A Conflict-Hysteresis Three-Equation Model: Stability, Policy Rules, and Brazilian Evidence

This paper revisits the canonical three-equation (IS–PC–MR) framework from a heterodox and structuralist perspective. We replace the conventional expectations-augmented Phillips curve with a conflict-inflation mechanism in which wage-share claims, mark-up conventions, external-cost pressures and institutional bargaining conditions shape inflation. Hysteresis is derived from an institutional-memory channel: the inflation-stabilizing benchmark adjusts gradually to persistent discrepancies between realized activity and the conflict-neutral position. The resulting continuous-time system features a continuum of steady states and transversal stability: monetary policy can anchor inflation and close the activity gap relative to an evolving benchmark, while the selected long-run real position remains history-dependent. The empirical exercise translates this mechanism into unemployment-based state-space models for Brazil. We compare a fixed NAIRU, a random-walk NAIRU and a hysteretic NAIRU, using free-price inflation deviations from expectations and selected controls for demand, exchange-rate, wage-cost, real external-cost and administered-price pressures. The fixed benchmark remains preferred by BIC, so the evidence is not a decisive rejection of fixed-NAIRU models. However, the random-walk benchmark is nearly time-invariant, whereas the hysteretic specification generates economically meaningful benchmark variation and positive tightness and adjustment parameters. The evidence therefore supports a qualified interpretation: benchmark drift is more persuasive when disciplined by a conflict-hysteresis mechanism than when left as unrestricted statistical movement.