  This study is concerned with estimating the inequality measures associated
with the underlying hypothetical income distribution from the times series
grouped data on the Lorenz curve. We adopt the Dirichlet pseudo likelihood
approach where the parameters of the Dirichlet likelihood are set to the
differences between the Lorenz curve of the hypothetical income distribution
for the consecutive income classes and propose a state space model which
combines the transformed parameters of the Lorenz curve through a time series
structure. Furthermore, the information on the sample size in each survey is
introduced into the originally nuisance Dirichlet precision parameter to take
into account the variability from the sampling. From the simulated data and
real data on the Japanese monthly income survey, it is confirmed that the
proposed model produces more efficient estimates on the inequality measures
than the existing models without time series structures.
