Representing structural change in U.S. migration patterns

This paper focuses on the identification of three sets of relationships exhibited by a time series of age-specific national migration rates and multiregional transition probability matrices: the relationship across time for the same age group, as defined by period (temporal) transformation coefficients or matrices; the relationships across age at a particular moment in time, as defined by age transformation coefficients or matrices; and the relationships across time and age, as defined by cohort transformation coefficients or matrices. Given any two of these relationships one can solve for the third. This feature of age-period-cohort relationships has a practical application in the development of improved methods for representing structural change in migration patterns over time and for indirectly estimating migration patterns using inadequate data.