Unlocking the Regression Space

TL;DR

This paper develops a flexible regression framework that handles heterogeneity in regressors and noise, providing robust standard errors and confidence intervals applicable to diverse models, including those with missing data.

Contribution

It introduces a general heterogeneity framework for regression models and proposes robust standard error estimators that extend White's heteroskedasticity-consistent approach.

Findings

Robust standard errors perform well in simulations.

The framework applies to models with missing data.

Estimates are computationally simple and broadly applicable.

Abstract

This paper introduces and analyzes a framework that accommodates general heterogeneity in regression modeling. It demonstrates that regression models with fixed or time-varying parameters can be estimated using the OLS and time-varying OLS methods, respectively, across a broad class of regressors and noise processes not covered by existing theory. The proposed setting facilitates the development of asymptotic theory and the estimation of robust standard errors. The robust confidence interval estimators accommodate substantial heterogeneity in both regressors and noise. The resulting robust standard error estimates coincide with White's (1980) heteroskedasticity-consistent estimator but are applicable to a broader range of conditions, including models with missing data. They are computationally simple and perform well in Monte Carlo simulations. Their robustness, generality, and ease of implementation make them highly suitable for empirical applications. Finally, the paper provides a brief empirical illustration.