Estimation of Treatment Effects Without an Exclusion Restriction: with an Application to the Analysis of the School Breakfast Program

While the rise in childhood obesity is clear, the policy ramifications are not. School nutrition programs such as the School Breakfast Program (SBP) have come under much scrutiny. However, the lack of experimental evidence, combined with non-random selection into these programs, makes identification of the causal effects of such programs difficult. In the case of the SBP, this difficulty is exacerbated by the apparent lack of exclusion restrictions. Here, we compare via Monte Carlo study several existing estimators that do not rely on exclusion restrictions for identification. In addition, we propose two new estimation strategies. Simulations illustrate the usefulness of our new estimators, as well as provide applied researchers several practical guidelines when analyzing the causal effects of binary treatments. More importantly, we find consistent evidence of a beneficial causal effect of SBP participation on childhood obesity when applying estimators designed to circumvent selection on unobservables.