Reversing disbursement rates to estimate stationary wealth processes for endowments with recursive preferences

Endowments have been accused of hoarding their wealth. However, the theoretically ideal spending plan remains unclear and, in practice, endowments follow a range of rules. Here we derive and estimate the optimal spending plans of an infinitely lived charity or endowment with an Epstein-Zin-Weil utility function, given general Markovian returns to wealth. We analyse two special cases: first, where spending is a power function of last period's wealth; and second where the endowment uses 'payout smoothing'. Via non-linear least squares, we estimate the optimal spending rate and the elasticity of inter-temporal substitution for an endowment with a typical diversified portfolio and for a portfolio of hedge funds. In a new approach, we use maximum entropy methods to characterize the returns distribution of an endowment whose spending plan conforms with the optimality condition. We confirm that the estimated returns distribution is largely consistent with the optimal spending plan.