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EKONOMETRIEKONOMETRITIME SERIESTIME SERIES

ASISTENSI :

SANJOYO

ASISTENSI EKON TIME SERIESASISTENSI EKON TIME SERIES-- SANJOYOSANJOYO 22

TOPIK TOPIK -- TOPIK TOPIK A.A. Pengertian DasarPengertian DasarB.B. PengujianPengujian StasioneritasStasioneritasC.C. ARMA & ARIMAARMA & ARIMAD.D. ARCH & GARCHARCH & GARCH

E.E. SIMULTAN EQUATIONSIMULTAN EQUATIONF.F. VARVARG.G. COINTEGRATION & ECMCOINTEGRATION & ECM


SIMULTAN EQ.SIMULTAN EQ.(1)(1)

SistimSistim PersamaanPersamaan SimulatanSimulatanModel Model StrukturalStrukturalModel Reduce formModel Reduce form-- statistical modelstatistical modelVarVar EndogenEndogenVarVar PredeterminedPredetermined

VarVar EksogenEksogenVarVar Lag EndogenLag Endogen

Rules for Rules for IndentificationIndentificationK K -- k < m k < m –– 1: 1: unidentified(underunidentified(under))K K -- k = m k = m –– 1: just1: just-- identifiedidentifiedK K -- k > m k > m –– 1: 1: overidentifiedoveridentified

K=# predet. var. dlm model inc. intercept; k=# predet. var. dlmsuatu pers.inc intercept; M=# endg. var. dlm model; m=# endg. var dlm suatu pers.


SIMULTAN EQ.SIMULTAN EQ.((22))

EstimasiEstimasi PersamaanPersamaan SimulatanSimulatanIndirect Least Squares (ILS)/ Indirect Least Squares (ILS)/ kuadratkuadrat terkecilterkecil taktaklangsunglangsungTwo Stage Least Squares (2SLS)/ Two Stage Least Squares (2SLS)/ kuadratkuadrat terkecilterkecil duaduatahaptahap

55

METODA ILSMETODA ILS((11))

CONTOH 1:CONTOH 1:Model Model StrukturalStruktural: :

F. D: F. D: QQddtt==αα00+ + αα11PPtt++αα22YYtt++μμ1t1t

F.S : F.S : QQsstt= = ββ00+ + ββ11PPtt++μμ2t2t

KeseimbanganKeseimbangan pasarpasar QQddtt= = QQss

tt, , PPtt=? =? dandan QQtt=?=?IndentifikasiIndentifikasi::

F.D F.D K=2(K=2(YYt t ,,αα00 atauatau ββ00); k=2(); k=2(YYt t ,,αα0 0 ); M=2(P); M=2(Ptt, Q, Qtt); m=2 ); m=2 KK--k (2k (2--2 )< m2 )< m--1(21(2--1)1) unidentifiedunidentifiedF.S F.S K=2(K=2(YYt t ,,αα00 atauatau ββ00); k=1(); k=1(ββ00); M=2(P); M=2(Ptt, Q, Qtt); m=2 ); m=2 KK--k k (2(2--1) = m1) = m--1(21(2--1)1) just just --identifiedidentified

66


Reduce formReduce form

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

=

++=

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

=

++=

11

1121

11

123

11

10012

32

11

12

11

21

11

000

10

;

;

βαμβμα

βαβαπ

βαβαβαπ

ππβαμμ

βααπ

βααβπ

ππ

ttt

ttt

ttt

ttt

w

wYQ

w

vYP

77


Dari data Lat11 Dari data Lat11 diperolehdiperoleh estimasiestimasi PersPers. Reduced . Reduced Form:Form:

PPtt = 72.30907579 + (0.004342974241)Y= 72.30907579 + (0.004342974241)Ytt PPtt==ππ00+ + ππ11YYtt

QQtt = 84.07020849 + (0.001982865402)Y= 84.07020849 + (0.001982865402)Ytt QQtt==ππ22+ + ππ33YYtt

Dari Dari persamaanpersamaan Reduce form Reduce form dptdpt dicaridicari koefisienkoefisienpersamaanpersamaan strukturalstruktural::

MakaMaka perspers. . StrukStruk. . utkutk fungsifungsi Supply:Supply:QQss

tt=51,0541+0,4565 P=51,0541+0,4565 Ptt

BilaBila fungsifungsi supply supply diestimatediestimate dg OLS dg OLS scrscr langsunglangsung ::QQss

tt=65.1719 + 0.3272 P=65.1719 + 0.3272 Ptt

4566,0004343,0001983,0

0541,5130908,72*)4566,0(07021,84

1

31

0120

===

=−=−=

ππβ

πβπβ

LAT11: ILS-1



SedangkanSedangkan utkutk perspers. . StrukStruk. . FungsiFungsi demand demand dg dg koefkoef. . αα00, , αα11, , dandan αα22, , tidaktidak dptdpt diselesaikandiselesaikankrnkrn underindentifiedunderindentified..

99


CONTOH 2:CONTOH 2:Model Model StrukturalStruktural::

F. D: F. D: QQddtt==αα00+ + αα11PPtt++αα22YYtt++μμ1t1t

F.S : F.S : QQsstt= = ββ00+ + ββ11PPtt++ββ22PPtt--11++μμ2t2t

KeseimbanganKeseimbangan pasarpasar QQddtt= = QQss

tt, , PPtt=? =? dandan QQtt=?=?IndentifikasiIndentifikasi::

F.D F.D K=3(K=3(YYt t ,P,Ptt--11,,αα00 atauatau ββ00); k=2(); k=2(YYt t ,,αα0 0 ); M=2(P); M=2(Ptt, Q, Qtt); m=2 ); m=2 KK--k (3k (3--2 ) = m2 ) = m--1(21(2--1)1) identifiedidentified

F.S F.S K=3(K=3(YYt t ,P,Ptt--11,,αα00 atauatau ββ00); k=2(); k=2(ββ00,P,Ptt--11); M=2(P); M=2(Ptt, Q, Qtt); m=2 ); m=2 KK--k (3k (3--2) = m2) = m--1(21(2--1)1) identifiedidentified

1010


Reduce formReduce form

Dari data Lat11 Dari data Lat11 diperolehdiperoleh estimasiestimasi PersPers. Reduced . Reduced Form:Form:

PPtt = 32.17152949 + 0.000680313607 = 32.17152949 + 0.000680313607 YYtt + 0.6818429413 P+ 0.6818429413 Ptt--11

PPtt = = ππ00 + + ππ11 YYtt + + ππ22 PPtt--11

QQtt = 68.00674178 + 0.0005259032821 = 68.00674178 + 0.0005259032821 YYtt + 0.2720386197 P+ 0.2720386197 Ptt--11

QQtt = = ππ33 + + ππ44 YYtt + + ππ55 PPtt--11

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

=

+++=

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

=

+++=

−

−

11

1121

11

215

11

124

11

10013

1543

11

12

11

22

11

21

11

000

1210

;

;

βαμβμα

βαβαπ

βαβαπ

βαβαβαπ

πππβαμμ

βαβπ

βααπ

βααβπ

πππ

ttt

tttt

ttt

tttt

w

wPYQ

w

vPYP

LAT12: ILS-2

1111


Dari Dari persamaanpersamaan Reduce form Reduce form dptdpt dicaridicarikoefisienkoefisien persamaanpersamaan strukturalstruktural::

ββ00=43,1381; =43,1381; ββ11=0,773; =0,773; ββ22==--0,255; 0,255; αα00=55,1703 =55,1703 αα11=0,399 =0,399 dandanαα22=0,00025=0,00025

MakaMaka model model strukturalstruktural::QQdd

tt==55,1703 55,1703 + + 0,399 0,399 PPtt++0,00025 0,00025 YYtt

QQsstt==43,1381 43,1381 + + 0,773 0,773 PPt t -- 0,2550,255 PPtt--11

1

1142

52

511

1

113

1

100

12521

410130

)(;)(

;)(

;;

βαβπα

πβπβα

ββαπ

βαβα

βππβππβπβπβ

−=

−−=

−−=

−==−=

1212

METODA Two Stage LSMETODA Two Stage LS((11))

Model Model StrukturalStruktural: : (1) Y(1) Y1t1t= = ββ1010+ + ββ1111YY2t2t++γγ1111XX1t1t+ + γγ1212XX2t2t+ + μμ1t1t

(2) Y(2) Y2t2t= = ββ2020+ + ββ2121YY1t1t+ + μμ2t2tYY11=income (GDP) ; =income (GDP) ; YY2 2 =stock of money (Money Supply);=stock of money (Money Supply);XX1 1 =investment expenditure; =investment expenditure; XX2 2 ==govtgovt expenditureexpenditure(1)=income function; (2)=money supply function(1)=income function; (2)=money supply function

IndentifikasiIndentifikasi::(1) (1) K=3(K=3(XX1t1t,X,X2t2t,,ββ1010 atauatau ββ2020); k=3(); k=3(XX1t1t,X,X2t2t,,ββ1010); M=2(); M=2(YY1t 1t ,Y,Y2t 2t ); m=2(); m=2(YY1t 1t ,Y,Y2t 2t ) ) KK--k (3k (3--3 ) < m3 ) < m--1(21(2--1)1) underidentifiedunderidentified(2) (2) K=3(K=3(XX1t1t,X,X2t2t,,ββ1010 atauatau ββ2020); k=1(); k=1(ββ1010); M=2(); M=2(YY1t 1t ,Y,Y2t 2t ); ); m=2(m=2(YY1t 1t ,Y,Y2t 2t ) ) KK--k (3k (3--1 ) > m1 ) > m--1(21(2--1)1) overidentifiedoveridentified

1313

METODA Two Stage LSMETODA Two Stage LS((22))

MetodaMetoda 2 stage LS2 stage LSStage 1: regress YStage 1: regress Y11 padapada semuasemua predetermined predetermined variabelvariabeldlmdlm system, system, dlmdlm halhal iniini YY11 padapada XX11 dandan XX22;;

Stage 2: Stage 2: subtitusikansubtitusikan nilainilai YY11 padapada fungsifungsi money supply money supply ((strukturalstruktural) :) :

ttt

tttt

XXY

XXY

221101

221101

ˆˆˆˆ;ˆˆˆˆ

πππ

μπππ

++=

+++=

LAT13: 2SLS

*12120

21212120

2121202

ˆ)ˆ(ˆ

;)ˆˆ(

tt

ttt

tttt

Y

Y

YY

μββ

μβμββ

μμββ

++=

+++=

+++=

1414

Test SimultaneityTest Simultaneity((11))

Model Model StukturalStuktural dandan reduced form reduced form samasama dg model dg model GDP & money supplyGDP & money supplyHausmanHausman Test:Test:

Step 1: Regress Step 1: Regress persamaanpersamaan reduce form: reduce form: untukuntukmendapatkanmendapatkan estimate Yestimate Y11 dandan μμtt ::

Step 2: Regress YStep 2: Regress Y22 terhadapterhadap estimate Yestimate Y11 dandan μμtt ::

Step 3: Reject Ho: Step 3: Reject Ho: ββ**2121=0 (no =0 (no corelationcorelation μμtt cap dg cap dg μμ2t2t / / no no simultanetysimultanety) ) bilabila tt--test > ttest > t--table. table.

ttt

tttt

XXY

XXY

221101

221101

ˆˆˆˆ;ˆˆˆˆ

πππ

μπππ

++=

+++=

LAT14: H-test

tttt YY 2*21121202 ˆˆ μμβββ +++=

1515

METODA 2SLSMETODA 2SLS--LanjutanLanjutan((11))

Model Model StrukturalStruktural: : (1) Y(1) Y1t1t= = ββ1010+ + ββ1111YY2t2t++γγ1111XX1t1t+ + γγ1212XX2t2t+ + μμ1t1t

(2) Y(2) Y2t2t= = ββ2020+ + ββ2121YY1t1t+ + γγ2323XX3t3t+ + γγ2424XX4t4t+ + μμ2t2tYY11=income (GDP) ; =income (GDP) ; YY2 2 =stock of money (Money Supply);=stock of money (Money Supply);XX1 1 =investment expenditure; =investment expenditure; XX2 2 ==govtgovt expenditureexpenditureXX3 3 =income (t=income (t--1); 1); XX4 4 =stock of money (t=stock of money (t--1)1)

IndentifikasiIndentifikasi::(1) (1) K=5(K=5(XX1t1t,X,X2t2t, , XX3t3t,X,X4t4t,,ββ1010 atauatau ββ2020); k=3(); k=3(XX1t1t,X,X2t2t,,ββ1010); ); M=2(M=2(YY1t 1t ,Y,Y2t 2t ); m=2(); m=2(YY1t 1t ,Y,Y2t 2t ) ) KK--k (5k (5--3 ) > m3 ) > m--1(21(2--1)1)overidentifiedoveridentified(2) (2) K=5(K=5(XX1t1t,X,X2t2t, , XX3t3t,X,X4t4t, , ββ1010 atauatau ββ2020); k=3(); k=3(XX3t3t,X,X4t4t,,ββ1010); ); M=2(M=2(YY1t 1t ,Y,Y2t 2t ); m=2(); m=2(YY1t 1t ,Y,Y2t 2t ) ) KK--k (5k (5--3 ) > m3 ) > m--1(21(2--1)1)overidentifiedoveridentified

1616

METODA 2SLSMETODA 2SLS--lanjutanlanjutan((22))

MetodaMetoda 2 stage LS2 stage LSStage 1: regress YStage 1: regress Y11 dandan YY22 padapada semuasemua predetermined predetermined variabelvariabel dlmdlm system, system, dlmdlm halhal iniini YY11 dandan YY22 padapada XX11,X,X22,X,X33, , dandan XX44;;

Stage 2: Stage 2: subtitusikansubtitusikan nilainilai estimasiestimasi YY11 dandan YY22 padapada fungsifungsiincome income dandan money supply :money supply :

(1) Y(1) Y1t1t= = ββ1010+ + ββ1111ŶŶ2t2t++γγ1111XX1t1t+ + γγ1212XX2t2t+ + μμ**1t1t

(2) Y(2) Y2t2t= = ββ2020+ + ββ2121ŶŶ1t1t+ + γγ2323XX3t3t+ + γγ2424XX4t4t+ + μμ**2t2t

1 10 11 1 12 2 13 3 14 4 1

2 20 21 1 22 2 23 3 24 4 2

ˆ ˆ ˆ ˆ ˆ ˆ ;ˆ ˆ ˆ ˆ ˆ ˆ ;

t t t t t t

t t t t t t

Y X X X XY X X X X

π π π π π μπ π π π π μ

= + + + + +

= + + + + +

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