Public and private investments in education yield

Question

Assignment:

Mankiw makes the point that human capital is an essential element in determining the long-run growth of any country. Mankiw notes also that human capital investments have both private and public benefits -- private benefits in the form of higher earnings and public benefits in terms of a more informed citizenry, a higher probability of inventions, etc.

Mankiw points out that public and private investments in education yield very large benefits in higher average earnings. Indeed, Mankiw notes  that (on average) there is about a 10% increase in average earnings for each additional year of formal schooling completed.

On the face of it, perhaps you will agree with me that this is an impressive claim (if it is true). A 10% earnings increase (for every year of your future worklife) is an impressive payoff to one additional year in school.

Because we do not want to take anything for granted, let's see if we can verify Mankiw's assertion using the actual earnings experience of American workers (from the Current Population Survey conducted by the United States Census Bureau each year).

To save you the trouble of negotiating the complete raw data, I have summarized the most general results (by gender) for 2013 (the most recent data available) in the two tables below.

In the first table, please note that "mean earnings" for all workers and all races are being shown for six different levels of educational attainment.

[All workers in Table 1 includes those who worked part-time only and those who did not work all year round even though they may have been full time for that portion of the year that they did work.]

In the second table, mean earnings are being shown for only those workers (again for all races) who worked full time for the entire year of 2013. In the last column of both tables, I have calculated the ratio of female earnings to male earnings for each level of educational attainment.

[You may be interested to see the magnitude of this ratio and how it varies by level of educational attainment.]

N.B.: Professional degrees include: MD, DDS, DVM, LLB, and JD.

For those of you who would like to see the raw data, it can be found at:

https://www.census.gov/hhes/www/cpstables/032014/perinc/pinc04_000.htm

Please respond to the following three questions (and show your work):

1. Considering the change in earnings from high-school graduate on to higher levels of educational attainment, is Mankiw correct in asserting that there is approximately a 10% gain per year for each additional year of schooling? Explain. [Note: that it will typically take more than one year to progress between the various categories of educational attainment.

For purposes of this exercise, assume that it takes two years (beyond high school graduation) to complete an Associates degree, two more years to earn a bachelors degree, two more years to complete a master's degree, and two additional years (beyond the master's) to earn a doctorate.

Assume also that it takes a minimum of three years (beyond the bachelor's degree) to earn a "professional" degree.In order to do these calculations correctly an important distinction must be made. There are two routes that an individual can go after receiving a bachelor's degree.

First, they can proceed directly to a master's degree (or a master's degree and a doctorate).  Second, they can proceed directly to a professional degree. Assume that they will not do both, and keep this in mind when calculating returns to schooling for a professional degree.]

2. For which gender (males or females) are the gains from additional schooling the greatest and for which additional degree (for males and females separately) is the payoff the largest? Explain

3. Notice that the Female/Male earnings ratio for "full-time, year round workers" is larger than the same ratio for "all workers." Is this a surprising result? Explain.

			Mean Earnings in 2013 (All Workers and All Races)
							Ratio:
			Males		Females		Females/
							Males
High School Grad.			$ 37,763		$ 26,322		.697
Assoc. Degree			$ 50,059		$ 33,946		.678
Bachelor's Degree			$ 72,124		$ 47,209		.655
Master's Degree			$ 97,365		$ 58,253		.598
Professional Degree			$ 169,135		$ 98,454		.582
Doctorate			$ 131,969		$ 80,501		.610
			Mean Earnings in 2013 (Worked Full Time, Year Round)
							Ratio:
			Males		Females		Females/
							Males
High School Grad.			$ 44,803		$ 34,951		.780
Assoc. Degree			$ 57,454		$ 42,136		.733
Bachelor's Degree			$ 81,066		$ 57,242		.706
Master's Degree			$ 108,997		$ 69,812		.641
Professional Degree			$ 188,338		$ 117,630		.625
Doctorate			$ 144,919		$ 94,035		.649