The college earnings premium and changes in college enrollment: Testing models of expectation formation

Labour Economics 49 (2017) 84–94

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The college earnings premium and changes in college enrollment: Testing models of expectation formation☆ Eleanor W. Dillon Department of Economics 306 Converse Hall Amherst College Amherst, MA 01002, USA

a r t i c l e Keywords: College premium College enrollment Belief formation

i n f o

a b s t r a c t This paper studies how students build expectations of the future price of college skills when making college enrollment decisions. I compare several possible proxies for students’ expectations of the lifetime earnings gains from college. Students may base their expectations on the earnings of current workers or they may have some information about future earnings. Since 1970, a forecast of future earnings based on static expectations has been a poor predictor of the ex post college premium for successive cohorts. Nonetheless, high relative earnings for college-educated workers at the time a student graduates high school increases his probability of enrolling in college, while his cohort’s future realized earnings do not. A 10 percentage point increase in the contemporaneous college premium is associated with a 1 percentage point rise in college enrollment rates, controlling for tuition and student characteristics. © 2017 Elsevier B.V. All rights reserved.

1. Introduction From 1980 to 2002, workers with a college degree moved from earning 45% more than workers with only a high school diploma to earning 94% more. This change in the price of college skills alters the costbenefit tradeoff for students who are considering enrolling in college. However, when students make this choice they are uncertain about future skill prices. Do students graduating high school now expect these new high prices to persist throughout their working lives? Did high school graduates in 1980 anticipate the future rise in prices? The supply of college-educated workers adjusts mainly through the education choices of young people entering the labor force. If these young workers over- or underestimate future skill prices they may not make optimal investments in education. In addition to being individually costly, these mistakes slow the pace at which the supply of high-skill workers adjusts to changes in labor demand. I consider how students build their expectations of future skill prices when deciding whether to enroll in college. I begin with a simple model where students choose whether to enroll in college based on the costs of attendance, including tuition, effort costs, and the opportunity cost not working, their expected delayed payoff of higher lifetime earnings with a college degree, and heterogeneous abilities that complement education. At the time they make this choice, students must build expectations of their future earnings with different levels of education. I compare

three models of student belief formation, static expectations, adaptive expectations, and perfect foresight, and test which assumption best fits observed patterns of college enrollment. These models of belief formation represent some of the most common assumptions in the existing literature on college enrollment choices. For example, Laitner (2000) and Fang (2006) model enrollment choices assuming students perfectly forecast future changes in the return to a degree. In contrast, Heckman et al. (1998) and Lee et al. (2015) model enrollment choices as a sequence of steady states, which is more aligned with a static expectations assumption where enrollment choices depend on contemporaneous returns to a college degree. Each model provides an appealingly clear mapping from observed data to expected earnings. They also reflect extreme assumptions about the information available to students: high school graduates forecast the future either perfectly or not at all. In an intermediate case where students have a noisy signal about future skill prices, which I will explore, we might expect both the current college premium and the perfect foresight projection to have some influence on college enrollment rates. I use data from the Current Population Survey March Supplement from 1964 to 2015 to construct average lifetime earnings with and without a college degree for each cohort of men graduating high school over this period. I first consider the case of static expectations, where students believe that skill prices will remain at their current levels. For this case, I use earnings for working men of all ages at the time each

☆ I thank John Bound, Charles Brown, Brad Hershbein, Matthew Shapiro, Daniel Silverman, Jeffrey Smith, Dmitriy Stolyrov, Matthew Wiswall, seminar participants at University of Michigan, the Federal Reserve Board of Governors, and Arizona State University, and several anonymous referees for helpful comments and suggestions. All errors are, of course, my own. E-mail address: [email protected]

https://doi.org/10.1016/j.labeco.2017.09.006 Received 31 March 2016; Received in revised form 23 September 2017; Accepted 26 September 2017 Available online 28 September 2017 0927-5371/© 2017 Elsevier B.V. All rights reserved.

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Labour Economics 49 (2017) 84–94

cohort graduates high school to forecast what they will earn at each age in the future. I also test an adaptive expectations model, a refinement of static expectations where students respond to a weighted average of current and past college premiums. Finally, for the earlier cohorts in the sample, I use observed realized earnings in all years to construct expected earnings under the assumption that students fully anticipate future skill prices. I use data from the CPS October Schooling Supplement to estimate the probability that an individual student will enroll in college, conditional on these measures of the expected earnings gain from a college degree and on other covariates. I find that the static expectations assumption fits observed patterns of college enrollment between 1970 and 1995 far better than the perfect foresight case. In fact, the perfect foresight measure has a weak negative correlation with college enrollment rates over time, suggesting that students have no information about the future path of the college premium. Moreover, past earnings gaps have no effect on enrollment when included along with contemporaneous earnings, suggesting that static expectations is a better description of student belief formation than an adaptive expectations model. Changes in the static expectations measure of the college premium have a substantial effect on college enrollment choices. On average, a 10% increase in the relative lifetime earnings for college-educated workers, $9,300 in 1980, raises the probability that a high school graduate will attend college by about 1 percentage point. If students responded to future earnings patterns instead of contemporaneous ones, college enrollment rates would have been 6 percentage points higher in 1980, and 2.6 percentage points lower in 1970. The identification of this relationship comes primarily from changes in the expected college premium over time, although I also allow expectations to vary by race. The static expectations measure of the expected lifetime gains to college fell through most of the 1970s, rose rapidly in the 1980s and 1990s, and has remained flat or declined slightly since 2002. While many factors that influence college enrollment have shifted over this period, this unique trend in the expected college premium allows me to isolate its effect. The estimated relationship between the return to college and college enrollment is robust to controlling for the demographics of high school graduates, college tuition, and family income. Several earlier papers have considered the relationship between college enrollment rates and average earnings for workers with and without a college degree. Freeman (1975, 1976) finds a positive relationship between the difference in log earnings and the share of young American men enrolling in college from 1951 to 1973. In contrast, Kane (1994) finds this earnings ratio is not an important predictor of enrollment choices and cannot explain differences in college enrollment rates between black and white men and women between 1973 and 1988.1 Heckman et al. (1998) and Laitner (2000) model how an increase in the returns to schooling, through a less progressive income tax in Heckman, Lochner, and Taber and through skill-biased technological change in Laitner, could theoretically increase educational attainment. Buchinsky and Leslie (2010) present a theory on how that adjustment will depend on the way students build their expectations of future skill prices under uncertainty, while Heckman et al. (2006) point out how dramatically the ex ante static expectation of the returns to college and the ex post realized returns have diverged over the past 40 years. Finally, Wiswall and Zafar (2015b) present experimental evidence that students update their beliefs about their own education-contingent future earnings in reasonable ways in response to accurate information

about current population average earnings. This result is consistent with my finding that students rely on the current labor market to form beliefs about their own future earnings. The key contribution of this paper is to test which model of belief formation best fits the observed patterns of college enrollment over time. I also find that a careful, theory-driven specification of the expected college premium is important when measuring the response of college enrollment. My static expectations measure of the discounted lifetime earnings gains from college, which places more weight on the current earnings of younger workers, has a large, positive, and statistically significant effect on college enrollment, which contrasts with some of the earlier work that had considered a simpler ratio of average earnings for all workers. Finally, I build on earlier work by considering a longer time horizon that covers both increases and decreases in the relative earnings of college-educated workers, which allows me to better identify the role of the college premium. The next section presents a simple model in which high school graduates decide whether to enroll in college based on the costs of college, their expectation of their future earnings with and without a college degree, and their own abilities, which affect their potential earnings and complement college skills. Section 3 summarizes my data and the trends in relative earnings and college enrollment. An important limitation of the Current Population Survey is that it does not include a measure of individual cognitive skills, which theory suggests will correlate with education.2 Section 4 details several approaches for constructing expected future lifetime earnings at each level of education, and discusses the consequences of not measuring ability in the earnings estimates. Section 5 estimates the relationship between expected relative lifetime earnings and college attendance and Section 6 concludes. 2. The labor market and college choice High school students choosing whether to enroll in college must compare the costs of attendance to their expected earnings gains. The expected monetary return to a college education will vary over time and across individuals, incorporating changes in the expected market price of college skills and differences in individual abilities that complement education. I assume that students know their own ability by the end of high school,3 and that they forecast the market return to college over their working lives using the best information available to them. I consider an economy with only two types of workers: those with a high school education and those with a college education. Earnings vary across workers, based on education, age, and other demographics, and over time. The model therefore has two time concepts: an individual’s working life and calendar. Throughout, s denotes age, or a year of working life, and t denotes calendar time, which identifies cohorts of high school graduates and snapshots of the labor market. 2.1. Determinants of earnings The first step in building students’ expectations of future earnings is to specify the determinants of earnings for each type of worker in each year. I consider a generalized Mincer (1974) model of earnings determination with only two levels of schooling in which the effects of experience vary by education. Log annual earnings in year t for workers with a high school education depend on a polynomial in experience at age s, xis , a single-dimensional measure of individual ability, 𝜃 i , and other worker characteristics, zi , 𝑙𝑜𝑔(𝑦0𝑖𝑠𝑡 ) = 𝑧𝑖 𝛼𝑡 + 𝛾𝑡0 (𝑥𝑖𝑠 ) + 𝜃𝑖 + 𝑢𝑖𝑠 ,

1

A related set of papers study the effect of idiosyncratic expectations of the return to college within a cohort rather than changes in the market price of college skills over time. Freeman (1976), Manski and Wise (1983), Dominitz and Manski (1996), and Attanasio and Kaufmann (2009) survey students about their subjective expected future earnings at different education levels and find that students who expect greater gains from college are more likely to enroll. Rosen and Willis (1979) and Cunha and Heckman (2007) find that, within a cohort of high school graduates, individuals’ college enrollment choices depend on their idiosyncratic ex post returns to college.

(1)

2 This limitation is shared with all long-running and representative cross-sectional surveys of U.S. earnings. 3 The framework and conclusions are the same if people continue to learn about their ability during college and their working lives and forecast their expected earnings with their best guess of their ability at the time they graduate high school.

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𝛽̂𝑖𝑡 summarizes the information about the value of a college education that is available to students graduating high school in year t. In addition to the opportunity cost of delaying work, which is captured in 𝛽̂𝑖𝑡 , attending college involves direct costs, Cit . These costs will vary across individuals because of differences in the psychic or effort costs of college, borrowing costs, tuition at nearby colleges, and the student’s parents’ ability to support him while he is studying instead of working. A student’s decision to enroll in college depends on both his ability and these costs. While higher ability individuals will have higher earnings at either education level, they are more likely to elect to go to college because their abilities multiply the returns to college. An incomemaximizing student will attend college if the expected returns to college exceed the costs. In log form, he will enroll in college if

where uis ∼ N(0, 𝜎 2 ) is an iid transitory earnings shock. Log annual earnings for workers with a college education are determined by 𝑙𝑜𝑔(𝑦1𝑖𝑠𝑡 ) = 𝑧𝑖 𝛼𝑡 + 𝑏𝑡 + 𝛾𝑡1 (𝑥𝑖𝑠 ) + 𝜃𝑖 + 𝑢𝑖𝑠 .

(2)

The coefficients of the wage equation vary by year t, capturing that average earnings will vary by cohort as well as worker characteristics. Earnings differ across the two education groups in two ways: collegeeducated workers have a baseline earnings boost of bt and also experience different earnings growth with experience, 𝛾𝑡1 instead of 𝛾𝑡0 . Allowing the effects of experience to differ across education groups adds an important degree of flexibility. Katz and Murphy (1992) find that gains from experience were higher for high school graduates than college graduates in the 1980s. Elsby and Shapiro (2012) and Heckman et al. (2006) find that gains from experience have since fallen for high school graduates and risen or remained steady for college graduates.

𝜃𝑖 ≥ log(𝐶𝑖𝑡 ) − 𝑙𝑜𝑔(𝛽̂𝑖𝑡 ) −

A student graduating high school in year t can anticipate discounted lifetime earnings of ( 2) 𝑇 ∑ ( ) 𝜎 (3) 𝛿 𝑠 𝑒𝑥𝑝(𝜃𝑖 )𝑒𝑥𝑝 𝑒𝑥𝑝 𝑧𝑖 𝛼 ̂𝑡𝑠 + ̂ 𝛾𝑡𝑠0 (𝑠) 2 𝑠=0

(4) 3. Trends in earnings and college enrollment

if he goes on to complete college, where 𝛿 is an annual discount rate and 𝑏𝑡𝑠 , ̂ all workers retire T years after they graduate high school. 𝛼 ̂𝑡𝑠 , ̂ 𝛾𝑡𝑠0 , and ̂ 𝛾𝑡𝑠1 indicate the graduate’s best guess, as of year t, of the parameters that will determine his earnings at age s. Under an assumption of static expectations, high school graduates expect the labor market to remain as it is, so 𝛼 ̂𝑡𝑠 = 𝛼𝑡 ∀s. Under perfect foresight, students have no uncertainty about future developments in the labor market, so 𝛼 ̂𝑡𝑠 = 𝛼𝑡+𝑠 . Finally, in the adaptive expectations framework, graduates’ beliefs are a weighted average of current and past labor market parameters. In this simplified model individuals either work or attend school and everyone completes their degree in four years, so the lifetime earnings for college graduates include four years of zero earnings while they finish their education. These years out of the workforce are also reflected in accumulated experience: s years after he graduates high school a worker who went directly to work would have s years of experience, while one who went on to college would have 𝑠 − 4. This assumption may slightly over- or understate the lifetime college earnings premium. As pointed out by Bound et al. (2010), many students take longer than four years to complete their degree. On the other hand, assuming zero earnings during college understates lifetime earnings for students who do some work while enrolled.4

I estimate the determinants of earnings and college enrollment using 52 years of U.S. data from the 1964–2015 March Annual Demographic Supplements and 1970–2015 October Schooling Supplements of the Current Population Survey (CPS). I use the additional earnings data from 1964 to 1969 to test the adaptive expectations model of belief formation. The March CPS supplement includes information on total earnings in the previous calendar year, so the March 1970 supplement surveys earnings over 1969. While the college earnings premium has risen for women, their labor force participation and college enrollment choices also changed over this period for reasons beyond the scope of this paper, so I restrict my analysis to men. My earnings sample includes approximately 1.8 million civilian men aged 18 to 65 who worked at least 14 weeks in the previous year and who did not spend any time out of the labor force. I use CPS-provided weights designed to make the earnings supplement sample representative of the U.S. working population. My earnings measure is total income from all jobs in the previous year including income from farms and other businesses.5 Fig. 1 plots the ratio of annual earnings for workers with exactly 4 years of college and workers with exactly a high school diploma.6 In 1976, the average college-educated worker made 144% of the average earnings for high school-educated workers. By the peak of the college premium in 2010, college-educated workers earned twice as much as workers with only a high school diploma. This rise in the relative earnings of college-educated workers occurred primarily between 1980 and 2002. Since then, relative earnings for college-educated workers have remained fairly stable, with slight dips around 2004 and since 2010.

2.3. The choice to enroll in college For each model of belief formation, I assume that all new high school graduates use the same information when developing their expectations of future earnings. Under this assumption, the difference in lifetime earnings with and without a college degree can be decomposed into privately observed ability, a variance term, and a publicly observed multiplier: ( 2) 𝜎 𝛽̂𝑖𝑡 , 𝑒𝑥𝑝(𝜃𝑖 )𝑒𝑥𝑝 (5) 2

5 Historically, the CPS has reported topcoded labor income, which could bias my estimates of the college wage premium because the topcode will disproportionately affect more educated workers. I use the Bureau of Labor Statistics-provided rank proximity swap method to accurately capture the top end of the earnings distribution from 1976 to 2015. From 1964-75 I adjust topcoded earnings with a race, education, and employment statusspecific multiplier equal to the average ratio of these uncensored earnings to the topcode value in 1976–1981. 6 The high school graduate sample does not include people who received a GED. Prior to 1992 the CPS did not distinguish between workers with 4 years of college and those with a college degree, so the college-educated group will include a small number of workers with 4 years of college credit but no degree.

where 𝛽̂𝑖𝑡 =

4

𝑇 ∑ 𝑠=4

(6)

that is, if his ability exceeds a threshold that depends on his individual costs of college and his expectation of the returns to college. This simple model assumes that the direct costs of college are independent of a student’s innate ability, 𝜃 i , and the empirical work will include only poor proxies for some dimensions of these costs, such as effort costs. As can be deduced from Eq. (6), the estimated relationship between 𝛽̂𝑖𝑡 and college enrollment will be unaffected if these omitted dimensions of the cost of college are orthogonal to innate ability or if the log of these costs is a linear function of ability, as is assumed in, for example, Cunha and Heckman (2007).

2.2. Belief formation

if he goes directly into the workforce and ( 2) ( 𝑇 ) ∑ 𝜎 𝑏𝑡𝑠 + ̂ 𝛿 𝑠 𝑒𝑥𝑝(𝜃𝑖 )𝑒𝑥𝑝 𝑒𝑥𝑝 𝑧𝑖 𝛼 ̂𝑡𝑠 + ̂ 𝛾𝑡𝑠1 (𝑠 − 4) 2 𝑠=4

1 2 𝜎 , 2

𝑇 ( ) ∑ ( ) 𝑏𝑡𝑠 + ̂ 𝛿 𝑠 𝑒𝑥𝑝 𝑧𝑖𝑠 𝛼 ̂𝑡𝑠 + ̂ 𝛾𝑡𝑠1 (𝑠 − 4) − 𝛿 𝑠 𝑒𝑥𝑝 𝑧𝑖𝑠 𝛼 ̂𝑡𝑠 + ̂ 𝛾𝑡𝑠0 (𝑠) . 𝑠=0

I evaluate this assumption in Section 4.2. 86

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the 1970s and rising with the premium through the 1980s and 1990s. I measure college enrollment using the annual October schooling supplement to the CPS. My sample includes 17 to 19 year old men who report in October that they graduated high school in the current calendar year (mostly in the spring). Students are considered to have started college if they report being currently enrolled in a four-year college. This definition somewhat understates the true share of the population that eventually attends college since it does not include students who take time off between high school and college. Cameron and Heckman (2001) track college enrollment among all 21 to 24 year old high school graduates, which better captures students who take time off, and find a very similar pattern in college enrollment rates over the same time period. two-year colleges represent a growing share of the college market. The share of new high school graduates enrolled in any college, plotted along the right axis of Fig. 2, has increased even more rapidly than four-year college enrollment. 4. Measuring the expected college premium Fig. 1. Ratio of Average Earnings by Education. Source: March CPS. Graph plots the ratio of average annual earnings for workers with exactly 16 and 12 years of schooling. The series are shown as three-year moving averages.

4.1. Determinants of annual earnings To construct the expected college premium under static expectations, I estimate year-specific determinants of annual earnings using data from the March CPS.7 For each year of the sample, I estimate the parameters of earnings Eqs. 1 and 2. zi includes a constant and indicators for Black, Hispanic, or other non-white workers. Earnings also depend on education-specific quartic functions of potential experience, xis . To reduce spurious changes in predicted earnings from measurement error, I include two years of lagged data when estimating the earnings parameters for each year.8 Table 1 presents the parameters estimated from the log earnings equation for select years. As expected, college-educated workers earn substantially more than high school educated workers. In keeping with Katz and Murphy (1992), Elsby and Shapiro (2012), and Heckman et al. (2006), high school graduates experience higher lifecycle earnings growth early in the sample, 98% over the first 10 years of work in 1970 in comparison to 80% for college graduates. This gap narrows by 2010, when high school graduates experience average earnings growth of 80% over the first 10 years of work and college graduates 77%. This gap in the returns to experience will temper the large differences in the intercept of earnings across education groups. As modeled in Eqs. (1) and (2), earnings also depends on individual innate ability. The CPS has no suitable measure of ability to include in the estimation equation.9 Many empirical studies, see Belley and Lochner (2007) for a recent survey, support the predictions of the college choice model: higher-ability high school graduates are more likely to enroll in college. Omitting ability from the earnings equation will therefore inflate the estimated college premium relative to the causal effect of college graduation on earnings. A student at the margin of attending college has lower ability than the average college student (or else unusually high costs of attendance) and should generally expect to earn less than the mean college graduate. Murnane et al. (1995), Taber (2001), and Heckman et al. use panel datasets to measure the return to college controlling for high school test scores. They find that the

Fig. 2. Share of New High School Graduates Enrolled in College. Source: October CPS. Graphs plot the share of 17 to 19 year olds who graduated high school in each year and enrolled in college the same fall. The series are shown as three-year moving averages.

The first line of Fig. 1 plots the ratio of total reported annual earnings. The sample includes only men who spent the full year in the labor force and worked at least 14 weeks, but within that sample the total earnings measure incorporates lower earnings for workers who spent part of the year un- or under-employed. College-educated workers have a higher employment rate and this pattern has become more pronounced over time (Juhn et al., 2002). Fig. 1 also plots the ratio of earnings adjusted to full-time full-year equivalent earnings using reported weeks worked and usual weekly hours. The ratio of these full-time equivalent earnings is consistently smaller than the ratio of total annual earnings and has risen more slowly, increasing 46 percentage points from 1980 to 2002 while the annual earnings ratio rose 51 percentage points. This adjusted measure is more comparable to other papers that have tracked the difference in weekly or hourly earnings, but it misses an important dimension of the differences in annual earnings across education groups. For the remainder of this paper I focus on total annual earnings. College enrollment roughly mirrors the movements in the college earnings premium over the past 46 years, providing suggestive evidence that enrollment decisions respond to the contemporaneous college premium. Fig. 2 shows enrollment rates falling with the college premium in

7 In theory, a more flexible alternative would be to construct cell-specific average earnings by year, education group, age, and other worker characteristics. In practice, even with the large annual sample of the March CPS, some of these year-education-race-age cells are sparsely populated. This flexible parametric approach allows me to smooth across these sparse cells. 8 That is, the parameters used to construct expected earnings for the 1980 cohort are estimated using data from 1978 to 1980. 9 As an alternative to individual-level ability measures, I experimented with a cohortlevel ability proxy based on average SAT scores and with instrumenting for college attendance using historical college tuition. Both proxies are too closely correlated with potential experience (which in a single year is simply an indicator of cohort and education) to provide a meaningful control for ability.

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Table 1 Determinants of real annual earnings.

Black

(1) 1970

(2) 1980

(3) 1990

(4) 2000

(5) 2010

−0.337∗ (0.018)

−0.189∗ (0.036) 0.542∗ (0.053) 0.188∗ (0.011) −1.194∗ (0.092) 0.320∗ (0.029) −0.309∗ (0.032) −0.033 (0.017) 0.196 (0.163) −0.039 (0.060) 0.014 (0.073) 9.491∗ (0.040)

−0.265∗ (0.019) −0.093∗ (0.013) −0.194∗ (0.026) 0.392∗ (0.034) 0.133∗ (0.008) −0.715∗ (0.073) 0.179∗ (0.025) −0.174∗ (0.029) −0.016 (0.012) 0.138 (0.122) −0.029 (0.045) 0.008 (0.055) 9.541∗ (0.022)

−0.303∗ (0.017) −0.217∗ (0.019) −0.247∗ (0.027) 0.749∗ (0.048) 0.158∗ (0.010) −0.906∗ (0.094) 0.245∗ (0.033) −0.251∗ (0.037) −0.034∗ (0.015) 0.087 (0.156) 0.018 (0.058) -0.064 (0.070) 9.283∗ (0.032)

−0.236∗ (0.017) −0.222∗ (0.017) −0.224∗ (0.028) 0.666∗ (0.038) 0.136∗ (0.008) −0.796∗ (0.083) 0.222∗ (0.031) −0.235∗ (0.036) −0.003 (0.013) -0.030 (0.141) 0.018 (0.055) −0.035 (0.069) 9.349∗ (0.019)

−0.258∗ (0.013) −0.224∗ (0.012) −0.156∗ (0.017) 0.711∗ (0.042) 0.137∗ (0.008) −0.728∗ (0.069) 0.176∗ (0.022) −0.161∗ (0.024) −0.006 (0.013) 0.035 (0.122) −0.007 (0.042) -0.010 (0.048) 9.277∗ (0.027)

41,367 0.168

56,346 0.156

58,558 0.174

46,889 0.145

71,560 0.224

Hispanic Other non-white College degree Experience Exper2 /100 Exper3 /1, 000 Exper4 /10, 000 College∗ exper Col∗ exper2 /100 Col∗ exper3 /1, 000 Col∗ exper4 /10, 000 Intercept Observations R2

Fig. 3. Difference in Discounted Lifetime Earnings by Education. Source: March CPS. The static expectation series plots the difference in expected discounted lifetime earnings for workers with exactly 16 and 12 years of schooling using a cross-section of workers in the labor market each year. The perfect foresight series plots the difference in realized discounted lifetime earnings for workers with exactly 16 and 12 years of schooling who turned 18 in each year. Both measures are described in more detail in Section 4.

Overall, these studies suggest that while some of the estimated college premium should rightly be interpreted as returns to unobserved ability, the movements in the causal return to college probably closely track the movements of the premium estimated here. In this case the estimated effects of the earnings gap on college enrollment will be too small in magnitude, since they are multiplying an earnings gap that is too large, but the qualitative results on how movements in this earnings gap affect college enrollment will be correct. High school students may also face the same difficulties as economists in disentangling returns to innate ability from the causal effect of college. In this case, the measures used in this paper will present a biased picture of the causal return to college, but perhaps an accurate picture of students’ beliefs.

Source: March CPS. Robust standard errors, clustered by education and cohort, in parentheses. ∗ indicates statistical significance at the 5% level. Regressions for each year include observations from the current and previous two years. Hispanics were not distinguished from other non-white workers before 1972. Weighted with CPS-generated inverse probability weights.

estimated college earnings premium falls between 25% and 50% when they control for these ability measures. The returns to unobserved ability could also vary across education groups. Heterogeneous returns to innate ability will further bias the estimated college premium away from the individual causal effect of college. Castex and Dechter (2014) and Heckman et al. both find that the returns to cognitive ability are somewhat higher for high school graduates than for college graduates. This discrepancy raises the gains from college for low ability students, since they face less penalty in the college market, and lowers the gains from college for high ability students. The key results of this paper will be most distorted if returns to innate ability have changed over time. A number of studies have attempted to quantify these changes with mixed results. Chay and Lee (2000), analyzing changes in residual earnings, conclude that changes in the earnings returns to innate ability explain at most 30% of the rise in the college premium between 1979 and 1991, while Castex and Dechter (2014), using direct measures of ability, conclude that returns to ability fell between 1980 and 2000, dampening growth in the college premium. Carneiro and Lee (2011) point out that increased college enrollment rates should have lowered the average ability of college graduates and that this compositional change has biased down the estimated increase in the college premium. In contrast, Bound et al. (2010) find that average test scores for four-year college starters did not change between 1972 and 1992 even though the share of students enrolling in college increased. Cunha et al. (2011) estimate a rich model that encompasses changes in the returns to college and innate ability and changes in composition using multiple panel datasets that include a direct measure of ability. They conclude that while there have been some changes in the return to innate ability, overall and across education groups, nearly all of the rise in the college premium since 1980 was generated by changes in the causal effect of college.

4.2. The college premium under static expectations I use the year-specific estimated earnings parameters to construct a projected gap in lifetime earnings for each year and within each race and ethnicity group, 𝛽̂𝑖𝑡 , following Eq. (5). For these calculations I assume that everyone discounts future earnings at 𝛿 = 1.105 . I set 𝑇 = 47, so that everyone retires at the age of 65 and high school graduates work for more years than college graduates. If high school students have static expectations, they treat current workers as a synthetic cohort and assume that when they are 35 they will earn what current 35 year-olds earn now and so on. For this model, I construct expected future earnings for each cohort of high school graduates using the earnings parameter estimates for that year. Specifically, the expected premia that influence enrollment choices for the high school class of 1980 are built using estimates from the 1978–1980 March CPS (which covers earnings during the 1977–1979 calendar years). The solid line in Fig. 3 plots this static-expectations measure of the gains in lifetime earnings for white men, the largest group of workers, from 1970 to 2015. This earnings gap differs from the ratio of average earnings plotted in Fig. 1 in several ways. The gap in expected earnings described in Eq. (5) incorporates the opportunity cost of college, which the average ratio ignores. In 2000, the average white male high school graduate could expect to earn $449,000 in present discounted dollars. If he went on to college he could expect to earn $649,000, or 45% more, far less than the 91% more in Fig. 1. This difference comes primarily from the opportunity cost built into the lifetime earnings gap. In 2000, the 88

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Labour Economics 49 (2017) 84–94

The construction of this expected lifetime earnings gap relies on three strong assumptions that merit some discussion. First, I assume that students do no work during college. Since 1986, the first year the March Earnings Supplement asks about school enrollment, 72% of 19–22 year olds who report being enrolled in college also report some earnings over the year. However, mean annual earnings for college students, including zeros, is $5,700 in 2010 dollars, less than 1% of discounted expected lifetime earnings, and these earnings do not exhibit clear time trends. Including these average earnings during college has no appreciable effect on the pattern of lifetime earnings gaps over time.10 Second, I assume that the variance of earnings is constant across time and education groups, so it can be pulled out of the sums over lifetime earnings and included as a constant in the college choice model.11 Meghir and Pistaferri (2004), Moffitt and Gottschalk (2011), and Christiansen et al. (2007) present evidence on the differences in the variance of wage shocks across education groups and how those differences have changed over time. However, changes in the variance of lifetime earnings over time is small relative to the changes in the mean. Koerselman and Uusitalo (2014) find that accounting for these differences in earnings risk does not meaningfully change estimates of the college premium. Finally, I assume that all workers retire at the same age, so that college graduates work for fewer total years. The last four years of earnings for high school graduates are heavily discounted, ( 1.105 )47 = 0.1, and contribute little to the earnings gap.12 4.3. The college premium under perfect foresight The second line of Fig. 3 plots the gap in discounted lifetime earnings constructed under the assumption that high school graduates perfectly foresee future changes in the labor market. To construct this measure of expected earnings I re-estimate Eqs. (1) and (2) pooling workers by birth cohort instead of calendar year. This approach is only feasible for the older cohorts in my sample, those who turned 18– and should have completed high school–between 1970 and 1995.13 As Heckman et al. (2006) point out, the perfect foresight projections of lifetime earnings look very different from the static expectations projections. During the 1970s, the static expectations earnings gap falls, tracking the declining price of college skills in the 1970s. However, high school graduates during that period would end up working during the 1980s and 90s when the relative wages of college workers rose rapidly. The perfect foresight earnings gap rises through the 1970s because successive cohorts of graduates will spend more time in these high college premium years.

Fig. 4. The College Premium by Age. Source: March CPS. The top panel plots the share of 22–51 year old male workers in each age range by year. The bottom panel plots the ratio of average annual earnings for workers with exactly 16 and 12 years of schooling, by age group. The series are shown as three-year moving averages.

4.4. The college premium under adaptive expectations A third possibility is that high school graduates cannot foresee the future path of earnings, but use both current and past earnings patterns to form their expectations of the future. Under the adaptive expectations model, high school students, recognizing that earnings in any one period include some transitory fluctuations, form their expectation of the college premium as a weighted average of the current current premium and the last period’s best expectation of the college premium. To evaluate this model of belief formation, I predict college enrollment using both the contemporaneous static expectations premium and several

first 4 years of earnings account for 12% of the total expected discounted lifetime earnings for high school graduates. The ratio of average earnings is also sensitive to the demographic mix of workers in each education group at a point in time, while the static expectations forecast of the difference in discounted lifetime earnings consistently places the heaviest weight on the youngest workers while discounting the earnings of older workers. The top panel of Fig. 4 plots the changing composition of the workforce as the baby boomers have aged through the sample. Young workers made up 45% of the workforce in 1980 but only 27% by 2002. The bottom panel of Fig. 4 shows that the relative earnings of college workers also differ by age (as has been pointed out by Card and Lemieux (2001), Heckman et al. (2006), and others). In the 1970s, the college premium fell more for younger workers, which is why the decline during these years is more pronounced in Fig. 3 than in Fig. 1. The steady rise in the ratio of average earnings during the 1990s, which is not mirrored in Fig. 3, is caused as much by the aging workforce, since the college premium is consistently larger for older workers, as by changes in relative earnings within age groups.

10 The correlation in the static-expectation 𝛽̂𝑖𝑡 with and without the inclusion of four years of mean earnings during college is 0.99. 11 If 𝜎 2 varies by education group it cannot brought out into the constant term and ) be ( ) ( ∑𝑇 𝑠 1 2 ∑𝑇 𝑠 1 2 𝛿 𝜎 𝛿 𝜎 ̂ 𝑒𝑥𝑝 𝑧𝑖𝑠 𝛼 ̂ 𝑒𝑥𝑝 𝑧𝑖𝑠 𝛼 ̂𝑡𝑠 + ̂ 𝑏𝑡𝑠 + ̂ 𝛾 1 (𝑠 − 4) − ̂𝑡𝑠 + ̂ 𝛾 0 (𝑠) . 𝛽̂𝑖𝑡 = 𝑠=4

12

2

1𝑡𝑠

𝑡𝑠

𝑠=0

2

0𝑡𝑠

𝑡𝑠

While the gap is not sensitive to retirement age assumptions it is sensitive to the discount rate. Changing my assumption about the discount rate substantially changes the magnitude of discounted lifetime earnings and the earnings gap, but does not change the movements in this gap over time. 13 Workers who were 18 in 1995 turned 38 in 2015, so their lifetime earning streams are extrapolated from their first 20 years of work experience. 89

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Labour Economics 49 (2017) 84–94 Table 2 Enrollment and expected earnings.

lags of this static premium. Because I use two years of lagged data when estimating the earnings parameters for each year, I include the static expectation measures at three-year intervals, so that each measure included reflects a distinct set of earnings observations. Following the formulation of expected permanent income in Friedman (1957), I define the adaptive expected college premium in year t, 𝛽̂𝑖𝑡𝐴𝐸 by the process ( ) 𝛽̂𝑖𝑡𝐴𝐸 − 𝛽̂𝑖𝑡𝐴𝐸 = 𝜂 𝛽̂𝑖𝑡𝑆𝐸 − 𝛽̂𝑖𝑡𝑆𝐸 (7) , −3 −3

Log 𝛽̂𝑖𝑡 , static expectations Log 𝛽̂𝑖𝑡 , perfect foresight

(2) 4 yr college

(3) 4 yr college

(4) 4 yr college 0.100∗ (0.031)

−0.067 (0.041)

0.089 (0.049) 0.002 (0.056)

0.098∗ (0.028)

Log 𝛽̂𝑖𝑡−3 , static expectations

0.007 (0.032) 0.009 (0.030) 0.931 (0.380)

Log 𝛽̂𝑖𝑡−6 , static expectations

where 𝛽̂𝑖𝑡𝑆𝐸 is the static expectations measure of the college premium using earnings data from year t to 𝑡 − 2 and 𝜂 captures the sensitivity of expectations to changes in the contemporaneous college premium. Rearranging Eq. (7) 𝛽̂𝑖𝑡𝐴𝐸 = 𝜂 𝛽̂𝑖𝑡𝑆𝐸 + 𝜂(1 − 𝜂)𝛽̂𝑖𝑡𝑆𝐸 + 𝜂(1 − 𝜂)2 𝛽̂𝑖𝑡𝑆𝐸 +… −3 −6

(1) 4 yr college

Dependent variable:

𝜂 : weight on 𝛽̂𝑖𝑡𝑆𝐸 in 𝛽̂𝑖𝑡𝐴𝐸 Observations Pseudo R2 P-stat: 𝜂 = 1

(8)

27,051 0.103

19,396 0.107

19,396 0.107

26,941 0.103 0.856

Source: October and March CPS. Bootstrapped standard errors from 250 draws in parentheses. ∗ indicates statistical significance at the 5% level. Coefficients reported are the average marginal effects from probit regressions. Weighted with CPS-generated inverse probability weights. 𝛽̂𝑖𝑡 measures the difference in discounted expected lifetime earnings for workers with a college degree and with only a high school diploma under different assumptions about how students form their beliefs about future earnings, as described in Section 4. 𝜂 is defined in Section 4.4. Regressions also include controls for log in-state college tuition, log family income, parents’ education, whether the parents own their home, a quadratic time trend, and indicators for race, living in a rural area, and Census division of the US. The estimated effects of these covariates for the static expectations forumulation, column (1), are presented in Table A.1.

As this formulation makes clear, when 𝜂 = 1, the adaptive expectations model simplifies to static expectations. In the next section, I test the ability of each of these three models of belief formation to predict college enrollment between 1970 and 2015. 5. Earnings expectations and college enrollment In the framework presented in Section 2, students condition their choice to go to college on their expectation at the time they are ready to start college of the additional discounted lifetime earnings they will receive with more education. To test this relationship I match the earnings gaps estimated in the previous section to the college choices of new high school graduates in the October CPS Schooling supplement. I assume that unobserved ability, 𝜃 i , has a normal distribution and estimate a probit model derived from Eq. (6). The probability that individual i in cohort t enrolls in college is ( ) 𝑃 𝑟(𝑐𝑜𝑙𝑖𝑡 ) = Φ 𝜙0 + 𝜙𝛽 log(𝛽̂𝑖𝑡 ) − 𝐶𝑖𝑡 𝜙𝐶 . (9)

has no clear relationship with enrollment rates.14 When included alone, the perfect foresight measure of earnings gains has a weak negative effect on the probability of enrollment, capturing the negative correlation between the static and perfect foresight measures over this period as shown in Fig. 3. If high school graduates have a noisy signal of future changes in the labor market we might expect that both current labor market conditions and future earnings gaps would have some positive effect on college enrollment. However, even after controlling the for static expectations measure, column (3), each cohort’s own future relative earnings have no substantial effect on enrollment rates. The last column of Table 2 uses the adaptive expectations model to test the role of past earnings data on students’ college enrollment choices. Including two lags of the static expectations earnings gap has almost no effect on the estimated marginal effect of the contemporaneous earnings gap on enrollment, while the estimated marginal effects of both lagged terms are imprecise zeros. The estimated weight on the current earnings gap in the adaptive expectations model, 𝜂 from Eq. (7), is 0.931.15 The data do not reject that this weight is equal to one, in which case the adaptive expectations model is equivalent to the static expectations model. Taken together, these results suggest that students are using the current labor market to forecast their own earnings, but have no accurate information about how earnings will evolve in the future and do not incorporate additional information from past labor markets. This finding is consistent with Betts (1996) and Dominitz and Manski (1996), who survey high school and early college students on their beliefs about current earnings for workers with different levels of education and their expectations about their own future earnings. While students vary widely in their perceptions of the current and future labor markets, their answers to these two questions are strongly correlated, consistent with a model where students use the current labor market to forecast their own future

Cit is a broad set of covariates chosen to capture the costs of college faced by each individual and perhaps heterogeneous preferences for college. The set of covariates includes log in-state tuition at public universities in the state where the student’s parents live, parents’ education and log income, and indicators for whether the parents own their home and the student’s race, ethnicity, and division of the U.S. To control for other changes in college enrollment trends over the period I also include a quadratic time trend. 𝜙𝛽 adjusts the scale of expected lifetime earnings relative to the variance of innate ability, which is set to one in the probit model. The constant term, 𝜙0 , incorporates the variance term − 21 𝜎 2 . 5.1. The information set of high school graduates The first two columns of Table 2 present estimates of Eq. (9) using estimates of 𝛽̂𝑖𝑡 constructed under the assumption that high school students have static expectations (column 1) and perfect foresight (column 2), as described in the previous section. In both cases I construct the differences in expected earnings adjusting the earnings intercepts to match the race/ethnicity of each high school student, using the relevant coefficients on the race and ethnicity indicators from the earnings equations. Because the estimated 𝛽̂𝑖𝑡 use non-linear transformations of pre-estimated parameters I report bootstrapped standard errors based on repeated draws from both the March and October data samples. The static expectations measure of expected lifetime earnings has a clear positive effect on the probability of enrolling in college. A unit increase in the log static expectation college earnings gap, slightly more than the rise between 1980 and 2002, is associated with a 9.8 percentage point average increase in college enrollment. In contrast, the ex post realized college premium for each cohort of high school graduates, which would predict college enrollment if these students had perfect foresight,

14 The regressions in columns (2) and (3) include only high school graduates from 1970 to 1995, since more recent graduates have too few years of earnings to calculate a perfect foresight lifetime earnings. Estimates using only these early cohorts and the static expectations earnings gap measure, available on request, look very similar to column 1. 𝜙 15 From Eq. (8), 𝜂 = 1 − 𝜙𝛽𝑡−3 where 𝜙𝛽t and 𝜙𝛽𝑡−3 are the coefficients on Log 𝛽̂𝑖𝑡𝑆𝐸 and Log 𝛽𝑡

, respectively. Note that this calculation uses the raw coefficients on these variables, 𝛽̂𝑖𝑡𝑆𝐸 −3 not the mean marginal effects reported in the first three rows of the table. 90

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and 2015, generating an increase in the log gap of 0.74. Holding college tuition and the characteristics of high school graduates and their families constant at 1983 levels, this change alone predicts 84% of the 8.5 percentage point growth in enrollment rates. However, changes in college tuition alone can also predict 60% of the growth in enrollment, while changes in parent characteristics alone can predict 30%. The demographic mix of high school graduates did not change enough between 1983 and 2015 to have a strong effect on enrollment rates. Instead, a negative estimated time trend prevents the fullf model from overpredicting the change in enrollment rates. Because most of the identification in this framework comes from changes in the college premium over time, I must assume that the effects of other covariates are the same within a cohort and over time. The estimated time trend may adjust for this misspecification. I discuss this possibility in more detail in Section 5.4. The final line of Fig. 5 plots the predicted college enrollment rates from a regression of enrollment rates on the static expectations 𝛽̂𝑖𝑡 without any covariates or time trends. Even with no control variables, this predicted college enrollment tracks actual enrollment well through the large rises and falls over the period. This univariate prediction misses the dips enrollment rates in the early 1990s and around 2008, which is captured in the full model through changes in family income during these recession years.

Fig. 5. Observed and Predicted College Enrollment, Static Expectations. Observed fouryear college enrollment rate from October CPS. Predicted four-year college enrollment rates are calculated based on changes in measures of expected earnings gains from a college degree for each cohort of high school graduates, with and without additional covariates, as described in the text. The series are shown as three-year moving averages.

5.3. The specification of the college premium

earnings. Rosen and Willis (1979) and Cunha and Heckman (2007) find that students’ college enrollment decisions are correlated with their future residual wages in a way that suggests individual students can forecast some of their own idiosyncratic returns to college; students who will benefit more than their classmates from a college education are more likely to enroll. My results suggest that students are less able to forecast the future changes in skill prices.

The results presented in Table 2 indicate that students use patterns of earnings in the labor market at the time they finish high school, rather than past or future earnings, to build their expectations of the returns to enrolling in college. Given these stark findings, the remainder of this section focuses on better understanding the relationship between contemporaneous earnings and college enrollment. Section 2 hypothesizes that high school students use a fairly sophisticated approach to forecasting their expected earnings gains from enrolling in college: they predict their earnings at each age and level of education, then compare the appropriately discounted stream of expected lifetime earnings. A more common measure of the college earnings premium is the ratio of average earnings for workers with exactly a college degree or exactly a high school diploma plotted in Fig. 1.18 As discussed in Section 4.2, this ratio describes the current labor market, but does not adjust for the changing composition of the workforce. Because of discounting, the static expectations measure also places more weight on the earnings of young workers. While there are some minor differences in these two measures over time, the broad movements are quite similar (correlation of 0.9 over the sample period). Unsurprisingly, therefore, this simpler college premium also has a strong positive relationship with college enrollment rates, as shown in the first column of Table 3, although the size of the effect is slightly smaller than the static expectations lifetime earnings gap used in Table 2. A standard deviation increase in log 𝛽̂𝑖𝑡𝑆𝐸 is associated with a 3.0 percentage point increase in college enrollment while a standard deviation increase in the log earnings ratio is associated with a 2.5 percentage point increase. Students might build their expectations of the college premium based on a subset of U.S. workers, for example considering only the earnings of young workers or of workers in their geographic area. Young workers may provide a better forecast of the experience of current students than older cohorts, and nearby workers provide a more accurate forecast if student plan to remain local. In practice, there is little evidence of this kind of focus. The second column of Table 3 presents an estimate of Eq. (6) using the log ratio of earnings by education for workers age 22 to 31 as the measure of students’ expected college premium. This measure of the college premium also has a positive relationship with enrollment,

5.2. Predicted enrollment patterns The rise in the college earnings premium during the 1980s and 1990s had a meaningful effect on college enrollment rates. Four-year college enrollment rates for men in the U.S. fell through the 1970s, to 34.4% in 1983, then rose somewhat unsteadily since then, to 42.9% in 2015. As plotted in Fig. 5, the static expectations model of college enrollment closely predicts these changes, falling early in the sample period and rising from 36.2% to 44.8% between 1983 and 2015. This prediction uses the estimated effects of all covariates included in the model, including a quadratic time trend. One way to isolate the role of students’ expectations is to compare this prediction to counterfactual enrollment if student beliefs had evolved differently. The third line in Fig. 5 plots predicted enrollment rates up to 1995 if students responded to the ex post college premium over their lives instead of the premium at the time they completed high school.16 Between 1983 and 1995, observed enrollment rates rose by 5.2 percentage points while the static expectation model predicts a growth of 5.6 percentage points. If students had instead responded to the ex post future college premium, enrollment rates would have risen only 2 percentage points. This perfect foresight counterfactual correctly predicts high college enrollment in 1995, but misses the growth. If students reacted to future earnings, enrollment would have already exceeded 40% in 1983. Another way to assess the importance of expected earnings in predicting college enrollment is to hold other factors constant at their 1980 levels.17 The gap in static expected lifetime earnings between workers with and without a college degree more than doubled between 1983

16 To predict this hypothetical, I use the static expectations model parameters from Column (1) of Table 2 to predict enrollment, but use the perfect foresight measure of the college premium in place of the static expectations measure. 17 The full set of estimated parameters for the static expectations model is presented in Table A.1.

18 See, for example, Freeman (1975), Katz and Murphy (1992), Card and DiNardo (2002), and Goldin and Katz (2009).

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Labour Economics 49 (2017) 84–94 Table 3 College enrollment, refining static expectations.

Dependent variable: Log ratio of avg. earnings

(1) 4 yr college

(2) 4 yr college

(4) 4 yr college

(5) Any college

0.052∗ (0.018)

0.077∗ (0.018)

27,051 0.103

27,051 0.106

0.223∗ (0.090) 0.119∗ (0.044)

Log ratio, age 22–31

0.082∗ (0.034)

Log ratio, by division Log 𝛽̂𝑖𝑡𝑆𝐸 , any college Observations Pseudo R2

(3) 4 yr college

27,051 0.103

27,051 0.103

27,051 0.103

Source: October and March CPS. Bootstrapped standard errors from 250 draws in parentheses. ∗ indicates statistical significance at the 5% level. Coefficients reported are the average marginal effects from probit regressions. Weighted with CPS-generated inverse probability weights. The first three rows present the estimated response of four-year college enrollment rates of the difference in average log earnings for workers with and with college education. 𝛽̂𝑖𝑡𝑆𝐸 measures the difference in discounted expected lifetime earnings for workers with a college degree and with only a high school diploma as described in Section 4. Regressions also include controls for log in-state college tuition, log family income, parents’ education, whether the parents own their home, a quadratic time trend, and indicators for race, living in a rural area, and Census division of the US.

but the magnitude of the effect is smaller than either the log ratio of earnings for all workers or the more complex construction of 𝛽̂𝑖𝑡𝑆𝐸 . A standard deviation increase in the log college premium for young people raises enrollment rates by an average of 1.7 percentage points. The third column of Table 3 uses the log ratio of earnings by education among workers in the same Census division as each high school graduate.19 Again, the estimated relationship between this measure of the college premium and enrollment is positive, but smaller than the effect of the baseline static expectations measure.20 Only half of students who enroll in a four-year college will complete their degree (Bound et al., 2010). Students may take these completion rates into account and weigh the costs of college against some weighted average of the returns to a college degree and to some college education. A very rough approximation of this adjusted college benefit would be the difference in discounted lifetime earnings for students with exactly a high school diploma and with any college education. This construction assumes that students give themselves the same probability of completion as the average college starter (the CPS does not distinguish between college credits earned at two-year and four-year colleges, so this measure includes all college enrollees). The fourth column of Table 3 presents the relationship between four-year college enrollment and this broader static expectations measure of the lifetime earnings gap. The gap in lifetime earnings between high school graduates and all college starters is about half as large as the gap with college graduates, but follows a similar pattern over time. It has a positive but smaller effect on college enrollment than the baseline static expectations measure. These expected gaps for college graduates and college starters are too tightly linked (correlation of 0.97) to establish which construction more influences college enrollment. As shown in Fig. 2, enrollment in two-year colleges has risen even more rapidly than enrollment in four-year colleges. The final column of Table 3 presents the effects of the broader measure of the return to starting any college on enrollment in either a two-year or four-year college. The estimated effect is positive, but not as large as the relationship between the baseline college premium measure and four-year enrollment. Many, though not all, students entering two-year college in the U.S. plan to eventually earn a four-year degree, but relatively few

achieve this goal (Reynolds, 2012). This heterogeneity makes it difficult to identify a single measure of the expected college premium that reflects the beliefs of all college starters, so the small estimated effect on enrollment could simply reflect a noisy measure of students’ actual expectations. 5.4. Policy changes and time trends In the U.S., each state operates its own system of public colleges and sets tuition, usually providing discounted tuition for residents of the state. College tuition is therefore correlated with college enrollment rates through several avenues. Holding college quality and availability equal, students in states with higher tuition face higher costs of attendance and will be less likely to enroll. However, states may charge higher tuition because they provide a higher quality public college system, which would draw more students into college. Finally, and most problematically, higher tuition may reflect a policy response to higher earnings for college graduates and higher demand for college, creating some reverse causality. Differences across states in college quality and average in-state tuition are highly persistent, so this third explanation is most likely to drive the positive relationship between enrollment and college tuition over time. Like enrollment and the college premium, average real college tuition fell from $2,052 in 1970 to $1,528 in 1980, then ballooned to $6,435 by 2015. The second column of Table A.1 estimates the college enrollment model using the static expectations measure of the expected college premium, but omitting state-specific college tuition. As expected, the estimated effect of the college premium rises slightly relative to the baseline specification, presented in column 1, suggesting that states’ decisions to increase tuition since 1980 has likely slightly dampened the enrollment response to the rising college premium. The baseline specification imposes that the cross-sectional relationship between each covariate and the probability of enrollment in each cohort is the same as the cross-time effects. This assumption is unlikely to hold for college tuition for the reasons discussed above. It is also likely violated for parental education. In 1970 26% of new high school graduates had no parent with a high school diploma and 17% had at least one parent with a college degree. By 2015, only 9% of new graduates had no parent with a high school diploma and 46% had at least one parent with a college degree. Within a cohort of high school graduates, parents’ education may proxy for many factors that affect college enrollment: financial resources not captured by one year of family income, higher cognitive ability passed on through either genetics or home environment, or a taste for education. In this case, the effect of parents’

19 There are too few observations in each year-division cell in the CPS to reliably estimate the experience profiles and construct division-specific 𝛽̂𝑖𝑡𝑆𝐸 . 20 The estimated effects of all three of these log earnings ratios are small and statistically indistinguishable from zero when included together with the baseline 𝛽̂𝑖𝑡𝑆𝐸 , although the high correlation between all four measures makes these horserace comparisons difficult to interpret.

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education on enrollment compared to other parents in their same cohort should be larger than the effect of rising average parental education over time. The model will therefore over-predict the response of college enrollment rates to the rise in parental education and college tuition over time. The negative estimated time trend may partially correct for this mis-specification. As shown in the third column of Table A.1, the estimated effect of the log earnings gap on college enrollment is not robust to the exclusion of the time trend. However, the estimated effect when the time trend, parental education, and college tuition are all omitted, column (4) is similar to the baseline specification. Parents’ characteristics are important determinants of students’ college enrollment, as illustrated by the fall in the R2 statistic between columns (2) and (4) of Table A.1. However, I only observe family characteristics for young people who are still part of their parents’ household in October of the year they graduate high school. This set includes graduates still living with their parents and graduates living in college dormitories or other institutional housing. I cannot link graduates to their parents if they have already moved into a home of their own. 84% of the young people in the October CPS sample are still part of their parents’ household. Recent graduates who have not enrolled in college are more likely than college students to be living independently, although that difference has narrowed over time. In my baseline specification I drop high school graduates if I do not observe their family background. The last column of Table A.1 shows that my results are largely robust to including these graduates in the sample if I set their parent characteristics to zero and include an indicator for missing parent information.

of current workers to predict his own future earnings would expect an additional $87,000 in real discounted earnings over his life if he went to college. In fact, college graduates from this cohort are on track to earn an average of $194,000 more than their contemporaries with only a high school diploma. The response of enrollment rates to the expected college premium is mainly identified by changes in this premium over time, controlling for a relevant but limited set of individual student characteristics. It therefore also reflects a different margin of adjustment than responses to policy changes such as the one analyzed by Dynarski (2003). Dynarski studies the choices of one cohort of students, some of whom are affected by a change in a grant program, but who otherwise face the same macroeconomic, social, and policy conditions. Changes in enrollment over time reflects individual responses to changes in earnings, but also policy responses. These policy changes could increase the response of enrollment rates, for example by expanding public college systems, or dampen enrollment rates, for example through increases in tuition. Finally, students’ responsiveness to changes in their expected college premium may be further tempered by an expectation that other students’ expectations have also changed, raising future college enrollment rates and driving down the equilibrium price of college skills. More broadly, the expected monetary costs and benefits of a college degree are only one of many factors that may influence enrollment decisions. Arcidiacono (2004), Beffy et al. (2012), and Wiswall and Zafar (2015a) all find that student tastes or comparative advantages are at least as important in determining college major choice as expectations about future earnings. Jacob et al. (2013) explore the importance of amenities, rather than qualities that map more directly to future earnings, in influencing the choice of which college to attend. It is likely that these non-pecuniary concerns also loom large in the decision of whether to enroll in college at all. These other concerns will decrease the elasticity of enrollment rates to changes in the monetary returns to college. The systemic response of enrollment rates to changes in the college premium measured here is the relevant margin for considering the adjustment of the supply of college graduates to changes in demand. One interpretation of the recent rise in the relative earnings of collegeeducated workers, as argued by Goldin and Katz (2009) and many others, is that growth in the demand for this type of worker has outpaced supply. Changing the skill mix of the labor supply is a slow process. Workers who decide to enter college will not emerge with a degree for at least four years, and adjustment takes place mainly through the decisions of young workers, who make up only a small share of the labor force. If students could anticipate future increases in skill prices, then the supply of skilled workers would begin to build even before demand increased. If, as I find, college enrollment rates respond only to the current price of college skills, then then this adjustment will take place very slowly and with a substantial lag. The rise in the college earnings premium between 1980 and 2000 accompanied and contributed to a dramatic increase in income inequality.21 As the more educated cohorts of recent high school graduates make their way into the labor market the earnings gap between more and less educated workers should gradually narrow, unless the forces increasing the earnings gap outpace the change in relative supply. This slow adjustment is consistent with multi-decade swings in skill prices and inequality. During these adjustment periods, individual workers may make costly miscalculations: foregoing college in periods when the ex post return would have made college worthwhile and enrolling in periods when, ex post, the investment in college may not pay off.

6. Conclusions Students deciding whether to enroll in college appear to rely mostly on the earnings of current workers when forecasting their own expected gains from a college degree. On average, a 10% increase in the expected lifetime earnings gains from college, constructed based on the earnings of workers at the time a student graduates from high school, increases the probability that this student enrolls in college by 1 percentage point. In contrast, cohort-specific enrollment rates do not respond to realized future earnings, or to past earnings alongside current averages. College enrollment rates for men rose from a recent low of 37% in 1983 to 44% in 2015, accompanying a large increase in the relative earnings of college graduates. If young men responded to their cohort’s future realized earnings instead of the contemporaneous labor market, enrollment might not have increased at all over the period because rates would have already reached 44% in 1983. Changes in the static expectations measure of the college premium, seemingly the best approximation of student beliefs, generate far smaller changes in college enrollment than changes in the direct costs of college. Dynarski (2003) finds that an additional $1,000 in grant tuition aid increases college enrollment by 3.6 percentage points. If students expect to get this grant for four years of college, then a $1,000 decrease in the discounted cost of obtaining a college degree raises enrollment by 1 percentage point. In 1982, the year of the policy reform Dynarski studies, a $1,000 increase in the expected discounted lifetime earnings gains from a college degree would have raised enrollment by 0.1 percentage points, an order of magnitude smaller than the effect of grant aid. This difference in responsiveness partially reflects the salience and uncertainty of changes in the expected lifetime earnings gains from college. High school graduates are probably not fully informed about the earnings of current workers. Moreover, while current earnings may reflect what high school students use to build their expectations of future earnings, they remain a bad predictor of realized earnings over this period. A student who graduated high school in 1982 and used the earnings

21 See, for example, Card and DiNardo (2002), Autor et al. (2006), and Goldin and Katz (2009).

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Appendix

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Table A1 Time trends and missing parent information. Dependent variable: Log 𝛽̂𝑖𝑡 , static expectations Log in-state tuition Log family income Parent HS dropout Parent some college Parent college graduate Parents own home Rural Black Hispanic Other non-white New England Mid Atlantic West North Central South Atlantic East South Central West South Central Mountain Pacific Time Time2 /1000

(1) 4 yr college

(2) 4 yr college

(3) 4 yr college

(4) 4 yr college

(5) 4 yr college

0.098∗

0.117∗

0.002

0.094∗

0.062∗

(0.028) 0.042∗ (0.013) 0.057∗ (0.006) −0.076∗ (0.012) 0.085∗ (0.013) 0.273∗

(0.028)

(0.020) 0.019 (0.011) 0.058∗ (0.006) −0.072∗ (0.012) 0.082∗ (0.013) 0.271∗

(0.012)

(0.025) 0.045∗ (0.012) 0.060∗ (0.006) −0.073∗ (0.013) 0.076∗ (0.014) 0.263∗

(0.013) 0.050∗ (0.010) −0.036∗ (0.009) 0.046∗ (0.015) −0.003 (0.016) 0.125∗ (0.019) 0.063∗ (0.014) 0.029∗ (0.013) 0.015 (0.015) −0.039∗ (0.014) 0.001 (0.019) 0.006 (0.016) −0.042∗ (0.018) −0.160∗ (0.017) −0.005∗ (0.002) 0.030 (0.026)

(0.013) 0.051∗ (0.010) −0.036∗ (0.009) 0.051∗ (0.015) −0.000 (0.016) 0.129∗ (0.019) 0.059∗ (0.014) 0.032∗ (0.013) 0.002 (0.015) −0.052∗ (0.014) −0.015 (0.019) −0.017 (0.015) −0.064∗ (0.018) −0.188∗ (0.015) −0.006∗ (0.002) 0.058∗ (0.025)

(0.013) 0.050∗ (0.010) −0.035∗ (0.009) 0.018 (0.014) −0.026 (0.015) 0.104∗ (0.018) 0.058∗ (0.014) 0.031∗ (0.013) 0.006 (0.015) −0.048∗ (0.014) −0.009 (0.019) −0.008 (0.016) -0.059∗ (0.019) −0.175∗ (0.017)

0.062∗ (0.010) −0.058∗ (0.009) 0.032∗ (0.014) −0.067∗ (0.015) 0.150∗ (0.018) 0.074∗ (0.014) 0.040∗ (0.014) 0.017 (0.016) −0.036∗ (0.014) −0.006 (0.019) 0.002 (0.016) −0.036∗ (0.018) −0.170∗ (0.015)

27,051 0.103

27,051 0.103

27,051 0.102

27,051 0.056

0.057∗ (0.006) −0.075∗ (0.012) 0.084∗ (0.013) 0.273∗

0.130∗ (0.006)

Not living with parents Observations Pseudo R2

(0.015) 0.054∗ (0.009) −0.033∗ (0.008) 0.044∗ (0.013) −0.005 (0.013) 0.145∗ (0.017) 0.067∗ (0.012) 0.034∗ (0.012) 0.018 (0.014) −0.027∗ (0.013) 0.007 (0.017) 0.011 (0.015) −0.027 (0.016) −0.135∗ (0.015) −0.002 (0.001) -0.010 (0.021) 0.107∗ (0.014) 32,158 0.099

Source: October and March CPS. Bootstrapped standard errors from 250 draws in parentheses. ∗ indicates statistical significance atthe 5% level. Coefficients reported are the average marginal effects from probit regressions. Weighted with CPS-generated inverse probability weights.

References Arcidiacono, P., 2004. Ability sorting and the returns to college major. J. Econ. 121 (1), 343–375. Attanasio, O., Kaufmann, K., 2009. Educational Choices, Subjective Expectations, and Credit Constraints. NBER Working Paper, 15087, NBER. Autor, D.H., Katz, L.F., Kearney, M.S., 2006. The polarization of the US labor market. Am. Econ. Rev. 96 (2), 189–194. Beffy, M., Fougere, D., Maurel, A., 2012. Choosing the field of study in postsecondary education: do expected earnings matter? Rev. Econ. Stat. 94 (1), 334–347. Belley, P., Lochner, L., 2007. The changing role of family income and ability in determining educational achievement. J. Hum. Cap. 1 (1), 37–89.

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