Economics Problem Set

Instructions: Start each part of the problem set on a new sheet of paper and staple all pages together.

Part I: Data Analysis

This first part of the problem set introduces you to Stata for simple data analysis. For each question, first copy and paste the Stata output into a word-processing document, then type your answer.

Note: There are at least three ways to copy your Stata output into your document:

• Copy the text from Stata into your document, then edit the text to Courier 10 point
• On a Mac: Print the Stata output to pdf ("open PDF in Preview"), then use rectangular selection (in the Tools menu) to copy and paste selected output into your document
• On a Windows machine: Use the "copy as picture" option

Use the dataset , which you can download from D2L. The extract is described in , also on D2L. Note that the extract includes UI claimants from only two of the four treatment groups in the WAWS experiment - the no work search group and the control group.

1. For all UI claimants assigned to the no work test and control groups (together), find the average earnings in the year before the UI claim (that is, the mean for variable earnyr_1). What are the lowest (minimum) and the highest (maximum) pre-claim earnings in the entire sample? (Hint: Use the "sum" command in Stata. The command is sum var1, where var1 is earnyr_1.)

2. How many claimants are in the no work search treatment group? In the control group? What percentage of the claimants are in each group? (Hint: Use the tab command in Stata: tab var1. For example, for the no work test group, type tab group_a.)

3. What were the average earnings in the year before the UI claim of claimants assigned to the no work test group? To the control group? Were the pre-claim earnings of workers in the no work test group smaller or larger than the pre-claim earnings of controls, on average? (Hint: There are at least two ways of doing this. A clunky way is to use the Stata command sum along with an if condition: sum var1 if var2==1, where var1 is earnyr_1 and var2 is group_a. A faster way is to type tab var2, sum(var1), where again var1 is earnyr_1 and var2 is group_a. You should try both methods.)

4. What is the average UI weekly bene?t amount (WBA) of all claimants in the sample? Of claimants assigned to the no work test group? Of claimants in the control group? Was the WBA of claimants assigned to the no work test treatment higher or lower than the average WBA of controls, on average? (Hint: Use the Stata commands you learned in questions 1, 2, and 3. In this case, var1 will be wba, rather than earnyr_1.)

5. What are the sample covariance and correlation between the variables earnyr_1 and wba? What is the sign of the covariance and what does it mean? What is the magnitude of the correlation coef?cient and what does it mean? Why might there be a relationship between pre-claim earnings and the UI weekly bene?t amount? [Hint: For the covariance, use the Stata command corr var1 var2, cov. (Note that cov is an option under the corr command.) For the correlation coef?cient, use the Stata command corr var1 var2 (that is, no cov option).]

Part II: The Summation Operator

Hint for Part II: See Wooldridge, Appendix A-1. For b, remember that anything that does not have a subscript can be treated as a constant and moved outside of the summation operator.

a. Let X₁ = 3, X₂ = -2, and X₃ = 5. Find _i=1∑³(2X₁ + 3).

b. Show that _i=1∑ⁿaX_i = a_i=1∑ⁿX_i, where n is the sample size.

Part III: Statistical Theory

Hint for Part III: See Wooldridge, Appendices C-1 and C-2.

a. Let Y₁, Y₂, Y₃, Y₄, and Y₅ be independent, identically distributed random variables from a population with mean μ and variance σ2. Let  = (1/5)(Y₁ + Y₂ + Y₃ + Y₄ + Y₅) denote the average of these five random variables.

What is the expected value of Y^- (in terms of μ)?

What is the variance value of Y^- (in terms of σ²)?

b. Consider a different estimator of μ:

W = (1/16)Y₁ + (1/16)Y₂ + (1/8)Y₃ + (1/4)Y₄+ (1/2)Y₅

This is an example of a weighted average of the Yi. (Note that the weights sum to 1.) Show that W is an unbiased estimator of μ, just as   is. Find the variance of W.

c. Based on your answers to a and b, which estimator of μ do you prefer,   or W? Explain your answer.

Attachment:- Assignment Files.rar