Calculate the average treatment effect of the policy E(T) using a simple difference in means.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. Randomization. This analysis will use the Dehijia and Wahba sample from the Lalonde dataset of the NSW experiment. The dataset is lalonde_nsw.csv. The outcome variable is re78 (real earnings in 1978). The treatment indicator is treat. The remaining variables are potential covariates. Assume for the purposes of this problem set that treat is completely randomly assigned.

(a) Calculate the average treatment effect of the policy E(T) using a simple difference in means. (b) Calculate the average treatment effect on the treated of the policy E(T; treat = 1). How does it compare to part a?

assume the treatment count would you do not need to fully do every

(c) Test the null of T = 0 for all i using a randomization test. N.B. Hold fixed the number of treated and control (e.g. be held fixed) and permute the labels randomly 1000 times permutation (there would be too many). Report the quantile that your estimate from the previous question falls.

2. Propensity Scores. We use lalonde_psid.csv. The new dataset is a sample of observations from the Panel Survey of Income Dynamics that can be used as alternative control observations. Importantly, these observations were not in the initial randomization.

(a) Using age, education, hispanic, black, married, nodegree, RE74 and RE75, construct a propen- sity score using the treated group in lalonde nsw.csv and the control sample of lalonde psid.csv. Use a logit regression model to do so. Report the average p-score for the treated and control samples, and plot the propensity score densities for the treatment and control groups.

(b) Compare the ATE in the previous question to the treatment effect estimated using a linear regression using the NSW treatment samples and PSID, with age, education, hispanic, black, married, nodegree, RE74 and RE75 as controls

(c) Using your p-score estimates, calculate the IPW and SIPW estimate for control and treated mean of the outcome, and the average treatment effect

3. Quantile Regression. This analysis will use the dataset lalonde_psid.csv.

(a) Do Quantile regression with dependent variable Y being re78 using the PSID dataset for X = education, for T = (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)

(b) Plot the coeffients with confidence intervals.

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