PUBPOL 5750 Causal Analysis and Impact Evaluation in Public Policy PROBLEM SET 2

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PUBPOL 5750

Causal Analysis and Impact Evaluation in Public Policy

PROBLEM SET 2

Spring 2026

Due 11:59pm, Thursday March 12

1. Taking a Sample of data, examining how estimates compare with the “population” In this problem we will treat the dataset CPS-ASEC-2017.dta as ifit were the population of interest, and imagine what we might estimate if we only had access to small samples from that dataset. In this exercise assume error term is homoscedastic.

a.   (8 points) First, run a regression of WAGE on EDUCATION.

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b.   (8 points) Next, create a dataset which has only the following two variables:

WAGE and EDUCATION.  (use STATA’s “keep” command.)  Then save this dataset with its own name. For example, I might “save ps2prob1.dta , replace”

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c.   (10 points) Next load up the data and take a random sample of 50 observations. You can do this with the commands:

i.   “use ps2prob1.dta , clear”

ii.   “bsample 50”

Summarize the new dataset to confirm you have 50 observations.  Run a regression of WAGE on education.  How do the results compare to the regression from the main sample in a.?

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d.   (10 points) Next, do step 1.c three more times.  Each time you draw a different sample of data, and get different regression output.  Use this output to fill the in the rows corresponding to “Sample 1” through “sample 4” of the Table below. (Fill in the “population” slope row with results from problem 1.c):

N

Population Slope

Population

61,305

Sample

N

Estimated Slope

Estimated Std. Error of Slope

95% CI for slope

1

50

2

50

3

50

4

50

5

200

6

200

7

200

8

200

e.   (8 points) Next, take 4 samples of size 200, in each sample run the same

regression (using education to predict WAGE), and fill in the remaining rows of the table.

f.    (8 points) For the N=50 samples, How do the “estimated” slopes compare to the “true” population slope?  How much variability do they have?  (give a statistical measure of variability)

g.   (8 points) Answer the same questions for the N=200 samples. Additionally, explain how the N=200 samples compare to the N=50 samples?

2. Dummy variables in bivariate regressions. For this problem, return to the main

dataset CPS-ASEC-2017.dta. For this question assume the error term is homoscedastic.

a.   (5 points) Summarize the dummy variable for FEMALE. Describe what the variable means and what the average tells us.

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b.   (5 points) Regress wage on this dummy.  What do the regression results tell us?

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c.   (5 points) Write down the “population line” model that corresponds to this

regression.  What must be true of,!  (the “slope” on FEMALE) in this model if men and women are paid the same?  Test this hypothesis.  Clearly state your hypothesis, show your steps, and clearly state and interpret your conclusion.

(You can implement the test however you would like.)

Model:

What must be true of β2:

Research Hypothesis:

Decision (including the numbers you used to come to your conclusion):

d.   (5 points) Use the regression output to determine the mean wages for men. Check this against a direct measure of the average.

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e.   (5 points) Use the regression output to determine the mean wages for women. Check this against a direct measure of the average.

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f.    (5 points) What does the regression let us do, that we could not easily do with simple summarize commands?

g.   (5 points) Some researchers suppose that the observed differences are due to

differences in education, age, etc.  Select a subsample of those with exactly a

BA/BS degree, and who are aged 25-35.  (use STATA’s “keep if … ” command.) How does the wage gap in this sample compare with the overall wage gap?

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h.   (5 points) In part (g) we were able to “hold constant” education and age by

restricting our sample based on these two variables.  What other variables would you like to “hold constant” when examining the differences in wages for men and women?


2026-03-10