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Table A.1. 
First-stage Estimates for Table 4 TSLS Models
(1)(2)(3)(4)(5)
Dependent Variable: Age at Start of K
Expected age at start of K 0.812 0.815 0.831 0.829 0.815 
 (0.015) (0.015) (0.016) (0.016) (0.014) 
Partial F-stat on instrument 2916 2972 2717 2837 3219 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsa 
School fixed effects 
(1)(2)(3)(4)(5)
Dependent Variable: Age at Start of K
Expected age at start of K 0.812 0.815 0.831 0.829 0.815 
 (0.015) (0.015) (0.016) (0.016) (0.014) 
Partial F-stat on instrument 2916 2972 2717 2837 3219 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsa 
School fixed effects 

Notes: Standard errors (in parentheses) are clustered on kindergarten classroom. Each column corresponds to the same numbered column in table 4.

aDummies for whether child is female, black, or received free/reduced-price lunch in K; fractions of K classmates with these characteristics; whether the kindergarten teacher is black, has an MA, or has 0 to 1 years of experience; and dummies for whether kindergarten class is small or regular sized with teacher's aide.

Table A.2. 
First-stage Estimates for Table 5 TSLS Models
(1)(2)(3)(4)(5)
 Panel A: First Stage Estimates forTable 5 , Panel A 
 Dependent Variable: Age at Start of K 
Expected age at start of K 0.642 0.634 0.675 0.672 0.625 
 (0.064) (0.066) (0.057) (0.060) (0.072) 
Expected age at start of K – average 0.169 0.179 0.155 0.155 0.189 
starting age of K classmates (0.059) (0.061) (0.051) (0.053) (0.067) 
Partial F-stat on instruments 1560 1583 1460 1549 1731 
 Dependent Variable: Relative Age at start of K 
Expected age at start of K −0.358 −0.366 −0.325 −0.328 −0.375 
 (0.064) (0.066) (0.057) (0.060) (0.072) 
Expected age at start of K – average 1.169 1.179 1.155 1.155 1.189 
starting age of K classmates (0.059) (0.061) (0.051) (0.053) (0.067) 
Partial F-stat on instruments 1991 1993 1972 2075 2126 
Observations 5,719 5,719 4,436 4,508 6,248 
 Panel B: First Stage Estimates forTable 5 , Panel B 
 Dependent Variable: Age at Start of K 
Expected age at start of K 0.880 0.879 0.936 0.938 0.871 
 (0.053) (0.052) (0.048) (0.048) (0.052) 
Expected age at start of K – average expected −0.067 −0.062 −0.103 −0.108 −0.055 
starting age of K classmates (0.052) (0.051) (0.048) (0.048) (0.051) 
Partial F-stat on instruments 1506 1523 1449 1513 1633 
 Dependent Variable: Relative Age at Start of K 
Expected age at start of K 0.025 0.023 0.072 0.077 0.008 
 (0.021) (0.021) (0.042) (0.038) (0.007) 
Expected age at start of K – average expected 0.788 0.792 0.759 0.752 0.806 
starting age of K classmates (0.026) (0.026) (0.042) (0.040) (0.017) 
Partial F-stat on instruments 1377 1419 1268 1321 1541 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsa 
School fixed effects 
(1)(2)(3)(4)(5)
 Panel A: First Stage Estimates forTable 5 , Panel A 
 Dependent Variable: Age at Start of K 
Expected age at start of K 0.642 0.634 0.675 0.672 0.625 
 (0.064) (0.066) (0.057) (0.060) (0.072) 
Expected age at start of K – average 0.169 0.179 0.155 0.155 0.189 
starting age of K classmates (0.059) (0.061) (0.051) (0.053) (0.067) 
Partial F-stat on instruments 1560 1583 1460 1549 1731 
 Dependent Variable: Relative Age at start of K 
Expected age at start of K −0.358 −0.366 −0.325 −0.328 −0.375 
 (0.064) (0.066) (0.057) (0.060) (0.072) 
Expected age at start of K – average 1.169 1.179 1.155 1.155 1.189 
starting age of K classmates (0.059) (0.061) (0.051) (0.053) (0.067) 
Partial F-stat on instruments 1991 1993 1972 2075 2126 
Observations 5,719 5,719 4,436 4,508 6,248 
 Panel B: First Stage Estimates forTable 5 , Panel B 
 Dependent Variable: Age at Start of K 
Expected age at start of K 0.880 0.879 0.936 0.938 0.871 
 (0.053) (0.052) (0.048) (0.048) (0.052) 
Expected age at start of K – average expected −0.067 −0.062 −0.103 −0.108 −0.055 
starting age of K classmates (0.052) (0.051) (0.048) (0.048) (0.051) 
Partial F-stat on instruments 1506 1523 1449 1513 1633 
 Dependent Variable: Relative Age at Start of K 
Expected age at start of K 0.025 0.023 0.072 0.077 0.008 
 (0.021) (0.021) (0.042) (0.038) (0.007) 
Expected age at start of K – average expected 0.788 0.792 0.759 0.752 0.806 
starting age of K classmates (0.026) (0.026) (0.042) (0.040) (0.017) 
Partial F-stat on instruments 1377 1419 1268 1321 1541 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsa 
School fixed effects 

Notes: Each column and panel of the table presents estimates from a different regression. Standard errors (in parentheses) are clustered on kindergarten classroom. Each column corresponds to the same numbered column in table 5.

aDummies for whether child is female, black, or received free/reduced-price lunch in K; fractions of K classmates with these characteristics; whether the kindergarten teacher is black, has an MA, or has 0 to 1 years of experience; and dummies for whether kindergarten class is small or regular-sized with teacher's aide.

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