Inferring cumulative advantage from longitudinal records

TL;DR

This paper demonstrates that longitudinal success records cannot distinguish between talent-based and cumulative advantage models, as both can produce identical success trajectories, highlighting an identification problem in understanding success dynamics.

Contribution

It formally proves the equivalence of talent and cumulative advantage models in generating success histories, revealing a fundamental identification challenge.

Findings

Longitudinal success data cannot differentiate between talent and cumulative advantage models.

For any talent model, an equivalent path-dependent model exists that produces the same predictions.

Models previously thought to support talent or cumulative advantage are mathematically indistinguishable.

Abstract

Inequality in human success may emerge through endogenous success-breeds-success dynamics but may also originate in pre-existing differences in talent. It is widely recognized that the skew in static frequency distributions of success implied by a cumulative advantage model is also consistent with a talent model. Studies have turned to longitudinal records of success, seeking to exploit the time dimension for adjudication. Here we show that success histories suffer from a similar identification problem as static distributional evidence. We prove that for any talent model there exists an analogous path dependent model that generates the same longitudinal predictions, and vice versa. We formally identify such twins for prominent models in the literature, in both directions. These results imply that longitudinal data previously interpreted to support a talent model equally well fits a model of cumulative advantage and vice versa.