• Non ci sono risultati.

Endogenous Fluctuations and the Role of Monetary Policy

N/A
N/A
Protected

Academic year: 2021

Condividi "Endogenous Fluctuations and the Role of Monetary Policy"

Copied!
56
0
0

Testo completo

(1)Fondazione Eni Enrico Mattei. Endogenous Fluctuations and the Role of Monetary Policy Mordecai Kurz*, Hehui Jin* and Maurizio Motolese** NOTA DI LAVORO 11.2002. JANUARY 2002 ETA – Economic Theory and Applications. *Stanford University **Catholic University of Milan. This paper can be downloaded without charge at: The Fondazione Eni Enrico Mattei Note di Lavoro Series Index: http://www.feem.it/web/activ/_activ.html Social Science Research Network Electronic Paper Collection: http://papers.ssrn.com/abstract=XXXXXX. Fondazione Eni Enrico Mattei Corso Magenta, 63, 20123 Milano, tel. +39/02/52036934 – fax +39/02/52036946 E-mail: letter@feem.it C.F. 97080600154.

(2) SUMMARY This paper studies the dynamic volatility properties of a monetary economy in which agents hold Rational Beliefs (see Kurz (1994), (1997)) rather than Rational Expectations. Except for this feature the examined Rational Belief Equilibrium (in short, RBE) is entirely standard: markets are competitive, prices are flexible and all information is symmetric. The paper demonstrates a) The RBE paradigm offers an integrated theory of real and financial volatility with a high volume of trade. Most volatility in an RBE is induced endogenously through the beliefs of agents. b) Although our RBE assumes fully competitive markets in which prices are fully flexible,the diverse expectations of agents can explain most of the familiar features of monetary equilibria. This includes, money nonneutrality, Phillips curve and impulse response functions with respect to monetary shocks. c) Agents with diverse but inconsistent beliefs may induce socially undesirable excess fluctuations even when the allocation is ex-ante Pareto optimal. Central bank policy should aim to reduce the endogenous component of this volatility..

(3) CONTENTS Introduction. 1. 1.. The economic environment. 8. 2.. A rational belief equilibrium. 16. 3.. What is the rationale for and object of. 37. monetary policy? References. 40.

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

(5)  D

(6) .XU]6FKQHLGHU 

(7) .XU]%HOWUDWWL 

(8) .XU]0RWROHVH 

(9)

(10) 8VLQJWKHWKHRU\RI5DWLRQDO%HOLHI(TXLOLEULXP KHQFHIRUWK5%( VHH.XU] 

(11)  

(12)

(13) WKHVHSDSHUVLQWURGXFHGDXQLILHGPRGHOZKLFKH[SODLQVVLPXOWDQHRXVO\D OLVWRIILQDQFLDOSKHQRPHQDUHJDUGHGDV³DQRPDOLHV´7KHPRGHO¶VNH\IHDWXUHLVWKHKHWHURJHQHLW\ RIDJHQW¶VEHOLHIV$WDQ\WLPHDQDJHQWPD\EHD³EXOO´ZKRLVUDWLRQDOEXWRSWLPLVWLFDERXWIXWXUH FDSLWDOJDLQVRUD³EHDU´ZKRLVUDWLRQDOEXWSHVVLPLVWLFDERXWVXFKJDLQV3KHQRPHQDVXFKDVWKH (TXLW\3UHPLXP3X]]OHDUHWKHQH[SODLQHGE\WKHIDFWWKDWSHVVLPLVWLF³EHDUV´ZKRDLPWRDYRLG FDSLWDOORVVHVGULYHLQWHUHVWUDWHVORZDQGWKHHTXLW\SUHPLXPKLJK IRUDXQLILHGWUHDWPHQWVHH.XU]. 7KLVUHVHDUFKZDVVXSSRUWHGE\DJUDQWRIWKH6PLWK5LFKDUGVRQ)RXQGDWLRQWRWKH6WDQIRUG,QVWLWXWHIRU (FRQRPLF3ROLF\5HVHDUFK 6,(35

(14) :HWKDQN.HQQHWK-XGGIRUFRQVWDQWDGYLFHZKLFKZDVFUXFLDODWVHYHUDOSRLQWV LQWKHGHYHORSPHQWRIWKLVZRUN:HWKDQN3HWHU+DPPRQG)HOL[.XEOHUDQG&DUVWHQ1LHOVHQIRUPDQ\LQVLJKWIXO FRQYHUVDWLRQVUHJDUGLQJWKHFRQWHQWDQGPHWKRGVRIWKLVSDSHU:HDOVRWKDQN$UWXUR5LFDUGR*RQ]DOH]GHOD0RWD $OEHUW&KXQDQG3H\URQ/DZIRUGHWDLOHGFRPPHQWVRQDQHDUOLHUGUDIWDQGIRUDVVLVWDQFHLQSUHSDULQJWKHGDWDLQWKH ,QWURGXFWLRQ:HDUHSOHDVHGWRKRQRU1HG3KHOSVZKRVHZRUNKDVDQWLFLSDWHGVRPHRIWKHGHYHORSPHQWVLQWKLV SDSHU. .

(15) DQG0RWROHVH 

(16)

(17) 7KH5%(WKHRU\ZDVXVHGE\.XU] E

(18) WRH[SODLQWKH)RUZDUG'LVFRXQW %LDVLQIRUHLJQH[FKDQJHPDUNHWVE\*DUPDLVH 

(19) WRH[SODLQWKHFDSLWDOVWUXFWXUHRIILUPVDQG E\:X 

(20) WRVWXG\VSHFXODWLRQDQGWUDGLQJYROXPHLQDVVHWPDUNHWV7KHSUHVHQWSDSHULQLWLDWHV RXUDSSOLFDWLRQRIWKH5%(WKHRU\WRWKHVWXG\RIHQGRJHQRXVIOXFWXDWLRQVLQDPRQHWDU\HFRQRP\ DQGWRDQH[DPLQDWLRQRIWKHLPSOLHGUROHRIPRQHWDU\SROLF\ 7KHLGHDWKDWGLYHUVHH[SHFWDWLRQVLVLPSRUWDQWLQDQHTXLOLEULXPDQDO\VLVLVQRWQHZWR HFRQRPLFV'LYHUVHEHOLHIVLQILQDQFLDOPDUNHWVDUHDFHQWUDOFRPSRQHQWRI7KRUQWRQ¶V 

(21) YLHZ RISDSHUPRQH\DQGILQDQFLDOPDUNHWV([SHFWDWLRQVDUHPHQWLRQHGRIWHQLQ.H\QHV 

(22) DOWKRXJK KHQHYHUGHYHORSHGDIRUPDOWKHRU\RILQGLYLGXDOEHOLHIV0DUNHWH[SHFWDWLRQVDUHFHQWUDOWR ³FXPXODWLYHPRYHPHQWV´LQ3LJRX VHH3LJRX¶V 

(23) &KDSWHU9,

(24) DQGH[SHFWDWLRQVDUHEDVLFWR WKHSURFHVVRIGHYLDWLRQVIURPDVWDWLRQDU\HTXLOLEULXPLQWKH6ZHGLVKVFKRRO HJVHH0\UGDO¶V YLHZRIPRQH\LQ0\UGDO 

(25) FKDSWHU,,,

(26) $OVRWKHFRQFHSWRI³VXEMHFWLYHYDOXHV´EDVHGRQ GLYHUVHH[SHFWDWLRQVLVDFRUQHUVWRQHRI/LQGDKO¶V 

(27) WKHRU\RIPRQH\DQGFDSLWDO)LQDOO\ GLYHUVHH[SHFWDWLRQVLVJHQHULFWRDQ$UURZ'HEUHXRUD5DGQHUHTXLOLEULXP $VWKLVZRUNLVGHGLFDWHGWR1HG3KHOSVZHREVHUYHWKDW3KHOSVVWUHVVHGRIWHQWKH LPSRUWDQFHRIH[SHFWDWLRQV,QDFFRUGZLWKD%D\HVLDQSHUVSHFWLYHKHVDZH[SHFWDWLRQVDV VXEMHFWLYHPRGHOVH[SUHVVLQJWKHDJHQW¶VLQWHUSUHWDWLRQRILQIRUPDWLRQDQGQHHGLQJDG\QDPLF XSGDWLQJZKLFKZRXOGOHDGWRVRPHFRQFHSWRIHTXLOLEULXP$OWKRXJKDWWUDFWHGE\WKHVLPSOLFLW\RI WKHVLQJOHEHOLHIPRGHOKHUHDOL]HGLWVODFNRIUHDOLVPEXWPRUHLPSRUWDQWLWVIDLOXUHWRFDSWXUHWKH FRPSRQHQWRIYRODWLOLW\LQGXFHGE\WKHLQWHUDFWLRQRIKHWHURJHQRXVH[SHFWDWLRQV0RUHVSHFLILFDOO\ LQHYDOXDWLQJWKHLPSDFWRIUDWLRQDOH[SHFWDWLRQV)U\GPDQDQG3KHOSV 

(28) VWUHVVWKHLPSRUWDQFH RIGLYHUVHEHOLHIV7KH\MXVWLI\WKHLUSRVLWLRQRQWKHJURXQGWKDWDQ\WKHRU\ZLWKXQLIRUPPDUNHW EHOLHIVRIDJHQWVLVIXQGDPHQWDOO\QRQUREXVWVD\LQJ SDJH

(29)  %XWRQFHWKHWKHRUHWLFDOGRRULVRSHQHGWRRQHRUPRUHK\SRWKHVHVRIRSWLPDOLW\LQWKHH[SHFWDWLRQVIRUPDWLRQ RIWKHLQGLYLGXDODJHQWVWKHLPSOLHGEHKDYLRURIWKH RWKHUZLVHLGHQWLFDO

(30) PRGHOLVRIWHQIRXQGWREHZUHQFKHG LQWRGLUHFWLRQVIDUIURPWKHEHKDYLRULPSOLHGE\WKHUDWLRQDOH[SHFWDWLRQVK\SRWKHVLV,QVKRUW3DQGRUD¶VER[RI GLVHTXLOLEULXPEHKDYLRULVRSHQHGXS. 7KHWKHRU\RI5DWLRQDO%HOLHIV 5%LQVKRUW

(31) SURYLGHVDQDQDO\WLFDOIUDPHZRUNDQGDYRFDEXODU\IRU WKHVHLGHDV,WVKRZVWKDWWKHLQWHUDFWLRQRIEHOLHIVDFWDVDSURSDJDWLRQPHFKDQLVPJHQHUDWLQJ YRODWLOLW\HQGRJHQRXVO\7KHFRPSRQHQWRIVRFLDOULVNJHQHUDWHGE\WKHGLVWULEXWLRQRIEHOLHIVLV. .

(32) FDOOHG³(QGRJHQRXV8QFHUWDLQW\´$OWKRXJK5%JHQHUDOL]HWKHFRQFHSWRIUDWLRQDOH[SHFWDWLRQVWKH 5%(WKHRU\UHYHDOVWKDWDV)U\GPDQDQG3KHOSV 

(33) FRQMHFWXUHGDQHFRQRP\ZLWKGLYHUVH EHOLHIVEHKDYHVGUDVWLFDOO\GLIIHUHQWIURPDQHFRQRP\ZLWKDVLQJOHXQLIRUPEHOLHI. 2QWKH'LYHUVLW\RI5DWLRQDO%HOLHIV 7DEOHSUHVHQWVDVDQH[DPSOHIRUHFDVWVRI*13JURZWKDQGLQIODWLRQPDGHLQ-DQXDU\ IRUDOORIE\SDUWLFLSDQWVLQWKH%OXH&KLS(FRQRPLF,QGLFDWRUV$ERXWKDOIRIWKH 7DEOH%OXH&KLS)RUHFDVWVRI*13*URZWKDQG,QIODWLRQIRU -DQXDU\. )RUHFDVWHG3HUFHQW&KDQJH 5HDO. *13. )RUHFDVWIRU. *13. 6HDUV5RHEXFN &R. +. . 3UXGHQWLDO%DFKH. . /. $PKROG 6%OHLFKURHGHU &KLFDJR&RUSRUDWLRQ. %RVWLDQ(FRQRPLF5HVHDUFK. 3ULFH'HIODWRU. . . . . . . )DLUPRGHO. . . :D\QH+XPPHU &R&KLFDJR. . . ,QIRUXP8QLYRI0DU\ODQG. . . 'XQ %UDGVWUHHW. . . &DKQHUV(FRQRPLFV. 1DW¶O&LW\%DQNRI&OHYHODQG &57*RYHUQPHQW6HFXULWLHV &RQIHUHQFH%RDUG. (FRQRFODVW. )LUVW1DWLRQDO%DQNRI&KLFDJR. 8QLYRI0LFKLJDQ04(0. . . . . . . . . . . . . . . 0DQXIDFWXUHUV1DWO%DQN'HWURLW. . . %URZQ%URWKHUV+DUULPDQ. . . 7XUQLQJ3RLQWV 0LFURPHWULFV

(34) 'HDQ:LWWHU5H\QROGV,QF /D6DOOH1DWLRQDO%DQN. 1RUWKHUQ7UXVW&RPSDQ\. . . . . . . . . (YDQV(FRQRPLFV. . . 3UXGHQWLDO,QVXUDQFH&R. . . 0RUULV&RKHQ $VVRFLDWHV &KU\VOHU&RUSRUDWLRQ. (FRQRYLHZV,QWHUQDWLRQDO,QF 867UXVW&R. 5HHGHU$VVRFLDWHV &KDUOHV

(35) 6LII2DNOH\0DUNV,QF. . . . . . (,'X3RQWGH1HPRXUV &R. . . &RUH6WDWHV)LQDQFLDO&RUS. 0RUWJDJH%DQNHUV$VVQRI$PHULFD. . . . %DQNRI$PHULFD. . . 0RUJDQ6WDQOH\ &R. (JJHUW(FRQRPLF(QWHUSULVHV,QF. +. . . . . . . . . . . . 1DWLRQDO$VVQRI+RPH%XLOGHUV. . . )RUG0RWRU&RPSDQ\. . . 86&KDPEHURI&RPPHUFH. . +. 0HWURSROLWDQ/LIH,QVXUDQFH&R &KDVH0DQKDWWDQ%DQN. 0DQXIDFWXUHUV+DQRYHU7UXVW&R. %DQNHUV7UXVW&R. . . . . . . . . /DXUHQFH+0H\HU $VVRF. . . 31&)LQDQFLDO&RUS. . . 6HFXULW\3DFLILF1DW¶O%DQN. . . 8&/$%XVLQHVV)RUHFDVW. . . *HRUJLD6WDWH8QLYHUVLW\. . . 0HUULOO/\QFK. (TXLWDEOH/LIH$VVXUDQFH. 0RUJDQ*XDUDQW\7UXVW&R 6KDZPXW1DWLRQDO&RUS. . . . . . . /. . IRUHFDVWHUVSUHGLFWHGDWWKDWWLPHWKDWZLOOEHDUHFHVVLRQ\HDUDQGWKHRWKHUKDOIGLVDJUHHG 7KHDFWXDOJURZWKUDWHLQZDVDQGWKHLQIODWLRQUDWH1RZSODFLQJRXUVHOYHVLQ. .

(36) -DQXDU\VXSSRVHZHPDNHDVWDWLRQDU\HFRQRPHWULFIRUHFDVWRI*13JURZWKZLWKRXWQRQ VWDWLRQDU\MXGJPHQWVDERXWWKHXQLTXHFRQGLWLRQVSUHYDLOLQJLQ:HXVHGDPRGHORI6WRFN DQG:DWVRQ D

(37)  E

(38)  

(39) HVWLPDWHGE\HPSOR\LQJDFRPELQDWLRQRIGLIIXVLRQLQGH[HV DYHUDJHGELYDULDWH9$5IRUHFDVWVDQGXWLOL]LQJDODUJHQXPEHURI86WLPHVHULHV$OOQRQ MXGJPHQWDOVWDWLRQDU\IRUHFDVWVRI*13WXUQHGRXWWREHKLJKHUWKDQPRVWRIWKHSULYDWHIRUHFDVWV )LJXUHSUHVHQWVWKHGLVWULEXWLRQRISULYDWHIRUHFDVWVRI*'3JURZWKUDWHVLQ 7KHVHIRUHFDVWVZHUHPDGHLQHDFKTXDUWHUIRU*'3JURZWKRYHUWKHIXOO\HDUIROORZLQJWKH\HDURI WKHIRUHFDVW+HQFHLQHDFKTXDUWHURIDJLYHQ\HDUWKHIRXUIRUHFDVWVDUHPDGHIRUWKHVDPH\HDU )RUH[DPSOHLQ0DUFK-XQH6HSWHPEHUDQG'HFHPEHURILQGLYLGXDOIRUHFDVWVDUHIRUWKHIXOO. ),*85(',675,%87,212)35,9$7()25(&$6762)*'3*52:7+. \HDU)LJXUHH[KLELWVWKHWKSHUFHQWLOHDQGWKHWKSHUFHQWLOHRIWKHIRUHFDVWGLVWULEXWLRQLQ HDFKTXDUWHUDQGWKHKRUL]RQWDOEDUVVKRZWKHUHDOL]DWLRQRI*'3JURZWKD\HDUODWHU)RUH[DPSOH WKHEDULQH[KLELWVWKHJURZWKUDWHUHDOL]HGLQDQGIRUHFDVWHGLQHDFKRIWKHIRXUTXDUWHUV RI7KHVWDWLRQDU\IRUHFDVWV QRWVKRZQ

(40) DUHQDUURZO\GLVWULEXWHGMXVWEHORZLQVRPH SHULRGVSULYDWHIRUHFDVWVDUHDERYHDQGLQRWKHUSHULRGVWKH\DUHEHORZWKHVWDWLRQDU\IRUHFDVWV 7KHHPSLULFDOUHFRUGWKXVUHYHDOVZLGHIOXFWXDWLRQVRILQGLYLGXDOIRUHFDVWVRIYDULDEOHVDERXW ZKLFKWKHUHLVQRSULYDWHLQIRUPDWLRQ0RUHRYHULQGLYLGXDOIRUHFDVWVIOXFWXDWHRYHUWLPHDURXQGWKH VWDWLRQDU\IRUHFDVWVVKRZLQJQRVLJQRIFRQYHUJHQFHWRWKHVHQRQGLVFUHWLRQDU\VWDWLRQDU\IRUHFDVWV 6RKRZGRHVWKHWKHRU\RI5DWLRQDO%HOLHIVH[SODLQWKHVHIDFWV" $QDFFRXQWRIWKH5%WKHRU\PD\EHIRXQGLQ.XU] 

(41) RU.XU]DQG0RWROHVH 

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

(43) FRQWUDGLFWHGE\WKHHPSLULFDOHYLGHQFH0RUHVSHFLILFDOO\LIRQHXVHVDQ5%WRVLPXODWHWKHGDWDRI WKHHFRQRP\LWZLOOUHSURGXFHWKHNQRZQHPSLULFDOGLVWULEXWLRQRIHTXLOLEULXPREVHUYDEOHV$Q5% PD\DWWLPHVH[KLELW³RSWLPLVP´RU³SHVVLPLVP´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

(44) 7HFKQRORJLFDOVKRFNVDQGLQYHVWPHQWV7UDGLWLRQDO5HDO%XVLQHVV&\FOH 5%&

(45) PRGHOVXVHGWKH 6RORZUHVLGXDODVDPHDVXUHRIWHFKQRORJLFDOVKRFNV+RZHYHUHPSLULFDOHYLGHQFHUHYHDOHGWKDW WKLVPHDVXUHGHSHQGVXSRQHQGRJHQRXVYDULDEOHVVXFKDVFDSDFLW\XWLOL]DWLRQ HJ*UHHQZRRG +HUFRZLW]DQG+XIIPDQ 

(46) %XUQVLGH(LFKHQEDXPDQG5HEHOR 

(47) DQG%DVX 

(48)

(49)  &RPSXWDWLRQDOOLPLWDWLRQVSUHFOXGHXVIURPLQWURGXFLQJHQGRJHQRXVFDSDFLW\XWLOL]DWLRQDQGZH IRFXVRQO\RQWKHVLJQDQGVL]HRISURGXFWLYLW\VKRFNV:HDJUHHZLWKWKHFULWLTXHRIPRVWZULWHUV HJ6XPPHUV 

(50) DQG(LFKHQEDXP 

(51)

(52) WKDWH[RJHQRXVWHFKQRORJLFDOVKRFNVFRQVWLWXWHD VPDOOIUDFWLRQRIWKH6RORZUHVLGXDODQGQHJDWLYHWHFKQRORJLFDOVKRFNVDUHXQMXVWLILHG :HWKXV FRQFOXGHWKDWWKHREVHUYHGGDWDRIHFRQRPLFIOXFWXDWLRQVFDQQRWEHH[SODLQHGE\DQH[RJHQRXV. ,QDUHFHQWSDSHU&ROHDQG2KDQLDQ 

(53) DUJXHWKDWWKH*UHDW'HSUHVVLRQUHVXOWHGIURPDFXPXODWLYH QHJDWLYHWHFKQRORJLFDOVKRFNWRWKH86HFRQRP\GXULQJ:HFDQQRWVXSSRUWVXFKDFRQFOXVLRQ. .

(54) SURFHVVRIQRQQHJDWLYHSURGXFWLYLW\VKRFNVZLWKVPDOOYDULDQFH)RUH[DPSOHVRIDOWHUQDWLYH DSSURDFKHVZLWKLQWKH5%&WUDGLWLRQVHH:HQ D

(55)  E

(56) DQG.LQJDQG5HEHOR 

(57)  :HDVVXPHDYHU\VPDOOYDULDQFHRIWKHH[RJHQRXVWHFKQRORJLFDOVKRFNVEXWH[SOLFLWO\ LQFRUSRUDWHDQLQYHVWPHQWJRRGVVHFWRUZKLFKWUDQVIRUPVFRQVXPSWLRQJRRGVLQWRFDSLWDOJRRGV ³PDFKLQHV´

(58) WRPRGHOWKHXQFHUWDLQW\DVVRFLDWHGZLWKWKHRXWFRPHRIQHZLQYHVWPHQWV7KHRXWSXW RIWKHLQYHVWPHQWVHFWRULVVWRFKDVWLFKHQFHLQYHVWPHQWGHFLVLRQVPXVWEHEDVHGRQWKHDVVHVVPHQW RIWKLVULVN7KHLQYHVWPHQWVHFWRULWVHOILVYHU\VLPSOHFRQVLVWLQJRIWZRSURMHFWVWKDWYDU\LQ SURGXFWLYLW\GHSHQGLQJXSRQVSHFLILHGUDQGRPVKRFNV:HWKHQLQYHVWLJDWHWKHLPSDFWRIWKH GLVWULEXWLRQRIEHOLHIVRQDJJUHJDWHIOXFWXDWLRQVRILQYHVWPHQWVRXWSXWVDQGSULFHV. LL

(59) $V\PPHWULFLQIRUPDWLRQ,QD5DWLRQDO([SHFWDWLRQV(TXLOLEULXP KHQFHIRUWK5((

(60) WKHVWXG\RI PRQHWDU\SROLF\IRFXVHGDWWKHHDUO\VWDJHVRQWKHHIIHFWVRILQIRUPDWLRQDODV\PPHWULHV/XFDV¶ 

(61) DUJXHGWKDWPRQH\KDVUHDOHIIHFWEHFDXVHSHRSOHFRQIXVHFKDQJHVLQSULFHOHYHOIRUFKDQJHV LQUHODWLYHSULFHV%\LPSOLFDWLRQPRQHWDU\SROLF\KDVDUHDOHIIHFWRQO\ZKHQLWLVXQDQWLFLSDWHG (PSLULFDOHYLGHQFHKDVQRWVXSSRUWHGWKLVFRQFOXVLRQ VHHIRUH[DPSOH0LVKNLQ 

(62)

(63) UHYHDOLQJ WKDWERWKDQWLFLSDWHGDVZHOODVXQDQWLFLSDWHGFKDQJHVLQPRQH\KDYHUHDOHIIHFWV,QDQ5%(DJHQWV KROGGLIIHUHQWFRQGLWLRQDOSUREDELOLWLHVDQGDUULYHDWGLIIHUHQWFRQFOXVLRQVZKHQWKH\FRQGLWLRQRQ FXUUHQWLQIRUPDWLRQ7KDWLVDJHQWVLQWHUSUHWFXUUHQWLQIRUPDWLRQGLIIHUHQWO\+HQFHHYHQIXOO\ REVHUYHGPRQHWDU\VKRFNVFRXOGEHLQWHUSUHWHGGLIIHUHQWO\E\DJHQWVDQGPRQH\QRQQHXWUDOLW\LV LPSOLHG IRUHDUOLHUZRUNVHH0RWROHVH 

(64)  

(65)

(66) )RFXVLQJKHUHRQWKHHIIHFWVRIEHOLHIVZH WKXVDVVXPHLQWKLVSDSHUWKDWWKHUHLVQRDV\PPHWULFLQIRUPDWLRQ. LLL

(67) 6WLFN\SULFHVPRQRSROLVWLFFRPSHWLWLRQDQGFUHGLW7KH'\QDPLF1HZ.H\QHVLDQ7KHRU\ '1.

(68) KDVGHYHORSHGDQLQWHJUDWHGYLHZRIPRQHWDU\HTXLOLEULXP,WLVHUHFWHGRQWZREDVLF DVVXPSWLRQV 

(69) 7KHPDUNHWFRQVLVWVRIPRQRSROLVWLFDOO\FRPSHWLWLYHILUPVWKDWDUHSULFHVHWWHUV DQG 

(70) SULFHVDUH³VWLFN\´GXHWRWKHH[LVWHQFHRIORQJWHUPFRQWUDFWV HJ7D\ORU 

(71) &DOYR 

(72) <XQ 

(73) *RRGIULHQGDQG.LQJ 

(74) &ODULGD*DOLDQG*HUWOHU 

(75) 5RWHPEHUJDQG :RRGIRUG 

(76) :RRGIRUG 

(77)  

(78)  D

(79)  E

(80) 0DQ\DXWKRUVZRUNZLWK&DOYR¶V 

(81) LGHDOL]DWLRQZKHUHDWDQ\GDWHRQO\DIUDFWLRQRIILUPVDUH³DOORZHG´WRFKDQJHSULFHV,Q. .

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

(83) %HUQDQNH*HUWOHUDQG*LOFKULVW 

(84) DQG &DOVWURPDQG)XHUVW 

(85) DUJXHWKDWIOXFWXDWLRQVLQWKHUHWXUQWRFDSLWDODQGLQDVVHWSULFHVDOWHU WKHFROODWHUDODYDLODEOHWRERUURZHUVJHQHUDWLQJDQDPSOLILFDWLRQZKLFKWKH\FDOOD³)LQDQFLDO $FFHOHUDWRU´$OWKRXJKZHDJUHHWKDWFUHGLWLVDQLPSRUWDQWFRPSRQHQWRIPRQHWDU\DQDO\VLVWKH ³)LQDQFLDO$FFHOHUDWRU´DERYHZDVGHYHORSHGXQGHUVWURQJDVVXPSWLRQV:HKRSHWRLQFRUSRUDWHLQ RXUPRGHODFUHGLWDPSOLILFDWLRQPHFKDQLVPZKLFKRSHUDWHVXQGHUZHDNHUDVVXPSWLRQV. LY

(86) 7KHUDWLRQDOHIRUPRQHWDU\SROLF\0RVW2SWLPDO3ROLF\PRGHOVGRQRWH[SODLQZK\DFHQWUDO EDQNVKRXOGIROORZDVWDELOL]DWLRQSROLF\7KH\DUHW\SLFDOO\IRUPXODWHGDVUHGXFHGIRUPV\VWHPRI HTXDWLRQVUHSUHVHQWLQJWKHSULYDWHVHFWRU7KH&HQWUDO%DQNWKHQVHOHFWVGLUHFWO\RSWLPDOLQIODWLRQ DQG*13JURZWKUDWHVVRDVWRPLQLPL]HDTXDGUDWLFREMHFWLYH HJ7D\ORU 

(87)  

(88)

(89) 7KH LPSOLFLWMXVWLILFDWLRQIRUVWDELOL]DWLRQSROLF\LVWKHYLHZWKDWWKHSULYDWHDOORFDWLRQLVQRW3DUHWR 2SWLPDOUHIOHFWHGE\IOXFWXDWLRQVRIWKHJURZWKUDWHRI*13DQGWKHUDWHRILQIODWLRQDURXQGWKHLU WDUJHWV7KHWDUJHWVWKHPVHOYHVDUHWUHDWHGDV3DUHWR2SWLPDOVWDWHV2XUREMHFWLYHVLQWKLVSDSHUDUH YHU\OLPLWHG:HGRQRWFKDUDFWHUL]HRSWLPDOPRQHWDU\SROLF\DQGRQO\XVHWKH³SROLF\´RI H[RJHQRXVYDULDWLRQVLQPRQH\VXSSO\2XUPRGHVWDLPLVWRVWXG\WKHLPSDFWRIGLYHUVHEHOLHIVLQ DQ5%(RQWKHG\QDPLFVRIDPRQHWDU\HFRQRP\:HGHPRQVWUDWHWKDWWKHGLVWULEXWLRQRIEHOLHIV FDXVHVHQGRJHQRXVDPSOLILFDWLRQRIIOXFWXDWLRQVDQGDUJXHWKDW3DUHWRRSWLPDOLW\LVQRWDQDGHTXDWH FULWHULRQIRUPRQHWDU\SROLF\$SUHOLPLQDU\YLHZRIVWDELOL]DWLRQSROLF\LVGLVFXVVHGLQ6HFWLRQ. :HWKXVIRUPXODWHDPRQHWDU\PRGHOZLWKWZRLQILQLWHO\OLYHGDJHQWVDQGVWXG\LWVYRODWLOLW\. .

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³SULFHOHYHO´

(92) DWW 3. ' B. 3. WKHUDWHRILQIODWLRQDWW. .  UHDOFDSLWDOVWRFNHPSOR\HGLQWKHSURGXFWLRQRIFRQVXPHUJRRGVDWW.  : T ×. . T. QRPLQDOZDJHDWW QRPLQDOSULFHDWWRIDXQLWRIFDSLWDOJRRGVLQVWDOOHG  T ×. . '. 3. WKHUHDOSULFHRIFDSLWDOJRRGVDWW. / ODERULQSXWLQWKHSURGXFWLRQRIFRQVXPHUJRRGVDWW 1 LQSXWDWWLQXQLWVRIFRQVXPSWLRQJRRGVLQWRWKHSURGXFWLRQRIFDSLWDOJRRGV . <  UHDORXWSXWRIFRQVXPHUJRRGVDWW , UHDORXWSXWRIQHZFDSLWDOJRRGVSURGXFHGE\WKHLQYHVWPHQWWHFKQRORJ\. 2XWSXWDQG3URGXFWLYLW\ 7KHUHDUHODUJHQXPEHURILGHQWLFDOFRPSHWLWLYHILUPVDQGDJJUHJDWHRXWSXWRIFRQVXPHU JRRGVLVGHILQHGE\DVWDQGDUGSURGXFWLRQIXQFWLRQ 

(93). <. '. $.

(94). L .  

(95) > /

(96). 

(97). .  W\SLFDOO\ZLWK$. 

(98) .

(99) 7KHSURGXFWLYLW\SURFHVV ^. >.  W.   ` LVDGHWHUPLQLVWLFWUHQGSURFHVVVDWLVI\LQJ. '. >. D

(100). 'L. >. ZKLOHUDQGRPSURGXFWLYLW\ ^. L. E

(101). ORJ.

(102). L. ' 8. W. . . '    ` LVD0DUNRYSURFHVVRIWKHIRUP . L

(103) % D. ORJ.  . D -. . F. 1  .

(104). LLG. 0RVWSURGXFWLYLW\VWXGLHVVHWWKHTXDUWHUO\PHDQUDWHRIWHFKQRORJLFDOFKDQJHDW. . L '  DQG. WKLVLVWKHYDOXHZHXVHLQDOORXUFRPSXWDWLRQV. 8  F. 7KHNH\SDUDPHWHUVIRUWKHWUDGLWLRQDO5%&OLWHUDWXUHDUH . F. IRUTXDUWHUO\GDWD(PSLULFDOHYLGHQFHVXJJHVWVWKDW.

(105) VHWDW. 8 '   F '  . LVDIUDFWLRQRIDQGIRUORZYDOXHVRI. WKLVSDUDPHWHUWKH5%&PRGHOIDLOVWRJHQHUDWHYRODWLOLW\ VHH.LQJDQG5HEHOR>@)LJSDJH. F '   8 '   F '  . 

(106) $FFRUGLQJO\ZHVHWWKHVHSDUDPHWHUVLQRXUPRGHODW. 7KHDJJUHJDWHFDSLWDODFFXPXODWLRQHTXDWLRQLVGHILQHGE\ 

(107). .. '. . & *. . . , . %. *LVWKHUDWHRIGHSUHFLDWLRQDQG, DUHQHZXQLWVRIFDSLWDOSODFHGLQWRSURGXFWLRQDWW. ZKHUH. LQSXWVRQZKLFKZRXOGKDYHEHHQH[SDQGHGDWW

(108) E\WKHLQYHVWPHQWJRRGVVHFWRU0RVWVWXGLHVVHW . *. .. DQGWKLVLVWKHYDOXHZHXVH'HILQH N . D

(109).  J . '. <. '. >. '. >. $. 6LQFH T . T ×. . '. 3. N. . '. . '. L / . L N . & *. L. . >. .  Z . :. '. > 3. DQG J. <. '. >. KHQFH.

(110). N . DQG E

(111). ,.  L . /. L . %. LVWKHUHDOSULFHRIDXQLWRIFDSLWDOLQHTXLOLEULXPWKHUHDOZDJHUDWH Z  DQGWKH. UHQWDOUDWHRQFDSLWDO 5  DUHGHILQHGE\WKHPDUJLQDOSURGXFWLYLW\FRQGLWLRQVLQFRQVXPSWLRQJRRGV D

(112). Z. E

(113).  5 . '. '. $. $. L  & F

(114). L F. N . L.

(115). /. N . L.

(116). /. . & * T. . . 7KH,QYHVWPHQW6HFWRU +HWHURJHQHLW\RILQYHVWPHQWDFWLYLWLHVDQGXQFHUWDLQW\LQWKHSURGXFWLYLW\RIWKHLQYHVWPHQW. .

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n 7KHUDQGRPRXWSXWRIWKHWZRDFWLYLWLHVLVVSHFLILHGLQWKHIROORZLQJZD\. D

(118) 7HFKQRORJ\, 0

(119) ,QSXWXQLWRIFRQVXPSWLRQJRRG 2XWSXW. ' 6. ' G %. G. &. G.  . .

(120). E

(121) 7HFKQRORJ\,, 6

(122) ,QSXWXQLWRIFRQVXPSWLRQJRRG 2XWSXW.

(123). ' 6 ' V %. %H V &. V.     . . %H. . ZKHUHWKHHPSLULFDOGLVWULEXWLRQRIWKHVKRFNLV. . HTXLOLEULXPXQGHUWKHEHOLHIWKDW. n - 1   F. WHUPIUHTXHQF\RIWKHVWDWHVLVUHSUHVHQWHGE\. n -. 1  . F.

(124) LLG7KH5((LVGHILQHGWREHWKH.

(125) LVWKHWUXWK,QDQ5%(DJHQWVNQRZWKDWWKHORQJ. . n - 1   F. :HDVVXPHWKDWUHODWLYHWRWKHGLVWULEXWLRQ.

(126) EXWWKH\GRQRWNQRZWKHWUXHSURFHVV. . n - 1   F.

(127) LWLVRSWLPDOWRIXOO\GLYHUVLI\. . LQYHVWPHQWVOHDGLQJWRDSHUIHFWKHGJHGSRVLWLRQDQGQRDJJUHJDWHXQFHUWDLQW\ 7RFODULI\WKLV. 2XUDVVXPSWLRQRIWKHRSWLPDOLW\RIDSHUIHFWKHGJHLVPDGHIRUFRQYHQLHQFHRQO\,WLVPRWLYDWHGE\. FRPSXWDWLRQDOHDVHVLQFHWKHSHUWXUEDWLRQPHWKRGXVHGKHUHHQDEOHVXVWRFRPSXWHWKHHTXLOLEULXPXVLQJWKHVWHDG\ VWDWHDVDUHIHUHQFHSRLQW7KHFDVHZKHUHIXOOGLYHUVLILFDWLRQLVQRWRSWLPDOUDLVHVRQO\FRPSXWDWLRQDOGLIILFXOWLHV QRWFRQFHSWXDORQHV. .

(128) LVVXHFRQVLGHUWKHFDVH G. '.   G. '.   V. . '   V '   P '  XVHGLQPRVWVLPXODWLRQVLQ . WKLVSDSHU,IDQDJHQWLQYHVWVXQLWZLWKSURSRUWLRQV ,.  .     ,. 

(129) KHHQVXUHVSURGXFWLRQRI. XQLWVRIFDSLWDOLQDOOVWDWHV+LVH[SHFWHGYDOXHLVDOVRKHQFHGLYHUVLILFDWLRQLVRSWLPDO. . :KHQDOODJHQWVEHOLHYHWKDW. n - 1   F.

(130) LVWKHWUXWKWKH\ZLOOKDYHDIXOO\GLYHUVLILHGLQYHVWPHQW. SRUWIROLRZLWKQRIOXFWXDWLRQVLQWKHDJJUHJDWHOHYHORUUHDOL]HGDJJUHJDWHFRVWRILQYHVWPHQWV ,QDQHFRQRP\ZLWKGLYHUVHEHOLHIVDJHQWVGRQRWIXOO\GLYHUVLI\7KH\EHOLHYHWKHPHDQ. n. YDOXHIXQFWLRQRI.  W. '      . YDULHVRYHUWLPH DQGWKLVLVSUREDEO\WUXH

(131) DQGWKH\KDYH. . VXEMHFWLYHPRGHOVDERXWWKLVYDOXH6LQFHWKHORQJWHUPPRPHQWVRI. n DUH   F.

(132) ZLWK. DXWRFRUUHODWLRQWKHUDWLRQDOLW\RIEHOLHIFRQGLWLRQVUHTXLUHWKHDJHQWV¶PRGHOVWREHVWDWLVWLFDOO\ FRPSDWLEOHZLWKWKHVHIDFWV+RZHYHUDWHDFKGDWHWKH\GRQRWEHOLHYHWKDWWKHPHDQYDOXHLV]HUR KHQFHWKHLURSWLPDOLQYHVWPHQWSRUWIROLRZLOOYDU\GHSHQGLQJXSRQWKHVHEHOLHIV. . 7KH,QILQLWHO\/LYHG$JHQWV :HILUVWLQWURGXFHWKHIROORZLQJQRWDWLRQIRUN. . FRQVXPSWLRQRINDWW. &  . OHLVXUHRINDWW. R '  & / . .. DPRXQWRIFDSLWDOVWRFNSXUFKDVHVE\NRQWKHRSHQPDUNHWDWW. .  DPRXQWRIFDSLWDORZQHGE\NDWWDQGXVHGLQSURGXFWLRQDWW 1. LQSXW LQXQLWVRIFRQVXPSWLRQJRRGV

(133) RINLQLQYHVWPHQWVWHFKQRORJ\0DWW.

(134). 1. LQSXW LQXQLWVRIFRQVXPSWLRQJRRGV

(135) RINLQLQYHVWPHQWVWHFKQRORJ\6DWW. 1. '. ,.

(136). 1. %. 1. WRWDOLQSXWRIDJHQWNLQLQYHVWPHQWVWHFKQRORJ\DWW. WRWDORXWSXWRIQHZLQYHVWPHQWV LQXQLWVRIFDSLWDOJRRGV

(137) RINDWGDWHW. . % DPRXQWRIRQHSHULRGQRPLQDOELOOSXUFKDVHGE\DJHQWNDWW. . T  WKHSULFHRIDRQHSHULRGELOODWWZKLFKLVDGLVFRXQWSULFH 0. DPRXQWRIPRQH\KHOGE\DJHQWNDWW. 0 0. . ' k UDQGRPJURZWKUDWHRIPRQH\VXSSO\ZKHQLWLVDSROLF\LQVWUXPHQW. + KLVWRU\RIDOOREVHUYDEOHVXSWRW %HIRUHIRUPXODWLQJWKHDJHQWV¶RSWLPL]DWLRQZHQHHGWRFODULI\WKHLVVXHRIWLPLQJ$WGDWHWDJHQWN.

(138). LQYHVWV 1.  1.

(139) DQGDWWKHVWDUWRIGDWHWWKHUDQGRPUHDOL]DWLRQWDNHVSODFHLQWKH. .

(140) LQYHVWPHQWJRRGVVHFWRUEHIRUHWKHUDWHRIWHFKQLFDOSURJUHVVLVUHDOL]HG7KHQHZFDSLWDO ,. . MRLQLQJSURGXFWLRQLVDGGHGWR .. ' 6. W7KLVLPSOLHV ,. ' .

(141).

(142). % 6. 1. WRIRUPWKHFDSLWDO . XVHGLQSURGXFWLRQDWGDWH. % .. 1. N. ZKLFKLVVRPHZKDWRGGQRWDWLRQ7KLV. RGGIHDWXUHLVXQDYRLGDEOHVLQFHZHFRPSUHVVLQWRRQHGDWHWZRUDQGRPUHDOL]DWLRQVILUVWRI. . WKHQRI. L WKHUDWHRIWHFKQRORJLFDOSURJUHVV1RZGHQRWHE\ 1 ' 1 % 1. LQYHVWPHQWVHFWRU2XWSXWRIQHZLQYHVWPHQWVDWGDWHWLVDIIHFWHGE\.

(143). ' 6. , .

(144). % 6. 1 . 1  . n DQG. WKHLQSXWVLQWRWKH. n DQGLVGHILQHGE\. N. .  :HWKXVGHILQH ,. WKHYDOXHRIQHZLQYHVWPHQWVSODFHGLQWRSURGXFWLRQDWGDWHWWREH.  ,. '. , .  DQG < . . . T ×. %. ZKLOH QRWLQJ WKDW , . . . ZKLFKLV*13E\ < . '. <. &. 1. J. &. Q. 'HILQH J. ,. %. . '. %. ' . <. . '. , . , 

(145). %.  Q . >. . WKHLQFRPHLGHQWLW\EHFRPHV J . . , 

(146). '.  . 1.  L. >. ,. '. >. DQG. . L. . 1RZIRUDQ\SUREDELOLW\EHOLHI4 RIDJHQWNKLVSUREOHPLVWRPD[LPL]HWKHXWLOLW\. D

(147). 0D[ (.    j  . >.  . $. . &. &(. .    . 

(148)

(149). R. %.  . . 0.

(150). 3. _ +  @.  . $.  . VXEMHFWWRWKHEXGJHWFRQVWUDLQW. E

(151)  3 & . %.. . T ×. .

(152). % 1. % 1. 

(153) 3 . % %. . T. & &R

(154). F

(155). ' 6. , . 1 . G

(156). 1RWHWKHGLVWLQFWLRQEHWZHHQ . . & . . T ×. . % 5 3

(157) & %  % 0 & 0  k '  .

(158). % 6 . .

(159) : . 1 . '.

(160) . . . %. 1. $. . . 1. $. ,  . SXUFKDVHGDWWRQWKHRSHQPDUNHWDQG .  XVHGLQSURGXFWLRQ &. DWWDQGRZQHGE\WKHDJHQWDWWKDWWLPH1RUPDOL]HWKHSUREOHPE\ F. . 0 3. >. '. P  . 0 3. >. '. 8VLQJ D

(161)  E

(162) DQG. P 3. 3. . 0 . 3. >. ' B. . P . '. B L .  Q . 1. '. >.  L . ,. '. >.  N . .. '. WKHPD[LPL]DWLRQSUREOHPEHFRPHV. . ' >. >  . .  E . .. '. ' >. % 3 . >. .

(163) . D¶

(164). . . $ j . 0D[ (. VXEMHFWWR. F. E¶

(165). '  & R. . & (. . > F . N.

(166) Z. %. > R. T . . L  ' 6. L. F¶

(167). % 5

(168) % . Q. . Q. & N. P. . >

(169). . T. 

(170)  @. & Q. . . $.  . % Q. 

(171).  . & E. T. . & P. . . Q. . . '. %. k % E. L  B . N. G¶

(172).  

(173) .

(174)

(175). P. % 6. $. . Q. . . $. N. L . %. 7RVLPSOLI\WKH(XOHUHTXDWLRQVZHLJQRUHWKHLQHTXDOLW\FRQVWUDLQWVLQ F¶

(176) DQGKDQGOHWKHPRQO\. 4. DVFRPSXWDWLRQDOLVVXHVUDLVHGE\WKHPRGHO +HQFHWKHILUVWRUGHUFRQGLWLRQVIRUODERUVXSSO\DUH F. D

(177). . '. .. R. Z . 1H[WWKHILUVWRUGHUFRQGLWLRQZLWKUHVSHFWWRFDSLWDOSXUFKDVHGRQWKHRSHQPDUNHW N .  F . E

(178).

(179). !.  . ". R.

(180)

(181). # !. $. ' $. T. (%. 7KHRSWLPDOLW\FRQGLWLRQZLWKUHVSHFWWR Q .  F . F

(182).

(183).  !.  . ". R.

(184)

(185). #  !. $. ' $. T. DQGWKHFRQGLWLRQZLWKUHVSHFWWR Q .  F . G

(186).

(187).  !.  . ". R.

(188)

(189). #  !. T.  !. #. F'&.

(190). . !. . #. R'&. ".

(191)

(192). # !. >. $. #. T'&.  LV. (%.  ! F'& #.

(193).  R'& #.  !. ".

(194)

(195). #  !. >. $ #. T'&. . $. LV. ' $. (%.  ! F'& #.

(196).  R'& #.  !. ".

(197)

(198). #  !. >. T'&. $. ) #. % 5'&. #. @ . !. #. % 5'&. L(

(199). !. #. @. #. @. 6'&. !. L(

(200). LV. #. % 5'&. L(

(201). . *. 6'&. 7KHILUVWRUGHUFRQGLWLRQZLWKUHVSHFWWR E  LV.  F . H

(202).

(203). . !. R.

(204). " + # !,. -. ' $. T. (%. !.  F'&. #. L.&. #. !. . R'&. "+ # !, #. . . !. L (

(205) B'&. #. )LQDOO\WKHRSWLPXPZLWKUHVSHFWWRPRQH\KROGLQJVUHTXLUHV. F . I

(206). 

(207) /

(208). R. '0 

(209) 21.

(210). & P . 

(211) /

(212). ' $. (. . 

(213) . > F3. L3. R3. 0 

(214)  1. k3. @.

(215) . . L 

(216) B3. 4. $Q$SSHQGL[%RQWKHFRPSXWDWLRQDOPRGHOLVQRWLQFOXGHGLQWKLVSXEOLVKHGYHUVLRQ$Q\LQWHUHVWHG. UHDGHUFDQREWDLQWKLV$SSHQGL[E\GRZQORDGLQJWKHSUHSXEOLVKHGYHUVLRQRIWKLVSDSHUZKLFKLVSRVWHGRQWKH KRPHSDJHRIWKHILUVWDXWKRUDWKWWSZZZVWDQIRUGHGXaPRUGHFDL7KHSUHSXEOLVKHGYHUVLRQDOVRFRQWDLQV $SSHQGL[$ZKLFKSURYLGHVDVKRUWDFFRXQWRIWKHWKHRU\RI5DWLRQDOEHOLHIVDQGRWKHUWHFKQLFDOGHWDLOVQRWLQFOXGHG KHUH. .

(217) . 0RQHWDU\3ROLF\ 7KHPRQHWDU\³SROLF\´LQWKHPRGHOLVWKHIDPLOLDUPRQHWDU\LQMHFWLRQWKHFHQWUDOEDQN. LQFUHDVHVWKHPRQH\VXSSO\E\DUDQGRPDPRXQWRI PRQH\KROGLQJRIDJHQWNLQFUHDVHVWR VLQFHWKH\REVHUYHWKHUHDOVKRFNV . 0. k3. +HQFH 0. k3 & 

(218) 0. ZKLFKLVWKHGDWHW. DWGDWHW$JHQWVREVHUYHWKHPRQHWDU\VKRFNDQG. L  n

(219) WKHH[RJHQRXVVWDWHLVIXOO\REVHUYHG. 5DQGRPYDULDWLRQVLQWKHPRQH\VXSSO\LVQRWDVHULRXVPRQHWDU\SROLF\WKDWPD\EHSXUVXHG E\DQ\FHQWUDOEDQN7KLVSDSHULVDWKHRUHWLFDOLQYHVWLJDWLRQDQGDQH[RJHQRXVPRQH\VXSSO\LVD VLPSOHGHYLFHIRUWKHVWXG\WKHHIIHFWRIEHOLHIVRQHFRQRPLFIOXFWXDWLRQV,WZLOODOVRHQDEOHXVWR GLVFXVVWKHUROHZKLFKDUHDOPRQHWDU\SROLF\VKRXOGSOD\LQHFRQRPLFVWDELOL]DWLRQ. . (TXLOLEULXP )RUHDFKVHWRISUREDELOLW\EHOLHIV 4. .

(220) RIWKHDJHQWVRQLQILQLWHVHTXHQFHVRIREVHUYHG.  4. YDULDEOHVDPRQHWDU\HTXLOLEULXPRIWKHHFRQRP\LVGHILQHGE\HTXDWLRQV D

(221)  E

(222)  D

(223)  E

(224)  E¶

(225)  D

(226)  I

(227) DQGE\WKHIROORZLQJDGGLWLRQDOFRQGLWLRQV 0RQH\JURZWK7KHPRQH\VXSSO\VDWLVILHV. k. P. D

(228). '. P . B L. 0DUNHWFOHDULQJFRQGLWLRQV*LYHQWKHDFFRXQWLQJLQ D

(229)  G

(230) ZHDJJUHJDWHWRHVWDEOLVKWZR HTXDWLRQV2QHDFFRXQWLQJLGHQWLW\VSHFLI\LQJWKHDPRXQWRIFDSLWDOHPSOR\HGDWGDWHW. .  .. '. .. %. .. DQGDPDUNHWFOHDULQJFRQGLWLRQLQWKHPDUNHWIRULQVWDOOHGFDSLWDODWGDWHW.  . .. .. %. . '. . . & *

(231) . 7KHG\QDPLFVRIFDSLWDOHPSOR\HGLVWKHQGHILQHGE\. .. ,. . '. ,. %. ,. ' 6. & *

(232) %. . . ' . . 1. . %. 1.

(233). ,. % 6. .  . 1. . %. 1

(234) . $IWHUQRUPDOL]DWLRQZHWKXVKDYHWKHLGHQWLWLHV. . N. . %. N. '. N. . IRUDOOW.

(235) . L. ' 6. . . Q. . % 6. . Q. . N. '.   . IRUDOOW. DQGWKHPDUNHWFOHDULQJFRQGLWLRQV. N. D

(236).  . N. E

(237). N. '. % . F

(238). E. G

(239).  . H

(240). P. %. . %. . N. E. & R. & *

(241). . L ' N. . '

(242). P. % . L. IRUDOOW. & *

(243). . %. IRUDOOW. . '. IRUDOOW. L. & R.

(244). '. / . P. IRUDOOW. IRUDOOW. :HWXUQQRZWRWKHFHQWUDOTXHVWLRQRIWKHEHOLHIVRIWKHDJHQWV. . $5DWLRQDO%HOLHI(TXLOLEULXP :HQRZFRQVWUXFWWKH5%(DQGH[SODLQWKHIDPLO\RI5DWLRQDO%HOLHIVZKLFKZHVWXG\)RU. DGHWDLOHGDFFRXQWRIWKHWKHRU\RI5DWLRQDO%HOLHIVVHH.XU] 

(245) DQGIRUDVXPPDU\RIWKH PHWKRGRIFRQVWUXFWLQJDQ5%(VHH.XU]0RWROHVH 

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

(247) RULQ$SSHQGL[$RIWKHSUHSXEOLVKHGYHUVLRQ DYDLODEOHDWWKHZHEDGGUHVVSURYLGHGDERYH$Q\VWDWHPHQWLQWKHWH[WDERXW³WKHVWDWLRQDU\PHDVXUH´RU³WKH HPSLULFDOGLVWULEXWLRQ´LVDOZD\VDUHIHUHQFHWRWKLVSUREDELOLW\PHDVXUHV,WVFHQWUDOLW\WRWKHWKHRU\DULVHVIURPWKH IDFWWKDWWKLVSUREDELOLW\LVGHULYHGIURPSXEOLFLQIRUPDWLRQDQGKHQFHWKHVWDWLRQDU\PHDVXUHLVNQRZQWRDOODJHQWV DQGDJUHHGXSRQE\DOOWRUHIOHFWWKHHPSLULFDOGLVWULEXWLRQRIHTXLOLEULXPTXDQWLWLHV. .

(248) FRQVWUXFWLYHDSSURDFKVHH.XU]0RWROHVH>@6HFWLRQ

(249) 6XFKFRQVWUXFWLYHSURFHGXUHLV SRVVLEOHRQO\ZKHQZHVWXG\DVSHFLILFIDPLO\RI5DWLRQDO%HOLHIVZKLFKLVWKHFDVHLQWKLVSDSHU :HFDUU\RXWWKLVSURFHGXUHLQVHYHUDOVWHSVVWDUWLQJZLWKWKHHTXLOLEULXPPDS 5HFDOOWKDWLQWKHRSWLPL]DWLRQ D¶

(250)  E¶

(251) DJHQWNGHULYHVRSWLPDOGHFLVLRQVE\XVLQJEHOLHI. 4. FRQGLWLRQDORQSXEOLFLQIRUPDWLRQDQGRQ \. WKHYDOXHRIKLVRZQDVVHVVPHQWYDULDEOH:H. DVVXPHWKDWDOOSRUWIROLRVDQGH[RJHQRXVVKRFNV [. '.   L  k  n  N.   Q.    Q.   E.   N. . ODJJHGHQGRJHQRXVYDULDEOHV [  \. ZLOOWKXVFRQGLWLRQRQ [  D

(252) E

(253) F

(254) G

(255) H

(256) I

(257). N. . Q. . Q E. . N. '. P. ' '. . L E E. R ' R. L  k  n.  [  T . L  k  n.  [  T . L   k  n. .  [  T  . . . L   k  n.  [  T  . L   k  n.  [  T . . . .  T. . .  T.  [  T . L  k  n. . . . . . . B

(258) 7RVLPSOLI\GHQRWH .  Q  E  P

(259) $JHQWN.

(260) DQGKHQFHRSWLPDOGHFLVLRQVDUHIXQFWLRQVRIWKHIRUP . . L. ' '. . '. L  k  n

(261) DUHREVHUYDEOH7KHREVHUYDEOHVDUH.       Q  Q  E  P  P  T   T           N  Q  Q  E  P  N  Q.  T. .  T. . . .  \. B. . B.  \. . B.  \. B.

(262) N. .

(263) N. .

(264) N. .

(265) N. .

(266) N. .

(267) N. .  \.  \. B. . . .  T.  T. .  \. B. . 0DUNHWFOHDULQJFRQGLWLRQVLPSO\WKDWWKHHTXLOLEULXPSULFHSURFHVV^ T . .  T.  . B

(268) W. `LV. WKXVGHILQHGE\DPDSRIWKHIRUP T 

(269). T. . . ' M L  k  n.  \. . .  \.  [

(270) . B 

(271) UHYHDOVWKDWWKHYRODWLOLW\RIHTXLOLEULXPSULFHVLVGHWHUPLQHGE\WKUHHIDFWRUVE\H[RJHQRXV . VWDWHV . L  k  n

(272) E\ODJJHGHQGRJHQRXVYDULDEOHV [. DQGE\WKHVWDWHVRIEHOLHI \. .  \.

(273) . ³(QGRJHQRXV8QFHUWDLQW\´ZDVGHILQHGE\.XU] 

(274)  

(275) DVWKDWFRPSRQHQWRIYRODWLOLW\ ZKLFKLVJHQHUDWHGE\WKHGLVWULEXWLRQRIEHOLHIVLQWKHPDUNHWUHSUHVHQWHGE\ \ ZHH[SODLQWKDWDQDVVHVVPHQWYDULDEOHV \ VWDWHRIEHOLHI \. .  \.

(276) ,Q6HFWLRQ. LVDVLPSOHPDWKHPDWLFDOUHSUHVHQWDWLRQRIDSULYDWH. LVDSULYDWHO\SHUFHLYHGSDUDPHWHURIWKHDJHQW¶VEHOLHIXQLTXHO\GHILQLQJKLV. FRQGLWLRQDOSUREDELOLW\EHOLHIRYHUREVHUYDEOHV7KHVWDWHVRIDQDJHQW¶VEHOLHIDUHUHVWULFWHGE\WKH UDWLRQDOLW\RIEHOLHIFRQGLWLRQVDQGWKHUHVWULFWLRQVDSSOLFDEOHWRRXUPRGHOZLOOEHVSHFLILHGODWHU 7KH(XOHUHTXDWLRQVDQGWKHGHILQLWLRQRIFRQVXPSWLRQLQ E¶

(277)  G¶

(278) VKRZWKDWDWDQ\GDWHW. .

(279) DJHQWNQHHGVWRIRUHFDVWWKUHHFDWHJRULHVRIYDULDEOHVGLVFXVVHGODWHU. L3  k3  n3. L

(280) H[RJHQRXVYDULDEOHV .  LL

(281) KLVRZQGHFLVLRQVDWW N3.   Q3.

(282) FRQGLWLRQDOXSRQLQIRUPDWLRQDWWDQGKLVDVVHVVPHQW \.     Q3. IXQFWLRQVDQGDIRUHFDVWRIKLVDVVHVVPHQW \3.  E3 . R3. . P3. . .

(283) EDVHGRQKLVRSWLPDOGHFLVLRQ. . . LLL

(284) 2WKHUHQGRJHQRXVYDULDEOHVSDUWLFXODUO\SULFHV T3  T3  DWWDQGKLVDVVHVVPHQW \. B3.

(285) FRQGLWLRQDOXSRQLQIRUPDWLRQ. . 7KHUDWLRQDOLW\RIEHOLHIFRQGLWLRQVUHTXLUHWKDWDOOPRPHQWVRIDQDJHQW¶VVXEMHFWLYHPRGHOEH H[DFWO\WKHVDPHDVWKHPRPHQWVRIWKHVWDWLRQDU\PHDVXUHGHULYHGIURPWKHHPSLULFDOGLVWULEXWLRQ RIWKHREVHUYDEOHVDIRUPXODWLRQRIWKHEHOLHIV RUSHUFHSWLRQPRGHOV

(286) RIDJHQWVQHFHVVLWDWHVRXU VSHFLI\LQJILUVWWKHJHQHUDOVWUXFWXUHRIWKHVWDWLRQDU\PHDVXUH  . &RQVWUXFWLRQRIWKHVWDWLRQDU\PHDVXUH 2XU5%(LVDQHTXLOLEULXPRIDVWRFKDVWLFHFRQRP\ZKLFKIOXFWXDWHVDURXQGVWHDG\VWDWH. YDOXHVGHQRWHGE\

(287) 6LQFHHTXLOLEULXPTXDQWLWLHVVDWLVI\WKHPDS 

(288) WKHHPSLULFDOGLVWULEXWLRQ. L k n. LVGHWHUPLQHGE\WKHHTXLOLEULXPPDSDQGWKHORQJWHUPEHKDYLRURI . . . .  \. . .  \ .

(289) 2XU. L  k  n  \. PHWKRGRIFRQVWUXFWLQJDQ5%(LVWRVSHFLI\ILUVWWKHHPSLULFDOGLVWULEXWLRQRI . .  \

(290) . 2QFHWKLVLVGRQHZHVSHFLI\WKHEHOLHIVRIDJHQWVDQGLPSRVHWKHUDWLRQDOLW\FRQGLWLRQV 7KHWUXHSURFHVVHVPD\H[KLELWQRQVWDWLRQDU\G\QDPLFV:HWKXVDVVXPHLQVWHDGWKDWWKH VWDWLRQDU\PHDVXUHRIH[RJHQRXVYDULDEOHV . L  k  n

(291) DQGRIVWDWHVRIEHOLHI \. .  \.

(292) KDYHWKH. IROORZLQJVWUXFWXUH D

(293). ORJ. L. E

(294). ORJ. k3 '. F

(295). n3 ' D3. 7KHVHTXHQFHRIVWDWHV^ \. G

(296) . . \. 3 . ' 8. . .  \. ORJ. ORJ .

(297) W. k  % 8. D. \. '. . D. . > ORJ. k &. ORJ. . k  @% D3. . . D - 1   F.

(298) LLG. D - 1   F .

(299) LLG. D - 1   F.

(300) LLG. . . `LVDUHDOL]DWLRQRIDVWRFKDVWLFSURFHVVRIWKHIRUP. . . L % D3. . . D. . D. -1.  . . F. . F. F. . F. LLG. (TXDWLRQV E

(301)  G

(302) DUHK\SRWKHWLFDO7KHDVVXPSWLRQVWKDWWKHLQYHVWPHQWVHFWRUVKRFNV WKHVWDWHVRIEHOLHI \. .  \. n DQG.

(303) H[KLELWQRORQJUXQSHUVLVWHQFHDUHPDGHIRUFRPSXWDWLRQDOVLPSOLFLW\. .

(304) 7KH\DUHYHU\VWURQJDQGWKHLULPSOLFDWLRQVZLOOEHHYDOXDWHGODWHU :HPDNHWKHIROORZLQJDGGLWLRQDOVLPSOLI\LQJDVVXPSWLRQV. D. D. $

(305). $

(306). k ' L. . . D. . . . . D. . D. . L L. KHQFH .

(307)

(308) DUHPXWXDOO\LQGHSHQGHQW.

(309) DUHWKHVWHDG\VWDWHYDOXHVRI . L  k

(310) LQWKHULVNOHVVHFRQRP\DQG. WKHORQJWHUPDYHUDJHLQIODWLRQUDWHLV]HURLQERWK5((DQG5%(. 8 ' . F '  . $

(311). $VGLVFXVVHGEHIRUH. $

(312). $VPRQHWDU\VKRFNVDQGWKHVWRFKDVWLFLQYHVWPHQWWHFKQRORJ\DUHK\SRWKHWLFDOZHVSHFLI\. F '   8  ' . . . F  '  7KLVLPSOLHVWKHVWDQGDUGGHYLDWLRQRIPRQHWDU\VKRFNVRYHU. WLPHLVSHUTXDUWHU7KHVHDVVXPSWLRQVDUHLQWHQGHGWRHQDEOHDTXDQWLWDWLYHHYDOXDWLRQ RIWKHZRUNLQJVRIRXUPRGHOE\SRVWXODWLQJSHUVLVWHQFHLQWKHPRQHWDU\VKRFNVZLWKD. . UHDVRQDEOHVWDQGDUGGHYLDWLRQ$VIRU \ FRUUHODWLRQFRHIILFLHQW. D \. . \.

(313).

(314) ZHDVVXPH. '  KHQFH F. . 7KH%HOLHI6WUXFWXUH. D. *HQHUDO$VVXPSWLRQV. D. 3URSHUWLHVRI$VVHVVPHQWYDULDEOHV $VVHVVPHQWYDULDEOHV \.  \. '. F ' F '.  DQGD.  . IRUN. DUHWKHWRROVZHXVHWRGHVFULEHDQDJHQW¶VEHOLHI:H. EULHIO\UHYLHZWKHLUSURSHUWLHVKHUH L

(315) 'HILQLWLRQ$VVHVVPHQWYDULDEOHVDUHDUWLILFLDOYDULDEOHVXVHGWRGHVFULEHQRQVWDWLRQDULW\EXW ZLWKRXWDQLQWULQVLFPHDQLQJRIWKHLURZQ7KXVOHW;EHDVSDFHRIREVHUYDEOHVDQGVXSSRVHZH ZDQWWRGHVFULEHWKHQRQVWDWLRQDULW\RIDG\QDPLFDOV\VWHPRQWKHVSDFHRILQILQLWHVHTXHQFHVRI. . REVHUYDEOHV ;

(316). % ;

(317). .

(318) ZKHUH% ;

(319). .

(320) LVWKH%RUHO. FILHOGRI ;

(321). . 7KH&RQGLWLRQDO. 6WDELOLW\7KHRUHP VHH.XU]DQG6FKQHLGHU 

(322) DQG1LHOVHQ 

(323)

(324) GHVFULEHVQRQVWDWLRQDULW\ YLDDUWLILFLDOYDULDEOHV \ SRVWXODWHV ; î<. ; î<. 4. . /4.

(325). . C

(326) _ \. ,<. ZLWKDPDUJLQDOSUREDELOLW\VSDFH <.

(327). . % <.

(328). . —

(329) ,W .

(330) WREHWKHVWDWHVSDFHLQWURGXFHVDXQLYHUVDOSUREDELOLW\PHDVXUH4 DQGVSDFH. % ; î<. .

(331). . . 4 

(332) DQGGHILQHVWKHGHVLUHGQRQVWDWLRQDU\SUREDELOLW\WREH.       

(333) WKHFRQGLWLRQDOSUREDELOLW\RI4 ZLWKUHVSHFWWRWKHVHTXHQFH\ 4 PXVW. VDWLVI\WKHFRQGLWLRQWKDWIRUDOO$. . ,% ; 4. .  

(334) DQG%. . $ î %

(335). ,% <. '. m. 4. . . . .

(336) . $

(337) — G\

(338) . .

(339) 7KHHIIHFWLYHFRQGLWLRQDOSUREDELOLW\VSDFH ;

(340). . % ;

(341). RIWKHREVHUYDEOHVVLQFHSUREDELOLWLHVRIHYHQWVLQ% ;

(342) ZLWKWKHSDUDPHWHUV \. . . 4. .

(343) LPSOLHVQRQVWDWLRQDU\G\QDPLFV.

(344) DUHQRWWLPHLQGHSHQGHQWWKH\FKDQJH. ZKLFKDUHWLPHGHSHQGHQW7KHDGYDQWDJHRIXVLQJDVVHVVPHQWYDULDEOHVLV. VWDWLVWLFDOVLQFHWKHVWRFKDVWLFVWUXFWXUHDERYHSLQVGRZQWKHHPSLULFDOUHJXODULW\RI \. LQUHODWLRQ. WRREVHUYDEOHVDQGWKLVUHJXODULW\ZLOOEHVHHQWREHWKHEDVLVIRUWKHUDWLRQDOLW\FRQGLWLRQV7KLV DSSURDFKLVFRPPRQLQHFRQRPHWULFVZKHUH<LVWKHVHWRISRVVLEOH³UHJLPHV´ \ LGHQWLILHVWKH UHJLPHDWWDQGKHQFHWKH \ DUHYLHZHGDV³UHJLPHYDULDEOHV´ $OWKRXJKWKHVSDFH ; î<.

(345). QRWEHWKHFDVH:HFRXOGUHSODFH < 4RYHUWKHSURGXFWVSDFH ;

(346). SUREDELOLW\WREH 4. . A <  . . /4. . . . % ; î<. . î. C

(347) _ \. A <  .

(348). .

(349). .         4 

(350) LVGHILQHGRYHUDIL[HGVHW< WKLVQHHG . . E\DQLQILQLWHQXPEHURIGLIIHUHQWVSDFHV <. DQGGHILQH.

(351) :HFDQWKHQGHILQHWKHGHVLUHGQRQVWDWLRQDU\.

(352) ZKLFKLVFRQGLWLRQDOXSRQDVHTXHQFHRIGLIIHUHQWREMHFWVLQ. ,QVKRUWDVVHVVPHQWYDULDEOHVRIDQDJHQWDUHSULYDWHO\SHUFHLYHGSDUDPHWHUVZKLFKWKH. DJHQWKLPVHOIJHQHUDWHVIRUDGHVFULSWLRQRIKLVEHOLHI7KH\PD\EHLQGLIIHUHQWVSDFHVDWGLIIHUHQW WLPHVDQGLQGLIIHUHQWVSDFHVDFURVVDJHQWVVRWKDWWKHUHLVQRVHQVHLQZKLFKWKH\FDQEHFRPSDUHG \. LVSULYDWHO\SHUFHLYHGE\DJHQWMDQGKDVPHDQLQJRQO\WRKLPDJHQWN. \. PHDQVHYHQLIKHFRXOG³REVHUYH´LW. úMZRXOGQRWNQRZZKDW. LL

(353) (FRQRPLF,QWHUSUHWDWLRQ 4 LVWKHGDWHWSUREDELOLW\EHOLHIRIIXWXUHREVHUYDEOHVDQG \. LV. XVHGWRGHVFULEHKRZWKHDJHQW¶VIRUHFDVWVGHYLDWHIURPWKHVWDWLRQDU\IRUHFDVWGXHWRKLVEHOLHILQ QRQVWDWLRQDULW\7KHUHDUHVHYHUDOLVVXHVWRQRWH)LUVWGHYLDWLRQVIURPWKHVWDWLRQDU\IRUHFDVWLVD MXGJHPHQWRI³VWUXFWXUDOEUHDNV´EDVHGRQOLPLWHGUHFHQWGDWD6XFKMXGJPHQWVDUHULJKWRUZURQJ KHQFHLQDQ5%(UDWLRQDODJHQWVDUHRIWHQZURQJ6HFRQGLQDQRQVWDWLRQDU\HQYLURQPHQWLWLV XVXDOO\QRWSRVVLEOHWRGHPRQVWUDWHZLWKKLJKOLNHOLKRRGWKDWDEHOLHIZDVULJKWHYHQLQUHWURVSHFW 7KLUGHYHQLIVXIILFLHQWGDWDEHFRPHVDYDLODEOHWRGHWHUPLQHLIDFKDQJHRIVWUXFWXUHRFFXUUHGVXFK LQIRUPDWLRQDUULYHVWRRODWHVLQFHDOOLPSRUWDQWGHFLVLRQVZRXOGKDYHDOUHDG\EHHQPDGH LLL

(354) 6WDWLVWLFDOVLPSOLFLW\5DWLRQDODJHQWVGRQRWGHYLDWHV\VWHPDWLFDOO\IURPWKHVWDWLRQDU\ IRUHFDVWVDQGWRHVWDEOLVKUDWLRQDOLW\RIEHOLHIZHQHHGDVWDWLVWLFDOPHDVXUHRIDQDJHQW¶VGHYLDWLRQ IURPWKHVHIRUHFDVWV$VVHVVPHQWYDULDEOHVSURYLGHVDVLPSOHWRROWRPHDVXUHVXFKUHJXODULW\ LY

(355) 7KHLQILQLWHO\OLYHGDJHQWLVDVHTXHQFHRIGHFLVLRQPDNHUVKHQFHDVVHVVPHQWYDULDEOHVDUHQRW VXEMHFWWRUDWLRQDOLW\FRQGLWLRQV$QHFRQRP\ZLWKFKDQJLQJWHFKQRORJ\DQGSURGXFWVLVRQHLQ. .

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³WHVW´KLVWKHRU\DQGQRUDWLRQDOLW\FRQGLWLRQVVKRXOGDSSO\WRWKHVHTXHQFHRI \. "7KH. VROXWLRQLVWRFRQVLGHUWKHLQILQLWHO\OLYHGDJHQWDVFRQVLVWLQJRIDQLQILQLWHVHTXHQFHRIPHPEHUV RI DIDPLO\RURUJDQL]DWLRQ

(357) HDFKPDNLQJHFRQRPLFGHFLVLRQVRYHUDUHODWLYHO\VKRUWWLPH(YHU\ GHFLVLRQPDNHUNQRZVRQO\KLVRZQ \. EXWQRWWKRVHRIKLVSUHGHFHVVRUV+HQFHHYHQLIDQDJHQW. KDVGDWDWRFRQYLQFHKLPVHOIWKDWKLVWKHRU\ZDVULJKWRUZURQJVXFKGDWDDUULYHVWRRODWHWREH XVHIXOVLQFHDOOLPSRUWDQWGHFLVLRQVZRXOGKDYHEHHQPDGH. D. 2WKHU$VVXPSWLRQV. $

(358) $QRQ\PLW\$VVXPSWLRQ,QDQHFRQRP\ZLWKWZRDJHQWVWKHEHOLHIRIHDFKKDVDQLPSDFWRQ SULFHV$JHQWVDFWFRPSHWLWLYHO\DQGLJQRUHWKHHIIHFWRIWKHLURZQEHOLHIVRQHTXLOLEULXPSULFHV. $JHQWVNQRZWKDWEHOLHIVLPSDFWSULFHVDQGWKHLUIRUHFDVWLQJPRGHOVQHHGWRIRUHFDVWWKH LPSDFWRIIXWXUHGLVWULEXWLRQRIEHOLHIVRQSULFHV7RH[SODLQKRZWKLVZRUNVLQRXUPRGHOQRWHWKDW NQRZLQJWKHVWDWLRQDU\PHDVXUHPHDQVNQRZLQJDOOORQJWHUPFRQGLWLRQDOGLVWULEXWLRQVJLYHQ . REVHUYHGYDULDEOHV+RZHYHUJLYHQIXQGDPHQWDOV [ . L  k  n

(359) WKHYDULDELOLW\RIHQGRJHQRXV. YDULDEOHVLVGHWHUPLQHGE\WKHYDULDELOLW\RIWKHVWDWHVRIEHOLHI \. . .  \ .

(360) 6LQFHVWDWHVRIEHOLHIDUH. QRWREVHUYHGWKH\GHGXFHWKHLULPSDFWIURPWKHORQJWHUPGLVWULEXWLRQRIHQGRJHQRXVYDULDEOHV . FRQGLWLRQDOXSRQ [ . L  k  n

(361) 6WDWHVRIEHOLHIDFFRXQWIRUWKHKLJKHUYRODWLOLW\RIWKH . HQGRJHQRXVYDULDEOHVXQH[SODLQHGE\ [ . L  k  n

(362) :HKDYHQDPHGWKLVFRPSRQHQWRIYRODWLOLW\. +HQFHRQHGHILQHVFRPPRGLWLHVE\WKHLUDWWULEXWHVVXFKDV³WUDQVSRUWDWLRQHTXLSPHQW´LQVWHDGRI ³DLUSODQHV´RU³FRPPXQLFDWLRQVHUYLFHV´LQVWHDGRI³WHOHSKRQH´2YHUWLPHZHWKHQH[SHULHQFHFKDQJHLQWKHFRVW RISURGXFLQJWKHVHVHUYLFHVDQGWKHLUSULFHVUDWKHUWKDQFKDQJHLQWKHGHILQLWLRQVRIWKHSURGXFWVRUVHUYLFHV WKHPVHOYHV. .

(363) ³(QGRJHQRXV8QFHUWDLQW\´ HJ.XU] 

(364)  

(365)

(366) DQGWKLVDUJXPHQWVKRZVWKDWLQOHDUQLQJWKH VWDWLRQDU\PHDVXUHDJHQWVDOVRGLVFRYHUWKHFRPSRQHQWRIWKHVWDWLRQDU\PHDVXUHLQGXFHGE\WKH GLVWULEXWLRQRIEHOLHIV)RUVLPSOLFLW\RIFRPSXWDWLRQVZHPDNHWKHDVVXPSWLRQ. $

(367) )RUHFDVWLQJ$VVXPSWLRQ,$JHQWVEHOLHYHWKDWWKHHQGRJHQRXVLPSDFWRIPDUNHWVWDWHVRI EHOLHIRQSULFHVDQGRWKHUHQGRJHQRXVYDULDEOHVLVWKHVDPHDVWKDWFRPSRQHQWZKLFKLVHVWLPDWHG IURPWKHVWDWLRQDU\PHDVXUH. :HILQDOO\WXUQWRRXUODVWVLPSOLI\LQJDVVXPSWLRQUHJDUGLQJWKHIRUHFDVWLQJRISULFHVLQWKHPRGHO  $

(368) )RUHFDVWLQJ$VVXPSWLRQ,,$JHQWVIRUHFDVWSULFHVXVLQJWKHPDS 

(369) DQGSHUFHLYHWKHLPSDFW RIVWDWHVRIEHOLHIRQSULFHVDQGRWKHUHQGRJHQRXVYDULDEOHVYLDDYDULDEOH ]  ZLWKWKHVDPH GLVWULEXWLRQDOSURSHUWLHVDVWKHORQJUXQSURSHUWLHVRIWKHXQREVHUYHGVWDWHVRIEHOLHI \. .  \.

(370) . $VVXPSWLRQ $

(371) LVQRWHQWLUHO\FRPSDWLEOHZLWKSRVWXODWHVRIWKH5%(WKHRU\ZKLFKKROG WKDWDJHQWVGRQRWNQRZHTXLOLEULXPPDSVRUWUXHSUREDELOLWLHVZHPDNHLWLQRUGHUWRIDFLOLWDWHWKH FRPSXWDWLRQVRI5%( $

(372) DPRXQWVWRDVVXPLQJWKDWRXU5%(DUHLQFRPSOHWH5DGQHU(TXLOLEULD VHH5DGQHU 

(373)

(374) ZLWKDQH[SDQGHGVWDWHVSDFHRIXQREVHUYHGVWDWHVRIEHOLHIV0DUNHWVDUH LQFRPSOHWHVLQFHDJHQWVKDYHRQO\WZRDVVHWVWRWUDGHPDUNHWXQFHUWDLQW\ . E. 7KH3HUFHSWLRQ0RGHOV *LYHQDVWDWLRQDU\PHDVXUHWUXHSUREDELOLWLHVSOD\DEVROXWHO\QRUROHLQGHILQLQJHTXLOLEULXP. :KDWPDWWHUVLVZKDWDJHQWVNQRZDQGKRZWKH\SHUFHLYHWKHIXWXUH:HKDYHDOUHDG\VHOHFWHGWKH EDVLFORQJWHUPVWDWLVWLFVDJHQWVNQRZDQGZHQRZWXUQWRWKHLUSHUFHSWLRQV2XUVWUDWHJ\LVWR VSHFLI\WKHDJHQWV¶EHOLHIVDQGWKHQUDWLRQDOL]HWKHP:HVWDUWZLWKWKHVWDWHVRIEHOLHIV G

(375) GHVFULEHVWKHORQJWHUPEHKDYLRURIWKHMRLQWVWDWHVRIEHOLHIEXWWKHUDWLRQDOLW\FRQGLWLRQVUHTXLUH PDUJLQDOGLVWULEXWLRQVRI \. WRKDYHFRPSDWLEOHDV\PSWRWLFSURSHUWLHV+HQFHZHSRVWXODWHWKDW. )RUDGLVFXVVLRQRIWKHUHODWLRQVKLSEHWZHHQDQ5%(DQGRWKHUHTXLOLEULXPFRQFHSWVLQFOXGLQJVXQVSRW HTXLOLEULDVHH.XU]DQG0RWROHVH 

(376) 6HFWLRQGSDJHV. .

(377) WKHVWDWHRIEHOLHIRIDJHQWNRQKLVRZQWDNHVWKHIRUP 

(378) ZKHUH ]. .  . \. . ' F ].  . . LVDUHDOL]DWLRQRIDQRUPDOLLGUDQGRPYDULDEOH ] ×. ZHVHWWKHSDUDPHWHU. F. IRUN. .  . a 1 

(379) ,QWKHVLPXODWLRQV. . 3HUFHLYHG3URGXFWLYLW\6KRFNVDQGWKHLU5DWLRQDOLW\&RQGLWLRQV 7KHEHOLHIVRIDJHQWNLVH[SUHVVHGDVDVWRFKDVWLFGLIIHUHQFHHTXDWLRQRIWKHIRUP 

(380). ORJ. L ' 8. 7KHDJHQWEHOLHYHVWKDW. 8. L % 8. ORJ. k.

(381) \. . % F 

(382) k.

(383) ] Ö. . . ] Ö. . a 1 

(384) . LVDVLQ D

(385) EXWWKHPHDQYDOXHYDULHVZLWK \. . 6LQFHWKHHPSLULFDO. GLVWULEXWLRQLQ D

(386) H[KLELWVQRORQJWHUPFRYDULDQFHEHWZHHQSURGXFWLYLW\VKRFNVPRQHWDU\ VKRFNVDQGVWDWHVRIEHOLHIUDWLRQDOLW\RIEHOLHIPXVWFRQIRUPWRWKDW+HQFHUDWLRQDOLW\UHTXLUHV WKHVWDWLVWLFVRIREVHUYDEOHVJHQHUDWHGE\ 

(387) DQG D

(388) WREHWKHVDPHZKHQWKHVWDWHVRIEHOLHI \. . DUHWUHDWHGDVXQREVHUYHGVKLIWVLQWKHPHDQYDOXHIXQFWLRQ1RUDWLRQDOLW\FRQGLWLRQVDUH. LPSRVHGRQ \. . RURQWKHFRUUHODWLRQEHWZHHQ \. ,Q 

(389) DJHQWVIRUPEHOLHIVWKDW. 8. k. . DQG ORJ.

(390) DQG. L

(391) . F

(392) k.

(393) GHSHQGXSRQ. k. UDWLRQDOLW\UHTXLUHVWKDWIRUREVHUYDEOHVSHUFHSWLRQHTXDOVUHDOL]DWLRQVKHQFH. :HZULWH. 7KHHPSLULFDOGLVWULEXWLRQRI. 8. k

(394) \ % F 

(395) k

(396) ]Ö . :HXVHDVSHFLILFIXQFWLRQDOIRUPLQZKLFKPRQHWDU\VKRFNVLPSDFW. 8. D

(397). k

(398) ' . %. 8  !. 8. LV 1  . EXW. k ' k *LYHQ. WKLVWKHEDVLFUDWLRQDOLW\FRQGLWLRQFDQEHVLPSO\VWDWHG 

(399) . k.  F.

(400) . k

(401) DQGWKLVIXQFWLRQLV. . H. ,Q D

(402) WKHIXQFWLRQLVLQFUHDVLQJLQWKHVL]HRIPRQHWDU\VKRFNVDQGKHQFHVXFKVKRFNVLQFUHDVH WKHHIIHFWRI \. . RQWKHSHUFHLYHGPHDQYDOXHRI ORJ. L. LQ 

(403) *LYHQRXUDVVXPSWLRQVLQWKLV. SDSHUZHVKDOOVKRZWKDWWKLVEHOLHILVUDWLRQDOL]HGLIZHUHTXLUHWKDWFRQGLWLRQDOXSRQ. . VHFRQGHPSLULFDOPRPHQWRI 8 k

(404) \  % F 

Riferimenti

Documenti correlati

In secondo luogo la conformazione della piazza — fortemente caratterizzata dalla presenza delle ci- sterne ipogee che, con la loro copertura a volta, generano un forte scoscendimento

As a consequence, the implementation of tuition fees also reinforces institutional autonomy, while the implementation of equality of opportunities funding incentives allows a

Qualche settimana dopo, la stessa restituzione di fedeltà feudali venne contemplata nel trattato con Ludovico di Savoia (30 agosto), tenuto a &#34;relassare le fidelità&#34; dei

Elisabetta Benelli | Università degli Studi di Firenze, Italy; Marta Berni | Università degli Studi di Firenze, Italy; Stefano Bertocci | Università degli Studi di

Wrong selection of measurements to be done In both situations a fair agreement must be find between car and loudspeaker manufacturers and we will present two case studies

Pur nella perdurante mancanza di una legge sugli archivi, si auspicava, e tra i proponenti di tali auspici vi era anche la novel- la Società storica della Valdelsa, «che si

These analytical procedures will be applied to different water samples (surface river waters, groundwater, samples taken at different stages in a water

Actors in such sectors are also especially sensitive to signals from the central bank, however, because the restrictive monetary policies that the bank wields not only depress