerr-.
> Point estimate of the Gini coefficient obtained from -inequdec- did not range from
> lower limit to upper limit calculated -ineqerr-!!!!
> How can I manage it?
>
> Thank you in advance
>
> Koichi
You must show us _exactly_ what you typed, and the output, for us to assess what
might be happening. Moreover, it is better to reproduce the apparent problem using
a data set all have access to (e.g. those available via -sysuse-). See an example
below which shows that the same point estimate is derived in comparable cases.
-ineqdeco- produces point estimates of the Gini, where the variable of interest is
assumed to have positive values (zero and negative values are not used), and you
can derive bootstrapped SEs. -ineqdec0- will also estimate the Gini, but allowing
variables with values of zero. The latest versions of these programs are available
from SSC, and illustrations of their use is shown in the help files.
See also -svylorenz- (on SSC) which allows zero values, and derives SEs by
linerarization methods
I have not used -ineqerr- (having preferred my own programs!). I note that it is a
version 5 program, and the others cited are version 8.2 or higher. It has 2 options
for handling weights, and this affects how SEs are computed. It does not use obs
with zero values.
Note also that derivation of bootstrapped SEs _using weighted data_ is a topic area
that has not received a lot of attention, and there is no consensus yet about how
to proceed.
. sysuse auto, clear
(1978 Automobile Data)
. replace price = 0 in 1/2
(2 real changes made)
. version 8: svyset [pw=mpg], psu(foreign)
pweight is mpg
psu is foreign
. svylorenz price
Warning: price has 2 values = 0. Used in calculations
Quantile group shares, cumulative shares (Lorenz ordinates),
generalized Lorenz ordinates, and Gini
Number of strata = 1 Number of obs = 74
Number of PSUs = 2 Population size = 1576.00
Design df = 1
---------------------------------------------------------------------------
Group | Linearized
share | Estimate Std. Err. z P>|z| [95% Conf. Interval]
---------+-----------------------------------------------------------------
1 | 0.055638 0.109694 0.507 0.612 -.159358 .270634
2 | 0.065121 0.021002 3.101 0.002 .0239579 .106284
3 | 0.076012 0.021170 3.591 0.000 .0345194 .117505
4 | 0.079359 0.022093 3.592 0.000 .0360576 .12266
5 | 0.075684 0.022154 3.416 0.001 .0322643 .119104
6 | 0.089191 0.020442 4.363 0.000 .049125 .129257
7 | 0.105285 0.020731 5.079 0.000 .0646534 .145917
8 | 0.105512 0.026994 3.909 0.000 .0526037 .15842
9 | 0.135774 0.035472 3.828 0.000 .06625 .205299
10 | 0.212423 0.080365 2.643 0.008 .0549114 .369935
---------+-----------------------------------------------------------------
Cumul. |
share |
1 | 0.055638 0.109694 0.507 0.612 -.159358 .270634
2 | 0.120759 0.088692 1.362 0.173 -.0530736 .294591
3 | 0.196771 0.067521 2.914 0.004 .0644317 .329111
4 | 0.276130 0.045429 6.078 0.000 .187092 .365169
5 | 0.351815 0.023275 15.115 0.000 .306196 .397433
6 | 0.441005 0.002833 155.669 0.000 .435453 .446558
7 | 0.546291 0.017898 30.523 0.000 .511211 .58137
8 | 0.651803 0.044892 14.519 0.000 .563815 .73979
9 | 0.787577 0.080365 9.800 0.000 .630065 .945089
10 | 1.000000
---------+-----------------------------------------------------------------
Gen. |
Lorenz |
1 | 316.381 91.057 3.475 0.001 137.913 494.849
2 | 686.687 85.824 8.001 0.000 518.475 854.899
3 | 1118.925 98.733 11.333 0.000 925.412 1312.438
4 | 1570.193 112.263 13.987 0.000 1350.161 1790.225
5 | 2000.567 119.006 16.811 0.000 1767.319 2233.814
6 | 2507.744 159.164 15.756 0.000 2195.787 2819.700
7 | 3106.440 225.903 13.751 0.000 2663.679 3549.202
8 | 3706.426 257.422 14.398 0.000 3201.888 4210.964
9 | 4478.496 293.800 15.243 0.000 3902.660 5054.333
10 | 5686.424 191.304 29.725 0.000 5311.475 6061.374
---------+-----------------------------------------------------------------
Gini | 0.2360649 .02180983 10.824 0.000 .1933185 .2788114
---------------------------------------------------------------------------
. ineqdeco price [aw=mpg]
Warning: price has 2 values = 0. Not used in calculations
Percentile ratios
----------------------------------------------------------
All obs | p90/p10 p90/p50 p10/p50 p75/p25
----------+-----------------------------------------------
| 2.563 2.057 0.803 1.490
----------------------------------------------------------
Generalized Entropy indices GE(a), where a = income difference
sensitivity parameter, and Gini coefficient
----------------------------------------------------------------------
All obs | GE(-1) GE(0) GE(1) GE(2) Gini
----------+-----------------------------------------------------------
| 0.07149 0.07662 0.08702 0.10550 0.21668
----------------------------------------------------------------------
Atkinson indices, A(e), where e > 0 is the inequality aversion parameter
----------------------------------------------
All obs | A(0.5) A(1) A(2)
----------+-----------------------------------
| 0.04010 0.07376 0.12509
----------------------------------------------
. ineqdec0 price [aw=mpg]
Warning: price has 2 values = 0. Used in calculations
Percentile ratios
----------------------------------------------------------
All obs | p90/p10 p90/p50 p10/p50 p75/p25
----------+-----------------------------------------------
| 2.563 2.061 0.804 1.493
----------------------------------------------------------
Generalized Entropy index GE(2), and Gini coefficient
----------------------------------
All obs | GE(2) Gini
----------+-----------------------
| 0.12086 0.23606
----------------------------------
. ineqerr price, weight(mpg) psu(foreign)
option weight() not allowed
r(198);
. ineqerr price [aweight = mpg], psu(foreign) reps(50)
price ------------------------------------------------------------------- Price
2 values = 0. Not used in calculations.
(obs=72)
Bootstrap statistics
Variable | Reps Observed Bias Std. Err. [95% Conf. Interval]
---------+-------------------------------------------------------------------
Gini | 50 .2166808 -.0055078 .0251136 .1662132 .2671483 (N)
| .1616089 .2496886 (P)
| .1616089 .2771308 (BC)
---------+-------------------------------------------------------------------
Theil | 50 .0870174 -.0010619 .0200851 .0466549 .1273799 (N)
| .048003 .1188811 (P)
| .048003 .1188811 (BC)
---------+-------------------------------------------------------------------
Varlogs | 50 .13249 -.0026397 .0284316 .0753545 .1896255 (N)
| .0774393 .1760419 (P)
| .0774393 .2187282 (BC)
-----------------------------------------------------------------------------
N = normal, P = percentile, BC = bias-corrected
Stephen (author of -ineqdeco-, -ineqdec0-, -svylorenz-)
-----------------------------------------
Professor Stephen P. Jenkins <[email protected]>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374. Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/
Downloadable papers and software: http://ideas.repec.org/e/pje7.html
*
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