ineqdeco for multiple categories (land inequality)?

[Cat Santos]

Dear Statalist Community,

I am having trouble calculating the theil index for land inequality using ineqdeco. I want to calculate this index for each of my municipalities. However, for each municipality, I have 10 categories of land plots by size. For each category I have data on the number of plots (num_cat*), and on the area of all plots by hectare (surfac_cat*).

I wanted to calculate land inequality taking into account the surface and the number of plots in each category. Basically, my goal was to replicate this formula of the theil index: https://psychology.fandom.com/wiki/I...t_computations.

However, I don't know how to operationalize that using ineqdeco, given that I have two things to consider (surface and number) and 10 categories...

Thank you so much!!

Cat

Variable    Obs    Mean    Std. dev.    Min    Max
                    
muni_code    3,330    3598.177    2027.443    4    7159
num_cat1    3,306    105.6086    167.9347    0    3295
num_cat2    3,306    70.99274    97.24655    0    2726
num_cat3    3,306    161.9897    168.7842    0    3361
num_cat4    3,306    66.8902    65.31594    0    903
                    
num_cat5    3,306    52.99335    59.39432    0    649
num_cat6    3,303    22.65789    34.31665    0    406
num_cat7    3,275    8.865954    18.14336    0    302
num_cat8    3,245    2.153467    6.430017    0    121
num_cat9    3,261    1.586017    4.444032    0    101
                    
num_cat10    3,229    .4168473    .9689932    0    14
surfac_cat1    3,204    23.85705    35.14102    0    890
surfac_cat2    3,204    55.17603    76.61556    0    2165
surfac_cat3    3,204    304.6957    313.7701    0    6267
surfac_cat4   3,204    255.9566    251.9805    0    3485
                    
surfac_cat5    3,204    363.7185    417.5487    0    4770
surfac_cat6    3,204    312.0147    485.0082    0    5657
surfac_cat7    3,204    261.8645    566.1812    0    10880
surfac_cat8    3,204    150.0268    459.4285    0    8735
surfac_cat9    3,204    324.7272    938.089    0    23031
                    
surfac_cat10    3,204    668.2612    1724.493    0    19849

[Nick Cox]

I don't know exactly what is a Theil index here. My recollection is that it is related to entropy in the Shannon sense.

Thanks for the link, but it didn't give me a quick and easy answer.

https://journals.sagepub.com/doi/pdf...6867X241276115 is a tutorial essay trying to underline that many of the indexes in this territory yield to a few lines of direct code. That essay may or may not be close to your set-up.

[Cat Santos]

Hi Nick,

Thank you very much! Yes the theil index is an entropy measure. I did calculate it by hand using the instructions on that link, but wanted to calculate it using a package just to double check.

I will look into the tutorial you sent me.

Many thanks again.

[Cat Santos]

Hello again,

I have a followup question.

I managed to restructure my dataset in a long format so that now I have four variables: an identification variable for each municipality (municipality_id), category (with each of my 10 categories of land plots by size), and the corresponding number of land plots in each category (number), as well as the area of land occupied by each category (superf). This means my dataset now has 10 categories for each municipality, allowing me to use ineqdeco.

If I'm not mistaken, I calculated it like this. So that the area occupied by each category is weighted by number of plots (if that makes sense ?).

However... I don't know how to create a variable that gives me the theil index for each municipality (which I understand is the GE(1) indicator). Is it possible to do that?

Once again thank you so much.


UPDATE: I believe I may have to create a variable (gen w = superf/number) to use the command correctly: ineqdeco w, by(category). But I'm not sure about this...

ineqdeco superf [fw=number], by(category)

Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
municipality_id |     32,020    3576.872    2033.534          4       7159
    category |     32,020         5.5    2.872326          1         10
      number |     32,020    49.29988    101.2329          0       3361
      superf |     32,020    271.9781    725.1904          0      23031

(Note, this is the total output from ineqdeco: )

. ineqdeco superf [fw=number], by(category)
 
Warning: superf has 45 values = 0. Not used in calculations
 
Percentile ratios

----------------------------------------------------------
  All obs |    p90/p10     p90/p50     p10/p50     p75/p25
----------+-----------------------------------------------
          |     38.793       4.182       0.108       7.210
----------------------------------------------------------
  
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
----------+-----------------------------------------------------------
          |    2.95430     0.82697     0.69088     1.24846     0.60462
----------------------------------------------------------------------
  
Atkinson indices, A(e), where e > 0 is the inequality aversion parameter

----------------------------------------------
  All obs |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
          |    0.31192     0.56263     0.85525
----------------------------------------------
  
Subgroup summary statistics, for each subgroup k = 1,...,K:
  

---------------------------------------------------------------------------------
 category |   Popn. share          Mean Relative mean  Income share     log(mean)
----------+----------------------------------------------------------------------
        1 |       0.21802      74.99103       0.15190       0.03312       4.31737
        2 |       0.14505     159.49305       0.32307       0.04686       5.07200
        3 |       0.32694     633.28712       1.28279       0.41940       6.45092
        4 |       0.13269     502.45646       1.01778       0.13505       6.21951
        5 |       0.10532     833.12444       1.68759       0.17774       6.72518
        6 |       0.04575    1051.79861       2.13054       0.09747       6.95826
        7 |       0.01786    1424.36883       2.88522       0.05152       7.26148
        8 |       0.00432    1539.20757       3.11784       0.01346       7.33902
        9 |       0.00322    2924.18567       5.92327       0.01906       7.98077
       10 |       0.00083    3743.00607       7.58188       0.00633       8.22764
---------------------------------------------------------------------------------
  
Subgroup indices: GE_k(a) and Gini_k

----------------------------------------------------------------------
 category |     GE(-1)       GE(0)       GE(1)       GE(2)        Gini
----------+-----------------------------------------------------------
        1 |    1.09650     0.60443     0.63483     1.17590     0.57118
        2 |    0.93962     0.56589     0.64026     1.37164     0.55858
        3 |    0.53610     0.37747     0.41143     0.68948     0.46557
        4 |    0.48688     0.31721     0.31252     0.42874     0.42156
        5 |    0.65181     0.36077     0.33359     0.42743     0.44161
        6 |    1.07054     0.46722     0.38325     0.45164     0.47924
        7 |    1.66760     0.65580     0.55023     0.74984     0.56184
        8 |    1.95316     0.84290     0.72246     0.98764     0.63344
        9 |    1.83596     0.77082     0.68199     1.02863     0.61329
       10 |    0.66375     0.44341     0.40515     0.49064     0.49453
----------------------------------------------------------------------
  
Within-group inequality, GE_W(a)

----------------------------------------------------------
  All obs |     GE(-1)       GE(0)       GE(1)       GE(2)
----------+-----------------------------------------------
          |    2.27350     0.45693     0.41607     0.97111
----------------------------------------------------------
              
Between-group inequality, GE_B(a):

----------------------------------------------------------
  All obs |     GE(-1)       GE(0)       GE(1)       GE(2)
----------+-----------------------------------------------
          |    0.68079     0.37003     0.27481     0.27735
----------------------------------------------------------
              
Subgroup Atkinson indices, A_k(e)

----------------------------------------------
 category |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
        1 |    0.26777     0.45361     0.68681
        2 |    0.25994     0.43215     0.65269
        3 |    0.17850     0.31440     0.51742
        4 |    0.14515     0.27182     0.49335
        5 |    0.15875     0.30286     0.56590
        6 |    0.19029     0.37326     0.68164
        7 |    0.26036     0.48098     0.76933
        8 |    0.33082     0.56954     0.79618
        9 |    0.30820     0.53737     0.78596
       10 |    0.19377     0.35816     0.57036
----------------------------------------------
  
Within-group inequality, A_W(e)

----------------------------------------------
  All obs |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
          |    0.18725     0.33901     0.57293
----------------------------------------------
 
Between-group inequality, A_B(e)

----------------------------------------------
  All obs |     A(0.5)        A(1)        A(2)
----------+-----------------------------------
          |    0.15340     0.33831     0.66107
----------------------------------------------

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