  We present a stylized model with feedback loops for the evolution of a
population's wealth over generations. Individuals have both talent and wealth:
talent is a random variable distributed identically for everyone, but wealth is
a random variable that is dependent on the population one is born into.
Individuals then apply to a downstream agent, which we treat as a university
throughout the paper (but could also represent an employer) who makes a
decision about whether to admit them or not. The university does not directly
observe talent or wealth, but rather a signal (representing e.g. a standardized
test) that is a convex combination of both. The university knows the
distributions from which an individual's type and wealth are drawn, and makes
its decisions based on the posterior distribution of the applicant's
characteristics conditional on their population and signal. Each population's
wealth distribution at the next round then depends on the fraction of that
population that was admitted by the university at the previous round.
  We study wealth dynamics in this model, and give conditions under which the
dynamics have a single attracting fixed point (which implies population wealth
inequality is transitory), and conditions under which it can have multiple
attracting fixed points (which implies that population wealth inequality can be
persistent). In the case in which there are multiple attracting fixed points,
we study interventions aimed at eliminating or mitigating inequality, including
increasing the capacity of the university to admit more people, aligning the
signal generated by individuals with the preferences of the university, and
making direct monetary transfers to the less wealthy population.
