Optimal growth with unobservable resources and learning

This paper examines the problem of choosing optimal resource consumption from an imperfectly observable aggregate capital, wealth or resource stock which the decision-maker learns about over time. Learning is complicated by the fact that the planner receives information about an object (the true resource stock) which is a moving target. Under the assumption that the utility of zero consumption is -∞ we show that the optimal policy follows a completely deterministic 'cautious' or 'minmax' policy that assumes the worst in each period and optimizes against that. When this model is compared to a model with completely observable wealth levels the following insights are obtained: (1) there is 'over-saving,' (2) investment and output processes are more volatile than consumption, and (3) regressions underestimate the risk aversion of agents. Information about the wealth or stock level is only valuable if it alters the support of the agent's beliefs. Thus, information may be statistically informative yet economically valueless. If information changes the support of the agent's beliefs then the optimal solution features an endogenous resource 'discovery' process.