A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints
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A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints Ayşe Kabukçuoğlu1 · Enrique Martínez‑García2 Accepted: 31 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We study a generalized version of Coleman (J Bus Econ Stat 8:27–29, 1990)’s time iteration method (GTI) for solving dynamic optimization problems. Our benchmark framework is an irreversible investment model with labor-leisure choice. The GTI algorithm is simple to implement and provides advantages in terms of speed relative to Howard’s (Dynamic Programming and Markov Processes. MIT Press, Cambridge, MA, 1960) improvement algorithm. A second application on a heterogeneous-agents incomplete-markets model further explores the performance of GTI. Keywords General equilibrium models · Occasionally binding constraints · Computational methods · Time iteration · Policy function iteration · Endogenous grid JEL Classification C6 · C61 · C63 · C68
* Enrique Martínez‑García [email protected] https://sites.google.com/view/emgeconomics/ Ayşe Kabukçuoğlu [email protected] 1
Department of Economics, Poole College of Management, North Carolina State University, Raleigh, NC, USA
2
Research Department, Federal Reserve Bank of Dallas, 2200 N. Pearl Street, Dallas, TX 75201, USA
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A. Kabukçuoğlu, E. Martínez‑García
1 Introduction Most dynamic models in macroeconomics are in the class of nonlinear rational expectations models, which are complex and rich in structure, and do not exhibit a closed-form, analytical solution. A solution, if it exists, can be obtained only through numerical techniques. A strand of literature has focused on solution methods that use the first order conditions (FOCs) of the optimization problem, such as Judd (1992), Maliar and Maliar (2005), and Maliar et al. (2011a). These methods, however, can still be time consuming or rely on the assumption that the decision rules are smooth, which may limit their applicability. Moreover, there may be problems with convergence, depending on the initial guess (see den Haan and Marcet 1990). Coleman (1990) and Baxter (1991) suggest methods which explicitly use Euler equations and a grid to approximate the decision rules. This type of approach is particularly useful as it does not rely on the assumption of the smoothness of decision rules. Therefore it can be useful for models with occasionally binding constraints, such as the irreversible investment model or heterogeneous-agents incomplete-markets models in the spirit of Aiyagari (1994). However, speed can be a major concern, as these models can become very sophisticated. We suggest a method that addresses this issue by generalizing the time iteration method of Coleman (1990), which makes use of policy function iteration on the Euler equation of a simple real business cycle (RBC) model. With time iteration, the aim is to solve a fixed-point equation of the form c = F(c) , where c is the optimal policy function and F is deri
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