Precautionary savings and wealth accumulation with parameter uncertainty and learning

This paper considers the intertemporal consumption/savings decision when income follows a random walk with drift and the drift coefficient is unknown. Instead agents are Bayesian learners, combining prior and sample information to form a posterior for the drift coefficient and future income. This parameter uncertainty increases by an order of magnitude the uncertainty of future income over that generated by unknown future shocks to income and can lead agents to have much more precautionary savings and hence to accumulate more wealth than otherwise. In a calibration exercise it is shown that for a plausible specification of the level of prior information and real interest rate, that the level of aggregate wealth due to this parameter uncertainty could be larger than that generated by unknown future shocks to income, the latter of which has been estimated elsewhere to potentially account for 60 percent of US aggregate wealth.