and Econ120C
Econ120C
Econ120C
Correlation Causality
Motivation
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Why do we care about beta ?
Econ120C
Consider the model
y = x*beta + u
In the last two lectures, we show that the OLS
estimator of beta enjoys some nice properties:
consistency and asymptotic normality.
Some students may know that OLS is BLUE (Best
Linear Unbiased Estimator).
But why do we care the value of beta in the model?
Often we say that beta is the effect of a one unit
change in x on y.
Why do we care about beta?
Econ120C
Econ120C
Suppose that we run a regression based on
y = x*beta + u
and get a statistically significant coefficient beta_hat = 5.
Can we say that one-unit change in x causes five-unit
change in y.
No. Regression alone can only establish the
correlation or association between two variables.
Correlation or association
Predict the future v.s.
predict the effect of interventions
Econ120C
Econ120C
Correlation or association can be used to predict the
future.
Econ120C
To predict the future, we just want the best currently
available predictors dont worry about causality.
Number of people carrying umbrella (X)
Probability of Raining (Y)
Even if X does not cause Y, we can still use X to
predict Y if the two variables co-vary.
So covariance helps predict the future. beta* =
Cov(X,Y)/Var(X) is for this purpose.
But most often in policy analyses, we want to
investigate whether X causes Y. This is necessary to
predict the result of policy changes and interventions.
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Predict the future v.s.
predict the effect of interventions
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Importance of Causal Knowledge
Econ120C
Econ120C
To predict the future, we are the passive observer and we
do not control the changes in the predictors.
If we observe that more people are carrying umbrellas,
then we predict that it is more likely to rain.
To predict the effect of interventions, we are the active
participant in the sense that we set the changes in the
predictors.
If we force more people to carry umbrellas, would this
change the probability of raining?
To predict the effect of interventions, we need to establish
the causal relationship between variables
Econ120C
Scientist/Engineers use causal knowledge to make things work
Economists use causal knowledge to design
better policies or institutional arrangements
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Econ120C
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Econ120C
If social scientists / economists have wrong causal
models, millions of people may die.
If social scientists / economists have wrong causal
models, millions of dollars may be wasted.
If scientists/Engineers have wrong causal
models, they will blow up their labs
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Econ120C
Econ120C
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Example 1: Hot Chocolate
Econ120C
A strong correlation has been found in a certain city in the
northeastern United States between weekly sales of hot
chocolate and weekly sales of facial tissues.
Alternatively, if you regress weekly sales of facial tissues on
weekly sales of hot chocolate, you find a statistically
significant relationship.
Correlation Does Not Imply Causation
Would you interpret that to mean that hot chocolate causes
people to need facial tissues? Explain.
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Example 2: TV
Econ120C
Econ120C
You will find a statistically significant relationship if
you regress the average life expectancy on the number
of TVs/person using cross country data.
Correlation Does Not Imply Causation
Econ120C
Econ120C
A Silly Correlation: Hot Chocolate
List of weekly tissue sales and weekly hot chocolate
sales for a city with extreme seasons would probably
exhibit a correlation because both tend to go up in
the winter and down in the summer.
Could we lengthen the lives of people in Rwanda by
shipping them more TVs?
Data from an observational study,
in the absence of any other evidence, simply cannot
be used to establish causation.
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Correlation Does Not Imply Causation
Econ120C
A Silly Correlation: TV Example
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Reasons of correlation (1)
Econ120C
X is the direct cause of Y
Omitted variable: wealth of the nation
Rich nations: more TV sets.
Rich nations: longer life expectancies because of
better nutrition, clean water, and better health care.
There is no cause-and-effect tie between TV sets and
length of life.
:
:
X
Causal Link
Correlation
Y
Examples:
X: Amount of fertilizer. Y: yield of corn
X: Weight of a car; Y: Mileage per Gallon
X: Dosage of a drug; Y: the survival rate of the mice
Again: data from an observational study,
in the absence of any other evidence, simply cannot
be used to establish causation.
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Reasons of correlation (2)
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Econ120C
Reasons of correlation (3)
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Econ120C
Mutual Causality (Simultaneity)
Y is the direct cause of X
X
X
Y
Y
Ex 1: X = advertising expenditures and
Y = occupancy rates for hotels.
Examples: Examples on the previous slide
but switch X with Y.
Ex 2: X = Police Spending
Y = Crime Rate.
If you run the regression by OLS
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Reasons of correlation (4)
Econ120C
Y
Z
Reasons of correlation (5)
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Econ120C
Both variables are changing over time.
Nonsensical associations result from correlating two
variables that have both changed over time.
Omitted Variable problem
X
Crime Rate = + Police Spending + u, you will find
that >0. (More police spending, more crime?)
X: Yrs of Schooling
Y: Hourly Salary
Z: Innate Ability
Example: weekly sales of facial tissues on weekly sales of hot
chocolate
X: life expectancy
Y: TVs/person
Z: Richness of the country
Causes responsible for one variable being high (or low)
are same as those responsible for the other being high
(or low).
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Reasons of correlation (5)
Econ120C
Econ120C
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Spurious Regression:
(Clive Granger, Nobel Prize Winner in Economics)
If you regress a random walk on another independent
random walk, you will find a statistically significant
relationship if you use standard regression methods.
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Correlation Does Not Imply Causation
Econ120C
A correlation between two variables x and y can
reflect many types of relationship among x, y, and
one or more omitted variables.
A correlation between a predictor x and a
response y, even if it is very strong, is not by itself
good evidence that changes in x actually cause
changes in y.
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Karl Pearson and correlation coefficient
Econ120C
Econ120C
Pearson invented the
correlation coefficient
He never talked about
causation, only about
correlation and
association between
variables.
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Econ120C
Econ120C
Establishing Causation
Econ120C
Scientists establish causality by holding other relevant factors
constant so they then can focus on the unique effects of a given
factor in a complex causal situation.
In order to formulate a causal relationship, it is usually
necessary to rule out factors which interfere with the
relationship.
Ceteris Paribus is a Latin phrase, meaning "all other things
being equal."
Experimentally, the ceteris paribus assumption is realized when
a scientist controls for all of the independent variables other
than the one under study, so that the effect of a single
independent variable on the dependent variable can be isolated.
Establishing Causation
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Establishing Causation
Econ120C
To evaluate the effectiveness of a drug, we hope that
we have two identical persons one takes the drug
and other does not.
By definition, all variables for the identical
persons two are the same. The only difference is that one
takes the drug and the other does not.
Any difference in the outcome of interest (for
example, blood pressure) must be caused by the drug.
This is exactly how we learn causality in every day
life.
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Establishing Causation
Econ120C
Treatment Group: Individuals who receive
treatment
Control Group: Individual who receive no
treatment or receive the placebo treatment.
Treatment is defined in general terms.
The importance of having a control group.
Example: Does everyone like to eat nails?
Example: Does everyone like to eat nails?
Econ120C
Econ120C
Econ120C
What does a magnet stick to?
Basic Science:
(i) A magnet only sticks to stuff with iron (fe) in it.
(ii) Anything that sticks to a magnet has the same
element fe in it.
On the pack of a Total Cereal, "iron, 100 percent"
is on the list of ingredients.
Cereal with iron fortification
By the way, a common fortified food is milk
(fortified with vitamin D)
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Example: Does everyone like to eat nails?
Econ120C
Is the iron (fe) in Total cereal the same iron as in the
nails?
Let smash some Total cereal and put a magnet on top
of the powder.
It sticks!
Perhaps
The importance of having a control group -- in this
case a box of cereal without the iron fortification.
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Establishing Causation
Econ120C
But it is impossible to find two identical persons.
(Some times econometricians use twins to ensure
certain crucial variables are approximately the same)
So what can we do?
To overcome the difficult, we change our goal
slightly. Instead of evaluating the causal effect for a
given individual, we ask: what is the average
treatment effects (ATE) for a group of individuals?
We try to make two groups of individuals look the
same
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Establishing Causation
Econ120C
Econ120C
We try to make two groups of individuals look
the same in a statistical sense.
The only legitimate way to try to establish a causal
connection statistically is to make all other things
statistically equal.
This can be achieved through the use of
randomized experiments.
Establishing Causation
Econ120C
Randomized experiments: participants are randomly
assigned to two groups. The group that receive the
treatment (are affected by the policy) is called the
treatment group. The group that do not receive the
treatment is called the control group.
Randomization eliminate the impact of confounding
variables because there is no systematic difference in those
variables across the two groups.
Since the only systematic difference between the two
groups is the treatment, the difference in the outcome is
caused by the treatment.
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Randomized Experiment
Econ120C
Randomized Experiment
Econ120C
Fisher found the data from experiments that had been going on for
decades to be basically worthless because of poor experimental
design.
Sir Ronald Fisher was sent
to Rothamsted Agricultural
Station in the UK to
evaluate the success of
various fertilizer treatments
Fertilizer had been applied to a field one year and not in another
in order to compare the yield of grain produced in the two years.
BUT
It may have rained more, or been sunnier, in different years.
The seeds used may have differed between years as well.
Sir Ronald Fisher invented
the randomized experiment.
This is the only
scientifically proven
method of testing causal
relations from data.
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Ronald Fisher: The father of statistics
The F test is named after him
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Or fertilizer was applied to one field and not to a nearby field in
the same year. BUT
The fields might have different soil, water, drainage, and
history of previous use.
Too many factors affecting the results were uncontrolled.
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Randomized Experiment
Econ120C
Econ120C
In the same field and same year,
apply fertilizer to randomly spaced
F
F
F
FF
F
FF F
F
FF
F
plots within the field. Analyze plants
FF FF
from similarly treated plots together.
F
F
This minimizes the effect of variation
FF
F
of drainage and soil composition within
F
the field on yield as well as controlling
F
F
FF
FFFF
F FF
F
New York Times : March 29,2007
Econ120C
Seeking new solutions to New Yorks vexingly high
poverty rates, the city is moving ahead with a bold
antipoverty experiment that will pay poor families
up to $5,000 a year to meet targets like
exemplary school attendance, going for
medical checkups or holding
down a full-time job, Mayor
Michael R. Bloomberg said
today.
F
for weather.
F: fertilizer
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New York Times : March 29,2007
Econ120C
Under the program, which is based on a similar
effort in Mexico but is believed to be the first of its
kind in the nation, families would receive
payments every two months for meeting any of
20 or so criteria per individual. The payments
would range from perhaps $25 for an elementary
school students attendance to $300 for greatly
improved performance on a standardized test,
officials said.
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New York Times : March 29,2007
Econ120C
Conceived as an experiment, the program, first
announced last fall and set to begin in
September, is to serve 2,500 randomly
selected families whose progress will be
tracked against another 2,500 randomly
selected families who will not receive
the assistance.
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Econ120C
Econ120C
Hot Disputes
Debating Causality
Econ120C
Does gun control reduce violent crime?
Does living near power lines cause cancer?
Does the use of fossil fuel cause global warming?
Does smoking cause lung cancer?
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Does smoking CAUSE lung cancer? Econ120C
Econ120C
causation: smoking causes lung cancer.
common response (Omitted Variable): people who
have a genetic predisposition to lung cancer also have
a genetic predisposition to smoking.
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Does smoking CAUSE lung cancer? Econ120C
Econ120C
confounding: people who drink too much, don't
exercise, eat unhealthy foods, etc. are more likely to
get lung cancer as a result of their lifestyle. Such
people may be more likely to be smokers as well.
Smoking
Smoking
Lung Cancer
Lung Cancer
certain life
style
Genetics
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Does smoking CAUSE lung cancer?
Econ120C
Econ120C
Econ120C
1969 Warning: The Surgeon General Has Determined That Cigarette
Smoking Is Dangerous to Your Health."
More Recent: SURGEON GENERALS WARNING: Smoking Causes
Lung Cancer, Heart Disease, Emphysema, and May Complicate
Pregnancy.
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Does smoking CAUSE lung cancer? Econ120C
Econ120C
It is now proved beyond doubt that
smoking is one of the leading causes of
statistics.
--------- Fletcher Krebel
Reader's Digest (December 1961)
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The Bottom Line
Econ120C
Econ120C
Causality is a difficult concept.
Equations Arent Enough.
But we cant 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.
Importance of subject knowledge: Economics
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Econ120C
Econ120C
A book on Causality
Econ120C
"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, UC Berkeley, Professor of
Statistics
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Hot Debate
Econ120C
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