The Dual Approach to Recursive Optimization: Theory and Examples. Issue 1 (5th February 2018)

• Record Type: Journal Article
• Authors: Pavoni, Nicola; Sleet, Christopher; Messner, Matthias
• Is Part Of: Econometrica. Volume 86:Issue 1(2018)
• Page Start: 133
• Page End: 172
• Publication Date: 2018-02-05
• Subjects: Dynamic contracts -- duality -- dynamic programming -- contraction mapping; Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA11905
• Languages: English
• ISSNs: 0012-9682

Abstract

Abstract : We develop a recursive dual method for solving dynamic economic problems. The method uses a Lagrangian to pair a dynamic recursive economic problem with a dual problem. We show that such dual problems can be recursively decomposed with costates (i.e., Lagrange multipliers on laws of motion) functioning as state variables. In dynamic contracting and policy settings, the method often replaces an endogenous state space of forward‐looking utilities with an exogenously given state space of costates. We provide a principle of optimality for dual problems and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate economic problems to their duals, address computational issues, and give examples.