Fixed Effects and First Differences comparison - part 1

This video explains some of the differences between Fixed Effects and First Differences estimators, indicating when it is preferable to use one over the other.
Check out oxbridge-tutor.co.uk/undergrad... for course materials, and information regarding updates on each of the courses. Check out ben-lambert.com/econometrics-... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.com/bayesian/ Accompanying this series, there will be a book: www.amazon.co.uk/gp/product/1...

[@lauragonzalez5584]

Why do we see efficiency in fixed effects? (I understand why there's a loss of efficiency in the case of first differences) But I don't know how to derive it

[@user-vm5el4zq6i]

Hi, do we need to conduct an Hausman test when using the first differences method ?
Thanks !

[@zues69696]

Hey man how did you get Var[u_i,t-1] = -.5?

[@brianathomas1661]

+Zues Sixtyne
First, for each t > 1, Var(Δui,t) = Var(ui,t - ui,t-1) = Var(ui,t) + Var(ui,t-1) = 2σ^2, where we use the assumptions of no serial correlation in {ut} and constant variance. Next, we find the covariance between Δuit and Δui,t+1. Because these each have a zero mean, the covariance is E(Δui,t⋅Δui,t+1) = E[(uit - ui,t-1)(ui,t+1 - ui,t)] = E(ui,t ui,t+1) - E((ui,t)^2) - E(ui,t-1 ui,t+1) + E(ui,t-1 uit) = −E((ui,t)^2) = -σ^2 because of the no serial correlation assumption. Because the variance is constant across t, Corr(Δui,t, Δui,t+1) = Cov(Δui,t, Δui,t+1)/Var(Δui,t) = -σ^2/2σ^2 = −.5.

[@mostafasaleh8158]

hi
do we use first difference when determining FE,RE and PRM or at level
regards

[@fur1ous112]

5:44 why - 0.5?

[@mitchellharding2423]

Beeta 1

[@StayForTheFireworks]

lol