Estimation of Treatment E¤ects 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 rami…cations 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 identi…cation of the causal e¤ects of such programs di¢ cult. In the case of the SBP, this di¢ culty 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 identi…cation. 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 e¤ects of binary treatments. More importantly, we …nd consistent evidence of a bene…cial causal e¤ect of SBP participation on childhood obesity when applying estimators designed to circumvent selection on unobservables. JEL Classi…cations: C21, C52, I18, J13 Key words: Treatment E¤ects, Propensity Score, Unconfoundedness, Selection on Unobservables, Obesity This study was conducted by Georgia State University and Southern Methodist University under a cooperative agreement with the U.S. Department of Agriculture, Economic Research Service, Food and Nutrition Assistance Research Program (agreement no. 58-5000-8-0097). The views expressed here are those of the authors and do not necessarily re‡ect those of the USDA or ERS. The authors bene…ted from discussions with Jay Bhattacharya, Chris Bollinger, Ozkan Eren, Juan Carlos Escanciano, Jason Fletcher, James Heckman, Keisuke Hirano, Michael Lechner, Arthur Lewbel, Salvador Navarro-Lozano, Denis Nekipelov, Je¤ Smith, Jessica Todd, Aaron Yelowitz, seminar participants at Clemson U, SMU, and U Kentucky, and conference participants at the 2009 Econometric Society Winter Meetings, the Fifth IZA Conference on Labor Market Policy Evaluation, the 2010 American Economic Association Annual Meetings, and Texas Camp Econometrics XV. Mehtabul Azam provided valuable research assistance. A previous version of this paper was circulated under the title “Minimizing Bias in Selection on Observables Estimators When Unconfoundness Fails.” Stata code to implement the estimators used is available from the authors. Corresponding author: Daniel L. Millimet, Department of Economics, Southern Methodist University, Box 0496, Dallas, TX 75275-0496, USA; Email: [email protected]; Tel. (214) 768-3269; Fax: (214) 768-1821.