ineqdeco - Theil index

[Katie Hulston]

Hello,

I am trying to calculate a Theil index for regions in the UK in order to analyse the within and between income inequality. I manage to get some output showing this however I believe it is not correct because it states the Popn. share as 0.08333 which is weighting the regions equally (1/12) however I have data about the population size I'm just not sure how to change it to that. I've tried using fweight(population) but it does not seem to work as it says option weight not allowed. The current command I've been using to get the output is ineqdeco decileincome, by(region).

Thanks for any help in advance!!

[Nick Cox]

ineqdeco is from SSC.

Weights in Stata are given separately from options. There is an example in the command help and

ineqdeco decileincome [fw=population], by(region)

may be closer to what you want.

That said, a variable called decileincome may or may not be suitable for this command, depending on what it is.

The author Stephen Jenkins may pop in as the authority.

[Katie Hulston]

Thank you so much that has worked!!

Also, I'm aware the Theil index can be decomposed indicating which region, in this case, has contributed more or less so to the overall inequalities. Do you know if this is shown by the individual GE(1) for each region? There is output that follows that gives the between and within inequalities from the regions as a whole but I'm not sure which figures denote the individual regions contribution to overall inequality. Theres also _00000F and _00000I figures for each regions so it could be them I suppose.

Thanks again!

[Nick Cox]

The ado file shows that I commented on the code circa 2006 but sorry, I don't retain detailed memories of anything much there. If there isn't,a better answer I would recommend experimenting with a very simple contrived example where you can work out independently what the results should be.

[Stephen Jenkins]

Nick's observations and recommendations are spot on, as ever. It's important to know the nature of the variable "decileincome" . -ineqdeco- is designed to be applied to unit record data, e.g. in this context, information about "income" for a large sample of individual units. For the within/between decomposition, you also need an additional variable with which to group individuals. Region is an example. If Katie only has, say, one observation per region, then -ineqdeco- is not applicable.
Bottom line: we need to know precisely what Katie's data structure is, in particular about the units for which 'income' is observed, as well as the grouping variable.

[Katie Hulston]

Thank you for the help Nick and Stephen I'm using decile income data for each region so I have ten for each region so I think its worked out now thanks!

[Stephen Jenkins]

Pedant speaking: surely if you have "deciles", you must have 9 incomes per region! 9 deciles; 10 deciles groups (4 quintiles; 5 quintile groups; etc). There are substantive points behind this remark. If you only have decile or decile group (income share? mean of the group?) information, then you have grouped data (a.k.a. banded) data. You do not have unit record data. You will be under-estimating overall inequality because you do not account for the inequality within the bands. [Just because Stata is not giving you a runtime error now, doesn't mean that the output is "correct".) And whether you have deciles (income values) or decile group shares or decile group means would make a difference to how you might estimate total inequality accounting for the within-band inequality not recorded.

[Katie Hulston]

Stephen Jenkins

I have 10 incomes per region the population is split into ten proportionate groups and they all have an average income between them. It is ordered from bottom to top income. However I thought that the Theil index is appropriate with group data as I am still weighting each decile per region according to the population of that particular region. Would within data not be accounted for between these different groups? I'm sure it would be less accurate but still to some degree accounts for the between and within inequalities.

[Nick Cox]

If your values are the mean of each decile bin, you're still understating the variability. The coarsened variable can't reach the extremes in data but only the outermost bin means.

If you can't do better because the raw data are inaccessible, fair enough, but your results are comparable most with calculations for similar data.

That's my understanding, which Stephen Jenkins may wish to qualify or correct. .

[Stephen Jenkins]

Nothing to add to Nick's words, except to point to the large literature dealing with estimation of inequality indices from banded/grouped/coarsened data. There are different approaches depending what sort of information is available to the analyst. A good starting place for Katie's case would be "The estimation and interpolation of inequality measures" by FA Cowell and F Mehta, Review of Economic Studies, 49 (1982), 273-290. (There is no publicly available Stata implementation of their estimators that I am aware of.)

[Katie Hulston]

Okay thank you very much Nick and Stephen!!