Interpreting Regression Results

Final Exam Study Guide
IA. Empirical Research Questions – Interpreting Regression Results: A randomly selected 2 out of
following 4 questions will appear on the exam for you to answer. All questions will remain the same
in content and structure, but variables in the regression and specific numbers will change for the exam.
Use the regression equation and table of results below to answer the questions below. The dependent
variable is the average 4th-grade test score for a school district, i, where the test is measured in points
out of 800. The independent variable STR refers to the student-teacher ratio in elementary schools in
the district (i.e., the number of students per teacher, which on average is about 20). Non-English is the
percent of non-native English speakers attending elementary schools in the district, which on average is
about 0.16. Free Lunch is the percent of elementary school students who are eligible for free lunch in
the district, which on average is about 0.25. The variable ln(Avg Income) is the natural logarithm of the
average income in the district.
Scorei = β0 + β1(STR)i + β2(Non-English)i + β3(Free Lunch)i + β4ln(Avg Income)i + i
Table 1: Dependent variable = Average Test Score in the District
OLS
Student-Teacher Ratio -0.73
(0.26)
Percent Non-Native English Speakers -1.76
(0.34)
Percent Eligible for Free Lunch -3.98
(0.33)
ln(Average District Income) 11.57
(1.81)
Intercept 658.6
(8.6)
Observations 420
R
2 0.73
Table Notes: The regression is Ordinary Least Squares. Standard errors are in parentheses below each
coefficient estimate.
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1. Consider the above regression equation and regression results reported in Table 1. In a sentence,
interpret the marginal effect of a one-percentage point increase in the number of students eligible for free lunch on the average district test scores. Is this effect statistically significant at the
5-percent level? Using the statistics, explain how you know this.
2. Consider the above regression equation and regression results reported in Table 1. Calculate the
marginal effect of adding ten more students per teacher (i.e., increasing the student-teacher ratio
by 10) on average district test scores? Is this effect statistically significant at the 5-percent level?
Using the statistics, explain how you know this.
3. Consider the above regression equation and regression results reported in Table 1. In a sentence,
interpret the marginal effect of average district income on average test scores. Is the effect statistically significant at the 5-percent level? Using the statistics, explain how you know this.
4. What percent of the variation in the dependent variable is explained by the regression model.
Briefly explain how you know this.
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IB. Empirical Research Questions – Research Methods: A randomly selected 1 of the next 4 questions
will appear on the exam.
1. Suppose you wanted to answer the following research question: Are students who graduate from
private colleges/universities more successful in the labor market than graduates from public colleges/universities?
(a) What would be your dependent variable? Be specific in your answer regarding a measurable
variable.
(b) What would be your key independent variable? Be specific in your answer regarding a
measurable variable.
(c) List 3 other independent variables you would need to control for. And, briefly state why
these are important to control for.
(d) What type of data (time series, cross sectional, or longitudinal) would you want? And, what
would be your unit of observation?
(e) List one concern, if any, that you might have with interpreting the coefficient estimate on
the key independent variable as a casual effect on the dependent variable? Briefly explain
your answer.
2. Consider the issue of causality.
(a) Briefly explain the difference between correlation and causality.
(b) Provide 1 possible threat to (i.e., potential problem with) interpreting a regression coefficient
estimate as a causal effect.
(c) Provide a clear and specific example of a regression equation that might suffer from this
problem, and briefly explain how your example illustrates this problem.
(d) Provide 1 possible solution to this problem, and amend your regression equation from (c) to
implement this solution.
3. Suppose you have a sample of children ranging from 5 to 18 years of age. You estimate a simple
regression of math scores on height and get a statistically significant positive coefficient estimate.
Your research assistant concludes that height has a causal effect on mathematical ability – being
taller makes children better at math. Bad luck for everyone who is short. Would you agree with
your research assistant’s interpretation of the regression results? If so, explain why. If not, offer a
more likely explanation for the positive correlation and suggest how you could alter your regression model to address this.
4. Select the type of data set you want to discuss for this question (clearly circle your choice):
Cross-sectional data / Time series data / Longitudinal (panel) data.
(a) Provide a concrete example of this type of data.
(b) List one possible concern for the error terms from an appropriate regression using this type
of data.
(c) List one method of statistically testing for this concern in your error terms.
(d) Briefly describe how you would interpret the results of this test. Specifically, what would
you look for to indicate the presence of the concern listed in part (b)?
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II. Current Policy Issues: A quasi-randomly selected (i.e., no more than one per topic) 2 of the next
10 questions will appear on the exam and you must answer both of them. All answers should be clear
and to the point. You will have an opportunity to upload pictures of hand-drawn, well-labeled, graphs,
equations, other work as needed to support your answers.
1. Based on the reading and class discussion, what are the three key criteria of effective fiscal stimulus. Briefly discuss the extent to which major components of the American Rescue Plan meet this
criteria. Be concrete and specific in your answer.
2. Olivier Blanchard writes, that some economists (himself included) support fiscal stimulus but
have “misgivings about the size of the Biden adminstrations’s $1.9 trillion coronavirus relief
plan.” Based on the reading and class discussion, briefly summarize his key concern, and provide a clear economic explanation for why he thinks the relief package will likely generate this
concerning outcome.
3. Suppose scientists estimate the global economic cost 50 years in the future of allowing a 2
o Celsius increase in global temperatures to be $70 trillion. (i) Assuming a discount rate (or interest
rate) of 2%, what is the present value of that future cost? (ii) Based on the reading and class
discussion, briefly discuss how this information might relate to current policy considerations.
4. Two of the most commonly discussed solutions to curb carbon emissions are cap-and-trade programs and carbon taxes. (i) Briefly explain each of these policies and how they aim to reduce
carbon emissions. (ii) Based on the reading and class discussion, provide one potential benefit
and one potential cost to each of these policies. Briefly justify your predicted costs and benefits
based on economic theory.
5. Briefly explain 2 key financial risks of climate change highlighted in the assigned IMF report. For
each, briefly discuss an appropriate fiscal, monetary, or private sector policy that could be taken
to mitigate these risks. Justify your answer using economic theory.
6. (i) Based on the reading and class discussion, briefly discuss 2 key factors that researchers believe
have contributed to rising inequality in the U.S. since the 1970’s. (ii) Provide a clear economic
argument for or against reducing inequality, while acknowledging at least one valid counter-point
to your argument.
7. The Peterson Institute provides a set of policy recommendations to reduce inequality in the assigned reading. Choose one specific policy recommendation, and design an empirical research
plan (unit of observation, necessary variables, and regression equation) to test the effectiveness of
the policy ten years into the future.
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8. President Biden’s Infrastructure Plan proposes to spend $2 trillion on investment in a variety of
infrastructure priorities. Given limited funding, and based on your knowledge of economic theory
and data, provide 3 key criteria that you would use to determine which priorities are most critical? Briefly explain your answer. (Note: you are not being asked to actually choose any spending
items from the plan, but rather to explain what method, process, or data should be looked at before
choosing which items to prioritize.)
9. Based on the reading and class discussion, briefly discuss at least two key expected social benefits
of stricter gun control laws, and at least two key expected social costs. (Recall that social benefits
and costs include both private and external benefits and costs.)
10. Based on the reading and class discussion, choose one of the recommended gun control policy
reforms. (i) Clearly state the selected reform, and provide a clear economic argument in favor it,
while acknowledging at least one cost of the reform. (ii) Design an empirical research plan (unit
of observation, necessary variables, and regression equation) to test the effectiveness of the policy
ten years into the future if it were implemented in different years across U.S. states (with some
states perhaps choosing not to comply).