# Structural Sieves

arXiv: https://arxiv.org/abs/2112.01377 · HTML: https://mlsanity.com/paper/2112.01377/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 54 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Reviving and Improving Recurrent Back-Propagation](https://mlsanity.com/paper/1803.06396/) (2018)
- [Deep vs. shallow networks : An approximation theory perspective](https://mlsanity.com/paper/1608.03287/) (2016)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)

## Abstract (arXiv)

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.