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Homework on matching/causality
Due: April 9, 2008

Use the Gilligan et al data. 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 propensity scores estimated with 'pscore' in Stata. 
   How close are the results? Any big differences?
     
6. Use matching (balancing on the propensity scores) to estimate the
   average treatment effect.

7. Visusally inspect and compare the matches.

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