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Table 10.
Effects of Voluntary Pre-Kindergarten Program (VPK) Participation (Instrumented with VPK Availability within 10 Miles) on Being Retained at Least Once by the Completion of Each Grade by Federal Meals Program Eligibility
Kindergarten1st Grade2nd Grade3rd Grade
First-stage effects of VPK availability on VPK participation 
Not Eligible 0.520*** 0.515*** 0.514*** 0.520*** 
 (0.012) (0.012) (0.011) (0.011) 
F-statistic for instrument 1,874.08*** 1,949.22*** 2,056.48*** 2,337.13*** 
R2 0.352 0.347 0.346 0.345 
Shea's partial R2 for instrument 0.063 0.061 0.061 0.064 
Reduced-Price 0.549*** 0.544*** 0.540*** 0.539*** 
 (0.014) (0.014) (0.015) (0.014) 
F-statistic for instrument 1,526.08*** 1,429.46*** 1,321.07*** 1,395.29*** 
R2 0.356 0.355 0.352 0.359 
Shea's partial R2 for instrument 0.064 0.063 0.063 0.064 
Free 0.459*** 0.456*** 0.455*** 0.458*** 
 (0.007) (0.007) (0.007) (0.007) 
F-statistic for instrument 4,120.65*** 4,048.23*** 4,030.11*** 3,785.47*** 
R2 0.262 0.262 0.261 0.278 
Shea's partial R2 for instrument 0.045 0.045 0.045 0.051 
Second-stage effects of VPK participation on retention 
Not Eligible −0.014*** −0.017*** −0.013* −0.003 
 (0.003) (0.005) (0.005) (0.006) 
Base rate 0.038 0.073 0.088 0.109 
% of base 36.8 23.3 14.7 2.8 
R2 0.015 0.024 0.027 0.029 
Reduced-Price −0.018* −0.020 −0.008 0.018 
 (0.008) (0.011) (0.012) (0.015) 
Base rate 0.054 0.107 0.132 0.175 
% of base 33.3 18.7 6.1 10.3 
R2 0.021 0.033 0.037 0.036 
Free −0.014 −0.007 0.003 0.024* 
 (0.008) (0.010) (0.010) (0.011) 
Base rate 0.094 0.178 0.226 0.300 
% of base 14.9 3.9 1.3 8.0 
R2 0.027 0.041 0.042 0.041 
Not Eligible N Students 639,780 614,590 592,086 504,392 
 N Communities 2,176 2,177 2,177 2,114 
Reduced-Price N Students 126,568 121,657 117,596 98,929 
 N Communities 2,111 2,111 2,109 2,060 
Free N Students 656,156 629,593 609,740 487,046 
 N Communities 2,186 2,182 2,179 2,118 
Kindergarten1st Grade2nd Grade3rd Grade
First-stage effects of VPK availability on VPK participation 
Not Eligible 0.520*** 0.515*** 0.514*** 0.520*** 
 (0.012) (0.012) (0.011) (0.011) 
F-statistic for instrument 1,874.08*** 1,949.22*** 2,056.48*** 2,337.13*** 
R2 0.352 0.347 0.346 0.345 
Shea's partial R2 for instrument 0.063 0.061 0.061 0.064 
Reduced-Price 0.549*** 0.544*** 0.540*** 0.539*** 
 (0.014) (0.014) (0.015) (0.014) 
F-statistic for instrument 1,526.08*** 1,429.46*** 1,321.07*** 1,395.29*** 
R2 0.356 0.355 0.352 0.359 
Shea's partial R2 for instrument 0.064 0.063 0.063 0.064 
Free 0.459*** 0.456*** 0.455*** 0.458*** 
 (0.007) (0.007) (0.007) (0.007) 
F-statistic for instrument 4,120.65*** 4,048.23*** 4,030.11*** 3,785.47*** 
R2 0.262 0.262 0.261 0.278 
Shea's partial R2 for instrument 0.045 0.045 0.045 0.051 
Second-stage effects of VPK participation on retention 
Not Eligible −0.014*** −0.017*** −0.013* −0.003 
 (0.003) (0.005) (0.005) (0.006) 
Base rate 0.038 0.073 0.088 0.109 
% of base 36.8 23.3 14.7 2.8 
R2 0.015 0.024 0.027 0.029 
Reduced-Price −0.018* −0.020 −0.008 0.018 
 (0.008) (0.011) (0.012) (0.015) 
Base rate 0.054 0.107 0.132 0.175 
% of base 33.3 18.7 6.1 10.3 
R2 0.021 0.033 0.037 0.036 
Free −0.014 −0.007 0.003 0.024* 
 (0.008) (0.010) (0.010) (0.011) 
Base rate 0.094 0.178 0.226 0.300 
% of base 14.9 3.9 1.3 8.0 
R2 0.027 0.041 0.042 0.041 
Not Eligible N Students 639,780 614,590 592,086 504,392 
 N Communities 2,176 2,177 2,177 2,114 
Reduced-Price N Students 126,568 121,657 117,596 98,929 
 N Communities 2,111 2,111 2,109 2,060 
Free N Students 656,156 629,593 609,740 487,046 
 N Communities 2,186 2,182 2,179 2,118 

Notes: Separate models were estimated for each grade-student subgroup combination. Students are weighted by their inverse propensity to be observed in a given school year. Robust standard errors in parentheses account for community clusters.

*p < 0.05; ***p < 0.001.

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