Optimal Consumption and Asset Allocation with Unknown Income Growth

I study an agent’s optimal consumption-saving and portfolio choice decisions when he cannot fully insure his income shocks and does not know his income growth rate. I show that the agent rationally saves for precaution against the risk of estimating his income growth, in addition to his standard precautionary saving demand induced by income volatility. I then extend the analysis to allow for the agent’s unknown growth rate to be stochastic. Finally, I generalize the model to allow the agent to trade risky assets to hedge against both his income risk and estimation risk. A more volatile and noisier underlying income process gives rise to a less volatile belief updating process. Hence, estimation risk (due to stochastic belief updating) is lower, and the implied hedging demand against estimation risk is smaller. The agent’s total hedging demand is thus non-monotonic in his income volatility because estimation risk decreases with income volatility, ceteris paribus.