2025/12/18 CRETA Seminar - Instrumental Variable Rectified Linear Unit Regression

Title：

2025/12/18 CRETA Seminar - Instrumental Variable Rectified Linear Unit Regression

Introduction：

This paper develops an instrumental variables method for endogeneity in rectified linear unit (ReLU) regression, where the ReLU transformation applies to the outcome variable. Building on the generalized method of moments (GMM) framework, our methodology requires only finite first moments and standard rank conditions for estimation and inference. The ReLU regression with instrumental variables yields explicit GMM solutions and avoids iterative optimization procedures. Through the Legendre-Fenchel transformation of ReLU regression outcomes, our framework enables the estimation of average quantile treatment effects between arbitrary quantiles, accommodating both continuous and non-continuous outcomes. We establish the asymptotic properties of the proposed estimators. In an empirical application examining the effect of 401(k) plans on household wealth accumulation, we find substantial heterogeneity in treatment effects across the wealth distribution, with larger impacts among households with greater financial capacity.

About speaker：

https://oka-econ.github.io/