Measurement Matters for Modeling U.S. Import Prices

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 883 December 2006 Measurement Matters for Modeling U.S. Import Prices Charles P. Thomas and Jaime Marquez NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. Measurement Matters for Modeling U.S. Import Prices Charles P. Thomas and Jaime Marquez Abstract: We focus on capturing the increasingly important role that emerging economies play in determining U.S. import prices. Emerging market producers differ from others in two respects: (1) their cost structure is well below that of developed-market producers, and (2) their wide profit margins induce pricing policies that seek to exhaust production capacity. We argue that these features have dampened the short-run responses of import prices to changes in the value of the dollar but that they have not altered the associated long-run response. To capture these considerations, we develop a new method to measure foreign prices and adopt a formulation that differentiates between short- and long-run responses. Our econometric work asks two questions: First, can one replicate the literature's dispersion of passthrough estimates? Second, is there any evidence of a change in the dynamic response of import prices to changes in the exchange value of the dollar? To address the first question, we estimate the parameters of our models using several alternative measures of U.S. and foreign prices, dynamic specifications, and sample periods. We find that these alternative inputs translate into a large range of parameter estimates, a finding that helps to rationalizing the existing dispersion of estimates. To address the second question, we compute the implied dynamic adjustment of import prices to a change in the value of the dollar using parameters estimated from two samples: 1974-2000 and 1974-2005. The long-run response of import prices is similar regardless of which sample is used---roughly one-half of the change in the exchange rate is passed through to import prices. However, the short-run response is quite sensitive to the sample period. Specifically, the short-run response based on data through 2005 is smaller than the short-run response based on data through 2000. We argue that one force behind the change in dynamics of the import-price process is the greater presence of producers from emerging economies and that their effect on import prices can be captured with their measure of foreign prices. JEL classifications: F17, F41, C51, C53 Keywords: aggregation methods, automated specification, exchange rates, pass-through, Penn World Tables. E-mail addresses are [email protected] and [email protected]. We are grateful to Neil Ericsson, Joe Gagnon, Jane Ihrig, Mario Marazzi, Trevor Reeve, Nathan Sheets, and Robert Vigfusson for their detailed comments. A previous version of this paper was presented in the workshop series of the Federal Reserve Board and the meetings of the Fall 2005 meetings of the Midwest International Economics Group. The calculations use PcGets; see Hendry and Krolzig (2001). The views in this paper are solely the responsibility of the author(s) and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/ . 4 Lqwurgxfwlrq Mxvw krz pxfk wkh groodu vkrxog ghsuhfldwh wr uhvwruh h{whuqdo edodqfh lv wkh vxemhfw ri dq rq0jrlqj ghedwh lq zklfk olwwoh djuhhphqw h{lvwv1 Wkh glvdjuhhphqwv vwhp iurp vhyhudo vrxufhv exw dq lpsruwdqw rqh lv wkh uhvsrqvlyhqhvv ri X1V1 lpsruw sulfhv wr fkdqjhv lq wkh ydoxh ri wkh groodu1 Vshflfdoo|/ Jrogehuj dqg Nqhwwhu +4<<:,/ dqg Fdpsd dqg Jrogehuj +5338, uhsruw wkdw kdoi ri wkh pryhphqwv ri wkh groodu duh sdvvhg wkurxjk wr lpsruw sulfhv zkhuhdv Rolyhl +5335, dqg Pdud}}l hw do1 +5338, qg wkdw wklv sdvv0 wkurxjk/ zkloh vljqlfdqw lq wkh sdvw/ kdv yluwxdoo| glvdsshduhg1 Xvlqj d qhz phdvxuh ri iruhljq sulfhv/ zh qg wkdw sdvv0wkurxjk lq wkh orqj0uxq  dw wkh whq0|hdu krul}rq  kdv ehhq vwdeoh dw rqh0kdoi zkhuhdv sdvv0wkurxjk lq wkh vkruw0uxq dw wkh wzr0|hdu krul}rq  kdv ghfolqhg pdunhgo| ryhu wkh sdvw ghfdgh1 Zh eholhyh wkhvh qglqjv frqwulexwh wr uhvroylqj wkh glvshuvlrq ri uhfhqw hvwlpdwhv1 Wkh jhqhudo iudphzrun wr prgho lpsruw sulfhv xvhg e| suhylrxv vwxglhv lv jlyhq lq htxdwlrq +4,= Sp @ i +S| / Si / Sfrp ,/ +4, zkhuh Sp lv wkh sulfh ri X1V1 lpsruwv> S| lv wkh sulfh ri X1V1 surgxfwv> Si lv wkh iruhljq sulfh h{suhvvhg lq grooduv> dqg Sfrp lv wkh sulfh ri lqwhuqdwlrqdoo| wudghg frpprglwlhv1 Htxdwlrq +4, doorzv iru wkh srvvlelolw| wkdw iruhljq h{sruwhuv vhhn wr uhwdlq vrph sdulw| zlwk jhqhudo X1V1 sulfhv e| dgmxvwlqj wkhlu h{sruw sulfhv wr fkdqjhv lq wkh sulfhv suhydlolqj lq wkh X1V1 pdunhw1 Vxfk d vwudwhj|/ nqrzq dv sulflqj wr pdunhw/ lpsolhv wkdw CSp CS|   A 31 Htxdwlrq +4, dovr doorzv iru wkh srvvlelolw| wkdw dq lqfuhdvh lq wkh ydoxh ri wkh groodu/ zklfk udlvhv Si > lv wkhq sdvvhg wkurxjk wr Sp = Vxfk d uhvsrqvh lv nqrzq dv wkh h{fkdqjh0udwh sdvv0wkurxjk dqg lw lpsolhv wkdw CSp CSi   A 314 Htxdwlrq +4, rhuv rqh zd| wr udwlrqdol}h wkh glvshuvlrq ri hvwlpdwhv ri  uhsruwhg lq wkh olwhudwxuh= hpslulfdo vwxglhv glhu lq wkhlu fkrlfh ri sulfh phdvxuhv/ hfrqrphwulf irupxodwlrqv/ vdpsoh shulrgv/ dqg hvwlpdwlrq whfkqltxhv1 Dqrwkhu h{sodqdwlrq lv wkdw wklv glvshuvlrq lv uh hfwlqj d vwuxfwxudo fkdqjh lq wkh ehkdylru ri h{sruwhuv wr wkh Xqlwhg Vwdwhv wkdw lv qrw dghtxdwho| fdswxuhg e| uhfhqw vwxglhv1 Lqghhg/ rqh uhfhqw ghyhorsphqw wkdw txdolhv dv d vwuxfwxudo fkdqjh lv wkh lqfuhdvhg lpsruwdqfh ri hphujlqj hfrqrplhv dv d vrxufh ri X1V1 lpsruwv15 Wr judvs krz wklv srvvlelolw| vkdshv rxu vwudwhj| lqyroyhv d eulhi h{srvlwlrqdo ghwrxu wr zklfk zh qrz wxuq1 Wkhuh duh wzr vdolhqw ihdwxuhv ri hphujlqj hfrqrplhv wkdw pd| dhfw wkh ehkdylru ri X1V1 lpsruw sulfhv1 Iluvw/ hphujlqj hfrqrplhv kdyh orz surgxfwlrq frvwv uhodwlyh wr ghyhorshg hfrqrplhv1 Vhfrqg/ 4 Qrw doo vwxglhv duh zloolqj wr h{whqg wkh ehqhw ri wkh grxew wr htxdwlrq +4,1 Lqghhg/ uhfhqw vwxglhv uhfrjql}h wkdw vwudwhjlf lqwhudfwlrqv dprqj surgxfhuv phdqv wkdw  dqg  duh qrw sdudphwhuhv wr eh hvwlpdwhg exw udwkhu hqgrjhqrxv rxwfrphv uhvxowlqj iurp ghpdqg0vxsso| lqwhudfwlrqv dw wkh plfur ohyho1 Vhh Jurq dqg Vzhqvrq +5333,/ Jurvv dqg Vfkplww +5333,/ Khoohuvwhlq +5337,> Ergqdu hw do1 +5335,> Jxvw hw do1 +5339,1 5 Uhfhqw gdwd vkrz wkdw Fklqd glvsodfhg Fdqdgd dv wkh odujhvw surylghu ri qrq0ixho jrrgv wr wkh Xqlwhg Vwdwhv1 hphujlqj hfrqrplhv kdyh ehhq lqfuhdvlqj wkhlu fdsdflw| wr surgxfh h{sruwdeoh jrrgv dw d udslg udwh1 Wr wkh h{whqw wkdw hphujlqj0pdunhw surgxfhuv duh sulflqj wkhlu h{sruwv wr dfklhyh d pdunhw vkduh wkdw h{kdxvwv wkhlu jurzlqj surgxfwlrq fdsdflw|/ zh zrxog h{shfw wzr glvwlqfw hhfwv rq lpsruw sulfhv1 Wkh uvw hhfw lv vwudljkw0iruzdug= zh zrxog h{shfw vrph grzqzdug suhvvxuh rq lpsruw sulfhv dv hphujlqj0 pdunhw h{sruwhuv sulfh vrphzkdw ehorz suhydlolqj sulfhv lq rughu wr jdlq pdunhw vkduh1 Zh zrxog h{shfw wklv h{sdqvlrq lq vxsso| wr erwk lqfuhdvh wkh wrwdo yroxph ri lpsruwv dqg wr glvsodfh vrph lpsruwv iurp kljkhu frvw surgxfhuv zkr duh qrz qr orqjhu deoh wr sulfh deryh wkhlu yduldeoh frvwv1 Wkh vhfrqg hhfw lv pruh vxewoh dqg lqyroyhv wkh uhvsrqvlyhqhvv ri lpsruw sulfhv wr fkdqjhv lq h{fkdqjh udwhv1 Li wkh hphujlqj pdunhw surgxfhuv idfh vkruw0uxq fdsdflw| frqvwudlqwv/ wkhq dv wkhlu vkduh lq X1V1 lpsruwv lqfuhdvhv/ zh zrxog h{shfw lpsruw sulfhv wr ehfrph ohvv uhvsrqvlyh wr h{fkdqjh udwh pryhphqwv dqg pruh uhvsrqvlyh wr X1V1 sulfh ghyhorsphqwv1 Wr xqghuvwdqg wklv fkdqjh lq sulfh uhvsrqvlyhqhvv/ lw lv khosixo wr irfxv rq wkh lpsruw0vxsso| vfkhgxoh1 Wr wkh h{whqw wkdw fdsdflw| frqvwudlqwv duh elqglqj/ wkh vkruw0uxq vxsso| vfkhgxoh ehfrphv pruh qhduo| yhuwlfdo1 Wkxv pryhphqwv lq h{fkdqjh udwhv ru iruhljq frvwv/ zklfk lqgxfh yhuwlfdo vkliwv lq wkh vxsso| vfkhgxoh/ zloo kdyh d uhodwlyho| vpdoo lpsdfw rq sulfhv zkloh d vkliw lq wkh ghpdqg vfkhgxoh zloo kdyh d uhodwlyho| odujh lpsdfw rq sulfhv1 Wklv vlwxdwlrq grhv qrw lpso| wkdw iruhljq sulfhv/ ru h{fkdqjh udwhv/ duh ehfrplqj ohvv lpsruwdqw lq wkh ghwhuplqdwlrq ri X1V1 lpsruw sulfhv exw/ udwkhu/ wkdw wkh g|qdplfv ri wkh surfhvv duh fkdqjlqj1 Lq sduwlfxodu/ wkh orqj0uxq +vhfxodu, pryhphqwv duh vwloo ghwhuplqhg lq odujh sduw e| iruhljq fdsdflw| dqg frvwv +zlwk vrph uljkwzdug guliw lq wkh vxsso| vfkhgxoh,/ exw wkh vkruw0uxq pryhphqwv duh pruh forvho| wlhg wr X1V1 ghpdqg dqg X1V1 grphvwlf sulfh ghyhorsphqwv +wkurxjk wkh vwhhshqlqj ri wkh vxsso| vfkhgxoh,1 Wr prgho wklv skhqrphqrq hfrqrphwulfdoo| uhtxluhv d phdvxuh ri iruhljq sulfhv wkdw h{solflwo| fdswxuhv erwk wkh jurzlqj fdsdflw| ri hphujlqj0pdunhw surgxfhuv dqg wkh idfw wkdw wkh frvw vwuxfwxuh ri wkhvh surgxfhuv lv zhoo ehorz wkdw ri ghyhorshg0pdunhw surgxfhuv1 Vhfwlrq 5 ghyhorsv vxfk d phdvxuh ri iruhljq sulfhv dqg frqwudvwv lw wr h{lvwlqj phdvxuhv ri djjuhjdwh iruhljq sulfhv1 Vhfwlrq 5 dovr orrnv dw wkh grphvwlf sulfh phdvxuhv dqg qrwhv wkdw glhuhqw phdvxuhv ri X1V1 sulfhv fduu| glhuhqw lpsolfdwlrqv iru prgholqj lpsruw sulfhv1 Li rqh fkrrvhv wkh X1V1 JGS gh dwru/ wkhq iruhljq surgxfwv duh dvvxphg wr frpshwh zlwk X1V1 jrrgv dqg vhuylfhv zkhuhdv li rqh xvhv wkh JGS gh dwru iru jrrgv/ wkhq iruhljq surgxfwv duh dvvxphg wr frpshwh zlwk X1V1 jrrgv16 Vhfwlrq 6 ghvfulehv vhyhudo glhuhqw hfrqrphwulf vshflfdwlrqv wkdw kdyh ehhq xvhg wr hvwlpdwh wkh sdudphwhuv ri htxdwlrq +4, dqg qrwhv krz wkhvh vshflfdwlrqv glhu lq wkhlu fkdudfwhul}dwlrq ri orqj0  6 .    -"  !     -"              2        -"      uxq ehkdylru1 Vhfwlrq 7/ xvlqj dqqxdo revhuydwlrqv iurp 4<:7 wr 5338/ hvwlpdwhv vhyhudo yhuvlrqv ri htxdwlrq +4, dqg uhsruwv rq wkh vhqvlwlylw| ri wkh hvwlpdwlrq uhvxowv wr fkdqjhv lq phdvxuhv ri X1V1 dqg iruhljq sulfhv/ g|qdplf vshflfdwlrqv/ dqg vdpsoh shulrgv1 Wkh vhfwlrq dovr hvwlpdwhv wkh sdudphwhuv xvlqj vdpsoh0vhohfwlrq whfkqltxhv wr h{foxgh revhuydwlrqv zkhq hphujlqj hfrqrplhv zhuh qrw lpsruwdqw lq zruog wudgh1 Dffruglqjo|/ Vhfwlrq 7 glylghv wkh glvfxvvlrq lq wzr sduwv= Ixoo0vdpsoh Hvwlpdwlrq dqg Vdpsoh0vhohfwlrq Hvwlpdwlrq1 Zh qg wkdw fkdqjhv lq hvwlpdwlrq ghvljq jlyh ulvh wr d glvshuvlrq ri hvwlpdwhv/ dv irxqg lq wkh olwhudwxuh1 Zh dovr qg/ xvlqj rxu qhz phdvxuh ri iruhljq sulfhv dqg uhfhqw revhuydwlrqv/ wkdw wkh vkruw0uxq h{fkdqjh udwh sdvv0wkurxjk lv forvh wr }hur exw wkdw wkh orqj0uxq sdvv0wkurxjk lv derxw rqh0kdoi1 Zh lqwhusuhw wklv uhvxow dv vxjjhvwlqj wkdw wkh jurzlqj lpsruwdqfh ri hphujlqj hfrqrplhv grhv qrw lpso| wkdw iruhljq sulfhv/ ru h{fkdqjh udwhv/ duh ehfrplqj ohvv lpsruwdqw lq wkh ghwhuplqdwlrq ri X1V1 lpsruw sulfhv exw/ udwkhu/ wkdw wkh g|qdplfv ri wkh surfhvv duh fkdqjlqj1 5 Phdvxuhphqw Pdwwhuv Zh phdvxuh wkh sulfh ri X1V1 lpsruwv/ S > dv wkh pxowlodwhudo sulfh gh dwru ri X1V1 phufkdqglvh lpsruwv h{foxglqj rlo/ frpsxwhuv/ dqg vhplfrqgxfwruv1 Iru zrun xvlqj glvdjjuhjdwh lpsruw sulfhv vhh \dqj +4<<:,/ Rolyhl +5335,/ Fdpsd dqg Jrogehuj +5338,1 Iru wkh sulfh ri udz pdwhuldov/ S / zh xvh wkh LPI*v qrq0ixho frpprglw| sulfh lqgh{1 Iru iruhljq dqg X1V1 grphvwlf sulfhv/ krzhyhu/ zh frqvlghu vhyhudo dowhuqdwlyhv zklfk duh glvfxvvhg ehorz1 514 Iruhljq Sulfhv +Si , Phdvxulqj iruhljq sulfhv lv ri lqwhuhvw ehfdxvh wkh| vhuyh dv sur{lhv iru iruhljq frvwv iru zklfk gdwd duh qrw uhdglo| dydlodeoh1 Wkh jhqhudo sudfwlfh iru phdvxulqj iruhljq sulfhv djjuhjdwhv iruhljq FSLv/ h{suhvvhg lq X1V1 grooduv/ xvlqj elodwhudo wudgh zhljkwv1 Zh ghsduw iurp wklv sudfwlfh lq vhyhudo zd|v1 Iluvw/ zh dujxh wkdw JGS gh dwruv duh d ehwwhu sur{| iru grphvwlf frvwv wkdq FSLv1 Vhfrqg/ udwkhu wkdq djjuhjdwlqj iruhljq JGS gh dwruv h{suhvvhg lq X1V1 grooduv/ zh frqvwuxfw rxu phdvxuh ri S vr dv wr hqvxuh frqvlvwhqf| zlwk wkh hyroxwlrq ri X1V1 lqwhuqdwlrqdo uhodwlyh sulfhv1 Zh dwwdlq wklv frqvlvwhqf| lq wzr vwhsv1 Wkh uvw vwhs lqyroyhv phdvxulqj X1V1 lqwhuqdwlrqdo uhodwlyh sulfhv/ T= T @ S  > S  +5, zkhuh S lv wkh sulfh ohyho ri X1V1 surgxfwv1 Wklv uvw vwhs lv qhhghg ehfdxvh gdwd iru devroxwh sulfh ohyhov dfurvv frxqwulhv duh qrw hdvlo| dydlodeoh zkhuhdv wkh ohyhov ri wkh dvvrfldwhg elodwhudo uhodwlyh sulfhv 3 duh dydlodeoh1 Wkh vhfrqg vwhs xvhv htxdwlrq +5, wr vroyh iru S wdnlqj dv jlyhq gdwd iru T dqg S = Lpsohphqwlqj wkhvh wzr vwhsv zrxog eh vwudljkwiruzdug li wkhuh zhuh djuhhphqw rq krz wr frqvwuxfw T= Dv Fklqq +5338, qrwhv/ krzhyhu/ vxfk dq djuhhphqw lv qrw fxuuhqwo| lq sodfh1 Lqghhg/ wkh h{lvwlqj phdvxuhv ri T frqvwuxfwhg e| wkh Ihghudo Uhvhuyh/ wkh LPI/ dqg wkh RHFG glhu lq wkhlu pl{ ri frxqwulhv/ lq wkhlu phdvxuh ri sulfhv/ lq wkhlu zhljkwlqj vfkhphv/ dqg lq wkhlu djjuhjdwlrq phwkrgv1 Wkh rqh ihdwxuh wkhvh phdvxuhv ri T kdyh lq frpprq lv wkhlu uholdqfh rq uhodwlyh sulfh lqgh{hv1 Dv glvfxvvhg ixuwkhu ehorz/ vxfk phdvxuhv fdqqrw ixoo| fdswxuh wkh jurzlqj lpsruwdqfh ri wkh orz0frvw surgxfhuv ehfdxvh lqgh{hv lqglfdwh/ e| frqvwuxfwlrq/ wkh shufhqw fkdqjh ri wkh yduldeoh uhodwlyh wr d edvh |hdu1 Rxu phdvxuh irfxvhv rq wkh ohyho ri lqwhuqdwlrqdo uhodwlyh sulfhv dqg qrw ri lwv fkdqjh1 51414 Phdvxulqj Lqwhuqdwlrqdo Uhodwlyh Sulfhv Fhqwudo wr rxu frqvwuxfw ri T lv wkh phdvxuhphqw ri wkh ohyho ri wkh sulfh ri X1V1 surgxfwv uhodwlyh wr wkh ohyho ri wkh sulfh ri wkh lwk frxqwu|/ t  = Zh phdvxuh wklv elodwhudo uhodwlyh sulfh dv t@ Hl ' S S S 'l  > zkhuh H 'l  lv wkh vsrw groodu h{fkdqjh udwh uhodwlyh wr wkh lwk fxuuhqf| +d ulvh lq H 'l frqvwlwxwhv dq dssuhfldwlrq ri wkh groodu,> dqg S S S l '  lv wkh SSS h{fkdqjh udwh uhsruwhg e| wkh Shqq Zruog Wdeohv17 Wklv SSS udwh lv d zhljkwhg dyhudjh ri wkh sulfhv ri wkh lwk frxqwu| uhodwlyh wr X1V1 sulfhv xvlqj dv zhljkwv wkh surgxfwlrq ohyhov ri wkh lwk frxqwu|1 Wkh sulfhv xvhg e| wkh Shqq gdwd duh edvhg rq kljko| frpsdudeoh surgxfwv dfurvv frxqwulhv dqg wkh dvvrfldwhg zhljkwv dffrxqw iru wkh ixoo ydoxh ri JGS1 Wkh Shqq gdwd duh frqvwuxfwhg wr doorz furvv0frxqwu| frpsdulvrqv dqg wkxv zhoo vxlwhg wr rxu sxusrvhv1 Qrwh wkdw t  glhuv lpsruwdqwo| iurp wkh sulfh lqgh{hv xvhg lq pdfurhfrqrplfv1 W|slfdoo|/ wkhvh sulfh lqgh{hv duh frqvwuxfwhg wr htxdo 433 lq d jlyhq |hdu/ vr lw zrxog pdnh qr vhqvh wr frpsduh wkh ohyho ri sulfh lqgh{hv lq wzr frxqwulhv1 Lq frqwudvw/ t  lv xqlwohvv dqg hdv| wr lqwhusuhw= D ydoxh ri 5 phdqv wkdw wkh edvnhw ri wkh lwk frxqwu| lv wzlfh dv h{shqvlyh lq wkh Xqlwhg Vwdwhv dv lw lv lq wkh lwk frxqwu|1 Zh djjuhjdwh wkhvh elodwhudo uhodwlyh sulfhv lqwr rxu frqvwuxfw T xvlqj wzr irupxodv= d jhrphwulf djjuhjdwh/ ghqrwhg dv T > dqg d Glylvld djjuhjdwh/ ghqrwhg dv T =8 Wkh jhrphwulf djjuhjdwh lv T @ +t4 ,4w  +t5 ,5w      +t ,qw > 7 /     6 " )  8 2      0 1  2   "    &  33           /   +  ! 4 )       5  ! !         !                      $%%% 4 zkhuh z  lv wkh vkduh ri wkh lwk frxqwu| lq wkh djjuhjdwh1 Vhyhudo idfwruv dhfw wkh djjuhjdwh T = dq lqfuhdvh lq X1V1 sulfhv udlvhv lw/ zkloh dq lqfuhdvh lq iruhljq sulfhv orzhuv lw> d qrplqdo dssuhfldwlrq ri wkh groodu +dq lqfuhdvh lq H l  , udlvhv T 1 Wkhvh wkuhh idfwruv zrun wkurxjk wkhlu hhfw rq wkh elodwhudo uhodwlyh ' sulfhvwkh t 3 v1 Lq dgglwlrq/ fkdqjlqj wkh zhljkwv dorqh zloo dhfw T hyhq li qrqh ri wkh xqghuo|lqj sulfhv ru h{fkdqjh udwhv fkdqjh1 Vshflfdoo|/ hphujlqj0pdunhw hfrqrplhv kdyh uhodwlyho| orz surgxfwlrq frvwv dqg wkhlu vkduh lq zruog wudgh kdv ehhq lqfuhdvlqj1 Wkh uhvxowlqj lqfuhdvh lq wkhlu vkduh lq zruog pdunhwv lv fdswxuhg e| wkh lqfuhdvh lq wkhlu zhljkwv1 Orrvho| vshdnlqj/ udlvlqj wkh zhljkw rq wkhvh orz0sulfh frxqwulhv orzhuv wkh cdyhudjh* sulfh deurdg dqg udlvhv X1V1 sulfhv uhodwlyh wr wkh dyhudjh iruhljq sulfh/ hyhq li qr xqghuo|lqj sulfhv fkdqjh1 Lq frqwudvw/ wkh Glylvld djjuhjdwh ri X1V1 lqwhuqdwlrqdo uhodwlyh sulfhv lv d zhljkwhg dyhudjh ri jurzwk udwhv ri elodwhudo uhodwlyh sulfhv=  T T @ T4 @4  t t 4 lw > +6, zkhuh e| frqyhqwlrq/ T@ lv vhw htxdo wr 433 wr d jlyhq shulrg dqg wkh lqgh{ ohyho iru doo rwkhu shulrgv lv ghqhg uhfxuvlyho|1 Wkh fklhi gudzedfn ri wklv phdvxuh iru rxu sxusrvhv lv wkdw lw fdqqrw ixoo| uhfrjql}h wkh lpsruwdqfh ri orz0sulfh frxqwulhv vxfk dv Fklqd dqg Ph{lfr1 Wr eh vxuh/ wkh zhljkwv iru wkhvh wzr frxqwulhv kdyh lqfuhdvhg exw wkhlu uhodwlyh sulfhv kdyh ehhq idluo| vwdeoh zklfk phdqv wkdw wkh odujh zhljkwv duh ehlqj pxowlsolhg e| qhjoljleoh jurzwk udwhv1 Wkh jhrphwulf djjuhjdwh grhv qrw vxhu iurp wklv olplwdwlrq ehfdxvh fkdqjhv lq zhljkwv dhfw wkh djjuhjdwh hyhq li doo wkh uhodwlyh sulfhv duh {hg1 Lq frqvwuxfwlqj wkhvh djjuhjdwhv/ zh frqvlghu wzr w|shv ri zhljkwv= X1V1 elodwhudo qrq0rlo lpsruwv dqg d eurdg phdvxuh ri X1V1 wudgh frpshwlwlyhqhvv1 Dv vkrzq lq wkh wrs sdqho ri jxuh 4/ xqolnh wkh fkrlfh ri zhljkwv/ wkh fkrlfh ri djjuhjdwlrq phwkrg pdwwhuv iru phdvxulqj wkh lqwhuqdwlrqdo uhodwlyh sulfh ri X1V1 surgxfwv1 Vshflfdoo|/ wkh jhrphwulf djjuhjdwh kdv dq xszdug wuhqg phdqlqj wkdw wkh sulfh ri X1V1 surgxfwv uhodwlyh wr iruhljq surgxfwv kdv ehhq lqfuhdvlqj ryhu wlph1 Vxfk d wuhqg rzhv sulpdulo| wr vkliwv lq frxqwu| zhljkwv dzd| iurp wkh uhodwlyho| kljk0sulfh lqgxvwuldo frxqwulhv wrzdug wkh orzhu0sulfh ghyhorslqj hfrqrplhv1 Lq frqwudvw/ wkh Glylvld djjuhjdwh ri uhodwlyh sulfhv hperglhv d grzqzdug wuhqg lq X1V1 lqwhuqdwlrqdo uhodwlyh sulfhv1 Dffrxqwlqj iru wkh glhuhqfh lq wuhqgv lqyroyhv uhfrjql}lqj wkdw wkh Glylvld djjuhjdwh irfxvhv rq wkh pryhphqwv lq wkh elodwhudo uhdo h{fkdqjh udwhv dorqh zkloh ljqrulqj wkh jhqhudo vkliw wrzdugv wkh uhodwlyho| orz0sulfh surgxfhuv1 Fdswxulqj wklv jhqhudo vkliw uhtxluhv djjuhjdwlrq ri wkh ohyhov ri elodwhudo uhodwlyh sulfhv/ zklfk lv zkdw jhrphwulf djjuhjdwlrq doorzv1  2     !       )          !     " 7  $%%8               !   9             !                      :             !           !     ! 5 51415 Hvwlpdwlqj Iruhljq Sulfhv lq Grooduv Jlyhq gdwd iru X1V1 grphvwlf sulfhvwkh JGS gh dwrudqg iru wkh djjuhjdwh ri X1V1 lqwhuqdwlrqdo uhodwlyh sulfhv/ zh xvh htxdwlrq +5, wr frqvwuxfw gdwd iru iruhljq sulfhv1 Vshflfdoo|/ wkh phdvxuh ri iruhljq sulfhv lq grooduv lpsolhg e| T lv S  @ S  = T Wkh phdvxuh ri iruhljq sulfhv lq grooduv lpsolhg e| T lv S  @ S  = T Wkh erwwrp sdqho ri jxuh +4, vkrzv wkdw/ jlyhq wkh gdwd iru S > glhuhqfhv lq wkh hyroxwlrq ri djjuhjdwh uhodwlyh sulfhv wudqvodwh lqwr glhuhqfhv iru wkh wzr phdvxuhv ri iruhljq sulfhv1 Vshflfdoo|/ diwhu prylqj lq orfn vwhs iurp 4<:5 wr 4<;9/ wkh vhulhv glyhujh zlwk S jurzlqj idvwhu wkdq S = Wkh jurzlqj jds ehwzhhq wkhvh wzr vhulhv uh hfwv wkh jurzlqj jds dvvrfldwhg zlwk wkh fkrlfh ri djjuhjdwlrq phwkrg1 515 X1V1 Sulfhv +S| , Wr phdvxuh wkh sulfhv ri X1V1 surgxfwv wkdw frpshwh zlwk lpsruwv zh frqvlghu wkuhh phdvxuhv= wkh Surgxfhu Sulfh Lqgh{/ wkh ryhudoo JGS gh dwru/ dqg wkh JGS gh dwru iru jrrgv dorqh1 Wkh glvwlqfwlrq ehwzhhq jrrgv dqg vhuylfhv pljkw pdwwhu li rqh dujxhv wkdw lpsruwv ri jrrgv frpshwh zlwk X1V1 jrrgv/ dqg qrw zlwk X1V1 jrrgv dqg vhuylfhv1 Wkdw vxfk d glvwlqfwlrq lv srwhqwldoo| uhohydqw lv fohdu iurp jxuh 51 Lqghhg/ vlqfh 4<:3/ wkh sulfh gh dwru iru X1V1 jrrgv dqg vhuylfhv kdv jurzq idvwhu wkdq wkh SSL dqg wkh JGS gh dwru iru jrrgv1 Ixuwkhupruh/ vlqfh 4<<8/ wkh jurzwk udwh ri sulfh gh dwru iru jrrgv kdv d qduurz udqjh ri xfwxdwlrqv durxqg }hur zkhuhdv wkh jurzwk udwh iru wkh ryhudoo JGS gh dwru lv srvlwlyh wkurxjkrxw wkh vdpsoh1 Iru wkh SSL/ wkh jurzwk udwh dovr xfwxdwhv durxqg }hur exw wkh udqjh ri wkh xfwxdwlrqv h{fhhg wkdw ri wkh gh dwru iru JGS jrrgv1 516 Phdvxulqj dqg Prgholqj Wkh ohiw sdqhov ri jxuh 6 uhyhdo d forvh uhodwlrq ehwzhhq S dqg wkh sulfh ri lpsruwv1 Wkh uljkw sdqhov uhyhdo/ lq frqwudvw/ d jurzlqj glvwdqflqj ehwzhhq S dqg wkh sulfh ri lpsruwv diwhu 4<;81 Vxfk d jds fdq eh frqvwuxhg dv vxjjhvwlqj d ghfolqh lq wkh uhvsrqvlyhqhvv ri X1V1 lpsruw sulfhv wr wkh h{fkdqjh udwh1 Wkh gdwd dovr uhyhdo d jurzlqj jds ehwzhhq wkh sulfh gh dwru iru lpsruwv dqg wkh sulfh gh dwru iru X1V1 jrrgv dqg vhuylfhv1 Wkdw glvwdqflqj lv qrw suhvhqw li rqh xvhv wkh X1V1 gh dwru iru jrrgv dorqh1    6 Wr hydoxdwh wkh wlph0vhulhv surshuwlhv ri wkhvh yduldeohv/ Wdeoh 4 vkrzv wkh uhvxowv iurp wkh Dxjphqwhg Glfnh|0Ixoohu whvwv ri vwdwlrqdulw|1 Zlwk rqh h{fhswlrq/ wkh DGI whvwv fdqqrw uhmhfw d xqlw0urrw iru wkhvh vhulhv> wkh h{fhswlrq lv wkh frpprglw| sulfh lqgh{ iru zklfk wkh DGI whvw vwdwlvwlf h{fhhgv e| d jrrg pdujlq wkh 4( fulwlfdo ydoxh1 Iru wkh sulfh ri lpsruwv/ wkh DGI whvw vkrzv d pdujlqdo uhmhfwlrq ri wkh xqlw0urrw k|srwkhvlv dw fhuwdlq odjv1 6 Hfrqrphwulf Vshflfdwlrqv Iru sdudphwhu hvwlpdwlrq zh vshfli| htxdwlrq +4, dv dq dxwruhjuhvvlyh glvwulexwhg odj= oq S  @  . +O,  oq S . +O,  oq S  . +O,  oq S  .   oq S  4  . x > +7, zkhuh O lv wkh odj rshudwru dqg x LQ +3>  5 ,= Wkh dsshdo ri htxdwlrq +7, lv lwv h{lelolw| lq glhuhqwldwlqj ehwzhhq vkruw0uxq hhfwv dqg orqj uxq hhfwv1 Wkh h{fkdqjh0udwh sdvv0wkurxjk lv +4, lq wkh vkruw0uxq  +4, +4, +4, dqg 4  lq wkh orqj0uxq1 Wkh uhpdlqlqj orqj0uxq frh!flhqwv duh 4 iru wkh sulflqj wr pdunhw dqg 4 iru wkh sulfh ri frpprglwlhv1 Wkh glhuhqfh ehwzhhq vkruw0 dqg orqj0uxq hhfwv lv ghwhuplqhg e| wkh sdudphwhu  zklfk phdvxuhv wkh shuvlvwhqfh ri lpsruw sulfhv1 D srsxodu dowhuqdwlyh wr htxdwlrq +7, h{sodlqv wkh jurzwk udwh ri lpsruw sulfhv lq whupv ri jurzwk udwhv ri lwv ghwhuplqdqwv= S  S S S  S @ 3 .  3 +O,  .  3 +O,  .  3 +O,  . 3  S 4 S 4 S 4 S 4 S   4  5  . y > +8, zkhuh y LQ +3> 5 , dqg zh dwwdfk dq c3 * wr wkh frh!flhqwv wr hpskdvl}h wkdw wkh| glhu iurp wkrvh lq htxdwlrq +7,1 Djdlq/ wkh h{fkdqjh0udwh sdvv0wkurxjk lv  3 +4, lq wkh vkruw uxq dqg 4+4, 3 lq wkh orqj0 3  +4, uxq1 Wkh uhpdlqlqj orqj0uxq frh!flhqwv duh 4+4, 3 iru wkh sulflqj wr pdunhw dqg 43 iru wkh sulfh ri 3 3 frpprglwlhv1 Htxdwlrqv +7, dqg +8, glhu lq wkhlu fkdudfwhul}dwlrq ri orqj0uxq ehkdylru1 Vshflfdoo|/ wkh orqj0uxq lpsruw sulfh lpsolhg e| htxdwlrq +8, lv duelwudu| ehfdxvh lw ghshqgv rq wkh ydoxh ri wkh lqlwldo frqglwlrq> wkh orqj0uxq lpsruw sulfh lpsolhg e| htxdwlrq +7, lv/ krzhyhu/ xqltxho| ghwhuplqhg1 Vshflfdoo|/ htxdwlrq +7, lpsolhv wkdw/ uhjdugohvv ri wkh lqlwldo frqglwlrq/ wkh orqj0uxq ohyho ri lpsruw sulfhv lv ghwhuplqhg dv oq S  /      @      .   oq S .   oq S .   oq S > 4     ) 7 $%%'(   0    , , +9, $%%' +4, +4, zkhuh  @ +4, 4 >  @ 4 > dqg  @ 4 = Iru wkhvh frh!flhqwv wr eh frqvlvwhqw zlwk wkh suhglfwlrqv ri wkhru|/ wkh| qhhg wr phhw wkh vljq uhvwulfwlrqv + A 3>  A 3/  A 3, dqg wkh krprjhqhlw| frqglwlrq + .  .  @ 4,> wkh orqj0uxq frh!flhqwv iru htxdwlrq +8, qhhg wr phhw frpsdudeoh frqglwlrqv1 7 Hfrqrphwulf Uhvxowv 714 Ixoo0vdpsoh Hvwlpdwlrq Sdudphwhu hvwlpdwlrq uhvwv rq wkh Jhqhudo0wr0Vshflf vwudwhj|1 Wkh jhqhudo irupxodwlrqv fruuhvsrqg wr htxdwlrqv +7, dqg +8, zkhuh zh lqfoxgh fxuuhqw ydoxhv dqg 4 odj iru hdfk suhghwhuplqhg yduldeoh> wkh vshflf irupxodwlrqv duh rewdlqhg e| lpsohphqwlqj wkh dxwrpdwhg0vshflfdwlrq dojrulwkp ghyhorshg e| Khqgu| dqg Nuro}lj +5334,1 Wkhlu dojrulwkp frpelqhv ohdvw vtxduhv zlwk d vhohfwlrq fulwhuld wkdw h{foxghv irupxodwlrqv odfnlqj sdudphwhu frqvwdqf|/ zklwh0qrlvh uhvlgxdov/ dqg lqvljqlfdqw yduldeohv1 Ixuwkhu/ wkh fulwlfdo ydoxhv xvhg lq prgho vhohfwlrq duh qrw {hg lq dgydqfh exw/ udwkhu/ duh fdofxodwhg vhtxhqwldoo| wr uhfrjql}h wkh mrlqw qdwxuh ri prgho vshflfdwlrq dqg sdudphwhu hvwlpdwlrq1 Wdeoh 5 uhsruwv wkh orqj0uxq frh!flhqw hvwlpdwhv iru wkh vshflf irupxodwlrq dvvrfldwhg zlwk htxdwlrq +7, dorqj zlwk wkh hydoxdwlrq ri wkh surshuwlhv ri wkh uhvlgxdov> Wdeoh 6 uhsruwv wkh dvvrfldwhg uhvxowv iru htxdwlrq +8,1 Wr idflolwdwh wkh glvfxvvlrq/ jxuhv 709 vkrz wkh vhqvlwlylw| ri wkhvh hvwlpdwhv wr fkdqjhv lq 41 wkh hfrqrphwulf vshflfdwlrq= htxdwlrq +7, yhuvxv htxdwlrq +8,> 51 wkh phdvxuh ri X1V1 sulfhv/ S = JGS gh dwru iru jrrgv dqg vhuylfhv +J)V,/ JGS gh dwru iru jrrgv +Jrrgv,/ Surgxfhu Sulfh Lqgh{ +SSL,> 61 wkh phdvxuh ri iruhljq sulfh/ S = jhrphwulf djjuhjdwh dqg Glylvld djjuhjdwh> 71 wkh zhljkwlqj vfkhph/ z  = X1V1 elodwhudo qrq0rlo lpsruwv +qrq0rlo, wr xvlqj X1V1 wudgh frpshwlwlyh0 qhvv +eurdg,> 81 wkh hvwlpdwlrq shulrg= 4<:705333 dqg 4<:7053381 Edvhg rq wkh ixoo vdpsoh/ jxuh 7 uhsruwv wkh orqj0uxq hvwlpdwhv ri wkh sulflqj wr pdunhw frh!flhqw/  e> e Lqvshfwlrq ri wkh uhvxowv uhyhdov vhyhudo qglqjv1 Iluvw/ dqg ri h{fkdqjh0udwh sdvv0wkurxjk frh!flhqw/ 1 dv vkrzq lq wkh wrs sdqho/  e lv srvlwlyh dqg vljqlfdqw h{fhsw zkhq wkh hvwlpdwlrq xvhv wkh irupxodwlrq lq ohyhov zlwk wkh Glylvld phdvxuh ri iruhljq sulfhv dorqj zlwk hlwkhu wkh X1V1 SSL ru wkh X1V1 ryhudoo             8        !              2 Sp        3  !           3 3 8 e lv srvlwlyh/ vljqlfdqwo| juhdwhu wkdq }hur/ dqg JGS gh dwru1 Vhfrqg/ dv vkrzq lq wkh erwwrp sdqho/  e edvhg rq wkh htxdwlrq lq ohyhov/ htxdwlrq +7,/ zlwk wkh jhrphwulf iruhljq h{fhhgv 4261 Wklug/ ydoxhv ri  sulfh duh forvh wr 318 dqg duh/ lq jhqhudo/ odujhu wkdq hvwlpdwhv edvhg rq wkh Glylvld iruhljq sulfh1 Wkh uroh ri frpprglw| sulfhv ghshqgv rq wkh vshflfdwlrq1 Iru wkh htxdwlrq lq ohyhov +Wdeoh 5, frpprglw| sulfhv duh qrw uhohydqw zkhuhdv iru wkh htxdwlrq lq jurzwk udwhv +Wdeoh 6,/ wkh| duh1 Vxfk d glhuhqfh lv qrw vxusulvlqj ehfdxvh/ dv Wdeoh 4 vkrzv/ wkh ohyho ri wkh sulfh ri frpprglwlhv lv vwdwlrqdu|1 Lq whupv ri wkh hvwlpdwh ri shuvlvwhqfh/ e / wkh uhvxowv iru wkh htxdwlrq lq ohyhov +Wdeoh 5, lqglfdwh wkdw e  lv vljqlfdqw dqg zhoo ehorz rqh> iru wkh htxdwlrq lq jurzwk udwhv +Wdeoh 6,/ e  lv qrw vwdwlvwlfdoo| glhuhqw iurp }hur1 Lq whupv ri wkh surshuwlhv ri wkh uhvlgxdov/ wkh hylghqfh fdqqrw uhmhfw wkh k|srwkhvhv ri vhuldo lqghshqghqfh dqg krprvnhgdvwlflw| iru hlwkhu vshflfdwlrq1 e h{fhhgv 426 lv dw rggv zlwk vwxglhv wkdw irfxv rq uhfhqw revhuyd0 Ilqglqj wkdw wkh vpdoohvw ydoxh ri  e forvh wr }hur1 Rqh srvvlelolw| lv wkdw uhfhqw revhuydwlrqv duh uhvsrqvleoh wlrqv dorqh dqg uhsruw ydoxhv ri  e Lq vxfk d fdvh/ rqh vkrxog h{shfw wkdw h{foxglqj wkhp iurp rxu vdpsoh zrxog udlvh iru d ghfolqh lq = e Wr h{soruh wklv srvvlelolw|/ zh uh0hvwlpdwh wkh frh!flhqwv zlwk d vdpsoh wkdw hqgv lq 5333 wkh ydoxh ri = dqg frpsduh wkh uhvxowlqj hvwlpdwhv wr wkrvh edvhg rq wkh ixoo vdpsoh1 e fkdqjhv lq uhvsrqvh wr dowhuqdwlyh vdpsoh shulrgv zkloh frqwuroolqj Iljxuh 8 vkrzv krz wkh ydoxh ri  iru sulfh phdvxuhv dqg ixqfwlrqdo irupv1 Zh qg qr hylghqfh ri d kljkhu orqj0uxq h{fkdqjh0udwh sdvv0wkurxjk iru wkh vdpsoh hqglqj lq 53331 Lqvwhdg/ iru wkh ohyho vshflfdwlrqv dqg vrph X1V1 sulfh e Dv vkrzq lq jxuh 9/ phdvxuhv/ zh qg wkdw h{whqglqj wkh vdpsoh lqfuhdvhv qrwlfhdeo| wkh ydoxh ri 1 wkh hvwlpdwhg sulflqj0wr0pdunhw frh!flhqw/  e> lv vrphzkdw pruh vhqvlwlyh wr vdpsoh shulrg/ hvshfldoo| iru wkh ohyho vshflfdwlrqv edvhg rq wkh Glylvld phdvxuh ri iruhljq sulfhv1 Vhyhudo frqfoxvlrqv hphujh iurp wkhvh hvwlpdwlrq uhvxowv1 Iluvw/ wkh orqj0uxq hhfw ri h{fkdqjh udwhv rq lpsruw sulfhv lv dw ohdvw rqh0wklug dfurvv doo uhjuhvvlrqv1 Vhfrqg/ wkh phuh lqfoxvlrq ri uhfhqw revhuydwlrqv e Wklug/ wkh phdvxuhphqw ri iruhljq sulfhv pdwwhuv iru hvwlpdwlqj grhv qrw vljqlfdqwo| orzhu wkh ydoxh ri = e edvhg rq wkh jhrphwulf iruhljq sulfh duh odujhu wkh h{fkdqjh0udwh sdvv0wkurxjk1 Vshflfdoo|/ ydoxhv ri  +forvh wr 318, dqg ohvv vhqvlwlyh wr fkdqjhv lq vshflfdwlrq wkdq hvwlpdwhv edvhg rq wkh Glylvld iruhljq sulfh1 Ilqdoo|/ fkdqjhv lq hvwlpdwlrq ghvljq jlyh ulvh wr d glvshuvlrq ri hvwlpdwhv/ dv irxqg lq wkh olwhudwxuh1 Vxfk d glvshuvlrq lv sureohpdwlf iru srolf| dssolfdwlrqv= vhhplqjo| plqru fkdqjhv lq hvwlpdwlrq ghvljq fduu| udglfdoo| glhuhqw lpsolfdwlrqv uhjduglqj wkh vwuhqjwk ri wkh h{shqglwxuh0vzlwfklqj hhfw ri d fkdqjh lq wkh h{fkdqjh ydoxh ri wkh groodu1 Wr glvfulplqdwh dprqj wkhvh vshflfdwlrqv/ zh dujxh wkdw srolf| dssolfdwlrqv ehqhw iurp irupxodwlrqv 2 #   "                   .        ;     !         9          wkdw h{klelw wkuhh surshuwlhv= frqvwdqf| ri orqj0uxq sdudphwhuv/ zklwh0qrlvh uhvlgxdov/ dqg frqvlvwhqf| zlwk sulfh krprjhqhlw|1 Dsso|lqj wklv fulwhuld |lhogv wzr vshflfdwlrqv/ uhsurgxfhg lq Wdeoh 71 Rqh vshflfdwlrq xvhv wkh irupxodwlrq lq ohyhov dorqj zlwk wkh jhrphwulf iruhljq sulfh dqg wkh X1V1 gh dwru iru JGS jrrgv> wklv vshflfdwlrq lv odehohg dv V 1 Wkh vhfrqg vshflfdwlrq xvhv wkh irupxodwlrq lq jurzwk udwhv dorqj zlwk wkh Eurdg zhljkwhg Glylvld phdvxuh ri iruhljq sulfh dqg wkh X1V1 SSL> wklv vshflfdwlrq lv odehohg dv V 144 e 318 iru V dqg 317 iru V = Krzhyhu/ wkhvh vshfl0 Wkhvh wzr vshflfdwlrqv kdyh vlplodu ydoxhv iru = fdwlrqv glhu lq wkhlu lpsolfdwlrqv iru wkh orqj0uxq= wkh frh!flhqw iru V uhihuv wr d orqj0uxq uhvsrqvh ri wkh ohyho ri lpsruw sulfhv zkhuhdv wkh frh!flhqw iru V uhihuv wr wkh vkruw uxq +rqh |hdu, uhvsrqvh ri wkh jurzwk udwh ri lpsruw sulfhv1 Wklv glvwlqfwlrq zrxog qrw eh uhohydqw li wkh hvwlpdwhg dgmxvwphqw ghod| lq V zhuh eulhi/ exw lw lv qrw1 Iljxuh : vkrzv krz lpsruw sulfhv uhvsrqg wr d k|srwkhwlfdo rqh0shufhqw vxvwdlqhg ghsuhfldwlrq ri wkh groodu145 Wkh uhvxowv uhyhdo vhyhudo ihdwxuhv ri lqwhuhvw1 Iluvw/ wkh prghov glhu juhdwo| lq wkhlu vkruw0uxq uhvsrqvhv1 Vshflfdoo|/ diwhu rqh |hdu/ V suhglfwv wkdw lpsruw sulfhv zloo lqfuhdvh e| 317 shufhqw +eoxh olqh, zkhuhdv V vkrzv d qhjoljleoh uhvsrqvh +eodfn olqh,146 Diwhu irxu |hduv/ krzhyhu/ wkh wzr vshflfdwlrqv suhglfw urxjko| wkh vdph hhfw rq lpsruw sulfhv1 Vhfrqg/ wr hpskdvl}h krz fkdqjhv lq wkh hvwlpdwlrq vdpsoh kdyh fkdqjhg wkh fkdudfwhu ri g|qdplf dgmxvwphqw/ wkh jxuh dovr lqfoxghv wkh uhvsrqvh iurp V xvlqj sdudphwhu hvwlpdwhv edvhg rq gdwd wkurxjk 5333 +uhg olqh,1 Wkh uhvsrqvhv iurp wkhvh wzr vdpsoh shulrgv frqyhujh wr yluwxdoo| lghqwlfdo ydoxhv lq wkh orqj uxq1 Wkhlu vkruw0uxq uhvsrqvhv duh/ krzhyhu/ txlwh glhuhqw= wkh vshflfdwlrq edvhg rq gdwd wkurxjk 5333 kdv d kljkhu vkruw0uxq uhvsrqvh dqg d txlfnhu dgmxvwphqw wr wkh orqj0uxq wkdq wkh hvwlpdwh edvhg rq gdwd wkurxjk 53381 Zh lqwhusuhw wklv qglqj dv ehlqj frqvlvwhqw zlwk wkh lghd wkdw wkh lqfuhdvhg lpsruwdqfh ri hphujlqj hfrqrplhv kdv fkdqjhg wkh g|qdplfv ri wkh surfhvv ri lpsruw0sulfh ghwhuplqdwlrq1 Eh|rqg vwdwlqj wkh reylrxvqdpho|/ wkdw wkhuh lv dq lpsruwdqw glhuhqfh ehwzhhq vkruw dqg orqj uxq hhfwv/ wkhvh uhvxowv duh qrw srzhuixo hqrxjk wr glvfulplqdwh ehwzhhq V dqg V = Wr wkdw hqg/ zh h{dplqh wkh rxw0ri0vdpsoh dffxudf| ri wkhvh wzr irupxodwlrqv1 Vshflfdoo|/ zh dsso| wkh Jhqhudo0wr0 Vshflf dojrulwkp zlwk gdwd wkurxjk 5333 dqg wkhq xvh g|qdplf vlpxodwlrqv wr jhqhudwh h{0srvw iruhfdvwv 44 2 '  5                           /                                        !         2             !!              <          !     =  >?     !  2   <   %'$ @%8A         %%3(         '*B 2 =  >?     ! 8C  DDD =   $%%* D%$  *B 2  !     9                        /  E !                             .    !                 45 2       E f n  u  u E n  u  n 2 u 2 n  46 2     j               <    f    !       f n  f 10 iru 533405338147 Iljxuh ; vkrzv wkh <8 shufhqw frqghqfh edqgv ri wkhvh h{0srvw iruhfdvwv148 Wkh uhvxowv lqglfdwh wkdw/ ryhu wkh uvw wzr |hduv/ erwk htxdwlrqv kdyh vwdwlvwlfdoo| lqvljqlfdqw suhglfwlrq huuruv exw wkdw V lv pxfk pruh dffxudwh wkdq V 1 Wkxv/ li wkh vroh sxusrvh ri hvwlpdwlrq lv vkruw0whup iruhfdvwlqj/ wkhq V lv wkh suhihuuhg vshflfdwlrq1 Wkh hylghqfh iru krul}rqv eh|rqg wzr |hduv lv/ krzhyhu/ ohvv vxssruwlyh ri V = Hyhq wkrxjk erwk htxdwlrqv vkrz vwdwlvwlfdoo| vljqlfdqw suhglfwlrq huuruv/ wkh urrw0 phdq vtxduhg huuru ryhu wkh yh0|hdu krul}rq lv vl{ shufhqw iru V exw hljkw shufhqw iru V = Wkxv/ li wkh srolf| dssolfdwlrq h{whqgv eh|rqg wzr |hduv wkhq V fduulhv juhdwhu suhflvlrq1 Dw wklv srlqw zh zrxog frqfoxgh wkdw/ ri wkh wzr irupxodwlrqv wkdw h{klelw zklwh0qrlvh uhvlgxdov dqg frqvlvwhqf| zlwk wkh krprjhqhlw| srvwxodwh/ wkh rqh zlwk wkh orzhvw dyhudjh iruhfdvw huuru lq wkh phglxp whup xvhv rxu jhrphwulf phdvxuh ri iruhljq sulfhv1 Lw kdv d orqj0uxq sdvv0wkurxjk ri rqh0kdoi1 Wklv irupxodwlrq fdswxuhv wkh fkdqjlqj qdwxuh ri wkh lpsruw0sulfh surfhvv e| xvlqj d phdvxuh ri iruhljq sulfhv wkdw uh hfwv wkh jurzlqj lpsruwdqfh ri hphujlqj hfrqrplhv1 Wkhuh lv/ krzhyhu/ dq dowhuqdwlyh vwudwhj| wkdw uhwdlqv wkh frqyhqwlrqdo phdvxuhv ri iruhljq sulfh dqg xvhv vdpsoh0vhohfwlrq phwkrgv vr dv wr h{foxgh revhuydwlrqv zkhq hphujlqj hfrqrplhv zhuh qrw lpsruwdqw lq zruog wudgh1 Lq wkh qh{w vxevhfwlrq zh zhljk wkh fkrlfh ri uhwdlqlqj fxuuhqw +Glylvld edvhg, phdvxuhv ri iruhljq sulfhv dqg vkruwhqlqj wkh vdpsoh shulrg djdlqvw uhsodflqj wkh Glylvld phdvxuhv ri iruhljq sulfhv zlwk wkh jhrphwulf dowhuqdwlyh dqg uhwdlqlqj wkh ixoo vdpsoh shulrg1 715 Vdpsoh0vhohfwlrq Hvwlpdwlrq Wkh uhvxow ri wkh uhfhqw ghfolqh lq wkh sdvv0wkurxjk lv edvhg rq txduwhuo| gdwd zkhuhdv rxu gdwd duh dqqxdo1 Wkxv zh ehjlq e| frquplqj wkdw wklv vdph ihdwxuh lv dovr suhvhqw lq wkh dqqxdo dqdorjxh wr wkhvh prghov1 Wr wklv hqg/ zh dsso| uroolqj uhjuhvvlrqv wr wkh jurzwk htxdwlrq +8, xvlqj wkh Glylvld phdvxuh ri S dqg wkh surgxfhu sulfh lqgh{ iru S  dqg d zlqgrz ri 48 |hduv vwduwlqj lq 4<:7149 Iljxuh e3 = < vkrzv wkh <8 shufhqw frqghqfh lqwhuydo iru wkh hvwlpdwhg sdvv0wkurxjk frh!flhqw ri htxdwlrq +8,/  e3 iurp 3178 lq 4<<8 wr 314: lq 5338/ d sdwwhuq lq olqh zlwk wkh Wkh uhvxowv uhyhdo d vxvwdlqhg ghfolqh lq  qglqjv ri Rolyhl +5335, Pdud}}l dqg Vkhhwv +5339,14: e3 lv urexvw wr prgho vshflfdwlrq1 Lq fkrrvlqj dq dowhuqdwlyh Zh qrz dvn zkhwkhu wklv ghfolqh lq  47 2      #   "     !          ;     !      $%%% 48 /                   !                        ! :   @   3    49 +                                          4: 2          !            ?    !          :                   6           # "                                2   !                    "                              pw p>w n pw 11 irupxodwlrq/ zh iroorz Hulfvvrq +5339/ Wdeoh 915, zkr vkrzv wkdw htxdwlrq +7, fdq eh h{suhvvhg dv dq huuru0fruuhfwlrq irupxodwlrq= S  S 4 @ 3 .  3 +O,  .h   oq S  S S S  S .  3 +O,  .  3 +O,  . 3  S 4 S 4 S 4 S 4  h  oq S 4 .  . h  oq S 4 . h   oq S  4    4  +:, 5  . x = Htxdwlrq +:, lv dsshdolqj ehfdxvh lw glhuhqwldwhv ehwzhhq vkruw0 dqg orqj0uxq uhvsrqvhv1 Wkh frh!flhqwv dvvrfldwhg zlwk wkh jurzwk udwhv ri wkh uljkw0kdqg vlgh yduldeohv uhsuhvhqw vkruw0uxq uhvsrqvhv> wkh frh!flhqwv dvvrfldwhg zlwk wkh yduldeohv lq ohyhov fdswxuh wkh dgmxvwphqw ri wkh sulfh ri lpsruwv wr lwv orqj0uxq ydoxh1 Lqghhg/ wkh uhvxowlqj h{suhvvlrq iru wkh orqj0uxq ohyho ri lpsruw sulfhv lv htxdwlrq +9, deryh zkhuh  @  h >  @  hh >  @  h > h  @ +  4,> dqg  lv wkh frh!flhqw ri wkh odjjhg lpsruw sulfh lq h h iru wkh htxdwlrq lq ohyhov/ htxdwlrq +7,1 Iru hvwlpdwlrq/ zh lpsohphqw uvw d Jhqhudo0wr0Vshflf vwudwhj| xvlqj wkh ixoo vdpsoh dqg wkhq dsso| uroolqj uhjuhvvlrqv wr wkh vhohfwhg vshflfdwlrq= Wkh wrs ohiw sdqho ri jxuh 43 vkrzv wkdw e3 ghfolqhv iurp 318 lq 4<<3 wr 315 lq 5338/ mxvw dv lq wkh uroolqj0uhjuhvvlrq uhvxowv uhsruwhg lq jxuh <1 Wklv qglqj vxjjhvwv wkdw wkh vkruw0uxq sdvv0wkurxjk kdv ghfolqhg uhjdugohvv ri ixqfwlrqdo irup/ d qglqj frqvlvwhqw zlwk wkh uhvxowv uhsruwhg e| Rolyhl +5335, dqg Pdud}}l dqg Vkhhwv +5339,1 Wkh wrs uljkw dqg erwwrp sdqhov ri e h vwduw dw }hur exw lqfuhdvh +lq devroxwh ydoxh, dqg uhpdlq frqvwdqw vlqfh jxuh 43 vkrz wkdw erwk e h  dqg  e @  h > kdv 4<<81 Lq sduwlfxodu/ jxuh 44 vkrzv wkdw wkh lpsolhg hvwlpdwh ri wkh orqj0uxq sdvv0wkurxjk/  e e h e ri V = Wkhvh xfwxdwhg ehwzhhq 317 dqg 318 zlwk d vdpsoh phdq ri 317;/ zklfk lv forvh wkh ydoxh ri  qglqjv vxssruw rxu ylhz wkdw wkh jurzlqj lpsruwdqfh ri hphujlqj hfrqrplhv grhv qrw lpso| wkdw iruhljq sulfhv/ ru h{fkdqjh udwhv/ duh ehfrplqj ohvv lpsruwdqw lq wkh ghwhuplqdwlrq ri X1V1 lpsruw sulfhv exw/ udwkhu/ wkdw wkh g|qdplfv ri wkh surfhvv duh fkdqjlqj1 Lqghhg/ wkh vkruw0uxq h{fkdqjh udwh sdvv0wkurxjk lv qrz forvh wr }hur exw wkh orqj0uxq sdvv0wkurxjk lv derxw rqh0kdoi1 Djdlq/ wklv glhuhqfh ehwzhhq vkruw0 dqg orqj0uxq uhvsrqvhv zrxog qrw eh uhohydqw li wkh dgmxvwphqw surfhvv zhuh vzliw1 Wr hvwlpdwh wkh ghod| lq dgmxvwlqj wr wkh orqj0uxq/ zh h{dplqh wkh uhvsrqvh ri lpsruw sulfhv wr d vxvwdlqhg/ rqh0shufhqw lqfuhdvh lq wkh ydoxh ri wkh groodu1  Iljxuh 45 vkrzv d vlplodulw| ri vkruw0uxq uhvsrqvhv= 314: iru wkh irupxodwlrq lq jurzwk udwhv +|hoorz olqh, dqg 3158 iru wkh huuru0fruuhfwlrq prgho +juhhq olqh,1 Wklv vlplodulw| lv/ krzhyhu/ vkruw0olyhg zlwk wkh uhvsrqvh iurp wkh huuru0fruuhfwlrq prgho ehlqj pruh wkdw wzlfh dv odujh dv wkdw iurp wkh jurzwk udwh htxdwlrq diwhu wkuhh |hduv1 Ixuwkhu/ jxuh 45 vxjjhvwv wkdw wkh glvshuvlrq lq hvwlpdwhv irxqg lq wkh olwhudwxuh pljkw eh gxh wr d idloxuh wr 1                12      33$%%8 glhuhqwldwh ehwzhhq vkruw0uxq dqg orqj0uxq uhvsrqvhv lq wkh ohyho ri lpsruw sulfhv1 Iljxuh 45 dovr vxjjhvwv wkdw rqh fdq fdswxuh wkh lqfuhdvhg uroh ri hphujlqj hfrqrplhv lq wzr zd|v= e| hlwkhu prgli|lqj phwkrgv wr phdvxuh iruhljq sulfhv +eodfn olqh, ru e| xvlqj frqyhqwlrqdo phdvxuhv ri sulfhv frpelqhg zlwk uroolqj uhjuhvvlrqv +juhhq olqh,1 Krzhyhu/ odfnlqj d whvw wr glvfulplqdwh ehwzhhq wkh wzr dssurdfkhv/ zh rhu wzr uhdvrqv zk| prgholqj lpsruw sulfhv ehqhwv iurp d vwudwhj| wkdw hpskdvl}hv phdvxuhphqw dv rssrvhg wr vdpsoh vhohfwlrq1 Iluvw/ uroolqj uhjuhvvlrqv hperg| d whqvlrq uhohydqw wr srolf| zrun= zkhuhdv wkh sdudphwhu hvwlpdwhv duh dvvxphg wr eh frqvwdqw gxulqj wkh iruhfdvw shulrg/ wkh| duh dvvxphg wr fkdqjh gxulqj wkh hvwlpdwlrq shulrg1 Vhfrqg/ dv Pdud}}l dqg Vkhhwv +5339, qrwh/ hvwlpdwhv iurp uroolqj uhjuhvvlrqv pd| eh vhqvlwlyh wr wkh fkrlfh ri wkh zlqgrz xvhg iru hvwlpdwlrq1 Zlwkrxw remhfwlyh fulwhuld iru fkrrvlqj wkh hvwlpdwlrq zlqgrz/ wklv lqwurgxfhv dqrwkhu vxemhfwlyh/ exw lpsruwdqw/ hohphqw wr wkh prgholqj surfhvv1 8 Frqfoxvlrqv Wklv sdshu rhuv dq hpslulfdo dqdo|vlv ri wkh ehkdylru ri X1V1 lpsruw sulfhv zlwk d irfxv rq dvvhvvlqj wkh glvshuvlrq ri hvwlpdwhg sdvv0wkurxjk ri h{fkdqjh udwhv1 Zh qg wkdw/ zkhuhdv wkh sdvv0wkurxjk lq wkh vkruw0uxq kdv ghfolqhg/ wkh orqj0uxq sdvv0wkurxjk kdv uhpdlqhg vwdeoh1 Zh eholhyh wkdw wkhvh qglqjv dujxh iru hpsor|lqj irupxodwlrqv wkdw glhuhqwldwh ehwzhhq vkruw0 dqg orqj0uxq uhvsrqvhv1 Zh dovr dujxh wkdw wkh rqh irufh ehklqg wkh fkdqjh lq g|qdplfv ri wkh lpsruw0sulfh surfhvv lv wkh juhdwhu suhvhqfh ri surgxfhuv iurp hphujlqj hfrqrplhv1 Dqg zh vkrz wkdw wkhlu hhfw rq lpsruw sulfhv fdq eh fdswxuhg zlwk rxu phdvxuh ri iruhljq sulfhv1 Uhihuhqfhv ^4` Ergqdu/ J1/ E1 Gxpdv/ dqg U1 Pduvwrq/ 5335/%Sdvv0wkurxjk dqg H{srvxuh/% Mrxuqdo ri Ilqdqfh/ 8:/ 4<<05641 ^5` Erzpdq/ G1/ 5333/ %Qrwhv rq LI H{fkdqjh Udwh Lqgh{hv/% plphr1 ^6` Exvvlhuh/ P1/ 5337/ %Qrq0olqhdu H{fkdqjh Udwh Sdvv0wkurxjkB%/ plphr/ Ihghudo Uhvhuyh Erdug1 ^7` Fdpsd/ M1 dqg O1 Jrogehuj/ 5338/ %H{fkdqjh Udwh Sdvv0Wkurxjk lqwr Lpsruw Sulfhv/% Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ ;:/ 9:<09<31 ^8` Fklqq/ P1/ 5338/ %D Sulphu rq Uhdo Hhfwlyh H{fkdqjh Udwhv= Ghwhuplqdqwv/ Ryhuydoxdwlrq/ Wudgh Iorzv dqg Frpshwlwlyh Ghydoxdwlrq/% QEHU Zrunlqj Sdshu Qr1 448541 13 ^9` Hulfvvrq/ Q1/ 5339/ Hpslulfdo Prghoolqj ri Hfrqrplf Wlph Vhulhv/ R{irug= R{irug Xqlyhuvlw| Suhvv +iruwkfrplqj,1 ^:` Jrogehuj/ S1 dqg P1 Nqhwwhu/ 4<<:/ %Jrrgv Sulfhv dqg H{fkdqjh Udwhv= Zkdw Kdyh Zh OhduqhgB/% Mrxuqdo ri Hfrqrplf Olwhudwxuh/ 68/ 4576045:51 ^;` Jurq/ D1 dqg G1 Vzhqvrq/ 5333/ %Frvw Sdvv0wkurxjk lq wkh X1V1 Dxwrpreloh Pdunhw/% Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ ;5/ 64906571 ^<` Jurvv/ G1 dqg Q1 Vfkplww/ 5333/ %H{fkdqjh Udwh Sdvv0Wkurxjk dqg G|qdplf Roljrsro|= Dq Hpslu0 lfdo Lqyhvwljdwlrq/% Mrxuqdo ri Lqwhuqdwlrqdo Hfrqrplfv/ 85/ ;<04451 ^43` Jxvw/ F1/ V1 Ohgxf/ dqg U1 Yljixvvrq/ 5339/ %Wudgh Lqwhjudwlrq/ Frpshwlwlrq/ dqg wkh Ghfolqh lq H{fkdqjh Udwh Sdvv0wukrxjk/% wklv frpshqglxp1 ^44` Khoohuvwhlq/ U1/ 5337/ %Zkr Ehduv wkh Frvw ri d Fkdqjh lq wkh H{fkdqjh UdwhB Wkh Fdvh ri Lpsruwhg Ehhu/% Ihghudo Uhvhuyh Edqn ri Qhz \run/ Vwd Uhsruw qr1 4:<1 ^45` Khqgu|/ G1 I1 dqg K1 Nuro}lj/ 5334/ Dxwrpdwlf Hfrqrphwulf Prgho Vhohfwlrq Xvlqj SfJhwv/ Orqgrq= Wlpehuodnh1 ^46` Oruhwdq/ P1/ 5338/ %Lqgh{hv ri wkh Iruhljq H{fkdqjh Ydoxh ri wkh Groodu/% Ihghudo Uhvhuyh Exoohwlq/ <4/ Qr14 +Zlqwhu,/ 40;1 ^47` Pdud}}l/ P1/ Q1 Vkhhwv/ U1 M1 Yljixvvrq/ dqg rwkhuv/ 5338/ %H{fkdqjh Udwh Sdvv0wkurxjk wr X1V1 Lpsruw Sulfhv= Vrph Qhz Hylghqfh/% Lqwhuqdwlrqdo Ilqdqfh Glvfxvvlrq Sdshu/ Qr1 ;661 ^48` Pdud}}l/ P1 dqg Q1 Vkhhwv/ 5339/ %Ghfolqlqj H{fkdqjh Udwh Sdvv0wkurxjk wr X1V1 Lpsruw Sulfhv= Wkh Srwhqwldo Uroh ri Joredo Idfwruv/% wklv frpshqglxp1 ^49` Rolyhl/ J1/ 5335/ %H{fkdqjh Udwhv dqg wkh Sulfhv ri Pdqxidfwxulqj Surgxfwv Lpsruwhg lqwr wkh Xqlwhg Vwdwhv/% Qhz Hqjodqg Hfrqrplf Uhylhz/ Iluvw Txduwhu/ 604;1 ^4:` Sroodug/ S1 dqg F1 Frxjkolq/ 5337/ %Vl}h Pdwwhuv= Dv|pphwulf H{fkdqjh Udwh Sdvv0wkurxjk dw wkh Lqgxvwu| Ohyho/% Ohyhukxoph Fhqwuh Uhvhdufk Sdshu 53372461 ^4;` Vxpphuv/ U1 dqg D1 Khvwrq/ 4<<4/ %Wkh Shqq Zruog Wdeoh +Pdun 8,= Dq h{sdqghg Vhw ri Lqwhuqd0 wlrqdo Frpsdulvrqv/ 4<8304<;;/% Txduwhuo| Mrxuqdo ri Hfrqrplfv/ 439/ 65:069;1 ^4<` \dqj/ M1/ 4<<:/ %H{fkdqjh Udwh Sdvv0Wkurxjk lq X1V1 Pdqxidfwxulqj Lqgxvwulhv/% Uhylhz ri Hfr0 qrplfv dqg Vwdwlvwlfv/ ;</ <804371 14 Table 1 : Augmented Dickey-Fuller Tests-1974-2005 Variable Import Price GDP Deflator Goods & Services Lags t-adf beta Y_1 SER AIC Variable Lags t-adf beta Y_1 SER AIC 3 -2.896 0.899 0.030 -6.891 Commodity 3 -4.712** 0.292 0.085 -4.783 2 -3.206* 0.907 0.029 -6.950 Price 2 -4.830** 0.243 0.090 -4.699 1 -2.173 0.938 0.032 -6.808 1 -4.936** 0.266 0.088 -4.755 0 -3.646* 0.906 0.034 -6.713 0 -3.952** 0.428 0.096 -4.620 3 -2.014 0.976 0.009 -9.321 GDP Deflator 3 -2.276 0.946 0.012 -8.756 Goods 2 -2.574 0.971 0.009 -9.338 2 -2.613 0.941 0.011 -8.810 1 -1.721 0.981 0.009 -9.234 1 -2.434 0.950 0.011 -8.841 0 -8.198** 0.940 0.012 -8.752 0 -8.198** 0.891 0.013 -8.556 Foreign Price: 3 -2.410 0.901 0.047 -5.954 Foreign Price: 3 -2.302 0.904 0.050 -5.857 Geometric 2 -2.281 0.912 0.047 -5.994 Geometric 2 -2.152 0.915 0.049 -5.894 Non-oil Weights 1 -2.214 0.917 0.046 -6.044 Trade Weights 1 -2.080 0.920 0.049 -5.942 0 -2.971* 0.882 0.052 -5.838 0 -2.760 0.887 0.055 -5.747 Foreign Price: 3 -1.790 0.947 0.049 -5.866 Foreign Price: 3 -1.860 0.944 0.050 -5.845 Divisia 2 -1.723 0.953 0.049 -5.920 Divisia 2 -1.711 0.951 0.050 -5.888 Non-oil Weights 1 -1.572 0.958 0.049 -5.955 Trade Weights 1 -1.547 0.957 0.050 -5.917 0 -2.137 0.937 0.055 -5.741 0 -2.108 0.935 0.056 -5.692 3 -2.238 0.942 0.027 -7.051 2 -3.118* 0.931 0.027 -7.089 1 0 -2.036 -4.723** 0.949 0.902 0.032 0.035 -6.823 -6.637 Producer Price Index Legend t-ADF: augmented Dickey-Fuller Test; an'*' means that the test rejects the hypothesis of a unit root beta Y-1: Coefficient of the level of the lagged dependent variable AIC: Akaike information criterion Rejection values 5%=-2.96; 1%=-3.67. Constant included. 15 Table 2: Long-run Coefficients: Level Specification--Sensitivity to Foreign Prices, U.S. Prices, Weighting Schemes, and Sample Periods Foreign U.S. Weights Sample Pricing to Market Price Price coeff. se Geometric 0.04 Goods & Nonoil 1974-2000 0.72 Services 1974-2005 0.49 0.05 Pass-through coeff. se Commodity coeff. se 0.26 0.46 0.03 0.04 0.10 0e 0.03 -- 0e 0.29 Lagged Dep. Var. coeff. se Intercept coeff. se Homogeneity coeff. se Residuals (a) SER Independ Homosk -0.06 -0.31 0.36 0.12 0.13 1.09 0.95 0.06 0.06 0.014 0.018 0.35 0.02 0.54 0.76 Broad 1974-2000 1974-2005 0.71 0.47 0.04 0.05 0.27 0.47 0.03 0.04 0.10 0e 0.02 -- 0e 0.29 -0.06 -0.27 0.41 0.11 0.13 1.08 0.94 0.05 0.06 0.013 0.017 0.36 0.02 0.36 0.66 Nonoil 1974-2000 1974-2005 0.51 0.56 0.07 0.12 0.52 0.47 0.08 0.12 0e 0e --- 0e 0.64 -0.09 0e 0e --- 1.03 1.03 0.11 0.17 0.028 0.026 0.07 0.39 0.57 0.69 Broad 1974-2000 1974-2005 0.50 0.53 0.06 0.09 0.52 0.49 0.06 0.10 0e 0e --- 0.33 0.58 0.06 0.09 0e 0e --- 1.03 1.03 0.08 0.13 0.025 0.026 0.08 0.18 0.78 0.62 Nonoil 1974-2000 1974-2005 0.52 0.35 0.08 0.16 0.48 0.57 0.09 0.12 0e 0e --- 0.56 0.66 0.16 0.15 0e 0.45 -0.35 1.00 0.91 0.12 0.20 0.020 0.020 0.16 0.49 0.76 0.51 Broad 1974-2000 1974-2005 0.54 0.46 0.05 0.05 0.46 0.50 0.06 0.05 0e 0e --- 0.41 0.27 0.16 0.08 0e 0.23 -0.13 1.00 0.95 0.08 0.07 0.018 0.020 0.12 0.05 0.76 0.52 1974-2000 1974-2005 0.77 0.26 0.07 0.21 0.18 0.48 0.05 0.18 0.13 0e 0.04 -- 0.33 0.69 0.08 0.08 -0.42 0.98 0.20 0.40 1.08 0.75 0.09 0.28 0.014 0.021 0.44 0.02 0.68 0.09 Broad 1974-2000 1974-2005 0.78 0.27 0.07 0.20 0.17 0.47 0.05 0.14 0.13 0e 0.04 -- 0.32 0.68 0.08 0.08 -0.39 1.02 0.19 0.38 1.08 0.74 0.09 0.24 0.014 0.022 0.40 0.16 0.50 0.05 Nonoil 1974-2000 1974-2005 0.55 0.73 0.04 0.08 0.42 0.35 0.04 0.04 0e 0.06 -0.03 0.30 0.18 0.08 0.09 0e -0.73 -0.25 0.97 1.14 0.06 0.09 0.022 0.018 0.03 0.01 0.53 0.96 Broad 1974-2000 1974-2005 0.79 0.78 0.07 0.06 0.34 0.34 0.03 0.03 0e 0e --- 0e 0e --- -0.70 -0.70 0.19 0.17 1.13 1.13 0.08 0.07 0.020 0.019 0.04 0.02 0.88 0.79 Nonoil 1974-2000 1974-2005 0.63 0.15 0.03 0.28 0.32 0.47 0.03 0.16 0e 0e --- 0.33 0.78 0.13 0.12 0e 1.51 -0.74 0.95 0.63 0.04 0.32 0.015 0.020 0.22 0.46 0.29 0.37 1974-2000 0.63 0.03 0.32 1974-2005 0.19 0.25 0.46 0e: Algorithm excludes explanatory variable from specification. 0.03 0.14 0e 0e --- 0.29 0.76 0.12 0.12 0e 1.41 -0.64 0.95 0.65 0.04 0.29 0.014 0.020 0.23 0.38 0.39 0.48 Goods PPI Divisia Goods & Nonoil Services Goods PPI Broad (a): Entries for "Independ" and "Homosk" are significance levels for rejecting the hypothesis of serial independence and homoskedasticity. 16 Table 3: Long-run Coefficients; Growth Specification--Sensitivity to Foreign Prices, U.S. Prices, Weighting Schemes, and Sample Periods Foreign U.S. Weights Price Price Geometric Goods & Nonoil Services Goods PPI Sample Pricing to Market coeff se Pass-through coeff se Commodity coeff se Lagged Dep. Var. Intercept coeff se coeff se Homogeneity coeff se SER Residuals(a) Independ. Homosk 1974-2000 1974-2005 0.73 0.71 0.11 0.11 0.37 0.36 0.09 0.09 0.09 0.07 0.03 0.03 0e 0e --- 0e 0e --- 1.18 1.14 0.15 0.14 0.022 0.022 0.91 0.96 0.82 0.44 Broad 1974-2000 1974-2005 0.75 0.72 0.11 0.11 0.35 0.35 0.08 0.08 0.09 0.08 0.03 0.03 0e 0e --- 0e 0e --- 1.19 1.15 0.14 0.14 0.022 0.022 0.23 0.89 0.91 0.69 Nonoil 1974-2000 1974-2005 0.83 0.85 0.16 0.15 0.42 0.41 0.10 0.09 0.10 0.09 0.04 0.04 0e 0e --- 0e 0e --- 1.36 1.36 0.19 0.18 0.026 0.024 0.70 0.76 0.98 0.97 Broad 1974-2000 1974-2005 0.86 0.88 0.16 0.14 0.40 0.39 0.10 0.08 0.11 0.10 0.04 0.04 0e 0e --- 0e 0e --- 1.37 1.37 0.19 0.17 0.026 0.024 0.60 0.62 0.97 0.88 Nonoil 1974-2000 1974-2005 0.58 0.52 0.10 0.11 0.47 0.44 0.08 0.09 0.06 0.08 0.03 0.05 0e 0e --- 0e 0e --- 1.11 1.04 0.13 0.15 0.022 0.024 0.57 0.57 0.05 0.23 Broad 1974-2000 1974-2005 0.60 0.49 0.09 0.12 0.45 0.46 0.07 0.10 0.06 0.11 0.03 0.06 0e 0.10 -0.11 0e 0e --- 1.11 1.05 0.12 0.17 0.022 0.024 0.35 0.53 0.04 0.67 1974-2000 1974-2005 0.72 1.01 0.12 0.16 0.33 0.36 0.09 0.08 0.09 0.08 0.04 0.03 0e 0e --- 0e -0.02 -0.01 1.14 1.44 0.15 0.18 0.023 0.021 0.96 0.99 0.55 0.71 Broad 1974-2000 1974-2005 0.72 1.00 0.12 0.16 0.33 0.34 0.08 0.08 0.10 0.08 0.04 0.03 0e 0e --- 0e -0.02 -0.01 1.14 1.43 0.15 0.18 0.023 0.022 0.94 0.96 0.79 0.70 Nonoil 1974-2000 1974-2005 0.83 0.77 0.16 0.15 0.39 0.36 0.09 0.08 0.10 0.15 0.04 0.05 0e 0e --- 0e 0e --- 1.33 1.28 0.19 0.17 0.026 0.023 0.68 0.49 0.89 0.95 Broad 1974-2000 1974-2005 0.83 0.77 0.16 0.15 0.39 0.35 0.09 0.08 0.11 0.16 0.04 0.05 0e 0e --- 0e 0e --- 1.32 1.28 0.19 0.17 0.026 0.023 0.64 0.40 0.93 0.93 Nonoil 1974-2000 1974-2005 0.55 0.59 0.10 0.12 0.41 0.44 0.07 0.09 0.12 0.08 0.05 0.06 0e 0e --- 0e -0.01 -0.01 1.08 1.11 0.13 0.16 0.022 0.024 0.24 0.68 0.87 0.82 0.40 0.42 0.07 0.09 0.13 0.09 0.05 0.06 0e 0e --- 0e -0.01 -0.01 1.07 1.09 0.13 0.16 0.022 0.025 0.20 0.60 0.72 0.78 Divisia Goods & Nonoil Services Goods PPI 1974-2000 0.54 0.10 1974-2005 0.58 0.12 0e: Algorithm excludes explanatory variable from specification. Broad (a): Entries for "Independ" and "Homosk" are significance levels for rejecting the hypothesis of serial independence and homoskedasticity. 17 Wdeoh 7= Orqj0uxq Frh!flhqw Hvwlpdwhv  ROV/ 4<:705338 Vhohfwhg Vshflfdwlrqv +vwdqgdug huuruv lq sduhqwkhvhv, Irupxodwlrqv V Sulflqj wr Pdunhw Sdvv0wkurxjk Shuvlvwhqfh Krprjhqhlw|  V 4<:705333 4<:705338 4<:705333 4<:705338 3183 3186 3187 318; +3139, +313<, +3143, +3145, 3185 317< 3173 3175 +3139, +3143, +313:, +313<, 3166 318; 0  +3139, +313<, 4136 4136 413: 413< +313;, +3147, +3146, +3148, Irupxodwlrqv V = Htxdwlrq +7, zlwk jhrphwulf phdvxuh ri iruhljq sulfhv dqg JGS0jrrgv gh dwru iru X1V1 sulfhv1 V = Htxdwlrq +8, zlwk Glylvld phdvxuh ri iruhljq sulfhv dqg SSL iru X1V1 sulfhv1  Vxp ri sulflqj wr pdunhw dqg sdvv0wkurxjk frh!flhqwv> vwdqgdug huuru frpsxwhg zlwkrxw wdnlqj lqwr dffrxqw wkh fryduldqfh ri wkh hvwlpdwhv1 18 U.S. Weighted Average Relative Prices* 120 Index with 1972 = 100 Geometric− 110 Trade weights Divisia Trade weights Non−oil weights 100 Non−oil weights 90 80 1970 1975 1980 500 Index with 1985 1990 1995 2000 2005 2000 2005 Measures of Dollar Foreign Prices 1972 = 100 Divisia 400 Non−oil weights Trade weights 300 Geometric− Trade weights Non−oil weights 200 100 1970 1975 1980 1985 1990 1995 * Series re−scaled to 100 in first common date Iljxuh 4= X1V1 Lqwhuqdwlrqdo Uhodwlyh Sulfhv dqg Djjuhjdwh Iruhljq0JGS Gh dwruv 19 Levels Measures of U.S. Prices Overall GDP deflator GDP−goods deflator PPI 140 120 Series re−scaled to 100 in First Data Common Date 100 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Growth Rates 0.15 0.10 0.05 0.00 1950 1955 Iljxuh 5= Dowhuqdwlyh Phdvxuhv ri X1V1 Sulfhv 20 Core Import Price Index Foreign Dollar Price − Geometric* GDP Deflator − Goods and Services 150 100 100 50 50 1970 1980 1990 2000 1970 Core Import Price Index Foreign Dollar Price − Geometric* GDP Deflator − Goods 150 100 50 50 1980 * Non−oil weights 1990 2000 1980 1970 1980 Iljxuh 6= Lpsruw Sulfhv/ Grphvwlf dqg Iruhljq Sulfh Ohyhov 21 1990 2000 Core Import Price Index Foreign Dollar Price − Divisia* GDP Deflator − Goods 150 100 1970 Core Import Price Index Foreign Dollar Price − Divisia* GDP Deflator − Goods and Services 150 1990 2000 1.20 Pricing to Market ( ) Sensitivity to Measure of Foreign Prices 1974-2005 1.00 Geometric Divisia 0.80 0.60 0.40 0.20 Not significant 0.00 G&S, nonoil G&S, Goods, Goods, PPI, broad nonoil broad nonoil PPI, broad G&S, nonoil Level eq. G&S, Goods, Goods, PPI, broad nonoil broad nonoil PPI, broad Growth Eq. 0.60 Geometric 0.50 Exchange-rate Pass-through ( ) Sensitivity to Measure of Foreign Prices 1974-2005 Divisia 0.40 0.30 0.20 0.10 0.00 G&S, nonoil G&S, Goods, Goods, PPI, broad nonoil broad nonoil PPI, broad G&S, nonoil Level eq. G&S, Goods, Goods, PPI, broad nonoil broad nonoil Growth eq. Iljxuh 7= Orqj0uxq Frh!flhqw Hvwlpdwhv  Vhqvlwlylw| wr Hvwlpdwlrq Ghvljq 22 PPI, broad Geometric Foreign Price 0.60 Level Eq. Growth Eq. 0.50 1974-2000 1974-2005 0.40 0.30 0.20 0.10 0.00 PPI, G&S, G&S, Goods, Goods, PPI, nonoil broad nonoil broad nonoil broad G&S, G&S, Goods, Goods, PPI, PPI, nonoil broad nonoil broad nonoil broad Divisa Foreign Price 0.60 Level Eq. Growth Eq. 0.50 0.40 0.30 0.20 0.10 0.00 G&S, G&S, Goods, Goods, PPI, PPI, nonoil broad nonoil broad nonoil broad G&S, G&S, Goods, Goods, PPI, PPI, nonoil broad nonoil broad nonoil broad e Dowhuqdwlyh Vdpsoh Shulrgv Iljxuh 8= Orqj0uxq Hvwlpdwhv ri H{fkdqjh0udwh Sdvv0wkurxjk +,= 23 Geometric Foreign Price 1.20 Growth Eq. Level Eq. 1.00 1974-2000 1974-2005 0.80 0.60 0.40 0.20 0.00 PPI, G&S, G&S, Goods, Goods, PPI, nonoil broad nonoil broad nonoil broad G&S, G&S, Goods, Goods, PPI, PPI, nonoil broad nonoil broad nonoil broad Divisia Foreign Price 1.20 Level Eq. Growth Eq. 1.00 0.80 0.60 0.40 n 0.20 n n n 0.00 G&S, G&S, Goods, Goods, PPI, PPI, nonoil broad nonoil broad nonoil broad G&S, G&S, Goods, Goods, PPI, PPI, nonoil broad nonoil broad nonoil broad Iljxuh 9= Orqj0uxq Hvwlpdwhv ri Sulflqj0wr0Pdunhw +e  ,= Dowhuqdwlyh Vdpsoh Shulrgv +q ghqrwhv qrw vwdvwlfdoo| vljqlfdqw,1 24 0.60 Hypothetical Response of U.S. Import Prices (percent change) to a One Percent Sustained Depreciation of the Dollar Level Specification, 1974-2000 Geometric Foreign Price 0.50 Growth-rate Specification, 1974-2005 Divisia Foreign Price 0.40 0.30 Level Specification, 1974-2005 Geometric Foreign Price 0.20 0.10 Years After Shock 0.00 1 2 3 4 5 6 7 8 9 10 11 Iljxuh := Vkruw0 dqg Orqj0uxq H{fkdqjh0udwh Sdvv0wkurxjk= Dowhuqdwlyh Irupxodwlrqv 25 12 Import Prices (logs) 4.90 4.85 Summary Measures Level Equation Growth Equation 4.80 Mean Forecast Error 5.8% −6.2% Growth Equation with Divisia Foreign Price RMSE 5.8% 8.1% 4.75 4.70 Actual 4.65 Level Equation with Geometric Foreign Price 4.60 4.55 4.50 1999 2000 2001 2002 2003 2004 2005 Iljxuh ;= <8( Frqghqfh Edqgv iru H{0srvw G|qdplf H{wudsrodwlrqv ri Lpsruw Sulfhv 26 2006 0.7 Pass−through Coefficient Rolling Regression − Window of 15 years Equation in Growth Rates 0.6 0.5 0.4 0.45 0.3 0.2 0.17 0.1 0.0 1990 1995 2000 2005 Iljxuh <= Hvwlpdwhg Vkruw0uxq H{fkdqjh0Udwh Sdvv0wkurxjk= Jurzwk0Udwh Prgho zlwk Uroolqj Uhjuhv0 vlrqv 27 0.75 ^ β’ 0.5 ^ ~ ρ 0.50 0.0 0.25 −0.5 0.00 −1.0 1990 1995 2000 2005 1990 1995 2000 2005 0.50 0.25 0.00 −0.25 ^ ^ ^ ~ ~ β =−β ρ −0.50 1990 1995 2000 2005 Iljxuh 43= Uroolqj Uhjuhvvlrq Hvwlpdwhv ri Huuru0Fruuhfwlrq Prgho 0.60 0.50 0.40 0.30 0.20 0.10 0.00 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 e h Iljxuh 44= Orqj0uxq Hvwlpdwh ri H{fkdqjh0Udwh Sdvv0wkurxjk ri HuuruFruuhfwlrq Prgho= 0 e h 28 0.60 Hypothetical Response of U.S. Import Prices (percent change) to a One Percent Sustained Depreciation of the Dollar Level Specification, 1974-2000 Geometric Foreign Price 0.50 Growth-rate Specification, 1974-2005 Divisia Foreign Price 0.40 ECM, 1991-2005 Divisia Foreign Price 0.30 Level Specification, 1974-2005 Geometric Foreign Price Growth-rate Specification Rolling Regressions (last), 1991-2005 Divisia Foreign Price 0.20 0.10 Years After Shock 0.00 1 2 3 4 5 6 7 8 9 10 11 12 Iljxuh 45= Vkruw0 dqg Orqj0uxq H{fkdqjh0udwh Sdvv0wkurxjk= Dowhuqdwlyh Irupxodwlrqv dqg Vdpsoh0 vhohfwlrq Phwkrgv 29