A new approach to measuring and studying the characteristics of class membership: The progress of poverty, inequality and polarization of income classes in urban China.

Classifying agents into subgroups in order to measure the plight of the "poor", "middle class" or "rich" is common place in economics, unfortunately the definition of class boundaries is contentious and beset with problems. Here a technique based on mixture models is proposed for surmounting these problems by determining the number of classes in a population and estimating the probability that an agent belongs to a particular class. All of the familiar statistics for describing the classes remain available and the possibility of studying the determinants of class membership is raised. As a substantive illustration we analyze household income in Urban China in the last decade of the 20th Century. Four income groups are classified and the progress of those "poor", "lower middle", "upper middle" and "rich" classes are related to household and regional characteristics to study the impact of urbanization and the one child policy on class membership over the period.