Matrix Representation of Structural and Circulation Mobility

Abstract

The conceptual foundation of the traditional approach to social mobility is compactly expressed in the equality, “circulation mobility = total mobility - structural mobility.” For more than two decades, this equality has been used without specifying the frequencies that express structural mobility. In contrast with common research practice, we analyze the matrix form of the classic equality. We provide a representation of structural and circulation mobility that meets face validity criteria, is theoretically grounded, and fulfills formal postulates. The matrix of observed mobility (N) is decomposed into the sum of three nonnegative matrices: immobility (1), structural mobility (S), and circulation mobility (C). The new decomposition N = 1 + C + S, based on linear programming, has various realistic and sociologically meaningful properties and interpretations.