▁the ▁C ram ér – R ao ▁bound ▁for ▁variance ) ▁if ▁the ▁normal ity ▁assumption ▁is ▁satisfied . ▁▁ ▁General ized ▁method ▁of ▁moments ▁ ▁In ▁i id ▁case ▁the ▁O LS ▁estim ator ▁can ▁also ▁be ▁viewed ▁as ▁a ▁G MM ▁estim ator ▁ar ising ▁from ▁the ▁moment ▁conditions ▁▁ ▁These ▁moment ▁conditions ▁state ▁that ▁the ▁re gress ors ▁should ▁be ▁un cor related ▁with ▁the ▁errors . ▁Since ▁x i ▁is ▁a ▁p - vector , ▁the ▁number ▁of ▁moment ▁conditions ▁is ▁equal ▁to ▁the ▁dimension ▁of ▁the ▁parameter ▁vector ▁ β , ▁and ▁thus ▁the ▁system ▁is ▁exactly ▁identified . ▁This ▁is ▁the ▁so - called ▁classical ▁G MM ▁case , ▁when ▁the ▁estim ator ▁does ▁not ▁depend ▁on ▁the ▁choice ▁of ▁the ▁weight ing ▁matrix . ▁ ▁Note ▁that ▁the ▁original ▁strict ▁ex ogene ity ▁assumption ▁ ▁implies ▁a ▁far ▁rich er ▁set ▁of ▁moment ▁conditions ▁than ▁stated ▁above . ▁In ▁particular , ▁this ▁assumption ▁implies ▁that ▁for ▁any ▁vector - function ▁ ƒ , ▁the ▁moment ▁condition ▁ ▁will ▁hold . ▁However ▁it ▁can ▁be ▁shown ▁using ▁the ▁G auss – Mark ov ▁theorem ▁that ▁the ▁optimal ▁choice ▁of ▁function ▁ ƒ ▁is ▁to ▁take ▁, ▁which ▁results ▁in ▁the ▁moment ▁equation ▁posted ▁above . ▁▁ ▁Properties ▁▁▁ ▁Ass um ptions ▁▁ ▁There ▁are ▁several ▁different ▁frameworks ▁in ▁which ▁the ▁linear ▁regression ▁model ▁can ▁be ▁cast ▁in ▁order ▁to ▁make ▁the ▁O LS ▁technique ▁applicable . ▁Each ▁of ▁these ▁settings ▁produces ▁the ▁same ▁formulas ▁and ▁same ▁results