Incomplete Markets and Volatility

This paper shows that the precautionary motive, combined with asset incompleteness, is a major source of volatility and indeterminacy in financial markets. Price fluctuations originate from agents' efforts to insure themselves through time by borrowing and lending instead of shifting income across states of nature by trading in risky assets. A high interest rate at a future date reduces the potential for future consumption smoothing across time via borrowing, leading to a strong precautionary motive and a low interest rate in the current period. The negative feedback between future and current interest rates generates fluctuations. This logic is developed in SPEC, a CARA-normal model with many periods, risky time-dependent endowments, and endogenous interest rates. Unlike existing frameworks, SPEC allows us to analyze the effect of financial structure on temporal fluctuations along a given path. In equilibrium, individual consumption is random, but the macro variables are deterministic and vary through time. When there is an intermediate level of market incompleteness and sufficient investor impatience, fluctuations in the real interest rate can be large, even though the aggregate endowment is constant. SPEC has a unique equilibrium under a finite horizon; on the other hand, with a finite number of infinitely-lived agents, there exists a robust continuum of equilibria that are neither bubbles nor sunspots.