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Table 5. 
Estimates of the Effect of School Entry Age and Relative Age
Dependent Variable
Eight Years Later:
Average Test Score, End of KAverage Test ScoreEver RetainedTook ACT or SAT
(1)(2)(3)(4)(5)
 Panel A: Two-Stage Least Squares— 
 Not Accounting for Lower Ability of Older Peersa 
Age at start of K 1.020*** 0.910*** 0.650*** −0.156* 0.155* 
 (0.282) (0.265) (0.181) (0.080) (0.092) 
Relative age in K classroom −0.310 −0.233 −0.429** −0.033 −0.151* 
 (0.265) (0.250) (0.167) (0.075) (0.086) 
Root MSE 0.900 0.855 0.890 0.405 0.465 
 Panel B: Two–Stage Least Squares— 
 Accounting for Lower Ability of Older Peersb 
Age at start of K 1.564*** 1.407*** 0.651*** −0.327*** 0.175 
 (0.429) (0.394) (0.251) (0.118) (0.107) 
Relative age in K classroom −0.847** −0.724* −0.430* 0.136 −0.172 
 (0.407) (0.374) (0.248) (0.115) (0.106) 
Root MSE 0.901 0.856 0.890 0.405 0.465 
 Panel C: Ordinary Least Squares 
Age at start of K 0.423 0.396 0.271 −0.107 0.069 
 (0.278) (0.263) (0.173) (0.079) (0.088) 
Relative age in K classroom −0.178 −0.112 −0.345** −0.043 −0.132 
 (0.267) (0.251) (0.167) (0.075) (0.085) 
Root MSE 0.885 0.844 0.885 0.404 0.464 
R2 0.230 0.302 0.219 0.146 0.147 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsc 
School fixed effects 
Dependent Variable
Eight Years Later:
Average Test Score, End of KAverage Test ScoreEver RetainedTook ACT or SAT
(1)(2)(3)(4)(5)
 Panel A: Two-Stage Least Squares— 
 Not Accounting for Lower Ability of Older Peersa 
Age at start of K 1.020*** 0.910*** 0.650*** −0.156* 0.155* 
 (0.282) (0.265) (0.181) (0.080) (0.092) 
Relative age in K classroom −0.310 −0.233 −0.429** −0.033 −0.151* 
 (0.265) (0.250) (0.167) (0.075) (0.086) 
Root MSE 0.900 0.855 0.890 0.405 0.465 
 Panel B: Two–Stage Least Squares— 
 Accounting for Lower Ability of Older Peersb 
Age at start of K 1.564*** 1.407*** 0.651*** −0.327*** 0.175 
 (0.429) (0.394) (0.251) (0.118) (0.107) 
Relative age in K classroom −0.847** −0.724* −0.430* 0.136 −0.172 
 (0.407) (0.374) (0.248) (0.115) (0.106) 
Root MSE 0.901 0.856 0.890 0.405 0.465 
 Panel C: Ordinary Least Squares 
Age at start of K 0.423 0.396 0.271 −0.107 0.069 
 (0.278) (0.263) (0.173) (0.079) (0.088) 
Relative age in K classroom −0.178 −0.112 −0.345** −0.043 −0.132 
 (0.267) (0.251) (0.167) (0.075) (0.085) 
Root MSE 0.885 0.844 0.885 0.404 0.464 
R2 0.230 0.302 0.219 0.146 0.147 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsc 
School fixed effects 

Notes: Each column and panel of the table presents estimates from a different regression. Test scores are standardized to have a mean of zero and a standard deviation of one using all available data. Standard errors (in parentheses) are clustered on kindergarten classroom.

aThe instrument for a child's age at the start of kindergarten is his expected age given his birthday and the 30 September kindergarten entry cutoff birthdate in Tennessee. The instrument for a child's relative age is his expected age − average age of his kindergarten classmates.

bThe instrument for a child's age at the start of kindergarten is his expected age given his birthday and the 30 September kindergarten entry cutoff birthdate in Tennessee. The instrument for a child's relative age is his expected age − average expected age of his kindergarten classmates.

cDummies 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.

*Statistical significance at 10% level; **statistical significance at the 5% level; ***statistical significance at the 1% level.

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