Sample Properties of the Least Squares and Instrumental Variables Estimators

Large-Sample Properties of the Least Squares and Instrumental Variables Estimators 

For the classical regression model y = XP + with no constant term and K regressors, what is 

be the rth residual in the ordinary least squares regression of y on X in the classical regression model and let s, be the corresponding true disturbance. Prove that plim(e, - e,) = 0. 

For the simple regression model, v, u + s s, N(0,a2), prove that the sample mean is consistent and 

For the model in (5-25) and (5-26), prove that when only x is measured with error, the squared correlation between y and x is less than that between y and x. (Note the assumption that y = y.) Does the same hold true ify is also measured with error  

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