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ARE 107 Assignment 1

Instructions. This is a group assignment. You have to work with your assigned group. However, each group member has to hand 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.

The problem sets 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 the estimates presented in columns (1)-(4) in words.

(b) Which of the following terms correctly defines the estimates presented in columns (1)-(4) given an outcome Yi,

-YQ =习栏i Yi/no, where individuals i = 1 constitute the subsample of individ

uals without the treatment

- Y¹ = i Yj/ni, where individuals j = 1,...,ni constitute the subsample of individ

uals with the treatment¹

-Y¹ _ W

-s.e.(Y⁰)

-s.e.(V-¹)

-s.e.(Y¹ — Y⁰)

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

1A more precise way to define Y⁰ and Y¹ is Y1 匕(1 一 D^/^₌ Jl 一 DQ and Y¹ = 匕Di, where Di equals one if an individual has the treatment and zero otherwise. Note that n = no + ni and no = £Li(¹ - Di)^{and n}i = 'LLi Di.

(c) For each outcome presented in the table, conduct a 5% t-test of the significance of its average treatment effect, i.e. a t-test of the null hypothesis, Ho : E[Yi《一Yoi\Di = 1] = 0.

III. Using the “Advertising” dataset, which consists of data on sales of computers in different locations as well as advertising spending on TV, radio and newspaper. Run the sample R program (“Advertising_Sample_Program”)provided to you on canvas.

(a) Perform the following regressions:

(i) regress Sales on TV,

(ii) regress Sales on TV and Newspaper,

(iii) regress Sales on Radio

(iv) regress Sales on Radio, TV.

(b) Does the coefficient on TV change in regressions (i)-(ii)? Explain in detail. Perform any additional regressions to support your reasoning.

(c) Does the coefficient on Radio change in regressions (iii)-(iv)? Explain in detail. Perform any additional regressions to support your reasoning.