Modeling the moral account: a system dynamics framework for brand-induced moral licensing and behavioral rebound in sustainable consumption

Introduction Quantitative models of sustainable consumption typically treat consumption as exogenous, assuming that every green purchase improves environmental outcomes. Behavioral research on moral licensing, however, suggests that purchases perceived as virtuous can license compensatory indulgence that erodes some of the benefit. Recent formal work treats licensing as an environmental rebound mechanism in static consumer models; this study contributes the first dynamic stock-and-flow formalization, developed from a recent conceptual framework of brand-induced moral licensing. Methods Four communication pathways (virtue attribution, identity conferral, effort signaling, and absolution framing) feed two moral accounts with opposite mechanics: credits, which deplete when spent, and credentials, which license behavior without being consumed. The model yields closed-form steady states and a licensing-resistance condition on the rebound ratio ρ> (backfire at ρ> 1). Communication parameters were calibrated through a preregistered content analysis of 120 verbatim-archived units from eight sustainable brands, with perfect dual-coder agreement on the reliability subsample; identity internalization was calibrated from a two-country survey of 3,293 adults. The behavioral conversion parameters are literature-anchored or illustrative, so all rebound magnitudes are model-derived, order-of-magnitude results rather than empirical estimates. Results Rebound stays far below backfire: steady-state values span 0.01 to 0.19 across archetypes, preserving 81 to 99% of gross benefit, across 8,000 uncertainty samples and under structural variants allowing credential depletion, sign reversal, and alternative licensing functions. Calibration inverts the theorized risk ordering: identity-positioned brands deploy almost no identity-conferring language, decoupling the typology's conceptual categories from their communication signatures. The model further predicts that 6-month evaluations understate long-run rebound nearly five-fold, implying measurement windows of 1 to 3 years. Absolution framing is absent from the corpus, consistent with the application timeline of Directive (EU) 2024/825; in counterfactual simulation, restoring such claims forfeits up to a third of gross benefit, whereas reducing the growth signal lowers cumulative modeled benefit without reducing rebound. Discussion Licensing rebound is projected to be real but bounded; message design, not demarketing, is the effective lever within the modeled mechanism. The model supplies an auditable communication-risk map and the design brief for the longitudinal study the field lacks.