Selection into Identification in Fixed Effects Models, with Application to Head Start

Douglas Miller, Na'ama Shenhav and Michel Grosz

No 26174, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: 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.

JEL-codes: C33 I28 I38 J13 (search for similar items in EconPapers)
Date: 2019-08
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (28)

Published as Douglas L. Miller & Na’ama Shenhav & Michel Grosz, 2023. "Selection into Identification in Fixed Effects Models, with Application to Head Start," Journal of Human Resources, vol 58(5), pages 1523-1566.

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