使用神经网络估计非线性异质代理模型

Estimating nonlinearheterogeneous agentmodels with neuralnetworks by Hanno Kase, Leonardo Melosi, Matthias Rottner Monetary and Economic Department January 2025 JEL classification: C11, C45, D31, E32, E52.Keywords:Neural networks,heterogeneous agents,nonlinearity, aggregate uncertainty, HANK, zero lowerbound. BISWorking Papers are written by members of the Monetary and EconomicDepartment of the Bank for International Settlements, and from time to time by othereconomists, and are published by the Bank. The papers are on subjects of topicalinterest and are technical in character. The views expressed in them are those of theirauthors and not necessarily the views of the BIS. This publication is available on the BIS website (www.bis.org). ©Bank for International Settlements 2025 All rights reserved. Brief excerpts may bereproduced or translated provided the source is stated. Estimating Nonlinear Heterogeneous Agent Modelswith Neural Networks∗ Hanno KaseEuropean Central BankLeonardo MelosiUniversity of Warwick,DNB, EUI, CEPRMatthias RottnerBIS,Deutsche Bundesbank January 13, 2025 Abstract We leverage recent advancements in machine learning to develop an integratedmethod to solve globally and estimate models featuring agent heterogeneity,nonlinear constraints, and aggregate uncertainty.Using simulated data, weshow that the proposed method accurately estimates the parameters of anonlinear Heterogeneous Agent New Keynesian (HANK) model with a zerolower bound (ZLB) constraint.We further apply our method to estimatethis HANK model using U.S. data.In the estimated model, the interactionbetween the ZLB constraint and idiosyncratic income risks emerges as a keysource of aggregate output volatility. Keywords:Neuralnetworks,likelihood,global solution,heterogeneousagents, nonlinearity, aggregate uncertainty, HANK, zero lower bound. JEL classification: C11, C45, D31, E32, E52. 1Introduction Over the past three decades, a significant advancement in macroeconomic researchhas been the integration of heterogeneity into dynamic general equilibrium models.These models enable the study of distributional issues, economic fluctuations, andstabilization policies within a single micro-founded framework.The complexity ofthese models often necessitates introducing tractability assumptions that largely pre-clude scholars from considering nonlinear aggregate dynamics and their interactionswith heterogeneity. Yet, accounting for these nonlinear dynamics is essential to un-derstand recent macroeconomic events, including recurring and prolonged periods atthe zero lower bound (ZLB), deep recessions, and the recent rise in inflation. In thispaper, we leverage recent advances in machine learning to develop a neural network(NN)-based method for solving and estimating models with heterogeneous agents,fully incorporating nonlinear aggregate dynamics. We apply our method to performlikelihood estimation of a nonlinear Heterogeneous Agent New Keynesian (HANK)model using US data. Estimating structural models entails searching for parameter values that globallymaximize an objective function, which could be a likelihood function, a posteriordistribution, or the distance between a set of empirical moments or impulse responsefunctions and their model counterparts. This search involves evaluating the objectivefunction at potentially numerous parameter values.For each parameter value, twosteps are typically taken.First, the model’s policy functions are characterized (so-lution step).Second, once the policy functions are properly approximated for thatparameter value, the objective function is evaluated (evaluation step). When estimating the parameters of an economic model, these two steps are re-peated multiple times to find the global maximum of the objective function.Thisrepetition is not problematic if the model can be solved within a fraction of a second,using a routine that can be easily automated.For instance, this is the case of lin-earized representative-agent models.However, repeatedly solving a highly complex nonlinear model, such as nonlinear HANK models with aggregate uncertainty, is un-manageable.Additionally, in the context of HANK models, the solution step mayinvolve computing the steady-state equilibrium afresh, which is a quite computation-ally intense task to perform. To overcome these computational hurdles, we approximate the model’s policyfunctions without conditioning on specific parameter values. By treating the param-eters as inputs, or pseudo-state variables, of the policy functions, we only need tosolve the model once, and only before launching the estimation. While this approachexpands the dimensionality of the model’s policy functions to approximate, NNs arehighly effective in managing high-dimensional problems (scalability), such that theincrease in computational burden remains manageable.1 Once the model’s policyfunctions are approximated over the parameter space, the model’s solution can beretrieved in a frac