Instructions.  This is a group assignment.  You can work with a group of up to four people. However, each group member has to turn in their own individual write-up to the answers to all questions. Copying and pasting answers, even from your group members, is considered plagiarism. In addition to the write-up, you have to include the R programs you use for the computational components.

These assignments are meant to help you understand the material. If you have any questions, please come to the instructor or TAs.

Note: Some of the problems here are from www.masteringmetrics.com.

I.  Consider the following in-class exercises:

- Exercise 2 in Lecture 2

- Exercise 2 in Lecture 3

- Exercise 3 in Lecture 3

- Exercise 5 in Lecture 4

Present your answer to each of the four exercises listed above and explain in words how you derived each of the results.

II. Table 1.5 in Mastering ‘Metrics presents the results for different outcomes from the Oregon Health Plan experiment.

(a) Explain in words the estimates presented in columns (1)-(4).

(b) Which of the following terms correspond correctly to estimates presented in columns

(1)-(4) given an outcome Yi ,

- 0  ✏ ➦1 Yi/n0 , where individuals i ✏ 1, . . . ,n0  constitute the subsample of individ- uals without the treatment

- 1  ✏➦ Yj /n1 , where individuals j ✏ 1, . . . ,n1  constitute the subsample of individ- uals with the treatment1

- 1 ✁ 0

- s.e.(0 )

- s.e.(1 )

- s.e.(1 ✁ 0 )

where s.e. denotes the standard error of the estimator in the parentheses?