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I am a little confused as to what the following line means. Do the authors mean they run a weighted least squares using the sample size as weights, or just weight the dependent variable using the sample size?

enter image description here

Here's the link to the original paper. The part I'm talking about is in page 19:

https://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/783.pdf

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    $\begingroup$ I won't offer a genuine contribution to this, because a serious treatment requires more time than I have. But it appears the 'weighting' has nothing to do with the removal of heteroskedasticity (i.e. weighting the error to make it homoskedastic), but more to do with a weighting process conducted on the data, in order for the sample to more accurately represent the population. I hope even if the statement I made is misguided, that it prompts thought/discussion. $\endgroup$
    – EB3112
    Nov 17 '20 at 22:18

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