  In order to describe the properties of the observed distribution of wealth in
a population, most economic models rely on the existence of an asymptotic
equilibrium state. In addition, the process generating the equilibrium
distribution is usually assumed to be ergodic, with a finite asymptotic average
and bounded inequality. Here we show, using data from Bank of Italy's Survey on
Household Income and Wealth and Forbes Italian billionaires lists, that the
last hypothesis is not justified in Italy. We find that, even if an equilibrium
asymptotic distribution exists, the average wealth has no finite asymptotic
value. As a consequence we find that - without changes in the parameters of the
wealth evolution process - wealth inequality is bound to diverge with time. In
addition we evaluate the equilibration time of the evolution process when its
parameters are chosen in order to admit both an equilibrium distribution and a
finite equilibrium average wealth. Even when both the equilibrium hypotheses
are satisfied, we find equilibration times much longer than the typical time
span between economic shocks.
