1 Human Capital 2

2 Example based on last section: Assume for a person there is just two years after high school. The individual could work in both years or go to school in the first year and work in the second. Say the individual works both years after high school and earns 20,000 each year. Then the present value is 20,000 + [20,000/(1+r)] (assuming a beginning of year convention and r =.05) = 39,048 If the individual goes to school the first year the cost is 5,000 but income the second year is then 47,000 for a present value = -5,000 +[47,000/(1+r)] = 40,238.

3 Since the present value for the school series is higher the person would choose school. Another way to see this is the way I mentioned at the end of the previous section - basically the differential cost in the first year has to be outweighed by the addition earning to make college pay off. Here we have -5, ,000 + [(47,000-20,000)/(1+r)] = 1,190. So, the year of schooling generates enough additional earnings in the second year to overcome the cost of school and forgone income in the first year. Now, in this example the interest rate was assumed to be 5%. But if the interest rate was 15% the year in school would not pay off. (please check the calculation)

4 The value of r is really determined in the market. Let’s call it the bank rate of interest you would earn if you put your money into a bank in some form (CD’s or something). Now, in reality each of us can choose between many different years of schooling. We next turn to a graph and analysis where years of schooling and yearly income are studied. On the next slide you will see the wage-schooling locus – a line showing the salary that employers are willing to pay a particular worker for every level of schooling. Note 12 on years of schooling is a high school diploma.

5 $ Years of schooling

6 Note three ideas in the graph on the previous slide: 1) The curve is upward sloping – more schooling translates into more yearly income. 2) The slope of the curve is change in income/change in school. If we take the change in school one year at a time then the slope is the change in income. For example, from 12 to 13 years of school we have (23000 – 20000)/(13-12) = 3000, and From 13 to 14 years of schooling we have (25000 – 23000)/(14 – 13) = 2000.

7 Note 3 – the curve is concave reflecting the fact that more schooling yields more income, but the additional income each year is less and less – the proverbial diminishing returns. From the three points in the graph I will put the values in a table and add some details. YearIncomeslopeMRR xxxxxx /20000 =.15 or 15% /23000 =.087 or 8.7% So, the slope can be used to calculate the MRR, the marginal rate of return to schooling.

8 Notice that when the person considers the 13 th year of school they will give up making after the 12 th year in the anticipation of making after the 13 th year. The additional 3000 on the 13 th year is the return on the given up, for a marginal rate of return of 15%. Since there are diminishing returns to school the marginal rate of return will be a curve that slopes downward from left to right, as seen on the next screen. I have included the values from our running example.

9 Years of Schooling Rates MRR % 8.7%

10 Decision rule on how much school to take: Add years of schooling as long as the MRR is greater than rate you can earn on funds in the bank (or other investment vehicles), stop adding when the MRR = bank rate and never add years when MRR < bank rate. On the next graph you see the general MRR graph with a bank rate added in horizontally. The amount of schooling to take is s*. The reason you would not take more than s* is that if you did you would give up money from working to be in school. But since the bank rate is higher than the MRR on that year of schooling if you work and put the money in the bank then you can have more than what you would have earned after the additional year of school. Plus you wouldn’t stop short of s* because schooling has the best return you can make at that point.

11 Years of Schooling Rates MRR S* Bank rate

12 Differences in “bank rates” Say you have two people who face the same wage schooling locus, and thus the same MRR curve. If they have different “bank rates” (really rates of return in other areas), then they will not take the same amount of schooling. The person who has lower alternatives elsewhere will take more schooling. With this scenario in mind, we have been talking theory but practice, or reality, can be used. If people only differ in their rates of return in other areas, then the person with more schooling and higher income can be compared with the person with less schooling and less and income and we can observe different points of the wage schooling locus. We get the extra income earned by the extra schooling.

13 But what if people have the same “bank rates” and differ in their abilities – in other words people have different wage schooling loci and hence different MRR’s to schooling? If person A gets more out of schooling than person B, then A’s wage schooling locus sort of rotates counterclockwise around the bottom left point on the locus (and is thus steeper and higher at every year of schooling) and the MRR curve would be farther to the right. Let’s see these graphs on the next screen. Person B takes less schooling and gets a lower wage.

14 $ Years of schooling Person A Person B rates Years of schooling Person A Person B

15 Conundrum When we observe different people having different years of schooling and different wages, we might want to fall into a line of thinking that says, well if we just get the lower wage earner more schooling they would have higher wages. They probably would, but not as much higher as we expect. Think back to person A and person B. In the real world we observe person A make more and have more schooling. What we may not observe is the differences in what each gets out of school. If we think person B, if encouraged to get as much schooling as person A, will have the same income as A after the additional schooling, we are wrong. Person B does not get as much out of schooling as person A. Person B will end up short of the income of person A

16 Public policy problem If there really is an ability bias in the data of the real world (meaning that the difference in earning comes from not only differences in schooling but also difference in what one gets out of school), then spending tax dollars to encourage more schooling 1. May leave some disillusioned because they won’t get as much as they had hoped, 2. May cost more than the benefits received – the encouragement will likely cost dollars and may be justified in that it will generate more income taxes. But the more income taxes may be overestimated.