Literature has shown that more non-maternal care and more center care was associated with more academic benefits but also more behavioral problems. However, most literature was correlational studies that did not eliminate, or at least mitigate, measurement error or omitted variable bias.

In order to draw causal inference on the impact of center care quantity, i.e. hours per week child spent in center care, we implemented instrumental variable approach using National Head Start Impact Study (NHSIS). NHSIS randomly assigned 4,484 children who applied to 383 Head Start centers to treatment group (receive Head Start services) or to control group (not receive Head Start services). We took advantage of the variance in center care quantity that was generated by NHSIS random assignment and estimated quantity effects on child outcomes. Specifically, we used interactions between Head Start center dummies and treatment assignment dummy as instrumental variable for child care quantity.

F-statistics for the exclusive instrumental variables indicate how much variance in center care quantity were generated by NHSIS random assignment and have a rule-of-thumb of above 10. We got slightly low F-statistics of about 7, which was due to several small centers. Hence several analysis for robustness check were also conducted. One robustness check method was limited information maximum likelihood (LIML) because LIML has the same asymptotic distribution as two-stage least square (2SLS) while LIML provides a finite-sample bias reduction. Also, LIML was proved to perform better than normal 2SLS in the presence of weak instruments (Hahn et al., 2004). Because our low F-statistics mainly came from small centers and NHSIS random assignment took place at center level, another robustness check analysis was conducted on large centers. All these analysis produced consistent estimates.

Our results show that for age 3 cohort, an additional hour per day in center care significantly increased .03SD in PPVT after one academic year of program implementation, .04SD in WJ-applied problem, .08SD in WJ-letter words, and significantly reduced behavioral problems by .03SD. Results for age 4 cohort was similar to those for age 3 cohort, except it was not significant at behavioral problems.

We worried about the only channel assumption of instrumental variable approach, i.e. random assignment within each site would impact child outcomes, not only through center care quantity, but also through the other channel, center care quality. We matched children in control group who were in center care with children in treatment group and compared ECERS and Arnett scores for these two matched groups. We did not find significant difference in child care quality between these two groups at center level, -- the 1st-stage F-statistics are merely 2 or 3. That ensures us about our causal inference of center care quantity effect on child outcomes.