Bootstrapping with weighted least squares

[Bert Lloyd]

I am running a regression where the dependent variable is a group-level mean, so following the advice of Angrist and Pischke (2009) and Solon et al. (2015), I am running Weighted Least Squares (WLS) where the weights are the group sizes:

reg y i.T [aweight=groupSize]

Because I have a small number of groups (36), I would like to conduce inference via the bootstrap. However, I find that the built-in vce(bootstrap)method returns an error when weights are specified, and the Stata manual ([R] Base Reference, pg. 154) states

bootstrap is not meant to be used with weighted calculations.

This leads me to wonder if there is a statistical reason that bootstrapping should not be combined with weighted estimators, or if this is just something that happens not to have been coded into Stata.

I have experimented with the user-written boottest command, and found that this does not return an error after a weighted regression. Neither its help file nor the accompanying Stata Journal paper (Roodman et al 2019) warn against weights, and Appendix A of the paper discusses observation weights (although it does not mention whether anything needs to be done in the boottest command to implement this).

Many thanks for any advice,

Bert

PS:

Stata 17.0 MP born_date = "08 Mar 2023"
Windows 11
boottest 4.1.0 13 July 2022

Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton University Press.

Roodman, D., Nielsen, M. Ø., MacKinnon, J. G., & Webb, M. D. (2019). Fast and wild: Bootstrap inference in Stata using boottest. Stata Journal, 19(1), 4–60. https://doi.org/10.1177/1536867X19830877

Solon, G., Haider, S. J., & Wooldridge, J. M. (2015). What Are We Weighting For? Journal of Human Resources, 50(2), 301–316. https://doi.org/10.3368/jhr.50.2.301

[Flor Carosa]

Hi, Bert,
Have you come up with an answer to your question? I'm encountering the same issue with bootstrapping + weights.
Thank you!

[Felix Bittmann]

I would also like to hear an explanation by StataCorp regarding this weights issue, as I am not aware of potential fatal problems when bootstrapping and probability weights are combined. You can either use boottest, and if you want to stick to the regular approach, you can write a wrapper for your regression command, as such:

clear all
sysuse nlsw88
set seed 123
gen w = runiform() * 0.1



cap program drop wrapper
program define wrapper, eclass
    syntax, cmd(string)
    `cmd'
    matrix res = e(b)
    ereturn post res
end



bootstrap _b, reps(100) seed(123): ///
    wrapper, cmd(reg wage hours tenure [pweight=w])
estat bootstrap

[Bert Lloyd]

TBH I don't remember how this turned out, although I do remember getting confused about whether, if I were to do it by hand, I would want to apply the group size weights as sampling probabilities for the bootstrap draws or if that would be "double-counting."