Exam Example Questions

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Name:________________________________________ Econometrics II – Example Exam Questions Instructor: Spencer Cooper Fall 2023 When instructed to do so, turn the page and begin your exam. This exam is worth a total of 105 points but you will only be graded out of 100 (meaning there is chance for extra credit). You may use a calculator but you may NOT use your phone, notes, books, your neighbor’s exam or any other materials. You must show your work on the short-answer questions. If you do the math wrong, you will get partial credit for writing the correct formula, graphs, or reasoning. Good Luck!

Q1. (35 points) Consider the example where we want to know the relationship between class size and student exam scores: i. Suppose I run a regression and I get the following output: ??𝑎? ????? 𝑖 = 56.20 − 1.21 ??𝑎?? ?𝑖𝑧? 𝑖 + 0.89 ??𝑎?ℎ?? ?????𝑖???? 𝑖 + ? 𝑖 (8.42) (0.44) (0.51) Determine whether the effect of class size on exam scores is statistically significant at the 5% level. – (5 points) ii. How do you interpret the effect of class size on exam score? Your answer should be specific about the numbers given in the results - (6 points) iii. How does your interpretation change of the result change if teacher experience is no longer included in the regression? – (6 points) iv. Is this estimated effect of class size on exam score causal? Explain your answer in one or two sentences - (10 points) a. Would your answer to question iv. change if you knew the 𝑅 2 = 0.05 ? Explain. – (4 points) b. Would your answer to question iv. change if you knew the 𝑅 2 = 0.85 ? Explain. – (4 points)

Q2. (30 points) Consider the example where I am looking at how years of education affects my wage: i. Suppose I have three different employment industries in my data – food, clothes, and automotive. Each of these is a binary variable that equals one if the observation works in that industry. Suppose I run the following regression: ?𝑎?? 𝑖 = 𝛽 0 + 𝛽 1 ??? 𝑖 + 𝛽 2 ???? 𝑖 + 𝛽 3 ????ℎ?? 𝑖 + 𝛽 4 𝑎??????𝑖?? + ? 𝑖 Which of the four assumptions are definitely violated in the above example? Explain in a couple of sentences – (5 points) ii. How could I fix the issue for this/these assumption(s)? – (5 points) iii. Suppose I instead ran the below regression with the following results: ?𝑎?? 𝑖 = 𝛽 0 + 0.511 ??? 𝑖 − 4.256 ???? 𝑖 + ? 𝑖 Interpret the coefficient on ???? 𝑖 if ?𝑎?? 𝑖 is measured in 1,000’s of dollars. This should only take one or two sentences. – (10 points) iv. Now interpret the effects on ???? 𝑖 and ????ℎ?? 𝑖 for the following regression: ?𝑎?? 𝑖 = 𝛽 0 + 0.433 ??? 𝑖 − 3.44 ???? 𝑖 + 1.10 ????ℎ?? 𝑖 + ? 𝑖 Your answer should only take two or three sentences – (10 points)

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Q3. (40 points) Consider the following questions about panel data: i. Explain the difference between cross-sectional and panel data – (7 points) a. Which data type would typically be preferred by an econometrician? Why? – (6 points) ii. Explain the difference between a balanced and unbalanced panel dataset – (7 points) iii. When we have panel data, we are able to use fixed effects. Suppose I have a panel dataset at the state level for 5 different states. a. Generally (not an example), what will including state fixed effects control for? – (10 points) b. Generally (not an example), what will including state fixed effects NOT control for? – (10 points)

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