Teacher Labor Market Policy and the Theory of the Second Best

The teacher labor market is a two-sided matching market where the effects of policies depend on the actions of both sides. We specify a matching model of teachers and schools that we estimate with rich data on teachers’ applications and principals’ ratings. Both teachers’ and principals’ preferences deviate from those that would maximize the achievement of economically disadvantaged students: teachers prefer schools with fewer disadvantaged students, and principals’ ratings are weakly related to teacher effectiveness. In equilibrium, these two deviations combine to produce a surprisingly equitable current allocation where teacher quality is balanced across advantaged and disadvantaged students. To close academic achievement gaps, policies that address deviations on one side alone are ineffective or harmful, while policies that address both deviations could substantially increase disadvantaged students’ achievement. *Bates, UC-Riverside: mbates@ucr.edu; Dinerstein, University of Chicago: mdinerstein@uchicago.edu; Johnston, UC-Merced: acjohnston@ucmerced.edu; Sorkin, Stanford: sorkin@stanford.edu. We thank Nikhil Agarwal, Claudia Allende, Peter Arcidiacono, Natalie Bau, Christina Brown, Jediphi Cabal, Dennis Epple, Felipe Goncalves, Caroline Hoxby, Peter Hull, Adam Kapor, Neale Mahoney, Richard Mansfield, Maxim Massenkoff, Derek Neal, Parag Pathak, Luigi Pistaferri, Jesse Shapiro, Camille Terrier, and numerous seminar and conference participants for helpful comments and conversations. Thanks to Ian Calaway for research assistance. We also thank representatives at an unnamed district, Kara Bonneau, and the North Carolina Education Research Data Center for data merging and access. Bates thanks the Blum Initiative and Sorkin thanks the Alfred P. Sloan Foundation for support. This research was approved by the Stanford IRB (#43865), the UC Merced IRB (UCM2019-88), and the UC Riverside IRB (HS-16-094). It was deemed non-human subjects research by the University of Chicago IRB (IRB17-1651). Mistakes are our own. Achievement gaps between economically advantaged and disadvantaged children are large and growing over time (Reardon, 2013). These large achievement differences correlate with differences in adult earnings (Chetty, Friedman, and Rockoff, 2014b). Recent work argues that this relationship is causal—teachers that causally improve achievement also improve adult income (Chetty, Friedman, and Rockoff, 2014b). Because teachers vary widely in their effect on student outcomes (Hanushek, Kain, and Rivkin, 2004), changing the allocation of teachers to students may be one of the most important policy instruments for helping the disadvantaged. The labor market, however, may be unlikely to achieve an inequality-reducing allocation of teachers to schools. Because wages usually do not vary across schools within a school district and teaching disadvantaged students may present various challenges, their schools might struggle to attract high-quality teachers. Such an unequal allocation of teachers to students may not only fail to close achievement gaps but even widen them.1 Policymakers have thus argued that interventions in the teacher labor market are necessary to deliver high-quality teachers to disadvantaged students. One policy that has nearly universal take-up is switching from a system of hiring based on seniority to one of mutual consent where both the teacher and the school principal must agree to an assignment. Mutual consent has risen sharply in the US over the last few decades (Engel, Cannata, and Curran, 2017) such that 92% of large districts have now adopted it (National Council on Teacher Quality, 2022). Mutual consent fundamentally changes the economics of the teacher labor market, from a one-sided market where principals have no say to a two-sided market, where both principals and teachers must agree to a match. In this paper, we study a large school district’s two-sided teacher labor market and how it allocates teacher quality across different student types. Like many school districts, our focal district has considerable sorting of students across schools by race and economic background, such that the within-district assignment of teachers has the potential to dramatically increase or decrease achievement gaps. We ask two questions: First, how effective are current policies in raising disadvantaged students’ achievement? Second, what policies would most effectively raise disadvantaged students’ achievement? While these questions have been the focus of large literatures, we generate new insights (at odds with inferences from the prevailing literature) by focusing on the economics of two-sidedness and using novel data. As a first-best benchmark, we assume that a district maximizes disadvantaged students’ achievement. The unifying theme 1Related concerns apply to many matching markets, as whenever a characteristic both confers an advantage and makes an individual more attractive to match to, the market can exacerbate inequality. Policymakers and economists have raised concerns about increasing wage inequality by worker education (e.g., Card, Heining, and Kline, 2013), the difficulty of rural hospitals attracting doctors through the US Residency Match (e.g., Agarwal, 2017), the under-representation of minority students at flagship universities (e.g., Kapor, 2020), and the increasing assortativity in the marriage market (e.g., Chiappori, 2020).