Inequality
regularly makes the news; when we see reports that inequality is rising,
there’s no need to complain too much that it doesn’t reflect everything in an
economy. Inequality as measured in a Gini coefficient is one important thing to
consider, and if inequality increases, people should wonder if we can stop
that.
But
the reverse isn’t true. When our inequality measure shows inequality
decreasing, it doesn’t necessarily mean that all is well with the economy, and
that’s my subject for today.
First
of all, let’s take a look at income inequality as it was in the UK for
income taxpayers, just to get an idea of what this sort of information looks
like.
Graph 1
This
graph shows the total income subject to tax for someone at each percentage
point for income in the population, for those with taxable income only (for
more information about the data, see HMRC’s Survey of Personal Incomes
2013-14). So, for example, the person with the middle income, at 50% of the population,
earned £20,020 after tax. The person at the top (the 99th
percentile) earned £103,427 in the year.
The
next bit is important, but a bit involved. The way to represent inequality
calculations is by summing the incomes and plotting the cumulative income for
everyone under that percentile. The graph looks like the lower plot on graph 2.
That curve shows the accumulated income of a segment of a population. For
example, the bottom 20% of taxpayers earned 9.8% of income. The bottom 90%
earned about 78% of income.
On
the same scale I’ve overlaid a plot of complete equality, in which everyone
earns the same amount. As everyone earns the same amount, the cumulative score
increases linearly as we add extra people to our total, and we get a straight
line. Inequality is calculated by comparing the area between the two lines to
the size of the whole triangle underneath the straight line (i.e the area
between the plot of perfect equality and the axes). That triangle represents
what this measure calls perfect inequality: if one person had all the income,
the cumulative total would remain 0 right until the very end, when it would
suddenly leap to 100% of all income. So what we’re doing is seeing how far
between complete equality and inequality we are; we measure the proportion of
complete inequality we see in the country.
Graph 2
I
do think it’s important to point out that of us regard perfect inequality as a
lot less troublesome than perfect equality. I, for one, wouldn’t like to earn
exactly the same as everyone else; it would be a pay cut, I’d feel unrewarded
for my expertise, and I’d have no incentive to work harder, learn or improve.
But I would hugely prefer that to earning nothing at all while someone else got
all the country’s income. So although inequality is measured on a scale of 0
(perfectly equal) to 1 (perfectly unequal), we should skew our expected range
to be closer to 0 than to 1. But in the end, measures like this are about
detecting change; we use them to compare different countries and change within
a country.
That means that
we’re looking for improvement that
represents improving lives, and as soon as we start using specific measures to
analyze general concepts such as wellbeing and inequality, we need to be aware
that no individual measure will incorporate everything that we understand in
the general term. We need a range of measures, and we need to understand how
and why they change, rather than just believing that a change in the number is
either good or bad. In other areas, such as targets within a company or the
NHS, using a measure can change behavior so that the measure improves but
overall circumstances don’t.
So why and how
can inequality change? We’ve already considered two extremes: perfect equality
and perfect inequality. But what about another scenario just to illustrate
other odd possibilities? How about graph 3? Here I’ve given half the population
no income and the remaining half share the income equally. This gives us an
inequality coefficient of 0.5. If we were thinking simplistically, we’d assume
that this was a tolerable situation. After all, we don’t like 0, and we don’t
like 1; we want something that’s a pleasing balance between the two. And 0.5 is
balanced between 0 and 1! Yet this distribution seems very unfair.
Graph 3
Graph
3 therefore nicely demonstrates that inequality as a simple number doesn’t mean
much. We have to assume that the rough shape of the Lorenz curve remains the
same and that a change in inequality represents just a slight shift one way or
another. Drastic leaps and jumps in which income varies hugely between
percentiles of the population can distort the measure. And graph 3 is based on
a very drastic leap in income at the 50th percentile, as shown in
graph 4, which plots the underlying incomes used for the cumulative totals of
graph 3.
Graph 4
I
hope this establishes perhaps the most important point I want to make here:
that fairness is not the same as inequality, or any other economic measure.
Economists measure whole-population effects, and a whole-population measure
typically can’t detect large leaps and dips: they’re ‘averaging’ across
everyone. The UK had a Gini coefficient (the measure usually used, and which I’m
describing here) of 0.356 in 2014. That’s not so far off the 0.5 of graphs 3
and 4. I could probably create a distribution very much like graph 4 which had
a Gini coefficient of 0.36.
But
what I have instead are some slight variations on the real income distribution
of graph 1.
Graph 5
Graph
5 shows something very similar to graph 1. Total income is roughly equivalent,
but the main difference is the top end (note the scale on the y axis). Graph 5
shows a similar gradual increase in income across the population, but without
the very big increases amongst the richest. Graph 6 shows the cumulative
distribution for the same data.
Graph 6
We can see that
although graph 5 isn’t a flat line with everyone earning the same, the Lorenz
curve (the name economists give to this cumulative income graph) is extremely
close to ‘perfect equality’, and the Gini coefficient very close to 0. The same
would apply with a doubled gradient on the slope of graph 5; graph 7 shows the
Lorenz curve if I double the changes from the midpoint. The inequality
coefficient for incomes that vary linearly from £4,000 to £44,000 (instead of
£14,000 to £34000) is still very close to 1.
Graph 7
This shows us
another feature of inequality measures: they’re insensitive to linear changes.
As long as the relationship is linear we need a massive change to make much
difference. For incomes to look even moderately unequal we need to leave the
linear relationship behind and try exponential relationships.
It’s very
important to point out here that I doubled the difference of a percentile’s
income from the midpoint. If I had doubled everyone’s income then inequality
wouldn’t have changed, because the measures have been deliberately designed to
detect proportional differences, not absolute differences. In graph 5 the
highest earners earn £20,000 p.a. more than the lowest, which is about 2.5
times their salary. If we double everything, the lowest earners would earn
£28k, the highest earners £68k and the difference would be £40,000. Inequality
would be exactly the same, even though the highest earners would now earn
£40,000 more than the lowest earners, not £20,000.
If I were to
keep the same slope, and keep the earnings difference between top and bottom at
£20k, but still double total income (i.e. give everyone an extra £24k each)
then inequality would drop.
This is
important, because earnings aren’t the only measure of quality of life. We also
need to understand what people can buy with their earnings. There’s a minimum
level of expenditure that’s required in order to live in the UK (yes, I know
that accommodation costs in particular vary a lot, but for the moment let’s
simplify and assume that the minimum applies across the whole country evenly).
We know that the
minimum wage doesn’t provide the minimum level of expenditure because there are
long-running campaigns about the ‘living wage’, which is higher than the
minimum wage. But just for this argument, I’ll set it at the lowest percentile
of income in graph 5.
If we assume
that the bare necessities cost this much, then the lowest earners have
absolutely no spare spending money for luxuries, mishaps, presents and personal
expenditure. The highest earners have £20k spare for such things; more than the
low earners’ entire income. Our measure of inequality suggests that this
distribution is close to perfect equality, but as soon as we introduce a minimum
necessary level of expenditure, we change our understanding of people’s lives.
Some people can afford no luxury or deviation from the absolute minimum, whilst
others have a wide choice. The ability to choose interests or activities to
pursue is an essential part of human flourishing (and, incidentally, an
assumption of free market economics). People who are trapped in only one set of
choices do not feel happy or wealthy, no matter what the Gini coefficient might
say.
Finally, let’s
look at something more realistic.
Graph 8
Graph 8 shows us
something a lot closer to the real distribution we saw in graph 1, but
accentuated a bit. As we have learned, the gradual increase across much of the
population in graph 1 makes little difference to inequality measures, so I’ve
left it flat. Now we’re looking at the tails of the population. Yet again,
total income is roughly similar.
If we plot the
Lorenz curve for this, we see that the tails do matter; that big leap at the
end drives a narrow wedge between our line and ‘perfect equality’. But overall
the equality coefficient is still very low. Most of the population (between the
4th and 97th percentiles, or 95% of the population) is
absolutely equal, and that’s what the measure detects. Those other 5% drag the
number away from perfect equality, up to about 0.3.Just by looking at the
measure of equality, we might say that this society is slightly more equal than
our own, and therefore a bit of an advance. Yet it’s a combination of perfect
equality, which we don’t like, and perfect inequality, which we hate.
Graph 9
Inequality isn’t
the same as fairness. For humans, those cases at the end matter. If I told you
that we could all live happily if we just sacrificed 3 in 100 of the
population, most people would say that human sacrifice isn’t an option. It’s
not right, and it’s not fair. But economic measures don’t account for this. A
few people here or there don’t change the bulk figures, but they matter
enormously for our perceptions of society. I haven’t even touched on how
enormous wealth differences distort power relations, or how greater ability to
spend on luxuries ‘distorts’ the market for goods /luxuries away from what the
population might want. Those are topics for you to ponder, bearing in mind that
the difference between people’s self-directed expenditure is proportionally
vastly greater than their plain incomes, due to our threshold effect.
Our society might be
slightly more equal, according to the Gini coefficient, but we need to
understand the distribution changes underlying this before we judge whether
this is good or not. Our society can easily have become more equal and yet also
become much less fair. If the 1% (or 0.01%) at the top earn millions of pounds
and do not deserve it (and yes, judging what a person deserves could occupy
many other essays) then we are right to complain about economic injustice even
if ‘inequality’, as measured by this one economic measure, is lower. Justice
and social equality is about whether a person’s situation is fair when compared
to any other person in society, not most others, all others, or the average.
