Heteregenous Beliefs Recovery

In a standard continuous-time economy with heterogeneous beliefs and constant relative risk aversion, equilibrium prices reveal the cross-sectional distribution of wealth and consumption shares across beliefs. Specifically, we establish a novel recovery theorem showing that the equilibrium paths of the risky asset price and the interest rate determine the evolution of these distributions. Motivated by this finding, we develop an optimization-based method to approximate the implied distribution of consumption shares across beliefs, given discrete time series of prices and interest rates. We confirm the accuracy of this method on simulated data and illustrate the versatility of our approach by providing extensions of our basic recovery theorem that allow for learning and multidimensional beliefs.