Download The Art and Science of Cause and Effect

The Art and
Science of
Cause and
Effect
Adapted from a
lecture by
Judea Pearl
available on his WEB site:
http://singapore.cs.ucla.edu/LEC
TURE/lecture_sec1.htm
In the ancient world, causal agents
were people or animals or deities.
The serpent made me do it...
• Even chance events were explained as
messages from the Gods.
• The Book of Jonah tells that the sailors
drew lots to determine who was responsible
for their ordeal.
• When Jonah lost, he was thrown into the sea
and had to live for 40 years in a whale.
• The view of causation
changed when people
began constructing
machines
• They had to figure out
how the machines
worked and how to
correct problems
• Ascribing motivations to
the machines did not
help
Galileo extended this model to
the universe as a whole
Galileo used the
strange new
language of
algebra to
describe
movement in
the physical
world. d = t2
Physicists discovered many useful
“laws” that explained things
•
•
•
•
Snell’s Law
Hooke’s Law
Olm’s Law
Joule’s Law
• all used equations
to describe how
the world actually
worked
Hooke’s law (1678)
Scottish
philosopher
David
Hume
argued that
the same
principle
could be
applied to
human
affairs
Causation and Correlation
• According to Hume, causation was a
learnable habit of the mind
• When we see that two things go together we
learn that one “causes” the other
• When the flame burns us, we learn to keep
away from it
But does the rooster’s crowing
cause the sun to rise?
Bertrand Russell thought
causation was a faulty concept
• “All philosophers imagine that
causation is one of the fundamental
axioms of science, yet oddly
enough, in advanced science the
word ‘cause’ never occurs.
• “The law of causality, I believe, is a
relic of a bygone age, surviving,
like the monarchy, only because it is
erroneously thought to do no harm.
Patrick Suppes thought causation
was just a shorthand for expressing
complex relationships
• “There is scarcely an issue of the
Physical Review that does not
contain at least one article using
either ‘cause’ or ‘causality’ in its
title.”
• Science is full of abbreviations. We
say “density” instead of “the ratio of
weight to volume.” Why pick on
causation?
Russell is not convinced
• “Causality is different.”
• “It could not possibly be an abbreviation, because
the laws of physics are all symmetrical, going both
ways while causal relations are uni-directional,
going from cause to effect.
• Thus, we say that force causes acceleration, not
the other way around, but the mathematical
formula f=ma can work either way
Karl Pearson agreed with Russell
• Pearson invented
chi-square and the
correlation
coefficient
• He never talked
about causation,
only about
correlation between
variables.
Pearson invented cross-tabulation and correlation but
never inferred causal relationships
The randomized experiment
offered the first solution
• Sir Ronald Fisher
invented the
randomized
experiment
• This is the only
scientifically
proven method
of testing causal
relations from
data.
Three Criteria of Causation
• Correlation: Cause and effect must vary
together
• Time Sequence: The cause must come
before the effect
• Non-Spuriousness: The relationship
between cause and effect cannot be
explained by any third variable
Experimental Proof
• Experiments establish time sequence by
manipulating the independent variable
• Experiments establish non-spuriousness
through random assignment to experimental
and control groups
• Experiments establish correlation by
measuring changes in the dependent
variable in response to manipulation of the
independent variable
Engineers Use Causal Knowledge
to Make things Work
• Their bottom line is
pragmatic
• If they could make the
sun rise earlier by
getting the rooster to
crow earlier, we might
change our model of the
universe
If we blow up the lab, something was
wrong with our model.
• In electronics, the
causal models can be
very complicated
and useful
• A circuit diagram
involves logic gates
that are either on or
off, 0 or 1
• They only work
one way, from input
to output
Path Diagrams Can Be Used to
Plot Causal Models
An example of a multiple regression analysis
displayed as a pathdagram. By David Garson.
Testing Causal Models is Difficult
and Often Controversial
• Experiments are the only guaranteed way to prove a causal
model.
• But experiments cannot be done on many important social
and criminal justice problems.
• So we approximate them as best we can with correlational
data.
• It is important to check each step in this process carefully,
paying close attention to time sequences and to controls for
antecedent and intervening variables
Equations Aren’t Enough
• Some social scientists just throw all their
data into one massive regression equation,
hoping that it will somehow control for all
the variables.
• But this doesn’t work, for a number of
technical reasons.
• And because equations are not as good as
diagrams for plotting time sequences
The Bottom Line
• Causality is a difficult concept.
• But we can’t do without it if we want to
know how the world works.
• Or if we want to change the world.
• We have techniques that are helpful, but it is
hard to get definitive answers because our
ability to manipulate variables is often quite
limited.
Econometrics is a term for complex statistical modeling
done by economists. It is very complex and
mathematical but it doesn’t work well on sociological
problems - see my paper on “Myths of Murder and
Multiple Regression.”
”If variations like unemployment, income inequality,
likelihood of apprehension and willingness to use the
death penalty are accounted for, the death penalty
shows a significant deterring effect." Isaac Ehrlich,
New York Times, 2000
"All of the scientifically valid statistical studies—
those that examine a period of years, and control for
national trends—consistently show that capital
punishment is a substantial deterrent." Senator Orrin
Hatch, 2002
"I do not think that regression can carry much
of the burden in a causal argument. Nor do
regression equations, by themselves, give much
help in controlling for confounding variables."
David Freedman
Regression on nationally aggregated data can never yield
reliable evidence on deterrence, pro or con. The signal, if
any, is hopelessly buried in the noise. John Lamperti
Just as Messrs. Lott and Mustard can, with one
model of the determinants of homicide, produce
statistical residuals suggesting that 'shall issue'
laws reduce homicide, we expect that a determined
econometrician can produce a treatment of the
same historical periods with different models and
opposite effects. Econometric modeling is a
double-edged sword in its capacity to facilitate
statistical findings to warm the hearts of true
believers of any stripe.
Franklin Zimring and Gordon Hawkins, “Concealed
Handguns: The Counterfeit Deterrent,” The Responsive
Community 7: 46-60, 1997
The Bell Curve by Herrnstein and Murray put
American social scientists in an uncomfortable
place. The conclusions of the book are unwelcome,
while the methods of the book appear to be the
standbys of everyday social science. The unstated
problem for many commentators is how to reject the
particular conclusions of The Bell Curve without
also rejecting the larger enterprises of statistical
social science, psychometrics, and social
psychology.
Clark Glymour in Intelligence, Genes and
Success: Scientists Respond to the Bell Curve
“there is much uncertainty as to the `correct’ empirical model
that should be used to draw inferences, and each researcher
typically tries dozens, perhaps hundreds, of specifications before
selecting one or a few to report. Usually, and understandably the
ones selected for publication are those that make the strongest
case for the researcher’s prior hypothesis.”
The data analyzed are not sufficiently strong to lead researchers
with different prior beliefs to reach a consensus regarding the
deterrent effects of capital punishment. Right-winger, rationalmaximizer, and eye-for-an-eye researchers will infer that
punishment deters would-be murderers, but bleeding-heart and
crime-of-passion researchers will infer that there is no significant
deterrent effect.
Walter McManus, Journal of Political Economy, 1985
ln Murder Rates in Philadelphia and Allegheny County (including Pittsburgh)
4
3.5
3
2.5
"Shall Issue" law went into
effect in Pittsburgh but not in
Philadelphia in 1989
2
1.5
1
0.5
0
76
78
80
82
84
Philadelphia
86
Allegheny
88
90
92
94
Executions and Homicide Rates in Texas and New York
45
Executions in Texas
40
35
No executions in New York
for the entire period.
30
25
20
Homicide Rate
in Texas
15
10
Homicide Rate
in New York
5
0
1965
1970
1975
1980
1985
1990
1995
2000
14
Louisiana
12
Murder Rate (2000)
10
8
Texas
Virginia
6
Florida
4
2
Oklahoma
North
Dakota
0
-10
0
10
20
Number of Executions (2000)
30
40
50
Graph A: Homicide Rates in Texas, New York and California
18
16
Texas 289
Executions
14
12
10
New York
no
executions
8
6
4
California
ten executions
2
0
1965
1970
1975
1980
1985
1990
1995
2000
2005
In many quantitative disciplines, most typically econometrics, the
appropriate method is to assume a statistical model, then collect
the data, then test the model by comparing the statistics with the
model. If the model does not fit it is rejected. This is supposedly
"sticking out one's neck," which is presumably the macho Popper
things to do. There are various things problematic with this
prescription… if you follow the prescription, and your data are any
good, your head gets chopped off… people know their head will
get chopped off, nobody follows the prescription. They collect
data, look at their data, modify their model, look again, stick out
their neck a tiny bit, modify the model again, and finally look
around with a proud look on their face and a non-rejected model
in their hand, pretending to have followed the Popperian
prescription. Thus the prescription leads to fraud.
Jam de Leeuw in Trends and Perspectives in Empirical
Social Research