[Martin Taylor 2011.06.28.10.52]
[From Rick Marken (2011.06.27.2230)]
Bill Powers (2011.06.27.1928 MDT)–
BP: The data do not suggest any causal relationship at all.
They describe concurrent variations which might prove to be
causal in one direction or the opposite direction, or they
might reflect, as Samuel Saunders pointed out, influences of
completely different kinds that account for both sorts of
variations so neither direction is causal: both are effects
of something else or of multiple covarying disturbances.
Yes, this is the usual interpretation of a correlation, based
on an understanding of the term “correlation does not imply
causation” to mean that data reported in terms of correlation
coefficients (r values) does not imply causation. But this is
not what the term means. The term “correlation does not imply
causation” means that non-experimentally obtained
relationships between variables do not imply causation.
That is not what it means. Any correlation DOES imply causation,
whether there’s an experiment involved or not.
As many people, including Rick, have shown, you can have a strong
causal connection between two variables but a complete absence of
correlation between them. The converse is not true. If there is a
correlation then there must be a causal relation, either directly
between the variables or from another variable to both. And that is
true in control systems, in non-experimental data, and whenever
there is sufficient data to indicate the correlation isn’t just a
coincidence.
The statement "correlation does not imply causation" simply means
that a correlation between A and B does not mean there is a causal
link between A and B. A and B may have no causal link whatever, but
if they don’t, then both must have a causal link to some other
variable. For example, there is a strong correlation between the
greenness of my grass and the leafiness of my deciduous trees, but
the leaves do not cause the grass to grow and neither does the grass
cause the trees to leaf. However, there is a causal relation,
because the same seasonal changes in solar angle influence both the
grass and the trees.
If there are several independent direct causal influences on a
variable, there are limits on how strong correlations can be. By
this I mean that if X is directly influenced by A, B, C, D,… and
these are all independent of one another, the second strongest
correlation cannot be greater than 1/sqrt(2), the third strongest
cannot be greater than 1/sqrt(3), and so forth. Usually the second,
third, etc., correlations are well below these limits, because the
limits actually will be reached only when both (all three, four,
…) correlations are equal.
Following Samuel Saunders, consider the case of taxes and prosperity
after the Second World War. High taxes were needed in order to pay
for the war effort. The high tax rates continued after the war, for
a while, and low unemployment also. But was the low unemployment
caused by the high taxes? It’s impossible to say, simply from the
correlation. One could argue, as Saunders does, that low
unemployment was due to the catchup on the lack of non-war
production during the war years, and to the need to fix war damage.
The war would then be a causal influence on both taxes and reduction
of unemployment.
On the other hand, when many apparently independent variables (such
as the grass and the leaves) correlate with the same independent
variable, there is a surface case for investigating whether that
common variable might be directly causal on the other variables.
Consider the correlations between a simple index of income
inequality (the ratio of the to 20% to the bottom 20%) and 29
different social indices across 23 developed nations or 50 US
states, from the book “The Spirit level: Why equality is better for
everyone” by Wilkinson and Pickett, Penguin 2010:
`
Indicator International data ``US data ``
`
*r*``*p-value*``*r p-value*
` Trust -0.66 <0.01
-0.70 <0.01 (percentage of people who say most people can
be trusted)
`
Life expectancy -0.44 0.04 -0.45 <0.01
Infant mortality 0.42 0.04 0.43 <0.01
Obesity 0.57 <0.01 0.47 <0.01
Mental illness 0.73 <0.01 0.18 0.12
Education score -0.45 0.04 -0.47 0.01
Teenage birth rate 0.73 <0.01 0.46 <0.01
Homicides 0.47 0.02 0.42 <0.01
Imprisonment 0.75 <0.01 0.48 <0.01
` Social mobility 0.93 <0.01
** The above were combined into an Index of quality of life (my term) as they were available for all the countries and states (not social mobility for the US index) **
** Index 0.87 <0.01 0.59 <0.01**
` The following were not available for all 23
countries or 50 states, so were not included in the above index.
`
Overweight children 0.59 0.01 0.57 <0.01
Drugs index 0.63 <0.01
Calorie intake`` 0.46`` 0.03
`
``
Public expenditure on health care``
-0.69`` <0.01`
`
``
Child well-being`` -0.63`` <0.01``
-0.51`` <0.01 `
`Triple education score
-0.44 0.04
`
Child conflict 0.62 <0.01
`Spending on foreign aid``
-0.61`` <0.01 `
`
``
Recycling`` -0.82`` <0.01 `
`
``
Peace index`` -0.45`` 0.03 `
`
``
Paid maternity leave``
-0.55`` 0.01 `
`
``
Advertising`` 0.60`` <0.01 `
`
``
Police`` 0.52`` 0.04 `
`
``
Social expenditure``
-0.45`` 0.04 `
`
``
Women’s status`` -0.50`` 0.02``
-0.30`` 0.03 `
Juvenile homicides`` 0.29 <0.05
` High school drop-outs
0.79 <0.01
`
``
Child mental illlness`` 0.36 0.01
Pugnacity`` 0.47 <0.01
Nothing in these correlations proves that income inequality causes
any of the adverse effects, but they do say either that it does or
that at least some of the factors such as government policies that
influence income inequality also influence these variables.
Obviously some of the variables are highly correlated, such as
“Obesity” and “Overweight children”, but others have no obvious
direct relationship, such as “teenage birth rate” and “imprisonment”
both of which correlate better than 1/sqrt(2) with income
inequality, or between “spending on foreign aid” and “mental
illness”, both of which correlate better than 1/sqrt(3) with income
inequality.
Given these correlations, one would be forgiven for thinking that
unless there is evidence to the contrary, income inequality probably
does have a direct effect on at least some of the social quality
indices. In the book, Wilkinson and Pickett suggest mechanisms for
some of the effects, but their suggestions certainly cannot be
considered definitive.
These correlations are data from respected sources, with no
cherry-picking. Any valid socio-economic model should produce a
similar pattern of correlations.
Martin