guidance for users who do not know which to choose

[ajdamico]

we ought to have a flowchart (like the asdfree one below, but serious) to help people choose a poverty measure. which poverty measure is most appropriate for your analysis? something like the https://choosealicense.com/ page. what is the relative strength of each poverty measure, compared to all the others?

[1] https://github.com/ajdamico/asdfree/raw/master/analyze%20survey%20data%20for%20free%20-%20the%20flowchart.pdf

[guilhermejacob]

This is an interesting idea. Inequality measures and poverty measures should be treated different in that sense. I'd start by looking at the desirable axioms of each.

[guilhermejacob]

aae80f580c17ea771351b3a7650078231c2cde32 added a section on this for inequality measures. Introduced in inequality .rmd only.

[ajdamico]

i've reverted because this commit broke the build. when you add it back in please build and debug the problem, thanks

[guilhermejacob]

I rewrote the commit and fixed the bugs. Website updated and online.

[ajdamico]

[ajdamico]

draft flowchart.txt

this file pastes into the open source flowchart generator at https://mermaid.live/

[ajdamico]

how and where do these four functions fit into this flowchart?

svyatk svyrich svyiqalpha svyisq

[guilhermejacob]

svyatk estimate the Atkinson index. This is an inequality measure that has a direct link with the concept of welfare, unlike the Gini and Generalized Entropy indices. The Atkinson index has an "inequality-aversion" parameter $\epsilon$: In economic terms, the elasticity of the marginal welfare of income equals $-\epsilon$. If $\epsilon$ is high, the larger is the welfare increase if the income of the poor is increased. Hoffmann, Botassio and Jesus (2019) have an interesting chapter about this, However, it has the same limitation of the Generalized Entropy indices: it does not work with zero or negative incomes.

Some richness measures can be estimated using the svyrich. Those are not poverty or inequality measures, with particular properties. Like poverty measures, it has a focus axiom -- it focuses on the top of the income distribution. They can also have an income inequality or income polarization aspect, depending on the effect of progressive transfers among the rich. An inequality-sensitive richness measure would say that richness is reduced with a progressive transfer among the rich, since the inequality in that part of the distribution has decreased. On the other hand, a polarization-sensitive richness measure would increase after a progressive transfer among the rich, since the rich are more clustered after this transfer.

svyiqalpha estimates the quantile (I do not think this is used anymore, but worth checking). svyisq estimates the total income held by bottom $p$% of the distribution. At the population level, it is similar to the Lorenz curve multiplied by the total income. However, even after the multiplication, they might differ a little at the sample level. This is because svylorenz uses a different estimator, producing an estimated curve more in line with the theoretical properties of the theoretical Lorenz curve.

[ajdamico]

from G

[9/13, 11:42 AM] Guilherme Jacob: AA --> FF["svyatk() computes the Atkinson index, an inequality measure with a direct link to social welfare functions"] [9/13, 11:47 AM] Guilherme Jacob: i think it is an option among inequality measures. Wherever svygei can be used, so can svyatk. The difference is that one is an Entropy based measure (a kind of statistical concept), while the other has a clearer link to a (hypothethized) social welfare function, which might make it more interpretable to economists. [9/13, 11:51 AM] Guilherme Jacob: GE indices are more common. I would point them, them point to Atkinson if they want something that can be interpreted int terms of a social welfare function.

[ajdamico]

Imagine that there is a function that assigns a welfare/happiness/satisfaction value to a given amount of money.

The marginal utility of money is the crucial part for SWF-based inequality measurement. It expresses the idea that more money gives more welfare, but at a diminishing rate. So $100 makes less difference in someone’s welfare as we move along the income distribution.