  Studies of wealth inequality often assume that an observed wealth
distribution reflects a system in equilibrium. This constraint is rarely tested
empirically. We introduce a simple model that allows equilibrium but does not
assume it. To geometric Brownian motion (GBM) we add reallocation: all
individuals contribute in proportion to their wealth and receive equal shares
of the amount collected. We fit the reallocation rate parameter required for
the model to reproduce observed wealth inequality in the United States from
1917 to 2012. We find that this rate was positive until the 1980s, after which
it became negative and of increasing magnitude. With negative reallocation, the
system cannot equilibrate. Even with the positive reallocation rates observed,
equilibration is too slow to be practically relevant. Therefore, studies which
assume equilibrium must be treated skeptically. By design they are unable to
detect the dramatic conditions found here when data are analysed without this
constraint.
