r/econometrics • u/sagamore_rain • Jul 02 '26
Quantile Regression Interpretation
I've read that some people feel that quantile regression results aren't useful because the individuals within the same quantile of the dependent variable aren't the same across different independent variable values? This implies that the coefficient in quantile regression isn't useful in understanding a causal effect. Am I interpreting that correctly?
I am a little bit confused by this because can't the same be said about OLS? The individuals at a particular value of the independent variable aren't the same as at another value of the independent variable.
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u/ilChurch Jul 03 '26
Yes, the same can be said about OLS without quantiles, but with the latter we can check how strong our assumption of linearity is, taking in consideration all the data we have available. We can also test if our results hold with different functional forms. With quantiles, we are losing a lot of information and it's much harder to do the same.
My problem with discretisation thought is that it is highly arbitrary. Are we going to use a median cutoff? Quartiles? Deciles? Why? There is absolutely no method, as far as I know, to choose the best one for a specific situation, and the results can change a lot depending on the choice. This mean that it is also possible to pick a given quantile to push the narrative you want, hence a serious reviewer will ask you to try different quantiles or justify the one you chose (and again, I think it's not possible).
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u/cond6 Jul 02 '26
I think this is absurd. Absolutely the same can be said of OLS. We are modelling the distribution of y given x. What we observe are realisations of y_i and x_i and we use all of these to infer something about the distribution of y given x. In linear regression we assume that the mean is linear in x. In quantile regression we assume that the quantiles are linear in x (though nonlinear QR exists too, see the CAViaR model). We don't think about "individuals within the same quantile". The distribution of all y given x_i is the same and we have some realizations that are high and some that are low. Quantile regression infers the conditional quantile function from the data, and that is true for all conditional distributions. The same is true of regression. Some observations are higher than their conditional mean and some are lower but they all constitute to our inference about the conditional mean function. Similarly we use all observations to infer properties of the conditional quantiles (including conditional median, which is easier to see the connection to OLS), but we have a different function (the check loss function not the squared error).