A look at income inequality in Bermuda – Gini Coefficients & Lorenz Curves

Another Inequality Measurement

Following on from my analysis of the 2010 Census data on incomes, I thought I’d try my hand at doing a Lorenz Curve and the related Gini Coefficient for the same data.

These two metrics of inequality are perhaps the most popular, the Palma Index I used in my previous analysis being a newer metric that tries to complement the Gini.  It’s also a lot easier to do, hence my focus on it in the earlier post.

Now, I know how to make a Lorenz Curve.

Or at least I thought I did.

Basically it’s an accumulative modelling of the stats from before, adding each deciles wealth at each stage.  So decile one stands alone, decile two is both decile one and decile two added together, etc.

This is then plotted as a line graph to get the Lorenz Curve.

A 45 degree straight line goes up the middle, indicating what ‘perfect equality’ would look like as a Lorenz Curve.

The Gini Coefficient is based on the difference between the actual Lorenz Curve and the line of perfect equality.

As I’m not too sure about calculating the Gini Coefficient (it involves calculus, which I need to improve on…), I double-checked my own attempt with an online modelling service.

The result?

Well, two different Lorenz Curves and two different Gini Coefficients.

I got a Gini of 0.63 (or 63, depending on how one prefers to record it) – Figure One.

Figure One - Gini

The online model, using my data, gave a Gini of 0.72 (72) – Figure Two.

Figure Two - The online model Lorenz Curve & Gini.

Figure Two – The online model Lorenz Curve & Gini.

So.  Yeah.

This one’s going to go back to the drawing board.

Hypothetically though, if one takes the actual Gini for 2010 Bermuda as the mean of these two, then Bermuda in 2010 had a GiniFigure Three Gini of  0.675 (67.5).

Using the same list of countries I used to compare our Palma Index, gives us Figure Three.

The high Gini for Bermuda is in red, the low in green and the mean in yellow.

A Big ‘IF’…

IF any of the Gini Coefficients calculated for Bermuda are correct, then based solely on them, Bermuda is either the most unequal country in the list, or the second most unequal country there after South Africa.

Now, I cannot stress this enough, I am not confident that I’ve calculated the Gini Coefficient for Bermuda properly.

I am simply hoping that by putting forward an initial calculation it inspires someone more skilled than me to refute the calculation and replace it with a better calculated one.

The same goes with my previous analyses of 2010 income inequalities in Bermuda.

They are but an initial attempt to shed some light on inequalities in Bermuda.

They need improved upon.

I will take another look at my Gini calculations and, if I subsequently redo it, I’ll post it here too.

Now, of course, if one of the above calculations of Bermuda’s Gini is correct, well, that alone should be some food for thought…


 

Wrong Data Set?

On a related note, I want to make clear that some people (primarily on Facebook, either in personal messages to me or in discussions sparked by my earlier post) have argued I’ve used the wrong data set.

I selected what I thought was the most appropriate data set to investigate income inequalities in Bermuda, however some disagree with that choice, it appears because that data set seems to include income data from expatriate workers.

They have suggested an alternative data set – and I hope to look at that and see if it’s possible to conduct a similar investigation using it instead of the data set I did.

Personally, I think the analysis I’ve done, if it includes expatriate incomes, is a perfectly valid investigation of total income inequalities in Bermuda as is, and provides an important insight in its own right.

Help Me Do It Better!

I encourage others to try their hand at improving on what I’ve tried to do.

If you want to refute my findings, please try and do so.

If you think you can refine my findings, please try and do so.

All I’m trying to do is provide an initial insight and indication into income inequalities in Bermuda.

I welcome assistance and alternative approaches!

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One thought on “A look at income inequality in Bermuda – Gini Coefficients & Lorenz Curves

  1. So, I’ve redone the calculations, and, yes, I’d erred.

    I’ll present the updated – and correct – Gini Coefficient and Lorenz Curve in a little bit. Going from memory, I think the Gini for 2010 Bermuda was around 0.42 or so.

    Basically I’d forgot to weight some figures, and then miscalculated another aspect, leading to the mistake.

    Even that figure is a very conservative estimate as I decided to err on the side of extreme conservatism in some of the necessary assumptions that had to be made, in terms of adopting the lowest figure possible for the highest income band, and means for all other income bands, which gives pretty much a lower than reality Gini.

    Having said that, I don’t think that would alter the Gini too much. It may be as high as 0.44 instead of the 0.42, but that’s about it.

    And again, this just measures income inequalities – true wealth inequalities would have to factor in wealth beyond income alone.

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