Deep Learning as a Projection Method for Solving Economic Models

Deep learning is increasingly presented in economics as a new paradigm for solving dynamic models, superseding the classical projection methods of numerical economics. We argue that this dichotomy rests on a misclassification. The neural-network solvers emphasized in this literature are least-squares projection methods with an adaptive nonlinear parameterization. Placing deep learning inside the projection family reorients the agenda. The issue is not a contest between paradigms, but suggests a single toolkit using a variety of approximation methods, residual criteria, and evaluation designs to be chosen on the merits for the model at hand. In low and moderate dimensions, linear-basis and sparsegrid methods are often more accurate, faster, and easier to verify than a trained neural network. In high dimensions, an appropriate choice for the space of permissible functions will often avoid the curse of dimensionality.