Pseudospectral Methods for Continuous-Time Heterogeneous-Agent Models

In this repository, you can find the code accompanying "Pseudospectral Methods for Continuous-Time Heterogeneous-Agent Models", forthcoming in the Journal of Economic Dynamics and Control.

Abstract

We propose a pseudospectral method to solve heterogeneous-agent models in continuous time. The solution is approximated as a sum of smooth global basis functions, in our case polynomials represented by their values at Chebyshev nodes. We illustrate the method by applying it to a Krusell-Smith model. It solves the differential equations characterizing the steady-state efficiently and precisely, despite using only very few nodes. System dynamics are then automatically differentiated to simulate a linearized model. The full solution is very fast and uses only standard software. A benchmark against finite differences shows at pseudospectral methods achieve far greater precision for a given number of nodes and for a given runtime. We conclude by discussing the methods' applicability, which is promising for smooth multi-dimensional models.

Code

There are six pieces of code, all written in Python and saved as Jupyter Notebooks:

• backend: contains various helper functions, notably for manipulating and assembling differentiation matrices, that are used in all other codes of this project
• two_state: code for the two-income Hugget model which is solved in Sections 3 and 4, and used for the static benchmark of Section 6
• krusell_smith: code for the two-income Krusell-Smith model which is solved in Section 5 and used for the Den Haan error calculation of Section 6
• two_state_weakly_binding: code for the two-income model with a weakly binding credit constraint in Appendix A
• diffusion: code for the diffusive income Hugget model solved in Appendix B
• power_law: code for the power law model and transition speed analysis in Appendix C
• life_cycle: code for the life-cycle model solved in Appendix D

To run without modification, all code should be put into a folder titled code, next to which one should create two folders called figures and tables to collect the outputs.

Beyond the standard Numpy and Scipy, there are only two important dependencies:

• DmSuite, to compute pseudospectral differentiation matrices, which you can download using Pip
• JAX, to automatically differentiate system dynamics for the linearized simulation, which you can also download using Pip

If you have any questions on the code or the paper itself, do not hesitate to message me at c.schesch@gmail.com.