Two Cycles, Not One: A Continuous-Time Point-Process Analysis of Reciprocal Violence in the Israeli–Palestinian Conflict

Whether violence in the Israeli–Palestinian conflict is reciprocal — each side's lethal action provoking the other's — has been studied largely through vector-autoregression on time-binned counts, an approach that obscures the timing, branching structure, and directionality of response. We model lethal violence in the two directions as a bivariate Hawkes process, a continuous-time self- and mutually-exciting point process, using individual-incident fatality records from the Second Intifada through October 2023. Reciprocal excitation is genuine but profoundly asymmetric: a single Palestinian-to-Israeli event triggers on the order of one subsequent Israeli lethal event, nearly thirty times the reverse coupling. The asymmetry survives placebo, regime-detection, and flexible-baseline checks designed to rule out a common-driver confound, and goodness-of-fit testing confirms the models describe the data adequately. Allowing the couplings to take either sign, we find no evidence of deterrence in either direction. The strength of the Israeli response is statistically indistinguishable across the conflict's two main eras, but its speed is not: the characteristic response lag roughly halves between the Intifada and the later Gaza-war period, a temporal change binned methods cannot represent. Resolving the Israeli-to-Palestinian direction into its Gaza and West Bank theaters reveals that they operate as nearly independent systems: violence within each is strongly self-exciting while cross-theater coupling is negligible, and the reciprocal dynamic that dominates the pooled analysis is localized almost entirely to the West Bank, whereas Gaza's violence is driven by internal escalation. What appears in aggregate as a single cycle is, spatially, two barely-interacting logics — a separation we argue reflects the differential governance of the two territories rather than any natural division of the conflict. A three-stream extension shows settler violence to be a distinct channel: reactive to Palestinian action, increasingly self-exciting, and temporally preceding rather than following state violence. All findings replicate on an independently constructed event dataset. We document these regularities for 2000–2023 and set out why we do not extend them through the subsequent war: individual-incident records for that period exist, but not on a footing commensurable with the present analysis.