Econometrics Problem Set #2

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Econometrics

Problem Set #2

Instructions

· Please submit your answers on Canvas

· You may work together in groups of up to four students as long as you each submit your work to Canvas and list group members at the top of the document.

· Please include your do file and log file (or rmd file) for Topic 4 in your problem set submission. Be sure to include selected Stata/R output (you may copy and paste) as indicated in the questions and answer all questions in one document.

Topic 1 – Omitted Variable Bias (OVB) in the News

We would like you to use the concept of omitted variable bias (OVB) that you learned in class to read and critically assess study findings.  Read the NYT article “Men Beware: The Dangers of Snow” (https://www.nytimes.com/2017/02/13/well/live/men-beware-the-dangers-of-snow.html).

1. What is the key question the study described in the article is trying to answer? What is the outcome of interest in the study? What predictor variables were included, according to the article?

2. The authors of the study believe that the spike in hospital admissions and heart attack deaths for men after snowstorms is due to snow shoveling. We can think about snow shoveling as an omitted variable in this model, and consider the bias introduced by this omission. Imagine regressing heart attack deaths on a given day (heartattack) on the number of inches of snow (snowinch) and percentage of local residents who shoveled snow (shovelpct) the previous day. What do you expect the sign of the coefficient on shovelpct to be, if the study’s authors are correct in their hypothesis?

3. What do you expect the sign of the correlation between snowinch and shovelpct to be?

4. Given your answers in 2. and 3., what do you expect the sign of the bias in the coefficient on snowinch in the short regression of heartattack on snowinch to be? Is the coefficient in the short regression likely to be an overstatement, an understatement, or incorrectly signed?

Topic 2 – More Practice with OVB

Recall that the sign of the bias in the coefficient on when omitting in the estimation of the regression: can be summarized in the table below.

Describe an example of the case illustrated by the upper right quadrant of the table (, ). Assume you would like to estimate but for some reason must omit from the regression. Feel free to draw on examples from class, but do not copy directly.

1. Describe clearly the hypothetical variables , , and .

2. Explain why you would expect the sign of the correlation between and to be negative.

3. Explain why you would expect the sign of to be positive.

4. Indicate how you know what the sign of the bias would be if you were to omit from the regression.

5. Indicate how your estimated is likely to change when omitting from the regression. Will it be larger or smaller in absolute value relative to the estimate you would get from the full regression (with both and as explanatory variables)? Is it likely to be overstated, understated, or incorrectly signed? In one to three sentences each, explain your reasoning in terms a policymaker can understand.

Topic 3: Michelle Rhee’s IMPACT Case Study

Recall the IMPACT case I posted here. You are a teacher in DC and are told IMPACT has determined you are an ineffective teacher. Which of these two arguments is a better defense of your teaching skills? Explain in terms of omitted variable bias. (HINT: You want to focus on what is and what is not controlled for in the regression in Exhibit 1 – shown on page 13 of the case study).

1. I had an unusually large number of students this past year with learning disabilities.

2. A fire alarm went off during the exam this year.

Topic 4 – Binary Dependent Variables

Download the data set burkinafaso.dta, which contains demographic and health data on 699 individuals in Burkina Faso from the DHS (Demographic and Health Surveys). The data includes information about HIV status for a quasi-representative sample of the adult population in Burkina Faso, and can be used to analyze the socioeconomic correlates of HIV infection and associated sexual behaviors.

1. Linear Probability Model

a. Run a regression that represents a linear probability model of the variable hivpositive on the variables wealth_index, catholic, secondary_educ, age_at_first_sex, and rural. (Note: The variable wealth_index reports an individual’s quintile ranking relative to the population. For the purposes of this problem, you can consider it a rough proxy for income). Use the “robust” option. Report your results by copying and pasting the Stata regression output into your solutions.

b. What does the coefficient on the dummy variable catholic tell you?

c. What does the coefficient on the dummy variable rural tell you?

d. Test the null hypothesis that living in a rural area has no effect on HIV status.

e. Calculate the predicted probability of having HIV for a Catholic with a wealth index of 2 and whose first sexual experience was at age 15, with all other characteristics at the sample averages based on the model in 1.a.

2. Probit Model

a. Now use a probit model to estimate the same model as in question 1 and answer the same questions (a.-e.) Can you interpret the coefficients? If not, what can you say?

b. For 1.b. and 2.b., do the linear and probit models give you consistent answers?

c. Now we’d like to predict the marginal effects at different points in the distribution. Calculate marginal effects using the mfx command for Catholics living in an urban area, with all other predictor variables set to their mean values. The below code (general form) should help

mfx, at([var1] = [value], [var2] = [value])

You can also use the margins command, if you prefer. Report your results by copying and pasting the Stata output into your solutions.

d. Interpret the results that you found in 2c. Is the marginal effect of the catholic variable consistent with your answer to 1.b. and 2.b.? Describe what these three estimates each tell you.