Biproportional Methods of Structural Change Analysis: A Typological Survey

Analysts often are interested in learning how much an exchange system has changed over time or how two different exchange systems differ. Identifying structural difference in exchange matrices can be performed using either 'directed' or 'undirected' methods. Directed methods are based on the computation and comparison of column- or row-normalizations of the matrices. The choice of row or column for the normalization implies a specific direction of the exchanges, so that the column-wise normalized results should not be compared to the row-wise normalized results. In this category fall the simple comparison of coefficient matrices and the causative method. Undirected methods do not impose such underlying constraints on exchanges. Hence, I present a set of undirected methods that can be used to compare structural matrices: the biproportional ordinary filter, the biproportional mean filter and the bi-Markovian filter. While doing so, I recall why the bicausative method must be dismissed. I then classify the methods according to their orientation and data needs, and illustrate how the results can differ from one method to the next using French tables for 1980 and 1997.