Title: Operator Learning in Macroeconomics

Abstract: This paper proposes a novel solution framework for the class of dynamic macroeconomic models with a continuum of heterogeneous agents and aggregate uncertainty. In these models, an agent's state variables include her individual state vector and a distribution function representing all agents' states, an infinite-dimensional object. Unlike the prevalent benchmark method that approximates the distribution function with a high-dimensional vector of simulated agents, this paper suggests the formulation of the policy function as an operator that maps between function spaces. The operator is parameterized by a cutting-edge neural network architecture known as the neural operator. This proposed framework offers significant computational advantages due to its three defining properties: discretization-invariance, permutation-invariance, and aggregation-sharing. The effectiveness of this approach is demonstrated by solving the Bewley-Huggett-Aiyagari model with aggregate uncertainty, a benchmark in computational economics literature. The proposed framework not only demonstrates computational efficiency as it manages tens of thousands of agents during simulations to precisely approximate the distribution function but also showcases its superior performance, achieving solutions with less than a one percent relative error in a shorter computational time compared to the benchmark method.