Ch6 - Solutions to Labor economics, Borjas PDF

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Solutions to Labor economics, Borjas...

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CHAPTER 6 6-1. Debbie is about to choose a career path. She has narrowed her options to two alternatives. She can either become a marine biologist or a concert pianist. Debbie lives two periods. In the first, she gets an education. In the second, she works in the labor market. If Debbie becomes a marine biologist, she will spend $15,000 on education in the first period and earn $472,000 in the second period. If she becomes a concert pianist, she will spend $40,000 on education in the first period and then earn $500,000 in the second period.Suppose Debbie can lend and borrow money at a 5 percent rate of interest between the two periods. Which career will she pursue? What if she can lend and borrow money at a 15 percent rate of interest? Describe in general terms how Debbie’s decision depends on the interest rate. Debbie will compare the present value of income for each career choice and choose the career with the greater present value. If the interest rate is 5 percent, PVBiologist = –$15,000 + $472,000/(1.05) = $434,523.81 and PVPianist = –$40,000 + $500,000/(1.05) = $436,190.48. Therefore, she will become a concert pianist. If the rate of interest is 15 percent, however, the present value calculations become PVBiologist = –$15,000 + $472,000/(1.15) = $395,434.78 and PVPianist = –$40,000 + $500,000/(1.15) = $394,782.61. In this case, Debbie becomes a biologist. As the interest rate increases, the worker discounts future earnings more, lowering the returns from investing in education. In this case, the higher interest rate makes the payoff from the $50,000 investment into becoming a concert pianist less valuable.

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6-2. Peter lives for three periods. He is currently considering three alternative educationwork options. He can start working immediately, earning $100,000 in period 1, $110,000 in period 2 (as his work experience leads to higher productivity), and $90,000 in period 3 (as his skills become obsolete and physical abilities deteriorate). Alternatively, he can spend $50,000 to attend college in period 1 and then earn $180,000 in periods 2 and 3. Finally, he can receive a doctorate degree in period 2 after completing his college education in period 1. This last option will cost him nothing when he is attending graduate school in the second period as his expenses on tuition and books will be covered by a research assistantship. After receiving his doctorate, he will become a professor in a business school and earn $400,000 in period 3. Peter’s discount rate is 20 percent per period. What education path maximizes Peter’s net present value of his lifetime earnings? The present discounted values of Peter’s earnings associated with each of the alternatives are

PVHS  100,000 

110,000 90,000   $254,167 , 1.2 1.2 2

PVCOL  50,000 

180,000 180,000   $225,000 , 1.2 1.2 2

PVPhD  50,000 

0 400,000   $227,778 . 1.2 1.2 2

and

Thus, the best option for Peter is to start working immediately upon completely high school.

6-3. Jane has three years of college, Pam has two, and Mary has one. Jane earns $21 per hour, Pam earns $19, and Mary earns $16. The difference in educational attainment is due completely to different discount rates. How much can the available information reveal about each woman’s discount rate? The returns to increasing one’s education from one to two years of college and then from two to three years of college are

r1to2 

$19  $16 $21  $19  18.75% and r2 to3   10.53% . $16 $19

Having observed their educational choices, we know that Mary’s discount rate is greater than 18.75 percent (otherwise she would have invested in a second year of education and earned 18.75% on the investment), Pam’s discount rate is between 10.53 percent and 18.75 percent, and Jane’s discount rate is less than 10.53 percent.

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6-4. Suppose the skills acquired in school depreciate over time, perhaps because technological change makes the things learned in school obsolete. What happens to a worker’s optimal amount of schooling if the rate of depreciation increases? If the rate of depreciation is very high, the payoff to educational investments declines. As a result, a worker’s optimal amount of schooling will also fall as the benefits of education erode more rapidly.

6-5. (a) Describe the basic self-selection issue involved whenever discussing the returns to education. People choose their level of education knowing their own abilities, preferences, and financial situation. Most important here is knowing one’s abilities. Highly capable people would likely earn a large salary even if they didn’t attend college, but they choose to attend because they earn even more (net of the cost of college) by doing so. Likewise, less capable people know they are less capable and that they will not get very high paying jobs even with a college degree. Consequently, highly capably people tend to go to college while less capable people are less likely to go to college, and the average wage of college graduates is higher than the average wage of non-college graduates largely because of self-selected education levels due to innate skills or abilities. To put numbers with the problem, suppose highly capable person would earn $50,000 without a college education and $65,000 with a college education. Similarly, a less capably person would earn $20,000 without a college education and $35,000 with a college education. All high ability people go to college, while none of the low ability people do. Clearly in this example, if one knows the numbers, one would say that the return to college is $15,000 (for either group). If one just saw the raw data of who went to college (and who did not) and each person’s income, one would falsely conclude that the return to college is $45,000. (b) Does the fact that some high school or college dropouts go on to earn vast amounts of money (e.g., Bill Gates dropped out of Harvard without ever graduating) contradict the self-selection story? No. One, there are always exceptions. And two, if the cost of education gets large enough (or the returns to education get small enough), even high ability people will forego college.

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6-6. Suppose Carl’s wage-schooling locus is given by Years of Schooling 9 10 11 12 13 14

Earnings $18,500 $20,350 $22,000 $23,100 $23,900 $24,000

Derive the marginal rate of return schedule. When will Carl quit school if his discount rate is 4 percent? What if the discount rate is 9 percent? The marginal rate of return is given by the percentage increase in earnings if the worker goes to school one additional year. Schooling 9 10 11 12 13 14

Earnings $18,500 $20,350 $22,000 $23,100 $23,900 $24,000

MRR 10.0 8.1 5.0 3.5 0.4

Carl will quit school when the marginal rate of return to schooling falls below his discount rate. If his discount rate is 4 percent, therefore, he will quit after 12 years of schooling; if his discount rate is 9 percent, he will quit after 10 years of schooling.

6-7. Suppose people with 15 years of schooling average earnings of $60,000 while people with 16 years of education average $66,000. (a) What is the annual rate of return associated with the 16th year of education? The annual rate of return is ($66,000 - $60,000) / $60,000 = 10%. (b) It is typically thought that this type of calculation of the returns to schooling is biased, because it doesn’t take into account innate ability or innate motivation. If this criticism is true, is the actual return to the 16th year of schooling more than or less than your answer in part (a)? It is typically argued that people who are innately skilled or motivated pursue more education than those who are less innately skilled or motivated, because the cost (psychic and in terms of the time spent in college) are less for the innately skilled or motivated. If true, then the returns to education are over-estimated by this type of simple calculation (i.e., a 10% rate of return is too high). Of course, the typical story might be wrong. The innately skilled or motivated might have to give up a lot in terms of foregone earnings in order to attend college, which they might not need in the first place (e.g., Bill Gates, NBA players). If so, then the returns to education could be under-estimated.

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6-8. Suppose there are two types of people: high-ability and low-ability. A particular diploma costs a high-ability person $8,000 and costs a low-ability person $20,000. Firms wish to use education as a screening device where they intend to pay $25,000 to workers without a diploma and $K to those with a diploma. In what range must K be to make this an effective screening device? In order for a low-ability worker to not pursue education, it must be that $25,000  K – $20,000, otherwise pursuing the diploma would be better than not pursuing the diploma for low-ability people. Thus, it must be that K  $45,000 to make sure low-ability people don’t pursue the diploma. Similarly, in order for a high-ability worker to pursue education, it must be that K – $8,000  $25,000, otherwise not pursuing the diploma would be better than pursuing the diploma for high-ability people. Thus, it must be that K  $33,000 to make sure high-ability people pursue the diploma. Thus, in order to use education as a signaling device in this example, it must be that educated workers are paid between $33,000 and $45,000.

6-9. Some economists maintain that the returns to additional years of education are actually quite small but that there is a substantial “sheepskin” effect whereby one receives a higher salary with the successful completion of degrees or the earning of diplomas (i.e., sheepskins). (a) Explain how the sheepskin effect is analogous to a signaling model. The sheepskin effect is analogous (in fact it is identical) to the signaling model in that purchasing the signal doesn’t actually change the person’s skills or productivity. Rather, purchasing the signal in effect documents or reveals that the person is a high-ability person. This is exactly the same as the sheepskin effect. That is, paying the money and sitting through classes and doing the work doesn’t change the person. Rather, no one without high skills would choose to do this, so acquiring a sheepskin is a tool by which to “signal” one’s productivity even though achieving the sheepskin had not direct effect on the individual. (b) Typically in the United States, a high school diploma is earned after 12 years of schooling while a college degree is earned after 16 years of school. Graduate degrees are earned with between 2 and 6 years of post-college schooling. Redraw Figure 6-2 under the assumption that there are no returns to years of schooling but there are significant returns to receiving diplomas.

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The Wage-Schooling Locus with Sheepskin Effects Dollars

$68,000

$42,000 $30,000

$18,000 12

16

20

Years of Schooling

The bold line in the above graph gives the wage-schooling locus with sheepskin effects. In particular, anyone without a high school diploma earns $18,000; anyone with a high school diploma (and no college diploma) earns $30,000; someone with a college diploma (but not a graduate school diploma) earns $42,000; and people with a graduate degree earn $68,000.

6-10. Consider a model with two periods—the first time period is the four years after high school and the second time period is the next 40 years. A person without a college education receives $120,000 of income during the first period and $1.2 million of income during the second period. A college graduate pays $200,000 during the first period to obtain a college degree and forgoes all earnings but then earns $2 million of income during the second period. Will the individual work or go to college in the first period if her individual rate of return between the two periods is 40%? The present value of working immediately (not going to college) is: PVNoCollege = 120,000 + 1,200,000/1.4 = $977,143 while the present value of getting a college degree is

PVCollege = –200,000 + 2,000,000/1.4 = $1,228,571. Therefore, as PVNoCollege < PVCollege, the individual will choose to attend college.

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6-11. One policy objective of the federal government is to provide greater access to college education for those who are less able to afford it. Recently many state governments have passed budgets that have significantly reduced funding for state universities. Using supply and demand analysis, what is the likely effect on the price of a university education to potential students? What does your model predict in terms of the number of people who will complete a university education? Less state funding will not change the demand for education; however, less state funding means that universities will need to pay for more expenses out of their own revenue, meaning that the marginal cost of providing a university education will increase. With the supply of university educations shifting in (up), the equilibrium will be associated with a higher price for a university education and imply that fewer people will complete a university education.

Price of Education S1 P1 S0 P0

D

E1

E0

Education

6-12. In 1970, men aged 18 to 25 were subject to the military draft to serve in the Vietnam War. A man could qualify for a student deferment, however, if he was enrolled in college and made satisfactory progress on obtaining a degree. By 1975, the draft was no longer in existence. The draft did not pertain to women. According to the 2008 edition of the U.S. Statistical Abstract, 55.2% of male high school graduates enrolled in college in 1970, but only 52.6% were enrolled in 1975. Similarly, 48.5% of female high school graduates were enrolled in college in 1970, while 49.0% were enrolled in 1975. Use women as the control group to estimate (using the difference-in-differences methodology) the effect abolishing the draft had on male college enrollment. The difference-in-differences table is

Men Women

1970 55.2 48.5

College Enrollment (percentage) 1975 Diff Diff-in-diff 52.6 -2.6 -3.1 49.0 0.5

Thus, abolishing the draft is estimated to have lowered the college enrollment rate of men by 3.1 percentage points.

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6-13. The textbook discusses in section 6–5 some strategies for correcting for ability bias when trying to estimate the rate of return to education. (a) What is the main argument for why using data on identical twins can control for ability bias? What problem arises if most pairs of identical twins pursue different levels of education? What problem arises if most pairs of identical twins pursue the same level of education? The main argument for why using data on identical twins can control for ability bias rests on the assumption that identical twins are also identical in ability. As long as this assumption is true, then wage models can be differenced between twins, the ability portion drops out, and the true rate of return remains. (This is shown in the textbook.) There are two issues with this method. First, if most pairs of identical twins actually pursue different levels of education, this calls into question the assumption that identical twins are identical in ability as differences in ability are a likely reason for the difference in education. Alternatively, if most pairs of identical twins pursue the same amount of education, then the rate of return to education is left to be estimated by just the small handful of twins in the sample who have pursued different levels of education. Looking at the equation in the text, Δs = 0 for any pair of twins with identical education, and therefore that observation lends no predictive information for b. (b) What is the main argument for why using certain birthdates can control for the bias? Do you think this method will be better as identifying the rate of return to different years of high school education or college education? Why? The main idea for using birthdates (or birth quarter as is common in the literature) is that education enrollment laws provide differences in kindergarten enrollment ages. Therefore, two people can be born relatively close together in time but have up to a year different in education when they drop out of high school at age 16. This method is likely better at estimating the rate of return to additional years of a high school education than additional years of a college education, because the mechanism by which birthdate is argued to serve this role pertains to dropping out of high school. It could be useful for college as well using maturity arguments, but this is a much less clear mechanism.

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6-14. A high school graduate has to decide between working and going to college. If he works, he will work for the next 50 years of his life. If he goes to college, he will be in college for 5 years, and then work for 45 years. In this model, the rate of discount that equates the lifetime present value of not going to college and going to college is 8.24% when the cost of each year of college is $15,000, each year of non-college work pays $35,000, and each year of post-college work pays $60,000. For each of the parts below, discuss how the rate of discount that equalizes the two options would change and who would make a different schooling decision based on the change. (Extra credit: Use Excel to show that the rate of return to schooling is 8.24% in the above case, and solve for the rates of discount associated with each of the parts below.) Calculating the rate of return for each case is straightforward in Excel by using the IRR function. In particular, list Years from 0 to 49. Then list the salary for co college in the next column. In the next list the cost of college or the salary from college for each year. Finally, create a fourth column that is the difference in value (college minus no college). Assuming the difference values are in cells E4 through E53, the Excel command is: =IRR(E4:E53). (a) Each year of college still costs $15,000 and each year of post-college work still pays $60,000, but each year of non-college work now pays $40,000. As the dollar benefit from not attending college has increased (from $35,000 to $40,000 annually), the return to college...