we return to a topic we looked at before
the distribution of income we do this
partly because it's such an important
issue in social science but also because
it enables us to review a number of
statistical topics that we've met
earlier in the series in a previous film
we looked at the difference between
wealth and income if we plot the data
for either of these variables for most
countries we get a positively skewed
distribution wealth is even more skewed
than income with most people having
little or no wealth at all and the
distribution of incomes is a skewed
distribution there are lots of people
who don't learn very much there are
quite a few people in the middle and
there are very small number of people
who earn an extraordinarily large amount
of money now if you choose to analyze
that by taking a mean you're going to
wind up with a rather high number simply
because a few billionaires can distort
it and you present that as an average
the average income in Britain is what in
fifty sixty thousand people so hang on a
minute there's not many of you one who
gets that and that's a classic case
where you really should be looking at
either the median or the mode if you
want to know so what does a typical
person in Britain earn you want the mode
and that is a surprisingly low number if
we want to measure the degree of
skewness of wealth we can do so with a
simple formula but we'll need to be
clear about the terms mean median and
standard deviation that we met in
earlier films but with that
understanding we can now develop a
measure of how skewed wealth
distribution is
the pier Sounion coefficient of skewness
sk is given us three times mean- median
over the standard deviation a
symmetrical distribution will give a
value of sk 0 0 and in general sk will
fall between plus 3 and minus 3 so with
a mean wealth of 5000 a median wealth of
4,500 and a standard deviation of a
thousand we have s k equals three times
five thousand minus 4500
over 1000
equals 1500 over a thousand gives us 1.5
so we can measure the degree of skewness
with a quite limited amount of data is
there a right distribution of income
most of us would say it depends upon
your view of justice to some people
justice means that people receive an
income which reflects their needs so if
that means redistributing income via the
tax system so be it to others justice
means receiving an income according to
what you produce in which case any
redistribution of income is by its
nature unjust Denmark like many European
nations has a very generous system of
wealth redistribution single mothers for
instance receive among other things
housing healthcare dental care and
asleep in the health care is that free
those free we have a dentist that's also
for free and that way it's a nice thing
and a really good thing it's a good deed
if we can say that way but even in the
most egalitarian European societies some
worried about the effect that taxes have
all incentives to work well it's
different societies and it's different
lifestyles under of course different
values well we need to have text to have
a foundation for our health care system
basic here which I say to our wealth but
it's also important that people who work
can't get feel that it's worth to work
the text shouldn't be too high and I
don't think it's right that we have so
high taxes as we have in Sweden but i
also think here is an awareness in
Sweden that we have the education we
have the health care we have the
structure in the society and I think
that's also something that we are all
very proud of in Sweden we we don't want
to get out of the social welfare
compared with European societies the
United States redistributes much less
income although there are some poverty
alleviation programs Americans tend to
believe in self-reliance the homeless
for instance must rely on the generosity
of others people see a problem and they
take it upon themselves to try to
address it as opposed to trying to force
the government entities to to deal with
the issue and that's how the shelter got
started some citizens saw the need and
decided to to make it happen and I think
that's that's the Genesis for a lot of
human service agencies the shelter for
the homeless receive 75% of its funding
from private donations the way the
United States is set up is that part of
the safety net system is provided by
private providers like the shelter we
are a private 501c3 you know we're not
part of of any governmental agency it's
very different than if you're in Sweden
or in France where the government has
taken on the role of providing that
safety net in totality the government in
the United States does a lot but it's
it's not the comprehensive approach that
is used in European countries if we
weren't here doing it the government's
not picking up the work so it has to
rely on private nonprofits or just
concerned individuals we're going to go
out and do the work
redistributing income will mean taxing
people who may then decide it isn't
worth working they take more leisure
instead produce less and society is
pouring that's why some are so keen on
the idea of the Laffer curve what's the
relationship between the tax rate and
the amount of government revenue
received art laffer was an American
economist and he was sitting in a
cocktail bar like this one day talking
to the economic advisor to the president
during a recession and he was asked what
should we do about tax rates and I
laugher said you should cut them and he
explained it like this he pushed his
drink aside took a cocktail napkin and
drew a diagram which has become the
stuff of economic textbooks he said if
you plot the tax rate along here from
zero to a hundred percent and the tax
take up here and you set a zero rate of
tax the government gets no revenue if
you raise the tax rate government
revenue increases but soon the
disincentive effects of increasing taxes
causes people to work less hard and the
government begins to receive less
revenue till when you reach a hundred
percent tax rate nobody does anything
and government revenue is reduced to
zero on the diagram which we've just
drawn is now in many textbooks and
explains why in the lap review using the
Laffer curve it's often a good idea for
governments not to increase taxes but to
decrease them what is true of taxes on
labor is in principle true of taxes on
profits as well a profits tax is likely
to reduce investment demand if there's
less investment there's less profits if
there's less prophets there's less
government revenue
let's have a look at some data to see if
we can see how true this is brilliant
hasit used nonlinear regression methods
to test the Laffer curve relationship
for corporate taxes is there a rate at
which increases in business taxes have
such a disincentive effect that
government revenue declines they tested
this question by looking at 29 OECD
countries in two separate periods the
earlier period 1985 to 1989 a letter
curve relationship is evident with a
peek at a tax rate of around thirty four
percent the tax later is lagged five
years because it takes some time for
companies to alter investment plans when
tax rates change
none of the period 2002 2005 where a
relationship still holds but the
inflection point is now lower at around
twenty eight percent notice also that
the curve is flatter for the earlier
period so that the cost in lost
government revenue is greater for having
rates above the peak capital has become
more mobile between countries over time
so this result is unsurprising
but how good a fit is the data will give
just a few of their results the fast
column shows the results for all
countries looked at the second when
they've excluded outlier countries
countries that are unusual for various
reasons and excluding these countries
makes little difference to the results
as you can see from the table the
r-squared is quite low but the tax
coefficient is significant not just at
the five percent level perhaps the most
common choice of significance level for
regression analysis but at the one
percent level so this important evidence
about the robustness of the Laffer curve
concept because regression analysis can
handle nonlinear relationships as well
as linear ones
let's look at some statistical analysis
which was undertaken with some
considerable care and see what happens
to the distribution of income when mean
average incomes are falling during a
recession when such a crisis comes to an
economy while averaging comes for it's
the poor who do relatively badly we can
see this particularly with reference to
the USA the figure plots data over time
for various percentiles in household
earnings in the USA the blue shaded
areas are periods of recession in the
economy it doesn't show all income it's
only income from labor and those at the
bottom of the distribution get help from
unemployment benefits and other
transfers which tend to rise in a
recession help not shown in this data
in the figure we taken the data and
divided for each year each percentiles
observation by the data for the first
year of the analysis 1967 this
normalization procedure means that all
groups would begin with a number of one
but here we've taken the logarithms of
the series remember that the log of 1 is
0 so that the starting point is 0 now we
can observe what happens over time to
the distribution between groups notice
in particular how households in the
bottom percentiles experience the
biggest relative falls during a
recession these declines can be
persistent the lowest percentile
earnings fell twenty percent in the
recession of the early 80s and only
return to pre-recession levels almost
two decades later
the data is log normalized to enable us
to see in the graph the proportionate
changes between the percentiles over
time rather than absolute changes
now Labor earnings are not the only
source of income for households in
particular at the bottom of the earnings
distribution governments and private
transfers such as unemployment insurance
and so on tends to rise when earnings
fall thereby mitigating widening
earnings inequality
one issue that society has to grapple
with is whether to worry about the
distribution of income or only to
concern itself with the poor they're not
the same thing let me show you how in
several previous films I introduced you
to my desert island economy in one of
those films three of us worked and
exchanged and produced income though it
wasn't evenly distributed we weren't had
a gini coefficient to give us a value
for the evenness or otherwise of our
income distribution now here's another
small island economy with which we trade
it also has a total income of a hundred
euros also has three people but the
income is shared out differently the
table shows our Island and how the two
societies weekly income is distributed
if you wish you can go back to film 15
calculate the Gini coefficient for the
other Island and establish that it's
more evenly divided
with the formula we used in an earlier
film we find our island has a
coefficient of 20 6.67 the other Island
has a coefficient of sixteen point six
seven you may recall that the closer to
one is the coefficient the more evenly
income is distributed
but now look at the poorest member in
each of the two societies observe that
on our Island our poorest member member
3 has a twenty-five percent higher
income than on the other Island where
income is more evenly distributed
income distribution and poverty are
closely linked but they are distinct
issues this phenomenon of both the
income and wealth bifurcation that's
going on in our country personally I
don't think is sustainable I think we're
headed down a path that is going to lead
to some real severe problems people have
argued forever about what constitutes a
fair distribution of income we haven't
been able to resolve this issue probably
no one ever will but if we understand
the statistics at least we're better
informed to make our own value judgments
statistics unlock your ideas if you look
through for instance the most recent
poverty figures and you're trying to
understand what it is that your policy
solutions might be to the problems that
we have with regards to poverty in this
country at the moment without
understanding the figures without really
looking at the numbers you could come up
with entirely the wrong solution to the
problem we are bombarded with data of
all types much of it used recklessly and
people's quote statistic it makes no
sense it frustrates me enormously and I
hear people saying something I say
that's possibly true I mean have a
feeling about data how to analyze data I
think everybody has to do that and
therefore statistics and caution
statistics is the best foundation for
getting some appreciation of how to go
about doing that