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Table 4.
First-Stage Estimates of the Effect of an Offer of Admission on Take-up
All Schools (1)School 1 (2)School 2 (3)School 3 (4)
IK bandwidth 0.314*** 0.324*** 0.314*** 0.251*** 
 (0.059) (0.043) (0.085) (0.088) 
28.2 57.1 13.6 8.1 
N 1,756 463 499 1,029 
Bandwidth = 6 0.278*** 0.359*** 0.368** 0.161 
 (0.061) (0.040) (0.118) (0.131) 
20.9 79.6 9.7 1.5 
N 1,023 463 156 404 
Bandwidth = 15 0.384*** 0.522*** 0.313*** 0.241*** 
 (0.056) (0.065) (0.096) (0.084) 
46.8 65.0 10.7 8.3 
N 2,606 1,102 406 1,098 
Bandwidth = IK, controls 0.309*** 0.298*** 0.291*** 0.245*** 
 (0.060) (0.059) (0.075) (0.088) 
26.8 25.2 15.1 7.8 
N 1,756 463 499 1,029 
Bandwidth = IK, low income 0.326*** 0.310** 0.372*** 0.352*** 
 (0.085) (0.134) (0.064) (0.072) 
14.7 5.4 34.1 23.7 
N 739 441 1,276 1,031 
Bandwidth = IK, high income 0.294*** 0.222*** 0.429*** 0.367*** 
 (0.068) (0.044) (0.070) (0.071) 
18.7 25.4 37.2 27.0 
N 1,017 582 1,761 1,420 
All Schools (1)School 1 (2)School 2 (3)School 3 (4)
IK bandwidth 0.314*** 0.324*** 0.314*** 0.251*** 
 (0.059) (0.043) (0.085) (0.088) 
28.2 57.1 13.6 8.1 
N 1,756 463 499 1,029 
Bandwidth = 6 0.278*** 0.359*** 0.368** 0.161 
 (0.061) (0.040) (0.118) (0.131) 
20.9 79.6 9.7 1.5 
N 1,023 463 156 404 
Bandwidth = 15 0.384*** 0.522*** 0.313*** 0.241*** 
 (0.056) (0.065) (0.096) (0.084) 
46.8 65.0 10.7 8.3 
N 2,606 1,102 406 1,098 
Bandwidth = IK, controls 0.309*** 0.298*** 0.291*** 0.245*** 
 (0.060) (0.059) (0.075) (0.088) 
26.8 25.2 15.1 7.8 
N 1,756 463 499 1,029 
Bandwidth = IK, low income 0.326*** 0.310** 0.372*** 0.352*** 
 (0.085) (0.134) (0.064) (0.072) 
14.7 5.4 34.1 23.7 
N 739 441 1,276 1,031 
Bandwidth = IK, high income 0.294*** 0.222*** 0.429*** 0.367*** 
 (0.068) (0.044) (0.070) (0.071) 
18.7 25.4 37.2 27.0 
N 1,017 582 1,761 1,420 

Notes: Heteroskedasticity robust standard errors clustered by score are in parentheses. First-stage estimates show the impact of receiving an offer of admission on actual enrollment in an RVTS. The estimates are generated using local linear regression in conjunction with a triangular kernel and the specified bandwidth and cohort-by-school fixed effects. An offer of admission is determined by having an admission score just above the cutoff specified for a given school and year for students in the 2007 through 2009 cohorts. The last two rows show heterogeneity in the first stage by low-income status in the IK bandwidth (Imbens and Kalyanaraman 2012). Below each coefficient is the F-statistic associated with the eligibility instrument. IK: Imbens and Kalyanaraman 2012.

**p < 0.05; ***p < 0.01.

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