Finite Elements in the Presence of Occasionally Binding Constraints

Abstract

This paper proposes and compares in terms of speed and accuracy two alternative approximation methods employing finite elements to parameterize the true policy functions that solve for the equilibrium of an optimal growth model with leisure and irreversible investment. The occasionally binding constraint in investment is efficiently handled on one algorithm by parameterizing the expectations of the marginal benefit of future physical capital stock and on the other by modifying the planner’s problem to include a penalty function. While both methods benefit from the high speed and accuracy achieved by a finite elements approximation, the algorithm incorporating a penalty function in the planner’s problem proved being of fastest convergence over a whole range of the model’s calibrations.