As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern
to policy makers and researchers alike. Of particular interest are the changes in inequality and
poverty over time, which are typically assessed through the estimation of income
distributions. From this, income inequality and poverty measures, along with their differences
and standard errors, can be derived and compared. With panel data becoming more frequently
used to make such comparisons, traditional methods which treat income distributions from
different years independently and estimate them on a univariate basis, fail to capture the
dependence inherent in a sample taken from a panel study. Consequently, parameter
estimates are likely to be less efficient, and the standard errors for between-year differences
in various inequality and poverty measures will be incorrect. This paper addresses the issue
of sample dependence by suggesting a number of bivariate distributions, with Singh-Maddala
or Dagum marginals, for a partially dependent sample of household income for two years.
Specifically, the distributions considered are the bivariate Singh-Maddala distribution,
proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of
multivariate distributions, which are an increasingly popular approach to modelling joint
distributions. Each bivariate income distribution is estimated via full information maximum
likelihood using data from the Household, Income and Labour Dynamics in Australia
(HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income
distribution are used to obtain values for mean income and modal income, the Gini inequality
coefficient and the headcount ratio poverty measure, along with their differences, enabling
the assessment of changes in such measures over time. In addition, the standard errors of each
summary measure and their differences, which are of particular interest in this analysis, are
calculated using the delta method.