Spread Regression, Skewness Regression, and Kurtosis Regression With an Application to the US Wage Structure

ABSTRACT Quantile regression provides a powerful tool for investigating the effects of covariates on key quantiles of a conditional distribution. However, we often lack a general picture of how covariates affect the overall shape of the conditional distribution. Using quantile regression estimation and quantile‐based measures of spread, skewness, and kurtosis, we propose spread regression, skewness regression, and kurtosis regression as empirical tools to quantify the effects of covariates on the spread, skewness, and kurtosis of the conditional distribution. This methodology is applied to US wage data during 1980–2019 with substantive findings, and a comparison is made with a moment‐based robust approach. In addition, we decompose changes in the spread into composition effects and structural effects to clarify rising inequality. We also provide the Stata commands spreadreg, skewreg, and kurtosisreg, which are available from the Statistical Software Components (SSC) archive, for easy implementation of spread, skewness, and kurtotis regressions.