https://github.com/babayara/deepequilibriumnets

https://github.com/babayara/deepequilibriumnets

Repository

https://github.com/BabaYara/DeepEquilibriumNets/blob/master/

# Deep Equilibrium Nets






Deep equilibrium nets (DEQN) is a generic, deep-learning-based framework to compute recursive equilibria in dynamic stochastic economic models. The method directly approximates all equilibrium functions and that are trained in an unsupervised fashion to satisfy all equilibrium conditions along simulated paths of the economy.

This repository contains example codes in [TensorFlow](https://www.tensorflow.org/). Its goal is to make DEQNs easily accessible to the computational economics and finance community.


### Authors
* [Marlon Azinovic](https://sites.google.com/view/marlonazinovic/home) (University of Zurich, Department of Economics)
* [Luca Gaegauf](https://www.bf.uzh.ch/en/persons/gaegauf-luca/team) (University of Zurich, Department of Banking and Finance)
* [Simon Scheidegger](https://sites.google.com/site/simonscheidegger/) (University of Lausanne, Department of Economics)

### The paper was published at the International Economic Review, and can be found here
* [Deep Equilibrium Nets -- IER version](https://onlinelibrary.wiley.com/doi/epdf/10.1111/iere.12575)
* [Deep Equilibrium Nets -- SSRN version](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3393482)

### Illustrative examples

**Analytic model:** To illustrate how DEQNs can be applied to solve economic models, we provide an example in python, which solves the model presented in [Appendix A.8](https://onlinelibrary.wiley.com/doi/epdf/10.1111/iere.12575) of the paper.
The presented model is taken from [Krueger and Kubler (2004)](https://www.sciencedirect.com/science/article/pii/S0165188903001118) and is based on [Huffman (1987)](https://www.journals.uchicago.edu/doi/10.1086/261445). We chose this model as an illustrative example for two reasons: first, it is closely related to the models we solve in the paper and second, it has an analytical solution, so the accuracy of the solution method can easily be verified.

**Benchmark model:** We provide the code used to solve our [benchmark model (section 3)](https://onlinelibrary.wiley.com/doi/epdf/10.1111/iere.12575) with the trained neural network weights.

**"continuum of agents" model:** We provide the code used to solve our ["continuum of agents" model (Appendix A.5)](https://onlinelibrary.wiley.com/doi/epdf/10.1111/iere.12575) with the trained neural network weights.

## Usage
We provide implementations which use python 3.

First, we provide our an implementation of the analytic model in two forms. A [jupyter-notebook](https://jupyter.org/) that is self-contained and also contains the model and all relevant equations:

[![Generic badge](https://img.shields.io/badge/jupyter%20nbviewer-DEQN-green)](https://nbviewer.jupyter.org/github/sischei/DeepEquilibriumNets/blob/master/code/jupyter-notebooks/analytic/Analytic_tf1.ipynb)

as well as a plain python script, which can be executed from the command line:

[![Generic badge 2](https://img.shields.io/badge/analytic-DEQN-green)](code/python-scripts/analytic)

The benchmark model code was also written in TensorFlow 1, however, as been made TensorFlow 2 compatible.

[![Generic badge 3](https://img.shields.io/badge/benchmark-DEQN-green)](code/python-scripts/benchmark)

The "continuum of agents" model code was written in TensorFlow 2.

[![Generic badge 4](https://img.shields.io/badge/continuum%20of%20agents-DEQN-green)](code/python-scripts/continuum_of_agents)

### Prerequisites / Installation

To run the code for the implementation with an analytical solution, follow the instructions below. For instructions on how to run the benchmark or "continuum of agents" model, see the corresponding: [benchmark README](code/python-scripts/benchmark) or ["continuum of agents" README](code/python-scripts/continuum_of_agents).

#### TensorFlow 1
```shell
$ pip install tensorflow==1.13.1
```

### Running Deep Equilibrium Nets in a local installation

#### Jupyter notebook

Launch with:
```shell
    $ cd /DeepEquilibriumNets/code/jupyter-notebooks/analytic/
    $ jupyter-notebook Analytic_tf1.ipynb
```


#### Plain Python
Launch with:
```shell
    $ cd /DeepEquilibriumNets/code/python-scripts/analytic/
    $ python Analytic_tf1.py
```

## Citation

Please cite Deep Equilibrium Nets in your publications if it helps your research:

```
@article{https://doi.org/10.1111/iere.12575,
author = {Azinovic, Marlon and Gaegauf, Luca and Scheidegger, Simon},
title = {DEEP EQUILIBRIUM NETS},
journal = {International Economic Review},
volume = {n/a},
number = {n/a},
pages = {},
year={2022}
doi = {https://doi.org/10.1111/iere.12575},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/iere.12575},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/iere.12575}
}
```


## Support

This work was generously supported by grants from the Swiss National Supercomputing Centre (CSCS) under project IDs s885, s995, the Swiss Platform for Advanced Scientific Computing (PASC) under project ID ["Computing equilibria in heterogeneous agent macro models on contemporary HPC platforms"](https://www.pasc-ch.org/projects/2017-2020/call-for-pasc-hpc-software-development-project-proposals), the Swiss National Science Foundation (SNF), under project IDs "Can Economic Policy Mitigate Climate-Change?", and "New methods for asset pricing with frictions".

Owner

GitHub Events