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Final Exam (Econometrics Summer 2020)

Name (print) _________________,__________________ (Last name) (First name)

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There are 90 possible points

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You may take up to three hours to complete this exam

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Your time clock begins when you view the exam’s contents

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The exam should be completed in one sitting, without books, notes, or other help

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If you don’t know the answer to one part of a question but you need the answer to work a subsequent part, then choose a value to use so that you can demonstrate your abilities on that subsequent part. Simply write that you are assuming an answer to the part that you couldn’t solve.

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To receive full credit for a free-response answer, you must show your work. A correct final answer without a complete demonstration of the steps leading to that number is not worth full credit. You might receive partial credit for an incorrect or an incomplete answer if you show your work or an appropriate diagram.

Honor code: "On my honor I have neither given nor received unauthorized information regarding this work, I have followed and will continue to observe all regulations regarding it, and I am unaware of any violation of the Honor Code by others.”

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Question 1 (5 points total). Carefully distinguish between the two terms below. Be precise. Residual, error term

Question 2: Suppose a data set of 1400 observations (NN=1400) was analyzed using OLS to examine the factors influencing the participation rate of employees in a 401(k) retirement plan sponsored by their employer. The regression results are as follows, with standard errors in parentheses:

Note: The match rate for a firm is the amount the firm contributes to a worker’s fund for each dollar the worker contributes. For example, if the match rate is 0.5, each time an employee contributes $1 the firm will contribute 0.5×$1=50 cents0.5×$1=50 cents. Question 2 (5 points, circle one) Use the information above. At the 1% significance level, with a twosided alternative hypothesis, the coefficient on mrate is statistically different from 0. (circle one) True

False

Question 3 (5 points, fill in the blank) Suppose mratemrate has a sample mean of 4% and a standard deviation of 1%, while the prateprate has a sample mean of 80% and a standard deviation of 4%. Based on the regression results, a 1% increase in the mratemrate results in a _____ increase in the participation rate in 401(k) plans.

Question 4 (5 points, circle one)

Question 5 (40 points total). Suppose that an econometrician is interested in estimating the effect of college grades (X, measured in GPA units) on post-graduation wages (Y, measured in millions of dollars per year), and the econometrician has data on each of these variables for individual college graduates. Suppose the econometrician is concerned about the influence of unobservable features (e.g. ability “Ai”) correlated with both X and Y. As a consequence, the econometrician cannot reasonably assume that E[ xu] 0 . The econometrician works down the hall from a young statistician who proposes the following work-around: “Assume the population model is linear, but that people with GPA=0 earn zero dollars. Then, you can estimate the following method-of-moments model:

yi  xi  ui E[ui ] 0

(1) (2)

…You can recover an estimate of gamma (  ) from a frequentist method of inference using (1) and (2), since these are just two equations and two unknowns. Thus, you can avoid making the zero-covariance assumption and need not worry about the unobserved effects of ability (Ai)”  Part A (12 points): Derive an expression for the estimator (gama-hat)  that emerges from the method of moments model (1) and (2) above. Show every step in your derivation.

Part D (8 points): Suppose the econometrician estimates this model and obtains the following estimates (the standard error appears in parenthesis below the coefficient estimate). Test the null hypothesis that the estimated coefficient equals zero and interpret the estimated magnitude, paying careful to the specific units of measurement. Is the estimated magnitude large or small? Explain.

y 5 x (0.2)

Part F (15 points) Verify whether this estimator of  is unbiased. Show every step of your work.

Part G (5 points): Given your findings in Parts D and F, how confident are you in the estimated causal effect of an additional GPA point is equal to $500,000 per year. Explain the basic issues.

Question 6 (30 points total): Suppose you observe individual-level data on hourly wages (Y) and education (X). You are interested in estimating the causal effect of education on hourly wages and you do Y  X u (1) so by estimating the model i  0  1 i  i .

 Part a (20 points) Suppose the econometrician estimates 1 via OLS under the assumption of (1). Suppose there exist two additional unobserved determinants of hourly wages, denoted Qj (‘amount of crime in neighborhood j in which the individual was raised) and Ri (‘work ethic’) that may influence a person’s wages. Formally derive an analytic expression that characterizes potential omitted variable bias associated with estimation of an equation that omits both Q and R. Show every step in your derivation.

Part B (10 points) Use the expression you derived to sign the bias associated with estimation of the  equation that fails to control for Q and R. Will  1 on average correctly estimate, over-estimate, or underestimate the true effect of education on wages. Comment on the possible magnitude of this bias. There is not a single right answer to this question, which is graded based on the quality of your analysis....