▁study ▁the ▁asympt otic ▁behavior ▁of ▁O LS , ▁and ▁in ▁which ▁the ▁number ▁of ▁observations ▁is ▁allowed ▁to ▁grow ▁to ▁infinity . Cor rect ▁specification . ▁The ▁linear ▁functional ▁form ▁must ▁co inci de ▁with ▁the ▁form ▁of ▁the ▁actual ▁data - gener ating ▁process . ▁ ▁Str ict ▁ex ogene ity . ▁The ▁errors ▁in ▁the ▁regression ▁should ▁have ▁conditional ▁mean ▁zero : ▁▁ ▁The ▁immediate ▁consequence ▁of ▁the ▁ex ogene ity ▁assumption ▁is ▁that ▁the ▁errors ▁have ▁mean ▁zero : ▁, ▁and ▁that ▁the ▁re gress ors ▁are ▁un cor related ▁with ▁the ▁errors : ▁. ▁ ▁The ▁ex ogene ity ▁assumption ▁is ▁critical ▁for ▁the ▁O LS ▁theory . ▁If ▁it ▁holds ▁then ▁the ▁re gress or ▁variables ▁are ▁called ▁ex ogen ous . ▁If ▁it ▁doesn ' t , ▁then ▁those ▁re gress ors ▁that ▁are ▁correl ated ▁with ▁the ▁error ▁term ▁are ▁called ▁end ogen ous , ▁and ▁then ▁the ▁O LS ▁estimates ▁become ▁invalid . ▁In ▁such ▁case ▁the ▁method ▁of ▁instrument al ▁variables ▁may ▁be ▁used ▁to ▁carry ▁out ▁inference . ▁▁ ▁No ▁linear ▁dependence . ▁The ▁re gress ors ▁in ▁X ▁must ▁all ▁be ▁linear ly ▁independent . ▁Mathemat ically , ▁this ▁means ▁that ▁the ▁matrix ▁X ▁must ▁have ▁full ▁column ▁rank ▁almost ▁surely : ▁▁ ▁Usually , ▁it ▁is ▁also ▁assumed ▁that ▁the ▁re gress ors ▁have ▁finite ▁moments ▁up ▁to ▁at ▁least ▁the ▁second ▁moment . ▁Then ▁the ▁matrix ▁ ▁is ▁finite ▁and ▁positive ▁semi - defin ite . ▁When ▁this ▁assumption