The Art and Science of Cause and Effect Adapted from a lecture by Judea Pearl available on his WEB site: TURE/lecture_sec1.htm.

The Art and Science of Cause and

Effect

Adapted from a lecture by

Judea Pearlavailable on his WEB site:

http://singapore.cs.ucla.edu/LECTURE/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

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

"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

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 ResponsiveCommunity 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, rational-maximizer, 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)

0

0.5

1

1.5

2

2.5

3

3.5

4

76 78 80 82 84 86 88 90 92 94

Philadelphia Allegheny

"Shall Issue" law went into effect in Pittsburgh but not in Philadelphia in 1989

Executions and Homicide Rates in Texas and New York

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5

10

15

20

25

30

35

40

45

1965 1970 1975 1980 1985 1990 1995 2000 2005

Executions in Texas

Homicide Ratein Texas

Homicide Ratein New York

No executions in New Yorkfor the entire period.

0

2

4

6

8

10

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14

-10 0 10 20 30 40 50

Number of Executions (2000)

Mu

rder

Rat

e (2

000)

Texas

Louisiana

Oklahoma

NorthDakota

Virginia

Florida

Graph A: Homicide Rates in Texas, New York and California

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2

4

6

8

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18

1965 1970 1975 1980 1985 1990 1995 2000 2005

Texas 289 Executions

New York no executions

Californiaten executions

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