Heteroskedasticity consistent (robust) and cluster robust standard errors

[@Eijgey]

One of the best teachers I have found to date together with Ben Lambert regarding econometrics (surpassing my own teachers far and wide). Your videos are very easy for me to follow and understand why what you are discussing is important & in which scenario. Thanks alot for taking the time to make this Mikko, it has helped me out alot!

[@mronkko]

Thanks. I have spent a lot of time with Ben Lambert's videos too. A funny fact: I have never taken a single course in econometrics. Beyond being entrepreneurship professor, I consider myself more of an applied research methods scholar than an econometrician.

[@datoubi]

cheers mate, you helped me. first guy who watched this but you helped me on my thesis with this

[@ivancabanillas3486]

When I was a student, I found Mikko's input to be great; he provides a fresh perspective on each topic at an intermediate level, but easy to understand. Now that I'm a teacher, he helps fill in the gaps in the textbooks; even basic texts often say "as the reader can anticipate, from this expression comes another"... but that is sometimes not easy even for teachers. Thanks Mikko, I'm your fan

[@mronkko]

Thanks a lot!

[@mustafizurrahman5699]

Mesmerizing explanation with simple mathematics and equations

[@mronkko]

You are welcome!

[@yashij8546]

Hi. This video is very helpful. I know not everyone wants to go through the math but they are also people who will feel so good and inspired ones they understand the mechanism. That’s why i’m so glad there’s someone like you to provide such lectures. Thanks.

[@mronkko]

You are welcome. I think that knowing the math in this case is useful because it will help you to understand in which cases the Session might be biased.

[@ethanthealien]

I had an ah! moment after watching this video. Thank you professor Mikko!

[@joyjunial1080]

Thanks, Mikko. I wish I was aware of this long time ago. Questions: 1. Assume we have OLS with dummy regressors only. There are applications of such regressions in practice. Does this H-consistent std errors hold up? Can they still be trusted to deliver robustness? 2. Assume the same regression as in '1'. If the problem is autocorrelation, can the H_consistent std errors deliver the robustness solution, reliably? Thanks again for opening the regression box for me.

[@joyjunial1080]

@@mronkko Thanks for response. A) I think this error may be application specific. My regression is as per 1. If I select 'cluster' robust option in Eviews I get: "Invalid specification for cluster series". B) Just a comment: Should you consider doing part 2 of this good learning please note - On the menu of robust std errors, there is many combinations of options in different softwares. We can start at random with EVews (ok, not robust random). It will be nice to have some kind of "rule of thumb" on choosing the appropriate set as appropriate. Thanks.

[@microeconomia2561]

Very interesting presentation and conference!

[@avalianiii]

Thanks! Your videos are great! but could you increase the volume please? Should be very easy to fix, while it diminishes the quality very much.

[@mronkko]

One would think that this is easy to fix, but unfortunately it is not. KZbin does not provide any tools to adjust volume of uploaded videos so the only way to adjust would be to reupload a video. It would probably take about 30 minutes for each video and I have 200+ videos which means about 3 weeks of work. That being said, all new material that I upload will have better audio levels.

[@SamirNeg]

Really helpful stuff mate

[@unknown-zx2df]

Thank you very much for your detailed explanation! I still have one questions. When I use Cluster robust standard errors, do they also adjust for heteroskedasticity? Maybe I was missing the point, but I hope you can clear me up

[@mronkko]

Yes, they do. The heteroskedasticity consistent SEs are a special case of cluster robust SEs.

[@Dawg_from_Hell]

Thank you for the videos. In the cluster robust standard errors section of the video, when looking at d_i and u_i, it looks like you’re treating d_i as a random variable. However, you’d previously mentioned that the X variables are considered fixed and not random. Can you explain which assumption holds for this derivation?

[@mronkko]

Where in the video do I use the term "fixed variable"? I cannot find it from the transcript. The assumptions of consistency of these SEs are 1) clusters are randomly sampled, 2) we have a random sample from each cluster, 3) no perfect collinearity of X, 4) linear model, 5) no endogeneity, X and u are uncorrelated. The assumptions can be stated in a few different ways.

[@krishnaiyer2556]

excellent sir. little complicated though. request you to simplify things both derivationwise and also matrix algebra but nonetheless value worth the effort

[@mronkko]

Yes, it is a bit complicated. The context for which I produced this video is an advanced course, where students have already studied two semesters with me. I have simpler explanations of heteroskedasticity and non-independence of observations, where I explain why they are problems for regression. In these videos I tell the students to apply robust SEs and this video is just about what exactly robust SEs do.

[@mattsisco4676]

Great video, thanks!

[@mronkko]

You are welcome.

[@fadijasmin1]

thank you very much

[@mronkko]

You are welcome

[@chaos2437]

I got a question, why the mean of y is equal to 0 which is 6:35 in the video?😵‍💫

[@mronkko]

The mean of y is not zero. sum (x_i-x-bar)y-bar is zero. This is because differences from mean (x_1-x-bar) sum to zero and we multiply that with constant y-bar. I agree that I am not 100% clear on this in the video.

[@yannicknovacek5566]

Thank you

[@mronkko]

You are welcome!

[@four9397]

Do you mean Homoscedasticity?

[@mronkko]

I am not sure what you mean with the comment. The video is about SEs that are consistent under heteroskedasticity. If you have homoskedastic and independent errors, you can use normal SEs.

[@johnspivack]

Overall you are an excellent teacher, thank you. But I have problems with this video. Your explanation of heteroskedasticity robust standard errors is great. But for cluster robust standard errors, your notation is very confusing. You don't clearly specify the data layout. Which index is for clusters, which index is for items within each cluster? You don't clearly define the X matrices or show their components. This is too confusing, sorry. It is not too hard to see the cluster robust standard errors as some kind of generalization of the heteroskedasticity case, but where you use the empirical variance in each cluster... but instead you go through a lot of unclear algebra where the meanings of the i and j are not fully clear and the covariance formulas appear strange Last time I checked var(a+b)= var a + var b + 2 cov(a,b). That doesn't seem to hold in your formulas. Please explain. Sorry for any misunderstanding, but I am likely not the only one. Thanks. ?

[@mronkko]

I agree that I could have explained the indexing of the data better. The context is that i referst to a case in the data. In the cluster robust SE case, the data are indexed by i and t, which refers to repeated observations. The u^_i in the cluster robust SE formula is the residual vector for case i. That is, i is the cluster index variable. Can you be more specific about "covariance formulas appear strange" part. I do not see where the variance of of sum equation would not hold in my presentation.

[@johnspivack]

@@mronkko Hello Professor, Thanks for being so responsive to feedback. I looked at it again, and still have real problems with your discussion of clustered standard errors. I believe from about 16:56 onward you are trying to establish the results given in the last two paragraphs here: en.wikipedia.org/wiki/Clustered_standard_errors I think the Wikipedia article is fairly clear and uses good notation. In the context of your presentation the clustered standard error formula would seem like straightforward generalizations of the previous formula dealing with heteroskedasticity in a univariate case. The transition is by substituting the outer product of vector u's instead of using the single scalar u's. The vector u's in the cluster setting now correspond to all the observations within a cluster, and sums are then of these outer products over the clusters to produce a variance estimate. I don't follow your explanation from 16:56 onward. I don't understand your i and j indices at 18:47 and 19:24, for instance, and how the discussion seems to alternate between vector u's (in bold) and their scalar components (non-bold). In your previous answer to me above you claim that i is the index for cluster and t is the index for components or individuals within cluster, but I don't see any t index as notation introduced in your slides. I think it would help to be clear about what the cluster structure is and which variable indexes the cluster as opposed to individual components of a u vector. I also don't see the motivation of avoiding matrix notation as much as you do, here it is fundamental to the expressing this content. In general I'm a fan of this channel and have found other videos to be really excellent. Apologies for anything I've misunderstood or mischaracterized here. Sincerely, John

[@mronkko]

@@johnspivack Thanks for the feedback. I am about to start a course where I use this video and might retake it soon because I do not explain the effects of samplep size as well as I could. Also, I agree that my choice of indexing is confusing. I mentioned i and t indices because those are used in Wooldridge 2002 from which the equation 7.26 comes from. The t index is not used in the equation because t indicates row of u-vector. So in vector equations i refers to a cluster. I scalar equations i and j are indices that indicate an observation. I agree that this is super confusing particularly that I do not explain my indexing choice. The reason why I switch to scalar notation is that that my students are much more used to reading that than vectors. Thus, my aim is to explain the matrix equation in scalar terms. Does this clarfy?

[@johnspivack]

@@mronkko I'm not sure, Professor. I think it is important to choose the clearest and most intuitive notation and to explain it fully, even if it takes an extra slide or two. In that matter I think the Wikipedia article has good notation, clearly explained. It is also the traditional notation used in biostatistics. I am not familiar with economics literature. I also think the explanation is important. Around 16:45 you talk about multiplying values across different individuals. This confused me at first because it wasn't fully clear you meant th clusters you were speaking of consisted of different individuals, I am more accustomed to correlated measurements on a given individual (cluster= individual), in which case different individuals would not be correlated . To make a long story short, clear notation, clear explanation, etc. would help students a lot. Perhaps the slides could be edited. Thanks very much for being open to feedback. Sincerely, John P.S. As for myself, I'll be fine. I got my PhD 10+ years ago, and they can't revoke it just for making annoying comments on other people's YT!

[@mronkko]

@@johnspivack Thanks for the feedback. I included it in my slide notes and will probably redo the video a bit later this fall. I agree that in this case more explanation definitely would be better.