Reinforcement generates systematic differences without heterogeneity

Inequality in outcomes may emerge through a reinforcement process in which stochastic variation in values is determined by prior values but may also originate in preexisting differences in unobserved factors. A common approach toward differentiating between these origins in longitudinal data is to attribute systematic differences between units—differences in means or differences proportional to a time-varying group average—to unobserved heterogeneity. We show that any longitudinal data with systematic differences can also be produced by a reinforcement-driven data generating process. This result reconciles findings in three distinct research areas—science of science, personal culture, and sexual networks—where reinforcement is a strong theoretical prior, yet longitudinal data analyses advance an explanation of interpersonal differences based on heterogeneity. Future studies may bound the role of heterogeneity and reinforcement from below by measuring fixed traits that systematically vary with the outcome and isolating random events that trigger emergent differences.