复旦大学计量经济学讲义08横截面时间序列模型

8.18.1()independentlypooledcrosssectionOLSBreush¡PaganWhiteWhiteR2N£R2»Â2kFWLSOLS8.2()F=SSR¡(SSR1+SSR2)SSR1+SSR2£n¡2(k+1)k+18.3():yit=¯0+±0dt+¯1xit+®i+uitunobservede®ect¯xede®ectunobservedheterogeneityidiosyncraticerroetime-varyingyit=¯0+±0dt+¯1xit+vitvit=®i+uit-145-8.1vitcompositeerror8.4()OLSheterogeneitybias8.5()NTAR1FGLS½Cochrane¡OrcuttestimationPrais¡Winstenestimation(1¡½)1=2®ifixedeffectstransformationyit=¯1xit+®i+uiti¹yi=¯1¹xi+®i+¹ui(8-1)time¡demeaneddata:yit¡¹yi=¯1(xit¡¹xi)+uit¡¹ui(8-2)Äyit=¯1Äxit+Äuit(8-3)withintransformaitonOLSfixedeffectsestimatorwithinestimator(8-3)OLStimevariation(8-1)OLSbetweenestimatoryxyx8.6()dummyvariableregression:i²¯j²yit=¯0+¯1xit+®i+uitFEFD®i®i®iCov(xitj;®i)=0-146-randomeffectsmodel®i¯jvit=®i+uitCov(vit;vis)=¾2a¾2a+¾2ut6=sOLSyit=®it+xit¯it+uit;i=1;¢¢¢;N;t=1;¢¢¢;T(8-4)NT(k+1)+N(NT(k+1)+T)NTNTyt=®+Xtb+ut(8-5)yi=®+xib+ui(8-6)N®¯(8-5)²pooledregressionmodel(8-7)²individual¡meancorrectedregressionmode(8-8)²unrestrictedmodel(8-9)yit=®+xit¯+uit;i=1;¢¢¢;N;t=1;¢¢¢;T(8-7)yit=®i+xit¯+uit;i=1;¢¢¢;N;t=1;¢¢¢;T(8-8)yit=®i+xit¯i+uit;i=1;¢¢¢;N;t=1;¢¢¢;T(8-9)8.2yit®i¯i(8-9)Wxx;i=TPt=1(xit¡¹xi)0(xit¡¹xi)Wxy;i=TPt=1(xit¡¹xi)0(yit¡¹yi)Wyy;i=TPt=1(yit¡¹yi)0(yit¡¹yi)-147-8.3¹xi=1TTPt=1xit¹yi=1TTPt=1yit(8-9)S1=NXi=1RSSi=NXi=1(Wyy;i¡W0xy;iW¡1xx;iWxy;i)(8-10)(8-8)Wxx=NPi=1Wxx;iWxy=NPi=1Wxy;iWyy=NPi=1Wyy;i(8-8)S2=Wyy¡W0xyW¡1xxWxy(8-11)(8-5)Txx=NPi=1TPt=1(xit¡¹x)0(xit¡¹x)txy=NPi=1TPt=1(xit¡¹x)0(yit¡¹y)tyy=NPi=1TPt=1(yit¡¹y)2¹x=1NTNPi=1TPt=1xit¹y=1NTNPi=1TPt=1yit(8-5)S3=tyy¡t0xyT¡1xxtxy(8-12)(1)S1=¾2u»Â2[N(T¡k¡1)](2)S3=¾2u»Â2[NT¡(k+1)](S3¡S1)=¾2u»Â2[(N¡1)(k+1)](3)Â2[NT¡(k+1)]S1=¾2uF2=(S3¡S1)=[(N¡1)(k+1)]S1=[NT¡N(k+1)]F1=(S2¡S1)=[(N¡1)k]S1=[NT¡N(k+1)]8.38.7()PanelDateYitit-148-BhargavaBhargavaetal;1982DWAbuafJorion1990SUR(seeminglyunrelatedregression)GLSSUR¡DF(1)(2)(3)Yit=®+¯Xit+iti=1;2;¢¢¢;Nt=1;2;¢¢¢;T(8-13)8.1Yit=®+¯Xit+°2W2t+¢¢¢+°NWNt+±2Zi2+¢¢¢+±TZiT+it(8-14)ii=2;¢¢¢;NWit=1ii=2;¢¢¢;NZit=1(N¡1)+(T¡1)NT¡2¡(N¡1)¡(T¡1)NT¡N¡TFN+T¡2;NT¡N¡T=(ESS1¡ESS2)=(N+T¡2)ESS2=(N¡T¡2)FH0:H1:FF=(SSEr¡SSEu)=(N¡1)SSEu=(NT¡N¡1)(8-15)SSErSSEuN¡1kNT¡N¡kYit=®+¯Xit+it(8-16)it=ui+vi+wit-149-8.3uiviVar(it)=¾2u+¾2v+¾2w(8-17)HausmanH0:¾2u=0H1:¾2u6=0(8-18):LM=NT2(T¡1)0B@PNi=1³PTt=1^uit´2PNi=1PTt=1^u2it¡11CA=NT2(T¡1)ÃT2¹^0u¹^u^u0^u¡1!2(8-19)¹^0u¹^u^u0^u18.14575Pit=¯0+¯1RNDi;t¡5+it-150-8.1SAS:1DATATEMP;2SETLI.RND;3P=LOG(P);4RUN;5/¤OLSEstimation¤/6PROCREGDATA=TEMP;7MODELP=RND;8RUN;8.2SAS:1DATARND;2SETLI.RND;3P=LOG(P);4RUN;PROCMEANSDATA=RNDNORPRINT;5CLASSCODE;6VARPRND;7OUTPUTOUT=ASUM=TOTALMEAN=MPMR;8RUN;DATATEM;9SETA;10IFN=1THENDELETE;11RUN;PROCREGDATA=TEM;12MODELMP=MR;13RUN;-151-8.38.3SAS:1DATATEMP;2SETLI.RND;3P=LOG(P);4RUN;56%MACROA;7%DOI=2%TO45;8DATATEMP;9SETTEMP;10B=7¤%EVAL(&I);11A=B¡6;12IFA=N=BTHENW&I=1;ELSEW&I=0;13OUTPUT;14RUN;15%END;16%MENDA;1718%A19PROCREGDATA=TEMP;20MODELP=RNDW2¡W45;21RUN;2223/¤Ftest¤/PROCREGDATA=TEMPNOPRINTOUTEST=A;24M1:MODELP=RNDW2¡W45/SSE;25M2:MODELP=RND/SSE;26RUN;DATANULL;27SETA;28IFFIRST.SSETHENCALLSYMPUT('ESS2',SSE);29ELSECALLSYMPUT('ESS1',SSE);30RUN;DATANULL;31Q1=FINV(0.95,50,269);32Q2=((&ESS1¡&ESS2)/50)/(&ESS2/269);33PUTQ1=Q2=;34RUN;8.4SAS(1)(2)-152-(3)(4)(5)(6)-153-