ECO375F - 2.4 - Unbiasedness of the Intercept Estimator (β0)

[@Alvaro-ph8nz]

Oh man, I love you. You literally explained in 6:27 minutes what my econometrics teacher couldn't explain well in 1 hour and a half. Thank you!

[@RemiDav]

Love you too ! 😋 I figured out that why most people hate stats/metrics is that they were in classes where the teacher focuses just on the math and goes too fast, providing 0 intuition. I'm glad I could help.

[@rorisanglesaoana3044]

Very insightful, thank you a thousand times.

[@rushy9895]

This is super helpful. You earned yourself a subscriber

[@uns6454]

Sir, could you explain why u bar is not equal to zero at 0:44? I thought E(y)=E(β0 + β1xi + ui) = E(β0) + E(β1xi) + E(ui) = β0+ β1x̅ since E(ui)=0. Thanks in advance!

[@RemiDav]

E(u_i) is not the same as u_bar, one is the population mean, the other the sample mean. You are right that E(u_i)=0, but that doesn't imply that the sample mean will be zero too.

[@josearturogf]

thanks. subscribed!

[@jananisreeganesh]

Thank you so much for these wonderful videos! And I have a query, is it compulsory to check for unbiasedness of the estimated parameters before moving on to calculate the variance and S.E.?

[@RemiDav]

It really depends. Usually you prefer unbiased estimators. But sometimes you might prefer a biased one. For instance suppose you have 2 estimators A and B. Estimator A is unbiased but the SE is very large (e.g. 10). Estimator B is a bit based (on the order of 0.1) but SE is very low (e.g 1). In that case you might prefer estimator B, because, even though you know that you make an error on average, it is so small and the estimator is so much more accurate (low SE) that it is a lot better than the unbiased one. There is another criterion to select estimators called Mean Integrated Squared Errors that takes into account both the Bias and Variance of the estimator. I hope this answers your question.

[@jananisreeganesh]

Yes! Thank you very much :)

[@andredevera1827]

why use the conditional expectation? thanks.

[@EconometricsAndAnalytics]

I am sorry but I do not really understand your question. It is very large, a bit like asking "why use an addition". The conditional expectation is a tool that is useful and appropriate to use here. It might be a bit confusing to understand how it works if you are not used to it. Maybe watching videos on conditional expectations would help. I have one here: kzbin.info/www/bejne/j5Wyi6WXbJaNY9E If it is still confusing, maybe check youtube channels on probability and statistics (or Kahn Academy). Good luck !

[@andredevera1827]

Thank you very much! You are such a big help!!