  This paper promotes the application of a path-independent decomposition
scheme. Besides presenting some theoretical arguments supporting this
decomposition scheme, this study also illustrates the difference between the
path-independent decomposition scheme and a popular sequential decomposition
with an empirical application of the two schemes. The empirical application is
about identifying a directly unobservable phenomenon, i.e. the changing social
gap between people from different educational strata, through its effect on
marriages and cohabitations. It exploits census data from four waves between
1977 and 2011 about the American, French, Hungarian, Portuguese, and Romanian
societies. For some societies and periods, the outcome of the decomposition is
found to be highly sensitive to the choice of the decomposition scheme. These
examples illustrate the point that a careful selection of the decomposition
scheme is crucial for adequately documenting the dynamics of unobservable
factors.
