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ABSTRACT
We evaluate the impacts of small high schools on youth risky behaviors and mental health in New York City, using a two-sample-instrumental-variable approach to address endogenous school enrollment. We find heterogeneous effects. School size, overall, has little effect. Among students most likely to attend small schools opened after an educational-achievement-oriented reform, however, diagnoses of violence-associated injuries and mental health disorders increased. Among students most likely to attend traditional small schools opened prior to the reform, pregnancy rates and diagnoses of mental health disorders declined. School focus is more important than school size as a determinant of student well-being outcomes.
Data availability statement
The data used in this research are confidential and HIPAA-protected.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 A related strand of literature shows that class size may also affect student outcome (Jakobsson, Persson, and Svensson Citation2013; Coupé, Olefir, and Alonso Citation2016; Green and Iversen Citation2022). While smaller schools may also have smaller class size compared to large schools, in our study we do not have data at the class level to study the impact of small class size.
2 Details about the difference between the two types of schools can be found in Bloom, Thompson, and Unterman (Citation2010), Schwartz, Stiefel, and Wiswall (Citation2013; Citation2016), and Stiefel, Schwartz, and Wiswall (Citation2015).
3 However, Schwartz, Stiefel, and Wiswall (Citation2016) do not find consistent evidence that students attending small schools in NYC perceive better learning environment.
4 The High School Application Processing System, which was introduced in NYC in the 2003–2004 academic year, requires all 8th graders in public schools in NYC to submit a list of up to 12 high schools in order of preference. Then the NYCDOE uses a computerized process to assign students to their highest-ranked high schools with available space whose admission criteria have been met. The students who are not assigned to any school on their list are informed of schools with empty places and asked to submit another list of up to 12 schools and the process repeats. Any remaining students after the second round are assigned administratively. See Schwartz, Stiefel, and Wiswall (Citation2013; Citation2016) and Stiefel, Schwartz, and Wiswall (Citation2015) for details about the high school application processing system in NYC.
5 The average straight-line distance between students’ homes and their first-choice high school is roughly 2.5 miles (about 4 kilometers) (https://ibo.nyc.ny.us/iboreports/preferences-and-outcomes-a-look-at-new-york-citys-public-high-school-choice-process.html), which is roughly the case for all the four boroughs included in this study.
6 We exclude Staten Island, where there are three small high schools. Generally, students do not travel to or from Staten Island to attend a small school.
7 If the potential benefits of a small school are due to smaller school size that generates positive peer effects and desirable schooling environment both inside and outside classrooms, co-location with other schools, which increases actual school size, may offset those benefits, particularly the ones outside classrooms.
8 New York State Medicaid claims data include personal identifiers, address history, Medicaid enrollment information, and codes for the types of service received, diagnoses, procedures, and service dates. We use both fee-for-service and managed care encounter claims data, which are comparable in quality (source: Mathematica. Medicaid Managed Care and Integrated Delivery Systems: Technical Assistance to States and Strengthening Federal Oversight.; 2013.)
9 From 2009 to 2014, the national income eligibility of guidelines for the reduced – and free-lunch program were 185% and 130% of the federal poverty line, respectively. Meanwhile, the NYC income eligibility of guidelines for Medicaid for children under 19 are 100–154% of the federal poverty line.
10 Census tract is a geographic region defined for the purpose of analyzing populations during census in the United States, established by the Bureau of Census. The primary purpose of census tracts is to provide a stable set of geographic units for the presentation of statistical data. Information such as demographic, socioeconomic, and housing statistics are collected and reported at the census tract level. Census tracts are small and relatively permanent subdivisions of a county. In 2020, a census tract had about 4,000 inhabitants on average. More information about census tracts can be found here: https://www2.census.gov/geo/pdfs/education/CensusTracts.pdf.
11 We have also examined substance use disorders. However, our results are implausibly large, which may have to do with discretion in identification of these disorders. Therefore, we exclude substance use disorders from the list of outcomes.
12 We also use overweight/obesity as outcomes for a validity check. However, as we will note later, we have inconsistent definitions of overweight/obesity across datasets. In the education dataset we define overweight/obesity by body mass index, while in the health dataset what we have are overweight diagnoses.
13 To save notations, we use lowercase rather than uppercase letter to denote the coefficient vector of . This rule applies throughout the entire paper.
14 Ideally, we could include census tract fixed effects. However, we would not have enough variation in school enrollment within census tract to estimate the first stage model. Our reduced-form results with census tract fixed effects (available upon request), especially the correlation between distance to old small schools and teen pregnancy, are similar to the results with census tract characteristics.
15 More details on instrument validity can be found in Schwartz, Stiefel, and Wiswall (Citation2013; Citation2016), which estimates the effects of small schools on educational outcomes using similar (one-sample) instrumental variable approaches.
16 Our models are overidentified with more instrumental variables than endogenous variables. It is essential that the distance to one type of schools is a strong determinant of enrollment in that type of schools, which is the case for all models. Although the enrollment in one type of schools may also be related to the distance to other type of schools, these coefficients tend to be small and statistically insignificant.
17 In our first stage, the F-statistics are above the recommended rule-of-thumb threshold of 10 (Staiger and Stock Citation1997; Stock, Wright, and Yogo Citation2002), indicating that overall, the instruments are strong. It is suggested that the exclusive first-stage F may not be appropriate when there are multiple endogenous variables (Angrist and Pischke Citation2008): The F statistic can be large when only a part of instrumental variables is strong, in which case the model may still be weakly identified. To account for that possibility in the separate models that distinguish old and small schools, we also conduct the modified first stage F test – the Sanderson-Windmeijer multivariate F test (Angrist and Pischke Citation2008; Sanderson and Windmeijer Citation2016) and get similar conclusions. We should note that for the baseline model the multivariate F-statistic test or the Sanderson-Windmeijer multivariate F test are equivalent because there is only one endogenous variable (small school enrollment).
18 New small schools are also much more likely to be co-located with other schools (Schwartz, Stiefel, and Wiswall Citation2013; Citation2016). In our sample the proportion of co-location is 95.2% and 60.5% for new and old small schools, respectively. One may argue that co-location with other schools, which may serve to increase size of the school community, may offset the potential benefits of a small school that are due to smaller school size that generates positive peer effects and desirable schooling environment both inside and outside classrooms. However, the disparity in the estimated effects between new and old small schools is unlikely to be driven by such a co-location effect because with distances to the nearest schools as instruments our estimated effects are mostly identified by schools that do not co-locate with others.
19 However, we should note that more male contraception may still contribute to the observed lower likelihood of teen pregnancy.
20 Boys are more likely to visit SBHC once (0.185, p-value<0.01) and report more claims (0.722, p-value = 0.07) in new but not old small schools, compared with those in large schools. Such differences in SBHC utilization between boys and girls may contribute to certain gender disparities in the estimated effects. For example, boys in new small schools may have more consultations for mental health than girls, thus, are less likely to be diagnosed with the issues.
21 Girls in new small schools are more likely to receive (moderately effective) contraceptives treatments, probably via more visits to school-based health centers. These may offset negative impacts such as riskier sexual behaviors, leading to an overall insignificant impact on pregnancy.
22 In another falsification test using the available data, we repeat our main regression models to examine whether small schools are correlated with student risky behaviors before high school enrollment, using the outcomes measured between January and August 2009 or 2010, when the students are supposed to be in grade 8. We do not find any statistically significant results (available upon request), indicating that small school placement may not be strategically related to the underlying risk of teenagers being involved in the examined outcomes before they are enrolled in high schools.
23 The authors conducted a test that regressed an indicator for student mobility on a set of student characteristics and after-move distance to old and new small schools. They did not find statistically significant evidence for the correlation. The test was performed using the whole sample, but the results should hold for low-income families given the high residential and moving costs in NYC.
24 Some families might make residential location decisions many years prior to student entry into grade 8, e.g. for school preferences for older siblings. However, that seems not matter in our case of cohort 2009 and 2010 in NYC, according to the two falsification tests conducted in Schwartz, Stiefel, and Wiswall (Citation2013) that examine cohort 2001 and 2002, and cohort 2007 and 2008, respectively. Moreover, given the cost of moving, including breaking family and social ties, such strategic moving in the past seems unlikely for low-income families studied here.
25 We should also note that starting from the 2012 to 2013 academic year, students in NYC whose families qualified for Medicaid received free school meals automatically, per the Medicaid direct certification program (Food Research & Action Center, Citation2018).
26 Note that since we control for age in all regressions, we still compare outcomes with the same length of measurement periods.
27 In the education dataset, there is information on BMI (Body Mass Index), from which we can generate overweight and obesity indicators. We use the cutoffs from the National Center for Chronic Disease Prevention and Health Promotion to define overweight and obesity. A child/teen is described as overweight if BMI is at or above the 85th percentile and below the 95th percentile for children and teens of the same age and sex, and as obesity if BMI is at or above the 95th percentile for children and teens of the same age and sex. Source: https://www.cdc.gov/obesity/childhood/defining.html (for definitions of overweight and obesity) and https://www.cdc.gov/healthyweight/assessing/bmi/childrens_bmi/about_childrens_bmi.html (for US children BMI percentile). In the Medicaid data we have diagnoses related to overweight/obesity.
28 We should note that the overweight variable in this study is likely to be closer to obesity (rather than overweight) by BMI, because our outcome is defined as whether the student had been diagnosed with problems related to overweight/obesity. Generally, a slight overweight is unlikely to cause health problems for teens or to be noticed by physician.
29 Given the difference in school age, small and large schools may also differ in school infrastructures, which have been shown to potentially affect student outcomes (Cellini, Ferreira, and Rothstein Citation2010; Martorell, Stange, and McFarlin Citation2016; Hong and Zimmer Citation2016).