The Trace-Agency Gap: A One-Sided Identification Frontier for Behavioral Evidence and Reflective Endorsement

Abstract

Randomization can establish that an external policy changed what people did. It cannot, by itself, establish whether the resulting action was understood, reflectively endorsed, or manipulative. This paper formalizes that separation as the trace-agency gap. Under reference concordance, no discordance without behavioral displacement, and binary monotonicity, its sharp identified set is ([0,\mathrm{ATE}]). The behavioral effect is therefore a ceiling on agency discordance—not evidence that the ceiling is attained. This creates a fundamental asymmetry: action evidence can rule out sufficiently large trace-agency gaps, but it can never certify a positive one. The framework maps increasingly demanding claims onto the evidence required to support them, from randomized behavioral effects to common-form post-disclosure audits and conservative dark-steering certificates. It also locates models of frame-dependent preference and bounded influence within the same identification structure. Reanalyses of published experiments demonstrate the distinction empirically. Action-only outcomes produce potentially informative ceilings while retaining zero. By contrast, a repeated keep-or-cash decision from Salvi, Cuevas, and Horta Ribeiro (2026) directly identifies a downstream valuation gap of 0.0394 and reveals that reference concordance fails in the comparison sample. The result is an evidence map for studying manipulation without inferring agency from behavior alone.