THE RETURN TO COLLEGE: SELECTION AND DROPOUT RISK

• Author: Lutz Hendricks,Oksana Leukhina
• Date: 01 August 2018
• DOI: http://doi.org/10.1111/iere.12297
• Published date: 01 August 2018

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 3, August 2018 DOI: 10.1111/iere.12297

THE RETURN TO COLLEGE: SELECTION AND DROPOUT RISK∗

BYLUTZ HENDRICKS AND OKSANA LEUKHINA1

University of North Carolina at Chapel Hill, U.S.A.; Federal Reserve Bank of St. Louis, U.S.A.

This article studies the effect of graduating from college on lifetime earnings. We develop a quantitative

model of college choice with uncertain graduation. Departing from much of the literature, we model in detail

how students progress through college. This allows us to parameterize the model using transcript data. College

transcripts reveal substantial and persistent heterogeneity in students’ credit accumulation rates that are strongly

related to graduation outcomes. From these data, the model infers a large ability gap between college graduates

and high school graduates that accounts for 59% of the college lifetime earnings premium.

1. INTRODUCTION

A large literature has investigated the causal effect of college attendance on earnings.2In

U.S. data, college graduates earn substantially more than high school graduates. However, part

of this differential may be due to selection, as students with superior abilities or preparation

are more likely to graduate from college. Although various approaches have been proposed to

control for selection, no consensus has been reached about its importance.

To understand why controlling for selection is hard, consider a simple model of lifetime

earnings. Each person starts life as a high school graduate, endowed with a random ability a.

He chooses to work as a high school graduate (s=HS) or as a college graduate (s=CG). Log

lifetime earnings are given by φa+ys, where φ>0 and ysdetermine the effects of ability and

schooling on lifetime earnings, respectively. The observed lifetime earnings gap between college

graduates and high school graduates can be decomposed into a term reflecting the return to

college, yCG −yHS, and a term reflecting ability selection, φ[E{a|CG}−E{a|HS}]. The challenge

is then to estimate the ability gap between college graduates and high school graduates and the

effect of ability on lifetime earnings φ.

If abilities were observable, for example, as test scores or high school grade point averages

(HS GPAs), estimating ability selection would be easy. The ability gap could be computed from

the joint distribution of HS GPAs and schooling, whereas φcould be estimated by regressing

log lifetime earnings on HS GPAs and schooling dummies. However, since HS GPAs are noisy

measures of abilities, these simple calculations would be biased. Since the precision of HS GPAs

as measures of abilities is not known, correcting for this bias is difficult.

The central idea of this article is that transcript data provide information about both of

the terms needed to estimate ability selection (the ability gap and φ). Transcripts reveal how

rapidly students progress toward earning a bachelor’s degree. We think of the number of credits

∗Manuscript received November 2014; revised January 2017.

1For helpful comments we thank the editor (Dirk Krueger) and three anonymous referees. We also thank David

Blau, V. V. Chari, Larry Jones, Patrick Kehoe, Rodolfo Manuelli, Luigi Pistaferri, Jos´

e-Victor Rios-Rull, Gianluca

Violante, Christoph Winter, as well as seminar participants at IFS, Indiana University, Ohio State, University of

Minnesota, University of Washington, Western University, Simon Fraser University, Tel Aviv University, Washington

State University, York University, the Federal Reserve Bank of Minneapolis, the 2011 Midwest Macro Meetings,

the 2011 SED Meetings, the 2011 Cologne Macro Workshop, the 2011 CASEE Human Capital Conference, the

2011 Barcelona Growth Workshop, the 2011 USC-Marshall mini macro labor conference, and the 2013 QSPS Summer

Workshop. Please address correspondence to: Oksana Leukhina, Federal Reserve Bank of St. Louis, Research Division,

P. O. Box 442, St. Louis, MO 63166. Phone: 314 444-3731. E-mail: oksana.m.leukhina@gmail.com.

2For a recent survey, see Oreopoulos and Petronijevic (2013).

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(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1078 HENDRICKS AND LEUKHINA

a student earns in each year as determined by ability and luck. Thus, credit accumulation rates

provide additional noisy measures of the relationship between abilities and college outcomes.

In contrast to commonly used test scores or HS GPAs, transcripts provide repeated observations

for the same individual. This helps to estimate how precisely HS GPAs measure abilities. It is

then possible to correct for the biases introduced when HS GPAs are used in lieu of abilities.

To implement this idea, we develop a quantitative model of college choice (Section 3).

The model follows a single cohort from high school graduation through college and work

until retirement. At high school graduation, agents are endowed with heterogeneous financial

resources and abilities. Following Manski (1989), we assume that students observe only noisy

signals of their abilities.3High school graduates choose between working and attempting college.

While in college, students make consumption–savings and work–leisure decisions.

Our main departure from the literature is to model students’ progress through college in

detail.4This allows us to map transcript data directly into model objects. We model credit

accumulation as follows: In each period, a college student attempts a fixed number of courses.

He passes each course with a probability that increases with his ability. At the end of each year,

students who have earned the required number of courses graduate. The remaining students

update their beliefs about their abilities based on the information contained in their course

outcomes. Then they decide whether to drop out or continue their studies in the next period.

Students must drop out if they lack the means to pay for college or if they fail to earn a degree

after six years in college.

We calibrate the model using a rich set of data moments for men born around 1960 (Section 4).

Our main data sources are High School & Beyond (HS&B) and the Postsecondary Education

Transcript Study (PETS, Section 2), from which we obtain college transcripts and financial

variables, and NLSY79, from which we estimate lifetime earnings.

Our model implies that ability selection is important (Section 5). We measure its contribution

as the fraction of the lifetime earnings gap between college graduates and high school graduates

that would remain if both groups worked as high school graduates. In the main specification, this

fraction is 59% of the observed 45% gap. We show that this result is robust (Online Appendix

F).

To understand why the model has this implication, we highlight the following features of

transcript data:

1. There is large dispersion in credit accumulation rates across students. By the end of the

second year in college, students in the 80th percentile of the credit distribution have earned

52% more credits compared to students in the 20th percentile.

2. Individual credit accumulation rates exhibit substantial persistence. The correlation be-

tween credits earned in adjacent years is 0.43.

3. Credit accumulation rates are strongly related to college graduation. By the end of their

second year in college, students who eventually graduate have earned 40% more credits

per year compared to those who eventually drop out.

4. Controlling for HS GPAs does not greatly reduce the dispersion in credits.

Our model of credit accumulation decomposes the dispersion in earned credits into persistent

heterogeneity (abilities) and shocks (luck). To account for the persistence of credits, the model

must limit the role of luck and instead rely on credit accumulation rates that rise sharply with

ability. Given the limited role of luck, the gap in credits between college graduates and college

dropouts identifies the ability gap between the two groups. The fact that controlling for HS

GPAs does not greatly reduce credit dispersion implies that HS GPAs must be noisy measures

of ability. Given these estimates of HS GPA noise and the ability gap, we can use the observed

3Based on surveys that elicit student expectations, Stinebrickner and Stinebrickner (2012, 2014) find that learning

about academic ability accounts for 45% of students’ dropout decisions during the first two years at Berea College.

4In much of the literature, college is a black box. Exceptions include Garriga and Keightley (2007), Arcidiacono

et al. (2012), and Stange (2012).