Quantile regression
Look beyond the conditional average
Quantile regression estimates selected quantiles of an outcome conditional on predictors. Median regression minimises absolute deviations; other quantiles use asymmetrically weighted deviations. It can reveal relationships that differ across a conditional distribution. A high conditional quantile is not simply a regression on the highest observed outcomes or the unconditional population percentile.
Use when inequality, tail outcomes or heterogeneous distributional associations matter, such as wages, expenditure or credit losses. Ensure the target quantiles have enough information for stable estimation and inference.
Strengths
- Reveals distributional differences hidden by mean regression
- Median regression is less sensitive to extreme outcomes than OLS
Limitations
- Extreme quantiles require substantial information
- Quantile crossing and dependent data complicate estimation
Know the boundary
Conditional quantile coefficients do not automatically identify effects on unconditional population quantiles.