General Equilibrium Dynamics For Incomplete Markets: Numerical Examples

Kubler and Schmedders (2005) showed that a competitive equilibrium can be far from an exact equilibrium when computed using first-order conditions. This paper shows that a competitive equilib- rium is implemented by recursive statistics with a minimal state space. This result allows us to develop an alternative method for computing the equilibrium without using first order conditions and smoothness assumptions. We compute the recursive equilibrium through a functional iteration algorithm and show that its implemented equilibrium allocation is arbitrarily close to an exact competitive equilibrium. In particular, we simulate some stochastic equilibrium processes in which agents anticipate exogenous un- certainty using some rules described in the literature of behavioral finance. An important stylized fact that is found suggests that incomplete markets favor agents with rational expectations when the expected asset return is high in relation to the risk-free asset.