CHAPTER 6

1. CHAPTER 6 “If you think education’s expensive, try ignorance!” -Derek Bok

2. Introduction People bring to the labor market a unique set of abilities and acquired skills known as human capital. Workers add to their stock of human capital throughout their lives via general and firm-specific work experience, education, and training.

3. Education: Stylized Facts Education is strongly correlated with: Labor force participation rates (positively) Unemployment rates (negatively) Earnings (positively)

4. Present Value Calculations Present value calculations allow comparisons of dollar amounts spent and received in different time periods. Present Value (PV) = Σ[yt/(1+r)t ] r is the per-period discount rate. y is the net benefit in time period t. t is an index of the time periods; t = 1, … T

5. Potential Earnings Streams Faced by a High School Graduate $ wCOL Goes to College Quits After High School wHS Age 0 18 22 65 -H A person who quits school after getting her high school diploma earns wHSfrom age 18 until retirement. If she decides to go to college, she foregoes these earnings and incurs a cost of H dollars for 4 years and then earns wCOLuntil retirement.

6. The Schooling Model Age-earnings profile: the wage profile over a workers lifespan. The higher the discount rate, the less likely it is that someone will invest in education (since they are less future-oriented). The discount rate depends on: the market rate of interest. time preference: the rate at which one is willing to sacrifice future consumption in exchange for additional current consumption.

7. The Wage-Schooling Relationship The wages firms are willing to pay workers, and workers are willing to accept, depend on the level of schooling. Properties of the wage-schooling relationship: Is upward sloping. Has a slope that indicates the increase in earnings associated with an additional year of education. is concave, reflecting diminishing returns to schooling.

8. The Wage-Schooling Relationship $ 30,000 25,000 23,000 20,000 Years of Schooling 0 12 13 14 18 The wage-schooling relationship gives the salary that a particular worker would earn if he completed a particular level of schooling. If the worker graduates from high school, he earns $20,000 annually. If he goes to college for 1 year, he earns $23,000. and so on.

9. Education and the Wage Gap Observed data on earnings and schooling does not allow us to estimate the return to schooling, because more able persons tend to get more education. Ability bias: the extent to which unobserved ability differences affect the wage differential across different levels of schooling and bias upwards estimates of the rate of return to schooling.

10. The Schooling Decision Rate of Discount r r MRR Years of Schooling s s* The MRR schedule gives the marginal rate of return to schooling, or the percentage increase in earnings resulting from an additional year of school. A worker maximizes the present value of lifetime earnings by going to school until the marginal rate of return to schooling equals the discount or time-preference rate. A worker with discount rate r goes to school for s* years.

11. Schooling and Earnings When Workers Have Different Rates of Discount Rate of Interest Dollars wHS PBO rAL wDROP PAL rBO MRR Years of Schooling Years of Schooling 12 11 11 12

12. Schooling and Earnings When Workers Have Different Abilities Rate of Interest Dollars Z Bob wHS Ace wACE wDROP PACE r MRRBOB MRRACE 11 Years of Schooling 12 Years of Schooling 11 12 Ace and Bob have the same discount rate (r) but each worker faces a different wage-schooling relationship. Ace drops out of high school and Bob gets a high school diploma. The wage differential between Bob and Ace (wHS - wDROP) arises both because Bob goes to school for one more year and because Bob is more able. As a result, this wage differential does not tells us by how much Ace’s earnings would increase if he were to complete high school (wACE - wDROP).

13. Estimating the Rate of Return to Schooling A typical empirical study estimates a regression of the form: log(w) =  + •s + •X +  w is the wage rate s is years of schooling  is the rate of return to an additional year of schooling X is a set of individual and firm characteristics  is a random variable (luck, unobservables)

14. Evidence from Twins Studies Studies of twins are able to control for otherwise unobservable aspects of an individual’s genetic and family background. Estimates of the annual rate of return to an additional year of schooling, using differences in educational attainment between twins, are imprecise, ranging from 10% to 15%.

15. School Quality and the Rate of Return to Schooling Source: David Card and Alan B. Krueger, “Does School Quality Matter? Returns to Education and the Characteristics of Public Schools in the United States,”Journal of Political Economy 100 (February 1992), Tables 1 and 2. The data in the graphs refer to the rate of return to school and the school quality variables for the cohort of persons born in 1920-1929.

16. Do Workers Maximize Lifetime Earnings? The schooling model assumes that workers select their level of education to maximize the present value of lifetime earnings. To test this hypothesis directly, we must observe the age-earnings profile at two points in time. Unfortunately, once a choice is made, we cannot observe the earnings associated with the non-choice. Thus, using the observed wage differential to determine if the worker selected the “right” earnings stream yields meaningless results.

17. Schooling as a Signal Education is a signal which provides information about a worker’s expected future productivity to potential employers. Information that is used to sort workers in the labor market is called a signal. There is a “separating equilibrium”: Low-productivity workers choose not to obtain post-high-school education, voluntarily signaling their low productivity. High-productivity workers choose to obtain a college degree and thereby separate themselves from their less-productive cohort members.

18. Education as a Signal Dollars Dollars Costs 300,000 300,000 Costs 250,001 y Slope = 25,000 200,000 200,000 Slope = 20,000 20,000 y y y Years of Schooling Years of Schooling 0 0 (b) High-Productivity Workers (a) Low-Productivity Workers Workers get paid $200,000 if they get less than y years of college, and $300,000 if they get at least y years. Low-productivity workers find it expensive to invest in college, and will not get y years. High-productivity workers do obtain y years. As a result, the worker’s education signals if he is a low-productivity or a high-productivity worker.

19. Implications of Schooling as a Signal For schooling to act as a signal, it must be more “costly” for low-ability workers to obtain than for high-ability workers. The social return to schooling (the percentage increase in national income) is likely to be positive even if a particular worker’s human capital is not increased by additional schooling. Although education may incorporate a signaling aspect, it is generally accepted that education is more than a signal. Education is at least partially an investment in human capital.

20. Post-School Human Capital Investments Three important properties of age-earnings profiles: Highly educated workers earn more than less educated workers at every post-schooling age. Earnings rise over time for more- and less-educated cohorts, and at a decreasing rate. The age-earnings profiles of different education cohorts diverge over time (they “fan outward”). Earnings increase faster over time for more-educated workers.

21. Age-Earnings Profiles

22. Age-Earnings Profiles

23. On-The-Job Training Most workers augment their human capital stock through on-the-job training (OJT) after completing their formal schooling. Two types of OJT: General: training that is useful at all firms once it is acquired. Specific: training that is useful only at the firm where it is acquired.

24. Who Pays for OJT? Firms only provide general training if they do not pay the costs. In order for the firm to willingly pay some of the costs of specific training, the firm must share in the returns to specific training. Engaging in specific training eliminates the possibility of the worker separating from the job in the post-training period.

25. The Acquisition of Human Capital Over the Life Cycle Dollars MC MR20 MR30 Efficiency Units Q30 Q20 0 The marginal revenue of an efficiency unit of human capital declines as the worker ages (so that MR20, the marginal revenue of a unit acquired at age 20, lies above MR30). At each age, the worker equates the marginal revenue with the marginal cost, so that more units are acquired when the worker is younger.

26. Age-Earnings Profiles and OJT Human capital investments are more profitable the earlier they are taken. The Mincer earnings function: Log(w) = a·s + b·t – c·t2 + other variables. The “overtaking age” is t* and indicates the time when the worker slows down acquisition of human capital to collect the return on prior investments so as to “overtake” earnings of those that did not undertake similar investments.

27. The Age-Earnings Profile Implied by Human Capital Theory Dollars Age-Earnings Profile Age The age-earnings profile is upward-sloping and concave. Older workers earn more because they are collecting the returns from earlier investments. The rate of growth of earnings slows down over time because workers accumulate less human capital as they get older and existing human capital depreciates.

28. Government Training Programs Aimed at enrolling disadvantaged and low-income workers in government-sponsored training programs. $4 billion annual federal spending on training programs. Many estimates of the rate of return to these training programs are unreliable, largely because of self-selection and attrition bias.

29. Experimental Evidence National Supported Work Demonstration Random assignment of disadvantaged individuals to treatment and control groups Treatment was a subsidized job for 9-18 months accompanied by job-search Results of the NSWD imply a 10% annual rate of return to investment in human capital for workers “treated” under the program, relative to the “control” group.