Balancing Flexibility and Interpretability: A Conditional Linear Model Estimation via Random Forest

TL;DR

This paper introduces a novel method combining random forests with linear modeling to estimate heterogeneous effects, balancing interpretability and flexibility in econometric analysis.

Contribution

It develops a new approach to estimate conditional linear models with heterogeneity using random forests, unifying parametric and nonparametric methods with theoretical guarantees.

Findings

The method achieves favorable finite-sample performance in simulations.

It provides consistent estimation and inference for heterogeneous effects.

The approach generalizes several existing models like varying-coefficient and additive models.

Abstract

Traditional parametric econometric models often rely on rigid functional forms, while nonparametric techniques, despite their flexibility, frequently lack interpretability. This paper proposes a parsimonious alternative by modeling the outcome $Y$ as a linear function of a vector of variables of interest $\boldsymbol{X}$, conditional on additional covariates $\boldsymbol{Z}$. Specifically, the conditional expectation is expressed as $\mathbb{E}[Y|\boldsymbol{X},\boldsymbol{Z}]=\boldsymbol{X}^{T}\boldsymbol{\beta}(\boldsymbol{Z})$, where $\boldsymbol{\beta}(\cdot)$ is an unknown Lipschitz-continuous function. We introduce an adaptation of the Random Forest (RF) algorithm to estimate this model, balancing the flexibility of machine learning methods with the interpretability of traditional linear models. This approach addresses a key challenge in applied econometrics by accommodating heterogeneity in the relationship between covariates and outcomes. Furthermore, the heterogeneous partial effects of $\boldsymbol{X}$ on $Y$ are represented by $\boldsymbol{\beta}(\cdot)$ and can be directly estimated using our proposed method. Our framework effectively unifies established parametric and nonparametric models, including varying-coefficient, switching regression, and additive models. We provide theoretical guarantees, such as pointwise and $L^p$-norm rates of convergence for the estimator, and establish a pointwise central limit theorem through subsampling, aiding inference on the function $\boldsymbol\beta(\cdot)$. We present Monte Carlo simulation results to assess the finite-sample performance of the method.