  In this paper, we identify two different sets of problems. The first covers
the problems that the iterative proportional fitting (IPF) algorithm was
developed to solve. These concern completing a population table by using a
sample. The other set concerns constructing a counterfactual population table
with the purpose of comparing two populations. The IPF is commonly applied by
social scientists to solve problems not only in the first set, but also in the
second one. We show that while it is legitimate to use the IPF for the first
set of problems, it is not the right tool to address the problems of the second
kind. We promote an alternative of the IPF, the NM-method, for solving problems
in the second set. We provide both theoretical and empirical comparisons of
these methods.
