Inequality Constraints and Euler Equation-based Solution Methods

Authors

  • Pontus Rendahl

    Corresponding author
    1. University of Cambridge, Centre for Macroeconomics (CFM) and CEPR
    • Corresponding author: Pontus Rendahl, Faculty of Economics, University of Cambridge, Austin Robinson Building, Sidgwick Avenue, Cambridge CB3 9DD, UK. Email: pontus.rendahl@gmail.com.

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  • This study is a substantially revised version of a chapter in my Ph.D dissertation written at the European University Institute, previously circulated under the title ‘Inequality Constraints in Recursive Economies’. I thank Wouter den Haan, Dirk Krueger, Albert Marcet, Karel Mertens, Morten Ravn, Sanne Zwart and two anonymous referees for helpful comments and suggestions. The usual disclaimer applies.

Abstract

Solving dynamic models with inequality constraints poses a challenging problem for two major reasons: dynamic programming techniques are reliable but often slow, whereas Euler equation-based methods are faster but have problematic or unknown convergence properties. This study attempts to bridge this gap. I show that a common iterative procedure on the first-order conditions – usually referred to as time iteration – delivers a sequence of approximate policy functions that converges to the true solution under a wide range of circumstances. These circumstances extend to a large set of endogenous and exogenous state variables as well as a very broad spectrum of occasionally binding constraints.

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