Economics 4261 Introduction to Econometrics Summer 2022 Midterm
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Economics 4261
Introduction to Econometrics
Summer 2022
Midterm
Multiple Choice
Circle your answer. 4 points per question
1. Which of the following experiments would most likely violate the stable unit treatment variable assumption (SUTVA)?
(A) You provide tuition assistance to some low-income students at UMN to see if financial aid increases GPAs
(B) You provide free preschool to some children in a small Kenyan village to see if early education raises reading levels
(C) You provide housing vouchers for some low income residents nationwide to move to higher income neighborhoods to see if neighborhood matters
(D) You provide varying levels of health insurance to a sample of US residents to see if lower costs increase health outcomes
2. Suppose you ran a well executed randomized control trial in rural Bangladesh to study how cash incentives affect vaccination rates in developing countries globally. Your study will likely have
(A) Low internal validity, low external validity
(B) Low internal validity, high external validity
(C) High internal validity, low external validity
(D) High internal validity, high external validity
Briefly explain your answer (credit will be given for convincing arguments):
3. Suppose all assumptions for OLS hold. What is the correct interpretation of β1 from the regression below?
log(Yi ) = β0 + β1Xi + εi
(A) A one unit increase in Xi will lead to a β1 /100 percent change in Yi (B) A one unit increase in Xi will lead to a 100 ∗ β1 percent change in Yi (C) A one percent increase in Xi will lead to a β1 unit change in Yi
(D) A one percent increase in Xi will lead to a β1 percent change in Yi
4. Which of the following regressions would violate (A1) Linearity from the CLRM assumptions?
(A) Yi = β0 + β1Xi(2) + εi
(B) Yi = β0 + β1 log(Xi ) + εi
(C) Yi = β0 + β1 β2Xi + εi
(D) log(Yi ) = β0 + β1 log(Xi ) + εi
5. An estimator βˆ of β is said to be consistent if (A) E[βˆ] = β
(B) βˆ β
(C) E[V [βˆ]] = σ 2
(D) i = βˆ0 + βˆ1Xi
Question 1 (35 points)
The Trade Adjusment Assistance (TAA) federal program offers job training, relo- cation services, unemployment insurance, etc. for workers in industries that were impacted by international trade (manufacturing, steel, etc.) Suppose you have data on whether a worker received job training through the TAA (Di = {0, 1} where Di = 1 indicates the worker received the training) and the worker’s wage (Yi ). You want to evaluate the causal effect of receiving the training on wages, so you write down a model of the relationship
Yi = β0 + β1 Di + εi
(a) - 10 points Write down the conditional expectation function for Yi given Di by taking the conditional expectation on both the left and right hand side. Assume E[εi |Di] = 0.
(b) - 5 points Express β0 and β1 only using the conditional expectation function evaluated at Di = 0, 1. Based on this, propose sample estimators for both.
During your research, you come upon this table from the US Department of La- bor:
and this graph from the Bureau of Labor Statistics:
(c) - 5 points Based on this information, what would be the sign (positive, negative, zero) of the conditional error term? Circle your answer for both.
E[ei |Di = 0] {> < =} 0 E[ei |Di = 1] {> < =} 0 |
(d) - 15 points Using this new information, show what would happen if you tried to use your previous estimator from (b). Is your old estimator for β1 going to overestimate or underestimate the true causal effect of the TAA on wages?
Question 2 (25 Points)
You are interested in how savings (sav) increase as a function of income (inc). You want to estimate the parameters to this equation:
log(savi ) = β0 + β1 log(inci ) + εi
where you know
E[εi |log(inci )] = 0
You run the regression on a sample dataset and get the following sample regression
equation:
lo—g(savi ) = −2 + 0.25log(inci )
(a) - 15 points What is the interpretation of βˆ1 = 0.25? That is, what is the expected change in savi for a change in inci ?
(b) - 10 points What is the interpretation of βˆ0 = −2? Does this interpretation have any relevance in real life?
Question 3 (30 Points)
You are interested if smaller classrooms lead to better educational outcomes of students, measured by standardized test scores. You run a regression of score on a standardized test (Yi ) on the number of students in the classroom (Xi )
Yi = β0 + β1Xi + ui
(a) - 5 points Intuitively, what do you expect the sign of β1 to be? Explain
your reasoning.
(b) - 15 points Show how the OLS estimator βˆ1 will converge in probability to β1 under a specific assumption. Explicitly note where you use the assump- tion.
βˆ1 = = |
(c) - 10 points Realistically, the assumption you used in (b) will likely fail. For example, schools in wealthier neighborhoods will have both smaller class sizes (because they’re better funded) and students who score better on standardized tests (because parents can afford tutoring). Let Wi be the average income in the school’s neighborhood. Write
ui = β2 Wi + εi
with
E[εi |Xi] = 0
Show how the assumption you made in (b) now fails. This leads to omitted variable bias. What is the sign (positive, negative, zero) of the bias? Does this suggest your OLS estimator on the under-specified regression will be an overestimate or an underestimate of the true causal effect?
2022-07-23