Role of vce(robust) in qreg

[Jake Carlam]

Good evening,

Thank you in advance for your assistance with this, I'm sure I am just missing a trick.

The STATA manual for qreg mentions the vce() option. The default is vce(iid) which computes standard errors under the iid assumption. The manual then specifies vce(robust) as the alternative to this.

Does this mean that using vce(robust) allows us to relax the iid assumption? This seems unrealistic! If not, why would I consider using robust standard errors when the qreg model already accounts for heteroscedasticity.

Best wishes.

[Joao Santos Silva]

Dear Jake Carlam,

I am not surprised you are puzzled. The default covariance matrix is indeed only valid when the errors are iid, in which case all quantiles are parallel to the mean and therefore QR is not interesting. In general, quantile regression is interesting when the errors are not iid, and in that case you have to specify the option vce(robust) in qreg. In contrast, that is the default in qreg2, which also allows you to cluster the standard errors.

Best wishes,

Joao

[Jeff Wooldridge]

The "iid" label is misleading here. In the usual paradigm of a superpopulation with random sample, the errors are always i.i.d. because they are necessarily independent of each other and identically distributed. The real key is, when we write,

y(i) = x(i)*b + u(i),

u(i) is assumed independent of x(i) in the vce(iid) default. The vce(robust) option allows u(i) and x(i) to be dependent -- for example, Var(u(i)|x(i)) can depend on x(i). There is another robust version that allows the linear quantile function to be misspecified, but that option is only allowed via bootstrapping when using qreg.