Panel Conditioning in Fixed-Effects Models: Identification and Bias Propagation

Abstract

Panel conditioning, the causal effect of prior survey participation on responses, can vary with tenure. Under an additive model of cell means in period, entry cohort, and tenure, we characterize which features of the conditioning path a staggered panel identifies on its observed support, and how the unidentified component affects common panel estimators. The identified set of the path is an affine translate of the tenure projection of the cell design's kernel, and a linear functional of the path is identified exactly when it annihilates that projection. It always contains an affine direction and, when the entry cohorts share a stride, periodic directions, which exhaust it under a connectivity condition on observed increments; second differences at that stride are then identified, and ordinary ones generally are not when the stride exceeds one. Under a recruitment condition, an interrupted schedule such as the four-eight-four rotation of the Current Population Survey (CPS) distinguishes a constant increment per interview from one per calendar month, which no equally spaced schedule can. We give support conditions for recovery under a plateau, entry-wave negative controls, or bounded cohort drift. A second set of results links identification to regression: two-way fixed effects absorb every unidentified direction, so the remaining conditioning bias is normalization-invariant and itself identified, and a two-way regression with tenure indicators corrects it under a residual-rank condition. When event time is aligned with tenure, conditioning shifts event-study coefficients by a known linear functional of the path, producing pre-trends without anticipation; bounds on identified curvature bound those shifts. Simulations verify the identities, a 19-wave Japanese panel illustrates the support calculations, and published CPS month-in-sample indices give a descriptive, not identifying, example.