When is quantile regression worse than OLS?

Question

Apart from some unique circumstances where we absolutely must understand the conditional mean relationship, what are the situations where a researcher should pick OLS over Quantile Regression?

I don't want the answer to be "if there is no use in understanding the tail relationships", as we could just use median regression as the OLS substitute.

Answer 1

If you are interested in the mean, use OLS, if in the median, use quantile.

One big difference is that the mean is more affected by outliers and other extreme data. Sometimes, that is what you want. One example is if your dependent variable is the social capital in a neighborhood. The presence of a single person with a lot of social capital may be very important for the whole neighborhood.

Answer 2

There seems to be a confusion in the premise of the question. In the second paragraph it says, "we could just use median regression as the OLS substitute". Note that regressing the conditional median on X is (a form of) quantile regression.

If the error in the underlying data generating process is normally distributed (which can be assessed by checking if the residuals are normal), then the conditional mean equals the conditional median. Moreover, any quantile you may be interested in (e.g., the 95th percentile, or the 37th percentile), can be determined for a given point in the X dimension with standard OLS methods. The main appeal of quantile regression is that it is more robust than OLS. The downside is that if all assumptions are met, it will be less efficient (that is, you will need a larger sample size to achieve the same power / your estimates will be less precise).

Answer 3

1. When there are outliers in our data set
2. When the distribution of data is skewed.
3. When we wanna have comprehensive view of the relationship between predictors and outcome of interest.
4. When the goel is to construct reference ranges for an outcome.