Quantile Regression

An OLS regression measures the impact of a one unit change in the explanatory variable on the mean of the dependent variable. In other words, regressions can be thought of estimation of the conditional mean of the dependent variable, given the value of the explanatory variable. Sometimes, however, the researcher is interested in the impact on certain quantiles (like the median, 90th percentile, or the first decile, etc.) of the distribution of the dependent variable instead of the mean. The statistical properties of the conditional quantile is very different from that of the conditional mean, and hence the standard OLS technique breaks down in a quantile regression.

A quantile regression can be implemented in STATA quite easily with the following command:

qreg y x1 x2, quantile(0.25)

The above command executes the quantile regression of the dependent variable y on the explanatory variables x1 and x2 for the 25th percentile of the distribution of y. The number for the option quantile() has to lie between 0 and 1.