Peer Influence on Academic Achievement: Mean, Variance, and Network Effects under School Choice

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1 Megan Andrew Cheng Wang Peer Influence on Academic Achievement: Mean, Variance, and Network Effects under School Choice Background Many states and municipalities now allow parents to choose their children s school in an effort to ensure all students receive a quality education under the auspices of No Child Left Behind and its revisions. Such school choice policies are intended to assuage educational inequality via quality curricula and instruction. But, these policies also induce important changes in students peer environments. This is especially the case for the low-income or otherwise disadvantaged public school students who move to higher-achieving charter and private schools under these policies. But, these changes may not always have the positive benefits the authors of school choice policy intended generally, however. Postsecondary policies that induce similar changes in peer environments lead to worse academic performance among already low achieving students and better academic performance among already high achieving students (Carrell et al. 2013). This is contrary to some research demonstrating few effects of increased variance or dissimilarity in peer environments on individual student achievement at the elementary and secondary levels (e.g, Hanushek et al. 2003). Observed heterogeneity in the effects of compositional peer influence likely stems from peer network ties and influence and how students integrate into and learn from close peers in school settings (Andrew and Flashman 2016, Sacerdote 2014, Carrell et al. 2013). But, such data are difficult to come by, especially at the primary and secondary school levels. Purpose and Research Design In this paper, we address the uneven evidence on peer influence effects using school choice policies in Indianapolis, Indiana. These policies induce differently changing school institutional settings and thus variation in peer environments that allow us to better identify the effects of peer environment for students with different prior achievement levels. Not incidentally, this variation occurs in the context of one of the nation s most robust school choice regimes. We make two key empirical contributions. First, using cohort by school and individual fixed effects, we evaluate mean and variance effects of peer achievement on a student s test achievement using a large administrative data set. We do so across a variety of specifications, paying particular attention to heterogeneity in peer effects by a student s initial achievement (Flashman 2012, Carrell et al. 2013). Second, we use new peer network data from Indianapolis schools to evaluate whether compositional peer effects may be driven by differential friend selection and influence processes by a student s initial achievement and across schools with different means and variance in student achievement. Preliminary results demonstrate that both the mean level of peer achievement and peer achievement variance have substantively and statistically significant implications for student achievement particularly lower achieving students. While higher mean peer achievement and peer achievement variance increases math and language arts test scores for other Indianapolis students, lower achieving students achieve lower test scores as peer mean and variance achievement increase. We are currently evaluating network data for a number of Indianapolis schools to test the hypothesis that differential compositional peer effects observed in Indiana 1

2 administrative data are driven by student-level peer selection and influence processes in dynamic network models. Data We use both administrative and student survey data in our analyses. Administrative data are from the Indiana Department of Education (IDOE). The IDOE tracks Indiana students longitudinally from the school year through the present for grades K-12. These administrative data include students basic demographic, free/reduced-price lunch status, English-as-a-second language status, special education status, state test scores, the type of school a student attends, whether the student receives a state voucher to attend a private school, and more. We focus on Indianapolis students in our data given the relatively large number of students in that city who attend public, charter, and private schools. Each of these types of schools presents varying mean levels of and variance in student body test achievement and other, and charter and private schools are cornerstones of Indianapolis school choice policies. We are in the process of modeling new longitudinal peer network data for Indianapolis students across public, private, and charter schools with varying levels of mean peer achievement and peer achievement variance. Preliminary Results: IDOE Administrative Data Using administrative IDOE data, we run analyses similar to those in Hanushek et al. (2003). That research suggests that all students benefit from higher achieving school peer environments, regardless of a student s prior achievement. That research also suggests that variance in peer achievement has no bearing on a student s own achievement. We evaluate these findings using more recent data for Indianapolis students under proto-typical school choice policies. Table I shows the linear regression results of students' academic achievement levels and gains measured in Indiana Statewide Testing for Educational Progress Plus (ISTEP+) English/Language Arts (ELA), Mathematics, and total test scores without and with school. Table II shows the linear regression models of subsamples of students staying the same schools and switching to other schools. Table III replicates the peer influence model by students' position in the school achievement distribution as in Hanushek et al. (2003). Table IV shows the effects of changes in peer group on score gains also using student and cohort or grade by school fixed effects. In Table V, we categorize all schools into low-achieving schools, medium-achieving schools and high-achieving schools by the average total scores of students attending each academic year and re-estimate student and grade-school fixed effects models. Generally, results demonstrate that increasing average peer test scores similarly increases a student s own test achievement. This finding replicates that of Hanushek et al. (2003). We also find that the higher the standard deviation of peers' achievement levels, the higher the focal student's achievement level. These coefficients are negative and statistically insignificant in Hanushek et al. (2003). The positive effects of mean peer achievement and variance in peer achievement, however, are limited to students in the second or higher of prior test achievement. Students in the bottom would suffer a loss of score gains from a higher standard deviation of peers' academic achievement (see Table III). In Table V specifically, we find that increasing average score of peers on a specific item still positively predict score gain of the focal student on that specific subject, whether the student 2

3 was switching from one school with a given achievement level to another school with another achievement profile. However, a student switching from a low-achieving to a medium-achieving school or from a medium-achieving to a low-achieving school experiences declines in his or her own achievement given greater variance in peers test achievement. On the other hand, a student switching from a low-achieving or medium-achieving school to a high-achieving school experiences an increase in test achievement given greater variance in peers test achievement. The statement that top students are "less responsive to peer achievement" by Hanushek et al. (2003) seems to apply to some degree when a student switches from a high-achieving school to a low-achieving or medium-achieving school. [Full citations available upon request.] 3

4 Table I. Estimated effects of peer group on levels and gains of ISTEP+ ELA, math, and total scores (absolute value of Huber White adjusted t-statistics in parentheses) ELA score level ELA score gain Average ELA score 0.79*** 0.79*** 0.29*** 0.30*** (324.39) (299.48) (162.08) (159.12) Standard deviation of ELA scores 0.03*** 0.02*** 0.05*** 0.05*** (7.45) (3.78) (15.63) (15.62) 0.14*** 0.15*** 0.19*** 0.19*** (52.20) (49.44) (96.71) (84.83) Sample size 2,948,306 2,572,341 2,948,306 2,572,341 Math score level Math score gain Average math score 0.86*** 0.86*** 0.34*** 0.35*** (454.16) (422.30) (253.81) (245.47) Standard deviation of math scores 0.06*** 0.04*** 0.05*** 0.08*** (14.86) (8.33) (19.37) (25.77) 0.22*** 0.22*** 0.23*** 0.23*** (77.76) (68.83) (119.84) (104.72) Sample size 2,948,306 2,572,341 2,948,306 2,572,341 Total score level Total score gain Average total score 0.84*** 0.83*** 0.28*** 0.29*** (401.91) (372.27) (217.64) (212.70) Standard deviation of total scores 0.05*** 0.03*** 0.04*** 0.05*** (12.82) (6.54) (14.37) (18.76) 0.37*** 0.38*** 0.37*** 0.37*** (71.91) (65.54) (119.77) (105.52) Sample size 2,948,306 2,572,341 2,948,306 2,572,341 Note: All specifications include personal (i.e., dummy variables for gender, black, Hispanic, reduced or free price lunch eligibility, school transfer, Title 1 programme eligibility, special education, and limited English proficient), school (i.e., percent black, percent Hispanic, number of teachers and enrolled students, dummy variables of school types), interaction terms (i.e., that between black and percent black, and that between Hispanic and percent Hispanic), and cohort-by-grade-by-year indicators. 4

5 Table II. Estimated effects of peer group on ISTEP+ ELA, math, and total score gains for stayers and movers (absolute value of Huber White adjusted t-statistics in parentheses) ELA score gain Stayers Movers Average ELA score 0.26*** 0.40*** (117.60) (106.89) Standard deviation of ELA scores 0.07*** 0.03*** (17.84) (4.68) 0.16*** 0.26*** (60.10) (62.01) Sample size 1,773, ,952 Math score gain Stayers Movers Average math score 0.32*** 0.44*** (192.69) (151.30) Standard deviation of math scores 0.09*** 0.05*** (26.13) (7.54) 0.21*** 0.29*** (80.85) (68.58) Sample size 1,773, ,952 Total score gain Stayers Movers Average total score 0.26*** 0.38*** (163.31) (134.75) Standard deviation of total scores 0.07*** 0.02** (22.33) (2.64) 0.32*** 0.49*** (78.80) (71.91) Sample size 1,773, ,952 Note: All specifications also include personal (i.e., dummy variables for gender, black, Hispanic, reduced or free price lunch eligibility, school transfer, Title 1 programme eligibility, special education, and limited English proficient), school (i.e., percent black, percent Hispanic, number of teachers and enrolled students, dummy variables of school types), interaction terms (i.e., that between black and percent black, and that between Hispanic and percent Hispanic), and cohort-by-grade-by-year indicators. Stayers are students who do not change school, while movers are those who do. 5

6 Table III. Estimated effects of peer group on ISTEP+ ELA, math, and total score gains by of each school's test score distribution, controlling for student and school-bygrade fixed effects (absolute value of Huber White adjusted t-statistics in parentheses) ELA score gain Bottom Second Third Top Average ELA score 0.24*** 0.16*** 0.16*** 0.27*** (56.12) (51.37) (54.06) (77.83) Standard deviation of ELA scores -0.05*** 0.04*** 0.06*** 0.16*** (-5.99) (6.53) (10.94) 0.10*** 0.09*** 0.10*** (20.40) (24.55) (27.56) Sample size 2,572,341 (25.84) 0.08*** (17.72) Math score gain Bottom Second Third Average math score 0.36*** 0.35*** 0.35*** (93.56) (126.77) (137.28) Standard deviation of math scores -0.11*** 0.01* 0.11*** (-13.43) (2.46) (21.00) 0.21*** 0.22*** 0.22*** (36.40) (52.24) (57.49) Sample size 2,572,341 Top 0.33*** (126.95) 0.23*** (42.43) 0.20*** (49.44) Total score gain Bottom Second Third Top Average total score 0.27*** 0.23*** 0.23*** 0.26*** (77.98) (91.80) (98.28) (107.75) Standard deviation of total scores -0.05*** 0.03*** 0.07*** 0.16*** (-7.47) (4.99) (14.67) (31.68) 0.27*** 0.27*** 0.28*** 0.22*** (30.39) (42.05) (47.13) (35.40) Sample size 2,572,341 Note: The specification also includes personal (i.e., dummy variables for gender, black, Hispanic, reduced or free price lunch eligibility, school transfer, Title 1 programme eligibility, special education, and limited English proficient), school (i.e., percent black, percent Hispanic, number of teachers and enrolled students, dummy variables of school types), interaction terms (i.e., that between black and percent black, and that between Hispanic and percent Hispanic), and cohort-by-grade-by-year indicators. 6

7 Table IV. Estimated effects of changes in peer group on ISTEP+ ELA, math, and total score gains, controlling for student and school-by-grade fixed effects (absolute value of Huber White adjusted t-statistics in parentheses) ELA score gain Math score gain Total score gain Change in average ELA score 0.37*** (152.54) Change in average math score 0.45*** (220.12) Change in average total score 0.38*** (192.85) Change in standard deviation of ELA scores 0.04*** (8.57) Change in standard deviation of math scores 0.02*** (3.85) Change in standard deviation of total scores (-1.66) Changes in proportion eligible for reduced price lunch 0.08*** 0.09*** 0.15*** (22.50) (25.70) (26.81) Sample size 795,715 Note: The specification also includes personal (i.e., dummy variables for gender, black, Hispanic, reduced or free price lunch eligibility, school transfer, Title 1 programme eligibility, special education, and limited English proficient), school (i.e., percent black, percent Hispanic, number of teachers and enrolled students, dummy variables of school types), interaction terms (i.e., that between black and percent black, and that between Hispanic and percent Hispanic), and cohort-by-grade-by-year indicators. 7

8 Table V. Estimated effects of changes in peer group on ISTEP+ ELA, math, and total score gains across schools of various academic achievement levels, controlling for student and school-by-grade fixed effects (absolute value of Huber White adjusted t-statistics in parentheses) ELA score gain -> -> Change in average ELA score 0.39*** (53.93) 0.41*** (65.03) 0.28*** (20.28) 0.50*** (89.89) 0.27*** (9.61) 0.26*** (14.29) Change in standard deviation -0.03* 0.06*** -0.05* 0.10*** of ELA scores (-2.03) (5.59) (-2.54) (9.77) Change in proportion eligible 0.15*** 0.15*** 0.14*** 0.10*** for reduced price lunch (14.15) (15.23) (7.21) (12.23) Sample size 795,715 (-0.84) 0.15*** (3.29) (-0.23) 0.12*** (4.40) Math score gain -> -> Change in average math 0.51*** 0.51***( 0.46*** 0.59*** score (83.24) 98.09) (39.06) (137.39) Change in standard deviation -0.04** 0.07*** -0.07** 0.06*** of math scores (-2.97) (6.44) (-3.02) (7.56) Change in proportion eligible 0.23*** 0.18***( 0.22*** 0.10*** for reduced price lunch (19.67) 19.26) (10.51) (13.27) Sample size 795, *** (15.06) 0.00 (0.05) 0.16*** (3.53) 0.35*** (22.66) 0.08* (2.39) 0.15*** (4.95) Total score gain -> -> Change in average total score 0.44*** 0.43*** 0.37*** 0.51*** 0.31*** 0.29*** (77.30) (83.16) (33.33) (119.04) (13.79) (19.67) Change in standard deviation of total scores -0.07*** (-5.99) 0.02 (1.67) -0.08*** (-3.91) 0.07*** (7.98) (-0.67) 0.04 (1.38) Change in proportion eligible for reduced price lunch 0.38*** (20.94) 0.30*** (20.09) 0.36*** (11.03) 0.16*** (13.93) 0.31*** (4.29) 0.26*** (5.55) Sample size 795,715 Note: The specification also includes personal (i.e., dummy variables for gender, black, Hispanic, reduced or free price lunch eligibility, school transfer, Title 1 programme eligibility, special education, and limited English proficient), school (i.e., percent black, percent Hispanic, number of teachers and enrolled students, dummy variables of school types), interaction terms (i.e., that between black and percent black, and that between Hispanic and percent Hispanic), and cohort-by-grade-by-year indicators. 8