# Estimation and Inference on Nonlinear and Heterogeneous Effects

## TL;DR

This paper introduces MDEI, a new method combining machine learning with traditional inference to estimate complex, heterogeneous effects in data, providing interpretable results with reliable uncertainty estimates.

## Contribution

The paper presents the Method of Direct Estimation and Inference (MDEI), a novel approach that captures complex heterogeneities while maintaining interpretability and providing valid uncertainty quantification.

## Key findings

- MDEI accurately estimates heterogeneous effects in simulations.
- The method provides reliable uncertainty intervals.
- Application demonstrates practical usefulness in real data analysis.

## Abstract

Multiple regression has been the go-to method for data analysis for generations of scholars due to its transparency, interpretability, and desirable theoretical properties. However, the method's simplicity precludes the discovery of complex heterogeneities in the data. We introduce the Method of Direct Estimation and Inference (MDEI) that embraces these potential complexities, is interpretable, has desirable theoretical guarantees, and, unlike some existing methods, returns appropriate uncertainty estimates. The proposed method uses a machine learning regression methodology to estimate the observation-level effect of a treatment variable. Importantly, we introduce a robust approach to uncertainty estimates. We provide simulation evidence and an application illustrating the performance of the method.