A Guide on Solving Non-convex Consumption-Saving Models

• Published in: Computational economics Vol. 58; no. 3; pp. 747 - 775
• Main Author: Druedahl, Jeppe
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2021; Springer Nature B.V
• Subjects: Accuracy; Adjustment; Algorithms; Behavioral/Experimental Economics; Computer Appl. in Social and Behavioral Sciences; Consumption; Cost control; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Endogenous; Grid method; Households; Iterative methods; Math Applications in Computer Science; Methods; Nesting; Operations Research/Decision Theory; Optimization; Endogenous grid method; C6; E21; Stochastic dynamic programming; Continuous and discrete choices; Post-decision states; Occasionally binding constraints; D91
• ISSN: 0927-7099; 1572-9974
• DOI: 10.1007/s10614-020-10045-x

Consumption-saving models with adjustment costs or discrete choices are typically hard to solve numerically due to the presence of non-convexities. This paper provides a number of tools to speed up the solution of such models. Firstly, I use that many consumption models have a nesting structure implying that the continuation value can be efficiently pre-computed and the consumption choice solved separately before the remaining choices. Secondly, I use that an endogenous grid method extended with an upper envelope step can be used to solve efficiently for the consumption choice. Thirdly, I use that the required pre-computations can be optimized by a novel loop reordering when interpolating the next-period value function. As an illustrative example, I solve a model with non-durable consumption and durable consumption subject to adjustment costs. Combining the provided tools, the model is solved almost 50 times faster than with standard value function iteration for a given level of accuracy. Software is provided in both Python and C++.