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Table 7. 
Two-Stage Least Squares Estimates of the Impacts of Relative Age, by Free/Reduced-Price Lunch Status
Dependent Variable
Eight Years Later:
Average Score End of K (1)Average Score (2)Retained in Any Grade (3)Took ACT or SAT (4)
 Panel A: Not Free/Reduced-Price Lunch in K 
Mean of dependent variable 0.268 0.467 0.155 0.623 
TSLS coefficients:     
Age at start of kindergarten 0.892*** 0.397 −0.060 0.088 
 (0.324) (0.243) (0.100) (0.130) 
Relative age in K classroom −0.124 −0.166 −0.127 −0.058 
 (0.309) (0.222) (0.090) (0.118) 
Root MSE 0.891 0.850 0.347 0.473 
Observations 2,951 2,398 2,420 3,217 
 Panel B: Free/Reduced–Price Lunch in K 
Mean of dependent variable −0.281 −0.284 0.360 0.313 
TSLS Coefficients:     
Age at start of kindergarten 0.911*** 0.856*** −0.270** 0.240* 
 (0.339) (0.295) (0.134) (0.134) 
Relative age in K classroom −0.319 −0.665** 0.082 −0.242* 
 (0.315) (0.270) (0.132) (0.127) 
Root MSE 0.804 0.925 0.460 0.454 
Observations 2,768 2,038 2,088 3,031 
p for age: low SES = high SES 0.161 0.042 0.089 0.183 
p for rel. age: low SES = high SES 0.401 0.047 0.290 0.120 
Dependent Variable
Eight Years Later:
Average Score End of K (1)Average Score (2)Retained in Any Grade (3)Took ACT or SAT (4)
 Panel A: Not Free/Reduced-Price Lunch in K 
Mean of dependent variable 0.268 0.467 0.155 0.623 
TSLS coefficients:     
Age at start of kindergarten 0.892*** 0.397 −0.060 0.088 
 (0.324) (0.243) (0.100) (0.130) 
Relative age in K classroom −0.124 −0.166 −0.127 −0.058 
 (0.309) (0.222) (0.090) (0.118) 
Root MSE 0.891 0.850 0.347 0.473 
Observations 2,951 2,398 2,420 3,217 
 Panel B: Free/Reduced–Price Lunch in K 
Mean of dependent variable −0.281 −0.284 0.360 0.313 
TSLS Coefficients:     
Age at start of kindergarten 0.911*** 0.856*** −0.270** 0.240* 
 (0.339) (0.295) (0.134) (0.134) 
Relative age in K classroom −0.319 −0.665** 0.082 −0.242* 
 (0.315) (0.270) (0.132) (0.127) 
Root MSE 0.804 0.925 0.460 0.454 
Observations 2,768 2,038 2,088 3,031 
p for age: low SES = high SES 0.161 0.042 0.089 0.183 
p for rel. age: low SES = high SES 0.401 0.047 0.290 0.120 

Notes: Each column and panel of the table presents estimates from a different regression. All models are estimated using two-stage least squares and are based on the specification presented in the final four columns of Table 4, Panel A. Thus, the models include the full set of controls; age at the start of kindergarten is instrumented with expected age at the start of kindergarten; and relative age is instrumented with own expected age – average age of kindergarten classmates. Standard errors (in parentheses) are clustered on kindergarten classroom. SES: socioeconomic status.

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

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