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, distinct from and largely 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. They minimize residuals of the model’s equilibrium conditions over finite evaluation points. Once the residual criterion, evaluation points, and weights are fixed, the remaining difference from classical projection is the approximating family, namely a linear approximation space versus an adaptive nonlinear parameterization. Placing deep learning inside the projection and weighted-residual family clarifies three recurring confusions, namely the meaning of “learning,” the source of the high-dimensional advantage, and the role of the accuracy criterion. It also reorients the agenda. The issue is not a contest between paradigms, but a single toolkit of approximating families, residual criteria, and evaluation designs to be chosen on the merits for the model at hand. In low and moderate dimensions, linear-basis and sparse-grid methods are often more accurate, faster, and easier to verify than a trained network.