國內油價與所得關係之探討-門檻向量誤差修正模型之應用

全文

(1)國立中山大學經濟學研究所碩士論文. 國內油價與所得關係之探討-門檻向量誤差修正模型之應用 An Examination of the Relationship between Oil Price and Income in Taiwan by Threshold Vector Error Correction Model.. 研究生：王鈺雯撰指導教授：李慶男博士. 中華民國九十六年六月.

(2) 謝辭一本著作得以完成，除了需要靈感，還需要許多的幫助。這本碩士論文紀錄著我兩年來所學的點點滴滴。論文能夠完成要感謝我的指導教授李慶男老師，老師平時教學認真，有著豐富的涵養及敏銳的心思。以及兩位口試委員，王俊傑老師與翁銘章老師，為學生的論文費心審查，並給予諸多寶貴的意見。此外，感謝所有老師的不吝教誨，以及秀燕姐和育萍姐的協助。論文寫作期間，特別感謝憲政學長在我徬徨無助的時候提供建議，真的是一個盡責的好學長。而可愛的學弟政揚也不時地給我加油打氣。宜璇，你讓我看到光明堅強的一面，讓我有了新的體會。而詩婷努力朝自己的理想邁進也讓我佩服。奕瑄則是一起研究論文的好伙伴。以及所有的同學們，有了你們，研究所的生活增添了不少的色彩，祝福你們。學生生涯至此告一段落，當學生的日子以來，總是過著無憂無慮的生活，感謝父親的辛苦持家與母親的慈愛，大姊和二姊的照顧。還有之元，總是在我最累的時候陪著我。我想我是幸福的孩子，在此，僅將這一小小的研究成果獻給我摯愛的家人。待在中山的時間不長，但中山的確很美，讓我擁有許多的回憶，藍色的大海，空無一人的沙灘，將是我懷念的地方。. 王鈺雯謹誌於中山大學經濟學研究所中華民國九十六年六月.

(3) 摘要石油屬於耗竭性資源，用完即不可再生，其蘊藏量分佈極為不均，半數以上集中在中東地區。近年來國際原油變化莫測，油價的絕對數據也一再突破新高。台灣地區自產石油極為有限，為國際油價之接受者，故油價對於經濟的影響不得不成為重要的議題。根據經濟學原理，油價上漲常造成停滯性通貨膨脹，故本文首先利用共整合方法探討國內油價與本國每人所得的關係，發現兩者之間存在負向的長期均衡關係。除此之外本文還以 Hansen andSeo(2003)門檻向量誤差修正模型來檢定國內油價與本國每人所得之間是否存在門檻效果，結果發現變數間符合門檻共整合的長期均衡關係，並且可表達成門檻向量誤差修正模型。. 關鍵字: 油價,停滯性通貨膨脹,門檻效果,門檻向量誤差修正模型。. 1.

(4) Abstract Since petroleum is a kind of exhaustive resource, it can not be regenerated after being consumed. And petroleum is distributed extremely uneven in the world, more than half of petroleum is distributed in the Middle East area. In the recent years, the oil price was so fluctuating and broke the record again and again. However, the productivity of petroleum in Taiwan is very low and we are a price taker. So it turns to be important that how the oil price affects the economy. According to Economics, high oil price often causes the staginflation. In the purpose of this study we examine the long run relationship between oil price and personal income in Taiwan by cointegration theory. And we find that there indeed exists a negative longrun relationship. In addition, we consider a nonlinear model, Threshold Vector Error Correction Model, to test a threhold effect in the long run relationship between variables. Finally we have a result that there is a threshold cointegrating relationship between the oil price and personal income in Taiwan.. keywords: oil price, threshold effect, threshold vector error correction.. 2.

(5) ê 1. ï¡ 1.1. G. 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. í´}¬ÈÿÇ . . . . . . . . . . . . . . . . . . . . . 1.1.2 í´}Ý; . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 @~^ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 @~êÝ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 @~/Úx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bz§¡8nZ¤/) 2.1 Bz§¡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 8nZ¤/) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . @~]° 3.1 ql . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Dickey-Fullerl(DFl) . . . . . . . . . . . . . . . . . . . . 3.1.2 Augmented Dickey-Fuller l(ADFl) . . . . . . . . . . . . 3.1.3 Phillips-Perron l(PPl) . . . . . . . . . . . . . . . . . . . 3.2 FÙJ)l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Engle and Granger Ë$ð£° . . . . . . . . . . . . . . . . . 3.2.2 Johansen tÃ«£° . . . . . . . . . . . . . . . . . . . . . 3.3 Granger.n;l . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Ô.l° . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 b'0-ÑÑÿl . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 £ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1. 2. 3. 3. 6 6 8 8 10 10 11 11 12 16 17 17 19 22 23 25 27 30 31 32 32 34.

(6) @J5 4.1 £]¼Ù

(7) § . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 ql . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 J)l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Engle and Granger Ë$ð£°l . . . . . . . . . . . . 4.3.2 JohansentÃ«£°l . . . . . . . . . . . . . . . . 4.4 '0-ÑÑÿlGranger causalityl? . . . . . . . . . . . . . . . . 4.5 b'0-ÑÑÿl . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 ¡ 5.1 ¡ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! ¢Z¤. 4. 4. 36 36 36 38 38 39 40 42 46 46 48 49.

(8) %ê )1.1*¬ÈÿÇ . . . . . . . . . . . . . . . . . . . . . . . . . )%×*»jæ´}T¬ÈÿÇ . . . . . . . . . . . . . . . . . . )4.1*o ql . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )4.2*y ql . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )4.3*Engle-grangerJ)l . . . . . . . . . . . . . . . . . . . . . . . )4.4*tÊa¡óóã . . . . . . . . . . . . . . . . . . . . . . . . . )4.5*JohansenJ)l . . . . . . . . . . . . . . . . . . . . . . . . . . )4.6*VECM;ó£ . . . . . . . . . . . . . . . . . . . . . . . . . . . . )4.7*Granger causality.l . . . . . . . . . . . . . . . . . . . . . . )4.8*bl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . )4.9*b'0-ÑÑÿl;ó£ . . . . . . . . . . . . . . . . . . . )4.10*b'0-ÑÑÿl;ó£ . . . . . . . . . . . . . . . . . . )%Þ*»/´T% . . . . . . . . . . . . . . . . . . . . . . . . . . . . )%ë*Í»NßXÿT% . . . . . . . . . . . . . . . . . . . . . . . . . .. 7 7. t. 37. t. 37. 5. 38 39 40 41 42 42 44 45 48 48.

(9) 1 1.1. G. ï¡. í´ßÆÌ

(10) ¼ÝtÎ¦Bzs"Ýú*í´)Î t±Ý×ËÙ!`í´ÝßP0lEy´ÙÏP®ÞÝ¶ÊÎ Ń »jæ´}¬È´2¥« ¾J´ãº¾ÀÎºH T ½´Ý{ÎÍºCWÀBzT£®½Ý\ÎÍºñ¼Bz<[ ´¼£Îî¬EßÆÝßþCW'ÝÅ( í´}Å(Bz`bö\3sßÏ×gí´^`-Â½2SRBz .ÝD¡Pierce and Enzler1974t"Dí´}ÀBzó Ýn ;Í@~s¨í´}î>ºE0JmO¦0l¿£î>CBzW £ìª¡|Hamilton1983 ´Ý@~.ïÆs¨´ÝîbrBzW £ìâÝ¨é.- ´Ý;ÀBzóbÛ6ÝnÐh¡8n@ ~-¼ Huang1989"D»j.ôE¬ÈÿÇÝÅ(s¨»jæ´}Ý ÎCW¬È»ÓXÿiã®Ýx.ôY»0JºÝEy¬È ÿÇ¬P½ÝÕæôµÎ1EylwBzlVÝ¬ÈÅ (ÍÿÇÝ»j.ôxÎ¼y@²«&0J« ^¼¬È´2¥ ¾J´ÃRãº¾Eyí´}Ýn¥ ãyí´ÝÅ(Î«PÝEyß®ïõðï/ªbDEÝ2 1.1.1 í ´ } ¬ È ÿ Ç ¬È ×lwBzvEÙ ýb{ÝµäP/)¬ÈÝ µ1973OÝÏ×gí´^Îãy|Z°» ÝMSsí´ /ºl `æ´}ã`¿íN[4Y-î16Y-´WÝ°¹r 1974OÕ1975O ¬ÈBz\á<[ÝÏÞgí´^sßy1978O9 Îãy¦ÏÞí´í»þksßÅ¸æ´®Þ3CW¦½º yþ»jæ´}ô`¿íN[13-îÕ1979O11`N[43.2Y-î 3.3¹H{Ý´ùr¬È31980OÕ1983O ÝBz<[Ïëgí 6.

(11) ´^ 1990O.þZ¸á+I©s®úÈ;Ê `»j´ã`¿ íN[17Y->`¿í33Y-¼ráÝ¦BzWÝXM¦ Bzùy1990OÕ1992O\á<[¬Î¬Èh`ÿ<[Ñ?3þZ¸á+I ©`@¬ÎåÕhgí´^Å(20tSÏ31988O9Õ2000O . OPECàÝ3®[TCWæ´ºm´¸»j´ã2000O¿íN[11Y.>Õ¿íN[25Y-|îÝiã Ý2000OÕ2001O¬Èÿ<[Ý¨é )1.1*¬ÈÿÇ. £]¼Ù ÅoBz' õºçìhttp://www.cepd.gov.tw/index.jsp.. )%×*»jæ´}T¬ÈÿÇ. 7.

(12) í´}Ý; À)»j´ðåÕß®®ÞmO|C»jÅ»TÝø!Å( ÃÍî»jæ´½ãyC¿ÇÄ3&]Tæ@ì½÷L9 .hÍ}&ðp|ï?Y»:T½(¼§¡ÇF»j´ ï?PáJ»jæ´}s"LúÿËÍ T 1.1.2. ´ÌÁ{®P qAY»ÙIX2µ£]îÎ¼æŃ[}Vy4060YÆbÞ20Y--yESAIï?óAîìôK-û10Y|î4QY»ÙIXèºæ´}ï?óAqÌ¢P¬ô 4tv«Q§2Z°r»B`»jæ´ÞîN[80Y-|C½ ºym`æ´}öÿN[40Y-|ìÝP 2 æ´}: 4Q»jæ´})böÿ¬} ½FÙæ´^ÇÛ Ï&FÙæ´sß®WÍ){Î¼»jæ´}Þ9ÿKN [40Y-Ý^£÷¼÷±Ç-¨ÍX¹ ôÞ÷¼÷y. 1. ãy»j´ÌbîÝ Tv®Ó¨èÝT¬È®í´Á b§¿{y5Üè"|îÄä ý.hN »j´®`¸¬ÈåÕÝ Å( G 1. 1.2. @~^. O¼»jî"DÙ}ÀBz nÐPÝZ¤K¬x½¿yË] '× @J"D]°²{ÎGranger.l'&]hl(VAR) õ' 0-ÑÑÿlVECM¨×J ×íÉtÊ;¼"D4Q8nZ a¾9¬¾1ýú. qA@oBzXU@Ù>0@~¼»j´îy5Þè»/´Þî>y5 èÎGDP¿3óÞîy5ëF°âBzWJÞìÿy5ëFÞÚ 1. 8.

(13) AHamilton1983|Granger.lÝ]°aBè¿OÝ@~¼´ îÝ\ÎBzÁfÝ- ×Hooker1996J×DGÝ@~Z ¤ú1973O|¡ÝY»ÀBz¨´>>8n¬%"~Íæ .QHamilton1996- í´}®; Ýn;º. £ ] Ý©PõóbÝ-CW5bX!Ý0 ¨b@~&aPÝ` ÿl|5 ËxøFÙÝ°Î|5` 6 ® x;Ý»5F"D ÿlÕósßx;Ý` FG¡ Õó Ýn;ÎÍbX!¨×vJÎ|Tong ( 1978 , 1990 Xèb ]h]° Ã|5ó6 x;Ý»5F53ÕóbÂî ìÕó Ýn;ÎÍbX!ãy|5` 6 »5FÝ5] °Ä6xÌÝ-sßxP;Ý` F]°î´Ì.hXÿÝ ¡ôµ8 5 h² Õó3y /¹2sß»Ý;`| ` x;»5FÝÿlºP°æ\ÿlÝx;8´ì| ó »5FÝ5]°|¹îÝþ´ bJ)ÿl´ãBalke and Fomby(1997)èBalke and Fomby- 3¾ ÕíÉÄ` ºb&=PÝJÆ¼ãyÅ83 Bz`Äm}×ÝJWÍX|ó3! 'íÉJÝÄ ºÓ¨×lÝ¨é.hJÄ3J¡Ý[ÇyWÍ`ôµÎÒ íÉ´`º¨&Æ- 9bÃyÕ ¢´Xÿ Ýn;`ú ¦`ß3FÙÝJ)©ÊÝó D3aPJ)n;8´ ìbJ) ×M"D` ÎÍ &aPJ)EyBz¨éÝÕ æÞ è ÆÍZ|Hansen and Seo (2002)èÝb'0-ÑÑÿ l(Threshold Vector Error Correction Model )!Ý«'NR»/´Í» NßGDP Ýn; 8n@~èº×Íf´. 9.

(14) 1.3. @~êÝ. ÍZÝ@~êÝ 1 @~Í»NßGDP»/´ÎÍD3J)n; 2 @~»/´Ý£ÎÍryÍ»NßGDPÝ£¸ÿBh D3. n; 3 @~Í»NßGDP»/´ÎÍD3bJ)Ýn; 4 £bÂ¬ãb'0-ÑÑÿl¼Ùó ÝyVíÉ 1.4. @~/Úx. ÍZÝÚx5 "aÏ×a ï¡1ÍZÝ@~eÿ@~^@ ~êÝCÍZÝ/ÚxÏÞa Bz§¡8nÝZ¤/)´+Û ´Å(XÿÝBz§¡#½+Û»/².ï@~bnyÉyBzÅ( ÝZ¤/)Ïëa @~]°+ÛÍZXàÝ8n§¡ÿlÀql J)lÿlGranger.l|Cb'0-ÑÑÿlÏ°a @ J5ÞÍZXk"DÝÀBz§¡¿àÿlXÿÕÝ@J ®×J§Ó¨Ï"a ¡EÍZÝ@J@~®×À1. 10.

(15) 2 2.1. Bz§¡. Bz§¡8nZ¤/). OÝí´^0lÝÝBzÁf¸ÿ9ó.ï@~Ù }Àó Ýn;Ù}¿yBzWÝÌFûÅ ¾X-!¬ Ù}~bÎBã¢ËÑ¼¼Å(JÍBzÕêG cJ$ÎÿÕ ×lPÝ¡|ìÃ¯1Ù}ºDÄø°H5Å(ÕJÍBz 1973. FÙº«\ h×Ñ¼ÎÞÙÚ xß®7áô× Ù}î>2âÙºT sßyþãyß®7á3KÞ0l®3Kz\jß®æ«½ìª qAz½ÝíÉf@²

(16) ££ÎãÎzÝ\jß®æX!X .h@²

(17) £ÝW£ôºìªA(ê

(18) £Ìb'ìÝüPJ ´¼£Þºî>×ßA- h×Ù}Ýî>ÎyõPÝ\Jº JÝðY|.Th×yõPÝ²3\ 0l@²¿£Ýî >¸7£Y3K 2 mO«.ô Ù}@Ý`ÎLÍ

(19) y3îÝðïº§PÝ;ô ð»AÃ¤º. ´î;cUÃ¦^ Ýið¾ô º.h3KØ°\òPÝóàÕÆÿáb´?ÝG> c.h9à #3KÝ¾Ýð7£w¸ÿÀmOìªÀõmOà¼É® 3K 3 XÿÉ»õÀ)mO í´}î>í´íá»ÝI XÿÞÉ»Õí´í»0lË»ó æÝ;2¸í´ ý»ÝðmOìªí´í»ÝðmOî> qAaªÝB39ËôæÝ8!Å(ìÀðmOÞìª; º¦. 1. 11.

(20) @²¿£«½ìª Ôk7£¼nÙI5ðYÝ3KQÀm Oìªº¸ÿÀmOà¼ÉCWÎìª®3K 4 @²õÜ[ Ù}î>¾ºE0JÝmO¦hù0J ÎC`¦0J º#3K0JºJº¸À)mOàÞ¼É¸ÿ¿£î>Î ìÿõ®ìª»AHoover and Perez1994¥Õ Y»ÍåÕÙ }\`Y»Ð¢£¿£Federal Fund Rates, FFRº«½î>. ¶Y»Ýÿ<[QÎãÙ}îXCWI5ÿ<[Ýæ. Å82ãå¹PÝ0JÅXl 2.2. 8nZ¤/). 9ó.ï-í´}ÿÇÌb8nP3@JÝZ¤]«Hamilton 1983Ç¿àSims1980XèÝÀBzóáí´}Ýó |Granger.n;Granger causality test)Ý]°jEY»ÝÀBzó l@ßîî31948OÕ1972O æ´}î>rY»Bz®<[ V34î´îÝ\31972O|GÎCWY»Bz<[Ý×Í¥. ô× ¡Burbidge and Harrison1984¿à'&]hl@~Y^Æ zJ

(21) ¼;»Ù}® Ýn;ÿÕHamiltonv«Ý¡ Mork1994 ×MÞÙ}® 5 Ñ'C'®tÝJÙ }\¿y@²Bzþ¬s¨DbEÌP[Íî ´îò `@@º¸Y»Ý®<[´ìÿ`®î>Ý[¬½ QHooker1996Ý5Jî1973O|¡Ýí´}Y»®¬^b ½Ý.n;70O|¡í´}ÝóÎÅ(Y»®Ý²ß ó®ï¿ËÕ»Aí´}ÎÍ» /ßó|'&] hÝ]°l.n;ô^b½Ý jEHookerX5ÝHamilton1996L5Net Oil Price Increase6 ¥±EHooker(1996)Ýó .lJY»1948OÕ1994OÝæ´}; 12.

(22) )ºrY»®Ý;©Î8ý1973O|GÝ5¼:1973O|¡Ýæ´ }E®Å(@@´¬yAHookerX5æ´}Îr® ;Ý²ßó Huang1989"D»j.ôE¬ÈÿÇÝÅ(¿à1961 1984 O £]@~»j.ôÀY»@²»Óß®gÜY»0JºY»ëÍ`» 0Ò¿£»jæ´}E»/@²»Óß®gÜõÎiãÅ(5½x &]h'ÿlVARCh&]h'ÿlBayesianVAR ² ó5¼ÌDó®åÍ¸óÅ(»s¨»jæ´}Ý ÎCW¬È»ÓXÿiã®Ýx.ôY»0JºÝEy¬È ÿÇ¬P½ÝÕæôµÎ1EylwBzlVÝ¬ÈÅ (ÍÿÇÝ»j.ôxÎ¼y@²«&0J« Daniel1997¿àYz^ë»1960OÕ1992O®£]CÌ3²ßP weakly exogenousæ´}¼"D»j ®W£n;¬ x P T5Íx&]h'ÿl(VAR)C0-ÑÑ'ÿl(ECM)¼ J)5s¨ó ÌbÞà; T 5 ß®æ T*.ôCæ ´} Tæ]7á¼óîYzÞ»® Tåæ´} T Å(8Eyß®æ TÅ(Q^Í® Tåß®æ TÅ(Q8E yæ´} TÅ(v ×M2 ï?0-²ó5îæ´ }Ý\EyYz^ÿÇ/Ìb¥ÝÕæ Clements and Krolzig (2000)¿àyG»ð(Markov Switching)ÿP¼¡´ EÿÇ!$ðÝÕæA¢¨²ôÌD´3!$ð`Ý&EÌÅ( P@JîyÿÇ!$ð`Bz®¬ºåÕ´ÝÅ(4Q ×°»ÝBz<[Îh.y´Ý»Q¡ÎÍbP´ÝÅ (Bz<[¦2»ðUùÝÅ(ÎyUù»ð<[Ý Lee, Huh and Harris2003¸à1959OÏ3Õ1996OÏ4Ý@²GDPõ»j ¿í´£]D¡æ´}Ý\õ?¼Y»õ^ÍEjöÿÇÝ \s¨æ´}EjöÝÅ(ý¼Ý@~- ÉjöBz ©bà#Ý\ºDÄ»²®Ý\Å( 13.

(23) ôbK.ï"DÉÀBzóÝÅ(»ABrown and Yucel (1999) ¢ã&]h'ÿl(VAR)ÿlÝ\DT(Impulse Response )¼¡´Ý A¢Å(Y»ÝBz51965O1997OÝ`£]@Jî´Ýy º¸ÿ»/ß®gÜ3±¬vCW¿£îò Chang and Wong2003¿à'0-ÑÑÿl(VECM)¬¤g¸à²ó5 (Variance Decomposition )õ\DTÐó(Impulse Response )5@~´® ±ÝÀBz Ýn;@~A!GZ¤X´Ý®EÀ óÌb¿ÝÅ(ÍEy±BzÝÅ(¬æ.J ± O¼Ù¸à* Ml¸ÙÛ/ìª Cunado and Gracia2003ÊÝ´Àó D3J)¿àJ )Ýl]P ó D3J)`|0-ÑÑÿl(ECM) ÑÑGranger.n ;Granger causality testsÝljEö9Í»5ÿÕ´ÝE 9» Ý;0µªõ®Å(¬8!h¡ô²î»j´ÝEyt &îÝXb»ÍÅ(ÝºY»Ý@~b8!¡ LeBlanc õChinn (2004)¿àÃ¿ûà]°EÁ¢Å(EG5»(Y z°ÆC^Í)Ý;0µªôè:°Í@Js¨´ÝîòE;0µªÝÅ (b§öõY»E´ÝAPô^b¢Ý-² Cunado and Gracia (2005)¿à1975OÏ×2002OÏÞÝ£]E±ö» (y¼±^Í±P8Ã;C»)Ý@~s¨´&ð½ ÝÅ(yÝBzþCÎ¼ó´õÀBz Å(n;Ý&EÌ Pô3×°»J Guo and Kliesen (2005)J¼×Íy´»Ý;¡ÍÎ}Ýîò Tìª/ºEY»ÝÀBz(Aü7£ð´¼£¿£õ}iã)® ß¿ÝÅ( rÕ(2005)J- ´{E&»BzWÅ(b§#»{Bzï ?Âxæ.;ãyæ´Û/æ´ð/@²GDP´Gìª!`Qô ¼´î¹350-îE¦Bz)ÞCW×J©½ÎD ÌÙWÍîXSsÝ;0µª®ÞâÞD9ðY ¼7£EB 14.

(24) z®ß¿Å( nyÉy®`Tz½Ý@~ô9b½

(25) »ADavis and Haltiwanger (2001)¸à'&]hÿP(VAR)5µ¼£Ù¸à

(26) Ã!ÿ 5¼lÑÝCÝÉy

(27) ®Ý0àCâcÝÅ(s¨´ Ýî Cìÿà#DTµ¼½¬Ó'n;Carruth et al. (1998)¸à0ÑÑÿl(ECM)ôs¨É´¼£b¥ÝÅ(´Ýî Þ!M¸´¼£î ò AHondroyiannis and Papapetrou2001|1984O1`Õ1999O9`Ý`£]@~ 6À¼ýÝVø!®àjEÙ{µä ýÝ6 5s¨æ´ }ºE6Ý

(28) ¼ß®ñ¼«\ ~¹(2004)"Dí´î%Ì²ß;¡´Å(ÍI3} ®õzÝÍ5 ´5½î10ªC50ª`3®`}]«| ÙÛ/{Ý®¼Å(t¼XåÝÅ(t3®C!Â] «Xå®CÝ®¼J×Ä6ÚÍ½®¼|í´ 7áÝ9>C®¼ ÝnÐ¼¾\µ¼ßý]«|¼XåÝ®Ct.J®Ýì ªº0l´¼£î>¼|z x7á.hº.®Ý3K¸z ßý3K.h´î>¬ñ¼BzÝ ¹mOÝ3K¸JBzåÕ¿ ÝÅ(#=ñ¸ÍzmOßý3K |îÎ&»nyÉyBzÅ(ÝZ¤/).ïÆ|!Ý] °nT&ÍÅ(·«. ´;ñ¼ÝÅ(*)P°@¬|ï]3 Î¼ãyí´ÝßPÞ¸ÿ´î'`ÉyBzÝ\Þ÷¼ ÷. 15.

(29) 3. @~]°. ¿àDickey-Fullerql°EY»£] l5 s¨ÀBzóûÅD3q¨éÇ` ÌPù & P(non-stationary)3FÙÝ@J@~ 92à]h]°¼£ó Ý n; Ý¹¨Ì]h(spurious regression)Ý®Þ

(30) §&` Ý ]PºbX!.h3¿à` ÀBz@J5G¾óÎÍ ÌPW @J5TþÝ×4M» |ì&ÆµP&PÝ+Û` £] 5 P &PPÝlVê5 úP3P3hL3P(weakly stationary Tcovariance stationary)A×` y |ìëÍfEyX bÝt t − s t − j Nelson and Plosser(1982). 2. t. E(yt ) = E(yt−s ) = µ E(yt − µ)(yt − µ) = E(yt−s − µ)(yt−s − µ) = σy2 E(yt − µ)(yt−s − µ) = E(yt−j − µ)(yt−j−s − µ) = γs. J&ÆÌh` y Ì3PÍTÂµ²óσ &²óγ í b§Ýðóº.` Ý;DEy×Í&Ýó²3 ÝWshockÞº ` ¦@´²óô© ï` 5 6 Ý!!k5×Í&Ý` óbËË]°|ÞÍÿÌb P× -5¿%× T¿% 1 -5¿%: ×&ó¢ã-5»ð óu©m-5×gÇ¾Õ PJB I(1)um-5dg¾ÕPJB I(d)u×ÍBÄdg -5¡ÝóîW×Í%CYÝ(invertable)ÝARM A(p, q)Aì 2 y. t. s. (1 − φ1 L − φ2 L2 − ... − φp Lp )(1 − L)d Yt = c + (1 + θ1 L + θ2 L2 + ... + θq Lq )εt (3.1). 3]h]°lT£@JÿlÝ`ÎAX2àÝ` óÎVJ]h b¸æÍmP.n;Ýó Q¨Ý.n; 2. 16.

(31) Íφ(L) = 0Cθ(L) = 0ÝXbq/a3i²(Outside Unit Circle)vε ×ç¯JÌY Î×ÍARIM A(p, d, q)óud = 1`J(3.1)P¶ t. t. (1 − L)Yt = c + ψ(L)εt. Íψ(L) = φ. −1. (3.2). v;ó EJ(3.2)PîW. (L)θ(L). Yt = y0 + ct + ψ(L). Íct ü Tψ(L) P 2 T¿%: ub×ó. t−1 X. εt−i. i=0. t−1 i=0 εt−i. ^ T. Xt = µ + ct + ψ(L)εt. Íψ(L)Ý;ó EE(X ) = µ+ctV ar(X ) = (1+ψ +ψ +...)σ . V ar(X ) < ∞.h©X ótctx J»W¿%óhÌ T¿%Ä t. t. 3.1. t. t. 2 1. 2 2. 2. t. ql. AD3×ÍAR(1)Äy = ρy + u Íu ç¯3ÊXÛÝ5ó qÝìρ > 1¡ÝXbÂKº¸ós÷Íρ = 1Ît|"DÝ X|&ÆÌρ = 1` qÄ(unit root process)lρÎÍy×J ql ÍZÞ+Û×@ß5ð¸àÝql°Dickey-Fuller lDFl Augmented Dickey-Fuller lADFlPhillips-Perron lPPl 3DFql0-4' ç¯ ¡Þ0-4Ý§×@w´ bADFlPPl 3.1.1 Dickey-Fullerl (DFl ) Dickey and Fuller(1979)Ê×ÍAR(1)Ý` lPlÎÍÌbq© P3T ÍøÍÌDÂÝµìDickey and Fuller J¿àOLS°X£ t. t−1. t. 17. t.

(32) ρÝ£ÂρˆÌb×lP!`3ÌnqÝÌP'ìtÙÝ5g ×ðV5gÎËÍ¾kº(Brownian Motion)8tÝP 'Ò]hP ×ÍAR(1)ÿl Yt = ρYt−1 + ut ρ=1. 3hY = 0vu i.i.d(0, σ ) ×ç¯ µÍÎÍâðó4(constant term)T` T(timetrend)]hP5 ì ëËlV ÿl×]hPPðó4C` T 0. 2. t. yt = ρ1 yt−1 + ut. 'l H : ρ = 1H ÝÁ§5g 0. 1. (3.3). 3ÌP'WñìDickey-Fuller0lÙ. :ρ<1. 1/2{[W (1)]2 − 1} R1 [W (r)]2 dr 0 1/2{[W (1)]2 − 1} t = (ˆ ρ − 1)/ˆ σρˆ → R 1/2 1 2 dr [W (r)] 0 T (ˆ ρ − 1) →. Íσˆ = [s ÷ P y ] vs = P (y − ρˆy àOLS£°ÿÕÝ£Â ÿlÞ]hPâðó4¬P` T ρˆ. 2. T t=1. 2 1/2 t−1. 2. T t=1. t. 2 t−1 ) /(T. yt = θ + ρyt−1 + ut = x0t ρ + ut. 18. − 1). ρˆÎã(3.3)P¿. (3.4).

(33) ]hPðó4'l H : ρ = 1(vθ = 0)H ñìDickey-Fuller0lÙÝÁ§5g R. θ. 0. 1. 3ÌP'W. :ρ<1. 1. 1/2{[w(1)]2 − 1} − W (1) · 0 W (r)dr T (ˆ ρθ − 1) → R1 R1 [W (r)]2 dr − [ 0 W (r)dr]2 0 R1 1/2{[W (r)]2 − 1} − W (1) · 0 W (r)dr tθ = (ˆ ρθ − 1)/ˆ σρˆθ → R1 R1 { 0 [W (r)2 ]dr − [ 0 W (r)dr]2 }1/2. Íσˆ = [s e (P x x ) e ] e = [01] vs = P ρˆ õÎã(3.4)P¿àOLS£°ÿÕÝ£Â ÿlë:]hPâðó4C` T ρˆθ. 2 0 2. 0 −1 1/2 t t 2. 0. 2. T t=1 (yt. 2. − θˆ − ρˆθ yt−1 )2 /(T − 2). . θ. yt = θ + ρyt−1 + δt + ut. (3.5). = x0t ρ + ut. ]hPðó4δ ]hP` T4'l H : ρ = 1(vδ = 0)H : ρ < 13ÌP'WñìDickey-Fuller0lÙÝÁ §5g R R R θ. 0. 1. 1. 1. 1. 1/2{[W (1) − 2 0 W (r)dr][W (1) + 6 0 W (r)dr − 12 0 rW (r)dr] − 1} T (ˆ ρτ − 1) → R 1 R R R R 2 dr − 4[ 1 W (r)dr]2 + 12 1 W (r)dr 1 rW (r)dr − 12[ 1 rW (r)dr]2 [W (r)] 0 0 0 0 0 tτ = (ˆ ρτ − 1)/ˆ σρˆτ. ˆ ρˆ y − δt) ˆ /(T −3) Íσˆ = [s e (P x x ) e ] e = [010] vs = P (y −θ− ρˆ Îã(3.5)P¿àOLS£°ÿÕÝ£Â ulP°`ÌP'Çy ×&PDy J ×P îëËÿlÝlÙÁ§5g¬&òy×ÝðV5gTÎt5g Î ¾kº(Brownian motion)X|Û&ÂP°¢ðVTÎt5gÎ ¢Dickey andFuller(1979)ÝÛ& 3.1.2 Augmented Dickey-Fuller l (ADFl ) DFlTà3AR(1)ÿlv0-4 ç¯Dickey-Fuller(1979) ×MÊ0 -4Ìb8n t8nmápa¡4¸0-4 ç ρˆτ. 2 0 3. 1/2 0 −1 t t 3. 0. 3. 2. T t=1. t. τ t−1. τ. t. t. 19. 2.

(34) ¯.hè|AR(p)` lP qlÌ ADFl(Augmented Dickey-Fullerl) 'Ò]h P×ÍAR(p)ÿl yt = φ1 yt−1 + φ2 yt−2 + . . . + φp yt−p + εt. (3.6). 3hε i.i.d(0, σ ) L 2. t. ρ ≡ φ1 + φ2 + . . . + φp ζj ≡ −(φj+1 + φj+2 + . . . + φp ). j = 1, 2, . . . , p − 1. BÄó.P»ð¡Þ(3.6)PJ§W. yt = ζ1 ∆yt−1 + ζ2 ∆yt−2 + . . . + ζp−1 ∆yt−p+1 + ρyt−1 + εt. (3.7). µÍÎÍâðó4T` T]hP5 ìëËlVÍÿlîAì. ÿl×:]hPPðó4T` T yt = ζ1 ∆yt−1 + ζ2 ∆yt−2 + . . . + ζp−1 ∆yt−p+1 + ρyt−1 + εt. (3.8). = x0t ρ + εt. 'l H Á§5g. 0. :ρ=1. H. 1. 3ÌP'WñìDickey-Fuller0ÙÝ. :ρ<1. R1 1/2{[W (1)]2 − 1} − W (1) · 0 W (r)dr T (ˆ ρ − 1) → (σ/λ) · R1 R1 [W (r)]2 dr − [ 0 W (r)dr]2 0 ∗. Í(σ/λ) 8nÝlÑ. vBJÄ¡ R1 1/2{[W (1)]2 − 1} − W (1) · 0 W (r)dr T (ˆ ρ∗ − 1) → R1 R1 1 − ζˆ1 − ζˆ2 − ... − ζˆp−1 [W (r)]2 dr − [ 0 W (r)dr]2 0 R1 X 1/2{[W (1)]2 − 1} − W (1) · 0 W (r)dr ∗ ∗ 2 0 0 −1 1/2 t = T (ˆ ρθ − 1)/[s ep+1 ( xt xt ) ep+1 ] → R1 R1 1/2 { 0 [W (r)]2 dr − [ 0 W (r)dr]2 } 20.

(35) Íe = [00 . . . 01] s = P (y − x ρˆ ) /(T − p) ρˆ Îã(3.8)P¿àOLS£ °ÿÕÝ£Â ÿlÞ:]hPâðó4¬P` T 0. p. T t=1. 2. 0 ∗ 2 t. t. ∗. yt = ζ1 ∆yt−1 + ζ2 ∆yt−2 + . . . + ζp−1 ∆yt−p+1 + α + ρyt−1 + εt. (3.9). = x0t ρ + εt. ]hPðó4'l H : ρ = 1(vθ = 0)H : ρ < 1 3ÌP' WñìDickey-Fuller0lÙÝÁ§5g: T (ˆρ − 1)Ct = (ˆρ − 1)/ˆσ Íe = [00 . . . 01] s = P (y − x ρˆ ) /(T − p − 1)ρˆ Îã(3.9)P¿ àOLS£°ÿÕÝ£Â ÿlë:]hPâðó4C` T α. 0. 1. θ. 0. p+1. T t=1. 2. θ. ∗ 2 0 t θ. t. θ. θ. ρˆθ. ∗. yt = ζ1 ∆yt−1 + ζ2 ∆yt−2 + . . . + ζp−1 ∆yt−p+1 + α + δt + ρyt−1 + εt. (3.10). = x0t ρ + εt. ]hPðó4δ ]hP` T4'l H : ρ = 1(vδ = 0)H : ρ < 13ÌP'WñìDickey-Fuller0lÙÝÁ §5gT (ˆρ − 1) Ct = T (ˆρ − 1)/[s e (P x x ) e ] Íe = P (y − x ρˆ ) /(T − p − 2)ρˆ Îã(3.10)P¿àOLS£° [00 . . . 01] s = ÿÕÝ£Â ADFlT (ρˆ − 1)ÙBÑÑ¡DFlT (ρˆ − 1)ÙÌb8!ÝÁ§ 5gADFlt ÙDFlt Ìb8!ÝÁ§5g.hADFlÝÛ &à!øãDFlÝÛ&. α. 0. 1. ∗ τ. 0. 2. ∗ τ. T t=1. t. ∗ τ. 2 0 p+2. ∗ 2 0 t τ. 0 −1 1/2 t t p+2 τ. p+2. ∗. ∗. ρˆ∗. ρˆ. ¡Said and Dickey(1984)?U"'-5¡Ý` ×ARMA(p, q)l Ppõq Îá(unknown)ÿlîAì (1 − φ1 L − φ2 L2 − . . . − φp Lp )∆yt = (1 + θ1 L + θ2 L2 + . . . + θq Lq )εt 21. (3.11).

(36) 'RÂy. 0. Îi.i.d(0, σ ) ×ç¯¬Þ(3.11)P¶W. = 0 εt. 2. η(L)∆yt = εt. Í η(L) = (1 − η1 L − η2 L2 − . . .) = (1 + θ1 L + θ2 L2 + . . . + θq Lq )−1 (1 − φ1 L − φ2 L2 − . . . − φp Lp ). .h×ARMA(p, q)Ý` »ð ×AR(∞) Ý` Ò]hP yt = yt−1 + η1 ∆yt−1 + η2 ∆yt−2 + η3 ∆yt−3 + . . . + εt. (3.12). ]hÿl yt = α + ρyt−1 + η1 ∆yt−1 + η2 ∆yt−2 + . . . + ηk ∆yt−k + etk. (3.13). = x0t β + etk. Í etk = ζk+1 ∆yt−k−1 + ζk+2 ∆yt−k−2 + . . . + εt. 3he ç¯uk → ∞vk¦Ý>yT J tk. p. etk − εt = ηk+1 ∆yt−k−1 + ηk+2 ∆yt−k−2 + . . . → 0. AkÂÈJARIM A(p, 1, q)3ÌP'ìÝlÙARIM A(p, 1, 0) 3ÌP'ìÝlÙb½8!ÝÁ§5g 3.1.3 Phillips-Perron l (PPl ) 3ADFl°4Ê"-4Ìb8nÝP¬QÎÊb D3²²P(heteroscedasticity)Ý®Þ.hPhillips(1987)Phillips and Perron(1988).ÌbqÝAR(1)ÿl;¨Õ?×;Ý'Êu ×Ímixing processÇ.&u b×Ý8µPC²²Pµs"Ýl]° t. t. 22.

(37) Ò]hPîAì yt = ρYt−1 + ut. (3.14). ρ=1. 3hY = 0vu ×Ímixing process ]hÿlîAì 0. t. yt = α + ρyt−1 + ut. (3.15). ¿àOLS°£P;óρˆ `Phillips and PerronÈÝÑÑlÙ T. 1 ˆ 2 − γˆ0 ) Zρ ≡ T (ˆ ρT − 1) − (T 2 σ ˆρ2ˆT ÷ ST2 )(λ 2 ˆ 2 − γˆ0 )/λ} ˆ × {T · σ ˆ 2 )1/2 · tT − { 1 (λ ˆρ2ˆT ÷ ST } Zt ≡ (ˆ γ0 λ 2. (3.16) (3.17). Í λˆ2 = γˆ0 + 2. l X. [1 − j/(l + 1)] · γˆj. j=1. γˆj = T −1 ·. T X. uˆt ut−j ˆ. t=j+1. ÀøÍóρˆ àOLS°£PÝρÂσˆ ρˆ Ý²óS ù¿àOLS£ POÿ"-4Ý²ó.hBÄÑÑ¡ÝlÙùDFlADFl °b8!ÝÁ§5gÆk¸àPPl°`ÍÛ&Â!ø¢Dickey and Fuller(1979)ÝÛ& T. 3.2. 2 ρˆT. T. FÙJ)l. T. 2 T. ` ]°31980O|¼@~¥Fæ¼ÝP` ó @~@U"ÕXÛ&` ]°Ý@~Í¥ÝMÓ1Î¼ yGranger and Newbold(1974)s¨&ó º¨XÛP]hÝ¨ é ÝXÌP]hÝ®ÞBz.ïè×°]°»AÞ&PÝ` -5(difference) T T£](detrended data)Q3 &` 5 23.

(38) `f´)§Ý]P GïÇ|-5¡ÝP ]h5h]°4 b[ÝXîÝ®ÞQôSsÍÝBz®Þ. Þ` -5¡Ý óÝÎ×Ë;ÝlV4Qz½2¡y/Ý;Qô¸ÿ ó ©P´l¸P°ló ÎÍD3½íÉn;yÎãEngle and Granger(1987)OèJ)§¡Æs¨&ó Ý]hn;A ¨J)Ç×à&Ý` óÝaPà)WÌPJÌ b J)¨éJ9øÝ]hn;)QbBzLvËÍó D3½%Ý íÉn;|ì Engle and Granger (1987)J)ÝL L×:u'y ÝXbàWô/ I(d)&PÝ` vD3×' a(6= 0)¸ÿz = a y ∼I(d − b)Íb > 0JÌ'y ÝàWô D3db$ J)n;ÐrB y ∼CI(d, b)'aJÌ J)'(cointegration vector) Engle and Granger (1987) èGranger Representation TheoremÊ×Í(n × 1)Ý'y v∆y ÌbWold representation. t. 0. t. t. t. t. t. t. (1 − L)yt = δ + Ψ(L)εt. Íε i.i.d.(0, Ω)v{s · Ψ } = 0EP(absolutely summable)' 'y ÝàWô D3hÍJ)n;JºD3×Í(h × n)ÝÎpA vÎ pA ÝN× aP}ñJ×(h × 1)Ý'z LW. t. ∞ s s. 0. t. 0. t. zt = A0 yt. X|z Î×ÍÌPÝ¨²ÎpA b×©P. 0. t. A0 Ψ(1) = 0. uÞîW×Íp$ÝV ARÿl. yt = a + Φ1 yt−1 + Φ2 yt−2 + . . . + Φp yt−p + εt. Tî. Φ(L)yt = a + εt 24.

(39) Í Φ(L) ≡ Ik − Φ1 L − Φ2 L2 − . . . − Φp Lp. JºD3×Í(n × n)ÎpB|. Φ(1) = BA0. ÍΦ(1) = I − Φ − Φ − . . . − Φ X|ºD3(n × n)Îpζ ,ζ ,. . . ,ζ ]hÿlîAì. k. 1. 2. 1. p. 2. p−1. ∆yt = ζ1 ∆yt−1 + ζ2 ∆yt−2 + . . . + ζp−1 ∆yt−p+1 + a − Bzt−1 + εt. (3.18). PÇ ×Í0-ÑÑÿl(vector error correction modelVECM)(z ) íÉ0-ãîDÄGranger Representation Theorem ÿáJ)n;Ä0 -ÑÑÿlETJ)ðÕ BzóÌbíÉn;2âÝ9°ó ÎÌb?íÉ]'JÝ©PùÇ3y`ó D3 ÒÝ¨é¬Î9ËyÒíÉÝ¨éTº@¹9ÍCWÒ íÉÿ|@XÝ^×µÎXÛÝ0-ÑÑ^ 3.2.1 Engle and Granger Ë $ ð £ ° Ê×Í£°. (3.18). t−1. yt = βxt + ut. Bãql@y x / I(1) lM»Aì. M»× ¿àOLS°£"-uˆ ¿àOLS£°£βˆ ÿÕ"-uˆ uËó D3½J)n; Juˆ ∼ I(0)ÇÌP3øÍÝµìβˆ[eÕË@Âβ¬&|×> √T [eÎ|y×>ÝT [e.hãOLS°£ÝβˆÂÌbø×l P(superconsistency) t. t. t. t. t. 25.

(40) M»Þ ¢ãlu ÎÍ I(1)ÿÕy x ÎÍD3J)n; 'l ÌP'H : u ∼ I(1)îy x DJ)n;Eñ' H : u ∼ I(0)¿àDF TADF ql°|îÝ? t·ÿlîA ì. t. t. 0. 1. t. t. t. t. t. ∆ˆ ut = ψ ∗ uˆt−1 +. p−1 X. ψ ∗ ∆ˆ ut−i + wt. i=1. Íw i.i.d.(0, σ )Aψ ½²yëJ`ÌP'îu ∼ I(0)y x Ë óD3J)n;ù¿à0-ÑÑÿlî. ∗. 2. t. t. t. ∆yt = a1 + ay (yt−1 − βxt−1 ) + A(L)∆yt−1 + B(L)∆xt−1 + w1t. (3.19). ∆xt = a2 + ax (yt−1 − βxt−1 ) + C(L)∆yt−1 + D(L)∆xt−1 + w2t. (3.20). ÍA(L)B(L)C(L)õD(L)í b§Ýa¡94P ε = y − βx 0-ÑÑ4 ˆ ¿àεˆ = y − βx ñáhÿlÿlîAì. t−1. t−1. t−1. t−1. t−1. t−1. ∆yt = a1 + ay · εˆt−1 + A(L)∆yt−1 + B(L)∆xt−1 + w1t. (3.21). ∆xt = a2 + ax · εˆt−1 + C(L)∆yt−1 + D(L)∆xt−1 + w2t. (3.22). ÿlÝ∆y ∆x ∆y õεˆ Xbó/ I(0)ÆàOLS¼£¢ óOó ÝyVJÄ QEngle and Granger Ë$ð£°4Q|U¬Q2Ý¿ÍE¯ Ýþ´. 1 ãyh]°Îó ÝJ)'©b×Í.h©ÊàyËóJ) n;Ýl ó ËÍ|î`D3ÝJ)'©×Íhù l `ÌJ)n;Í¬ó ÇD3J)n; 2 D3½b§øÍ-(finite sample bias)Ý®Þ4Q3J)]hÿl5 βˆÌbø×lPÝ©P¬AøÍóÄK`|ly-Ý®Þ)P° E¯ t. t−1. t−1. t−1. 26. t.

(41) 3Phillips and Durlauf (1986)çîβˆÝÁ§5g &ðV5g(nonnormal)vt lÙ¬&t5gÆ¿àht lÙ 'l ÎP[Ýl 3.2.2 Johansen t Ã «£ ° ãyEngle and Granger Ë$ð£°b|îÝþ´ÆBz.ïXè&9 !Ýl]°|RîïÍ|Johansen èÝtÃ«£°tÌ PôÎêG ct Â½¿àÝJ)l£° Johansen tÃ«£°ÎãJohansen(1988)Johansen(1991)è|ló ÝJ)n;3JohansentÃ«£°Î'ÿlÍ '&]h ÿl(vector autoregression modelVAR)v£lJ)'ÝÍó. h8ýEngle and Granger ÝË$ð£°?

(42) §ËÍ|îÝó®Þ 'b×Í(n × 1)Ý'y v'y ÝN×ôí I(1)|V AR(p) î. 3. t. t. yt = µ + Π1 xt−1 + Π2 xt−2 + . . . + Πp xt−p + εt. t = 1, 2, . . . , T. (3.23). ∆yt = µ + ξ1 ∆yt−1 + ξ2 ∆yt−2 + . . . + ξp−1 ∆yt−p+1 + ξyt−1 + εt. (3.24). ÍµÎðó4vε i.i.d.N (0, Ω) Þ(3.23)P|0-ÑÑÿlî. t. Í ξ = −(In − Π1 − Π2 − . . . − Πp ) = −Π(1) ξi = −(In − Π1 − Π2 − . . . − Πi ). t = 1, 2, . . . , p − 1. ''y ÝN×Í½óy í I(1)v¸Æ ÌbrÍJ)n; Jξ = αβ αβ/ (r × n)ÝÎpβÌ J)ÎpαJ J;óÎp ÎpξÝè(rank)¼D3yó íÉn;ÝóêÇJ)'ÝÍ óD3bëË. t. it. 0. 27.

(43) rank(ξ) = nÇξÎp G>ÎpÇè(full rank)î'y Ý& ó/ PÝ` 2 0 < rank(ξ) = r < nî'y Ýó D3rÍJ)' 3 rank(ξ) = 0Çξ Îp èÎpÇ ëè(null rank)½'y ¬D 3¢J)n; .hlÄx3y@ξÎpÝèùE(3.24)P 'lÌP' H : rank(ξ) = r|@rank(ξ)J)Ý'Íó JohansentÃ«£°M»Aì. M»×Õ§]h(Auxiliary Regressions) ∆y y 5½E∆y ,. . . ,∆y ®]hÿlÞ(3.24)P;¶W. 1. t. t. t. 0. t. t−1. t−1. t−p+1. Z0t = ΓZ1t + ξZpt + εt. Í Z0 t = ∆yt Z1t = 1, ∆yt−1 , . . . , ∆yt−p+1 Zpt = yt−p Γ = (µ, ξ1 , . . . , ξp−1 ). ¿àOLS£ÿÕ"-4R CR v"-Ý¿]õ. 0t. pt. Sij = Mij − Mi1 M−1 11 M1j. (i, j = 0, p). JÍf¹ÝÃ«Ðó(concentrated likelihood function)î. T. −T /2. L(α, β, Ω) = |Ω|. 1X (R0t − ξRpt )0 Ω−1 (R0t − ξRpt )} exp{− 2 t=1. M»Þ ÕÑø8n(Canonical Correlations) 28. (3.25).

(44) kOtÃ«£POìP. |λSpp − Sp0 S−1 00 S0p | = 0. .hÿÕ©Pq(eigenvalues) λˆ > λˆ > . . . > λˆ > 0Cýã;¡Ý©P' (eigenvectors) Vˆ = (ˆv , vˆ , . . . , vˆ )vVˆ S Vˆ = I M»ë ÕÃ«ÐóÝ£¢ó(MLE Estimation of Parameters) uD3rÍJ)n;Jβ£Ç GrÍ©PqXETÝGrÍ©P'X àWÝÎpÇβˆ = (ˆv , vˆ , . . . , vˆ )vξ = αβ Þ(3.25);¶W(3.26). 1. 1. 1. 2. 2. 2. n. 0. n. pp. 0. r. T. −T /2. L(α, β, Ω) = |Ω|. 1X exp{− (R0t − αβ 0 Rpt )0 Ω−1 (R0t − αβ 0 Rpt )} 2 t=1. (3.26). βÂüì|ÿÕìP. ˆ = S0p β( ˆ βˆ0 Skk β) ˆ −1 α( ˆ β) ˆ = S00 − S0p (βˆ0 Skk β) ˆ −1 βˆ0 S0k ˆ β) Ω( ˆ = (M01 − ξMp1 )M11 −1 Γ. èËËl°¼lJ)'ÝÍó. 1 ªl(Trace Test). 3Î@D3¿àJ)n;GãîXÿÕÝ©Pqàyl ÿlt9D3rÍJ)'ÝÌP'ÎÍWñ H : rank(ξ) ≤ r (9brÍJ)') H : rank(ξ) > r (byrÍJ)') lÙ. Johansen. 0. 1. −2 ln(H0 |H1 ) = −T. n X i=t+1. î) ln(1 − λ. Í 5g|¾ ×Í(n − r)îÝ¾k¹º(Brownian Motion) vlÙÝÁ§5gºyQÎpÝª 29.

(45) t©Pql(Maximum Eigenvalues Test). 2. H0 : H1 :. brÍJ)' br+1ÍJ)'. lÙ. ˆ r+1 ) −2 ln(H0 |H1 ) = −T ln(1 − λ. 8!2Í 5gù¾W×Í(n − r)îÝ¾k¹º(Brownian Motion)vlÙÝÁ§5gºyQÎpÝt©Pq 3.3. .n;l. Granger. 3BÄJ)l¡¾W0-ÑÑÿl30-ÑÑÿlóB Ä×g-5Ó¨PyÎ&Æ|ºàGranger.n;lÍ Ý.n ;Granger.n;¼ÝÎÙîÝ.n;¯@î¼ÝÎó ` îÝ ra¡n;Hamilton(1983)©½úGranger.n;¬&ìîÝ.n ;Granger.n;ÝÎ3ÙîØÍóÝ;ÎÍ\y¨×ÍóÝ ;Granger(1969).n;ÝLAì LÞ bX õY ËÍI(0)Ý` ÍLG>/)AìX:âX |² ÄÝXb£GY :âY |²ÄÝXb£GX :âX õÄÝX b£GY :âY õÄÝXb£GF M SE(X |X, Y ):îâX õY |²ÝÄXb£Gìï?í]0- Granger.lbì°Ëµ t. t. t. a. t. a. t. t. t. }ñn;. 1. F M SE(Xt |X) = F M SE(Xt |X, Y a ) = F M SE(Xt |X, Y ). 30. t. t.

(46) v F M SE(Yt |Y ) = F M SE(Yt |X a , Y ) = F M SE(Yt |X, Y ). îfáEX ¦ÝY TÝXb£GT¦ ÝY |²ÝÄXb£G/P°EX Ýï?í]0-®ßÅ(! §EY X óÝáôEY Ýï?í]0-^b¢;.h |¾X õY Î8!^b.n;Ý 2 '.n; F M SE(X |X) > F M SE(X |X, Y )áY |²ÝÄXb £GbÃyX Ýï?æÆáY ºÅ(X !§uF M SE(Y |Y ) > F M SE(Y |X, Y )JX ºÅ(Y 3 .n; F M SE(X |X, Y ) < F M SE(X |X, Y ) ÝY ºñÇÅ(X !§ uF M SE(Y |X , Y ) < F M SE(Y |X, Y )JX ºñÇÅ(Y 4 /n; F M SE(X |X) > F M SE(X |X, Y )vF M SE(Y |Y ) > F M SE(Y |X, Y ) áÍóÝ£GEyóKb´·Ýï?[£J Ô'Ý.n; 3.3.1 Ô . l ° Granger(1969)èº×ÍÔ.n;ÝluÊPAì t. t. t. t. t. t. t. t. t. t. t. t. t. t. t. t. t. t. a. t. t. t. t. t. a. t. t. t. t. t. zt = a0 + a1 zt−1 + ... + ap zt−p + b1 xt−1 + . . . + bp xt−p + et. t. t. t. (3.27). î ` 4pî tÊa¡óùÇGranger.lÝÌP' H :x does not Granger cause zlxóÎÍÙîEÎ¼Ýz Ìb£GÇÎEt ¿]°Ý]h;ób b Ð)ll]h;óÎÍ½²yë ÆGranger.lÝÌP'ô H : b = . . . = b = 0AóxEÎ¼Ý ózÌb£GÝFlÝlÙº`ÌP'îxÝ;|EÎ¼zè t. 0. 1. p. 0. 1. 31. p.

(47) º£GDu`ÌP'Jî^bÈJAîx|EÎ¼Ýzèº £G lÙ F =. (RSSr − RSSu )/p RSSu /(T − 2p − 1). ÍRSS å§×Ý"-¿]õRSS Îå§×Ý"-¿]õpa¡ ó r. 3.4. u. b'0-ÑÑÿl. FÙÝJ)©ÊÝó D3aPJ)n;#½&ÆÊBzó J)¨é|&=ÝòP¼ JÞÍU &aPÝÿlG ¸ÿlæî>EyBz¨éÝÕæô è bJ)ÿlÎãBalke and Fomby(1997)èBalke and Fomby- 3¾Õ íÉÄ` ºb&=PÝJ ` 3ñÒíÉHG `J)n;´ ú¦Q ` ÒíÉ8 Ý`ÎJJ)n ;´ ß3Æ¼ãyÅ83Bz`Äm}×ÝJWÍX |ó3! 'íÉJÝÄºÓ¨×lÝ¨é.hJÄ 3J¡Ý[ÇyWÍ`ôµÎÒíÉ´`º¨ Hansen and Seo(2002) ×M¿àË ½bJ)'0-ÑÑÿl l hÿlÝ¥F3ylÎÍD3×Íb[ÍÝbó 0-ÑÑ 4Ç@~ 0-ÑÑ4ybÂÝ`Î0-ÑÑ4ybÂÝ`Îó 3Õ¾íÉÄÝJ ÎÍ8!Hansen and Seo È¸àSup LMÙ lb[D3Í¬èÐ)lÙ 5g 3.4.1 £ aP'0-ÑÑÿl 'x ×pîI(1)Ý` ux D3×p × 1ÝJ)'βJw (β) = β x I(0)Ý0-ÑÑ4u|'0-ÑÑÿlîJ2PAì t. 0. t. t. t. ∆xt = A0 Xt−1 (β) + ut 32. (3.28).

(48) Í∆x x Ý×g-5X (β) = [1, w , ∆x , ∆x , · · · , ∆x ] k × 1Î pvl tÊa¡ó(lag length)A k × p;óÎpÍk = p × l + 2' 0-4u ×martingale difference sequencevE(u u ) = Σ ×b§²Îp ÝÿÕ°×PmÞÎpβÑð;(Normalization)ÇÞβÍ×-ô' 1 30-4u iid Gaussian'ìÍ¢ó(β, A, Σ)ãtÃ«°(Maximum ˜ A, ˜ "˜ Σ) ˜ îJu˜ = ∆x − AX ˜ Likelihood)£ÿÍ£Â|(β, (β) ' bË ½'0-ÑÑÿl Hansenõseo(2002)qAaP'0-ÑÑÿlÞÍU" bË ½Ý' 0-ÑÑÿl t. t. t−1. t−1. t. t−1. t. t−2. t−l. 0 t. t. t. ∆xt =. t. t−1. A01 Xt−1 (β) + ut if wt−1 (β) ≤ γ A02 Xt−1 (β) + ut if wt−1 (β) > γ. (3.29). Íγ bÂîÿlù;¶ . ∆xt = A01 Xt−1 (β)d1t (β, γ) + A02 Xt−1 (β)d2t (β, γ) + ut. (3.30). Pd (β, γ) = 1(w (β) ≤ γ)d (β, γ) = 1(w (β) > γ)Ç w (β) ≤ γ `d (β, γ) = 1Dd (β, γ) = 0 w (β) > γ `d (β, γ) = 1D d (β, γ) = 0vb[°b30 < P (w ≤ γ) < 1Çw ≤ γsß^£ +y0õ1 bLÍJhÿlÞ;WaPJ)X|áÊ Ý§×f (constraint)': 1t. t−1. 2t. 1t. t−1. 1t. t−1. 1t. t−1. t−1. 2t. t−1. π0 ≤ P (wt−1 ≤ γ) ≤ 1 − π0. Íπ > 0 ×J¢ó(trimming parameter)Í@~¢Hansen and Seo(2002)3@JÄ'π = 0.05qAHansen and Seo(2002)30-4u iid Gaussian'ìÍtÃ«£ÝGaussian likelihood. 0. 0. ln(A1 , A2 , Σ, β, γ) = − n2 log|Σ| −. Í. t. 1 2. Pn. t=1. ut (A1 , A2 , β, γ)0 Σ−1 ut (A1 , A2 , β, γ). ut (A1 , A2 , β, γ) = ∆xt − A1 0 Xt−1 (β)d1t (β, γ) − A2 0 Xt−1 (β)d2t (β, γ) 33.

(49) |M LE(Aˆ , Aˆ , Σ,ˆ β,ˆ γˆ) ln(A , A , Σ, β, γ) tÃ«£ÂAˆ (β, γ) CAˆ (β, γ) ãI5øÍw (β) 6 γõw (β) > γ Í½|∆x EX (β) ]h ÿAì 1. 2. 1. 2. t−1. 2. 1. t−1. t. t−1. n n X X 0 −1 ˆ A1 (β, γ) = ( Xt−1 (β)Xt−1 (β) d1t (β, γ)) ( (β)∆xt 0 d1t (β, γ)) t=1 n X. Aˆ2 (β, γ) = (. t=1 n X. Xt−1 (β)Xt−1 (β)0 d2t (β, γ))−1 (. t=1. (β)∆xt 0 d2t (β, γ)). t=1. uˆt (β, γ) = ut (Aˆ1 (β, γ), Aˆ2 (β, γ), β, γ) n 1X ˆ Σ(β, γ) = uˆt (β, γ)uˆt (β, γ)0 n t=1. .hÿÕ|ì;Ã«]P. np n ˆ ˆ γ)| − (3.31) ln(β, γ) = ln(Aˆ1 (β, γ), Aˆ2 (β, γ), Σ(β, γ), β, γ) = − log |Σ(β, 2 2 P ˆ γˆ ) MLE(β, β π0 6 n−1 1(xt 0 β 6 γ) 6 1 − π0. 3J)' ðV;C § ˆ ×ìÿt;log |Σ(β, γ)|3ðV;CG§×ìβ γ -BãÏ(3.30)P tÃ«Â£QÏ(3.30)P¬&¿âÐó.hP°|FÙÝVÉ. Õ°(gradient hill-climbing algorithms)OHansen and Seo(2002)ÈãË î(β, γ)ÝF£(grid search)OÿÃ«ÂtÝà)|® J)'(β)b Â(γ)£Â 3.4.2 l b[ÝlÍ@~JÎ|Hansen and Seo(2002)èSupLMl ãJÍÙ5g`½Îãbootstrapÿa®ßtÝ"-&ýã;5 g|CW¢ó®ÞlÿlÊ)aPÝ'0-ÑÑÿlTÎ&aP b'0-ÑÑÿlÌP'H (3.28)PÝaP'0-ÑÑÿlEñ 'H (3.29)PÝb'0-ÑÑÿl (3.30)PÝA = A `ÿlÞ ; (3.28)PÝFÙaP'0-ÑÑÿlhl°½¥y|ÿl ÃÝl (model-based statistical tests)v.&ÿlà#Ýf´.h3ÿlïIî´ ÍPÒól(nonparametric tests)?Ì[æ 0. 1. 1. 34. 2.

(50) hl ¿àLM(Lagrange Multiplier)Ù¼Æ'(β, γ) ávü JÌP'Eñ'5½Aì. ∆x H ∆x. H0. t. = A0 Xt−1 (β) + ut. 1. t. = A1 0 Xt−1 (β)d1t (β, γ) + A2 0 Xt−1 d2t (β, γ) + ut. A ½2yA `î×b[D3uJ)(β)õbÂ(γ) á`qAHansen and Seo(2002)lÙ. 1. 2. LM (β, γ) = vec(Aˆ1 (β, γ) − Aˆ2 (β, γ))0 (Vˆ1 (β, γ) + Vˆ2 (β, γ))−1 × vec(Aˆ1 (β, γ) − Aˆ2 (β, γ)). Í ˆ i = Mi (β, γ)−1 Ωi (β, γ)Mi (β, γ)−1 i = 1, 2 V Mi (β, γ) = Ip ⊗ Xi (β, γ)0 Xi (β, γ) i = 1, 2 Ωi (β, γ) = ξi (β, γ)0 ξi (β, γ) i = 1, 2. PX (β, γ) X. ÀP'(stacked vector)£Pξ (β, γ) ˆ (β, γ) 0-ÑÑ4! ½ u˜ ⊗ X (β)d (β, γ)ÀP'£PvecA 4x EX (β)d (β, γ) ]h;óÀP'£PVˆ (β, γ)J vecAˆ (β, γ) ²Îp£P uβõγ ÎááH ÌP'ìÝF£Â.hβ|(3.28)PXÿ£ Âβ˜ áãyH ì¬PbÂ.hlÙJ. t−1 (β)dit (β, γ). i. t. t−1. t. i. it. t−1. i. it. i. i. 0. 0. SupLM =. ˜ γ) LM (β,. sup. (3.32). γL ≤γ≤γU. γ¨´Pγ Þyw˜ π y5fγ Þyw˜ (1 − π )y5 ft¡3µAHansen and Seo(2002)èÝü]hPdí°(fixed regressor bootstrap)|C"-dí°(residual bootstrap)¼ÕÍ `½p-value|l ÿlb[. [γL , γU ]. L. t−1. 0. 35. U. t−1. 0.

(51) 4 4.1. £]¼Ù

(52) §. @J5. ÍZ@~ 1987OÏ°2006OÏ°|£] 577ÍÌ DÂÍZ;¿àHansen and Seo(2002)b0-ÑÑÿlXóãÝó »/ ´Í»NßGDP 3»/´]«µï´2¥Ý´`ê4Q´2¥Ý´`4ê¾9 ¬´`îìÿÝ TÎ×lÝÆÍZóãÜÞPÕ_´Ý}¼»/´ ¬BÄÐ³ÎJ @²´ìµÝæ£]£] `£]lVã3Í `¿íW £]vÎB;PJ£]¼Ù5 ËI51999O1`|¡Ý£ ]¼y´2¥Ýçì1999O|GÝ£]¼y¬È2 ÙÙ£]0 3h©½1´2¥Ý´J®¼æJÍJ¼ý NYMEX WTI(Y»ÆLùæ´)[8ãóÞ¼ýÝ» N ×WTI}î×WTI}f´»y5fâWãóÞãh á»/´)6¢»jÝæ´}¬»´ õc35î«2à »/´G»/¨µì5ÝôÞ? Þã3Í»NßGDP] «£]ÝlV £]£]¼Ù ¬ÈBz± £]0X¸àÝóAì »/@²ó =log(ÜÞPÕ_´}/Ð³Î¼ó) 2 Í»NßGDPy =log(NßGDP) 1. t. t. 4.2. ql. 3EBzó n=P"DGÄ6|ql PÝl| ¹®ßÌ]hÝ®ÞÍZ¸àADFl°PPl° E»/´Í»N ßGDPPÝ@-ql@JA. 36.

(53) )4.1*o ql H :o iãÂ q t. l. ADF. Ù. t -2.8708. Ù. 0. t. Ù H :o ×$-5 q. PP. Ù. PP. p-value 0.1778. l. 0. t -3.0202. p-value 0.1337. t. ADF. t -7.3173***. l. p-value 0.0000***. l. t -7.2873***. p-value 0.0000***. !Û 1. ***31¥½iãì|`ÌqÝÌP' 2.X¸àÝÿlvl âðó4` T4Ýÿl 3.Û&Â¢Fuller(1979). )4.2*y ql H :y iãÂ q t. Ù. l. ADF. t -2.5886. Ù. t -6.8734***. 0. t. Ù H :y ×$-5 q. PP. Ù. PP. p-value 0.2867. l. 0. l. t -1.9231. p-value 0.6327. t. ADF. p-value 0.0000***. t -10.7942***. l p-value 0.0000***. !Û 1. ***31¥½iãì|`ÌqÝÌP' 2.X¸àÝÿlvl âðó4` T4Ýÿl 3.Û&Â¢Fuller(1979). l¼NßGDP»/´Ý` P¡31¥5¥T10¥Ý½iã ì/Ìbq©PvBÄ×g-5¡Ó¨VùÇNßGDP»/´ / I(1)` Æ»/´Í»NßGDP5m ×M¸àJ)l ¼ï-ËïÝÉíÉn; 37.

(54) 4.3. J)l. 3G×;Í@~EyNßGDP»/´ qllîË ïí &Ý` 3@ó/ I(1)¡ ×MÊó D3 J)n;ÍZ#½J)lÍðÝJohansen(1988)J)l° Balke and Fomby(1997)- Johanson(1988)J)l]°3bJ)l æ· ¬Engle and Granger(1987))býÝlº[ÆuÎËÍ®ß ×lÝ`Î|Engle and GrangerË$ð£°Ý ã 4.3.1 Engle and Granger Ë$ ð £ °l 3h®Engle and Granger(1987)Ë$ð£° M»×|y |Co óEBh t¿]]hÿìËf]hP 3. t. t. yt = α1 + β1 ot + e1t ot = α2 + β2 yt + e2t. M»Þ35½E"-4e e ql lA 1t. 2t. )4.3*Engle-grangerJ)l H :e q ADFl PPl tÙ tÙ -3.10597** -3.05035 ** H :e q ADFl PPl tÙ tÙ 0. 1t. 0. 2t. -2.57647*. -2.47149*. !Û 1. ***5½310¥õ5¥½iãì|`ÌqÝÌP' 2.Û&Â¢Phillips and Ouliaris(1990) Balke and Fomby(1997)- JohansenJ)l]°ðVP'Þ.bJ)D3`" - &ýã5gCWÿl0'Ýµsß 3. 38.

(55) 3P¡Î|ADFl°TÎPPl°3½iã10¥ì`]hP "-4ÌqÝÌP'µh.\NßXÿ»/´D3J)n; É Tù.hÿÕÿlÝ@- 4.3.2 Johansent Ã «£ °l dyEngle and Granger(1987)Ýl°D3A(3.2.1);Xè