Long horizon versus short horizon planning in dynamic optimization problems with incomplete information

Abstract

This paper compares the implications of short and long horizon planning in dynamic optimization problems with the structure of a standard one-sector growth model if agents have incomplete knowledge about the production function. Agents know the output and rate of return at the current capital stock and use an estimation of the production function based on this knowledge to determine current consumption. For standard utility functions without wealth-effects both long and short planning horizons yield convergence to the steady state - however at a faster rate than optimal -, or fluctuations around the steady state, and in both cases, long horizon planning yields a policy which locally at the steady state is closer to the optimal one than short horizon planning. On the other hand, for preferences with wealth effects where the intertemporal optimal path exhibits fluctuations, long horizon planning destabilizes the path and short horizon planning can generate paths which are qualitatively closer to the optimal one and yield higher discounted utility.