My employer has assigned me the project of trying to understand where our current and potential International Private Banking clients are, and where they are moving to.
To understand this, we are buying compiled data (Income as an indicator of wealth [no wealth tax in these countries, so no wealth data] combined with the destination countries of the emigrants) from statistical bureaus of certain countries but have run into a privacy issue. Any identified "class" with fewer than five members is excluded. Say there are 500 people moving to Japan, but only 3 of those earn enough to be considered potential clients, then that data would be withheld. This is very likely to be a problem for a number of our important markets, enough so that it is not worth our buying this data in its current format.
We have considered a number of alternatives: average incomes, combining years of data, a lower income threshold, etc... but have concluded that combining enough years of data/lowering the threshold enough for data not to be suppressed would render our data not useful, and that comparing average incomes doesn't give a fair representation of the distribution of income.
Additionally, we have identified that classes with such small numbers of people can vary wildly (percentage-wise) from year to year along a normal distribution, meaning that trends will be difficult to assess.
So finally, we are considering using an index for income inequality to measure how big the spread of income is. Given the definition that someone earning more than 150k p.a.is considered to be a potential client and a very small percentage of people earn that (for one of our countries it's 0.7% including capital income), and that data that is excluded is impossible to establish any trends from - how do we do this?
Which measure of income inequality is best for this use case, and why, how should the data be handled? Should anyone earning below say 80k be discounted, and then an income inequality measure be used there? How do the different measures handle small datasets? Does a bias appear when there are fewer than say 100 people in a class?
So... is there a best answer? Were we unfair in dismissing any of the alternatives as a good measure? Is there an alternative I haven't considered?
Thanks for all the help it's really appreciated!