# Counterfactual Averages

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## Counterfactual Averages

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- Lecture number:
- 24
- Pages:
- 2
- Type:
- Lecture Note
- School:
- Cornell University
- Course:
- Econ 3120 - Applied Econometrics
- Edition:
- 1

**Unformatted text preview: **

Econ 3120 1st Edition Lecture 24 Outline of Last Lecture I Dependent Variable Errors Outline of Current Lecture II Counterfactual Averages Current Lecture 2 We can also define what we don t observe counterfactual averages E Y0i T 1 average outcome for individuals facing the policy in the state where they didn t face the policy E Y1i T 0 average outcome for individuals not facing the policy in the state where they faced the policy Now let s return to the regression Yi 0 1Ti ui I showed above that this estimates 1 E Yi T 1 E Yi T 0 or in our new notation E Y1i T 1 E Y0i T 0 Note that if I omit the state of the world in the subscript for Yi you can assume it s the observed state of the world But the way we ve the treatment effect the causal effect on the policy on the treated group is actually E Y1i T 1 E Y0i T 1 Thus we have to assume that E Y0i T 1 E Y0i T 0 Sometimes I call this the critical assumption of causal inference It turns out that this is just a more detailed way of expressing the zero conditional mean assumption E ui Ti 0 E ui T 0 E ui T 1 0 Why Because it turns out that ui represents the actual outcome for the control group and the counterfactual outcome for the treatment group The easest way to see this is a situation where 0 0 so Yi 1Ti ui For the control group ui Yi This is the outcome for the control group in the absence of the treatment For the treatment group ui Yi 1Ti But think about the hypothetical situation where the treatment goup did not get treated the counterfactual Using the model we take the treatment group and set T 0 yielding ui Yi0 So the zero conditional mean assumption that E ui T 0 E ui T 1 is the same thing as E Yi0 T 0 E Yi0 T 1 One way to think about the critical assumption is that there unobserved characteristics in this case the counterfactual that differ between the two groups 2 3 When can we assume that E Y0i T 1 E Y0i T 0 Let s take a simple example Suppose we are interested in whether a college scholarship program increases

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