  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.
