4. Consider the model y = XB+ u, where X is an (nx1) vector and all...

 

Transcribed Image Text:

4. Consider the model y = XB+ u, where X is an (nx1) vector and all the standard assumptions above are satisfied. The problem in this model is that X is not observed. Instead, a variable with a measurement error, X, is observed, that is, X=X+e. Thus the observed model is y=X'B+(u- eß)= XB+v. (Xu) = =plim (X'=)= plim(eu)=0, n n (X) = Q n plim X'X matrices. (a) Let us assume that plim im (1²) = Q Qce where Q and Q are finite positive definite ce =Q₁, and plim Show that the OLS estimator of the observed model, B=(X'X') 'X''y, is inconsistent. [10] 4. Consider the model y = XB+ u, where X is an (nx1) vector and all the standard assumptions above are satisfied. The problem in this model is that X is not observed. Instead, a variable with a measurement error, X, is observed, that is, X=X+e. Thus the observed model is y=X'B+(u- eß)= XB+v. (Xu) = =plim (X'=)= plim(eu)=0, n n (X) = Q n plim X'X matrices. (a) Let us assume that plim im (1²) = Q Qce where Q and Q are finite positive definite ce =Q₁, and plim Show that the OLS estimator of the observed model, B=(X'X') 'X''y, is inconsistent. [10]