Solving Models of Economic Dynamics with Ridgeless Kernel Regressions

This repository contains the replication code and extra examples for Solving Models of Economic Dynamics with Ridgeless Kernel Regressions by Mahdi Ebrahimi Kahou, Jesse Perla, and Geoff Pleiss

Full replication code is provided for Python, and additional Julia code is in progress.

Python Setup

We recommend installation with uv (on all platforms, but especially on MacOS and Linux). If you wish to use conda see notes at the end of these instructions.

Windows Ipopt Installation

Ipopt binary installation is tricky, and we find the most reliable method is to use Anaconda (even if you will otherwise use uv). To do so, install ipopt in your base Anaconda with

conda install -n base -c conda-forge ipopt=3.11.1 pkg-config

• For Windows, version 3.11.1 seems to be essential.
• If you have clutter in your base Anaconda which prevents this from correctly installing, then you may need to reinstall Anaconda.
• If you run into issues the binary dependencies in Julia are bullet-proof and seamless.

Setup with uv

uv is a much faster alternative to Conda, even if it has incomplete support for challenging binary dependencies.

1. Install uv. This is a usually a one-line installation:
   • On Linux/MacOS: curl -LsSf https://astral.sh/uv/install.sh | sh
   • On Windows: powershell -ExecutionPolicy ByPass -c "irm https://astral.sh/uv/install.ps1 | iex" or with winget winget install --id=astral-sh.uv -e
   • If you have any installation issues, see the docs for troubleshooting
2. Install optimizer dependencies.
   • On MacOS: brew install ipopt pkg-config
   • Linux: sudo apt-get install coinor-libipopt-dev pkg-config
   • Windows: See note above if you have not previously installed Ipopt or JAX
3. Synchronize the environment

  uv sync

4. Finally, you will want to make sure you activate the python environment each time you use it.
   • In VS Code you can activate the default environment with >Python: Select Interpreter to be the .venv local to the directory
   • If the debugger isn't working in that case, sometimes setting the vscode terminal.integrated.shellIntegration.enabled: true in the settings can help
   • Outside of vscode, a simple, platform specific CLI line will activate .venv in your terminal.

Troubleshooting:

• If you receive JAX errors about DLL load failures, you may need to update https://learn.microsoft.com/en-us/cpp/windows/latest-supported-vc-redist?view=msvc-170#visual-studio-2015-2017-2019-and-2022
• See notes above on Windows Ipopt installation challenges

Figure Replication

After installation, to generate all of the figures in the paper and the appendices,

python all_figures.py

The output will be in the ./figures folder

Example Usage

The individual files support CLI arguments. To pick specific points rather than the linspace grid, pass in --train_points_list as below

python neoclassical_growth_matern.py
python neoclassical_growth_matern.py --train_points=5
python neoclassical_growth_matern.py --rho=5.0
python neoclassical_growth_matern.py --train_points_list="[0.0,2.0,5.0,10.0,20.0]"
python neoclassical_growth_matern.py --train_points=20 --train_T=10.0 --test_T=10.0 --k_0=0.5

These functions can also be imported and called directly, for example,

from neoclassical_growth_matern import neoclassical_growth_matern
sol = neoclassical_growth_matern(rho=10.0)
print(sol["c_rel_error"].mean())~~~~

Python Conda Installation

If you prefer to use conda for your entire environment management, install uv as above, then generate a requirements file and a conda environment

uv pip freeze > requirements.txt
conda create -n kernels python=3.11
conda activate kernels
pip install -r requirements.txt
conda install -c conda-forge ipopt=3.11.1

Julia Setup

Julia is more straightforward and cross-platform

1. If required, install Julia from juliaup. This can be done in a one-line terminal command:
   • MacOS/Linux: curl -fsSL https://install.julialang.org | sh
   • Windows: winget install --name Julia --id 9NJNWW8PVKMN -e -s msstore
2. Install the VS Code Julia extension. See here for more details.
3. Then activate and instantiate the environment to get the required packages. See here for more.
   • If you start a Julia REPL is VS Code, then you just need: ] instantiate