Structural Sieves
This addresses the curse of dimensionality in economic modeling for researchers and practitioners, though it appears incremental by adapting existing deep learning methods to a specific domain.
The paper tackles the challenge of semiparametric estimation in economic models with nonlinear latent variables by proposing deep neural networks as a nonparametric sieve to approximate regression functions, showing that this approach allows for straightforward imposition of economic restrictions like shape or sparsity.
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.