### Far from equilibrium: Wealth reallocation in the United States

### Alex Adamou

LML Resident Fellow

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.

Joint work with Yonatan Berman (Tel-Aviv University) and Ole Peters (London Mathematical Laboratory, Sante Fe Institute).

### Location

University of Manchester.

### Date & Time

5th – 8th September 2016.