Abstract
Since 1980, 25% of US students repeated a grade during their academic career. Despite this, few economists account for retention when measuring education and experience, causing bias when retention is correlated with other regressors of interest. Rising minimum dropout ages since 1960 have increased retention, causing positive bias in 2SLS estimates of the returns to education. Retention also causes endogenous measurement error in potential experience. In addition to distorting experience-wage profiles across countries, this endogenous measurement error causes the residual Black-White wage gap and the returns to a high school diploma to be overstated. Proxying for age instead of potential experience reduces this bias, suggesting age, not potential experience, should be a standard control variable.
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Notes
Similarly high retention rates can be found in other datasets: 38% of the National Longitudinal Survey of Youth Children and Young Adults (CNLSY) repeated at least one grade in their academic career, and 18% of the National Education Longitudinal Study of 1988 (NELS88) repeated at least one grade from Kindergarten to 8th grade.
The General Educational Development (GED) tests are high school equivalency exams used in the USA and Canada to certify the test taker has achieved high school-level academic skills.
The US Census, the American Community Survey (ACS), the Current Population Survey (CPS), the National Longitudinal Survey of Youth (NLSY), the Panel Study of Income Dynamics (PSID), and many others report educational attainment as the default education variable.
When actual labor market experience is observed, researchers conventionally still use a potential experience proxy. Observed labor market experience (e.g., lifetime weeks worked) is highly endogenous as it is directly caused by labor force participation and employment decisions. (Eckstein and Wolpin 1989).
I cannot replicate the Heckman et al. (1998) approach with a correction for grade retention due to a lack of appropriate data, but their method would similarly suffer from overstating the potential experience in high-grade retention countries.
The mean of 9th grade repeats is about 5% because 0.7% of the sample repeated the 9th grade multiple times. 6.6% of the sample repeated multiple grades, causing overall grade retention to have a mean of 37.6%.
This is considered a separate change from minimum competency testing as high-stakes testing tests students on skills appropriate for their grade level, while minimum competency testing tests far below grade level.
This equation does not estimate the overall effect of compulsory schooling on 9th grade retention, as there are no states without compulsory education. As a result, I only able to test the marginal effect of a higher minimum dropout age on 9th grade retention, not the aggregate effect of compulsory education on 9th grade retention.
Other well-known critiques of the TWFE design include Goodman-Bacon (2018) and Callaway and Sant’Anna (2019). These critiques do not have derivations or solutions analogous to the estimates presented in Table 2, because in my context (i) all units are always treated with a minimum dropout age > 0; and (ii) the changes in treatment are non-binary changes in treatment intensity.
The Stata package presented in de Chaisemartin et al. (2019) was used for these estimates.
Borusyak and Jaravel (2017) show that the “lags and leads” design can only identify deviations from a perfectly linear pre-existing trend when all units are treated. They recommend setting the omitted periods “far apart” to increase precision, so I omit the year before treatment begins and the earliest non-pooled year, 4 years before treatment.
The confidence interval at k = − 4 does not exist, but is displayed as the linear interpolation between k = − 5 and k = − 3 for ease of viewing.
A small number of individuals may have repeated the same grade more than once; however, the question asked in the CNLSY does not permit separate observation of these multi-time repeaters. I do observe individuals who repeat multiple, different grades; these make up about 10% of all high school grade repeaters. I do not observe whether students who are retained in early high school are able to “catch up” to their peers; because of this, there is likely a small amount of non-classical measurement error in retention in the CNLSY. Any student who was retained due to a lack of credits in early high school, received those credits and caught up to their peers so that their educational attainment appeared “on track” (whether a high school dropout or graduate), and still self-reported as a grade repeater would overstate the true number of off-track grade repeaters affected by CSLs. In the NLSY97, this pattern represents less than 1% of all repeaters.
Acemoglu and Angrist (2000) note that related literature (e.g., Imbens and Angrist 1994) shows 3 quarter of birth instruments cause the 2SLS estimate to be strongly biased toward the OLS estimate due to its 1st stage weakness, while the quarter of birth interacted with year of birth produces estimates largely unaffected by weak instrument bias.
The coefficients on grade retention in this and all other tables are positive, which should not be surprising. These represent a positive return to grade retention, conditional on educational attainment and independent of unobservables. For two otherwise identical people who have the same final educational attainment, we should expect the retained student to have higher human capital because they remained in school for an additional year, though this human capital gain is almost certainly smaller than the gain from an additional year of educational attainment.
This is somewhat common, especially delayed school entry. Delayed school entry cannot be distinguished from retention in Kindergarten in the NLSY, but the corrections to potential experience presented in the following sections are agnostic to this issue.
The major exceptions to this pattern are Canada, which has a relatively flat profile, and Germany, which has a relatively steep profile.
The ELFE (Étude Longitudinale Française depuis l’Enfance) in France will eventually allow this type of correction in one of the highest-retention countries in the world. However, the ELFE began with the 2011 birth cohort, so such a correction cannot be done for at least 20 more years. In addition, many Nordic countries have appropriate restricted-access longitudinal datasets, but have overall retention rates less than 5%.
See Section B.2 for a derivation of the resulting bias.
Given the sample restrictions I describe in Sect. 2, this corrected potential labor market experience measure is equal by construction to the number of years since an individual left high school, either by drop** out or by graduating. If individuals who skipped grades were included in the sample, corrected potential experience would not equal years since leaving high school.
Cameron and Heckman (1993) use lifetime weeks worked as their primary experience measure. As mentioned previously, this measure is not subject to measurement error from repeated grades, but is endogenous with factors influencing labor force participation, and is rarely used today.
This measure of annual hours worked also partially includes labor supply on the extensive margin. It includes the decision to work a part-time or full-time job, as well as some changes in employment status. Observations of 0 h worked in a year are dropped.
Though the proxy error associated with age as a proxy for actual labor market experience is likely larger than the proxy error associated with potential experience, the error associated with age should, at worst, attenuate the estimate of the parameter of interest, rather than biasing it in an unpredictable direction and.
The point estimates and repeated grades bias when using this experience measure are almost identical (18–20% Black-White wage gap, 13% bias) to the previous estimates in Table 5.
This similarity between linear and nonlinear age controls is partially due to the age composition of the NLSY97. Age-earnings profiles become highly nonlinear after mid-career (Card et al., 2013), but all NLSY97 workers are under 40 years old.
References
Acemoglu D, Angrist J (2000) How large are human-capital externalities? Evidence from compulsory schooling laws. NBER Macroecon Annu 15:9–59
Angrist JD, Krueger AB (1991) Does compulsory school attendance affect schooling and earnings? Q J Econ 106(4):979–1014
Berlinski S, Galiani S, Manacorda M (2008) Giving children a better start: preschool attendance and school-age profiles. J Public Econ 92(5–6):1416–1440
Borusyak K and Jaravel X (2017) Revisiting event study designs. Available at SSRN 2826228
Bound J, Freeman RB (1992) What went wrong? The erosion of relative earnings and employment among young Black men in the 1980s. Q J Econ 107(1):201–232
Buckles KS, Hungerman DM (2013) Season of birth and later outcomes: old questions, new answers. Rev Econ Stat 95(3):711–724
Bureau of Labor Statistics, U.S. Department of Labor, and National Institute for Child Health and Human Development. Children of the NLSY79, 1979–2014. Produced and distributed by the Center for Human Resourse Research, The Ohio State University. Columbus, OH: 2015
Bureau of Labor Statistics, U.S. Department of Labor. National longitudinal survey of youth 1997 cohort, 1997–2013 (rounds 1–16). Produced by the National Opinion Research Center, the University of Chicago and distributed by the Center for Human Resource Research, The Ohio State University. Columbus, OH: 2015
Callaway, B. and Sant’Anna, P. H. (2019). Difference-in-differences with multiple time periods. Available at SSRN 3148250
Cameron SV, Heckman JJ (1993) The nonequivalence of high school equivalents. J Labor Econ 11(1, Part 1):1–47
Card D, Heining J, Kline P (2013) Workplace heterogeneity and the rise of West German wage inequality. Q J Econ 128(3):967–1015
de Chaisemartin C, D’Haultfœuille X, Guyonvarch Y (2019) Fuzzy differences-indifferences with stata. Stand Genomic Sci 19(2):435–458
De Chaisemartin C, d’Haultfoeuille X (2018) Fuzzy differences-in-differences. Rev Econ Stud 85(2):999–1028
Deaton A (1997) The analysis of household surveys: a microeconometric approach to development policy. The World Bank
Dustmann C, Meghir C (2005) Wages, experience and seniority. Rev Econ Stud 72(1):77–108
Eckstein Z, Wolpin KI (1989) Dynamic labour force participation of married women and endogenous work experience. Rev Econ Stud 56(3):375–390
Goodman-Bacon A (2018) Difference-in-differences with variation in treatment timing. Technical report, National Bureau of Economic Research
Hall RE (1968) Technical change and capital from the point of view of the dual. Rev Econ Stud 35(1):35–46
Haney W, Madaus G, Abrams L, Wheelock A, Miao J, Gruia I, and Gruia I (2004) The education pipeline in the United States, 1970–2000
Heckman J (1974) Life cycle consumption and labor supply: an explanation of the relationship between income and consumption over the life cycle. Am Econ Rev 64(1):188–194
Heckman JJ, Lochner L, Taber C (1998) Explaining rising wage inequality: explorations with a dynamic general equilibrium model of labor earnings with heterogeneous agents. Rev Econ Dyn 1(1):1–58
Heubert JP, Hauser RM (1998) High stakes: testing for tracking, promotion, and graduation. National Academies Press, National Research Council Committee on Appropriate Test Use
Imbens GW, Angrist JD (1994) Identification and estimation of local average treatment effects. Econometrica 62(2):467–475
Jacob BA, Lefgren L (2009) The effect of grade retention on high school completion. Am Econ J Appl Econ 1(3):33–58
Kleibergen F, Paap R (2006) Generalized reduced rank tests using the singular value decomposition. J Econ 133(1):97–126
Kreitzer AE, Madaus GF and Haney W (1989) Competency testing and dropouts
Lagakos D, Moll B, Porzio T, Qian N, Schoellman T (2018) Life cycle wage growth across countries. J Polit Econ 126(2):797–849
Lemieux T (2006) The “mincer equation” thirty years after schooling, experience, and earnings. In Jacob Mincer a pioneer of modern labor economics, pages 127–145. Springer
Lochner L, Moretti E (2004) The effect of education on crime: evidence from prison inmates, arrests, and self-reports. Am Econ Rev 94(1):155–189
Mackey PE and Duncan TG (2013) Does raising the state compulsory school attendance age achieve the intended outcomes
Manacorda M (2012) The cost of grade retention. Rev Econ Stat 94(2):596–606
Mincer JA (1974) The human capital earnings function. In Schooling, experience, and earnings, pages 83–96. NBER
Oreopoulos P (2006) Estimating average and local average treatment effects of education when compulsory schooling laws really matter. Am Econ Rev 96(1):152–175
Planty M, Hussar WJ, Snyder TD (2009) Condition of education 2009. Government Printing Office
Sable J, Gaviola N and Hoffman L (2007) Numbers and rates of public high school dropouts: school year 2004–05. First Look (NCES 2008–305). National Center for Edu-cation Statistics
Sanderson E, Windmeijer F (2016) A weak instrument F-test in linear IV models with multiple endogenous variables. J Econ 190(2):212–221
Shepard LA and Smith ML (1989) Flunking grades: research and policies on retention (New York, NY: Falmer)
Stephens M, Yang D-Y (2014) Compulsory education and the benefits of schooling. Am Econ Rev 104(6):1777–1792
Further Readings
Aragon S (2015) Free and compulsory school age requirements. The Education Commission of the States
Elementary/Secondary Information System. U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics
Historical tables & reports: elementary and secondary enrollment. U.S. Department of Education. Institute of Education Sciences, National Center for Education Statistics
OECD (2016). Pisa 2015 results (volume ii). policies and practices for successful schools
Statistical reports: grade retention. Massachusetts Department of Elementary & Secondary Education, Information Services
U.S. Department of Education Office of Planning, E., Policy, P. D., and Service, P. S. (2018). Issue brief: credit recovery
Acknowledgements
Thanks to editor Alfonso Flores-Lagunes and three anonymous referees for their helpful comments and suggestions. Additional thanks to Timothy Bond, Christopher Candelaria, Jillian Carr, David Figlio, Scott Imberman, Justine Mallatt, and Kevin Mumford, seminar participants at Bowling Green State University, Mississippi State University, NC State University, Purdue University, and the University of Toledo, and participants and discussants at SEA 2017, APPAM Fall 2017, EALE 2018, and the NBER Spring 2019 Education Program Meeting for many helpful comments and discussions. The author thanks Philip Oreopoulos for providing a list of compulsory schooling laws in the USA. This research was conducted with restricted access to Bureau of Labor Statistics (BLS) data. The views expressed here do not necessarily reflect the views of the BLS. The data can be obtained by filing a request with the BLS (https://www.bls.gov/nls/geocodeapp.htm).
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Kennedy, K.J. Hidden schooling: endogenous measurement error and bias in education and labor market experience. J Popul Econ 36, 2691–2723 (2023). https://doi.org/10.1007/s00148-022-00918-w
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DOI: https://doi.org/10.1007/s00148-022-00918-w