EC2020 Econometrics I: Christmas Project This is the project for this module that counts 60%. All questions carry the same weight.The submission deadline is 3:00pm, Tuesday 12th of January 2021. Collusion and plagiarism will not be tolerated, and punished ruthlessly according to the strict University regulations on academic integrity.
1. Consider the following model:yi=α+βxi+i;i= 1,2,···,n(1)where xiis fixed in repeated sampling, and the random disturbance termi satisfies the usual assumptions of E(i) = 0∀iE(2i) =σ2∀iE(ij) = 0∀i6=j Let ˆα andˆβ denote the ordinary least squares (OLS) estimators ofαandβ, respectively. There is no need to derive the least squares estimators for this question. Also, let ˆy ide note the fitted value of y i obtained by the least squares estimation.a) Show that n∑i=1ˆyi=n∑i=1yi.(2)[30%]b) Show that E[(ˆβ−β)] = 0where=1nn∑i=1i.(3)[30%]c) Find the covariance between ˆα andˆβ.
