Working Paper: NBER ID: w26174
Authors: Douglas L. Miller; Naama Shenhav; Michel Z. Grosz
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.
Keywords: Fixed Effects; Head Start; Causal Estimation; Selection Bias; Reweighting Methods
JEL Codes: C33; I28; I38; J13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Selection into identification (C52) | FE estimator bias (C51) |
| Switching treatment status (C22) | Systematic difference between switchers and non-switchers (C34) |
| Larger families with lower parental education and income (I24) | Switchers (Y90) |
| FE estimates (C33) | Cannot be generalized to overall population (C90) |
| Reweighting methods (C83) | Recover ATE (Y60) |
| Head Start participation (I21) | 26 percentage point increase in likelihood of attending some college (I24) |
| Traditional FE estimate (C51) | 12 percentage point increase in likelihood of attending some college (I24) |
| Impact of Head Start (I24) | Varies by family size (D19) |