Structural and Exchange Mobility as Additive Components of Social or Economic Mobility

An unambiguous delineation between structural and exchange (circulation) components of mobility has been a long-standing challenge in social and economic mobility. This article presents a solution to this problem by conceptualising the transition matrix as an ensemble of elementary combinations of movements rather than an ensemble of individual movements. This representation embraces a vector space approach, which permits an additive decomposition of the transition matrix. Every transition matrix is represented as a deviation from an ideal matrix representing immobility or perfect mobility. The deviation matrices can be split into structural and exchange parts. A precise definition of structural mobility emerges from this framework. A linear representation in terms of elementary or basis movements opens up the possibility fresh modeling and statistical analysis around the concepts of structural and exchange mobility. In the cases of ordinal and grouped data, these representations lead to some partial orders among transition matrices in respect of individual, exchange and structural mobility.