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PCaMS: Simon Scheidegger - Deep Equilibrium Nets

  • PWBM's Philadelphia Office 3440 Market Street, Suite 300 Philadelphia, PA 19104 United States (map)

Simon Scheidegger is an Assistant Professor at the Department of Finance, HEC Lausanne, Switzerland. His research focuses on developing computational methods for high-dimensional dynamic stochastic economic modeling and applying them to macroeconomics, monetary policy, option pricing, and optimal tax policy. His articles have been published in leading journals such as Econometrica. He will present the paper Deep Equilibrium Nets.

Deep Equilibrium Nets

Abstract: In order to develop large-scale overlapping generations models, which are consistent with findings at the micro-level, one has to be able to include a substantial amount of heterogeneity, significant uncertainty, and financial frictions. Studying such models demands that one can compute equilibria in situations jointly featuring a high-dimensional state space, kinks in the equilibrium functions, and irregular state space geometries. To this end, we introduce deep equilibrium nets—neural networks that directly approximate all equilibrium functions in discrete-time dynamic stochastic economic models and that are trained in an unsupervised fashion to satisfy all equilibrium conditions along simulated paths of the economy. Since the neural network approximates the equilibrium functions directly, neither sets of non-linear equations nor optimization problems need to be solved in order to simulate the economy. Consequently, training data can be generated at virtually zero cost. To demonstrate the performance of the proposed method, we study the effects of borrowing constraints and adjustment costs on the cross-sectional consumption response to aggregate shocks in overlapping generations models with 60 generations, aggregate uncertainty, a one-period bond, and occasionally binding constraints. We obtain average relative errors in the Euler equations of the order ∼ 10^-4 when applying a densely connected deep neural network with two hidden layers. To study the effect of borrowing constraints on the cross-sectional consumption response to stochastic shocks to total factor productivity and depreciation of capital, we compare two economies that differ in the level of the exogenous borrowing constraint. In one economy, agents are not allowed to take up debt; in the other, agents can take up debt up to an exogenously fixed value that we set to −84% of mean yearly per-capita consumption. The effect of looser borrowing constraints differs across age-groups: the consumption response to a shock with high total factor productivity and high depreciation, for example, decreases from 14.4% to 4.1% for 21-year-old agents, while it increases from 12.6% to 21.6% for 32-year-old agents and decreases from 4.1% to 3.6% in the aggregate.