EconomicsInspired Neural Networks with Stabilizing Homotopies
Abstract
Contemporary deep learning based solution methods used to compute approximate equilibria of highdimensional dynamic stochastic economic models are often faced with two pain points. The first problem is that the loss function typically encodes a diverse set of equilibrium conditions, such as market clearing and households' or firms' optimality conditions. Hence the training algorithm trades off errors between those  potentially very different  equilibrium conditions. This renders the interpretation of the remaining errors challenging. The second problem is that portfolio choice in models with multiple assets is only pinned down for low errors in the corresponding equilibrium conditions. In the beginning of training, this can lead to fluctuating policies for different assets, which hampers the training process. To alleviate these issues, we propose two complementary innovations. First, we introduce Market Clearing Layers, a neural network architecture that automatically enforces all the market clearing conditions and borrowing constraints in the economy. Encoding economic constraints into the neural network architecture reduces the number of terms in the loss function and enhances the interpretability of the remaining equilibrium errors. Furthermore, we present a homotopy algorithm for solving portfolio choice problems with multiple assets, which ameliorates numerical instabilities arising in the context of deep learning. To illustrate our method we solve an overlapping generations model with two permanent risk aversion types, three distinct assets, and aggregate shocks.
 Publication:

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.14802
 arXiv:
 arXiv:2303.14802
 Bibcode:
 2023arXiv230314802A
 Keywords:

 Economics  General Economics