The Recursive Lagrangian Method: Discrete Time

Marcet and Marimon (1999) propose a recursive Lagrangian-based method for solving dynamic incentive problems. We show that this method is applicable to a large class of concave contracting problems that encompass many in the literature. This class includes problems with (potentially persistent) private information, non-commitment, differential private and societal discounting and potentially unbounded returns. The dynamic programming problems associated with the method are non-standard in several respects: their state spaces may be unknown and their constraint correspondences are not continuous or compact-valued. We propose resolutions for these difficulties.