The dynamics of leverage and the belief distribution of wealth

The scale and terms of borrowing in an economy depend on the manner in which wealth is distributed across potential creditors with heterogeneous beliefs about the future. This distribution evolves over time as uncertainty is resolved, in favor of optimists if loans are repaid in full, and in favor of pessimists if there is widespread default. We model this process in an economy with two assets—risky bonds and risk-free cash. Within periods, given the inherited distribution of wealth across belief types, the scale and terms of borrowing are endogenously determined. Following good states, aggregate borrowing and the face value of debt both rise, and the interest rate falls. In the absence of noise, wealth converges to beliefs that differ systematically from the objective probability governing state realizations, with greater risk-aversion associated with greater optimism. In the presence of noise, the economy exhibits periods of high performance, punctuated by periods of crisis and stagnation.