b=(X'X)^{-1}X'Y \\ =[(X^*+u)'(X^*+u)]^{-1}(X^*+u)'( X^* \beta + \epsilon +v ) \\ =( (X^*)'(X^*) +u'u )^{-1}( (X^*)'(X^*) \beta+ u'u \beta -u'u \beta ) \\ =\beta [I -( (X^*)'(X^*) +u'u )^{-1}u'u ]
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