ECON 628 – 3^rd Empirical Assignment

Due on Tuesday, November 29 2005

This is a follow-up on the first assignment based on Lalonde’s data. The goal of this assignment is to use propensity score and matching methods to compare experimental and non-experiment estimates of the impact of training programs on earnings. For this assignment, simply focus on “PSID-1” as the (non-experimental) control group. There is no need to perform the below analysis using the experimental control group.

1. Estimate the propensity score using a logit model and compare the distribution of the propensity score for the treatment and control group using an histogram.
2. Now use the propensity score to estimate the treatment effect using regression methods. First, estimate a regression model without interaction terms between the propensity score and the treatment dummy. Do you find that a cubic specification for the propensity score is adequate or do you need higher order terms? Second, estimate a model with interactions between the propensity score and the treatment dummy. For the cubic model, do you reject the more restrictive model without interactions? Finally, compute the “treatment effect for the treated” and the ATE (assuming that PSID-1 represents the whole population) in the model with interactions. Do you get different treatment effects for these two groups? Discuss.
3. Dehajia and Wahba use various “matching” methods to estimates that ATE. There are now several programs available in Stata to perform matching estimation in practice. In particular, the “match” procedure is available on Guido Imbens home page at http://emlab.berkeley.edu/users/imbens/estimators.shtml. Other procedures, including a propensity score matching approach (psmatch2), are also available on the web. Using one of the available approach (or an algorithm of your own!), estimate the ATE using a matching approach and compare your results with those obtained using the above regression approach.
4. An alternative and simpler (in my view) estimator is based on re-weighting observations using the propensity score. Let p(x) be the propensity score. Reweighting the control group by p(x)/(1-p(x)) yields a counterfactual sample that now has the same distribution of the propensity score as the treatment group. The treatment effect (on the treated) can now be computed as a simple difference in mean outcomes between the treatment group and this counterfactual group. Similarly, reweighting the treatment group by (1-p(x))/p(x) yields a counterfactual sample that now has the same distribution of the propensity score as the control group. It is then easy to compute the ATE by assuming, as in 2, that PSID-1 represents the whole population. Use the reweighting approach to compute the treatment effect on the treated and the ATE, and compare your results to those in 2.
5. Use the reweighting approach to compute the effect of the training programs on the distribution, as opposed to just the mean, of log earnings. First compute the effect of the treatment on the variance of log earnings. Then compute the 10^th, 25^th, 50^th, 75^th, and 90^th centiles of log earnings and show the impact of the treatment at each of these points in the earnings distribution. Finally, compute kernel density estimates of the distribution of log earnings for the treatment and the (reweighted) control group using the “kdensity” procedure in Stata.