Talk:Heteroskedasticity-consistent standard errors
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When the error terms do not have constant variance (i.e., the assumption of {\displaystyle \operatorname {E} [uu^{\operatorname {T} }]=\sigma ^{2}I_{n}}{\displaystyle \operatorname {E} [uu^{\operatorname {T} }]=\sigma ^{2}I_{n}} is untrue),
[edit]Is this statement an if and only if? 68.134.243.51 (talk) 19:56, 23 August 2022 (UTC)
Do heteroskedastic SEs constitute model mis-specification?
[edit]The final paragraph, that heteroskedasticity most often is due to model mis-specification seems very strong to me for a lot of data structures, at least those being used in (micro-)economics. I would consider either removing or substantially softening the imperative presented in it. Instead the paragraph should point out that in some cases, the heteroskedasticity could be removed by considering alternative specifications instead.
While it is true that often transformations are appropriate (log specifications) or additional polynomial terms should be included. In particular, recent quasi-experimental approaches to Causal inference, especially those based on potential outcomes, are explicitly Reduced form. While correct specification of variables to avoid heteroskedasticity is clearly desirable, this is secondary to the specification fulfilling the identifying assumptions of the Causal Inference method. Furthermore, some phenomena are likely to be inherently heteroskedastic or close to it. Instead of oversaturating the regression, or going all in with possible specification of the variables, the use of robust standard errors (or weighted / adaptive least squares) seems very acceptable to me. Finally, it is likely to fall into the trap of pretesting (if the inference method is based on a test of the inference method's validity, due to false discoveries, the test size is usually distorted), if users start to amend their regression until it happens to be homoskedastic. Instead, heteroskedastic standard errors should be the inference norm. Oragonof (talk) 21:04, 10 December 2022 (UTC)