spread regression, skewness regression and kurtosis regression with an application to the u.s. wage structure

Quantile regression provides a powerful tool to study the effects of covariates on key quantiles of conditional distribution. Yet we often still lack a general picture about how covariates affect the overall shape of 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 conditional distribution. This methodology is then applied to the U.S. 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 as an effort to understand rising inequality. We also provide Stata commands spreadreg, skewreg and kurtosisreg available from SSC for easy implementation of spread, skewness and kurtosis regressions.