1.) We’ll plot some ROC curves using the spam example from lec03--regression .nb .html. You can use the R function for plotting ROC curves, uploaded to Blackboard.

a.) Estimate the logit specification from the lecture notes on the full data set (you can just copy the code from the lecture). Plot an ROC curve for classifying spam vs not-spam from this logit regression.

b.) Plot an out-of-sample ROC curve by estimating the same logit specification on 4/5 of the data (sampled randomly), and evaluating classification error on the remaining 1/5 of the data.

2.)  The data set dw_data .csv is taken from Dehejia and Wahba1 .  It contains data on individuals who participated in a job training program (for whom treated equals TRUE) and “control” individuals from the PSID (for whom treated equals FALSE). Additional variables are:  age, education, Black (1 if black, 0 otherwise), Hispanic (1 if Hispanic, 0 otherwise), married (1 if maried, 0 otherwise), RE74 and RE75 (earnings in 1974 and 1975), UE74 and UE75 (indicator for unemployment in 1974 and 1975), and RE78 (earnings in 1978).  The training program was done before 1978, so the last varible is post-training earnings.

a.) Estimate a linear model with constant treatment effects by regressing RE78 on the treatment indicator and the remaining variables.  Report the estimate of the average treatment effect from this regression (using the assumptions of selection-on-observables and correct specification of this regression).

b.) Add interactions of the treatment indicator with the remaining variables to the regres- sion in (a). Compute an estimate of the average treatment effect from this regression (using the assumptions of selection-on-observables and correct specification of this re- gression).

c.) The data set dw_experimental_data .csv includes both the treated observations in the dw_data .csv data set and a set of true control individuals, such that treatment was randomized among this population. Parts (a) and (b) can thus be considered an attempt to recover the outcome of this experiment using observational data where a true control group is not available.

Using the data set dw_experimental_data .csv, estimate the average treatment effect by taking the difference in means between treated and control groups.  Is the answer similar to (a) and (b)?