1. Human Capital: Education and Earnings Wages will vary among workers because workers are different. We each bring into the labor market a unique set of abilities and acquired skills, or human capital. We begin our study of human capital by focusing on the decision to acquire formal education. The skills we acquire in school make up an increasingly important component of our stock of knowledge.

2. 1.Education in the Labor Market: Some Stylized Facts 教育程度七十年七十五年八十年八十五年九十年九十五年九十七年 國中及以下 56.6958.8956.5553.0047.7144.3442.84 高中（職） 54.7657.8760.2260.5361.3463.5263.74 大專及以上 63.1366.1967.2767.9766.8267.3868.26 表一 勞動參與率與教育程度 單位： % 表二 就業者與教育程度 單位： % ，千人 教育程度七十年七十五年八十年八十五年九十年九十五年九十七年 國中及以下69.3164.0554.2644.3435.6427.4024.75 高中（職）20.0823.8529.8933.6935.9735.9135.38 大專及以上10.6112.1115.8521.9628.3936.7039.87

3. 表三 失業率與教育程度 單位： % 教育程度七十年七十五年八十年八十五年九十年九十五年九十七年 國中及以下 0.701.630.981.834.593.213.59 高中（職） 1.953.892.053.004.654.364.12 大專及以上 1.232.931.782.413.203.984.06

4. 2. The Schooling Model What factors motivates some workers to remain in school while other workers dropout before they finish high school? We assume that workers acquire the skill level that maximizes the present value of lifetime earnings. What factors motivates some workers to remain in school while other workers dropout before they finish high school? We assume that workers acquire the skill level that maximizes the present value of lifetime earnings.

5. (1) Present Value of Age-Earnings Profiles The present value of the earnings stream if the worker only gets a high school education is: (1) The parameter r is the worker’s rate of discount. There are 47 terms in this sum, one for each year that elapses between the ages of 18 and 64.

6. The present value of the earnings stream if the worker gets a college diploma is: Direct Costs of Attending College Post-College Earnings Stream The first four terms in this sum give the present value of the direct costs of a college education, while the remaining 43 terms give the present value of lifetime earnings in the post-college period. (2)

7. We assume that a person’s schooling decision maximizes the present value of lifetime earnings. Therefore, the worker attends college if the present value of lifetime earnings when he gets a college education exceeds the present value of lifetime earnings when he gets only a high school diploma, or: (3) Goes to College Quits after High School FIGURE 1 Earning Streams Faced by a High School Graduate Dollars Age w COL w HS -H 18 2265

8. (2) The Wage-Schooling Locus The wage-schooling locus gives the salary that employers are willing to pay for every level of schooling. The wage-schooling locus is market-determined. In other words, the salary for each level of schooling is determined by the intersection of the supply of workers with that particular schooling and the demand for those workers. Years of schooling FIGURE 2 The Wage-Schooling Locus Dollars 20000 23000 25000 30000 0 12131418

9. The wage-schooling locus has three important properties: The wage-schooling locus has three important properties: a. The wage-schooling locus is upward sloping. More educated workers must earn more as long as educational decisions are motivated only by financial gains. To attract more educated workers, employers must compensate those workers for the costs incurred in acquiring an education. b. The slope of the wage-schooling locus tells us by how much a worker’s earnings would increase if she/he were to obtain one more year of schooling. c. The wage-schooling locus is concave. As with most production process, there are diminishing returns to getting an education.

10. Defn. The Marginal Rate of Return to Schooling Defn. The Marginal Rate of Return to Schooling The percentage change in earnings resulting from one more year of school is defined to be the marginal rate of return to schooling. The percentage change in earnings resulting from one more year of school is defined to be the marginal rate of return to schooling.

11. (3) The Stopping Rule, or When Should I Quit School? Suppose that the worker has a rate of discount r that is constant; that is, it is independent of how much schooling the worker gets. The stopping rule that maximizes the worker’s present value of earnings over the life cycle is given by: Suppose that the worker has a rate of discount r that is constant; that is, it is independent of how much schooling the worker gets. The stopping rule that maximizes the worker’s present value of earnings over the life cycle is given by: Quit school when the marginal rate of return to schooling = r

12. This stopping rule maximizes the worker’s present value of earnings over the life cycle. Years of Schooling FIGURE 3 The Schooling Decision Rate of interest MRR r’ r s’s*

13. 3. Is Education a Good Investment? (1) Is Education a Good Investment for Individuals? The rate of return typically estimated for the U.S. generally fall in the range of 5-15 percent. The rate of return typically estimated for the U.S. generally fall in the range of 5-15 percent. At first glance, an investment in education is about as good as an investment in stocks, bonds, or real estate. At first glance, an investment in education is about as good as an investment in stocks, bonds, or real estate.

14. 資料來源：中央產經論文 - 台灣地區大學教育報酬率時間變化之分析 ( 邱麗芳 )

16. A. The Upward Bias The typical estimates of the rate of return on further schooling overstate the gain an individual student could obtain by investing in education because they are unable to separate the contribution that ability makes to higher earnings from the contribution made by schooling. The typical estimates of the rate of return on further schooling overstate the gain an individual student could obtain by investing in education because they are unable to separate the contribution that ability makes to higher earnings from the contribution made by schooling. i.e., Some of the added earnings college graduates typically receive would probably be received by an equally able high school graduates who did not attend college. i.e., Some of the added earnings college graduates typically receive would probably be received by an equally able high school graduates who did not attend college.

17. Methods to correct this bias: Methods to correct this bias: a. Separating effects of ability and schooling by including the aptitude-test scores such as IQ. b. Controlling for all the unmeasured aspects of ability by using data on twins. Part of earnings differentials associated with higher levels of schooling are due to inherently abler persons obtaining more schooling. Part of earnings differentials associated with higher levels of schooling are due to inherently abler persons obtaining more schooling.

18. B. The Downward Bias a. Some benefits of college attendance are not necessarily reflected in higher productivity. b. Most rate-of-return studies fail to include fringe benefits. Fringe benefits, usually as a fraction of total compensation, tend to rise as money earnings rise. Fringe benefits, usually as a fraction of total compensation, tend to rise as money earnings rise. a. Some of the job-related rewards of college are captured in the form of psychic or nonmonetary benefits.

19. C. Selection Bias The measured rate of return on a college education may understate the actual return for those who choose to attend college. Likewise, the measured rate of return may overstate the return that would have been received by those terminating schooling with higher school had they instead chosen to attend college. The measured rate of return on a college education may understate the actual return for those who choose to attend college. Likewise, the measured rate of return may overstate the return that would have been received by those terminating schooling with higher school had they instead chosen to attend college.

20. : the earnings in a college-level job of those who : the earnings in a college-level job of those who choose to go to college. choose to go to college. : the earning in a high school-level job of those who : the earning in a high school-level job of those who choose not to go to college. choose not to go to college. Let : the earnings in a high school-level job of those who choose to attend college terminating who choose to attend college terminating schooling at high school. schooling at high school. is perhaps less than is perhaps less than Measured benefit B t :

21. :the earnings in a college-level job of those who choose not to attend college were to alter their decisions. is perhaps less than → When abilities are diverse, the principle of comparative advantage is an important factor in making choices about schooling and occupations.

22. (1) Is Education a Good Social Investment? Some critics have suggested that to a large degree, education acts merely as a “sorting device”. Some critics have suggested that to a large degree, education acts merely as a “sorting device”. → Schooling does nothing to alter productive characteristics. The education is simply as a filter that has the effect of “signaling” which people are likely to be most productive. → Schooling does nothing to alter productive characteristics. The education is simply as a filter that has the effect of “signaling” which people are likely to be most productive. Note: Even if schooling were only a screening device, it could have social value. Employers need a reliable method by which to select employees. Investment in schooling sends a signal to the labor market that one has a certain level of ability. Note: Even if schooling were only a screening device, it could have social value. Employers need a reliable method by which to select employees. Investment in schooling sends a signal to the labor market that one has a certain level of ability.

23. →School would have net social value if the decision to attend and the success one attained in school sent accurate signals about productive characteristics to employers in the least costly way. Either education does enhance worker productivity or it is a cheaper screening tool than any other that firms could use. In either case, the fact that employers are willing to pay a high price for an educated work force seems to suggest that education produces social benefits. Either education does enhance worker productivity or it is a cheaper screening tool than any other that firms could use. In either case, the fact that employers are willing to pay a high price for an educated work force seems to suggest that education produces social benefits.