# Reinforcement generates systematic differences without heterogeneity

## TL;DR

This paper shows that differences in outcomes over time might be due to reinforcement processes rather than unobserved individual differences.

## Contribution

It introduces a new explanation for systematic differences in longitudinal data using reinforcement mechanisms.

## Key findings

- Systematic differences in longitudinal data can be generated by reinforcement processes.
- Reinforcement can explain findings in science of science, personal culture, and sexual networks.
- Future studies can better understand heterogeneity by measuring fixed traits and random events.

## Abstract

In analyses of longitudinal records, it is standard practice to attribute systematic differences across units to heterogeneity in unobserved characteristics. In this paper, we show that such systematic differences might instead be the result of a reinforcement mechanism, where present outcomes are driven by past outcomes. Because reinforcement is not a mere mechanical possibility but also a strong theoretical prior in many research areas, our results suggest that heterogeneity might have been overestimated in previous studies. An explanation that bases interpersonal differences on reinforcement instead of heterogeneity not only changes our understanding of social processes but it can also suggest different targeted interventions for achieving a given policy goal.

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.