Optimal Savings under Transition Uncertainty and Learning Dynamics

TL;DR

This paper analyzes how agents optimally save and consume when facing uncertain economic regime transitions, incorporating Bayesian learning of transition probabilities and examining the effects on wealth accumulation and consumption behavior.

Contribution

It introduces a model with unknown Markov transition probabilities and Bayesian updating, establishing existence, uniqueness, and structural properties of optimal policies.

Findings

Transition uncertainty influences precautionary savings.

Learning dynamics affect wealth accumulation and consumption.

Uncertainty about regime persistence shapes long-term household wealth.

Abstract

This paper studies optimal consumption and saving decisions under uncertainty about the transition dynamics of the economic environment. We consider a general optimal savings problem in which the exogenous state governing discounting, capital returns, and nonfinancial income follows a Markov process with unknown transition probability, and agents update their beliefs over time through Bayesian learning. Despite the added endogenous state from belief updating, we establish the existence, uniqueness, and key structural properties of the optimal policy, including monotonicity and concavity. We also develop an efficient computational method and use it to study how transition uncertainty and learning interact with precautionary motives and wealth accumulation, highlighting a dynamic mechanism through which uncertainty about regime persistence shapes consumption dynamics and long-run household wealth.