Estimating Nonlinear Heterogeneous Agents Models with Neural Networks

Economists routinely approximate away features of their models – nonlinear dynamics, aggregate uncertainty, agent heterogeneity – to make estimation feasible, but it is often unclear how much these simplifications distort a model’s predictions. This paper develops a neural-network-based solution and estimation method designed to avoid such approximations entirely. The key device is to treat a model’s structural parameters as additional “pseudo state variables” fed into the neural networks that approximate its policy functions, so that a single (more expensive) training run yields the model’s entire solution mapping across the whole parameter space, rather than the solution at one parameter point – exploiting the fact that neural networks scale cheaply to extra inputs. Because likelihood-based estimation of nonlinear models also requires a computationally costly Monte Carlo (particle) filter at every parameter draw, the paper trains a second “surrogate” neural network – the neural network particle filter – on a modest sample of particle-filter-evaluated likelihoods, giving a near-instant approximate mapping from parameters to likelihood that can be plugged into a standard Metropolis-Hastings sampler. After validating the approach on a linearized New Keynesian model (where the true solution is known analytically) and on a tractable representative-agent model with an aggregate zero-lower-bound nonlinearity (where results closely match a conventional particle-filter estimation), the paper applies its method to a fully nonlinear Heterogeneous Agent New Keynesian (HANK) model with 100 households, idiosyncratic labor-productivity risk, an individual borrowing limit, and a zero lower bound on the nominal interest rate – a model with hundreds of state and pseudo-state variables and 12 estimated structural parameters, including parameters that directly govern the degree of household heterogeneity. Using the calibrated model as the true data-generating process and 500 simulated periods of output growth, inflation, and the interest rate, a 1-million-draw Bayesian estimation recovers all 12 parameters, with the true value falling inside the 90% credible interval in every case, completed in under two days on a modern desktop computer – what the authors describe as the first estimation of a HANK model in its fully nonlinear specification. The exercise also reveals a strong asymmetry in identification: parameters governing aggregate dynamics (habit formation, price-adjustment costs, monetary-policy responses, shock persistences) are estimated precisely, while the posteriors for parameters governing idiosyncratic risk and the borrowing limit are “rather flat,” suggesting standard macro aggregate data contains little information about the underlying degree of heterogeneity and that richer, distributional data would likely be needed to pin these down.

Matthias Rottner | Macro Paper Warehouse

Estimating Nonlinear Heterogeneous Agents Models with Neural Networks