Bayesian Optimization on the Equilibrium Manifold

Abstract

Computing optimal policy in heterogeneous-agent economies is complicated by the possibility of multiple equilibria. We overcome this difficulty by showing that when the equilibrium manifold has a low-dimensional Negishi-weight parameterization, Bayesian optimization reliably finds approximate solutions and can be used to certify candidate solutions with high probability. This insight brings recent machine learning advances to bear on a core problem in macroeconomics. We apply Bayesian optimization to a dynamic economy with heterogeneous agents and climate change and compute optimal carbon taxes in this setting. Although in principle the presence of the carbon externality creates scope for multiple equilibria, we show that in an example with realistic calibration of damages competitive equilibra are most likely unique.