Notes:

↵* refers to a statistical difference between the HSIS and model impact estimates at a 5% significance level. For the model, standard errors (in parentheses) are calculated by drawing 100 times from the asymptotic distribution of the final parameter estimates and rerunning the counterfactual simulations.

↵a Design refers to the two arms of randomization in the HSIS. The four-year-old cohort was a group of children randomized to receive Head Start or not at age four. The three-year-old cohort consisted of a treatment and a delayed treatment control starting at four years old.

↵b The ITT (intent to treat) columns report the average change in cognitive achievement at kindergarten entry conditional on being eligible for Head Start (in the model) and for children who were offered Head Start services (in the HSIS).

↵c The LATE (local average treatment effect) columns report the average impact on individuals induced to switch treatment status by the offer. In the simulations, this average can be directly constructed, while the HSIS reports estimates form an IV procedure using the offer as an instrument.