Chapter Study Outline

  • Investment: any costly activity that potentially yields future benefits
    • Like physical and financial investments, workers may also make investments in human capital investments. These are investments in the individual’s mind or body that are expected to reap future rewards, including:
    • Migration
    • Job search
    • Education—the focus of the chapter
    • Health

5.1 Human Capital: An Overview

  • Human capital is acquired over the course of several distinct phases and involves a number of sources, including:
    • Family
    • Schools and colleges
    • Firms
    • Government
  • The demand for education by workers in one period is the primary determinant of the available supply of trained workers in later periods.
  • The link between human capital and worker productivity connects the theory with
    • (a) earnings patterns
    • (b) economic growth and development
    • (c) public finance
  • Formal education is the term for schooling in kindergarten through college.
    • By 2009 about 25% of the U.S. population was either enrolled in a school or college or teaching in one.
      • The United States spent $1 trillion on education in the same year.
    • In recent years there have been significant changes in the level, type, and composition of enrollment in formal education.
      • In 1909 barely 9% of the population had a high school diploma, while today nearly 30% of people over the age of 25 have a bachelor’s degree or higher.
      • These changes can be explained as the outcome of rational purposive behavior in response to the market and informational constraints of the economy.
    • The evidence shows that there is a positive relationship between educational attainment and both employment and earnings.

5.2 The Individual Investment Decision

  • The individual’s lifetime wealth, V, equals the discounted value of his earnings stream net of his educational costs.
    • $s0 = the cost of education
    • $w0 = any earnings generated during time of education
    • t = the individual years in the person’s life to date
    • T = the person’s lifespan
    • r = the interest rate
      • The individual’s future returns to education must be discounted by the interest rate using the concept of net present value.
      • The working life span, T, is an important determinant in the value of education.
        • The young are more likely to enroll in college than the old because the young have longer expected working lifespans.
        • An increase in working lifespan may induce individuals to decide to increase educational attainment.
    • Model 5.1: The College Attendance Decision: A Two-Period Framework: this model is comprised of only the present, in which the individual makes a human capital investment decision, and the future, in which she reaps the rewards
      • (a) The cost of college, including out-of-pocket expenses and the value of intellectual effort, is $s0.
      • (b) Capital markets are perfect and the individual can borrow to finance education at the constant interest rate r ≥ 0.
      • (c) The individual can earn $w0 ≥ 0 while in college; she earns $w after she graduates. If she does not attend college, she earns $wn in both periods. She knows the values of $w0 < $w < $wn when she makes her educational choice.
        • If the individual attends college, her discounted lifetime wealth is V(s) = (w0 - s) + [w / (1 + r)]
        • If the individual does not attend college, her discounted lifetime wealth is V(n) = (wn - s) + [wn/(1 + r)]
    • The individual will choose college if –{s + wn - w0}} + (w - wn)/(1 + r) ≥ 0
      • A key component of this human capital framework is the opportunity cost of the net earnings the individual forgoes while in school, w - wn.
        • This opportunity cost increases with the length of schooling.
        • It is equally as important as the cost of schooling itself.
      • The discounted benefits of education increase with the college-wage premium, w - wn, and decrease with the interest rate.
  • Evidence from U.S. college attendance rates in the last 40 years indicates that a decrease in the college wage premium,Δw = w - wn, renders college less attractive at the margin and decreases enrollment.
    • Meanwhile, a decrease in the earnings of non-college-educated workers, wn, increases the wage premium, w - wn, and increases enrollment.
  • sr* = the reservation schooling cost, or the value of schooling cost at which an individual is just indifferent between attending and not attending college. The reservation cost depends on w0, wn, w, and r.
    • If s ≤ sr, the individual will attend college.
    • If s > sr, the individual will not attend college.
    • A worker is more likely to attend college or invest in human capital:
      • as the wages w0 and w increase
      • as the educational cost, s, the non-college wage, wn, and the interest rate, r, decrease

5.3 The Level of Human Capital Investments

  • Model 5.2: A Two-Period Model of Human Capital Accumulation
    • (a) The individual attends college and picks a level of education, $s > 0.
    • (b) Second-period earnings are given by $w = w(s), this number increases with s, but at a diminishing rate.
      • This model indicates that there are positive and diminishing returns to educational investments.
      • The marginal return to schooling, MW(s), equals the increase in future earnings that results from an additional dollar investment in education.
        • MW(s) =Δw(s) /Δs
        • The marginal return to schooling, MW(s), depends on s itself.
      • The marginal cost of increasing human capital investment by $1 is simply MC = $1.
      • The marginal benefit of increasing human capital investment by $1 is MB = MW(s)/(1 + r).
  • The optimal investment level, s*, exists where MB = MC.
    • MC = 1 = MW(s)/(1 + r) = MB
    • Rearrangement yields the optimal level of investment at r = MW(s*) – 1 = i(s*).
      • r is the market rate of interest.
      • MW(s) – 1 = i(s) is the net rate of return to human capital investments.
    • The individual may transfer wealth from the present to the future by means of investment in a bank at r or investment in human capital at MW(s) - 1, and his choice of the optimal level of investment (s) occurs when these two marginal rates of return are equal.
      • If the economy is perfectly competitive, this choice will be Pareto efficient at ŝ.
      • The same inequality holds for society as a whole, implying that government intervention will be harmful under the flawed assumption that capital markets are perfectly competitive.

5.4 Extensions

  • The models thus far have assumed that workers are homogeneous, labor markets are perfect, and capital markets are perfect.
  • Assumption 5.1: Heterogeneous Abilities: relaxing the assumption of homogeneous worker ability allows for a model in which workers have heterogeneous abilities and:
    • (a) There are two types of workers: those with high innate ability, (aH), and those with low innate ability, (aL) .
    • (b) In the first period, each worker earns the common wage, $w0. Second-period wages, wH(s) and WL(s), satisfy
      • w(0)H =w(0)L = w0
      • MW(s)H > MW(s)L for all values of s
    • Absent schooling, s = 0 and both workers are equally productive.
    • With more schooling, workers with high innate ability are faster learners, giving them greater earnings as s increases.
      • $w(s)H > $w(s)L
    • Given the market interest rate, r0, the optimal educational choice for both workers is governed by r0 = i(sH*)H = i(sL*)L
      • sH* > sL*, indicating that high-ability workers will accumulate more human capital than low-ability ones.
      • The positive correlation between ability and education offers a possible explanation for the right-handed skew of the earnings distribution.
  • Assumption 5.2: Imperfect Capital Markets: relaxing the assumption that labor markets are perfect and considering the possibility of unemployment, u, the worker’s optimal level of educational investment is located at r = MW(s*)(1 - u) – 1 = i(s).
    • A higher unemployment rate discourages the accumulation of human capital, leading to a low average level of worker skills in the population.
    • Furthermore, firms will be discouraged from entering areas with uneducated labor markets, increasing the level of unemployment and compounding the negative effect on human capital investment.
  • If capital markets are imperfect, the level of wealth may affect the educational decision.
    • Under the assumption that capital markets are perfect, two individuals with equal innate ability and unequal parental wealth will both borrow enough funding to afford the level of schooling, s* = MW(s*) = 1 = r.
    • In this case, wealth does not affect s*, since funds in excess of s* would be better invested in a trust fund at the bank.
    • In practice, though, the level of wealth will affect interactions in capital markets.
      • Despite innate ability equal to that of the wealthier individual, an individual with less wealth may be unable to afford s*.
    • In imperfect capital markets, r(s) denotes the interest rate charged on the sth dollar of a loan, where r(s) increases with s.
      • Here, the interest rate increases with the amount that is borrowed, indicating that banks are more willing to finance small unsecured loans than the large loans required to finance the education of a less-wealthy person.
        • Under these conditions, the worker’s optimal choice of education to maximize lifetime wealth, V(s), satisfies the condition r(s*) = MW(s*) – 1 = i(s*).
    • In imperfect capital markets, high innate ability encourages the acquisition of human capital and results in a higher rate of return.
      • sH* > s0* > sL* and iH* > i0* > iL*
    • In imperfect capital markets, low borrowing cost (high wealth) also encourages the acquisition of human capital but depresses the rate of return.
      • sl* > s0 * > sh* and il* < i0* < ih*, where l refers to low borrowing cost

5.5 The Return to Investments in Human Capital

  • There is an overwhelming body of evidence that points to a positive correlation between education and earnings.
    • One hypothesis is that this correlation is causal.
    • Investments in education may raise workers’ human capital levels and hence their productivities on employment.
    • Higher productivity may be rewarded in the marketplace through higher earnings.
      • If this causal relationship is true, a policy to increase educational attainment will increase earnings.
    • Alternatively, correlation does not imply causation, and there may be a spurious positive correlation between education and earnings.
      • Education may have no effect whatsoever on productivity.
      • Workers may possess heterogeneous innate abilities which determine their earnings.
      • High-ability workers may choose more education than low-ability workers, regardless.
        • If this is a spurious relationship, a policy to increase educational attainment will affect neither the level of earnings nor their distribution.
    • Mincer’s earnings function measures the relationship between schooling and earnings.
      • lnw =ρ ∙ s + controls + ε
        • lnw = the natural logarithm of the wage
        • ρ = the causal net rate of return from an additional year of schooling, s
        • controls = the other variables that determine wages
        • ε = an error term that satisfies the standard properties
        • ρ = MW(s)/w(s) by definition
      • The object is to estimate ρ and use it to test whether i(s) equals the market rate of interest, r.
        • If i(s) ≠ r, educational investments are inefficient, and government policies may increase social well-being. If the error term possesses standard properties, OLS estimators may be used to obtain an unbiased estimate of ρ.
        • However, some of the core OLS assumptions may be violated, and ρ may be biased.
        • Moreover, there is reason to believe that there are omitted variables that they are correlated with s. One of the largest difficulties is unmeasured differences in innate ability.
    • After controlling for bias, studies find that:
      • The OLS estimates are biased downward and hence too small.
      • The causal rate of return to human capital investments in the United States is between 9% and 16%, or about 60% larger than the OLS estimated rate of return.