Skip to Main Content
Table 4.
Fitted Parameters from Two-Stage Least Squares (2SLS) Models of the Probability of Being Retained at Least Once by the Completion of Kindergarten through Third Grade
Kindergarten1st Grade2nd Grade3rd Grade
VPK participant, instrumented −0.017*** −0.016** −0.009 0.009 
 (0.004) (0.006) (0.006) (0.006) 
Linear cohort trend, centered on 2006 −0.001 −0.006*** −0.008*** −0.009*** 
 (0.001) (0.001) (0.001) (0.001) 
Month of birth, centered on September 0.007*** 0.011*** 0.012*** 0.014*** 
 (0.000) (0.000) (0.000) (0.000) 
Female −0.034*** −0.060*** −0.070*** −0.085*** 
 (0.001) (0.001) (0.001) (0.001) 
Asian/Pacific Islander −0.018*** −0.040*** −0.052*** −0.064*** 
 (0.001) (0.002) (0.002) (0.002) 
Black 0.018*** 0.032*** 0.041*** 0.066*** 
 (0.001) (0.002) (0.002) (0.002) 
Hispanic 0.006*** 0.011*** 0.012*** 0.018*** 
 (0.001) (0.001) (0.001) (0.002) 
Other race −0.001 −0.002 −0.003 −0.002 
 (0.001) (0.002) (0.002) (0.002) 
Immigrant student −0.000 −0.008** −0.011*** −0.023*** 
 (0.002) (0.003) (0.003) (0.004) 
First-generation student −0.010*** −0.019*** −0.021*** −0.020*** 
 (0.002) (0.003) (0.004) (0.004) 
Speaks language other than English at home 0.007*** 0.010*** 0.019*** 0.035*** 
 (0.001) (0.002) (0.002) (0.002) 
Parents speak non-English language at home 0.003 0.006 0.007 0.007 
 (0.002) (0.003) (0.004) (0.005) 
Free lunch eligible 0.061*** 0.107*** 0.129*** 0.159*** 
 (0.001) (0.002) (0.002) (0.002) 
Reduced-price lunch eligible 0.018*** 0.032*** 0.040*** 0.050*** 
 (0.001) (0.001) (0.001) (0.002) 
Constant 0.000 0.000* 0.000*** 0.000*** 
 (0.000) (0.000) (0.000) (0.000) 
N students 1,422,504 1,365,840 1,319,422 1,090,367 
N communities 2,206 2,202 2,202 2,144 
R2 0.032 0.050 0.056 0.064 
2SLS base rate 0.066 0.125 0.156 0.199 
2SLS treatment effect as % of base 25.8 12.8 5.8 4.5 
OLS-estimated VPK participant (observed) coefficient −0.019*** −0.030*** −0.033*** −0.038*** 
 (0.001) (0.001) (0.001) (0.001) 
OLS base rate 0.067 0.130 0.164 0.212 
OLS treatment effect as % of base 28.4 23.1 20.1 17.9 
Kindergarten1st Grade2nd Grade3rd Grade
VPK participant, instrumented −0.017*** −0.016** −0.009 0.009 
 (0.004) (0.006) (0.006) (0.006) 
Linear cohort trend, centered on 2006 −0.001 −0.006*** −0.008*** −0.009*** 
 (0.001) (0.001) (0.001) (0.001) 
Month of birth, centered on September 0.007*** 0.011*** 0.012*** 0.014*** 
 (0.000) (0.000) (0.000) (0.000) 
Female −0.034*** −0.060*** −0.070*** −0.085*** 
 (0.001) (0.001) (0.001) (0.001) 
Asian/Pacific Islander −0.018*** −0.040*** −0.052*** −0.064*** 
 (0.001) (0.002) (0.002) (0.002) 
Black 0.018*** 0.032*** 0.041*** 0.066*** 
 (0.001) (0.002) (0.002) (0.002) 
Hispanic 0.006*** 0.011*** 0.012*** 0.018*** 
 (0.001) (0.001) (0.001) (0.002) 
Other race −0.001 −0.002 −0.003 −0.002 
 (0.001) (0.002) (0.002) (0.002) 
Immigrant student −0.000 −0.008** −0.011*** −0.023*** 
 (0.002) (0.003) (0.003) (0.004) 
First-generation student −0.010*** −0.019*** −0.021*** −0.020*** 
 (0.002) (0.003) (0.004) (0.004) 
Speaks language other than English at home 0.007*** 0.010*** 0.019*** 0.035*** 
 (0.001) (0.002) (0.002) (0.002) 
Parents speak non-English language at home 0.003 0.006 0.007 0.007 
 (0.002) (0.003) (0.004) (0.005) 
Free lunch eligible 0.061*** 0.107*** 0.129*** 0.159*** 
 (0.001) (0.002) (0.002) (0.002) 
Reduced-price lunch eligible 0.018*** 0.032*** 0.040*** 0.050*** 
 (0.001) (0.001) (0.001) (0.002) 
Constant 0.000 0.000* 0.000*** 0.000*** 
 (0.000) (0.000) (0.000) (0.000) 
N students 1,422,504 1,365,840 1,319,422 1,090,367 
N communities 2,206 2,202 2,202 2,144 
R2 0.032 0.050 0.056 0.064 
2SLS base rate 0.066 0.125 0.156 0.199 
2SLS treatment effect as % of base 25.8 12.8 5.8 4.5 
OLS-estimated VPK participant (observed) coefficient −0.019*** −0.030*** −0.033*** −0.038*** 
 (0.001) (0.001) (0.001) (0.001) 
OLS base rate 0.067 0.130 0.164 0.212 
OLS treatment effect as % of base 28.4 23.1 20.1 17.9 

Notes: Students are weighted by their inverse propensity to be observed in a given school year. Robust standard errors in parentheses account for community clusters. Parameters for community characteristics omitted due to space limitations but include demographic measures (school and community racial/ethnic composition and school enrollment), economic measures (school free/reduced-price lunch eligibility, median household income, under age 18 years poverty rate, unemployment rate, and home sale prices), and other measures (student–teacher ratio and household size). OLS = ordinary least squares.

*p < 0.05; **p < 0.01; ***p < 0.001.

Close Modal

or Create an Account

Close Modal
Close Modal