An Adversarial Approach to Structural Estimation

Abstract

We propose a new simulation-based estimation method, adversarial estimation, for structural models. The estimator is formulated as the solution to a minimax problem between a generator (which generates synthetic observations using the structural model) and a discriminator (which classifies if an observation is synthetic). The discriminator maximizes the accuracy of its classification while the generator minimizes it. We show that, with a sufficiently rich discriminator, the adversarial estimator attains parametric efficiency under correct specification and the parametric rate under misspecification. We advocate the use of a neural network as a discriminator that can exploit adaptivity properties and attain fast rates of convergence. We apply our method to the elderly's saving decision model and show that including gender and health profiles in the discriminator uncovers the bequest motive as an important source of saving across the wealth distribution, not only for the rich.

Fast Simulation-Based Bayesian Estimation of Heterogeneous and Representative Agent Models using Normalizing Flow Neural Networks

“…Thus, the density of the posterior p(θ|x) = r(x, θ)p(θ), where p(θ) is the prior. This extends Kaji, Manresa and Pouliot (2020) GAN approach in allowing estimation of models with a latent time dimension. One can extend this to multi-round inference where one uses the GAN as a better proposal distribution 1) for n = 1...S with MCMC;…”

“…Other machine learning approaches use techniques that have both robustness and efficiency guarantees like GANs. Most relevant to this paper, Kaji, Manresa and Pouliot (2020) whose GAN approach to structural modelling open the door to robust and near efficient point estimation using only simulations from the model and not a likelihood.…”

“…When thought in this way, it's intuitive to recognize that the GAN is nearly a full information and efficient estimation procedure. For more thorough proofs see Kaji, Manresa and Pouliot (2020).…”

“…Finding the mode of the posterior with a uniform prior allows one to derive MLE estimation from the Bayesian procedure as well. Econometrically, this approach extends Kaji, Manresa and Pouliot (2020) to the Bayesian setting and when there is a time series component that is not iid. I next will discuss briefly the Sequential Neural Posterior Estimation (SNPE) algorithm (Greenberg, Nonnenmacher and Macke, 2019), (Tejero-Cantero et al, 2020) that can perform this likelihoodfree Bayesian and MLE estimation.…”

Deep Structural Estimation: With an Application to Option Pricing

“…Liu, Borovykh, Grzelak, and Oosterlee (2019b) introduce a framework called Calibration Neural Networks to calibrate financial asset pricing models and provide numerical experiments based on simulated data. Kaji, Manresa, and Pouliot (2020) propose a simulation-based estimation method for economics structural models using a generative adversarial neural network.…”