E560095DwTF - Fortin Econ 560 V Social Mobility and Social Interactions Plan D Evidence of Neighbourhood Network and Peer Effects 1 Peer Effects in

E560095DwTF - Fortin Econ 560 V Social Mobility and Social...

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Unformatted text preview: Fortin – Econ 560 V. Social Mobility and Social Interactions Plan D. Evidence of Neighbourhood, Network and Peer Effects 1. Peer Effects in Education 2. Neighbourhood Effects 3. Network Effects Lecture 5D Fortin – Econ 560 Lecture 5D 1. Peer Effects in Education • Expressions of the popular belief in sizeable peer interaction effects in schooling is reflected by the actions of parents who pay sizeable tuition fees to send their children to private schools or sizeable housing premium for schools in better neighbourhoods. • The literature on peer-group in education really began with the Coleman Report (1966) which indicated that the educational achievement of black students was positively related to the fraction of students in their school that were white. • This early and controversial study were very influential as it has been held as primarily responsible for the school busing desegregation movement in the US, but it was plagued with all the problems noted earlier, except with the simultaneity problem (that the extent that being white is a characteristic rather than an interaction effect). • Since the early studies, there have been numerous papers on peer effects in education. Many, if not the majority of studies (see for example, Schofield, 1995) find non-existent or weak effects of peers, that are fragile and non-robust to specification and the inclusion of controls. • Studies of peer effects in education that find stronger results use a definition of closer peers, namely roommates. Fortin – Econ 560 Lecture 5D • Another study by Bruce Sacerdote (2001) that is based on random assignment exploits the fact that Freshmen entering Dartmouth College (a highly selective, medium-sized, liberal arts institution located in New Hampshire) are randomly assigned to dorms and to roommates thereby eliminating the problem of peers selecting each other based on observable and unobservable characteristics. • Sacerdote (2001) finds that peers have an impact on GPA and on decisions to join social groups such as fraternities, which can be important for career networks and for lifelong friendships which ultimately may have a high impact on outcomes. • Peer effects in GPA occur at the individual room level, whereas peer effects in fraternity membership occur both at the room level and the entire dorm level. In contrast, the peer effect in GPA does not display any dorm level or floor level effect; it is observed only at the room level. • On the other hand, he finds that residential peer effects are markedly absent in other major life decisions such as choice of college major. • This provides some evidence that the reference group or relevant peer group can differ dramatically across different activities and outcomes. 692 Source: Sacerdote (2006) TABLE III PEER EFFECTS IN ACADEMIC OUTCOMES Roommates’ GPA HS academic score (self) HS academic score (roommates’) roommates’ academic score bottom 25 percent roommates’ academic score top 25 percent roommates’ intention to graduate w/honors (1–4) own academic score bottom 25 percent (2) Fresh year GPA w/ dorm f.e. (3) Senior year GPA 0.120** (0.039) 0.014** (0.0008) Ϫ0.001 (0.001) 0.068** (0.029) 0.015** (0.0007) Ϫ0.0003 (0.0009) 0.008 (0.026) 0.013** (0.0009) 0.0009 (0.001) (4) Fresh year GPA (5) Fresh year GPA (6) Fresh year GPA 0.014 (0.025) 0.017 (0.025) 0.060** (0.028) 0.047* (0.026) 0.043* (0.026) 0.082** (0.037) Ϫ0.284** (0.025) Ϫ0.282** (0.025) (8) Econ major Ϫ0.0001 (0.0003) 0.0003 (0.0003) 0.016 (0.028) (7) Graduate late 0.003** (0.0006) Ϫ0.0001 (0.0006) QUARTERLY JOURNAL OF ECONOMICS (1) Fresh year GPA Dummies for housing questions F test of roommate background coefficient ϭ 0 R2 N 0.174** (0.025) 0.175** (0.025) 0.008 (0.029) yes .38 1589 yes .18 1441 yes yes yes F ϭ 2.31 P ϭ 0.10 .24 1589 yes F ϭ 1.63 P ϭ 0.20 .19 1589 .19 1589 .06 1589 .07 1589 F ϭ 2.74 P ϭ 0.04 .05 1589 yes Ϫ0.018 (0.026) yes Standard errors are in parentheses and are corrected for clustering at the room level. In cases with more than one roommate, roommate variables are averaged. ** ϭ p-value Ͻ .05. * ϭ p-value Ͻ .10. Regression (1) is OLS of own GPA on roommate GPA and controls. If own and roommate academic indices are excluded, the coefficient on roommate GPA falls to .111, and the standard error falls to 0.037. Regression (2) adds dorm fixed effects. The coefficient on roommate GPA falls, but remains significant. Regression (3) is OLS of own senior year GPA on freshman year roommates’ senior year GPA. Senior year GPA includes all grades in final year and excludes grades from earlier years. Regressions (4)–(6) are OLS of own GPA on own and roommate background. These regressions use dummies for own and roommate academic index are in the bottom 25 percent, middle 50 percent (excluded category), or top 25 percent of their respective distributions. Regression (4) shows that “roommate top 25 percent” is significant in predicting own GPA. The level of significance on “roommate top 25 percent” falls to .10 when two dummies for own academic index are added. (This is regression (5).) Regression (6) shows that roommate intention to graduate with honors also predicts own GPA. This variable is a self-assessed probability of graduating with honors and is coded as a 1, 2, 3, or 4 for the responses of no chance, very little chance, some chance, or a very good chance. Regression (6) also includes a dummy for “roommate intend to graduate with honors” missing. See text for more discussion of this variable. Regressions (7) and (8) are probits of own “graduate late” and own “major choice ϭ econ” on roommate graduate late and roommate major choice ϭ econ. ‫ ץ‬y/‫ ץ‬x is shown. PEER EFFECTS WITH RANDOM ASSIGNMENT own academic score top 25 percent Roommate graduate late Roommate econ major 693 Source: Sacerdote (2006) PEER EFFECTS WITH RANDOM ASSIGNMENT 699 TABLE V PEER EFFECTS IN SOCIAL OUTCOMES (1) Member frat/ soror (2) Member frat/ soror roommate member of fraternity/sorority/coed dorm average of fraternity/sorority/coed roommate varsity athlete 0.078** (0.038) 0.056 (0.037) 0.321** (0.135) HS academic score (self) 0.0098 (0.0010) Ϫ0.0017 (0.0011) 0.0011 (0.0011) Ϫ0.0016 (0.0011) yes yes 0.0010 (0.0011) Ϫ0.0016 (0.0011) 0.135** (0.038) Ϫ0.025 (0.026) (0.026) 0.287** (0.146) yes .02 1589 .02 1589 .03 1589 HS academic score (roommates’) Own use of beer in high school (0–1) Roommates’ use of beer in high school (0–1) Dormmates’ use of beer in high school (0–1) Dummies for housing questions R2 N (3) Member frat/ soror (4) Varsity athlete 0.045 (0.033) Ϫ0.004** (0.001) Ϫ0.0002 (0.0007) yes .05 1589 Standard errors are in parentheses and are corrected for clustering at the room level. In cases with more than one roommate, roommate variables are averaged. ** ϭ p-value Ͻ .05. Columns (1)–(4) are Probits. ‫ ץ‬y/‫ ץ‬x is shown. In regression (2), dorm average of frat membership excludes own observation, and standard errors are corrected for clustering at dorm level. In regression (3), use of beer in past year is coded 0 –1 as follows: 0 ϭ not at all, occasionally or frequently ϭ 1. Dorm use of beer excludes own room and standard errors are corrected for clustering at dorm level. tials are reported rather than probit coefficients.) If my freshman year roommate joins a fraternity, I am 8 percent more likely to do so myself. This occurs in spite of the fact that students do not even execute this decision during their freshmen year. Students are not allowed to join until sophomore year, and only 16 percent of people keep any of the same roommates. More remarkable is the frequency with which students join the same house as their randomly assigned roommate. When I limit the sample to rooms of two where both roommates have joined a fraternity, I find that 27 percent of the roommate pairs Fortin – Econ 560 Lecture 5D • When one is not fortunate enough to find a situation where there is random assignment, one can exploit some bureaucratic idiosyncrasies. A few recent studies have exploited such idiosyncracies in school environment to use an identification strategy based on instrumental variables. • For example, Angrist and Lang (2004) study the impact of busing on students in Metco schools, a voluntary program that sent mostly black students out of the Boston district into schools in the surrounding, mostly white suburban districts. • In particular, they estimated the effect of Metco students on the achievement of non-Metco students using school/grade/year average national percentile rank of non-Metco students on the fraction Metco in a grade, school, and year as well as individual data. • Their OLS estimates for black residents of Brookline show that most estimates are not significant, except for some of the estimates for third graders which are negative and significant. • They also perform an IV estimation that exploits the fact that Metco students are assigned to Brookline schools partly on the basis of a space constraint of 25 students, a strategy similar to what Angrist and Lavy (1999) termed Maimonides' rule, after the biblical scholar, who proposed a maximum class size of 40 in a Talmudic commentary. VOL. 94 NO. 5 ANGRIST AND LANG: DOES SCHOOL INTEGRATION GENERATE PEER EFFECTS? 1621 TABLE 4--TEST SCORES RACEAND METCO BY STATUS Non-Metco Grade 3 Subject Core Reading Math Language 5 Core Reading Math Language 7 Core Reading Math Language Metco All (1) Black (2) Hispanic (3) Asian (4) White (5) All (6) Black (7) Non-black (8) 71.6 (24.2) 16.81 70.7 (24.7) 15.91 72.0 (24.7) V.31 67.8 51.2 (27.6) 54.2 (27.6) 71.9 (22.8) 74.3 (22.7) 47.2 (25.1) 60.1 (25.2) 51.7 (28.4) 54.9 (26.4) 63.7 (23.8) 74.8 (22.8) 46.1 (26.8) 58.8 (24.8) 50.8 (28.4) 54.9 (28.0) 76.4 (22.6) 74.0 (23.3) 49.0 (25.5) 122.21 47.9 (26.8) [2 1.41 47.9 (26.4) 122.91 45.7 (26.3) 62.0 (23.4) i2.3(22.7) [5.11 72.4 (22.7) L4.31 70.6 (23.2) L6.11 69.2 (24.4) l6.1I 76.4 (21.8) 14.71 77.0 (22.6) L4.41 74.0 (23.4) 15.01 73.9 (22.4) 15.31 49.8 (25.7) 49.9 52.2 (25.9) 47.8 Notes: Columns (1) to (5) show statistics for the population of tested non-Metco students. Columns (6) to (8) show statistics for the population of tested Metco students. Reported test scores are means of the National Percentile Rank from the Iowa Test of Basic Skills administered from the 1994-1995 school year through the 2000-2001 school year. Standard deviations are reported in parentheses. Standard deviations for schooL/grade/year cell means appear in brackets. from Boston, a project we hope to pursue in the future. C. Metco and the School Environment Differences in average achievement between Brookline residents and Metco students are large enough for the presence of Metco students to reduce average test scores in Brookline. This can be seen in the top panel of Table 5. Columns (1) to (4) of the table report unweighted estimates of the grouped equation (1) Yg,, = ag + p, + yr + Sms,, + As,, + ugjr where y,,, is the average score in the grade glschool jlyear t cell, s,., is class size in the cell, including Metco, and m,, is fraction Metco (based on tested students) [where g X j X t = 3 X 8 X 7 = 168 cells]. Columns ( 5 ) to (8) report estimates treating individual students as the unit of observation and replacing y,, with y,gr(,,, average score of students in the cell, the excluding student i. These estimates capture the Source: Angrist and Lang (2004) 1622 THE AMERICAN ECONOMIC REVIEW TABLE 5-METCO EFFECTS ON THE DECEMBER 2004 SCORE DISTRIBUTION ALL STUDENTS FOR Grouped data Subject (1) Pooled (2) 3rd (3) 5th Micro data (4) 7th (5) Pooled (6) 3rd (7) 5th (8) 7th Panel A. Dependent variable: mean test score Peer means Cell means Core Reading Math Language N Panel B. Dependent variable: second decile of test score Cell quantiles Core Reading Math Language N -51.4 (14.4) -45.2 (15.2) -37.6 (17.1) -35.7 (14.1) 168 -61.7 (31.8) -58.3 (35.1) -48.3 (34.6) -43.0 (3 1.2) 56 -37.8 (23.3) -41.3 (22.0) -31.4 (28.7) -1.79 (23.4) 56 Quantile regression -48.6 (23.1) -41.1 (23.8) -35.3 (29.3) -44.5 (21.7) 56 -48.6 (15.5) -43.3 (16.5) -44.4 (14.5) -40.3 (15.6) 8,629 -56.7 (38.0) -57.5 (33.8) -40.5 (47.1) -47.4 (42.8) 2,798 -43.0 (3 1.2) -45.8 (25.8) -40.0 (36.7) -23.0 (3 1.5) 2,966 -51.9 (28.1) -31.7 (32.0) -31.2 (33.2) -49.6 (29.5) 2,865 Notes: The table reports the coefficient on fraction Metco estimated from the Riverside testing data using equation (1) in the text. Standard errors are reported in parentheses. Standard errors in columns (1) to (4) are robust. Standard errors in columns (5) to (8) of panel (A) are clustered by grade/school/school-year cell. Standard errors in columns (5) to (8) of panel (B) are boostrapped. In columns (1) to (4) of panel (A) the dependent variable is the mean test score for the grade/school/school year cell. In columns (5) to (8) of panel (A), the dependent variable is the peer mean score. The peer mean score is the grade/school/school year cell mean score omitting the student's own score from the mean. In columns (1) to (4) of panel (B) the dependent variable is the second decile of the test score. Columns (5) to (8) of panel (B) report microdata quantile regression estimates for the second decile of the test score. Covariates include class size and fixed effects for school and school year. Columns (1) and (5) include cohort and grade fixed effects. The N row displays the number of observations (or cells) in the regression. For columns (5) to (8), the N row displays the number of observations in the core test score regression. effect of fraction Metco on non-Metco students' peer means, since Metco students are included in y,,(,, but excluded from the estimation sample. Except for the fact that the dependent variable is a peer mean and the equation includes individuallevel controls, the resulting estimates are similar to estimation using cell means weighted by the number of non-Metco students in a ce11.13 The results tell a similar story for both estimation strategies. As with the school-level data, the presence of Metco students has a marked l 3 The standard errors in columns (5) to (8) are adjusted for cell-clustering. All models using data p l e d across grades include a set of cohort effects (for 11 graddyear cohort groups). Models using microdata include dummies for sex and race. negative effect on average performance. Increasing the number of Metco students by ten percentage points in Brookline (about two per class) lowers average scores by almost 2% percentage points, or about 40 percent of the standard deviation of the group averages. Of course, this may be a pure composition effect arising from the large gap between the scores of Metco and non-Metco students, a point to which we return below. Because Metco students' scores are concentrated in the lower tail of the Brookline residents' score distribution, increasing the fraction Metco shifts the overall score distribution most sharply in the lower tail. To illustrate this point, the bottom panel of Table 5 shows the effect of Source: Angrist and Lang (2004) 1624 DECEMBER 2004 THE AMERICAN ECONOMIC REVIEW Grouped data Subject Pooled (1) 3rd (2) Micro data 5th (3) 7th (4) Pooled (5) 3rd (6) 5th (7) 7th (8) -1.60 (10.9) -3.93 (9.74) 4.46 (12.1) -11.5 (1 1.6) 2,672 -6.50 (10.2) -5.82 (1 1.2) -11.8 (12.9) -3.18 (10.2) 2,796 -3.45 (8.16) 0.067 (6.89) -2.86 (9.42) -4.96 (8.11) 2,678 Panel A. All non-Metco students Core Reading Math Language N 3.19 (7.52) 5.30 (6.91) 4.53 (8.72) 0.53 1 (8.11) 168 1.41 (14.2) -2.06 (13.9) 4.66 (16.7) -4.63 (14.1) 56 1.57 (13.7) -1.14 (13.5) -0.322 (17.5) 4.91 (13.9) 56 6.62 (12.3) 10.2 (10.1) 8.34 (14.1) 5.42 (12.3) 56 -5.18 (5.88) -2.78 (5.09) -4.81 (7.03) -8.38 (6.57) 8,146 Panel B. Black non-Metco students Core Reading Math Language N -78.1 (36.6) -66.2 (36.0) -50.0 (37.0) - 102 (41.O) 146 -218 (92.8) -288 (94.9) -92.1 (81.O) -237 (65.7) 45 21.8 (79.8) 14.9 (62.1) 22.5 (81.6) 0.529 (88.9) 49 -68.0 (45.0) -2.40 (43.6) -61.2 (5 1.9) -83.4 (52.5) 52 -33.1 (24.5) -29.7 (24.5) -5.4 (28.3) -47.3 (25.0) 534 - 170 (54.4) - 180 (56.6) -31.1 (66.1) -175 (52.9) 169 26.9 (49.8) 20.0 (39.5) 32.7 (55.6) 29.4 (57.8) 183 -3.75 (30.4) 19.2 (33.2) 2.62 (36.5) - 12.4 (32.0) 182 Notes: Columns (1) to (4) report OLS estimates of the coefficient on the fraction Metco variables in equation (2) using cell means. Columns (5) to (8) report student-level estimates from equation (3). The fraction Metco variable was constructed from the Riverside testing data. Robust standard errors are reported in parentheses in columns ( I ) to (4). Standard errors in columns (5) to (8) are clustered by grade/school/school-year. The dependent variable is the relevant test score. Covariates include class size and fixed effects for school and school year. Models for columns (5) to (8) also include race, gender, ESLiTBE, and special education indicator variables as covariates. Models for columns (1) and (5) contain grade and cohort fixed effects. The N row shows the number of observations in the core regression (or the number of cells). command. In practice, the standard errors from this procedure may be misleading, especially when there are few clusters, and inference using grouped data has been shown to be more reliable (see, e.g., Ziding Feng et al., 2001; Stephen Donald and Kevin Lang, 2001). This leads us to report results using both cell means and individual data. Both the grouped and micro equations use the fraction Metco tested for in,, since this is more consistently measured and probably more accurate than the fraction Metco enrolled (though estimates using both measures are similar). Pooled estimates of equation (2) generate small positive, but insignificant, effects-of fraction Metco on average non-Metco scores in each subject. This can be seen in the first four columns of panel (A) in Table 6. The estimates using microdata, reported in columns (5) to (8), are negative but again small and insignificant, suggesting that the proportion Metco has no effect on non-Metco students. On the other hand, it should be noted that the standard errors for the microdata estimates in column (5) are such that the smallest negative effect that could be detected (i.e., the effect that would be significant at the 5-percent level in a one-tailed test) is about 5.9 X 1.64 = -9.7. Since the effect of fraction Metco tested on peer means is -24 (see column [5] in Table 5 ) , the smallest detectable peer effect that operates solely through the test scores of all classmates is about 0.4. On the other hand, if the lower tail of the score distribution matters for achievement, then peer effects as small as 0.2 would be significant. The results therefore reject effects in the upper range of those found in prior research on peer effects, but smaller effects cannot be ruled out. For example, using data from Texas schools, Hoxby (2000) reports estimates of the effect of the average peer score ranging from 0.1 to 0.55. Our estimates for Brookline rule out Source: Angrist and Lang (2004) 1628 THE AMERICAN ECONOMIC REVIEW TABLE 7-OLS, FIRST-STAGE, AND DECEMBER 2004 REDUCED-FORM ESTIMATES ALLNON-METCO FOR THIRD GRADERS Dependent raiable Math Core (71 (8) Language (91 (10) (11) 112) -1 64 (1.63) -0037 (0.082) -0.530 -0.429 (1.53) 0.015 (0.080) 0.620 (0.243) - 1.85 (1.49) -3.13 (1 75) 0.025 (0.076) -0.530 Panel A. OLS Number Metco In class Number non-hletco enrolled Number non-hletco ~n class N 0.586 (0.601) -0.033 (0.0761 0 658 (0.215) 0 162 (0.626) -0 145 (0.713) -0.038 (0.077) -0.530 2.672 Panel B. First-stage-Dependent Instrument Number non-hletco enrolled Number non-Metco ~n clasc N 0.921 (0 185) 0 0014 (0.0 16) 0.0205 (0.0401 0 875 (0.163) variable is number Metco In class 0.873 (0.170) 0.0016 (0 016) 2,812 Panel C Reduced form Instrument Number non-hletco enrolled Number non-Metco tn class N -0.069 11.39) -0.029 (0.078) 0.610 (0.259) -1.50 (1.33) 2.672 -2.67 ( I 60) -0.021 (0.073) -0.530 0.280 (1.01) -0.00?0 (0.062) 0 586 (0.241 -1 10 (1.02) 2,773 -2.36 (1 32) 0.0087 (0.058) -0.530 0 3...
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