šš¸É3
¦³Á¸¥ª·›¸ª·‹´¥
3.1 ‹Îµ¨°Šš¸ÉčoĜ„µ¦«¹„¬µ
Ĝ„µ¦«¹„¬µ‡¦´ÊŠœ¸ÊÁž}œ„µ¦«¹„¬µ™¹Š Ÿ¨„¦³š…°ŠÁŠ·œš»œÁ‡¨ºÉ°œ¥oµ¥˜n°—´œ¸‡nµÁŠ·œš¸Éšo‹¦·Š
ץčo˜´ªÂž¦š´ÊŠ®¤—2 ˜´ªÅ—o„nÁŠ·œš»œÁ‡¨ºÉ°œ¥oµ¥­»š›·£µ‡Á°„œ (NF) ¨³—´œ¸‡nµÁŠ·œš¸Éšo‹¦·Š
(REER)ץčo„¦°Âœª‡·—…°Š¤´œÁ—¨-Á¢¨¤¤·ÉŠÂ¨³Âœª‡·—…°Š—°¦rœ»­r¤µž¦³¥»„˜rčo„´
œª‡·—Á„¸É¥ª„´—´œ¸‡nµÁŠ·œš¸Éšo‹¦·ŠÁ¡ºÉ°°›·µ¥™¹ŠŸ¨…°ŠÁŠ·œš»œÁ‡¨ºÉ°œ¥oµ¥¦³®ªnµŠž¦³Áš«Â¨³
°´˜¦µÂ¨„Áž¨¸É¥œÃ—¥Â‹Îµ¨°Š‡ªµ¤­´¤¡´œ›r…°ŠÁŠ·œš»œÁ‡¨ºÉ°œ¥oµ¥„´—´œ¸‡nµÁŠ·œš¸Éšo‹¦·ŠÂ­—Š
ŗo—´Šœ¸Ê
REER
f ( NFi )
×¥š¸É REER ‡º°—´œ¸‡nµÁŠ·œš¸Éšo‹¦·Š
NFi ‡º°ÁŠ·œš»œÁ‡¨ºÉ°œ¥oµ¥­»š›·£µ‡Á°„œ
3.2 ª·›¸„µ¦«¹„¬µ
čoÁš‡œ·‡šµŠÁ«¦¬“¤·˜·š¸ÉÁ¦¸¥„ªnµ Vector Autoregression Model (VAR) ×¥…o°¤¼¨š¸ÉčoĜ
‹Îµ¨°Šœ´ÊœÁž}œ˜´ªÂž¦Äœ¨´„¬–³…°Š°œ»„¦¤Áª¨µ( Time Series) —oª¥Á®˜»š¸Éªnµ„µ¦­¦oµŠ
‹Îµ¨°Š…°Š VAR œ´ÊœÅ¤nŗo¥¹—˜µ¤š§¬‘¸š¸ÉÁž}œÃ‡¦Š­¦oµŠ( Structure) ÁšnµÄ—œ´„Ánœ
‹Îµ¨°Š¦³­¤„µ¦š¸ÉÁ„¸É¥ª¡´œ„´œ (Simutaneous Equation Model) °¸„š´ÊŠ˜µ¤š§¬‘¸…°Š
‹Îµ¨°ŠÂ¨oªVAR ¥´ŠÄ®oŸ¨„µ¦ž¦³¤µ–„µ¦®¦º°šÎµœµ¥ (Forcast) š¸É—¸„ªnµª·›¸…°ŠÂ‹Îµ¨°Šš¸É
Áž}œÃ‡¦Š­¦oµŠÁnœÂ‹Îµ¨°Š¦³­¤„µ¦š¸ÉÁ„¸É¥ª¡´œ„´œš¸É¥»nŠ¥µ„¨³Áž}œÃ¤Á—¨š¸É­µ¤µ¦™‹´—„µ¦
„´ž{®µ Simultaneity Bias ŗo—¸(Gujarati, 2003) Ž¹ÉŠ„µ¦Äo‹Îµ¨°Š VARœ´Êœ¤¸‡ªµ¤
ŗoÁž¦¸¥ÄœÂŠn…°ŠÄœ„¦–¸š¸ÉÁ¦µ°µ‹‹³Å¤nš¦µ‡ªµ¤­´¤¡´œ›rš¸Éšo‹¦·ŠÄœ¦³®ªnµŠ˜´ªÂž¦š´ÊŠ®¤—š¸É
50
Á„¸É¥ª…o°Š„´œ®¦º°°µ‹‹³Å¤nš¦µªnµ˜´ªÂž¦Ä—Áž}œ Endogenous Variable ®¦º°Exogenous Variable
„´œÂœn˜nš¦µªnµÃ—¥¦ª¤Â¨oª˜´ªÂž¦š»„˜´ªÄœÂ‹Îµ¨°ŠVAR¤¸Ÿ¨˜n°„´œ
—´Šœ´Êœ‹¹Š­µ¤µ¦™Äo‹Îµ¨°ŠVARĜ„µ¦«¹„¬µ™¹ŠŸ¨„¦³š®¦º°‡ªµ¤­´¤¡´œ›r…°Š˜´ªÂž¦
˜´ªÄ—˜´ª®œ¹ÉŠÄœÂ‹Îµ¨°Š˜n°˜´ªÂž¦°ºÉœÄœÂ‹Îµ¨°ŠÅ—o×¥ª·›¸˜nµŠÇŗo„n„µ¦ª·Á‡¦µ³®r
ž’·„·¦·¥µ˜°­œ°Š˜n°‡ªµ¤Âž¦ž¦ªœ (Impulse Response Function) „µ¦Â¥„­nªœ…°Š‡ªµ¤
ž¦ž¦ªœ(Variance Decomposition) ×¥¤·˜o°Š„´Šª¨„´„µ¦˜´—­·œÄ‹Äœ„µ¦­¦oµŠ­¤„µ¦ÄœÂ
Structural Model Á¡¦µ³ÄœVAR ‹³Ä®o˜´ªÂž¦š»„˜´ªÁž}œ Endogenous Variable°¸„š´ÊŠÄœ„µ¦Äo
Simutaneous Equation ModelĜ„¦–¸š¸ÉŤnš¦µ‡ªµ¤­´¤¡´œ›rš¸Éšo‹¦·Š…°Š˜´ªÂž¦˜nµŠÇĜ
‹Îµ¨°Š°µ‹Á„·—ž{®µÁ¤ºÉ°šÎµ„µ¦˜´—š·ÊŠ®¦º°Á¡·É¤˜´ªÂž¦µŠ˜´ªÄœ¦³­¤„µ¦Ž¹ÉŠ°µ‹Á„·—ž{®µ
ÁnœIdentification Error ŗo
Ĝ„µ¦«¹„¬µŸ¨„¦³š…°ŠÁŠ·œš»œÁ‡¨ºÉ°œ¥oµ¥˜n°—´œ¸‡nµÁŠ·œš¸Éšo‹¦·ŠÃ—¥Äo…o°¤¼¨š»˜·¥£¼¤·Áž}œ
…o°¤¼¨°œ»„¦¤Áª¨µŽ¹ÉŠ˜o°ŠœÎµ…o°¤¼¨¤µš—­°¨´„¬–³œ·ÉŠ…°Š…o°¤¼¨®¦º°„µ¦š—­° unit root ¨³
šÎµ„µ¦ž¦´…o°¤¼¨Ä®o¤¸¨´„¬–³œ·ÉŠ(Stationary) ®¦º°Å¤n¤¸ Unit Roots ¤·Ánœœ´Êœ‹³šÎµÄ®oÁ„·— Spurious
Problem ŗo Œ³œ´Êœ‹¹Š˜o°Šš—­°—¼ªnµ…o°¤¼¨°œ»„¦¤Áª¨µš¸ÉœÎµ¤µÄoœ´Êœ¤¸Ÿ¨…°Š Trend Ÿ­¤°¥¼n
®¦º°Å¤n‹¹Š˜o°Šš—­° Unit Roots „´…o°¤¼¨…°Š˜´ªÂž¦š»„˜´ª ×¥ª·›¸ Augmented Dickey-Fuller
(ADF) Test Ž¹ÉŠ™oµŸ¨„µ¦š—­°œ´Êœž¦µ„’°°„¤µªnµ˜´ªÂž¦Ä—¤¸ Unit Roots ­—Šªnµ…o°¤¼¨
°œ»„¦¤Áª¨µ…°Š˜´ªÂž¦—´Š„¨nµªš¸ÉœÎµ¤µÄoœ´ÊœÅ¤nÁž}œ Stationary „¨nµª‡º°¤¸Ÿ¨…°Š Trend °¥¼nĜ
°œ»„¦¤…°Š…o°¤¼¨—´Šœ´Êœ˜´ªÂž¦—´Š„¨nµªÄœÂ‹Îµ¨°Šœ´Êœ°µ‹‹³˜o°ŠÄoÁž}œ¨´„¬–³…°Š
Difference šœŽ¹ÉŠ‹³˜o°ŠšÎµ„µ¦š—­°˜n°Åžªnµ˜´ªÂž¦—´Š„¨nµªœ´ÊœÁž}œ Stationary š¸ÉDifference
š¸ÉOrder ėץčoª·›¸„µ¦…°Š Augmented Dickey-Fuller (ADF) Test ÁnœÁ—·¤ ¨³Á¨º°„Lag ®¦º°
‡ªµ¤¨nµoµš¸ÉÁ®¤µ³­¤
‹µ„œ´ÊœœÎµ¤µ š—­°‡ªµ¤­´¤¡´œ›rĜ¦³¥³¥µª®¦º°„µ¦®µ
Cointegration„µ¦ ­¦oµŠ
‹Îµ¨°ŠVector Autoregression Model (VAR) ¨³­»—šoµ¥„µ¦ÄoŸ¨„µ¦ž¦³¤µ–‡nµš´ÊŠ„µ¦
ª·Á‡¦µ³®rž’·„·¦·¥µ˜°­œ°Š˜n°‡ªµ¤Âž¦ž¦ªœ (Impulse Response Function) ¨³„µ¦Â¥„­nªœ
…°Š‡ªµ¤Âž¦ž¦ªœ(Variance Decomposition) ץ˜n¨³…´Êœ˜°œ¤¸¦µ¥¨³Á°¸¥——´Š˜n°Åžœ¸Ê
3. 2.1„µ¦š—­°Unit Root
Ĝ„µ¦«¹„¬µœ¸Êčo…o°¤¼¨„µ¦ž¦³¤µ–‡nµ¤¸¨´„¬–³Áž}œ°œ»„¦¤Áª¨µ˜´ªÂž¦ž{‹‹»´œÂ¨³Äœ
°—¸˜¤´„¤¸‡ªµ¤­´¤¡´œ›r„´œšÎµÄ®o˜´ªÂž¦¤¸¨´„¬–³Å¤nœ·ÉŠ (Non-stationary) œ°„‹µ„œ´Êœ®µ„˜´ªÂž¦
51
š¸ÉčoĜ„µ¦ž¦³¤µ–‡nµÄœÂ‹Îµ¨°Š¤¸‡»–­¤´˜·Å¤nœ·ÉŠ‹³šÎµÄ®oÁ„·—ž{®µ‡ªµ¤­´¤¡´œ›rš¸ÉŤn
šo‹¦·ŠSpurious ®¦º°˜´ªÂž¦Á®¤º°œ¤¸‡ªµ¤­´¤¡´œ›r„´œÂ˜nĜ‡ªµ¤Áž}œ‹¦·ŠÅ¤n­´¤¡´œ›r„´œ
—´Šœ´Êœ…´Êœ˜°œÂ¦„„n°œ„µ¦ž¦³¤µ–‡nµÁ¦µ‹³˜o°Š¡·‹µ¦–µ¨´„¬–³…o°¤¼¨Ã—¥š—­°
‡»–­¤´˜· Stationary ®¦º°Unit root —oª¥„µ¦š—­°Augmented Dickey-Fuller (ADF) ¡·‹µ¦–µ
­¤„µ¦™—™°¥3 ¦¼žÂš¸É˜„˜nµŠ„´œÄœ„µ¦š—­°ªnµ¤¸ Unit root ®¦º°Å¤nŽ¹ÉŠ3 ­¤„µ¦—´Š„¨nµª
ŗo„n
p
' Xt
TX t 1 ¦Ii ' X t i H t
(random walk process)
(3.1)
i 1
p
' Xt
D TX t 1 ¦I ' X t i H t
(random walk with drift) (3.2)
i 1
p
' Xt
D E TX t 1 ¦Ii ' X t i H t
(random walk with drift y (3.3)
i 1
and linear time trend)
×¥„µ¦š—­°­¤¤˜·“µœÅ—o—´Šœ¸Ê
H0 :T
0 ˜´ªÂž¦Áž}œ
H1 : T 0 ˜´ªÂž¦Áž}œ
Non-stationary
Stationay
„µ¦š—­° Unit root ®µ„­µ¤µ¦™ž’·Á­›­¤¤˜·“µœÅ—o®¤µ¥‡ªµ¤ªnµ˜´ªÂž¦œ´Êœ¤¸
¨´„¬–³Áž}œStationay ¤¸Integration of order zeroœ´Éœ‡º°Ž¹ÉŠÄœ„¦–¸š¸ÉÁž}œ Non-stationary Á¦µ
­µ¤µ¦™šÎµ­nªœ˜nµŠ…°Š˜´ªÂž¦œ´ÊœÂ¨³š—­°Unit root °¸„‡¦´ÊŠ®¦º°‹œ„ªnµž’·Á­›­¤¤˜·“µœŽ¹ÉŠ
Á¦µ‹³Á¦¸¥„˜´ªÂž¦š¸ÉšÎµ­nªœ˜nµŠÂ¨oªStationary š¸É¨Îµ—´š¸É p ªnµ I ( p) ®¦º°Integrated Order pth
3.2.2 „µ¦Á¨º°„‡ªµ¤¨nµoµ(Lag) š¸ÉÁ®¤µ³­¤
Ĝ„µ¦«¹„¬µœ¸ÊčoÁ„–”r Akaike Information Criteria (AIC) ¨³ 6FKZDU]us Bayesian
Information Criterion (SC, BIC ®¦º° SBC) Áž}œÁ„–”rĜ„µ¦¡·‹µ¦–µ‡ªµ¤Á®¤µ³­¤…°Š‹Îµœªœ
‡ªµ¤¨nµoµ®¦º°Lag …°ŠÂ‹Îµ¨°Š¤¸­¼˜¦—´Šœ¸Ê
52
AIC
×¥š¸É
VÖ 2 ‡º°
log VÖ 2 2
pq
T
‡nµž¦³¤µ–…°Š‡ªµ¤Âž¦ž¦ªœ…°Š
SC
log VÖ 2 2
(3.4)
et
pq
log T
T
(3.5)
Á„–”rš´ÊŠ­°ŠÁž}œÁ„–”rš¸É°µ«´¥‡ªµ¤‡ª¦‹³Áž}œ(
likelihood-based) ¨³Â­—ŠÄ®oÁ®Èœ™¹Š
‡ªµ¤­¤—»¨(š¸É¤¸Ÿ¨ÄœšµŠ˜¦Š„´œ…oµ¤) ( trade off) ¦³®ªnµŠvILWwŽ¹ÉŠª´—×¥‡nµ…°Š‡ªµ¤‡ª¦‹³Áž}œ
¨³ v˜¦³®œ¸É (parsimonywŽ¹ÉŠª´—×¥‹Îµœªœ…°Š¡µ¦µ¤·Á˜°¦r°·­¦³p+q ™oµ‡nµ‡Šš¸É™¼„œÎµÅž¦ª¤°¥¼n
Ĝ‹Îµ¨°Š—oª¥‹Îµœªœ…°Š¡µ¦µ¤·Á˜°¦r—´Š„¨nµª„È‹³Á¡·É¤…¹ÊœÁž}œ p+q+1 ­Îµ®¦´®¨´„Á„–”rĜ
„µ¦˜´—­·œÄ‹Á¨º°„‹Îµ¨°Š„ȇº°Á¦µ‹³Á¨º°„‹Îµ¨°Šš¸É¤¸‡nµ AIC ®¦º° SC š¸É¤¸‡nµœo°¥š¸É­»— ‡nµ
AIC ¨³ SC ‹³œo°¥‹µ„­µÁ®˜»—´Š˜n°Åžœ¸Ê‡º°¤¸‡ªµ¤Âž¦ž¦ªœÂ¨³‡ªµ¤Âž¦ž¦ªœ¦nª¤œo°¥¤¸
‹Îµœªœ…°Š˜´ªÂž¦Â¨³‹ÎµœªœLag œo°¥Â¨³­»—šoµ¥¤¸‹Îµœªœ…o°¤¼¨Äœ„µ¦ž¦³¤µ–‡nµ¤µ„
Ĝ…–³š¸ÉÁ„–”rš´ÊŠ­°Š—´Š„¨nµª¤¸‡ªµ¤Â˜„˜nµŠ„´œÄ®oÁ¨º°„čoSC Ūo„n°œÁ¡¦µ³ªnµSC ¤¸
‡»–­¤´˜·ªnµ SC ‹³Á¨º°„‹Îµ¨°Šš¸É™¼„˜o°ŠÁ„º°Âœnœ°œ ­Îµ®¦´ AIC œ´Êœ¤¸ÂœªÃœo¤š¸É‹³Áž}œ
¨´„¬–³Á·ŠÁ­oœ„ε„´ÄœÂ‹Îµ¨°Šš¸É¤¸¡µ¦µ¤·Á˜°¦r¤µ„Á„·œÅž œ°„‹µ„œ´ÊœÄœ„µ¦«¹„¬µœ¸Ê‹³šÎµ
„µ¦Áž¦¸¥Áš¸¥Ÿ¨„µ¦Á¨º°„Lag „´Á„–”r°ºÉœ—oª¥‡º°Final Prediction Error (FPE) ¨³HannanQuinn Information Criterion (HQIC) Ž¹ÉŠÄ®o‡ªµ¤®¤µ¥Äœ¨´„¬–³Ä„¨oÁ‡¸¥Š„´œ
3.2.3 „µ¦š—­°®µCointegration ª·›¸„µ¦…°ŠJohansen
Johansen (1988) ¨³Stock and Watson (1988) ŗoÁ­œ°˜´ªž¦³¤µ–‡nµÂ maximum
likelihood (maximum likelihood estimator) Ž¹ÉŠšÎµÄ®o­µ¤µ¦™®¨¸„Á¨¸É¥Š„µ¦Äo˜´ªž¦³¤µ–‡nµ 2
…´Êœ˜°œÅ—o( two-step estimators) ¨³­µ¤µ¦™š¸É‹³ž¦³¤µ–‡nµÂ¨³š—­°„µ¦¤¸°¥¼n‹¦·Š…°Š
cointegrating vectors ®¨µ¥vectors ŗoœ°„‹µ„œ¸Ê¨oª„µ¦š—­°—´Š„¨nµª¥´ŠšÎµÄ®oÁ¦µ­µ¤µ¦™
š—­°„µ¦Ä­n…o°‹Îµ„´—…°Š¡µ¦µ¤·Á˜°¦r…°Š cointegrating vectors ¨³‡ªµ¤Á¦Èª…°Š„µ¦ž¦´˜´ª
(speed of adjustment) ŗo°¸„—oª¥
°¥nµŠÅ¦„Șµ¤š´ÊŠª·›¸„µ¦…°Š Johansen (1988) ¨³ Stock and Watson (1988) ˜nµŠ„È°µ«´ ¥
‡ªµ¤­´¤¡´œ›r¦³®ªnµŠ rank …°ŠÁ¤š¦·„Žr¨³ characteristic roots …°ŠÁ¤š¦·„Žr—´Š„¨nµª°¥nµŠ¤µ„
53
¨³Á¡ºÉ°š¸É‹³Á…oµÄ‹…´Êœ˜°œ…°Šª·›¸„µ¦…°Š Johansen (1988) ‹¹ŠÁž}œ„µ¦­¦»žª·›¸„µ¦Â¨³…´Êœ˜°œ…°Š
Johansen (1988) —´Šœ¸Ê
¡·‹µ¦–µautoregressive process
yt
A1 yt 1 A2 yt 2 ... Ap yt p H t
(3.6)
‹µ„­¤„µ¦(3.6) Á°µ yt 1 ި°°„š´ÊŠ­°Š…oµŠ‹³Å—o
'yt
( A1 I ) yt 1 A2 yt 2 ... Ap yt p H t
(3.7)
‹µ„­¤„µ¦(3.7) ª„Á…oµÂ¨³¨°°„šµŠ…ªµ¤º°—oª¥ ( A I ) yt 2 ‹³Å—o
'yt
( A1 I ) yt 1 ( A2 A1 I ) yt 2 A3 yt 3 ... Ap yt p H t
(3.8)
šÎµÁnœœ¸ÊŞÁ¦ºÉ°¥Ç‹³Å—o
p 1
'yt
¦S 'y
i
t i
Syt p H t
(3.9)
i 1
×¥š¸É
S
p
ª
º
« I ¦ Ai »
i 1
¬
¼
­·ÉŠ­Îµ‡´Äœ­¤„µ¦ (3.9) „ȇº°‡nµ¨Îµ—´´Êœ (rank) …°ŠÁ¤š¦·„Žr S œ´Éœ‡º°‡nµ¨Îµ—´´Êœ (rank) …°Š
S ‹³Ášnµ„´‹Îµœªœ…°Šcointegrating vector Ž¹ÉŠ­µ¤µ¦™Â­—ŠÅ—oĜ¦µ¥¨³Á°¸¥——´Šœ¸Ê
1. ™oµ‡nµ¨Îµ—´´Êœ(rank) Ášnµ„´«¼œ¥rÁ¤š¦·„Žr S ‹³Áž}œÁ¤š¦·„Žr«¼œ¥r¨³­¤„µ¦(3.9)
„ȇº°Â‹Îµ¨°ŠVAR Ĝ¦¼ž…°ŠŸ¨˜nµŠš¸É®œ¹ÉŠ(first difference)
2. ™oµ‡nµ¨Îµ—´´Êœ(rank) …°Š S Ášnµ„´ n (Ž¹ÉŠ„ȇº° ¤¸‡nµ¨Îµ—´´Êœ (rank) Á˜È¤š¸É®¦º°š¸É
Á¦¸¥„ªnµfull rank Ž¹ÉŠvector process ‹³¤¸¨´„¬–³œ·ÉŠÂ¨³Áž}œ VAR Ĝlevel Ž¹ÉŠ‡º°
­¤„µ¦(3.6)
54
3. ™oµ‡nµ ¨Îµ—´´Êœ(rank) …°Š S Ášnµ„´1 Á¦µ„È‹³¤¸ cointegrating vector Á¡¸¥Švector
Á—¸¥ªÂ¨³ Syt p „ȇº°ž{‹‹´¥„µ¦ž¦´˜´ª…°Š‡ªµ¤‡¨µ—Á‡¨ºÉ°œ( error-correction
factor)
4. Ĝ„¦–¸Ž¹ÉŠ1 < rank ( S ) < n Á¦µ„È‹³¤¸ cointegrating vectors ®¨µ¥cointegrating
vectors
­Îµ®¦´
„µ¦š—­° Cointegration ®¦º°„µ¦š—­°‡ªµ¤­´¤¡´œ›r¦³¥³¥µª¦³®ªnµŠ˜´ª
ž¦Á¡ºÉ°ÄoĜ„µ¦Á¨º°„‹Îµ¨°Šš¸ÉčoĜ„µ¦ž¦³¤µ–‡nµ¦³®ªnµŠ VAR ¨³ VEC Ĝ„µ¦«¹„¬µœ¸Ê
ŗočo„µ¦š—­° Johansen Trace …°ŠJohansen and Juselius (1990) Á¡ºÉ°®µ‹Îµœªœ…° Š
‡ªµ¤­´¤¡´œ›r Cointegration ŗo—oª¥„µ¦Äo„µ¦š—­° Likelihood Ratio test statistic £µ¥Ä˜o…o°
­¤¤˜·“µœ®¨´„‡º°
¨³
×¥š¸É
H 0 : rank(–)
r
H1 : rank(–)
r t1
0
– ‡º°Á¤˜¦·„Žr­´¤ž¦³­·š›·Í…°Š‡ªµ¤­´¤¡´œ›r¦³®ªnµŠ
r
'Yt ¨³ 'Yt 1 Ĝ
‹Îµ¨°ŠVEC
‡º°‹ÎµœªœRank …°ŠÁ¤˜¦·„Žr –
×¥Á¤ºÉ°‡nµš—­° Trace ¤µ„„ªnµ‡nµª·„§˜šÎµÄ®o­µ¤µ¦™ž’·Á­›­¤¤˜·“µœ®¨´ „(null
hypothesis) ®¤µ¥‡ªµ¤ªnµ˜´ªÂž¦Äœ Yt Ťn¤¸‡ªµ¤­´¤¡´œ›r„´œ ®µ„‡nµš—­°Trace ¤¸‡nµœo°¥„ªnµ
‡nµª·„§˜‹³¥°¤¦´­¤¤˜·“µœ®¨´„ ®¤µ¥‡ªµ¤ªnµ˜´ªÂž¦Äœ Yt ¤¸‡ªµ¤­´¤¡´œ›r„´œ°¥nµŠœo°¥®œ¹ÉŠ
‡ªµ¤­´¤¡´œ›r¨Îµ—´˜n°Åž„È‹³Áž}œ„µ¦š—­°ŽÊεץčo­¤¤˜·“µœ‡º°
H 0 : rank(–)
¨³
×¥š¸É
r
H1 : rank(–) t r 1
– ‡º°Á¤˜¦·„Žr­´¤ž¦³­·š›·Í…°Š‡ªµ¤­´¤¡´œ›r¦³®ªnµŠ
r
‹Îµ¨°ŠVEC
‡º°‹ÎµœªœRank …°ŠÁ¤˜¦·„Žr –
'Yt ¨³ 'Yt 1 Ĝ
55
Ž¹ÉŠÄœ„¦–¸š¸É­µ¤µ¦™ž’·Á­›­¤¤˜·“µœ‡¦‹œ„¦³š´ÉŠ Full Rank Á¦µ­µ¤µ¦™Äo
‹Îµ¨°ŠVAR Ĝ„µ¦ž¦³¤µ–‡nµ ŗo®µ„Ťnčn Full Rank ¤¸‡ªµ¤­´¤¡´œ›r¦³®ªnµŠ˜´ªÂž¦š´ÊŠ
­°ŠŽ¹ÉŠšÎµÄ®o­µ¤µ¦™®µ‡ªµ¤­´¤¡´œ›rĜ¦³¥³­´ÊœÂ¨³¦³¥³¥µªÅ—o Á¦µ‹³Äo‹Îµ¨°ŠVEC šœ
3.2.4 ‹Îµ¨°ŠVector Autoregression
Á¡ºÉ°˜°‡Îµ™µ¤…°Š„µ¦«¹„¬µ„µ¦«¹„¬µœ¸Êŗo„ε®œ—‹Îµ¨°Š VAR Áž}œÂ‹Îµ¨°Šš¸É
Á®¤µ³­¤Á¡ºÉ°ÄoĜ„µ¦«¹„¬µÁœºÉ°Š‹µ„¨´„¬–³Â¨³‡ªµ¤­´¤¡´œ›r…°Š˜´ªÂž¦°µ‹Å¤n´—Á‹œÂ¨³Áž}œ
‡ªµ¤­´¤¡´œ›rĜÁ·Š¡¨ª´˜¦ž¦³„°„´…o°­¤¤˜·Ä®o˜´ªÂž¦Â˜n¨³˜´ªÅ¤n­nŠŸ¨˜n°˜´ªÂž¦°ºÉœÇ
ĜnªŠÁª¨µÁ—¸¥ª„´œ°¸„š´ÊŠ„µ¦«¹„¬µ‡¦´ÊŠœ¸Ê­nªœ®œ¹ÉŠÁ¡ºÉ°˜°‡Îµ™µ¤™¹ŠŸ¨„¦³š
…°ŠÁŠ·œš»œ
Á‡¨ºÉ°œ¥oµ¥š¸É¤¸˜n°—´œ¸‡nµÁŠ·œš¸Éšo‹¦·Š ™¹Š…œµ—š·«šµŠ¦³¥³Áª¨µ‡ªµ¤‡Š°¥¼n( Persistence) ¨³
­´—­nªœ…°ŠŸ¨„¦³šš¸É¤¸˜n°—´œ¸‡nµÁŠ·œš¸Éšo‹¦·Š
ÁœºÉ°Š‹µ„‡ªµ¤­´¤¡´œ›r…°Š˜´ªÂž¦Â˜n¨³˜´ª¤¸‡ªµ¤­´¤¡´œ›rš¸ÉŤnœnœ°œÂ¨³­nŠŸ¨„¦³š
¦³®ªnµŠ„´œš´ÊŠšµŠ˜¦ŠÂ¨³šµŠ°o°¤…o°­¤¤˜·ž¦³„µ¦®œ¹ÉŠš¸É‹ÎµÁž}œÂ¨³Á®¤µ³­¤˜n°„µ¦«¹„¬µÄœ
‡¦´ÊŠœ¸Ê‡º°˜´ªÂž¦Â˜n¨³˜´ª‹³Å¤n­nŠŸ¨„¦³š˜n°˜´ªÂž¦˜´ª°ºÉœÄœnªŠÁª¨µÁ—¸¥ª„´œ ®¦º°Å¤n­nŠŸ¨
„¦³š°¥nµŠš´œš¸Á¤ºÉ°˜´ªÂž¦®œ¹ÉŠÁž¨¸É¥œÂž¨ŠÁ¡¦µ³„µ¦˜°­œ°Š˜n° Shock š¸ÉÁ„·—…¹ÊœÂ¨³š¸É¤¸Ÿ¨
˜n°˜´ªÂž¦˜nµŠÇĜ¦³Á«¦¬“„·‹œ´Êœ¥´Š¤¸‡ªµ¤¨nµoµ(Non-Contemporaneous Effect)
Á¦µ­¦oµŠÂ‹Îµ¨°Š…°ŠÁª„Á˜°¦rœ¸ÊĜ¦¼ž…°Š‡nµš¸ÉŸnµœ¤µÄœ°—¸˜…°ŠÁª„Á˜°¦r—´Š„¨nµªœ¸ÊŸ¨
š¸Éŗo„ȇº°Vector Autoregression (VAR) ­µ¤µ¦™Á…¸¥œÅ—o—´Šœ¸Ê
yt
=
m A1 yt 1 A2 yt 2 ... Ap yt p H t
(3.10)
Ender (1995) ŗo¥„˜´ª°¥nµŠ¦³°¥nµŠŠnµ¥š¸É¤¸­°Š˜´ªÂž¦—´Šœ¸Ê
yt
b10 b12 z t J 11 yt 1 J 12 z t 1 H yt
zt
b20 b21 yt J 21 yt 1 J 22 zt 1 H zt
(3.11)
(3.12)
56
3.2.4.1 „µ¦ª·Á‡¦µ³®rž‘·„·¦·¥µ˜°­œ°Š˜n°‡ªµ¤Âž¦ž¦ªœ(Impulse Response
Function: IRF)
ÁœºÉ°Š‹µ„„µ¦ª·Á‡¦µ³®r‹Îµ¨°ŠVAR Ťn­µ¤µ¦™ª·Á‡¦µ³®r‹µ„‡nµ­´¤ž¦³­·š›·Í
š¸Éŗo‹µ„„µ¦ž¦³¤µ–‡nµ‹¹Š˜o°Š°µ«´¥ª·›¸„µ¦°ºÉœÄœ„µ¦nª¥ª·Á‡¦µ³®r
Impulse Response
Function(IRF) Áž}œ°¸„®œ¹ÉŠª·›¸„µ¦š¸É°µ«´¥Âœª‡·— Moving Average Á¡ºÉ°¡·‹µ¦–µ„µ¦Á‡¨ºÉ°œÅ®ª
…°Š˜´ªÂž¦š¸ÉÁž}œ°œ»„¦¤Áª¨µÃ—¥Â‹Îµ¨°Š VAR ‹³°µ«´¥‡»–­¤´˜· Stability …°ŠÂ‹Îµ¨°Š
Ĝ„µ¦Á…¸¥œÂ‹Îµ¨°ŠÄ®o°¥¼nĜ¦¼ž…°ŠVector Moving Average (VMA) —´Šœ¸Ê
ª yt º
«z »
¬ t¼
ª yt º f
«z » ¦
¬ t¼ i 0
i
ªI11 i . I12 i º ªH yt i º
»
«I i I i » «
22
¬ 21
¼ ¬H zti ¼
(3.13)
‹µ„œ´ÊœšÎµ„µ¦®µ˜´ª‡¼– Multiplier ( Iij (i) ) …°Š‡nµ‡ªµ¤Ÿ·—¡¨µ— (H i ) Ĝ‹Îµ¨°Š
VMA Ĝ˜n¨³nªŠÁª¨µÂ¨³œÎµ˜´ª‡¼–œ´Êœ¤µ Plot „¦µ¢Áš¸¥„´Áª¨µ‹³Å—o IRF ®¨´Š‹µ„š¸Éŗo IRF
‹³­µ¤µ¦™ª·Á‡¦µ³®r‡ªµ¤­´¤¡´œ›r…°Š˜´ªÂž¦®œ¹ÉŠ˜n°°¸„˜´ªÂž¦®œ¹ÉŠÄœÂ˜n¨³nªŠÁª¨µŽ¹ÉŠÄ
œ
„µ¦«¹„¬µœ¸Ê IRF ­µ¤µ¦™°„š·«šµŠÂœªÃœo¤„µ¦Áž¨¸É¥œÂž¨ŠÂ¨³…œµ—…°ŠŸ¨„¦³šÄœÂ˜n¨³
nªŠÁª¨µÅ—o×¥˜´ªÂž¦š¸É¤¸Ÿ¨˜n° —´œ¸‡nµÁŠ·œš¸Éšo‹¦·Š š¸É­Îµ‡´‡º°‡ªµ¤®œº—…°Š —´œ¸‡nµÁŠ·œš¸É
šo‹¦·Š(Persistence) ¨³˜´ªÂž¦°ºÉœ
3.2.4.2 „µ¦ª·Á‡¦µ³®r„µ¦Â¥„­nªœ…°Š‡ªµ¤Âž¦ž¦ªœ(Variance Decomposition)
‹µ„IRF Áž}œ„µ¦ª·Á‡¦µ³®r˜´ªÂž¦š¸É«¹„¬µÂÁž}œ‡¼nÁœºÉ°Š‹µ„­´¤ž¦³­·š›·Í…°Š
Error
…°Š˜´ªÂž¦Á—¸¥ª
‡nµ‡ªµ¤Ÿ·—¡¨µ— (H i ) š¸É‡Îµœª–Å—oÁž}œ‡nµš¸ÉÁ„·—‹µ„
VarianceDecomposition (VD) ‹¹ŠÁž}œª·›¸„µ¦®œ¹ÉŠÄœ„µ¦ª·Á‡¦µ³®r£µ¡¦ª¤Äœ¦³Ã—¥‹µ„
‹Îµ¨°Š VMA š¸Éŗo‹µ„„µ¦®µIRF Á¦µ­µ¤µ¦™¡¥µ„¦–r( Forecast) ˜´ªÂž¦Å—o(®¦º°¡¥µ„¦–r
‹µ„VAR ®¦º°VEC „Èŗo)
Á¡¦µ³Œ³œ´Êœ­nªœž¦³„°…°Š‡ªµ¤Âž¦ž¦ªœ…°Š‡ªµ¤‡¨µ—Á‡¨ºÉ°œ…°Š„µ¦¡¥µ„¦–r‹³
°„Á¦µÁ„¸É¥ª„´­´—­nªœ…°Š„µ¦Á‡¨ºÉ°œÅ®ªÄœ®œ¹ÉŠ sequence °´œÁœºÉ°Š¤µ‹µ„ shocks …°Š˜´ªÂž¦
œ´ÊœÁ°ŠÁ¤ºÉ°Áš¸¥„´ shocks °´œÁœºÉ°Š¤µ‹µ„˜´ªÂž¦°ºÉœÃ—¥„µ¦¡·‹µ¦–µ­´—­nªœ…°ŠŸ¨„¦³š…°Š
˜´ªÂž¦

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