Structural Sieves

TL;DR

This paper proposes using deep neural networks as nonparametric sieves for semiparametric estimation in economic models, effectively capturing complex interactions without restrictive assumptions.

Contribution

It introduces a novel approach of employing deep neural networks as flexible sieves to approximate complex regression functions in latent variable models of economic behavior.

Findings

Deep networks effectively approximate nonlinear latent variable models.

Restrictions are more straightforwardly imposed using flexible latent variable models.

The approach handles rich interaction effects without separability assumptions.

Abstract

This paper explores the use of deep neural networks for semiparametric estimation of economic models of maximizing behavior in production or discrete choice. We argue that certain deep networks are particularly well suited as a nonparametric sieve to approximate regression functions that result from nonlinear latent variable models of continuous or discrete optimization. Multi-stage models of this type will typically generate rich interaction effects between regressors ("inputs") in the regression function so that there may be no plausible separability restrictions on the "reduced-form" mapping form inputs to outputs to alleviate the curse of dimensionality. Rather, economic shape, sparsity, or separability restrictions either at a global level or intermediate stages are usually stated in terms of the latent variable model. We show that restrictions of this kind are imposed in a more straightforward manner if a sufficiently flexible version of the latent variable model is in fact used to approximate the unknown regression function.