1. Among the preferred explanations for the increase in wage inequality over the last several years are skill-biased technical change (SBTC), and trade with Less Developed Countries (LDCs). For each of the following facts about the evolution of the wage structure, say whether they are consistent with the SBTC explanation, with the trade explanation, both, or neither.
- The college wage premium has increased, even though the relative supply of college graduates has also increased.
- Most of the increase in the share of skilled workers in manufacturing can be explained by within-industry skill-upgrading, rather than a reallocation of workers across industries.
- Wage inequality has increased in Mexico and China as well as in the US.
- Job polarization: there has been in the share of jobs in high-skill and low-skill occupations, and a decrease in the share of jobs in middle-skill occupations.
2. (Borjas, Chapter 7, Problem 10) Ms. Aura is a psychic. The demand for her services is given by Q = 2,000 – 10P, where Q is the number of one-hour sessions per year and P is the price of each session. Her marginal revenue is MR = 200 – 0.2Q. Ms. Aura’s operation has no fixed costs, but she incurs a cost of $150 per session (going to the client’s house).
(a) What is Ms. Aura’s yearly profit?
(b) Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new demand for her services is Q = 2500 – 5P. Her new marginal revenue is MR = 500 – 0.4Q. What is her profit now?
(c) Advances in telecommunications and information technology revolutionize the way Ms. Aura does business. She begins to use the Internet to find all relevant information about clients and meets many clients through teleconferencing. The new technology introduces an annual fixed cost of $1,000, but the marginal cost is only $20 per session. What is Ms. Aura’s profit? Assume the demand curve is still given by Q = 2500 – 5P.
(d) Summarize the lesson of this problem for the superstar phenomenon.
3. Consider a modified version of the Becker-Tomes-Solon model of intergenerational mobility studied in class. Families contain one parent and one child. The parent must choose how to allocate lifetime earnings (yt-1) between own consumption (ct-1) and investment in the child (It-1). The parent’s budget constraint is therefore:
yt-1 = It-1 + ct-1.
The parent’s utility function is
U = (1-α)log ct-1 + α log yt
The technology translating one unit of investment into the child’s lifetime earnings is:
yt = Iγt-1 exp(Et)
a) Calculate the optimal amount of investment (It-1) chosen by the parent.
b) Show that log yt is a linear function of log yt−1. What is the intergenerational elasticity of lifetime earnings (i.e., the slope of the linear relationship) based on this model?
c) If you estimate a regression of log yt on log yt−1 , do you expect to obtain an consistent estimate of the structural parameter you found in part b)?
4. (Borjas, Chapter, Problem 6) Suppose the firm’s production function is given by
q = 10√(Ew + Eb)
where Ew and Eb are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is then
MPE = 5/√(Ew + Eb)
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. How many workers does this firm hire? How much profit does it earn?
(c) Finally, consider a firm that has a discrimination coefficient equal to 1.25. How many workers does this firm hire? How much profit does it earn?
5. Consider the following simplified version of the job search model studied in class. An unemployed worker lives two periods, 1 and 2. The timing of events in period 1 is the following:
i) The worker receives a job offer with probability α. The offered wage is drawn from a continuous uniform distribution on the interval [μ - θ/2 , μ + θ/2] . [See below for properties of the uniform distribution.]
ii) Given a wage offer w, the worker must decide whether to accept it or reject it. If she accepts an offer she is employed at wage w in both periods 1 and 2. If she rejects the offer, she receives unemployment benefits b in period 1, and she can search again next period.
If a worker is still unemployed in period 2, she faces the same sequence of events: receives a job offer with probability α from the same wage offer distribution, and must decide whether to accept it or reject it. If she accepts the offer, she receives w in period 2. Otherwise, she receives b. The world ends after period 2.
The worker wants to maximize the sum of total income (from wages and/or unemployment benefits) over her lifetime. The discount rate is zero, i.e., future payments are equivalent to present payments.
a) What is the worker’s reservation wage in period 2?
b) Write down the worker’s decision problem for setting the reservation wage in period 1, and calculate the worker’s reservation wage in period 1 as a function of α, b, μ and θ.
c) What is the effect of each of the following parameters on the reservation wage in period 1, and on the probability of exiting unemployment in period 1?
- The level of unemployment benefits b
- The mean of the wage offer distribution μ?
- The range of the wage offer distribution θ?
- The probability of receiving a job offer α? (Hint: more difficult!)
6. For this question, you will download the data set nlsy_ps4.dta. The data set contains information on weekly wages, years of schooling, actual and potential experience for a panel of more than 5000 individuals from the National Longitudinal Survey of Youth. Even though the data is a panel (the same individuals are observed multiple times), we will disregard this aspect, and instead treat each observation as independent.
Use the describe and summarize commands in Stata to familiarize yourself with the data set. The key variable, wkwage, is in nominal terms. Deflate it using the CPI (you can download the CPI time series from the BLS website), and answer the following questions.
a) Potential experience is calculated as age-highest grade completed-6. Actual experience is the number of years in which an individual has worked more than 500 hours since age 18. Actual full-time experience is the number of years in which an individual has worked more than 1500 hours since age 18. Discuss the advantages and disadvantages of these three measures of experience.
b) Using only males (sex==1), estimate the following three regressions (no need to report the results), and calculate and store the predicted values.
i. Log real weekly wages on actual experience and experience squared.
ii. Log real weekly wage on actual experience, experience squared, experienced cubed, and experience to the fourth.
iii. Log real weekly wage on a full set of experience dummies.
On the same graph, plot the predicted values from the three regressions against actual experience. Which parametric specification does a better job of capturing the wage-experience profile? The quadratic or quartic specification?
c) Repeat part b) using only females (sex==2).
d) Plot on the same graph the wage-experience profile for males and females (i.e., plot the predicted values from the regressions with a full set of experience dummies). Are there visible differences in the returns to experience by gender?
e) Pool the male and female samples together. Estimate a regression of log real weekly wages on a quartic in experience, a gender dummy, and the interaction between the gender dummy and the quartic in experience. Test whether the difference in predicted wage between a worker with 0 and 10 years of experience is the same for men and women. How about the difference in predicted wages between a worker with 10 and 20 years of experience?
f) Repeat parts d) and e), but now using:
- Potential experience instead of actual experience.
- Actual full-time experience instead of actual (overall) experience.
Comment on the results.
g) Do the results in parts d)-f) support the notion that women invest less in on-the-job training?
h) Calculate the raw gender gap in log weekly wages.
i) Use the Oaxaca decomposition to evaluate what portion of the gap is due to differences in observed characteristics, and what part is due to discrimination. Do this in three ways:
a. In the regressions, control for years of schooling, race dummies, marital status dummies, year dummies, and a quartic in actual experience.
b. As in part a, but now control for a quartic in potential experience.
c. As in part a, but now control for a quartic in actual years of full-time experience.
Comment on the results.