PROBLEM SET 5 – EC356 (A1)
Spring 2024
Due: no later than Wednesday, May 1 at 11:59pm Eastern time
Problem Set must be uploaded on Blackboard in the appropriate section.
INSTRUCTIONS: Please submit your problem set as a single PDF file titled PS5_[LastName][Firstname].pdf. Example: PS5_PasermanDaniele.pdf. This is an individual problem set. You are encouraged to discuss your papers with each other but must turn in separate work demonstrating independent thought and investigation.
Please TYPE the text of your answers to the extent possible. It is OK to have handwritten figures, but make sure to label them clearly and to make them as clear as possible.
Total: 100 points. Considerable weight will be given to effort, even if the final answer is not 100% correct.
1. (20 points) Returns to Schooling Using a Twins Sample. In this exercise, you will
reanalyze the data set used by Ashenfelter and Krueger in their study on the returns to
schooling using data on identical twins. Download the data set ps5_twins.dta from the course website. The data includes 680 twins (this is a slightly larger sample than the one used by Ashenfelter and Krueger in their final regressions). You are interested in estimating the following equation:
ln wagei = β0 + β1 educi + Y ′xi + ui
Answer the following questions (For all regressions, make sure to report coefficients and standard errors on the key variables of interest.)
a. Estimate an OLS regression of log wages (lwage) on years of schooling (educ), pooling together the data from both twins. What is the percentage change in wages associated with an additional year of schooling?
b. Now add to the regression controls for age, age squared, a female dummy, a racial dummy, and a marital status dummy. What happens to the estimated returns to schooling?
c. Add to the regression in part (b) controls for mother and father’s years of
schooling. What is the sign and significance of the parental education controls?
What happens to the estimated returns to schooling? Is this what you would have expected? Explain.
d. Estimate the regression in part (c) using first differences (i.e.., regress the
difference in log wages between twin 1 and 2 on the difference in years of schooling, the difference in age, etc. The variables in first differences are aleady included in the data set: d_lwage, d_educ, …). What is the rationale for running this regression? What happens to the estimated returns to schooling relative to the estimate in part (c)? Is this what you would have expected? Is this the same result obtained by Ashenfelter and Krueger?
2. (15 points) The returns to attending a selective college.
In the country of Utopia there is one selective university (University of Utopia, or UU), and several other non-selective ones. To be admitted to UU, students must score at least 1300 points on the U-SAT (the Utopian SAT). Some students that score above 1300 choose not to attend UU (they choose to study in neighboring Dystopia, or they enroll in a less selective university), while some students who score below 1300 are able to attend UU anyway because of other outstanding admission credentials. Researchers are interested in estimating the causal effect of attending UU on earnings. They collect data on earnings of recent Utopian university graduates, and plan to estimate the following regression:
ln eaTningsi = β0 + β1Attendeduui + ui
a. Researcher A: “To estimate the causal effect of attending UU, we can simply
compare the earnings of recent UU graduates to recent graduates of other universities.” Do you think Researcher A’s strategy recovers the causal effect of attending UU? Explain.
Researcher B: “I suggest instead that we use an instrumental variable strategy: create a dummy variable zi defined as follows:
1 if i scored above 1300 on U-SAT
zi = {
0 otherwise
Then use zi as an instrument for Attendeduui .”
b. What do you think of researcher B’s proposed strategy? Specifically, do you think that the instrument satisfies the relevance condition (Cov(zi, Attendeduui ) ≠ 0)? Does it satisfy the exclusion restriction Cov(zi, ui ) = 0)? Explain.
c. Researcher C: “I like Researcher B’s proposal, but I would restrict the sample to only those students who scored between 1200 and 1400 on the U-SAT.” What do you think of Researcher C’s strategy? Do you think that the instrument satisfies the two conditions for a valid instrument in this restricted sample?
3. (20 points) Two-period model
Ann lives two periods (period 0 and period 1), and draws utility from consumption in both periods. Her utility function is U(C0, C1). Ann must decide between two alternative income paths:
- “No College”: Ann works full time in both periods, and receives an income of 200 in both periods (Y0,NC = Y1,NC = 200).
- “College”: In period 0, Ann goes to college, works part time and earns 120 (Y0,C = 120). In period 1, Ann works full time and earns 300 (Y1,C = 300).
Assume that Ann does not derive any direct utility from going to college, and that the amount of leisure is identical under both income paths. Assume also that tuition is zero. For parts a-c, assume that there are perfect capital markets, i.e., Ann can borrow and lend any amount at interest rate r.
a) For r = 0, draw Ann’s budget constraint under the two possible income paths. Your graph should have consumption in period zero on the horizontal axis, and consumption in period 1 on the vertical axis. Make sure to mark on the graph the initial income allocation (Y0,NC and Y1,NC for the No College path, and Y0,C and Y1,C for the College path). Which income path will Ann choose? Does your answer depend on Ann’s indifference curves?
b) Repeat part (a), but assuming that r = 0.5. Which path will Ann choose now?
c) What is the internal rate of return of going to college, i.e., the interest rate that makes Ann indifferent between going and not going to college?
d) Assume now that capital markets are not perfect, and that it’s impossible to borrow.
People can still save at interest rate r=0, but the interest rate for borrowing is effectively infinite. Under these circumstances, Ann chooses to go to college. On the other hand Beth, Ann’s friend, chooses not to go to college. Explain Ann’s and Beth’s decisions using a graph with the new budget constraint and indifference curves. What can be said of Ann’s rate of time preference relative to Beth’s?
4. (15 points) Post-schooling investments and the shape of the age-earnings profile.
a. The age-earnings profile is steeper for workers with a college degree than for workers with only a high school degree. One likely explanation for this is that workers with a college degree have lower costs of investment in on-the-job training. True / False? Explain
b. The age-earnings profile for women has become steeper over time, suggesting that recent cohorts of women invest more in on-the-job training, as they expect stronger attachment to the labor force. True / False? Explain.
c. An increase in life expectancy is expected to lead to a steeper age-earnings profile. True / False / Uncertain. Explain.
5. (15 points) Wage inequality
a. If the relative demand for high skilled workers grows more rapidly than the
relative supply of high skilled workers, the skill wage premium will increase / decrease / stay the same. Explain.
b. Over the past 40 years, the US labor market has been characterized by the
phenomenon ofjob polarization: an increase in the share of workers employed in very low-skill and very high-skill occupations, and a decrease in the share of workers employed in middle-skill occupations. This phenomenon is consistent with the simple theory of skill-biased technical change outlined in Lecture Note 9, slides 15- 19. True / False? Explain.
c. The North American Free Trade Agreement (NAFTA) led to a large increase in trade between Mexico and the United States. Because Mexico specialized in the production of goods intensive in low-skill labor, we would have expected wage inequality in Mexico to increase / decrease / stay the same. Explain
6. (15 points) Oaxaca decomposition.
Suppose years of schooling, s, is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by:
wm = 600 + 80s
and
wf = 400 + 60s
On average, men have 14 years of schooling and women have 12 years of schooling.
a) What is the male-female wage differential in the labor market?
b) Using the Oaxaca decomposition, calculate how much of this wage differential is explained by differences in years of schooling, and how much of it is unexplained.
7. (20 points) Discrimination
Suppose the firm’s production function is given by
q=10 ,
where Ew andEb are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is then
5
MP = .
/E + E
Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each unit of output is $100.
(a) How many workers would a firm hire if it does not discriminate? How much profit does this non-discriminatory firm earn if there are no other costs?
(b) Consider a firm that discriminates against blacks with a discrimination coefficient of .25. That is, the firm acts as if the wage it has to pay to black workers is w~b = (1 + d)wb ,
with d = 0.25, How many workers does this firm hire? How much profit does it earn?
(c) Consider instead a firm that has a discrimination coefficient equal to d = 1.25. How many workers does this firm hire? How much profit does it earn?
(d) What does this model teach us about the likelihood of discriminating firms to survive in the long run? What other factors may lead to the existence of discriminating firms in the long run?