Realizing Common Random Numbers: Event-Keyed Hashing for Causally Valid Stochastic Models

TL;DR

This paper identifies a fundamental mismatch in how stateful pseudorandom number generators are used in agent-based models for causal inference, and proposes event-keyed hashing with counter-based RNGs as a solution to ensure causally valid paired simulations.

Contribution

It formalizes the causal inconsistency caused by stateful PRNGs in ABMs and introduces event-keyed hashing with counter-based RNGs to restore causal validity.

Findings

Stateful PRNGs cause causal incoherence in ABMs.

Event-keyed hashing with counter-based RNGs restores causal consistency.

Proposed method improves validity of paired counterfactual simulations.

Abstract

Agent-based models (ABMs) are widely used to estimate causal treatment effects via paired counterfactual simulation. A standard variance reduction technique is common random numbers (CRNs), which couples replicates across intervention scenarios by sharing the same random inputs. In practice, CRNs are implemented by reusing the same base seed, but this relies on a critical assumption: that the same draw index corresponds to the same modeled event across scenarios. Stateful pseudorandom number generators (PRNGs) violate this assumption whenever interventions alter the simulation's execution path, because any change in control flow shifts the draw index used for all downstream events. We argue that this execution-path-dependent draw indexing is not only a variance-reduction nuisance, but represents a fundamental mismatch between the scientific causal structure ABMs are intended to encode and the program-level causal structure induced by stateful PRNG implementations. Formalizing this through the lens of structural causal models (SCMs), we show that standard PRNG practices yield causally incoherent paired counterfactual comparisons even when the mechanistic specification is otherwise sound. We show that a remedy is to combine counter-based random number generators (e.g., Philox/Threefry) with event identifiers. This decouples random number generation from simulation execution order by making random draws explicit functions of the particular modeled event that called them, restoring the stable event-indexed exogenous structure assumed by SCMs.