Eco311, First Midterm Exam, Fall 2017

Prof. Bill Even

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Your Name (Please print) ________________________________________

Your row (Please circle) 1 2 3 4 5

Directions

Place your answers to all questions in the space provided. Organize your answer so it is easy for me to

see the logic behind your answer. Clearly circle your answer to each question so it can be easily

distinguished from your work. If the logic of your work looks correct but there is a math error, you may

receive partial credit for your answer. Itâ€™s important that you present your work in a way that is easy to

follow.

Round all numerical answers to the nearest 100th (e.g. 1.23) unless specifically told otherwise. Unless

indicated otherwise, each question is worth 4 points.

The formula sheet and a table with the standard normal CDF are attached to the last page of the exam.

Eco311, First Midterm Exam, Fall 2017

Prof. Bill Even

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To answer the next 3 questions, consider the following relationship between annual labor earnings

(incwage), age, and age-squared that was estimated using data from the 2015 American Community

Survey.

Incwage = -72000 + 5240**age â€“ 51*age2

1. If a worker is 40 years old, use a derivative to calculate the marginal effect of one more year of age on

annual earnings.

In the ACS data, workers range between 16 and 97 years of age.

2. What age maximizes annual earnings? (Your answer must be somewhere in the range of 16 to 97

years of age).

3. What age minimizes annual earnings? (Your answer must be somewhere in the range of 16 to 97

years of age).

4. As an alternative to the linear model above, consider the following log-linear model of annual

earnings:

ln(incwage)=5.4 + .22*age- .002*age2

For a worker who is 40 years old, use a log-approximation to estimate the percent change in earnings

associated with an additional year of age. Be sure to give your answer as a percent (e.g. 20.32%, not

.2032).

Eco311, First Midterm Exam, Fall 2017

Prof. Bill Even

-3-

Consider the alternative to the earlier equation for annual earnings where earnings are allowed to

depend on age and years of education (educ)

Incwage= -27000 + 265*age +5700*educ + 60*(age*educ)

5. Based on this equation for annual earnings, use a first order approximation to estimate the marginal

effect of an additional year of age for a person who is 40 years old with 12 years of school.

6. Based on the above equation, which of the following is true?

a. The marginal effect of age on income is greater for more educated workers.

b. The marginal effect of education on income is greater for older workers

c. Both of the above are true

d. None of the above are true.

To answer the next 3 questions, consider the following data on the number of times a person has been

married drawn from the 2015 American Community Survey. Those who were married more than 3

times are recorded as a 3. You can ignore this issue in answering the questions. I also rounded the

probabilities to the nearest .05 to make calculations easier. Show the basic steps behind your work for

each answer.

Number of

times married

0

1

2

3

Probability

.30

.55

.10

.05

7. What is the expected number of times that a person has been married?

8. What is the variance of number of times married?

9. What is îœ§[(îœº âˆ’ îŸ¤î¯«) 3 ] where X is number of times married and îŸ¤î¯« is the expected value of X?