Quantile regression: number of observations

[Peter Sutton]

Hello all!

I am wanting to conduct quantile regressions at 25% and 75% of my panel data sample. This is advised by my thesis tutor on checking the robustness of my model.

However, I am struggling with how to interpret this. Does the quantile regression refer to only looking at the bottom and top 25% (in my case) of your sample?

Additionally, I read that specifying -fe- for fixed effects is not possible, and this model (automatically?) assumes that heteroscedasticity is present.

When I run the quantile regression, the number of observations above the output is the exact same as my regular multiple linear regression model that excludes the quantile command. Fyi I use the -xtqreg- command.

Could someone please clarify?

All the best and have a good Christmas,
Peter

[Clyde Schechter]

Does the quantile regression refer to only looking at the bottom and top 25% (in my case) of your sample?

No, it doesn't mean anything remotely like that.

Let's step back a bit and review what ordinary linear regression does. When you run -regress DV IV1...- what you get is a linear combination of the IVs that represents a "best" (in the sense of least total squared error) estimate of the mean value of DV given the values of the IV.

When you do a quantile regression, say for the 25th percentile, what you get is a linear combination of IVs that represents a "best" (in the sense of maximum likelihood) estimate of the 25th percentile of the DV given the values of the IV. So it's very similar to ordinary linear regression except that the model is targeting the prediction of the 25th (or whatever) percentile of the DV instead of the mean. The sample size should indeed be the same, as both procedures use all observations in the data set that have non-missing values for all model variables.

Additionally, I read that specifying -fe- for fixed effects is not possible,

That is literally correct, but conceptually off the mark. -xtqreg- does not have an -fe- option. But it has an -id()- option that is, for practical purposes, the same thing. You use -id()- to tell Stata the name of your panel variable, and it includes that variable as a fixed effect in the model.

and this model (automatically?) assumes that heteroscedasticity is present

I don't know.

[FernandoRios]

To complement on Clyde’s answer
xtqreg assumes the full model is hereoskedastic
that is how it identifies the quantile. Coefficients.
as a matter of fact it estimates a model that assumes the standard of the error is linear in parameters.

Hth
Fernando