Practice Midterm

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Economics

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Feb 20, 2024

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Page 1 of 6 ECON 140 Econometrics Practice Midterm Exam Spring 2024 (1 hour and 20 minutes, 25 percent of final grade) --Closed-Book Exam and No Calculators-- Answer all questions (total of 100 points in this exam) Do not communicate with anyone during the exam. Before starting, fill out the following: LAST NAME: FIRST NAME: Student (Cal) ID: SECTION DAY: SECTION TIME: Answer all questions (total of 100 points in this exam)

Page 2 of 6 Question 1 Define in one or two sentences any 5 of the following 6 concepts. If you use an equation or a graph, make sure that you explain what it shows. Do not answer more than 5 (4 points each, total of 20 points). A) Probability distribution B) Sample covariance C) Ordinary least squares estimation D) Median value E) p-value

Page 3 of 6 F) Central limit theorem Question 2 True or false, and briefly explain why. Select any 5 of the following 6 statements and do not answer more than 5 (6 points each, for a total of 30 points). Zero points for true/false labels without an explanation. A) The slope coefficient in a univariate OLS regression only correctly measures the ratio of the covariance between the independent and dependent variables over the variance of the independent variable IF there is no bias from omitted variables or other sources of bias. B) In a univariate regression of Y on 𝑋 ଵ , where we omit a second independent variable ( 𝑋 ଶ ) that has a positive effect on the outcome of interest, then the slope coefficient for 𝑋 ଵ will be positively biased.

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Page 4 of 6 C) Knowing the point estimate for a slope coefficient and the sample standard deviation of the independent variable for that coefficient are sufficient for testing the statistical significance of the slope coefficient. D) The slope coefficient of the interaction term between two independent variables, 𝑋 ଵ and 𝑋 ଶ , in an OLS regression measures the change in the intercept for 𝑋 ଵ ൌ 0 as 𝑋 ଶ changes by one unit. E) In a log-log OLS regression specification, a point estimate of 𝛽 ଵ ൌ 0.5 implies that a 10% change in 𝑋 ଵ is associated with a 5% change in Y. F) Measurement error in the independent variable leads to a negative bias of the point estimate of the slope coefficient if the true coefficient is positive.

Page 5 of 6 Question 3 Answer all questions (50 points in total). Suppose you were interested in analyzing the effects on test scores of a scholarship program that was randomly assigned in equal proportions to a group of 5th and 6th graders. To test these effects, you collected data on test scores and created the following variables: treatment – 1 if in a treatment school and 0 if not raven – this is the score on a Raven’s test (a test used to measure intellectual aptitude). grade5 - 1 if the pupil began in grade5 and 0 if the pupil began in grade 6 treat_grade5 - the interaction between treatment and grade5 Now suppose we ran the following command in Stata, which yielded the output below: A) What does the constant term measure? (10 points) B) Based on these estimates, what is the effect of the intervention for 6th graders? What is the level of statistical significance of this estimate? What is the average test score among 6 th graders in the treatment group? (15 points)

Page 6 of 6 C) What is the treatment effect on 5 th graders? Is it statistically significantly different from that of 6 th graders? At what level? (10 points) D) Using the potential outcomes framework, explain why (or why not) the estimated treatment effects you describe above correspond to average treatment effects (ATE). (15 points)

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