# Iterative Estimation of Nonparametric Regressions with Continuous Endogenous Variables and Discrete Instruments

arXiv: https://arxiv.org/abs/1905.07812 · HTML: https://mlsanity.com/paper/1905.07812/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2019.

## Built on by (most cited first, 2 of 2)

- [Fairness constraint in Structural Econometrics and Application to fair estimation using Instrumental Variables](https://mlsanity.com/paper/2202.08977/) (2022)
- [Nonlinear Causal Discovery via Kernel Anchor Regression](https://mlsanity.com/paper/2210.16775/) (2022)

## Abstract (arXiv)

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied research, its implementation is challenging, as the regression function becomes the solution to a nonlinear integral equation. We propose a simple iterative procedure to estimate such models and showcase some of its asymptotic properties. In a simulation experiment, we detail its implementation in the case when the instrumental variable is binary. We conclude with an empirical application to returns to education.