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Endogenous - nyu.edu
NotesonIdenti cationMostlyFromGujarati,BasicEconometri cs,Chapter19 Copyright-JonathanNagler;April11,2001Un- identi ed:Wecannotdeterminethevaluesoftheparame tersofthemodelbasedonwhatweobserve( ,basedonthedatathemodelgenerates).Themod eldescribeshowthedataaregenerated(orhowt heendogenousvariablesaregenerated).Anuni denti edmodelisnotidenti edevenifitgeneratesanin :Theseare`jointlydependent'variables;or, , :Ct= 0+ 1Yt+ tYt=Ct+ItReducedForm:Substitutethe rstequationintothesecondequation:Yt= 0+ 1Yt+ t+ItYt 1Yt= 0+ t+ItYt(1 1)= 0+It+ tYt= 01 1+11 1It+ t1 1Yt= 0+ 1It+!twhere: 0= 01 1 1=11 1!t= t1 13 Ifthemodelisidenti ed,wecanestimatethestructuralcoe cientsfromthereducedformcoe 12Y2t+:::+ 1 MYMt+ 11X1t+ 12X2t+::: 1 KXKt+u1tY2t= 21Y1t++:::+ 12 MYMt+ 21X1t+ 22X2t+::: 2 KXKt+u2tYMt= M1Y1t+ M2Y2t+:::+ M 1;MYM 1;t+ M1X1t+ M2X2t+::: MKXKt+uMt Ysaretheendogenousvariables.
The Order Condition This is a NECESSAR Y, but not su cien t, condition for iden ti cation. The follo wing t w o statemen ts are equiv-alen t. These are statemen ts for meeting
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