European Central Bank publishes working paper on sequential deep learning for DSGE models and non-linear tariff shock effects

The European Central Bank has published a working paper by Massimo Ferrari Minesso and Carla Frenzel that develops a sequential deep learning method for solving dynamic stochastic general equilibrium models. The paper presents a four-phase training approach in which a deep neural network is anchored to the analytically known steady state, then trained through exploration around that state, simulation on the model’s ergodic set, and Monte Carlo integration of stochastic expectations. According to the authors, this avoids the need for a pre-computed starting approximation and addresses the circularity between the solution and the data used to train it. The paper notes that the views expressed are those of the authors and do not necessarily reflect those of the ECB. In tests on a standard real business cycle model, the authors find that shallow networks with two or three hidden layers, moderate width, and an intermediate steady-state penalty deliver the best accuracy at the lowest computational cost. Applied to a two-country open-economy model, the method produces strongly non-linear responses to tariff shocks that local solution methods do not capture. In particular, large tariff shocks can reverse the direction of the exchange-rate response, with the currency of the tariff-imposing country moving from appreciation under a small shock to depreciation under a large one, while a second-order perturbation solution misses that sign change.