Sufficient statistics for economic mobility: when do measures agree?

Empirical studies of intergenerational mobility use different statistics—elasticities, rank–rank slopes, transition matrices, axiomatic indices—that sometimes produce conflicting conclusions. I show that a single property determines when they agree: concordance, capturing how rank-preserving the parent–child joint distribution is. When one economy is everywhere more rank-preserving, all standard measures agree on which is more mobile. Any change in a mobility measure decomposes into a dependence component and an inequality component; rank-based measures isolate dependence while level-based measures conflate both. Concordance arises naturally in a Becker–Tomes–Loury model and is robust to proxies and measurement error. Twentieth-century U.S. data confirm the predictions, rank-based measures co-move while the intergenerational elasticity diverges as inequality rises.