Human Capital Investment, Inequality and Economic Growth

Human Capital Investment, Inequality

and Economic Growth

Kevin M. Murphy & Robert H. Topel

The University of Chicago

February 2014

Revised March 2015

This paper was prepared in honor of our friend Eddie Lazear, and presented at the Journal of Labor Economics Conference in Honor of Edward Paul Lazear, Stanford University, February 7-8, 2014. We are grateful to conference participants for helpful comments, especially James Heckman, Canice Prendergast, Chinhui Juhn and our late friend and colleague Gary Becker. We also appreciate the useful comments of two anonymous referees. And Eddie. Thanks for everything Naz.

Abstract

We treat rising earnings inequality as an equilibrium outcome in which endogenous human capital investment fails to keep pace with steadily rising demand for skills, driven by skill-biased technical change (SBTC). We focus on the supply side, where human capital choices of individuals and families affect the skill composition of the labor force, and hence skill prices, on three margins: (i) the type of human capital in which to invest; (ii) how much human capital to acquire via investment; and (iii) the intensity with which human capital is applied in producing earnings. We refer to first of these as the extensive margin of skill production, and the latter two decisions as occurring on the intensive margins of human capital acquisition and utilization. Intensive margin choices are substitutes for the creation of new skilled workers on the extensive margin, and we provide evidence that the extensive margin has stalled as a source of skilled labor. Yet intensive margin choices are strongly complementary with each other. Greater incentives to invest in human capital also raise the returns to using human capital intensively, while the opportunity to use skills intensively increases the returns to investment. Though the extensive margin supply elasticity always dampens the impact of SBTC on inequality, greater elasticities on the intensive margins magnify inequality. We also show that when SBTC is the main driver of economic growth, greater inequality reduces the rate of economic growth.

1. 
   Introduction
   

Economists recognized the emergence of rising earnings inequality in developed economies, especially the United States, decades ago.¹ The basic facts are well known—in the U.S., wage growth of low skilled individuals stagnated after the mid-1970s, and their employment rates declined, while individuals near the top of the wage distribution enjoyed rapid and sustained wage growth. More recently the seeming permanence of this change in the income distribution has motivated a number of policy proposals meant to mitigate its impact, such as more progressive income taxation, wealth and inheritance taxes, pay regulation and greater empowerment of labor unions. We argue that most of these interventions would treat the symptom rather than the disease, exacerbating the underlying scarcity of skilled labor that is the root cause of greater inequality of labor market outcomes.

We treat rising earnings inequality as an equilibrium outcome in which endogenous human capital investment fails to keep pace with steadily rising demand for skills, driven by skill-biased technical change (SBTC) or other shifts in economic fundamentals, such as a decline in the price of capital, that favor highly skilled labor.² Our main focus is on the supply side, where the human capital choices of individuals and families affect the skill composition of the labor force, and hence skill prices, on three margins. The first is a choice of the type of human capital in which to invest—“skilled” or “unskilled” in our analysis—say by deciding whether to attend or complete college. We refer to this source as the extensive margin because responses to a rising demand for skills add more individuals to the ranks of skilled labor, just as the output of an industry expands by entry of new firms. Second, given choice of a skill type, an individual decides how much human capital of that type to acquire; when skill prices are high, more investment occurs. Third, for a chosen skill type and amount of human capital, an individual must also decide how intensively their skills will to be applied to the market sector, say through effort, labor supply or occupational choice. We refer to the latter two decisions as occurring on the intensive margins of human capital acquisition and utilization, similar to an expansion of output by infra-marginal firms when rising market demand increases price in a competitive market. All of these choices are affected by heterogeneous opportunities and abilities to acquire human capital, and each is a source of greater skill supply that can “meet” rising demand for skills and so dampen its impact on skill prices.

Among other results, we show that while investment and utilization on the intensive margins are substitutes for the creation of new skilled workers on the extensive margin, intensive margin choices are strongly complementary with each other. Greater incentives to invest in human capital, due to a higher price of skills, also raise the returns to using human capital intensively, while the opportunity to use skills intensively increases the returns to investment. Unlike the extensive margin supply elasticity, which always dampens the impact of SBTC on earnings inequality by increasing the number of skilled workers, greater elasticity of response on the intensive margins magnifies the impact of SBTC on earnings inequality because the increased per-worker supply of human capital increases the earning power of high ability workers.

We argue that these forces are important in light of the evident slowdown in educational attainment in the US, which has been especially prominent for men. When the extensive margin flow of individuals who are able to join the ranks of skilled labor slows or declines—which raises the price of skills—the incentives for the more “able” to acquire even more human capital and to apply it intensively magnify the effects of rising skill demand on overall earnings inequality. This effect is especially important in an intergenerational context, where the skills and resources of high income families beget greater human capital investment in their offspring. As James Heckman (2008) has recently put it, “Children in affluent homes are bathed in cognitive and financial resources” that reduce the costs of acquiring human capital. These resources include better inputs from parents, who are themselves more skilled, as well as financial resources, superior schools and interactions with comparably advantaged peers. All of these factors facilitate human capital investment. These “able” investors benefit disproportionately from an increase in the relative scarcity of skilled labor because they are well positioned to exploit the resulting higher returns to human capital investment and utilization. With diminished supply growth of skilled labor from the extensive margin, the incentives of advantaged investors to acquire even more human capital and to use it more intensively magnify earnings inequality.

Many view rising inequality itself as an important social problem worthy of corrective policies. We don’t take a position on these concerns, but we do argue that effective policies meant to limit or reduce inequality should, if possible, attack its source, which is a relative scarcity of skilled labor. We also emphasize a less normative concern about rising earnings inequality, which is that greater inequality reduces the rate of overall economic growth that can be realized from a given rate of skill-biased technical progress. Specifically, we embed the human capital investment incentives mentioned above in a model of economic growth with both human and physical capital deepening. In our model, productivity growth accrues to human capital because physical capital is elastically supplied at a constant return. When technological progress or other economic fundamentals favor skilled labor—which has evidently been the case—the induced growth rate of overall productivity is proportional to the labor income share of skilled workers. Other things equal, greater earnings inequality reduces this share because the relative demand for skilled labor is price elastic—the elasticity of substitution between skilled and unskilled labor exceeds 1.0. This means that factors causing greater inequality lower the rate of economic growth associated with a given rate of SBTC, because employers substitute away from relatively expensive skilled labor.

Our analysis is motivated by several empirical facts regarding the earnings distribution and the returns to various measures of skill, which are documented in the next section. The primary fact is the well-known increase in wage and earnings inequality, which began in the 1970s for the U.S. We demonstrate that this rise in inequality is not restricted to any particular part of the wage distribution—such as the very top or the very bottom. Instead, rising inequality occurs throughout the distribution—the wages of persons at the 99^th percentile increased relative to those at the 95^th, but so did the wages of those at the 60^th percentile relative to the 50^th and at the 20^th percentile relative to the 10^th. Similarly, educational wage premiums also began a steady increase around 1980 and the premium associated with college relative to high school completion had roughly tripled by the late-1990s. Though less pronounced than in the United States, these changes in relative earning power of more versus less skilled individuals also occurred in other developed economies, and at about the same time.³ These outcomes indicate that rising inequality is mainly a skill-based phenomenon and the result of changes in economic fundamentals, such as technical change that raises the relative productivities of more skilled workers or, similarly, a decline in the price of factors (such as capital) that are more complementary with skilled than unskilled labor, rather than particular institutions or policies that might have favored one group or another.

The evident increase in skill “prices” has occurred in an environment of greater relative skill abundance. For example, the average educational attainment of the workforce and the fraction of the workforce who are college graduates have increased, which again point to changes in economic fundamentals—growth in demand for skills has outpaced growth in supply, so that the relative price of skill has risen. While there is compelling evidence that individual investments in education respond to rising returns, we show most of this response involves persons who leave college before obtaining a four-year degree. This is especially apparent for men, for whom the fraction completing a four-year college education has remained roughly constant at 30 percent since 1980.

2. 
   Background: Rising Skill Prices and Human Capital Investment
   

We begin by documenting some new and old facts about rising inequality and human capital investment in the U.S., using data from the March Current Population Surveys of 1963-2013, the U.S. Censuses since 1940, and the American Community Surveys since 2001.

Figures 1A and 1B and show the magnitudes of rising wage inequality for “full-time” men and women aged 18-64 in the indicated years.⁴ The figures graph average real weekly wages (deflated by the GDP price deflator for personal consumption expenditures (PCE)) at selected percentiles of the wage distribution since 1962. Figure 1A shows that real weekly wages roughly doubled for men in the 95^th percentile of the wage distribution, driven by a well-known acceleration of wage growth that began in the late 1970s. In contrast, real wages of men at the 10^th percentile did not grow at all, though neither did they materially decline.⁵ The timing of rising wage inequality is virtually the same among women, though magnitudes are different than for men—even the least skilled (lowest wage decile) women experienced rising real wages. These points are further illustrated in Figure 2, which graphs cumulative real wage growth at each percentile of the male and female wage distributions over 40 years (1972-2012).⁶ Note that wage growth was monotonically increasing over the entire wage distribution, which is perhaps the key fact about rising inequality in the U.S.—the trend toward rising wage disparities was not unique to the top or bottom of the distribution, but occurred at all skill levels for both men and women.

The patterns in Figure 2 undermine “theories” that attribute rising inequality to an outbreak of self-dealing conspiracies or rent-seeking among the very rich, while wage growth for everyone else languished.⁷ The monotonic increase in wage growth across percentiles for both men and women strongly indicates that market fundamentals favoring more skilled workers are the driving force behind rising inequality. This important fact motivates our emphasis below on demand-side changes that have increased the relative productivity of more skilled workers.

It is also worth noting that use of the PCE deflator rather than the CPI makes some difference for gauging the magnitudes of real wage growth. It is well known that various biases in the CPI cause it to overstate increases in the cost of living, and that some of these biases are at least partially corrected by the PCE index, which is chain-weighted and which includes prices paid by a broader population of consumers as well as a different mix of goods.⁸ Over short periods these differences don’t matter much, but over long ones they do. Had we used the CPI, estimates of wage growth would have been slightly lower though there would be no impact on inequality because we deflated all wages by a common index. Though we do not pursue the point here, this common index assumption could be misleading in terms of calculations of relative welfare—for example, we would overstate the growth in inequality if nominal prices of goods purchased by low income households rose by less than those for high income households, which some have conjectured.⁹¹⁰

Skilled-biased technical change and other factors that affect skill demand raise the relative demand for skills, but its impact on inequality is also determined by the supply of skills—the propensity of workers, especially new workers, to acquire skills through human capital investment. Figure 3 shows the evolution of college attainment for male and female high-school cohorts from 1918 through 2003. For these calculations high-school “cohorts” are defined by the calendar year in which individuals turned 18; the typical age of high-school graduation. The figures shows that college completion rates (defined as 16 or more years of completed schooling) for pre-1935 cohorts were quite low, but then grew rapidly for the next 30 years. For men, the college completion rate peaked at 33 percent for high-school cohorts of the mid-1960s—who, it should be noted, received a deferment from the Vietnam-era military draft while in college. After falling through the 1970s male college completion again exceeded 30 percent in the mid 1980s, but declined slightly thereafter. Similarly, the fraction of men who have completed some college (one year or more post high school) has also never surpassed the peak that was achieved in by cohorts from the mid-1960s. In contrast, college completion rates for female cohorts continued to grow—with some noteworthy deceleration in the 1970s—and have exceeded men’s completion rates since about 1980. For cohorts reaching college age after 2000 the fraction of women completing four or more years of college reached about 35 percent, exceeding the 1960s peak of male college completion.

A key ingredient of our analysis is the response of human capital investment to an increase in the “price” of skills. Using college attendance and completion as our measures of investment on the extensive margin, Figures 4A and 4B show the evolution of the college/high-school wage ratio for full-time workers along with the fractions of each cohort that have some college or have completed college.¹¹ Note that the college wage premium for both men and women bottomed out in the late 1970s. This nadir corresponds almost exactly to the minimum of men’s college participation (and coincides with an inflection point in college participation for women). After 1979 the fraction of men who had completed some college (at least one year) rises with the wage premium, suggesting substantial human capital investment in response to greater potential returns, but even this growth stalls after the mid-1980s. And note that any possible investment response is far more muted for actual college completion. In spite of a rough tripling of the college premium after 1979, male college completion rates are not much changed—fewer than 30 percent of men in the most recent cohorts complete college before age 30—which indicates that the supply of these skills has proven highly inelastic over the indicated time interval. The picture for women in Figure 4B is somewhat different—the 1970s decline in the college premium does seem to have slowed the growth of women’s investments in schooling, but subsequent growth in the premium was associated with renewed growth in the shares of women with some college training and who have completed college.

The modal college experience is a four-year continuation of full-time schooling after high-school, culminating with graduation at age 22. Figures 5A and 5B graph college completion rates by age for 5-year high-school cohorts since 1960, showing that this prototype accounts for only about half of individuals who report completing college. For men, the fraction completing college by age 23 (the vertical line) is about 15 percent for every cohort except those of 1965 and 1970—who benefitted from the availability of draft deferments during the Vietnam War. Thus there is little evidence that rising educational premiums after 1980 caused more men to acquire a college education via the traditional route. Yet cohorts after 1980 do have higher (and rising) college completion rates—all of the increase is accounted for by rising shares of individuals who complete college at older ages. Indeed, completion rates continue to rise up to nearly age 40. The picture for women is again somewhat different. For them, each new cohort is more likely to have graduated college by age 23 than the ones before it. But as for men, college completion continues to rise after age 30, and an increasing fraction of college completion occurs after age 23. About 40 percent of the women in the youngest cohort (age 18 in 2000) had completed college by age 32, which is double the corresponding rate for the 1965 cohort.

Why did growth of male educational attainment stall, and why have men fallen behind women in terms of overall educational attainment? Whatever the core sources might be, the evidence suggests that men are simply less prepared, on average, for post-secondary education.¹² Figure 6 shows grade point averages of male and female graduating high school seniors from 1990 to 2009.¹³ Though GPAs of both genders are rising—which may reflect grade inflation more than improved performance—the important point is that there is a substantial gap between the measured high school performance of males and females; females average about 0.2 grade points higher than males, and there is no indication that the gap has narrowed. This gender gap in high school academic performance persists in the population that continues on to college. Table 1 reports the distributions of first year college GPAs for men and women attending four-year non-profit colleges and universities, broken out by broad areas of intended study. Not only do women perform better overall, but the performance gap is at least as large in traditionally “male” majors (science, engineering and mathematics) as it is in majors with a heavier representation of female students (social sciences and humanities). For example, in the 2003-04 cohort two-thirds of women majoring in the sciences and engineering had GPAs above 3.0, compared to only 48 percent of men. The gap between the fractions of college women and men earning high GPAs also widened over time.

The model developed in the next section emphasizes that rising returns to skill increase the incentives of able individuals to invest in human capital and, once it is produced, to use human capital more intensively. Some supportive evidence on the latter point is in Figures 7A and 7B, which show average weekly hours worked by percentile of the weekly wage distribution in 1970-72 (before the increase in wage and earnings inequality) and 2010-12. For both men and women, the evidence indicates that rising returns to skill (see Figure 2) are associated with increased utilization—relative weekly hours increased in the right tail of the wage distribution, where wages increased the most.¹⁴ For men the range of increased effort is confined to the upper half of the distribution, with monotonically larger increases in the highest percentiles. The pattern for women is similar, though only the bottom quartile of their wage distribution is associated with declining hours worked.

The data summarized above are the empirical context for our following modeling effort. Especially for men, the data suggest that human capital investment via schooling (measured by college graduation) has been unresponsive to the large increase in the educational wage premium, which we interpret as indicating that the supply of college graduate human capital has low price elasticity during the era of rising inequality, at least on the “extensive” margin of producing a larger stock of college and higher educated workers. Though we don’t explore the issue further here, we also think it is noteworthy that much of the correspondence between rising educational premiums and completed schooling is accounted for by two sources. First, a much larger fraction of both men and women report completing some schooling post high-school, though they do not complete a traditional four-year program. Second, especially for men, the expansion of college “graduates” is due in large part to completion at older ages. Human capital from these sources is likely to be qualitatively and quantitatively different, on average, than from the relatively unresponsive margin of continued schooling after high school, culminating in a college or advanced degree. And for the range of skills that experienced sharply rising returns—the upper reaches of the distribution—the evidence is that “gainers” have magnified their advantage by applying their skills more intensively.

3.