Understanding the Quantile Regression

Abstract

In linear regression, the regression coefficient represents the change in the response variable produced by a one unit increase in the preditcor variable associated with that coefficient. The quantile regression parameter estimates the change in a specified quantile of the response variable produced by a one unit change in the predictor variable. In investigating the relationship between the employment growth and a set of predictors, the quantile regression allows comparing how some percentiles of the employment growth of firms may be more affected by certain firm’s characteristics than other percentiles. This is reflected in the change in the size of the regression coefficient. The quantile regression shows the effects of outliers are important when testing the Gibrat’s law.