# Family background and university quality

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Family background and university quality

Story 1: Destiny at age 6? In Project STAR, 11,571 students in Tennessee and their teachers were randomly assigned to classrooms within their schools from kindergarten to third grade. One study demonstrates that kindergarten test scores are highly correlated with outcomes such as earnings at age 27, college attendance, home ownership, and retirement savings.

Story 1: Destiny at age 6? They document four sets of experimental impacts: Students in small classes are significantly more likely to attend college and exhibit improvements on other outcomes. Students who had a more experienced teacher in kindergarten have higher earnings. Students who were randomly assigned to higher quality classrooms in grades K-3 – as measured by classmates' end-of-class test scores – have higher earnings, college attendance rates, and other outcomes. The effects of class quality fade out on test scores in later grades but gains in non-cognitive measures persist.

Story 2: Born on the first of September
Researchers have found that the single start day of schooling every year leads to discrepancy in education outcome. In the case of Taiwan, Elliott Fan has found that September 1st born children are 34% more likely to attend university than those born on August 31st.

Introduction People bring into 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, especially via job experience and education.

Education: Stylized Facts
Education is strongly correlated with: Labor force participation rates Unemployment rates Earnings

Present Value Calculations
Present value allows comparison of dollar amounts spent and received in different time periods. (An idea from finance.) Present Value = PV = y/(1+r)t r is the per-period discount rate. y is the future value. t is the number of time periods.

Potential Earnings Streams Faced by a High School Graduate
A person who quits school after getting her high school diploma can earn A from age 18 until retirement. If she decides to go to college, she foregoes these earnings and incurs a cost of B dollars for 4 years and then earns Stream B until retirement.

Present value of age-earnings profiles

The Schooling Model Real earnings (earnings adjusted for inflation).
Age-earnings profile: the wage profile over a worker’s lifespan. The higher the discount rate, the less likely someone will invest in education (since they are less future oriented). The discount rate depends on: the market rate of interest. time preferences: how a person feels about giving up today’s consumption in return for future rewards.

The Wage-Schooling Locus
The salaries firms are willing to pay workers depend on the level of schooling. Properties of the wage-schooling locus. The wage-schooling locus is upward sloping. The slope of the wage-schooling locus indicates the increase in earnings associated with an additional year of education. The wage-schooling locus is concave, reflecting diminishing returns to schooling.

The Wage-Schooling Locus
13 14 18 12 30,000 20,000 23,000 25,000 Years of Schooling Dollars The wage-schooling locus 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.

The Schooling Decision
Years of Schooling Rate of Discount s* s r r MRR 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 rate of discount. A worker with discount rate r goes to school for s* years.

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

Schooling and Earnings When Workers Have Different Abilities
Years of Schooling Rate of Interest 12 11 r MRRACE MRRBOB Dollars wHS wACE PACE wDROP Z Bob Ace Ace and Bob have the same discount rate (r) but each worker faces a different wage-schooling locus. 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).

Education and the Wage Gap
Observed data on earnings and schooling does not allow us to estimate returns to schooling, because more able persons tend to get more education. Ability bias: The extent to which unobserved ability differences exist affects estimates on returns to schooling, since the ability difference may be the true source of the wage differential.

Estimating RRS using a family model
Y is earnings for individual i of family j E is years of schooling X are individual characteristics Z are family characteristics

Estimating RRS using a family model
Assuming that the errors can be decomposed into two components – a family specific term u and an idiosyncratic term v. We can apply family fixed-effects model on identical twins However, there are limitations on the twin method.

Estimating RRS using IV
Candidates for IV are Quarter of birth or month of birth Policy changes such as the extension of mandatory education years from 6 to 9 years in Taiwan in 1968. Discontinuity caused by institutional designs, such as the cutoff score set by province government in the university education system in China.

Some Evidence In studies of twins, presumably holding ability constant, valid estimates of rate of return to schooling can be estimated. Estimates range from 3% to 15% annual return to a year of education. Generally, the rate of return to schooling is higher for workers who were born in states with well-funded education systems. RRE is found larger in developing countries than rich countries.

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

Does class size matter? Non-experimental evidence appears to be mixed.
Using two well-known experiments – STAR in the US and Maimonide’s rule in Israel, researchers have found a negative correlation between class size and education outcomes.

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.

Schooling as a Signal Education reveals a level of attainment which signals a worker’s qualifications or innate ability to potential employers. Information that is used to allocate workers in the labor market is called a signal. There could be a “separating equilibrium.” Low-productivity workers choose not to obtain X years of education, voluntarily signaling their low productivity. High-productivity workers choose to get at least X years of schooling and separate themselves from the pack.

Schooling as a Signal Suppose there are 2 types of workers:
In the case of asymmetric information, a pooled equilibrium is reached, and average wage is paid to both types of workers. Work types % of work force productivity High productivity q 200k Low productivity 1-q 300k

Education as a Signal 300,000 250,001 y 20,000 y Dollars Years of Schooling Costs Slope = 25,000 200,000 Slope = 20,000 (a) Low-Productivity Workers y (b) High-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.

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

On the job training Using the PV method in a 2-period model:

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

Age-Earnings Profiles

Age-Earnings Profiles

On-The-Job Training Most workers augment their human capital stock through on-the-job training (OJT) after completing education investments. 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.

Implications 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.

The Acquisition of Human Capital Over the Life Cycle
MC MR20 MR30 Dollars Q30 Q20 Efficiency Units 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.

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.

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 invest less in human capital and 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.

Policy Application: Evaluating Government Training Programs
Aimed at exposing disadvantaged and low-income workers to training programs. \$4 billion of federal spending per year. Studies of the return to these human capital investments are unclear, largely because of self-selection bias.

Social Experiments National Supported Worker Demonstration (NSW).
Results of the NSW suggest a 10% return to investments in human capital for workers treated under the program.