Theil decomposition- decompose income inequality between and within regions using "ineqdeco"

[Yang Zhou]

Hi all,

I am trying to do Theil decomposition using the STATA module “ineqdeco", but I am not sure how to exactly use the syntax for my situation. I have done some readings but could not find enough tutorials or examples of how to use ineqdeco, so could someone kindly answer my questions in details?

In my research, there are three regions, east, central and north, and in each region, there are some states. I have the population and average income data for each state, and I want to decompose income inequality within and between the regions.

The syntax is ineqdeco varname [weights] [if exp] [in range] [, bygroup(groupvar) welfare summarize ].

My questions are: What my command should be like? Should the "varname" be total income or average income of each state? Does "weights" mean the number of population in each state? Could someone explain the full syntax for me? I would appreciate it if you can also provide some examples or tutorial resources.

I wrote the following command (I am not sure if it is correct):

ineqdeco incomepercapita [w=population] if year==2015,by(region_n)

Thank you in advance,

Yang

[Stephen Jenkins]

The answers to your questions can be derived from a close reading of the help file for ineqdeco (or ineqdec0), both on SSC (you're supposed to tell us where user-written modules come from -- please read the Forum FAQ).

I want to decompose income inequality within and between the regions

But you only have average income for states within a region, and I suspect there are few states within a region. (Perhaps you also have state-, region- or national-level population data but you don't tell us.)

As the help for ineqdeco explains, the program is intended for application to individual-level data only; it is not intended to be applied to grouped data -- which is what you have.

For each member of the family of Generalised Entropy inequality indices, Total inequality = Within-Region inequality (weighted sum of inequality within regions) plus Between-Region inequality (what inequality would be if each person received the average income of the region in which they reside). You have insufficient information to calculate this accurately, it appears. You might be able to calculate some estimate of Between-Group inequality, depending on what information you have about population sizes.