Risk Sensitivity and Stationary Equilibrium in Incomplete Markets

We study stationary equilibrium and comparative statics in an incomplete market economy with risk-sensitive preferences. We provide conditions under which a stationary equilibrium exists for every nonnegative degree of risk sensitivity. Under independent income, greater risk sensitivity strictly raises aggregate saving at fixed prices unless both economies have zero saving, and strictly lowers the smallest and the largest equilibrium interest rates. Under stochastically monotone Markov income, these comparisons hold whenever one of the two levels of risk sensitivity being compared is sufficiently low or sufficiently high. For pairs of intermediate values, however, greater risk sensitivity can strictly lower saving, contrary to an existing result in the literature, and can strictly raise the smallest and largest equilibrium rates. An exact decomposition identifies the forces driving these reversals.