I've have a variable that has a regression coefficient of 5 using OLS, but when I use quantile regression (examining every 5th percentile, 5, 10, 15, etc.), I find a coefficient that is anywhere from 1/100th to 1/5th of the size of the OLS coefficient. It never really approaches the OLS coefficient. What is causing that? Does that indicate problems with either the quantile regression or OLS approach?
Furthermore, I have another variable that has a significantly positive OLS coefficient, but at pretty much each percentile (again, by 5ths), the coefficient is negative. What could be driving this?