Transcription of Endogenous - nyu.edu
1 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.
2 Xsaretheexogenousorpredeterminedvariable s. and , ; ,thenthesystemofequationsisidenti ,thentheequationisunidenti edorunderidenti edandunderidenti edmeanthesamething,theyaresynonyms! ed(unidenti ed). cation: M=numberofendogenousvariablesinthemodel. m=numberofendogenousvariablesinagivenequ a-tion. K=numberofexogenousvariablesinthemodel. k= ,butnotsu cient,conditionforidenti cation,theyshouldnotbereadlit-erallytoin dicatethatthemodelisnecessarilyidenti ed.(1)InamodelofMsimultaneousequations,i norderforanequationtobeidenti ed,itmustexcludeatleast(M-1)variables(ex ogenousorendogenous)appearinginthemodel.
3 (Gujarati, )(2)InamodelofMsimultaneousequations,ino rderforanequationtobeidenti ed,thenumberofexoge-nousvariablesexclude dfromtheequationmustbenotlessthan(thenum berofendogenousvariablesincludedinthateq uationminus1);thatis:K k m 1(1)(Gujarati, )7 TheRankConditionTheRankconditionisnecess aryandsu cientforidenti- ,anequationisidenti edi atleastonenonzerode-terminantoforder(M-1 )(M-1)canbeconstructedfromthecoe cientsofthevariablesexcludedfromthatequa -tionbutincludedinotherequationsinthemod el.(Gu-jarati, ) ,codeavalueof1wheretheithvariableisinclu ded, ,thenthegthequationisidenti , , (Gujarati, ) k>m 1andtherankofthematrixAisM 1,theequationisoveriden-ti k=m 1andtherankofthematrixAisM 1,theequationisexactlyidenti k m 1andtherankofthematrixAislessthanM 1,theequationisunderidenti ed(notidenti ed).
4 K<m 1,theequationisunderidenti ed(notidenti ed).10 SupplyandDemand:Dt= 0+ 1Pt+ 1tQSt= 0+ 1Pt+ 2t11
![SFPE Equation Sheet [KL 10-19-2015]](/cache/preview/c/f/3/c/2/1/e/4/thumb-cf3c21e48064d8fdafc6507dedc08886.jpg)
