test for heteroskedasticity using robust regressions (rreg, robreg)

[Max Langer]

Hi everyone,

i got a problem regarding tests for heteroskedasticity. After running the robreg command, i would like to perform this test to further evaluate if i should include clustered standard errors on county level.

I guess my first question would be, if there is still a necessity to test for heteroskedasticity after using a robust regression. If no, there is no need to cluster.

If yes, i wonder how i can perform such test, because the tests i have seen so far do only work with the reg command (e.g. estat hetest).

Any help is highly appreciated!

Max

[Joao Santos Silva]

Dear Max Langer,

You can, and should, test for heteroskedasticity, and you can do it based on the OLS results. Heteroscedasticity is characteristic of the population, so it is independent of the estimator you use. However, the interpretation of the robust estimators you are using may depend on the presence of heteroskedasticity, so it is important to test for it and use suitable standard errors. BTW, I wonder what flavour of robust regression you are using and I would be interested to learn about your motivation to use it.

Best wishes,

Joao

[Max Langer]

Dear Joao,

thanks for the reply.

I am using robreg m, which is not up to debate for some reasons. The original motivation to use this robust regression was to control for outliers.

Now, I did tests for heteroskedasticity and these were positive.

If I understood the robreg command correctly, it implies robust standard errors (therefore, heterskedasticity should be already controled for). However, if I cluster the standard erros on county level, the results im interested in change from significant to insignifcant. Is there a way to tell which way is "better"? (FYI, there are other levels of clustering available, which also deliver different significance levels)

And, following that question, is it suitable to use bootstrapping instead?

Best regards,

Max

[Joao Santos Silva]

Dear Max Langer,

If that is the estimator you are using, you should probably read this. Anyway, clustering is not about heteroskedasticity but about independence; we would need to know much more about what you are doing to be able to advise.

Best wishes,

Joao

[Max Langer]

Dear Joao Santos Silva,

thanks again, and sorry for the confusion. Let me give a short overview of my data and the question im trying to answer. Basically, i am still trying to figure out what i should cluster over.

I got Panel Data from 2009-2017 consisting of 396 observations each year. Each municipality has the right to impose its own taxes. Most of these municipalities (374) are part of a county. The rest of the muncipalities are counties at the same time. So the latter counties consist of 9 observations, while a county with 10 municpalities consists of 90 observations.

Now what i would want to find out is what the legal status of a municipality (part of a county or a county itself) does to the tax rate of a municipality.

Does it make sense to cluster at county level? i feel like that is not the right way to do, because the tax rate is not correlated within these counties. In fact, municipalities are extremely heterogenous within counties (except when the municipality is a county itself). Also, there is no reason to believe that two municipalities which are equal in every aspect, but are located in different counties, may impose different tax rates. I believe that the tax rate highly depends on the centrality of a municipality, so my approach would be to cluster at that level, making it a total of 5 clusters (I know though, that this is not a sufficient number)

Depending on the cluster level, i get completely different standard errors. With cluster on county level, they are the highest.

If i believed that it is soley the legal status of a municipalty that is causing the different tax rate, wouldnt it make more sense to cluster over the legal status, so that there are only two clusters (again, this is by far not a sufficient number)?

Sorry for the long and detailed question, i also dont know if this is the right place to ask for such questions, Anyway, thanks for your time!

Best whishes,

Max

[Joao Santos Silva]

Dear Max Langer,

Thanks for the additional information. I guess that in this case most people would cluster at the municipality level, irrespective of whether it is one of many in a county, or the only one. That is, cluster at the tax setter level. BTW, if you are worried about outliers, I would recommend quantile (median) regression rather that a "robust" estimator of the mean (the mean is not a robust measure of location, so I find it difficult to interpret robust estimators of something that is not robust).

Best wishes,

Joao