[t,re78,education,re74,re75]
ans =
For this problem set use the Lalonde experimental data set (the Dehejia-Wahba version of these data) in the file lalonde experimental.txt. The data set contains 445 observations on five variables, t, the binary treatment indicator, re78 (earnings in 1978, the outcome), re74, earnings in 1974 (prior to the program), re75, earnings in 1975 (prior to the program), and educ, years of education. The earnings measures are in thousands of dollars. We focus on estimating the average effect of the treatment on 1978 earnings.
Estimate the average effect as the difference in means for the two groups, using the robust standard errors, and using the bootstrap.
Estimate the average effect of the treatment by first estimating the conditional expec-tation of Yi (0) and Yi(1) given Xi , and then averaging the di ff erence. You may use a linear model for the conditional expectation. Use the bootstrap to get standard errors.
Estimate the average effect by inverse propensity score weighting. Use a logistic model for the propensity score, and make sure you normalize the weights. Use the bootstrap to get standard errors.
Use the doubly robust estimator and use the bootstrap to get standard errors.
Assuming homoskedasticity, estimate the semiparametric e ffi ciency bound. Compare those to the standard errors in the previous parts.
Imbens, Problem Set IV, MGTECON640/ECON292 Fall ’18
2
Do a small simulation study, where you take the estimates of the conditional mean and the propensity score from the previous parts as the data generating process. Use normal homoskedastic errors. Keep the covariates in the simulations identical to those in the data. Compare the performance of the three estimators in parts 2-4, and compare their performances to what the semiparametric efficiency bound suggests.
