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Table 4. 
Conventional Estimates of the Effect of School Entry 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 Squaresa 
Age at start of kindergarten 0.707*** 0.674*** 0.215*** −0.189*** 0.002 
 (0.057) (0.054) (0.065) (0.026) (0.024) 
Root MSE 0.900 0.855 0.890 0.404 0.465 
First stage partial F on instrument 2,916 2,972 2,717 2,837 3,219 
 Panel B: Ordinary Least Squares 
Age at start of kindergarten 0.242*** 0.282*** −0.079* −0.151*** −0.064*** 
 (0.038) (0.036) (0.046) (0.019) (0.015) 
Root MSE 0.885 0.844 0.885 0.404 0.465 
R2 0.230 0.302 0.219 0.146 0.147 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsb 
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 Squaresa 
Age at start of kindergarten 0.707*** 0.674*** 0.215*** −0.189*** 0.002 
 (0.057) (0.054) (0.065) (0.026) (0.024) 
Root MSE 0.900 0.855 0.890 0.404 0.465 
First stage partial F on instrument 2,916 2,972 2,717 2,837 3,219 
 Panel B: Ordinary Least Squares 
Age at start of kindergarten 0.242*** 0.282*** −0.079* −0.151*** −0.064*** 
 (0.038) (0.036) (0.046) (0.019) (0.015) 
Root MSE 0.885 0.844 0.885 0.404 0.465 
R2 0.230 0.302 0.219 0.146 0.147 
Observations 5,719 5,719 4,436 4,508 6,248 
Additional controlsb 
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.

bDummies 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 the 10% level; ***statistical significance at the 1% level.

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