Causality (introduction)
Lukˊaˇs Laffˊers
Matej Bel University, Dept. of Mathematics
MUNI Brno
11.11.2021
Credibility revolution (Econ Nobel 2021)
https://www.nobelprize.org/prizes/economic-sciences/2021/summary/
Correlation = Causation
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Randomized experiment as a gold standard
Y(1) Y(0)
Randomized experiment as a gold standard
Y( ) Y( )
Randomized experiment as a gold standard
Y(1) Y(0)
Adam 4
Boris 5
Cyril 6
Diana 7
Ema 3
Filip 3
... ... ...
Missing observations
Y(1) Y(0)
Adam 4 ???
Boris 5 ???
Cyril ??? 6
Diana ??? 7
Ema 3 ???
Filip ??? 3
... ... ...
Y(1) Y(0) Y(1)−Y(0)
Adam 4 6 -2
Boris 5 7 -2
Cyril 8 6 2
Diana 3 7 -4
Ema 3 4 -1
Filip 1 3 -2
... ... ... ...
Y(1) Y(0) Y(1)−Y(0)
Adam 4 6 -2
Boris 5 7 -2
Cyril 8 6 2
Diana 3 7 -4
Ema 3 4 -1
Filip 1 3 -2
... ... ... ...
mean 5.1 6.8 -1.6
Y(1) Y(0)
Adam 4 ???
Boris 5 ???
Cyril ??? 6
Diana ??? 7
Ema 3 ???
Filip ??? 3
... ... ...
mean 4.5 6.0
Estimated effect is
4.5 −6.0 = −1.5
We need the intervention to be random.
D ∈ { , }
Y(1),Y(0) ⊥⊥ D
And this is the problem
To answer many many interesting question we simply cannot conduct a
proper experiment
Do veterans have lower wages because of the war?
Does education increase wages?
What is the slope of a demand curve?
How does minimum wage affect unemployment?
Does classroom size affect students’ performance?
Does alcohol consumption increase the probability of a car crash?
Will a job training improve candidate’s chances of getting a job?
Does more information improve market efficiency?
...
Solution nr.1 (?)
Make use of information (X) for prediction of D.
Y(1),Y(0) ⊥⊥ D|X
We compare similar units.
Solution nr.2 (?)
We need a
SOURCE OF RANDOMNESS
Solution (?)
”Quasi-experiment”
D → Y
Z → D → Y
Z → Y
ˆβ =
effect(Z → Y)
effect(Z → D)
ˆβ =
Cov(Y,Z)
Cov(D,Z)
ˆβ =
E[Y|Z = 1]−E[Y|Z = 0]
E[D|Z = 1]−E[D|Z = 0]
Vietnam draft lottery (Angrist, 1990)
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Vietnam draft lottery Z → Y
Is education worth it? (Angrist and Krueger, 1991)
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Is education worth it?
log(wage) = β0 +β1education+β2age+ε
log(wage) = β∗
0 +β∗
1 education+β∗
2 age+β∗
3 ability+ε
ability = γ0 +γ1education+ε
log(wages) = (β∗
0 +β∗
3 γ0)+(β∗
1 +β∗
3 γ1)
β1
education+β∗
2 age+(β∗
3 ε +ε)
Is education worth it?
Is education worth it? Z → D
Is education worth it? Z → Y
Is education worth it?
Results
one year of extra schooling predicts and wage increase in about 7%
Critique
Is the quarter of birth truly random?
The association between the quarter of birth and years of schooling is
only weak.
Demand for fish (Angrist, Graddy and Imbens 2000)
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Demand curve
Demand curve
Demand curve
The effect of minimum wage on unemployment (Card and
Krueger, 1994)
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The effect of minimum wage on unemployment
Classroom size: does it matter? (Angrist and Lavy, 1999)
www.fishownerguide.com
Does classroom size predict students’ performance?
40 students → 1 class
41 students → 2 classes
(Angrist and Lavy, 1999)
Access to information and market efficiency (Jensen,
2007)
Access to information and market efficiency
Access to information and market efficiency
Radioactive fallout
(Almond et al. 2007) (Black et al. 2019)
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Radioactive fallout
Problems
Can we generalize from the sample to the whole population?
The effect can be heterogenous.
Are the ”natural” experiments truly random?
More difficult problems - we need a model
Model as a map
The model should be useful and not true.
Broken experiment
There are many other problems even with proper experiments
People do not respond.
Measurement error.
Sample is too specific.
Conditions has changed.
Qualitative support for causality
Effect is strong.
Effect is consistent.
Effect is specific.
Effect is time consistent.
Effect is monotonous.
Effect is plausible.
Effect is confirmed by an experiment.
Summary
We need a source of randomness
lottery
nature
legislative change
...
Results
are based on models. These could be sensible or less sensible.
we should be critical
relevant for a specific subpopulation.
Despite all these problems
some questions are so important that even an imperfect answer is
better than nothing.
This was the soft intro, now we are ready to start.
References
Angrist, Joshua D. ”Lifetime earnings and the Vietnam era draft lottery: evidence from social security administrative records.” The American Economic Review (1990):
313-336.
Angrist, Joshua D., and Alan B. Keueger. ”Does compulsory school attendance affect schooling and earnings?.” The Quarterly Journal of Economics 106.4 (1991):
979-1014.
Angrist, Joshua D., Kathryn Graddy, and Guido W. Imbens. ”The interpretation of instrumental variables estimators in simultaneous equations models with an
application to the demand for fish.” The Review of Economic Studies 67.3 (2000): 499-527.
Card, David, and Alan B. Krueger. ”Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania.” American Economic
Review 84.4 (1994): 772-93.
Angrist, Joshua D., and Victor Lavy. ”Using Maimonides’ rule to estimate the effect of class size on scholastic achievement.” The Quarterly journal of economics 114.2
(1999): 533-575.
Jensen, Robert. ”The digital provide: Information (technology), market performance, and welfare in the South Indian fisheries sector.” The quarterly journal of
economics 122.3 (2007): 879-924.
Almond, Douglas, Lena Edlund, and M˚arten Palme. ”Chernobyl’s subclinical legacy: prenatal exposure to radioactive fallout and school outcomes in Sweden.” The
Quarterly journal of economics 124.4 (2009): 1729-1772.
Black, Sandra E., et al. ”This is only a test? Long-run and intergenerational impacts of prenatal exposure to radioactive fallout.” Review of Economics and Statistics
101.3 (2019): 531-546.