Quantile Regression
Also known as: conditional quantile regression, regression quantiles, Kantil Regresyon
Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.
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When to use it
Use quantile regression when the outcome is continuous (or a count) and you care about effects beyond the average - for instance the tails of the distribution or heterogeneous effects that differ across low, middle, and high values of the outcome. It assumes a linear quantile function and is preferred over OLS when heterogeneous effects are the question of interest. A reasonable sample is needed (at least about 50 observations), and standard errors should be computed by bootstrap.
Strengths & limitations
- Estimates effects across the whole distribution, not just the conditional mean, exposing tail behaviour and heterogeneous effects.
- Does not require normally distributed errors and is robust to outliers in the outcome.
- Directly preferred over OLS when the research question is about heterogeneous treatment or predictor effects.
- Assumes a linear conditional quantile function.
- Standard errors must be obtained by bootstrap, which is more computationally involved than closed-form OLS inference.
- Needs a reasonable sample size (around 50 or more) to estimate extreme quantiles reliably.
Frequently asked
How is quantile regression different from OLS?
OLS estimates the conditional mean of the outcome, while quantile regression estimates conditional quantiles such as the median or the 25th and 75th percentiles. This lets a predictor have different effects at different points of the distribution instead of a single average effect.
Why are bootstrap standard errors recommended?
The check-loss estimator does not have a simple closed-form variance like OLS, so its standard errors and confidence intervals are usually estimated by bootstrap resampling, which gives reliable inference without strong distributional assumptions.
What is the check (pinball) loss?
It is an asymmetrically weighted sum of absolute residuals: positive and negative residuals are weighted by τ and 1−τ respectively. Minimising it yields the τ-th conditional quantile, just as minimising squared residuals yields the conditional mean.
When should I prefer quantile regression over OLS?
Choose it when you care about effects in the tails of the distribution or suspect that a predictor's effect is heterogeneous across low, middle, and high outcome values. If only the average effect matters, OLS is simpler and sufficient.
Sources
- Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50. DOI: 10.2307/1913643 ↗
- Koenker, R. (2005). Quantile Regression. Cambridge University Press. DOI: 10.1017/CBO9780511754098 ↗
How to cite this page
ScholarGate. (2026, June 1). Quantile Regression. ScholarGate. https://scholargate.app/en/econometrics/quantile-regression
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