Returns to Head Start by Family Size and Implications for Regression Estimates
PSID | CNLSY | ||||
---|---|---|---|---|---|
Some College | HS Grad | Idle | Learning Disability | ||
CX (1) | FE (2) | FE (3) | FE (4) | FE (5) | |
Panel A: Effects by Family Size | |||||
Head Start × 1 child family | 0.169* (0.091) | ||||
Head Start × 2 child family | 0.038 (0.079) | −0.126 (0.099) | 0.058 (0.050) | −0.075 (0.060) | −0.018 (0.025) |
Head Start × 3 child family | −0.030 (0.087) | 0.152** (0.075) | 0.042 (0.063) | −0.001 (0.071) | −0.073 (0.046) |
Head Start × 4 child family | −0.053 (0.100) | 0.251*** (0.091) | 0.135 (0.087) | −0.063 (0.118) | −0.042 (0.052) |
Head Start × 5+ child family | 0.572*** (0.119) | 0.348*** (0.126) | 0.305*** (0.095) | −0.317** (0.132) | −0.161* (0.091) |
Head Start × Unknown child family | −0.099 (0.108) | ||||
Observations | 4,258 | 2,986 | 1,251 | 1,251 | 1,247 |
Head Start switchers | 213 | 668 | 668 | 668 | |
Effective obs. (individs. 2-person families) | 235.9 | 644.3 | 644.3 | 644.3 | |
Effective obs. (CX individs.) | 731.8 | 558.9 | 558.9 | 558.9 | |
Panel B: Simulated Estimates across Samples Using Family-Size Regression Weights | |||||
All | 0.046 | ||||
Siblings | 0.037 | 0.083 | 0.081 | −0.071 | −0.047 |
Switchers | 0.069 | 0.123 | 0.093 | −0.077 | −0.054 |
Sources: Panel Study of Income Dynamics 1968–2011 waves and Children of the National Longitudinal Study of Youth.
Notes: Panel A of this table shows the coefficients from regressions of outcomes on a series of indicators for whether an individual attended Head Start interacted with an indicator for the number of children in one’s family. The data source and specification varies across columns. Columns 1 and 2 use our main PSID sample, and the outcome is attainment of some college. Columns 3–5 use the CNLSY79 sample, and the outcomes are indicators for graduating from high school, being idle, and having a learning disability, respectively. Column 1 includes controls, but not mother fixed effects, and standard errors are clustered at the family ID level. Columns 2–5 include mother fixed effects, and standard errors are clustered by mother ID. The number of Head Start switchers is equal to the number of individuals in families that have variation in Head Start. “Effective Obs. (CX Individs.)” is the equivalent number of cross-sectional units that provide the same amount of variation as switchers. “Effective Obs. (Individs. 2-Person Families)” is the equivalent number of individuals in two-person switching families that provide the same amount of variation as switchers. Both of these are calculated using Equation 3, where the denominator is the variance of Head Start, residualized by the family mean of the covariates in the analysis, or 0.125, respectively. Panel B shows the weighted average of the coefficients when using regression weights, ωz (defined in Section III), determined by the overall distribution of families (“All”), the distribution of 2+ child families (“Siblings”), and the distribution of 2+ child families that have variation in Head Start attendance (“Switchers”).
↵* p < 0.10,
↵** p < 0.05,
↵*** p < 0.01.