Ineqdec0 bygroup() - individual subgroup's contribution to overall GE measure

[Janene Brown]

Hello,

I am trying to use the ineqdec0 var, bygroup() command to calculate unique population subgroups' contribution to a global GE(1) statistic.

The values that I am interested in calculating I would like to be able to sum to equal the global population level statistic:

GE(1) global = GE(1) pop A + GE(1) pop B + GE(1) pop C + ... etc.

While working with a sample dataset I see that the ineqdec0 command does not calculate these results, but instead treats each subgroup as if it were a unique population and returns that decomposed value for each subgroup.

How can I calculate each population subgroup's contribution to a global inequality measure using ineqdec0 that will sum to the global value?

Thank you for your advice.

[William Lisowski]

I am a little confused by your statement of your problem. You say you seek a decomposition of the GE(1) index, but you also say you used the ineqdec0 command, presumably because your variable has some zero values.

But the output of help ineqdec0 tells us

The indices estimated by ineqdec0 are the percentile ratios p90/p10 and p75/p25, GE(2) = half the squared coefficient of variation, the Gini coefficient, and Sen's welfare index.

which contradicts my understanding that you are decomposing a GE(1) index.

So your question really isn't clear without more detail, or at a minimum it is too difficult to guess at a good answer from what you have shared. Please help us help you. Show your code. Show us what Stata output. Tell us what precisely is wrong. The Statalist FAQ provides advice on effectively posing your questions, posting data, and sharing Stata output.

In particular, please copy from Stata's Results window the command(s) you ran and the output Stata provided, and paste it into a post, surrounding it with code delimiters [CODE] and [/CODE] to ensure that the results are readable.

[Janene Brown]

Thank you for your reply.

Ineqdec0 and Ineqdeco will decompose the GE(1) or Theil entropy index of inequality as well as the other measures you reference. I am interested in decomposing Theil's entropy index, GE(1).

One of the main advantages of using this index versus the Gini coefficient for example, is that GE(1) is additively decomposable, meaning that a global GE(1) index can be decomposed by population subgroups into additive components that will sum to the global index, and this is precisely the data that I am interested in obtaining.

Here is my code:

 ineqdec0 income, bygroup(education)

Here is the output that inspired this question:

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
    
0.49405     0.34765     0.37684     0.71645    0.44371

To recap, I'm interested in GE(1) which has a value of 0.37684 and the output that ineqdec0 shows for the decomposition piece is:

Subgroup indices: GE_k(a)    and Gini_k

                
education
1              GE(-1)    GE(0)    GE(1)    GE(2)    Gini
                
0     0.48258    0.35054    0.37818    0.70023    0.44684
1     0.38096    0.28083    0.27461    0.35347    0.40273
2     0.40880    0.30181    0.32797    0.54804    0.41696
3     0.29329    0.21769    0.20621    0.23892    0.35395
4     0.38664    0.28349    0.30148    0.47299    0.40436
5     0.34201    0.36465    0.61710    2.05701    0.45096
6     0.28082    0.22916    0.23015    0.28140    0.37202
7     0.32906    0.28343    0.27844    0.31081    0.40519
8     0.34437    0.24781    0.25503    0.37241    0.36706
.

My understanding of a property of GE(1) is that there is additive decomposability, or that each population subgroup has an additive contribution to inequality.
It is clear that the values in the GE(1) column do not sum to the global measure GE(1) = 0.37684, and I am asking how I can obtain the values that will sum to the global total using ineqdec0. Reading through the documentation, ineqdec0 is treating each population subgroup as a distinct population leading to the output shown here.

I hope this clarifies what precisely I am asking about!

[William Lisowski]

GE(1) is additively decomposable, meaning that a global GE(1) index can be decomposed by population subgroups into additive components that will sum to the global index

That is not my understanding of an additively decomposable inequality index as the term is commonly used.

Because you presented only the output you considered relevant, rather than the full output from the command, we'll discuss the example below. Because your output included GE(1) which, as I noted in post #2 above, is not output from (at least the most recent versions of) ineqdec0, my example uses ineqdeco.

. sysuse nlsw88, clear
(NLSW, 1988 extract)

. ineqdeco wage, by(race)
 
Percentile ratios

----------------------------------------------------------
  All obs |    p90/p10     p90/p50     p10/p50     p75/p25
----------+-----------------------------------------------
          |      3.967       2.037       0.513       2.253
----------------------------------------------------------
  
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
----------+-----------------------------------------------------------
          |    0.19892     0.18123     0.19978     0.27444     0.33253
----------------------------------------------------------------------
   
Atkinson indices, A(e), where e > 0 is the inequality aversion parameter

----------------------------------------------
  All obs |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
          |    0.09062     0.16576     0.28461
----------------------------------------------
  
Subgroup summary statistics, for each subgroup k = 1,...,K:
  

-------------------------------------------------------------------------------------
     race |   Popn. share           Mean  Relative mean   Income share      log(mean)
----------+--------------------------------------------------------------------------
    white |       0.72885        8.08300        1.04069        0.75851        2.08976
    black |       0.25957        6.84456        0.88124        0.22875        1.92345
    other |       0.01158        8.55078        1.10092        0.01274        2.14602
-------------------------------------------------------------------------------------
  
Subgroup indices: GE_k(a) and Gini_k 

----------------------------------------------------------------------
     race |     GE(-1)       GE(0)       GE(1)       GE(2)        Gini
----------+-----------------------------------------------------------
    white |    0.19545     0.17909     0.19811     0.27123     0.33070
    black |    0.19335     0.17738     0.19622     0.27454     0.32957
    other |    0.22626     0.17528     0.16270     0.17845     0.31159
----------------------------------------------------------------------
  
Within-group inequality, GE_W(a)

----------------------------------------------------------
  All obs |     GE(-1)       GE(0)       GE(1)       GE(2)
----------+-----------------------------------------------
          |    0.19621     0.17860     0.19722     0.27195
----------------------------------------------------------
              
Between-group inequality, GE_B(a):

----------------------------------------------------------
  All obs |     GE(-1)       GE(0)       GE(1)       GE(2)
----------+-----------------------------------------------
          |    0.00271     0.00263     0.00256     0.00249
----------------------------------------------------------
              
Subgroup Atkinson indices, A_k(e)

----------------------------------------------
     race |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
    white |    0.08977     0.16397     0.28104
    black |    0.08885     0.16254     0.27886
    other |    0.08093     0.16078     0.31154
----------------------------------------------
  
Within-group inequality, A_W(e)

----------------------------------------------
  All obs |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
          |    0.08945     0.16360     0.28093
----------------------------------------------
 
Between-group inequality, A_B(e)

----------------------------------------------
  All obs |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
          |    0.00129     0.00258     0.00512
----------------------------------------------

.

I have highlighted in red the additive decomposition of the value of GE(1) - 0.19978 - into the contribution from "within-group inequality" - 0.19722 - and "between-group inequality" - 0.00256 - suggesting that the bulk of the observed inequality is due to the inequality of income separately within each of the three groups - the numbers highlighted in brown..

[Ahmed Zohirul ISLAM]

Dear William Lisowski,

I am analyzing the level of inequality and change in inequality between two periods.
I got a guideline in carrying out my analysis from your above suggestion. I used the same ineqdeco command to analyze the level of inequality. The command is perfectly working to decompose within-group and between-group inequality.

Now the question is - Can I use the ineqdeco to decompose the change in inequality between two periods? What would be the command in this case?

Thank you so much in advance.

[Stephen Jenkins]

#5: -search msdeco- (but I should say I have never used it. Alternatively, you can run -ineqdeco- (or -ineqdec0-) twice and used the saved results from each to calculate the expressions of interest. (See e.g. Jenkins, Accounting for inequality trends, Economica, 1995). So, run the command for the first year. Relevant information is saved in r(); put this stuff into differently-named local macros. Then repeat the exercise for the second year; and then calculate the relevant statistics from the locals created at each step. I suspect that this is what -msdeco- does. (You could bootstrap the whole procedure to get SEs.)

[Ahmed Zohirul ISLAM]

Thank you so much Professor Stephen for your guidelines.