Optimal Grid Selection for the Numerical Solution of Dynamic Stochastic Optimization Problems
- PDF / 725,296 Bytes
- 46 Pages / 439.37 x 666.142 pts Page_size
- 102 Downloads / 193 Views
Optimal Grid Selection for the Numerical Solution of Dynamic Stochastic Optimization Problems Karsten O. Chipeniuk1 Accepted: 18 November 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract This paper unites numerical literature concerning the optimal linear approximation of convex functions with theory on the consumption savings problems of households in macro economies with idiosyncratic risk and incomplete markets. Construction of a grid for the linear approximation of household savings behavior which is optimal in the sense of minimizing the largest absolute error is characterized in a standard environment with income fluctuations and a single savings asset. For wealthy households, the grid is characterized asymptotically as having a density which decreases in household wealth. For domains which include resource poor households, the optimal grid is seen to have non-monotonic grid point density for standard parameters. This feature contradicts conventional rules for constructing grids, and is related to nonmonotonic curvature in the savings function for low resource holdings. Approximate optimal grids are seen to outperform standard grid constructs according to a variety of accuracy measures at the cost of significantly increased computational time, and efficiency-improving alternatives are given. Keywords Numerical approximation · Heterogeneous agents · Incomplete markets JEL Classification C61 · E21 · D52
The views expressed in this article are solely those of the author and do not necessarily reflect the position of the Reserve Bank of New Zealand. The author thanks Todd Walker, Eric Leeper, Amanda Michaud, Juan Carlos Hatchondo and Nets Katz, colleagues at Indiana University, Bloomington and the Reserve Bank of New Zealand, and participants at the 2017 Workshop of the Australasian Macroeconomic Society at the Australian National University for comments and suggestions. Much of the work underpinning this paper was completed while the author was a graduate student at Indiana University, Bloomington. Any remaining errors are the author’s.
B 1
Karsten O. Chipeniuk [email protected] Reserve Bank of New Zealand, 2 The Terrace, Wellington 6011, New Zealand
123
K. O. Chipeniuk
1 Introduction Robust and accurate global solution methods are indispensable in the solving of dynamic stochastic optimization problems characteristic of heterogeneous agent macroeconomics models. This class of models features substantial nonlinearity and high dimensionality inherent in the optimization problems facing the various economic agents, which are largely absent in the representative agent framework. Consequently, the numerical methods applied must be finely tuned to each individual model and its parameters. This has led to a large body of literature in recent decades aiming to address the accuracy, speed, and versatility of the numerical solution of baseline heterogeneous agent models (Krusell and Smith 1998; Algan et al. 2008; Reiter 2009; Den Haan 2010a; Kim et al. 2010; Maliar e
Data Loading...
