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.