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When I studied linear regression analysis, one of the assumptions taught was that of homoskedatiscity. I understood that homoskedasticity was required for significance testing on the coefficients. Then in my econometrics class, my professor said that we actually don't need homogeneity assumption since it was too strong. Instead, in order to conduct hypothesis testing on the coefficients, we could use "t-robust test" or Wald test.

So then why is homoskedasticity still widely assumed and taught in linear regression class? How do I reconcile these?

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  • $\begingroup$ Hi: it's taught that way because getting involved in teaching the wald lrt, lm tests and other robust tests iis a more advanced topic. for large n, the latter tests are better than the standard inference procedures ( like t-tests ) but not optimal theoretically so there are more difficulties teaching those topics. $\endgroup$ – mark leeds Oct 18 '18 at 17:50
  • $\begingroup$ I see. Whenever I look up "assumptions behind linear regression" online, the "homogeneity" assumption shows up. Is this because the default in statistical packages is to use t test? $\endgroup$ – Rainroad Oct 18 '18 at 20:20
  • $\begingroup$ That's probably largely the reason. But even the test of homog has its issues too. So, you have to test whether a test is valid, yet the former test probably has its own issues. So, it might be best to assume heteroscedasticity.. Usually, regression estimates are robust to heterosced. So, if you're really worried about the homog assumption, I would suggest dropping it and then either using 1) bootstrapping or 2) Halbert White's results for constructing a heterosced consistent covar estimate when there is heterosced. If you're interested in 1) or 2) I can try to think of references. $\endgroup$ – mark leeds Oct 19 '18 at 6:30
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    $\begingroup$ Re the meaning of homogeneity in a regression context, this question on Cross Validated SE is relevant, especially answer by gung. $\endgroup$ – Adam Bailey Oct 19 '18 at 12:36
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    $\begingroup$ My bad. it should be homoskedatiscity. $\endgroup$ – Rainroad Oct 20 '18 at 1:39
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For the same reason you're taught the very simple supply and demand model of perfect competition in econ 101. It's not that it's wrong, it's a simplification of the real world and a good place from where to start. Once you've mastered the basics, you can learn more advanced topics. Heteroskedasticity isn't that advanced of a topic tho, most undergraduate students who take a second econometrics course get to learn about robust tests and all that.

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