This paper addresses the intergenerational mobility question by examining the role of
family structure in the transmission of educational attainment within a family using the
one percent Integrated Public Use Microsample Series (IPUMS) of the decennial Census
for the decades 1970 and 1990. We first introduce mobility indices and tests which
examine the proximity of the transition matrix to that which would pertain in the
perfectly mobile state. Unlike existing transition matrix based mobility indices, these
indices and tests can be employed when the transition matrix is not square, and when the
transition matrix is between states that are defined multivariately or more generally when
the quantiles of the marginal states are unmatched. Using educational attainment as a
proxy for permanent income for children and both educational attainment and income as
proxies for parents, the tests indicate that mobility significantly increased, both in the
population as a whole and within intact parent and single parent sub-populations, over the
period. Within the single parent group there was much less evidence for significant
mobility change for children from exogenous single parent families than for children
from endogenously single parent families, which accords with theoretical predictions.
There is also some evidence of convergence between intact and single parent groups,
suggesting that there is a trend towards equal opportunity for children of intact and
endogenously single parent families.