<p>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 <em>wrong</em>, 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 <em>that</em> advanced of a topic tho, most undergraduate students who take a second econometrics course get to learn about robust tests and all that.</p>

CC BY-SA 4.0
2018-10-21T16:40:47.723Z
2018-10-21T16:40:47.723Z
Pedro Cavalcante
<p>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. </p>

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

CC BY-SA 4.0
2018-10-18T17:50:11.093Z
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.
mark leeds
CC BY-SA 4.0
2018-10-18T20:20:34.747Z
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?
Rainroad
CC BY-SA 4.0
2018-10-19T06:30:46.723Z
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.
mark leeds
CC BY-SA 4.0
2018-10-19T06:34:27.710Z
Note that,m above,  the assumption I'm suggesting to make is that only heteroscedasticity exists. I'm still assuming that the the error term is independent across observations. If both are not true, then things get way more complicated.
mark leeds
CC BY-SA 4.0
2018-10-19T12:36:18.213Z
Re the meaning of homogeneity in a regression context, [this question](https://stats.stackexchange.com/questions/96105/what-are-key-differences-between-homoscedasticity-and-homogeneity) on Cross Validated SE is relevant, especially answer by gung.
Adam Bailey
CC BY-SA 4.0
2018-10-19T17:04:36.220Z
Thanks Adam but, to be honest, I found the linked discussion unnecessarily confusing.  I assumed that, by "homogeneity", Rainroad  just meant constant variance across observations in a regression.
mark leeds
CC BY-SA 4.0
2018-10-20T01:38:36.387Z
Note that by constant variance across observations,  I mean that $\epsilon \sim N(0, \sigma^2)$.  and my assumption was standard fixed effects, classical OLS.
mark leeds
CC BY-SA 4.0
2018-10-20T01:39:17.370Z
My bad. it should be homoskedatiscity.
Rainroad
CC BY-SA 4.0
2018-10-20T02:43:06.713Z
no problem. I knew what you meant from context. and I think I remember having seen homogeneity used sometimes.
mark leeds
CC BY-SA 4.0
2018-10-20T02:50:49.520Z
@Rainroad: The specific bootstrap implementation required depends critically on the type of non-homogeneity you think there is but this link can atleast give you an idea of what bootstrapping is  about if you want to pursue it. http://statweb.stanford.edu/~tibs/sta305files/FoxOnBootingRegInR.pdf. Note that I'm assuming that  you're not familiar with boostrapping. If you are, then sorry for noise.
mark leeds
CC BY-SA 4.0
2018-10-20T03:37:47.110Z
Yes I am familiar with bootstrapping, but your document helps a lot! Thanks so much!
Rainroad
CC BY-SA 4.0
2018-10-20T03:40:27.150Z
on the same note, why is the assumption residuals are normally distributed needed for linear regression? Or is this purely for teaching's purpose too?
Rainroad
CC BY-SA 4.0
2018-10-20T06:00:23.187Z
that's less of an issue than changing variance but it too will cause bias in the t-test of the coefficients because normalty of residuals makes the t-test optimal.  If they're not normal, one can try various transformations of the response that end up making the residuals closer to having a normal distribution.. But any decent regression text should discuss this, I would think. Sanford and Weisberg wrote one. ( never read it ) John Fox text is decent and Draper and Smith text is well known. Reviews are subjective so best to check them out and see for yourself.
mark leeds
<econometrics><regression>
Linear Regression Assumptions of Homoskedasticity
Rainroad
# Linear Regression Assumptions of Homoskedasticity

(Asked by: username_0 on 2018-10-18)

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?

**Tags:** econometrics, regression
> **Comments:**
> **username_1**: 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.  
> **username_0**: 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?  
> **username_1**: 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.  
> **username_1**: Note that,m above,  the assumption I'm suggesting to make is that only heteroscedasticity exists. I'm still assuming that the the error term is independent across observations. If both are not true, then things get way more complicated.  
> **username_2**: Re the meaning of homogeneity in a regression context, [this question](https://stats.stackexchange.com/questions/96105/what-are-key-differences-between-homoscedasticity-and-homogeneity) on Cross Validated SE is relevant, especially answer by gung.  
> **username_1**: Thanks Adam but, to be honest, I found the linked discussion unnecessarily confusing.  I assumed that, by "homogeneity", Rainroad  just meant constant variance across observations in a regression.  
> **username_1**: Note that by constant variance across observations,  I mean that $\epsilon \sim N(0, \sigma^2)$.  and my assumption was standard fixed effects, classical OLS.  
> **username_0**: My bad. it should be homoskedatiscity.  
> **username_1**: no problem. I knew what you meant from context. and I think I remember having seen homogeneity used sometimes.  
> **username_1**: @Rainroad: The specific bootstrap implementation required depends critically on the type of non-homogeneity you think there is but this link can atleast give you an idea of what bootstrapping is  about if you want to pursue it. http://statweb.stanford.edu/~tibs/sta305files/FoxOnBootingRegInR.pdf. Note that I'm assuming that  you're not familiar with boostrapping. If you are, then sorry for noise.  
> **username_0**: Yes I am familiar with bootstrapping, but your document helps a lot! Thanks so much!  
> **username_0**: on the same note, why is the assumption residuals are normally distributed needed for linear regression? Or is this purely for teaching's purpose too?  
> **username_1**: that's less of an issue than changing variance but it too will cause bias in the t-test of the coefficients because normalty of residuals makes the t-test optimal.  If they're not normal, one can try various transformations of the response that end up making the residuals closer to having a normal distribution.. But any decent regression text should discuss this, I would think. Sanford and Weisberg wrote one. ( never read it ) John Fox text is decent and Draper and Smith text is well known. Reviews are subjective so best to check them out and see for yourself.  

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## 1 answers

### Answer by username_3 on 2018-10-21. Score: 1

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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