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Title: Selection into Identification in Fixed Effects Models, with Application to Head Start
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Miller, Douglas L. Shenhav, Na'ama Grosz, Michel Z. |
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Selection into Identification in Fixed Effects Models, with Application to Head Start NBER Working Paper No. 26174, National Bureau of Economic Research, August 2019. Also: https://www.nber.org/papers/w26174 Cohort(s): Children of the NLSY79, NLSY79 Young Adult Publisher: National Bureau of Economic Research (NBER) Keyword(s): Educational Attainment; Head Start; High School Completion/Graduates; Modeling, Fixed Effects; Panel Study of Income Dynamics (PSID) Many papers use fixed effects (FE) to identify causal impacts of an intervention. In this paper we show that when the treatment status only varies within some groups, this design can induce non-random selection of groups into the identifying sample, which we term selection into identification (SI). We begin by illustrating SI in the context of several family fixed effects (FFE) applications with a binary treatment variable. We document that the FFE identifying sample differs from the overall sample along many dimensions, including having larger families. Further, when treatment effects are heterogeneous, the FFE estimate is biased relative to the average treatment effect (ATE). For the general FE model, we then develop a reweighting-on-observables estimator to recover the unbiased ATE from the FE estimate for policy-relevant populations. We apply these insights to examine the long-term effects of Head Start in the PSID and the CNLSY. Using our reweighting methods, we estimate that Head Start leads to a 2.6 percentage point (p.p.) increase (s.e. = 6.2 p.p.) in the likelihood of attending some college for white Head Start participants in the PSID. This ATE is 78% smaller than the traditional FFE estimate (12 p.p). Reweighting the CNLSY FE estimates to obtain the ATE produces similar attenuation in the estimated impacts of Head Start. |
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Bibliography Citation
Miller, Douglas L., Na'ama Shenhav and Michel Z. Grosz. "Selection into Identification in Fixed Effects Models, with Application to Head Start." NBER Working Paper No. 26174, National Bureau of Economic Research, August 2019. |