Econometrics Midterm UNCC PDF

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Midterm Exam (Econometrics UNCC, Summer I, 2020)

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

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There are 85 possible points

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You may take up to two 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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Due electronically in a single file to Canvas submission portal by Midnight on Friday June 5 2020.

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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 an 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.”

Pledged ______________________________________________________________ (your signature)

Question 1: (5 points): This exam is submitted to Canvas in a single electronic file (MS Word or PDF). Circle one: Yes No Question 2: (5 points, circle one). The term used to distinguish the distribution of an estimator is a. Cumulative distribution b. Data generating process c. Probability distribution d. Sampling distribution Question 3: (5 points, circle one)

Question 4: (5 points, circle one)

Question 5: (5 points, circle one)

Question 6: (5 points, circle one) Which of the following refers to panel data? a. Data on the average share price of a company over the course of a year b. Data on the unemployment rate in a country for each of 5 years c. Data on the income of each of 5 members of a family in a particular year d. Data on the birth rate in various developing countries for five consecutive years

Question 7: This is a free-response section. It is graded based on demonstrated knowledge. For full credit show every step used to arrive at your answer. Consider the following dataset on last quarter’s corporate profitability (P, measured in percent) and CEO salary (S, measured in millions of dollars), for each firm i . The sample average of S equals 2.66 . The sample variance of S equals 2.33 . Firm 1 2 3

P 7 2 5

S 4 3 1

Part 1 (5 points): is this a time-series, pooled cross section, panel, or cross-sectional dataset?

Part 2 (10 points). Compute the sample mean and variance of P. Write the formula for the average using the summation operator and show how you use the formula to obtain your answer.

Part 3 (10 points) Compute the sample covariance between P and S. Write the formula for the sample covariance using the summation operator and show how you use the formula to obtain your answer.

Part 4 (10 points): Now suppose you want to measure CEO salary in hundreds of thousands instead of millions of dollars. To do this you would create a new variable “CEO salary in hundreds of thousands of dollars”, denoted S’, as follows: S’=10*S. Use the properties of the summation operator to prove that Cov(P, S’) = 10*Cov(P, S). Show every step in your derivation and indicate at each step which property of the summation operator you use. Finally, write the numerical value of the covariance between P and S’.

 2 0.5 Part 5. Suppose you know (from other sources, e.g. your analytics team, that s , and your objective s is to conduct a two-tailed test the hypothesis that =2. The estimator we will consider is the sample average of S. 5.1 (10 points) Use the properties of the expectation and summation operator to show that the sample mean is an unbiased estimator for this population moment. Show every step in your work and list each property used as you go along.

2 5.2 (10 points). Suppose you know from elsewhere (e.g. your analytics team) that S 4. Conduct a twotailed test of the hypothesis that s =2 at the 5% level. What do you conclude based on your dataset? Is the true CEO salary statistically distinguishable from 2 million dollars? Show every step in your work....