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The Fundamental Problem of Causal Inference Alexander Tabarrok January 2007

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Page 1: The Fundamental Problem of Causal Inference Alexander Tabarrok January 2007

The Fundamental Problem of Causal Inference

Alexander Tabarrok

January 2007

Page 2: The Fundamental Problem of Causal Inference Alexander Tabarrok January 2007
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The Gold Standard• The gold standard is randomization. If units are randomly

assigned to treatment then the selection effect disappears.

• i.e. with random assignment the groups selected for treatment and the groups actually treated would have had the same outcomes on average if not treated.

• With random assignment the average treated minus the average untreated measures the average treatment effect on the treated (and in fact with random assignment this is also equal to the average treatment effect).

• In a randomized experiment we select N individuals from the population and randomly split them into two groups the treated with Nt members and the untreated with N-Nt.

Page 7: The Fundamental Problem of Causal Inference Alexander Tabarrok January 2007

• In a regression context we can run the following regression:

• and Bt will measure the treatment effect. It's useful to run through this once in the simple case to prove that this is true. See handout.

Yi BT Ti i

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Matching

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Propensity Score0 1

E(Wages| _)Union

Non-Union

Wages of Union and Non-Union Members Against PropensityScore (Prob. of belonging to Union)

Effect of Observableson Wages for UnionMembers

Effect of Observableson Wages for NonUnion Members

TreatmentEffect

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The circle labeled "earnings" illustrates variation in the variable to be explained. Education and Ability are correlated explanatory variables and Ability is not observed. The blue area within the instrument circle represents variation in education that is uncorrelated with Ability and which can be used to consistently estimate the coefficient on education. Note that the only reason the instrument is correlated with Earnings is through education.

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Instruments in Action(Angrist and Krueger 1991)

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Instrumental variables with weak instruments and correlation with unobserved influences.

Bias in the IV estimator is determined by the covariance of the instrument with education (blue within instrument circle) relative to the covariance between the instrument and the unobserved factors (red within instrument circle). Thus IV with weak instruments can be more biased than OLS.

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Prison Population (1000s) Violent Crime Rate

Violent Crime Rate is violent crimes per 1000 pop over the age of 12Source: Bureau of Justice Statistics, http://www.ojp.usdoj.gov/bjs/

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From Did Securitization Lead to Lax Screening? Evidence From Subprime Loans (Benjamin J. Keys, Tanmoy Mukherjee, Amit Seru, Vikrant Vig)

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1093137

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