Random Effects Estimator - an introduction

[@juancarlosmatosgarcia960]

you have helped me throuugh all my courses of economietrics, I am infinitely in gratitude wit you

[@JMRG2992]

Mate, one question, what is the intepretation of B1 in a random effect model Yit = B0 + B1Xit + b2Zit +c+u ? i haven't been able to find the interpretation of the estimator anywhere. so it implies a change on Xit produces B1 change in Yit... or how?

[@lastua8562]

@@JMRG2992 Mate the way he wrote the comment it is unlikely he would respppond! I guess it is the same as OLS since alpha is assumed to be somewhat irrelevant (i.e. countries are homogenous in the independent variable we are trying to estimate). Did you find your answer?

[@JMRG2992]

@@lastua8562 Well, I did require it for my barchelor thesis in economics, but the interpretation of betha remains the same, by an increase of 1 unit, there's a change in b units, ceteris paribus, (and here's the new trick for random effects), in average across countries in time.

[@xiaolu8334]

Thank you, Ben. Clear and inspirational explanation.

[@etibo]

You should get my teacher's salary.

[@m.wufuer2610]

Etienne Grenier 🤝

[@we_love_ji]

very much agreed.

[@enteetne6704]

This also counts for binary and multinomial logit models right? If my DV is either 1 or 0 and my IVs are both continuous or binary.

[@Swetter1000]

But when you calculate the covariance of the errors, wouldn't subtract the mean alpha_i from the alpha_i (covariance formula) which gives 0 as alpha_i is constant? And thus get a covariance = 0?

[@bouguenadrien1278]

Thanks for this again very clear video on RE. You are doing a fantastic job here! About the assumption for the consistency of the RE, you mention that it might hold if all factors are being controlled for. But is it the case that if you include more control variables in the regression, then these will also need to be uncorrelated with the alpha_i and hence would make this assumption even less likely? I am still looking for a situation where this assumption would be valid... Best

[@alexmarsh8464]

I know this is a year old, but I too had a similar thought. Imho, the best examples of random effects being valid are in actual random expirements. The fertilizer example is a great one. Different types of fertilizer is placed on different fields randomly. However, due to randomness in measurement error (the amount placed on each field) or just in soil quality, some fields might produce more or less yield independent of the brand or quality of the fertilizer used.

[@TheRealDCoy]

This is wonderful, thanks. One question, though. Should we be talking about Cov(alpha_i, X) or even Cov(alpha_i, X_i) instead of Cov(alpha_i, X_it)? Or have I misunderstood something about the notation?

[@wanjadouglas3058]

Forever grateful 🌻

[@TheMagic0wnz]

if alpha_i is a constant how can it have a variance?

[@MyMpc1]

+Bob S I am also wondering this vary same thing! I've also read alpha_i being described as 'time invariant'.

[@SpartacanUsuals]

+MyMpc1 Thanks for your message. Something can have a variance if it varies. Whilst alpha_i is time invariant, it varies with i - the cross sectional unit. This variance across cross sectional units is what we are representing by allowing it to be a random effect. Does that make sense? Best, Ben

[@MyMpc1]

+Ben Lambert Ahhhh I see it now! Thanks so much for your quick reply and answering my question ;-)

[@niccolomurtas3691]

@@SpartacanUsuals Thank you for your videos sir. However, I'm still struggling to understand your answer to this sub-question. The thing is, here we are actually considering the covariance between the unobserved heterogeneity of unit i at time t and unit i at time t+1. This heterogeneity is for the same unit, is time-constant, and we are considering it at the two times. It shall be reasonable to assume that, conditional on such heterogeneity being for the same unit, there is not such covariance (or variance) between the same unobserved heterogeneity at two different point in time. Am I getting it wrong? Am i wrong in A- thinking that you are considering the possibility of what can be stated as an "autocorrelation" of the unobserved heterogeneity, but also B- that these same unobserved heterogeneity at two different point in times shall not vary at all? thank you for your videos, they are great.

[@misi7259]

clear and direct, Thank you so much!!!!!!!!!!!!!!

[@louisaerts927]

If eit and eis were correlated, would we then use a random effects estimator with cluster-robust standard errors?

[@JMRG2992]

What is the interpretation of b1 (crime rate) in random effects ? By the increase of 1% in the crime rate over the time, the house price increase by B1 ceteris paribus ?

[@TheShushanmargaryan]

Hi Ben. When you mention that POLS has the problem of serial correlation of the error term, would not clustering solve this problem ? Thanks

[@lastua8562]

I am not sure about clustering here, though I thought of using SC robust SE. Did you find the answer?

[@rexevan6714]

So Random Effect is basicly FGLS for Pooled OLS, right?

[@lastua8562]

I think pooled OLS is only one possible random effects estimation. We use fGLS to correct for SC. Did you find a different answer?

[@mehradghazanfaryan640]

You are the best

[@kulsoomabid7379]

plz share the procedure of estimating the parameters by using the linear model keeping the explanatory variable random..kindly help ....

[@dimasmukhlas3952]

Thanks Ben!

[@Michael-yu9ix]

I don't understand why the error term still consists of alpha if we assume that all factors have been controlled for.

[@eepaul1981]

awesome. very understandable. Thank you!!!!!

[@simonmartin5704]

Dude you rock. Thank you.

[@szpacur]

champion

[@kangtoby]

you are godlike

[@drewbryk]

so random XD