Theil Index

[Farjana Misu]

Hello Everyone,

I will be grateful if anyone could advance my understanding of STATA in relation to the question below.

Is it possible to calculate Confidence Interval for Theil Index?
Please help me with STATA commands.


Thanks
Farjana

[Nick Cox]

Please cross-reference your previous thread of 17 June, explaining what different answer you seek.

[William Lisowski]

The previous thread at https://www.statalist.org/forums/for...76-theil-index asked for the calculation of the Theil index to measure the inequality by region for a health indicator variable.

The current thread asks for the calculation of confidence intervals for that index.

If you believe that the health indicator variable values are perfectly accurate, then the Theil index perfectly reflects the inequality in the data. And I think this is typical of applications of inequality indices in the context you describe.

Consider an analogy. Suppose you have a group of 10 apples and you measure their total weight. Now, how would you put a confidence interval around that total? It just "is what it is" - there's nothing random to do statistics with.

That's a different question than assuming that the 10 apples were sampled from a larger population of apples whose weights followed a normal distribution with a given mean and standard deviation, and you want to calculate an estimate of the mean of the distribution and a confidence interval for that estimate.

Perhaps Stephen Jenkins - the author of the package recommended in the previous thread - can express this more fluently. As an expert in measures of inequality I'm certain he's had to address questions like this.

There's also proof-by-Wikipedia - if there were a standard way of calculating a confidence interval for a Theil index, I'm sure some fan of the Theil index would have included it in the article.

[Jared Greathouse]

proof-by-Wikipedia

This should be the first thing they cover in real analysis courses (which I do wish I took in undergrad).

"And today class, we are going to continue to cover.... methods of proof. We've went over contradiction and induction. However, using the Cauchy–Schwarz inequality as an example, we shall today be covering the most valuable and coveted method of proof: proof, by Wikipedia, the free encyclopedia."

[Farjana Misu]

Thank you so much all. I hope I understand.