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Disruption, learning, and the heterogeneous benefits of smaller classes

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Abstract

Prior research suggests that the benefits from smaller classes may vary along multiple dimensions. In this paper we develop a flexible model of education production that incorporates the classroom-level time lost to disruption and the rate of learning during productive time as a function of teacher quality and individual propensity to acquire knowledge. We then investigate heterogeneity in class size effects by school poverty share, family income, teacher experience, and achievement percentile using data from Project STAR. We find that the benefits of small classes are consistently higher in schools with a larger low-income enrollment share. Conditional on school poverty share, we find little or no evidence that lower-income or lower-achieving students tend to realize larger benefits of smaller classes. Instead, we find that the return to smaller classes tends to increase with achievement regardless of school poverty share. Given the generally higher levels of disruption reported in higher poverty schools, this set of findings is consistent with, though not direct evidence of, the notion that reduced time lost to disruption is a primary mechanism through which smaller classes raise achievement and a compelling explanation for the empirical finding that class-size effects tend to be larger for lower-income children.

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Notes

  1. There are also a number of papers that rely on quasi-random variation in class size to identify effects. Angrist and Lavy (1999), Bressoux et al. (2009), Fredriksson et al. (2013), Hoxby (2000), Jepsen and Rivkin (2009), Leuven et al. (2008), and Rivkin et al. (2005) use plausibly exogenous variation in class size in Israel, France, Sweden, Connecticut, California, Norway, and Texas, respectively. With the exception of Hoxby (2000) and Leuven et al. (2008), these studies generally support the finding that smaller classes significantly increase achievement in the early grades (grade 5 and below).

  2. In order to identify the channels through which smaller classes raise achievement for lower- income children, Babcock and Betts (2009) use information from report cards to classify baseline effort and academic achievement prior to a change in class size. The authors find that students who were previously graded with low effort realize larger benefits from class size reduction, while there appears to be little heterogeneity on the basis of achievement. To the extent that effort is negatively related to disruptive behavior, this finding is also consistent with Lazear’s emphasis on disruption as a mechanism that contributes to heterogeneity in class-size effects.

  3. The classroom average propensity to disrupt is determined by teacher skill at classroom management as well as underlying student behavior. Differences in classroom management skill introduce another pathway through which teacher performance can influence the benefits of smaller classes.

  4. At a value of \(\rho \) below 0.95, nln(\(\rho )\) +1 becomes negative, but at such a low value of \(\rho \) the share of class time available for instruction is well below 50 %.

  5. If the underlying propensity to disrupt is positively correlated with the poverty level, the elements that primarily determine the relationship between the poverty rate and benefit of smaller classes are \(\rho (d)^{n-1}, [n\mathrm{{ln}}(\rho (d))+1]\), and \(\frac{\partial \rho (d)}{\partial d}\). Because \(\rho (d)^{n-1}\) and \([n\mathrm{{ln}}(\rho (d))+1]\) decrease in magnitude as d rises and \(\rho \) declines, these terms would tend to make the benefit of class size reduction increase at a decreasing rate as d and presumably the rate of poverty rise. Therefore in order for the increase in the benefit of class size reduction to be larger at higher levels of d the term \(\frac{\partial \rho (d)}{\partial d}\) would have to be larger in magnitude. This may well be the case, particularly if high-poverty schools find it very difficult to attract and retain teachers and administrators and if they experience a severe lack of resources for support services.

  6. Hanushek (1999) documents the extensive attrition and classroom switching that took place following kindergarten in the STAR experiment and highlights the limited information on teacher quality available in the study. Ding and Lehrer (2010) estimate dynamic treatment effects for STAR.

  7. The average share eligible for a subsidized lunch in each category are 11.9, 35.6, 59.2, and 90.8 %.

  8. See Firpo (2007), Hao and Naiman (2007) and Koenker and Hallock (2001) for further information on quantile regression.

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Authors and Affiliations

  1. Department of Economics, Princeton University, Princeton, NJ, USA

    Graham McKee

  2. Department of Economics, Amherst College, Amherst, MA, USA

    Katharine R. E. Sims

  3. Department of Economics, University of Illinois at Chicago, Chicago, IL, USA

    Steven G. Rivkin

  4. National Bureau of Economic Research, Cambridge, MA, USA

    Steven G. Rivkin

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  1. Graham McKee
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  2. Katharine R. E. Sims
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  3. Steven G. Rivkin
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Correspondence to Steven G. Rivkin.

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McKee, G., Sims, K.R.E. & Rivkin, S.G. Disruption, learning, and the heterogeneous benefits of smaller classes. Empir Econ 48, 1267–1286 (2015). https://doi.org/10.1007/s00181-014-0810-1

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  • DOI: https://doi.org/10.1007/s00181-014-0810-1

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