bc-MC Operator

Artificial Neural Networks to Solve Dynamic Programming Problems: A Bias-Corrected Monte Carlo Operator

This repository contains the code for the paper "Artificial Neural Networks to Solve Dynamic Programming Problems: A Bias-Corrected Monte Carlo Operator", available here: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4476122

Folders and Files

Folder 6.Brock_Mirman_Colab

Folder to solve the simple textbook Brock and Mirman (1972) model with full depreciation.

Notebooks (BM_1.ipynb, ..., BM_8.ipynb) were executed on Google Colab. Notebooks and output files (initially saved on Google Drive) were then downloaded locally in this folder. Notebooks are for different optimizers (ADAM or SGD) and different values of the learning rate.

To create Figures 1 and 2 (saved in the folder output), use the notebook plot_BM.ipynb. Functions are stored in the notebook functions_BM.ipynb.

The notebook plot_BM.ipynb also creates Figures 8 - 21 in the online Appendix.

Folder 7.model_with_bc_2

Folder to solve the consumption-savings problem with a borrowing constraint.

The notebook bc-MC-consumption-savings_bc_0.ipynb solves the model with $b=0$. It creates panel A of Figure 3. The notebook bc-MC-consumption-savings_bc_1.ipynb solves the model with $b=1$. It creates panel B of Figure 3.

Folder 8.model_with_bc_2_Colab

Folder to solve the consumption-savings problem with a borrowing constraint.

Notebooks (bc-MC-consumption-savings_bc_hyperparams_1.ipynb, ..., bc-MC-consumption-savings_bc_hyperparams_4.ipynb) were executed on Google Colab. Notebooks and output files (initially saved on Google Drive) were then downloaded locally in the folder. Notebooks are for different optimizers (ADAM or SGD) and different values of the learning rate.

To create Figures 4 and 5 (saved in the folder output), use the notebook plot_bc.ipynb. Functions are stored in the notebook functions-bc-MC-consumption-savings.ipynb.

The notebook plot_bc.ipynb also creates Figures 22 - 35 in the online Appendix.

Folder 9.large_scale_model_2

Folder to solve variants of the consumption-savings problem, varying the dimension for the state vector and the shock vector. Compare the bc-MC operator to the Time Iteration (TI) algorithm with a dense grid, a sparse grid, as well as an adaptive sparse grid.

The notebook bc-MC-consumption-savings_large_scale_1.ipynb creates Figures 6 and 7.

Folder 10.OLG_model

NOT in the paper. The notebook OLG.ipynb shows how the bc-MC operator can be used to approximate global solutions of economic models with overlapping generations (OLG).

References

• Pascal, Julien, Artificial Neural Networks to Solve Dynamic Programming Problems: A Bias-Corrected Monte Carlo Operator (June 12, 2023). BCL Working Papers n°172., Available at SSRN: https://ssrn.com/abstract=4476122 or http://dx.doi.org/10.2139/ssrn.4476122

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Computational details

Folders 6.Brock_Mirman_Colab and 8.model_with_bc_2_Colab

Calculations performed with Google Colab. See the results of "cpuinfo" in the notebooks for details on the machines.

Folders 7.model_with_bc_2, 9.large_scale_model_2 and 10.OLG_model

All calculations performed on the same laptop: Intel® Core™ i7-8850H CPU @ 2.60GHz × 12, Ubuntu 20.04.6 LTS. Python 3.8.10.