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Homework on matching/causality
Due: Dec. 10, 2007

Use the Gilligan et al data as in the lab. Use the programs discussed
in the lab. For your DV use duration of peace. For the purposes of
this homework, use linear methods, that is, do OLS and not duration modeling.

1. Precisely state a causal hypothesis in terms of counterfactuals.

2. What is the "naive" (no balancing) estimator of the average treatment effect? 

3. What is the (linear) regression estimator of the average treatment
   effect (no balancing)?

4. Calculate propensity scores by hand (using logit). Put in what you
   think needs to be put in.

5. Compare the result with King's propensity scores (plotting is
   good). How close are the results? Any big differences?

6. Use matching (balancing on the propensity scores) to estimate the
   average treatment effect. (Do not use a caliper for this.)

7. Repeat with a reasonable caliper. (What gets dropped by this caliper?)

8. Repeat but use nearest neighbors (Mahalanobis distance).

9. Repeat but use genetic matching.

10. Visusally inspect and compare the matches.

11. Compare 2, 3, 6, 7, 8 and 9 results. What differences do you observe?