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In the remainder of this section, we check if there are differences in observable characteristics across the VLBW cutoff by estimating our baseline model with the covariates as dependent variables. If the RD design is valid, then there should be no discontinuities at the VLBW cutoff.16 Table 1 provides the results. Panels A, C, and D use the FC/parent sample and check whether focal child and parental characteristics are balanced, while panel B uses the sibling sample to check for discontinuities in the covariates of siblings. Column 1 provides the conventional point estimate from the local-linear regression, and columns 2 and 3 present the bias-corrected estimate and the robust standard error (Calonico et al., 2019). We report sharpened q-values, that is, p-values based on the numbers in columns 2 and 3 further corrected for multiple inference and in column 4 (see section III and Anderson, 2008, for details). Finally, column 5 reports the mean of the covariate in the sample of (family members of) focal children with birth weight of at least 1,500 g. The results show that observations just below the VLBW cutoff are generally similar to those just above the VLBW cutoff. There are few characteristics with marginally significant discontinuities at the threshold, and none of these survive the adjustment for multiple inference: the lowest q-value is 0.5.

Table 1.

Distribution of Covariates across the VLBW Cutoff

EstimateBias-Corrected EstimateRobust Standard ErrorSharpened q-ValueMean of Dependent Variable
(1)(2)(3)(4)(5)
A. Focal child characteristics (N = 2,156) 
Boy −0.028 [−0.079] (0.077) {0.919} 0.456 
Birth order 0.229 [0.166] (0.173) {0.919} 1.911 
Multiple birth 0.065 [0.092] (0.070) {0.851} 0.208 
Gestational age −0.353** [−0.508] (0.258) {0.576} 34.097 
Family size 0.054 [0.009] (0.160) {1.000} 2.937 
Has younger siblings −0.066 [−0.020] (0.078) {1.000} 0.611 
Number of younger siblings −0.189 [−0.205] (0.133) {0.713} 0.899 
B. Sibling characteristics (N = 3,311) 
Boy −0.003 [−0.033] (0.068) {1.000} 0.520 
Birth order −0.115 [−0.154] (0.147) {0.919} 2.121 
Multiple birth 0.026 [0.011] (0.017) {1.000} 0.023 
Gestational age −0.319 [−0.464] (0.449) {0.919} 38.209 
Birth weight −128.494* [−188.938] (105.751) {0.618} 2,898.7 
VLBW 0.012 [0.019] (0.033) {1.000} 0.046 
Age difference–older sibling −0.119 [−0.397] (0.782) {1.000} 6.586 
Age difference–younger sibling −0.400 [−0.691] (0.449) {0.713} 4.515 
C. Mother's characteristics at the birth of the focal child (N = 2,156) 
Age 1.118 [1.040] (0.800) {0.851} 27.735 
Education (years) −0.246 [0.218] (0.389) {1.000} 11.239 
Immigrant −0.021** [−0.052] (0.027) {0.576} 0.068 
Married 0.047 [0.003] (0.080) {1.000} 0.535 
D. Father's characteristics at the birth of the focal child (N = 2,116) 
Age 2.044** [2.132] (0.873) {0.507} 30.547 
Education (years) 0.172 [0.465] (0.400) {0.919} 11.608 
Immigrant 0.013 [−0.006] (0.039) {1.000} 0.074 
Not reported −0.008 [−0.004] (0.023) {1.000} 0.021 
EstimateBias-Corrected EstimateRobust Standard ErrorSharpened q-ValueMean of Dependent Variable
(1)(2)(3)(4)(5)
A. Focal child characteristics (N = 2,156) 
Boy −0.028 [−0.079] (0.077) {0.919} 0.456 
Birth order 0.229 [0.166] (0.173) {0.919} 1.911 
Multiple birth 0.065 [0.092] (0.070) {0.851} 0.208 
Gestational age −0.353** [−0.508] (0.258) {0.576} 34.097 
Family size 0.054 [0.009] (0.160) {1.000} 2.937 
Has younger siblings −0.066 [−0.020] (0.078) {1.000} 0.611 
Number of younger siblings −0.189 [−0.205] (0.133) {0.713} 0.899 
B. Sibling characteristics (N = 3,311) 
Boy −0.003 [−0.033] (0.068) {1.000} 0.520 
Birth order −0.115 [−0.154] (0.147) {0.919} 2.121 
Multiple birth 0.026 [0.011] (0.017) {1.000} 0.023 
Gestational age −0.319 [−0.464] (0.449) {0.919} 38.209 
Birth weight −128.494* [−188.938] (105.751) {0.618} 2,898.7 
VLBW 0.012 [0.019] (0.033) {1.000} 0.046 
Age difference–older sibling −0.119 [−0.397] (0.782) {1.000} 6.586 
Age difference–younger sibling −0.400 [−0.691] (0.449) {0.713} 4.515 
C. Mother's characteristics at the birth of the focal child (N = 2,156) 
Age 1.118 [1.040] (0.800) {0.851} 27.735 
Education (years) −0.246 [0.218] (0.389) {1.000} 11.239 
Immigrant −0.021** [−0.052] (0.027) {0.576} 0.068 
Married 0.047 [0.003] (0.080) {1.000} 0.535 
D. Father's characteristics at the birth of the focal child (N = 2,116) 
Age 2.044** [2.132] (0.873) {0.507} 30.547 
Education (years) 0.172 [0.465] (0.400) {0.919} 11.608 
Immigrant 0.013 [−0.006] (0.039) {1.000} 0.074 
Not reported −0.008 [−0.004] (0.023) {1.000} 0.021 

Sample of (family members of) focal children with birth weight within a 200 g bandwidth around the 1,500 g cutoff and gestational age of at least 32 weeks. Column 1 reports the estimated coefficient of the VLBW variable from a separate local-linear regression with a triangular kernel of the characteristic listed in the row for the family member indicated in the panel heading. Column 2 reports the corresponding bias-corrected estimate, column 3 the robust standard error (Calonico et al., 2014, 2019), column 4 the sharpened q-value for the set of tests included in the table (Anderson, 2008), and column 5 the mean of the variable in the row calculated among (family members of) focal children with birth weight above 1,500 g. Asterisks indicate statistical significance (significant at **5% and *10%), based on robust confidence intervals centered on the bias-corrected estimates (for details, see Calonico et al., 2014, 2019).

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