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?

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    $\begingroup$ Is the confindence interval around the ols-estimate wide? Do you have high leverage observations, i.e. outliers in the predictors? $\endgroup$ – Michael M Nov 27 '13 at 16:52
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    $\begingroup$ Have you plotted your data? Extreme percentiles are necessarily sensitive to the details of the tails of the data. $\endgroup$ – Nick Cox Nov 27 '13 at 16:56
  • $\begingroup$ My dependent variable is highly skewed (positive skew of 12), which is why I am using quantile regression as an alternative to OLS + bootstrapped errors. Approximately 3% of my observations have a Cook's D with a value greater than 4/n. These are actually the interesting observations in my sample though. Deleting them eliminates the OLS result. None of the observations have a Cook's D greater than 1, however. The confidence around my OLS coefficient is fairly wide (about 2x the coefficient). $\endgroup$ – KSL Nov 27 '13 at 17:29
  • $\begingroup$ Additionally, using predict h, hat, I'm not finding an leverage statistics above 0.5 (a few are 0.3 or higher, but deleting them doesn't change much). $\endgroup$ – KSL Nov 27 '13 at 19:17

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