Question

1. Consider a regression model Yi = x;ß +ei, i = 1,...,n. You estimate this model using the OLS estimator. (a) Present and discuss assumptions for the OLS estimation.

Answer 1

The Assumptions for the OLS (Ordinary LEast Squares) are:

1) The regression model should be linear in parameters. This condition is fulfiled.

2) The expected value of stochastic term should be zero.This may not be always true.

3) The error term is homoskedastic i.e. the variance is same for the whole sample.

4) The correlation between x variable and error term should be zero. But this condition may not fulfiled here.

5) There should be no autocorrelation among the disturbance. This is true for the given model.

6) The error term should be normally distributed with mean zero and variance equal to 1. This condition is satisfied in the model.

7) There should be no specification biased in the model. This may or may not be true in the model as the intercept has been dropped. There should be a robust argument in favor of dropping such a crucial parameter from the model.

The regression in (= 1 1 ...im 1 yi=xi ßtei OLS model La ruim 2 yi-xib) -- < Cy;22B ! +B? Exiy (B is constant {Bxi = B Exi) L=&y,²_ zßExi'yi + B² Exit differentiating with respect to B - - 2 Exi'yi + 2B Exiao . Exil +2 Exilli=+zB B. = {xilli X12کے Scanned with CamScanner