Model uncertainty and equilibrium wealth and consumption dynamics

Abstract

In this paper, I consider a infinite horizon consumption-saving problem where (i) the agent's preference takes a recursive exponential utility (REU) form; (ii) labor income follows a continuous-time Ornstein-Uhlenbeck process with conditional heteroskedasticity; and (iii) households have preference for robustness due to fear about model misspecification. There are three major findings: (i) The marginal propensity to consume (MPC) out of labor income decreases upon switching to a new income process and is a decreasing function of the degree of robustness. This finding differs from Luo, Nie and Young (2018) as the MPC in their model is independent from robustness; (ii) robustness affects optimal consumption both directly and indirectly, resulting in a larger response of consumption to model uncertainty and larger welfare losses; and (iii) the estimated labor income process using PSID data and the recursive WLS method indicates a positive and significant effect of income level on income volatility.

The extension follows the recursive formulation method developed by Wang (2007), and derives equilibrium wealth and consumption distribution of ambiguity averse households using the explicit consumption-saving rules under both approximating and distorted models. For financial wealth, the equilibrium relative moments suggest that under the approximating model, only the mean and variance of wealth distribution increase with robustness while higher order moments are unaffected. For equilibrium consumption distribution, the effect of robustness is even more mixed than that of the wealth distribution, where relative moments show opposite and non-monotonic effect of robustness. The results generally confirm the conclusion of Wang (2007) that "stationary cross-sectional (standardized) wealth is less skewed and less fat-tailed than stationary cross-sectional (standardized) income'' and show that such properties are strengthened by the presence of robustness.