Solving Models of Economic Dynamics with Ridgeless Kernel Regressions

Mahdi Ebrahimi Kahou, Jesse Perla and Geoff Pleiss

Papers from arXiv.org

Abstract: This paper proposes a ridgeless kernel method for solving infinite-horizon, deterministic, continuous-time models in economic dynamics, formulated as systems of differential-algebraic equations with asymptotic boundary conditions (e.g., transversality). Traditional shooting methods enforce the asymptotic boundary conditions by targeting a known steady state -- which is numerically unstable, hard to tune, and unable to address cases with steady-state multiplicity. Instead, our approach solves the underdetermined problem without imposing the asymptotic boundary condition, using regularization to select the unique solution fulfilling transversality among admissible trajectories. In particular, ridgeless kernel methods recover this path by selecting the minimum norm solution, coinciding with the non-explosive trajectory. We provide theoretical guarantees showing that kernel solutions satisfy asymptotic boundary conditions without imposing them directly, and we establish a consistency result ensuring convergence within the solution concept of differential-algebraic equations. Finally, we illustrate the method in canonical models and demonstrate its ability to handle problems with multiple steady states.

Date: 2024-06, Revised 2025-10
New Economics Papers: this item is included in nep-big, nep-cmp and nep-inv
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2406.01898 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2406.01898

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().