Nominal rigidities and the dynamic effects of a shock to monetary policy

Nominal Rigidities and the Dynamic

Effects of a Shock to Monetary Policy

By: Lawrence J. Christiano, Martin

Eichenbaum and Charles L. Evans

L4?@* +}_|it @?_ |i #)?@4U ,giU|t Lu @

5LU! |L L?i|@h) L*U)



w@hi?Ui a ht|@?L

_{@h|? ,Ui?M@4}

@h*it w ,@?t

@)c 2ff

Zh suhvhqw d prgho hperg|lqj prghudwh dprxqwv ri qrplqdo uljlgl0 wlhv zklfk dffrxqwv iru wkh revhuyhg lqhuwld lq lqdwlrq dqg shuvlvwhqfh lq rxwsxw1 Wkh nh| ihdwxuhv ri rxu prgho duh wkrvh wkdw suhyhqw d vkdus ulvh lq pdujlqdo frvwv diwhu dq h{sdqvlrqdu| vkrfn wr prqhwdu| srolf|1 Ri wkhvh ihdwxuhv/ wkh prvw lpsruwdqw duh vwdjjhuhg zdjh frqwudfwv ri dyhudjh gxudwlrq wkuhh txduwhuv/ dqg yduldeoh fdslwdo xwlol}dwlrq1

MHO= H6/ H7/ H8

_{Wkh uvw wzr dxwkruv duh judwhixo iru wkh qdqfldo vxssruw ri d Qdwlrqdo Vflhqfh Irxqgdwlrq}

judqw wr wkh Qdwlrqdo Exuhdx ri Hfrqrplf Uhvhdufk1 Zh zrxog olnh wr dfnqrzohgjh khosixo frpphqwv iurp Oduv Kdqvhq/ Fkulv Vlpv dqg Pdun Zdwvrq1 Zh sduwlfxoduo| zdqw wr wkdqn Ohyrq Eduvhjk|dq iru klv vxshue uhvhdufk dvvlvwdqfh1 Wklv sdshu grhv qrw qhfhvvdulo| uhhfw wkh ylhzv ri wkh Ihghudo Uhvhuyh Edqn ri Fklfdjr/ ru wkh Ihghudo Uhvhuyh V|vwhp1

|_{Qruwkzhvwhuq Xqlyhuvlw|/ Qdwlrqdo Exuhdx ri Hfrqrplf Uhvhdufk/ dqg Ihghudo Uhvhuyh}

Edqnv ri Fklfdjr dqg Fohyhodqg1

}_{Qruwkzhvwhuq Xqlyhuvlw|/ Qdwlrqdo Exuhdx ri Hfrqrplf Uhvhdufk/ dqg Ihghudo Uhvhuyh Edqn}

ri Fklfdjr1

 W?|hL_U|L?

At T@Tih tii!t |L ?_iht|@?_ |i LMtihi_ ?ih|@* Mi@Lh Lu ?@|L? @?_ Tihtt|i?Ui ? @}}hi}@|i ^@?||it AL |t i?_c i uLh4*@|i @?_ it|4@|i @ _)?@4Uc }i?ih@* i^*Mh4 4L_i* U ?ULhTLh@|it t|@}}ihi_ @}i @?_ ThUi UL?|h@U|t `i ti Lh 4L_i* |L ?it| }@|i @| 4 Lu uhU|L?t U@? @UUL?| uLh |i i_i?Ui Lu ?ih|@ @?_ Tihtt|i?Ui 6Lh |t i ihUti |L Mi i** _i€?i_c i 4t| U@h@U|ih3i ?ih|@ @?_ Tihtt|i?Ui ThiUti*) `i _L tL t?} it|4@|it Lu |i _)?@4U hitTL?ti Lu ?@|L? @?_ @}}hi}@|i @h@M*it |L @ 4L?i|@h) TL*U) tLU! `| |t U@h@U|ih3@|L?c |i ^it|L? |@| i @t! hi_Uit |LG @? 4L_i*t | 4L_ih@|i _i}hiit Lu ?L4?@* h}_|it }i?ih@|i ?ih|@* ?@|L? @?_ Tihtt|i?| L|T|

4Li4i?|t ? hitTL?ti |L @ 4L?i|@h) TL*U) tLU!q< _{h @?tih |L |t ^it|L? tc )it<}

Ai 4L_i* |@| i UL?t|hU| @t |L !i) ui@|hit 6ht|c | i4Mi_t @*L t|)*i ?L4?@* ThUi @?_ @}i UL?|h@U|t 5iUL?_c |i hi@* t_i Lu |i 4L_i* ?ULhTLh@|it |hii _iT@h|hit uhL4 |i t|@?_@h_ |i |MLL! L?i tiU|Lh _)?@4U t|LU@t|U }hL| 4L_i* Aiti @hi 4L| @|i_ M) hiUi?| hiti@hU L? |i _i|ih4?@?|t Lu UL?t4T|L?c @tti| ThUitc ?it|4i?| @?_ ThL_U||) Ai tTiU€U _iT@h|hit U i ?U*_i @hi @M| Tihtt|i?Ui ? Thiuihi?Uit uLh UL?t4T|L?c @_t|4i?| ULt|t ? ?it|4i?| @?_ @h@M*i U@T|@* |*3@|L?

h !i) €?_?}t @hi @t uL**Lt 6ht|c |i @ih@}i _h@|L? Lu ThUi @?_ @}i UL?|h@U|t ? |i it|4@|i_ 4L_i* t hL}*) 2 @?_  ^@h|ihtc hitTiU|i*) #itT|i |i 4L_it| ?@|hi Lu |iti ?L4?@* h}_|itc |i 4L_i* _Lit @ ih) }LL_ LM Lu @UUL?|?} ^@?||@|i*) uLh |i it|4@|i_ hitTL?ti Lu |i N5 iUL?L4) |L @ TL*U) tLU! W? @__|L? |L hiThL_U?} |i _)?@4U hitTL?ti Lu ?@|L? @?_ L|T|c |i 4L_i* @*tL @UUL?|t uLh |i _i*@)i_c 4T t@Ti_ hitTL?ti ? UL?t4T|L?c ?it|4i?|c ThL€|tc ThL_U||) @?_ |i i@! hitTL?ti Lu

|i hi@* @}i2 _{5iUL?_c |i Uh|U@* ?L4?@* uhU|L? ? Lh 4L_i* t @}i UL?|h@U|tc ?L| ThUi}

UL?|h@U|t  ihtL? Lu |i 4L_i* | L?*) ?L4?@* @}i h}_|it _Lit @*4Lt| @t i** @t |i it|4@|i_ 4L_i* W? UL?|h@t|c | L?*) ?L4?@* ThUi h}_|itc |i 4L_i* TihuLh4t ih) TLLh*) L?tt|i?| | i t|?} hit*|t ? |i *|ih@|hic |t ihtL? Lu |i 4L_i* U@??L| }i?ih@|i Tihtt|i?| 4Li4i?|t ? L|T| ?*itt i @tt4i ThUi UL?|h@U|t Lu i |hi4i*) *L?}

_h@|L? _{Ai 4L_i* | L?*) ?L4?@* @}i h}_|it _Lit ?L| @i |t ThLM*i4}

Ah_c i tL |@| ?uihi?Ui @ML| ?L4?@* h}_|it t ti?t|i |L }i||?} |i hi@*

4_{Wklv lv wkh vdph txhvwlrq wkdw lv wkh irfxv ri d odujh dqg jurzlqj olwhudwxuh1 Vhh/ iru h{dpsoh/}

Fkdul/ Nhkrh dqg PfJudwwdq +5333,/ Pdqnlz +5334,/ Urwhpehuj dqg Zrrgirug +4<<<, dqg wkh uhihuhqfhv wkhuhlq1

5_{Lq uhodwhg zrun/ Verugrqh +5333, dujxhv wkdw/ wdnlqj dv jlyhq djjuhjdwh uhdo yduldeohv/ d}

prgho zlwk vwdjjhuhg zdjhv dqg sulfhv grhv zhoo dw dffrxqwlqj iru wkh wlph vhulhv surshuwlhv ri zdjhv dqg sulfhv1

6_{Vhh iru h{dpsoh Fkdul/ Nhkrh dqg PfJudwwdq +5333,1}

t_i Lu |i 4L_i* h}|<e _{,t|4@|i_ ihtL?t Lu |i 4L_i* U _L ?L| ?ULhTLh@|i Lh}

_iT@h|hit uhL4 |i t|@?_@h_ }hL| 4L_i* 4T*) 4T*@tM*) *L?} ThUi @?_ @}i UL?|h@U|t 6Lh|c i €?_ |@| u L?i L?*) @?|t |L 4@|U |i ?ih|@ ? ?@|L? @?_ Tihtt|i?Ui ? L|T| | 4L_ih@|i @}i @?_ ThUi t|U!?ittc |i? L?*) @h@M*i U@T|@* |*3@|L? t hi^hi_ AL ?_iht|@?_ ) |t ui@|hi t tL 4TLh|@?| ?L|i |@| ? Lh 4L_i*c €h4t ti| ThUit @t @ 4@h!T Lih 4@h}?@* ULt|t Ai 4@Lh UL4TL?i?|t Lu 4@h}?@* ULt|t @hi @}it @?_ |i hi?|@* h@|i Lu U@T|@* ) @**L?} |i tihUit Lu U@T|@* |L ?Uhi@ti @u|ih @ TLt|i 4L?i|@h) TL*U) tLU!c @h@M*i U@T|@* |*3@|L? i*Tt _@4Ti? |i *@h}i hti ? |i hi?|@* h@|i Lu U@T|@* |@| L*_ L|ihti LUUh At ? |h? _@4Ti?t |i hti ? 4@h}?@* ULt|t @?_c i?Uic ThUit Ai hit*|?} ?ih|@ ? ?@|L? 4T*it |@| |i hti ? ?L4?@* tTi?_?} |@| LUUht @u|ih @ TLt|i 4L?i|@h) TL*U) tLU! ThL_Uit @ Tihtt|i?| hti ? hi@* L|T| 54*@h ?||L? i T*@?t ) t|U!) @}it T*@) @ Uh|U@* hL*i ? @**L?} Lh 4L_i* |L i T*@? ?@|L? ?ih|@ @?_ L|T| Tihtt|i?Ui

6?@**)c i €?_ |@| Lh 4L_i* i4ML_it t|hL?} ?|ih?@* ThLT@}@|L? 4iU@?t4t 6Lh i @4T*ic ii? ? hitTL?ti |L @? _ tLU! ? |i }hL| h@|i Lu 4L?i)c |i 4L_i* }i?ih@|it @ *@h}ic Tihtt|i?| 4T t@Ti_ hitTL?ti ? @}}hi}@|i L|T| @?_ @? ?ih|@* hitTL?ti ? ?@|L? Lhi }i?ih@**)c |i 4L_i* 4T*it |@| |i igiU|t Lu @ tLU! |L 4L?i|@h) TL*U) L? @}}hi}@|i @h@M*it Tihtt| i** Mi)L?_ |i igiU|t Lu |i tLU! L? |i ?|ihit| h@|i @?_ |i }hL| h@|i Lu 4L?i)

`i Thti @ T@h|U*@h *4|i_ ?uLh4@|L? iUL?L4i|hU t|h@|i}) |L it|4@|i @?_ i@*@|i Lh 4L_i* Ai M@tU _i@ Mi?_ |t t|h@|i}) U@? Mi t44@h3i_ @t uL**Lt `i U@h@U |ih3i 4L?i|@h) TL*U) @t @ h*i U i Thittit |i ?|ihit| h@|i @t @ u?U|L? Lu @}}hi}@|i iUL?L4U @h@M*it @?_ @ 4L?i|@h) TL*U) tLU! h @tt4T|L?t @ML| |i tLU! 4T*) @ T@h|U*@h tihit Lu ThLiU|L? i^@|L?t U U@? Mi i T*L|i_ |L it|4@|i |i _)?@4U

igiU|t Lu @ 4L?i|@h) TL*U) _t|hM@?Ui L? @}}hi}@|i iUL?L4U @h@M*itD _{h iUL?L4i|hU}

t|h@|i}) UL4T@hit |iti ThLiU|L?t ? |i 4L_i* @?_ ? |i _@|@

W? Lh 4L_i*c |i ThLiU|L?t ULhhitTL?_ |L |i _)?@4U hitTL?ti Lu |i iUL?L4) |L

7_{Rwkhu dxwkruv kdyh dovr dujxhg wkdw lqihuhqfh derxw qrplqdo uljlglwlhv fdq eh glvwruwhg lq}

lpsruwdqw zd|v li wkh uhdo vlgh ri wkh hfrqrp| lv plvvshflhg1 Vhh iru h{dpsoh Ixkuhu +5333,/ PfFdooxp dqg Qhovrq +4<<;, dqg Vlpv +4<<;,1 Vhh dovr wkh lqwhuhvwlqj sdshu e| Hgjh +5333,/ zklfk lqfrusrudwhv kdelw irupdwlrq/ wlph0wr0exlog fdslwdo/ dqg lqyhvwphqw dgmxvwphqw frvwv lqwr d Fdoyr0vw|oh vwlfn| sulfh prgho1 Vkh vkrzv wkdw wkhvh uhdo shuwxuedwlrqv vxevwdqwldoo| lpsuryh wkh shuirupdqfh ri wkh Fdoyr prgho1

8_{D sduwlfxoduo| vlpsoh h{dpsoh fdq eh irxqg lq Fkdul/ Nhkrh dqg PfJudwwdq +5333, dqg}

Frroh| dqg Kdqvhq +4<;<,1 Wkh| dvvxph wkdw wkh prqhwdu| srolf| vkrfn lv wkh huuru lq d uvw rughu dxwruhjuhvvlyh uhsuhvhqwdwlrq iru prqh| jurzwk1 Xqghu wkhvh frqglwlrqv/ wkh srolf| vkrfn lv wkh huuru lq wkh surmhfwlrq ri prqh| jurzwk rq rqh odj ri lwvhoi1 Wkh g|qdplf uhvsrqvh ri d yduldeoh wr wkh vkrfn lv wkh surmhfwlrq ri wkdw yduldeoh rq fxuuhqw dqg sdvw ydoxhv ri wkh vkrfn1

@ TL*U) tLU! h 4L_i* @t |i ThLTih|) |@| |i ThLiU|L?t @hi ?_iTi?_i?| Lu |i

?@|hi Lu |i ?L?4L?i|@h) tLU!tS _{At t @? 4TLh|@?| @_@?|@}ic t?Ui | @**Lt t}

|L @L_ |@!?} @ t|@?_ L? |i ?@|hi Lu |i ?L?4L?i|@h) tLU!t 6Lh UL?i?i?Uic i

t4T*) ti| |i L|ih tLU!t |L 3ihL. _{AL LM|@? i4ThU@* it|4@|it Lu |i ThLiU|L?tc}

i i T*L| |i i**!?L? hit*| |@| iU|Lh @|Lhi}hittL?t EV+<t ThL_i @? i Ui**i?| U@h@U|ih3@|L? Lu |i tiUL?_ 4L4i?| ThLTih|it Lu |i _@|@ t tUc i it|4@|i @ V+ uLh |i !i) @h@M*it ? Lh 4L_i* iUL?L4) @?_ UL4T|i |i ThLiU|L?t 4T*i_ M) |t hiThiti?|@|L? W? Th@U|Uic |t @4L?|t |L UL4T|?} t|@?_@h_ 4T*ti hitTL?ti u?U|L?t |L @ T@h|U*@h Lh|L}L?@*3i_ ??L@|L? ? |i V+ `i t|hitt |i ThLiU|L? ?|ihThi|@|L? Lu Lh ThLUi_hi ? Lh_ih |L _h@ @||i?|L? |L |i ti?ti ? U i @hi UL4T|?} |i t@4i

LMiU| ? |i 4L_i* @?_ ? |i _@|@H

W| t Lh| UL?|h@t|?} Lh t|h@|i}) | @? @*|ih?@|ic Tih@Tt 4Lhi |h@_|L?@*c L?i At @*|ih?@|i t|h@|i}) uLUtit L? |i 4L_i*<t Thi_U|L?t uLh @hLt tiUL?_ 4L4i?|t Lu |i _@|@c tU @t @|L @?_ UhLtt ULhhi*@|L?t Lu _gihi?| @h@M*it `*i |i @_@?|@}it Lu |t t|h@|i}) @hi i** !?L?c |i) UL4i @| @ ULt| 5?Ui |iti |)Tit Lu tiUL?_ 4L4i?|t hiiU| |i LTih@|L? Lu @** |i tLU!t _h?} |i iUL?L4)c |i 4L_i* ti_ ? |i @?@*)tt 4t| ?ULhTLh@|i @** Lu |iti tLU!t |LL 5Lc |i @?@*)t| 4t| ?L| t| |@!i @ t|@?_ L? ThiUti*) L 4L?i|@h) tLU!t i?|ih |i iUL?L4) Ai @?@*)t| 4t| @*tL |@!i @ t|@?_ L?

|i ?@|hi Lu tLU!t |L }Lih?4i?| tTi?_?}c |iU?L*L})c 4L?i) _i4@?_c Thiuihi?Uitc i|Ub

Ai @_@?|@}i Lu |i *4|i_ ?uLh4@|L? t|h@|i}) t |@| | @**Lt t |L *i@h? @ML| tL4i @tTiU|t Lu |i t|hU|hi Lu |i iUL?L4) |L| |@!?} @ t|@?_ L? |iti L|ih tLU!t

Ai hi4@?_ih Lu |t T@Tih t Lh}@?3i_ @t uL**Lt W? tiU|L? 2 i Mhi) _itUhMi Lh it|4@|it Lu L |i N5 iUL?L4) hitTL?_t |L @ 4L?i|@h) TL*U) tLU! 5iU|L?  _tT*@)t Lh iUL?L4U 4L_i* W? 5iU|L? e i _tUtt Lh iUL?L4i|hU 4i|L_L*L}) h i4ThU@* hit*|t @hi Thiti?|i_ ? 5iU|L? D L?U*_?} UL44i?|t @hi UL?|@?i_ ? tiU|L? S

9_{Wklv lv dfwxdoo| rqo| wuxh dv dq dssur{lpdwlrq1 Lw lv d ihdwxuh ri wkh olqhdu srolf| uxohv zh}

xvh wr dssur{lpdwh wkh vroxwlrq wr wkh prgho1 D pdlqwdlqhg dvvxpswlrq ri rxu dqdo|vlv lv wkdw wklv dssur{lpdwlrq lv uhdvrqdeo| dffxudwh1

:_{Wklv lv qrw wuxh iru doo prghov1 Iru h{dpsoh/ wkh vljqdo h{wudfwlrq sureohp lq Oxfdv* +4<:5,}

prqhwdu| plvshufhswlrq prgho lpsolhv wkdw wkh uhvsrqvh ri wkh hfrqrp| wr d prqhwdu| srolf| vkrfn ghshqgv vhqvlwlyho| rq wkh qdwxuh ri wkh rwkhu vkrfnv1 Vr/ hyhq li rqh lv rqo| lqwhuhvwhg lq nqrzlqj wkh hhfwv ri d prqhwdu| srolf| vkrfn lq d prqhwdu| plvshufhswlrq prgho/ rqh vwloo fdqqrw dyrlg wdnlqj d vwdqg rq wkh qdwxuh ri wkh rwkhu vkrfnv1

;_{Fkulvwldqr/ Hlfkhqedxp dqg Hydqv +4<<;,/ Hgjh +5333, dqg Urwhpehuj dqg Zrrgirug}

+4<<:, kdyh dovr dssolhg wklv vwudwhj| lq wkh frqwh{w ri prqhwdu| srolf| vkrfnv1

<_{Vhh iru h{dpsoh Fkdul/ Fkulvwldqr dqg Hlfkhqedxp +4<<8,/ Luhodqg +4<<:,/ Nlp +5333,/ dqg}

Ohhshu dqg Vlpv +4<<7,1 Dq h{wuhph yhuvlrq ri wklv vwudwhj| dvvxphv wkdw wkh rqo| glvwxuedqfhv wr wkh hfrqrp| duh prqhwdu| srolf| vkrfnv +vhh Fkdul/ Nhkrh dqg PfJudwwdq +5333,1

2 Ai L?ti^i?Uit Lu @ L?i|@h) L*U) 5LU!

Ai t|@h|?} TL?| Lu Lh @?@*)tt t |i uL**L?} U@h@U|ih3@|L? Lu 4L?i|@h) TL*U)G

-|' sEl| n 0| E2

Oihic -| t |i 6i_ih@* 6?_t h@|ic s t @ *?i@h u?U|L?c l| t @? ?uLh4@|L? ti|c @?_ 0| t

|i 4L?i|@h) TL*U) tLU! h ?|ihThi|@|L? Lu E2 t |@| |i 6i_ @**Lt 4L?i) }hL| |L Mi @|iih t ?iUitt@h) |L }@h@?|ii |@| E2 L*_t h M@tU _i?|u)?} @tt4T|L?

t |@| 0| t Lh|L}L?@* |L |i i*i4i?|t ? l| i*Lc i _itUhMi |i @h@M*it ? l| @?_

i*@MLh@|i L? |i ?|ihThi|@|L? Lu |i Lh|L}L?@*|) @tt4T|L?

`i ?L Mhi) 4L|@|i Lh ThLUi_hi uLh it|4@|?} |i ThLiU|L? Lu iUL?L4U @h@M*it

L? Uhhi?| @?_ T@t| 0|<t W? Th?UT*ic |ihi @hi |L @)t |L it|4@|i |t ThLiU|L?c @*tL

!?L? @t @? 4T*ti hitTL?ti u?U|L? Ai €ht| Mi}?t M) it|4@|?} |i 0|<t t?} |i €||i_

hit_@*t uhL4 @ hi}hittL? Lu -| L? l| Ai 4T*ti hitTL?ti Lu @ @h@M*i |L |i 0|<t t |i?

it|4@|i_ ? @ tiUL?_t|@}i hi}hittL? Lu |i @h@M*i L? Uhhi?| @?_ T@t| @*it Lu |i €||i_ hit_@*t Aihi @hi |L _U*|it | |t @TThL@UG E |L LM|@? tiih@* )i@ht< Lh| Lu hitTL?titc L?i 4t| ti T @ tMt|@?|@* ?4Mih Lu ?|@* LMtih@|L?tc |t hi_U?} t@4T*i t3i( @?_ E |i ULiUi?|t ? |i tiUL?_t|@}i hi}hittL? |i?_ |L Mi 4ThiUti*) it|4@|i_ `i Thti @? @*|ih?@|i @TThL@U M@ti_ L? @ iU|Lh @|Lhi}hittL? EV+ €| |L

|i iU|Lh Lu @h@M*it ?U*_i_ ? l| V+<t @hi i** !?L? |L ThL_i @? i Ui**i?| t44@h)

Lu |i tiUL?_ 4L4i?| ThLTih|it Lu |i _@|@ `| |t ? 4?_c i it|4@|i @ V+ uLh |i !i) @h@M*it ? Lh 4L_i* @?_ |i? UL4T|i |i ThLiU|L?t 4T*i_ M) |t hiThiti?|@|L? At t i^@*i?| |L |i t|@?_@h_ ThLUi_hi uLh UL4T|?} 4T*ti hitTL?ti u?U|L?t |L @ T@h|U*@h Lh|L}L?@*3i_ ??L@|L? ? @ V+ iU@ti |i ?4Mih Lu *@}t ? @ V+ t ^|i t4@** ? Th@U|Uic |t @TThL@U @L_t |i *Ltt Lu ?|@* LMtih@|L?t ? |i €ht|t|@}i hi}hittL? _tUtti_ @MLi W? @__|L?c i i TiU| |@| |i t|hU|hi 4TLti_ M) |i V+ *i@_t |L hi*@|i*) ThiUti it|4@|it Lu |i 4T*ti hitTL?ti u?U|L?t

`i ?L Mhi) _itUhMi |i _i|@*t Lu Lh V+ @?_ Lu Lh _i?|u)?} @tt4T|L?t wi|

t| _i?L|i |i iU|Lh Lu @h@M*it ?U*_i_ ? |i @?@*)tt `i T@h||L? t| @t uL**LtG

t|' 5 7 t_-|_| t2| 6 8 

Ai iU|Lhc t|c t UL4TLti_ Lu |i @h@M*it Lti |4i | i*i4i?|t @hi UL?|@?i_ ? l|c @?_

@hi @tt4i_ |L ?L| hitTL?_ UL?|i4TLh@?iLt*) |L @ 4L?i|@h) TL*U) tLU! Ai iU|Lh t2|

UL?tt|t Lu |i |4i | @*it Lu @** |i L|ih @h@M*it ? l| W? Th@U|Uic |i @h@M*it ? t|

@hi hi@* B#c hi@* UL?t4T|L?c |i B# _i@|Lhc hi@* ?it|4i?|c |i hi@* @}ic @?_ *@MLh D

ThL_U||) Ai @h@M*it ? t2| @hi hi@* ThL€|tc |i }hL| h@|i Lu 2c @?_ |i 5:Dff

?_i c tU@*i_ M) |i UL?t4ih ThUi ?_i  ** |iti @h@M*itc i UiT| 4L?i) }hL|c @i

Mii? *L}}i_ `i 4i@thi |i ?|ihit| h@|ic -|c t?} |i 6i_ih@* 6?_t h@|i

Ai Lh_ih?} Lu |i @h@M*it ? t| i4ML_it |L !i) _i?|u)?} @tt4T|L?t 6ht|c

|i @h@M*it ? t| @hi @tt4i_ |L ?L| hitTL?_ UL?|i4TLh@?iLt*) |L @ 4L?i|@h) TL*U)

tLU! 5iUL?_c |i |4i | ?uLh4@|L? ti| Lu |i 4L?i|@h) @|Lh|) UL?tt|t Lu Uhhi?| @?_

*@}}i_ @*it Lu |i @h@M*it ? t| @?_ L?*) T@t| @*it Lu |i @h@M*it ? t2| Ai 4L_i*

UL?t|hU|i_ ? |i ?i | tiU|L? ?ULhTLh@|it ML| @tt4T|L?t

Ai V+ UL?|@?t e *@}t Lu i@U @h@M*i @?_ |i t@4T*i TihL_ t bSD"  bbD"f

W}?Lh?} |i UL?t|@?| |ih4c |i V+ U@? Mi h||i? @t uL**LtG

t|' t|3n  n et|3en #|c E22

ihi  t @ f  f *Lih |h@?}*@h 4@|h | _@}L?@* |ih4t i^@* |L ?|)c @?_ #| t

@ f_4i?tL?@* iU|Lh Lu 3ihL4i@?c tih@**) ?ULhhi*@|i_ tLU!t | _@}L?@* @h@?Ui

UL@h@?Ui 4@|h  5?Ui |ihi @hi t @h@M*it ? t|c |i 4L?i|@h) TL*U) tLU!c 0|c t

|i .| i*i4i?| Lu #|  TLt|i tLU! |L 0| ULhhitTL?_t |L @ UL?|h@U|L?@h) 4L?i|@h)

TL*U) tLU! `i it|4@|i |i T@h@4i|iht  c  ' c c ec c @?_ |i @h@?UiUL@h@?Ui

4@|h Lu #|  t?} t|@?_@h_c *i@t| t^@hitc 4i|L_t Nt?} |iti T@h@4i|ih it|4@|itc

i UL4T|i |i _)?@4U T@| Lu t| uL**L?} @ L?it|@?_@h__i@|L? tLU! ? 0|c ti||?}

?|@* UL?_|L?t |L 3ihL At T@|c U ULhhitTL?_t |L |i ULiUi?|t ? |i 4T*ti

hitTL?ti u?U|L?t Lu ?|ihit|c t ?@h@?| |L |i Lh_ih?} Lu |i @h@M*it |? t| @?_

|? t2| Etii ht|@?Lc ,Ui?M@4 @?_ ,@?t Ebbb

Ai 4T*ti hitTL?ti u?U|L?t Lu @** @h@M*it ? t| @hi _tT*@)i_ ? 6}hi  w?it

4@h!i_ n< ULhhitTL?_ |L |i TL?| it|4@|it Ai t@_i_ @hi@t ?_U@|i bDI UL?€_i?Ui ?

|ih@*t @ML| |i TL?| it|4@|it _{Ai tL*_ *?it Tih|@? |L |i ThLTih|it Lu Lh t|hU|h@*}

4L_i*c U ** Mi _tUtti_ ? tiU|L?  Ai hit*|t t}}it| |@| @u|ih @? i T@?tL?@h) 4L?i|@h) TL*U) tLU! |ihi t @G

 4Tt@Ti_c hitTL?ti Lu L|T|c UL?t4T|L? @?_ ?it|4i?|c | |i Ti@! igiU| LUUhh?} @u|ih @ML| D )i@htc

 4Tt@Ti_ hitTL?ti ? ?@|L?c | @ Ti@! hitTL?ti @u|ih @ML| 2 )i@htc  u@** ? |i ?|ihit| h@|i uLh hL}*) L?i )i@hc

 hti ? ThL€|tc hi@* @}it @?_ *@MLh ThL_U||)c @?_

43_{Wklv vdpsoh shulrg lv wkh vdph dv lq Fkulvwldqr/ Hlfkhqedxp dqg Hydqv +4<<<,1}

44_{Zh xvh wkh phwkrg ghvfulehg lq Vlpv dqg ]kd +4<<<,1}

 @? 44i_@|i hti ? |i }hL| h@|i Lu 4L?i)

Ai hLMt|?itt Lu |i ^@*|@|i ui@|hit Lu |iti €?_?}t |L @*|ih?@|i _i?|u)?} @tt4T |L?tc @*|ih?@|i t@4T*i tMTihL_t @?_ |i ti Lu 4L?|*) _@|@ t _tUtti_ ? ht|@?Lc ,Ui?M@4 @?_ ,@?t Ebbb

 Ai L_i* ,UL?L4)

W? |t tiU|L? i _itUhMi Lh 4L_i* iUL?L4) @?_ _tT*@) |i ThLM*i4t tL*i_ M) €h4t @?_ LtiL*_t W? @__|L?c i _itUhMi |i Mi@Lh Lu €?@?U@* ?|ih4i_@hit @?_ |i 4L?i|@h) @?_ €tU@* @|Lh|it

 6?@* BLL_ 6h4t

| |4i |c @ €?@* UL?t4T|L? }LL_c t|c t ThL_Ui_ M) @ TihuiU|*) UL4Ti||i €h4 Ai

€h4 _Lit tL M) UL4M??} @ UL?|?4 Lu ?|ih4i_@|i }LL_tc ?_i i_ M)  5 dfc oc t?} |i |iU?L*L}) t| ' ] _ f t|  bs_{_} bs E

ihi   bs 4c @?_ t| _i?L|it |i |4i | ?T| Lu ?|ih4i_@|i }LL_  wi| | @?_

| _i?L|i |i |4i | ThUi Lu |i UL?t4T|L? }LL_ @?_ ?|ih4i_@|i }LL_ c hitTiU|i*)

hL€| 4@ 43@|L? 4T*it |i ,*ih i^@|L?  | |  bs bs 3 ' t_t| | E2

UULh_?} |L E2c |i _i4@?_ uLh ?|ih4i_@|i }LL_  t @ _iUhi@t?} u?U|L? Lu |i hi*@|i

ThUi Lu |@| }LL_ @?_ @? ?Uhi@t?} u?U|L? Lu @}}hi}@|i L|T|c t| W?|i}h@|?} E2 @?_

4TLt?} Ec i LM|@? |i uL**L?} hi*@|L?tT Mi|ii? |i ThUi Lu |i €?@* }LL_ @?_ |i ThUi Lu |i ?|ih4i_@|i }LL_G

|' ] _ f   3bs | _ E3bs  E .

2 W?|ih4i_@|i BLL_ 6h4t

W?|ih4i_@|i }LL_  5 Efc  t ThL_Ui_ M) @ 4L?LTL*t| L tit |i uL**L?} |iU?L*L})G

t| '

&k

|u3k|   u &k|u3k|  

fc L|ihti Ee

ihi f k  Oihic u| @?_ &| _i?L|i |4i | *@MLh @?_ U@T|@* tihUit ti_ |L ThL_Ui

|i | _{?|ih4i_@|i }LL_ *tLc  : f _i?L|it |i € i_ ULt| Lu ThL_U|L? `i h*i L|}

i?|h) @?_ i | ?|L |i ThL_U|L? Lu ?|ih4i_@|i }LL_  W? |i i4ThU@* @?@*)ttc  t ti| |L }@h@?|ii |@| ThL€|t @hi 3ihL ? t|i@_) t|@|i At t UL?tt|i?| | @t @?_ 6ih?@*_ Ebbec O@** EbHHc @?_ +L|i4Mih} @?_ `LL_uLh_ EbbDc L @h}i |@| iUL?L4U ThL€|t @hi U*Lti |L 3ihL L? @ih@}i

W?|ih4i_@|i €h4t hi?| U@T|@* @?_ *@MLh ? TihuiU|*) UL4Ti||i u@U|Lh 4@h!i|t hL€|t

@hi _t|hM|i_ |L LtiL*_t @| |i i?_ Lu i@U |4i TihL_ wi| -&

| @?_ `| _i?L|i |i

?L4?@* hi?|@* h@|i L? U@T|@* tihUit @?_ |i @}i h@|ic hitTiU|i*) `Lh!iht 4t| Mi

T@_ ? @_@?Ui Lu ThL_U|L? t @ hit*|c |i | _{€h4 4t| MLhhL |t @}i M**c `}

|u|c

uhL4 |i €?@?U@* ?|ih4i_@h) @| |i Mi}???} Lu |i TihL_ +iT@)4i?| LUUht @| |i

i?_ Lu |4i TihL_ | @| |i }hLtt ?|ihit| h@|ic -| L?ti^i?|*)c |i €h4<t |L|@* |4i | ULt|t

@hi }i? M) -|`|u|n -&|&| Ai €h4<t hi@* 4@h}?@* ULt| t }i? M)G

r|'     k 3k_ k k_ o& | k E|-|3k ED ihi o&

| ' -|&*| @?_ |' `|*| Ai €h4<t |4i | ThL€|t @hiG

 | |  r|  |t|c ihi | t €h4 <t ThUi

`i @tt4i |@| €h4t ti| ThUit @UULh_?} |L @ @h@?| Lu |i 4iU@?t4 tTi**i_ L| ?

@*L EbH W? i@U TihL_c @ €h4 u@Uit @ UL?t|@?| ThLM@M*|)c   1Rc Lu Mi?} @M*i |L

hiLT|43i |t ?L4?@* ThUi Ai @M*|) |L hiLT|43i |t ThUi t ?_iTi?_i?| @UhLtt €h4t @?_ |4i Wu @ €h4 U@? hiLT|43i |t ThUic | _Lit tL MiuLhi |i hi@*3@|L? Lu |i |4i | }hL| h@|i Lu 4L?i) `i UL?t_ih |L tTiU€U@|L?t Lu @| @TTi?t u @ €h4 U@??L| hiLT|43i |t ThUi W? i@U U@ti ThUit @hi hiti| @|L4@|U@**) @UULh_?} |L @ t4T*i h*i Ai €ht| tTiU€U@|L?c U ULhhitTL?_t |L |i t|@?_@h_ L?i ti_ ? |i *|ih@|hic t

|' 7Zc|3c ES

ihi 7Z t |i t|i@_) t|@|ic }hLtt h@|i Lu ?@|L? Etii ,hUi}c Oi?_ihtL? @?_ wi?c 2fff

@?_ v?c bbS2 _{`i hiuih |L ES @t |i t|@|U ThUi T_@|?} tUi4i}

Ai tiUL?_ tTiU€U@|L? t 4L|@|i_ M) U*@4t ? |i *|ih@|hi |@| |i €ht| tTiU€U@|L? _Lit ?L| }i?ih@|i tUi?| ?ih|@ ? ?@|L? W? |t tTiU€U@|L?c €h4  4t| ti| |t ThUi @UULh_?} |L

|' Z|3c|3 E.

i*Lc i i T*@? |i |iLhi|U@* @?_ ^@?||@|i 4T*U@|L?t Lu |t _)?@4U ThUiT_@|?} tUi4i

`i ?|ihThi| |i @*L ThUiti||?} 4iU@?t4 @t U@T|h?} €h4t< hitTL?ti |L @hLt ULt|t Lu U@?}?} ThUit Ai M@tU _i@ t |@| ? |i Thiti?Ui Lu |iti ULt|t €h4t u**) LT|43i ThUit L?*) TihL_U@**)c @?_ uL**L t4T*i h*it uLh U@?}?} |ih ThUit @| L|ih |4it Ai |)Ti Lu ULt|t i @i ? 4?_ @hi |Lti @ttLU@|i_ | LT|43@|L? Ei}c ULt|t @ttLU@|i_ | ?uLh4@|L? }@|ih?}c _iUtL? 4@!?}c ?i}L|@|L? @?_ UL44?U@|L? Aiti ULt|t @hi _gihi?| uhL4 4i? ULt|tc U @TT*) |L @** ThUi U@?}it ~M@h@U!c +|tL?c wi)c #||@ @?_ ih}i? E2fff ThL_i tL4i 4UhLiUL?L4U i_i?Ui |@| ULt|t @ttLU@|i_ | hiLT|43@|L? @hi 4U 4Lhi 4TLh|@?| |@? 4i? ULt|t

W? @| uL**Lt i uLUtc uLh UL?i?i?Uic L? tTiU€U@|L? E. wi| | _i?L|i |i @*i

Lu | ti| M) @ €h4 |@| U@? hiLT|43i @| |4i | h ?L|@|L? _Lit ?L| @**L | |L _iTi?_

L?  `i _L |t ? @?|UT@|L? Lu |i i** !?L? hit*| |@| ? 4L_i*t *!i Lhtc @** €h4t L U@? hiLT|43i |ih ThUi @| |4i | ULLti |i t@4i ThUi Etii `LL_uLh_c bbS @?_ v?c bbS

Ai €h4 ULLtit | |L 4@ 43iG

.|3 " [ ,'f Eq1R,v|n, k  |f|, r|n,|n, l tc|n,c EH

tMiU| |L E2c ED @?_

f|, '

Z| Z|n     Z|n,3 uLh ,  

 , ' f  Eb

W? EHc v| t |i 4@h}?@* @*i Lu @ _L**@h |L |i LtiL*_c U t |hi@|i_ @t i L}i?Lt

M) |i €h4 w@|ihc i tL |@| |i @*i Lu @ _L**@hc ? |*|) |ih4tc t UL?t|@?| @UhLtt

LtiL*_t *tLc .|3 _i?L|it |i i TiU|@|L?t LTih@|Lhc UL?_|L?i_ L? *@}}i_ }hL|

h@|it Lu 4L?i)c >|3,c ,   At tTiU€U@|L? Lu |i ?uLh4@|L? ti| U@T|hit Lh @tt4T|L?

|@| |i €h4 ULLtit | MiuLhi |i hi@*3@|L? Lu |i |4i | }hL| h@|i Lu 4L?i)

45_{Rwkhuv/ olnh Grwvh|/ Nlqj dqg Zropdq +4<<<,/ dqg Zrrgirug +4<<9, dvvxph S}

mw@ Sm>w4=

AL ?_iht|@?_ EHc ?L|i |@| | ?i?Uit €h4 <t ThL€|t L?*) @t *L?} @t | U@??L|

hiLT|43i |t ThUi Ai ThLM@M*|) |@| |t @TTi?t uLh , TihL_t t E1R,c ? U U@ti

c|n, ' |f|, Ai Thiti?Ui Lu E1R, ? EH @t |i igiU| Lu tL*@|?} u|hi hi@*3@|L?t Lu

_Lt)?Uh@|U ?Uih|@?|) ? U | UL?|?it |L @giU| |i €h4<t ThL€|t

Ai €ht| Lh_ih UL?_|L? @ttLU@|i_ | |i €h4<t ULUi Lu | tG

.|3 " [ ,'f Eq1R,v|n,tc|n, k  |f|,  bs|n,r|n, l ' f Ef

`i? 1R ' fc Ef hi_Uit |L |i u@4*@h UL?_|L? |@| |i €h4 ti|t |t ThUic |c i^@*

|L @ 4@h!T Lih i TiU|i_ 4@h}?@* ULt|c |r|cUL?_|L?@* L? ?uLh4@|L? @| |   `i?

1R : fc |i €h4 ti|t | |L @ 4@h!T Lih |i i}|i_ @ih@}i Lu 4@h}?@* ULt|t Lih |4i

AL }@? uh|ih ?||L? ?|L |i €h4<t ThLM*i4c | t UL?i?i?| |L *?i@h3i Ef @ML| |i t|i@_) t|@|i @*it Lu |i hi*i@?| @h@M*itG

eR| ' .|3 % r|n " [ ,' Eq1R,E r|n,  r|n,3 n " [ ,' Eq1R,E Z|n,  Z|n,3 &  E

Oihic R| ' |*|c @?_ @ @| Lih @ @h@M*i ?_U@|it |i TihUi?| _i@|L? uhL4 |t t|i@_)

t|@|i @*i A@| tc eR| ' ER| R*Rc ihi @ @h@M*i |L| @ @| Lh @ tMtUhT| ?_U@|it

|t ?L?t|LU@t|U t|i@_) t|@|i @*i _{5iih@* ui@|hit Lu E @hi Lh| ?L|?} 6ht|c u}

?@|L? @?_ hi@* 4@h}?@* ULt| @hi i TiU|i_ |L hi4@? @| |ih |4i | *ii*tc |i? |i €h4

ti|t eR| ' .|3 r| 5iUL?_c tTTLti |i €h4 i TiU|t hi@* 4@h}?@* ULt|t |L Mi }ih ? |i

u|hi |@? @| |4i | ?|UT@|?} |Lti u|hi 4@h}?@* ULt|tc |i €h4 ti|t eR| }ih |@?

.|3 r| W| _Lit tL MiU@ti | ?_iht|@?_t |@| | 4@) ?L| Mi @M*i |L h@ti |t ThUi i?

|Lti }ih 4@h}?@* ULt|t 4@|ih@*3i `i hiuih |L |t |)Ti Lu uLh@h_ *LL!?} Mi@Lh @t

uhL?| *L@_?}< Ah_c tTTLti €h4t i TiU| ?@|L? ? |i u|hi |L hti @MLi .|3 Z| Ai

L?i TihL_ *@} ? |i _)?@4U ThUiti||?} h*ic E.c 4T*it |@| |i €h4<t hi*@|i ThUi L*_ u@** AL UL4Ti?t@|ic |i €h4 uhL?| *L@_t i TiU|i_ u|hi U@?}it ? |i ?@|L? h@|i

?|L eR|

5TTLti |@| ?t|i@_ Lu @_LT|?} E. i @_ ThLUii_i_ @t ? |i *|ih@|hic M) @tt4?} |i t|@|U ThUiT_@|?} tUi4ic ES Ai?c |i @?@*L} i ThittL? |L E tG

eR|' .|3 % r|n " [ ,' Eq1R,E r|n, r|n,3 n " [ ,' Eq1R, Z|n, &  E2

46_{E| cqrqvwrfkdvwlf* zh phdq rqo| wkdw wkh djjuhjdwh vkrfn lv khog dw lwv xqfrqglwlrqdo phdq1}

Wkh lglrv|qfudwlf vkrfnv dvvrfldwhg zlwk Fdoyr sulflqj duh qrq0wulyldo udqgrp yduldeohv lq wkh qrqvwrfkdvwlf yhuvlrq ri wkh prgho1

`| |t tTiU€U@|L?c |i €h4 uhL?| *L@_t i TiU|i_ u|hi U@?}it ? |i ThUi *ii*c h@|ih |@? |i ?@|L? h@|i AL U*@hu) |i ?@|hi Lu uhL?| *L@_?} ?_ih |i _gihi?| T_@|?}

tUi4itc 4@}?i .|3 Z|' .|3 Z|n : f `| tTiU€U@|L? E.c c|nhtit M) |i @4L?|

Lu ?@|L? @| |4i |c tL |ihi t ?L ?ii_ |L uhL?| *L@_ |i i TiU|i_ ?@|L? ?|L eR| W?

UL?|h@t|c | |i t|@?_@h_ tTiU€U@|L? ESc c|n _Lit ?L| @_t| ? hitTL?ti |L Z|c tL

|i €h4 @t @? ?Ui?|i |L uhL?| *L@_ .|3 Z|n _hiU|*) ?|L eR|

W| uL**Lt uhL4 i**!?L? hit*|t ? |i *|ih@|hi |@| E U@? Mi i Thitti_ @tGe

|'  E  1R   |   3bs _{n 1} REZ|3|3  3bs 3bs  E #_?} M) |c *?i@h3?} @?_ hi@hh@?}?}c i LM|@?G eR| ' _{  1}1R R E Z| Z|3  Ee

+i*@|L?t E @?_ Ee 4T*)G

Z|' _{ n q} Z|3n _{ n q}q .|3 Z|nnE  q1_{E n q 1}RE  1R

R .|3 r| ED 5L*?} |t uLh Z| Z|3c 4TLt?} .|3qE Z|n  Z|n3 $ fc i LM|@?G Z| Z|3 ' E  q1R₁E  1R R .|3 " [ 'f q _r |n ES

Ai @?@*L} i ThittL?tc LM|@?i_ t?} |i t|@|U ThUiT_@|?} tUi4ic ESc @hiGD

Z|' q.|3 Z|nnE  q1R₁E  1R R .|3 r| E. Z|' E  q1R₁E  1R R .|3 " [ 'f q _r |n EH

AL 4L|@|i Lh ?|ihit| ? |i _)?@4U ThUiT_@|?} tUi4ic UL?t_ih |i hi_Ui_ uLh4 uLh ?@|L?c E.c 4T*i_ M) |i t|@?_@h_c t|@|U ThUiT_@|?} tUi4i |Lht

47_{Vhh/ iru h{dpsoh/ Fdoyr +4<;6,1}

48_{Wkh dqdorj h{suhvvlrq wr +6147, lv es}

w@ 4ssaw=

*!i 6hih @?_ LLhi EbbD @?_ B@* @?_ Bih|*ih Ebbb @h}i |@| |i @Mti?Ui Lu *@}}i_ ?@|L? ? E. Thii?|t |i 4L_i* uhL4 Mi?} @M*i |L @UUL?| uLh |i LMtihi_ _i}hii Lu tih@* ULhhi*@|L? ? ?@|L? Aiti @|Lht 4L_u) |i @*L uh@4iLh! ? ?L?|h@*

@)t |L ?_Ui @ *@}}i_ ?@|L? |ih4 ?|L E.S _{t U@? Mi tii? uhL4 EDc |i _)?@4U}

ThUiT_@|?} tUi4i ThL_it @? @*|ih?@|i @) |L @UUL4T*t |t. _{W?|ihit|?}*)c |i UL}

iUi?|t L? *@}}i_ @?_ u|hi ?@|L? ? ED h|@**) UL?U_i | |i @*it it|4@|i_

M) B@* @?_ Bih|*ih Ebbb @?_ |i @*i Lu %2 Lu|i? @tt4i_ ? |i *|ih@|hiH

`i UL?U*_i |t tMtiU|L? M) i4T@t3?} |hii hit*|t 6ht|c ?_ih i|ih tTiU€U@|L?

Z| _Lit ?L| hitTL?_ |L @ TihL_ | 4L?i|@h) TL*U) tLU! 5Lc |i 4L_i* t UL?tt|i?|

| @ !i) _i?|u)?} hit|hU|L? ? Lh i4ThU@* Lh!G |i ThUi *ii* _Lit ?L| hitTL?_ UL?|i4TLh@?iLt*) |L @ 4L?i|@h) TL*U) tLU! 5iUL?_c ?_ih i|ih tTiU€U@|L? ?@|L? _iTi?_t L? i TiU|i_ u|hi 4@h}?@* ULt|t +i*@|L? ED 4T*it |@| 4@h}?@* ULt| t @? ?Uhi@t?} u?U|L? Lu |i @}i h@|ic |i hi?|@* h@|i L? U@T|@* @?_ |i ?|ihit| h@|i W? tiU|L? 2 i uL?_ |@| ?@|L? hitTL?_t L?*) t*L*) |L @ 4L?i|@h) tLU! ||?} |iti LMtih@|L?t |L}i|ihc i @?|UT@|i |@| Lh iUL?L4i|hU it|4@|it ** T*@Ui tMt|@?|@*

i4T@tt L? |i ui@|hit Lu Lh 4L_i* |@| 4|i |i i TiU|i_ u|hi hitTL?tit Lu o&

|c |@?_

-||L @ 4L?i|@h) TL*U) tLU! Ah_c uLh @?) }i? ThLUitt _itUhM?} r|hi*@|L?t ES @?_

EH 4T*) |@| ?@|L? ** Mi 4Lhi ?ih|@* ?_ih |i _)?@4U ThUiT_@|?} tUi4i |@? ?_ih |i t|@|U ThUiT_@|?} tUi4i

49_{Dqrwkhu frqfhuq kdv ehhq udlvhg zlwk wkh Fdoyr sulflqj vfkhph1 Ixkuhu dqg Prruh +4<<8,}

dqg rwkhuv dujxh wkdw wkh vwdqgdug irupxodwlrq frxqwhuidfwxdoo| lpsolhv wkdw lqdwlrq ohdgv rxwsxw1 Krzhyhu/ dv Jdol dqg Jhuwohu +4<<<, srlqw rxw/ wklv uhvwv rq d vshflfdwlrq lq zklfk

avw lv phdvxuhg e| wkh rxwsxw jds1 Jdol dqg Jhuwohu +4<<<, srlqw rxw wkdw wklv fulwlflvp grhv

qrw dsso| wr prghov olnh rxuv lq zklfk avw fruuhvsrqgv wr uhdo pdujlqdo frvw1 Lq dgglwlrq/ wkh|

surylgh hylghqfh lq vxssruw ri vshflfdwlrqv olnh wklv1

4:_{Edoo +4<<7, dqg Pdqnlz +5333, dqg rwkhuv kdyh udlvhg dqrwkhu remhfwlrq wr Fdoyr0vw|oh}

vwlfn| sulfh prghov= d fuhgleoh glvlqdwlrq lv dvvrfldwhg zlwk dq h{sdqvlrq lq hfrqrplf dfwlylw|1 Wklv fulwlflvp lv edvhg rq d yhuvlrq ri +614:, lq zklfk d phdvxuh ri wkh rxwsxw jds dsshduv lqvwhdg ri pdujlqdo frvwv/ av= Lw lv qrw fohdu wkdw wkhlu fulwlflvp dssolhv wr rxu prgho1 Iluvw/ zh lqfrusrudwh pdujlqdo frvwv dqg qrw wkh rxwsxw jds1 Vhfrqg/ rxu phdvxuh ri pdujlqdo frvw lqfoxghv wkh lqwhuhvw udwh1 Lq rxu prgho/ zh frqmhfwxuh wkdw d fuhgleoh glqvlqdwlrq zrxog eh dvvrfldwhg zlwk d wudqvlwru| ulvh lq wkh lqwhuhvw udwh dqg wkhuhiruh d ulvh lq pdujlqdo frvwv1 Vr/ lw lv srvvleoh wkdw rxu prgho lv qrw vxemhfw wr wklv fulwlflvp1 Wklv lv dq lqwhuhvwlqj lvvxh zklfk zh ohdyh wr ixwxuh uhvhdufk1

4;_{Vhh Fdvduhv dqg PfFdooxp +5333,/ Pdqnlz +5334, dqg Zdovk +4<<;/ s1 5570558,1}

 OLtiL*_t

Aihi t @ UL?|?4 Lu LtiL*_tc ?_i i_ M)  5 Efc  Ai | _{LtiL*_ 4@!it @}

ti^i?Ui Lu _iUtL?t _h?} i@U TihL_ 6ht|c | 4@!it |t UL?t4T|L? _iUtL?c |t U@T|@* @UU4*@|L? _iUtL?c @?_ | _iU_it L 4@?) ?|t Lu U@T|@* tihUit |L tTT*) 5iUL?_c | ThU@tit tiUh|it Lti T@)Lgt @hi UL?|?}i?| TL? i|ih | U@? hiLT|43i |t @}i _iUtL? Ah_c | ti|t |t @}i h@|i @u|ih €?_?} L| i|ih | U@? hiLT|43i Lh ?L| 6Lh|c | hiUiit @ *4Tt4 |h@?tuih uhL4 |i 4L?i|@h) @|Lh|) 6?@**)c | _iU_it L 4U Lu |t €?@?U@* @tti|t |L L*_ ? |i uLh4 Lu _iTLt|t | @ €?@?U@* ?|ih4i_@h) @?_ L 4U |L L*_ ? |i uLh4 Lu U@t

5?Ui |i ?Uih|@?|) u@Ui_ M) |i LtiL*_ Lih i|ih | U@? hiLT|43i |t @}i t _Lt)?Uh@|U ? ?@|hic LtiL*_t Lh! _gihi?| @4L?|t @?_ i@h? _gihi?| @}i h@|it 5Lc ? Th?UT*i |i) @hi @*tL i|ihL}i?iLt | hitTiU| |L UL?t4T|L? @?_ @tti| L*_?}t  t|h@}|uLh@h_ i |i?tL? Lu @h}4i?|t ? ,hUi}c Oi?_ihtL? @?_ wi? E2fff @?_ `LL_uLh_ EbbSc it|@M*t |@| |i i t|i?Ui Lu t|@|i UL?|?}i?| tiUh|it i?thit |@| ? i^*Mh4 LtiL*_t @hi L4L}i?iLt | hitTiU| |L UL?t4T|L? @?_ @tti| L*_?}t +iiU|?} |t hit*|c Lh ?L|@|L? @tt4it |@| LtiL*_t @hi L4L}i?iLt | hitTiU| |L UL?t4T|L? @?_ @tti| L*_?}tc @?_ i|ihL}i?iLt | hitTiU| |L |i @}i h@|i |@| |i) i@h? @?_ Lht Lh!i_

Ai Thiuihi?Uit Lu |i | _{LtiL*_ @hi }i? M)G}

. |3 " [ ,'f q,3|_dES

|n,  KS|n,3  5Ec|n, n E^|n,o c Eb

ihi .|3 t |i i TiU|@|L? LTih@|Lhc UL?_|L?@* L? @}}hi}@|i @?_ LtiL*_  _Lt)?

Uh@|U ?uLh4@|L? T |Lc @?_ ?U*_?}c |4i |( S|_i?L|it |4i | UL?t4T|L?( | _i?L|it

|4i | Lht Lh!i_( ^|  '|*| _i?L|it hi@* U@t M@*@?Uit( @?_ '| _i?L|it ?L4?@* U@t

M@*@?Uit

`i? K : fc Eb @**Lt uLh @M| uLh4@|L? ? UL?t4T|L? Thiuihi?Uit |Lht tU @t 6hih E2fffc @?_ U@**4 @?_ i*tL? EbbH @i @h}i_ |@| |t t 4TLh|@?| uLh ?_iht|@?_?} |i 4L?i|@h) |h@?t4ttL? 4iU@?t4 ?i @) |L 4L|@|i |ih @h}4i?| t |L hiU@** |@|c @UULh_?} |L Lh it|4@|itc @ TLt|i 4L?i|@h) TL*U) tLU! *i@_t |L @ Tihtt|i?| _iU*?i ? |i hi@* ?|ihit| h@|i @?_ @ 4Tt@Ti_ hti ? UL?t4T|L?  4L_i* | t|@?_@h_c |4itiT@h@M*i Thiuihi?Uit U@??L| Mi 4@_i UL?tt|i?| | |t T@||ih? At t MiU@ti LtiL*_ LT|43@|L? 4T*it |@| @ *L hi@* ?|ihit| h@|i t @ttLU@|i_ | } Uhhi?| UL?t4T|L? hi*@|i |L |i u|hi |c @UULh_?} |L Lh it|4@|itc @u|ih @ 4L?i|@h) TL*U) tLU! Uhhi?| UL?t4T|L? t *L hi*@|i |L |i u|hi  4L_i* | @M| Tihtt|i?Ui Lih|h?t |i 4T*U@|L? Lu t|@?_@h_ 4L_i*t MiU@ti ? igiU| | hiT*@Uit

|i *ii* Lu UL?t4T|L? | |t }hL| h@|i ? |i |*|) u?U|L? 5Lc @ *L hi@* ?|ihit| h@|i t @ttLU@|i_ | } Uhhi?| UL?t4T|L? }hL| hi*@|i |L |i u|hi  @t ? |i _@|@

Ai LtiL*_<t @tti| iL*|L? i^@|L? t }i? M)G

|n ' -|d| '|n E>| |@o n c|n '|n `c|c| E2f n-& ||7&|n (| |  |n S|n @E|7&|  

Oihic | t |i LtiL*_<t Mi}???} Lu TihL_ | t|LU! Lu 4L?i)c `c|c| t |4i | *@MLh

?UL4i W? @__|L?c 7&|c (| @?_ c| _i?L|ic hitTiU|i*)c |i T)tU@* t|LU! Lu U@T|@*c €h4

ThL€|t @?_ |i ?i| U@t ?L uhL4 T@h|UT@|?} ? t|@|iUL?|?}i?| tiUh|it @| |4i |

Ai @h@M*i >| hiThiti?|t |i }hLtt }hL| h@|i Lu |i iUL?L4)_i Tih U@T|@ t|LU! Lu

4L?i)c @

| Ai ^@?||)c E>| |@ t @ *4Tt4 T@)4i?| 4@_i |L LtiL*_t M) |i

4L?i|@h) @|Lh|) Ai ^@?||)c | |^|n E>| |@c t _iTLt|i_ M) |i LtiL*_

| @ €?@?U@* ?|ih4i_@h)c ihi | i@h?t |i }hLtt ?L4?@* h@|i Lu ?|ihit|c -|

Ai hi4@??} |ih4t ? E2fc @t_i uhL4 |S|c Tih|@? |L |i t|LU! Lu ?t|@**i_ U@T|@*c

U i @tt4i t L?i_ M) |i LtiL*_ Ai LtiL*_<t t|LU! Lu U@T|@* iL*it @UULh_?} |LG

7&|n' E  B7&|n 8 E|c |3 E2

Oihic B _i?L|it |i T)tU@* h@|i Lu _iThiU@|L? @?_ |_i?L|it |4i | ThU@tit Lu ?it|4i?|

}LL_t Ai u?U|L?c 8c t44@h3it |i |iU?L*L}) U |h@?tuLh4t Uhhi?| @?_ T@t| ?it|4i?| ?|L ?t|@**i_ U@T|@* uLh ti ? |i uL**L?} TihL_ `i _tUtt |i ThLTih|it Lu 8 Mi*L

@T|@* tihUitc &|c @hi hi*@|i_ |L |i T)tU@* t|LU! Lu U@T|@* M)

&| ' |7&|

Oihic | _i?L|it |i |*3@|L? h@|i Lu U@T|@*c U i @tt4i t ti| M) |i LtiL*_b

W? E2fc -&

||7&| hiThiti?|t |i LtiL*_<t i@h??}t uhL4 tTT*)?} U@T|@* tihUit Ai

?Uhi@t?}c UL?i u?U|L?c @E|7&|c _i?L|it |i ULt|c ? ?|t Lu UL?t4T|L? }LL_tc Lu

ti||?} |i |*3@|L? h@|i |L | h 4L|@|L? uLh @**L?} U@T|@* tihUit |L Mi i*@t|U t

|LuL*_ 6ht|c | _@4Tt 4Li4i?|t ? 4@h}?@* ULt|t M) hi_U?} U|@|L?t ? |i hi?|@* h@|i Lu U@T|@* 5iUL?_c | hi_Uit |i u@** ? *@MLh ThL_U||) |@| L*_ L|ihti LUUh

4<_{Rxu dvvxpswlrq wkdw krxvhkrogv pdnh wkh fdslwdo dffxpxodwlrq dqg xwlol}dwlrq ghflvlrqv lv}

d pdwwhu ri frqyhqlhqfh1 Dw wkh frvw ri d pruh frpsolfdwhg qrwdwlrq/ zh frxog zrun zlwk dq dowhuqdwlyh ghfhqwudol}dwlrq vfkhph lq zklfk upv pdnh wkhvh ghflvlrqv1

@u|ih @ TLt|i 4L?i|@h) TL*U) tLU!2f

W? |i hi4@?_ih Lu |t tiU|L?c i Mhi) _tUtt |i €ht| Lh_ih UL?_|L?t Lu |i Lti

L*_ Ai €ht| Lh_ih UL?_|L? uLh S| tG

.|3Sc|' .|3|c E22

ihi | ' v||c @?_ v| t |i @*i Lu @ _L**@h |L |i LtiL*_ Ai @h@M*ic v|c t |i

4*|T*ih L? E2f ? |i w@}h@?}@? hiThiti?|@|L? Lu |i LtiL*_ ThLM*i4 W| t i@t)

|L ihu) |@| v| t @ u?U|L? Lu |i Uhhi?| TihL_ hi@*3@|L? Lu >| W? @__|L?c Sc| t |i

hi@*3i_ @*i Lu |i 4@h}?@* |*|) Lu UL?t4T|L? @| _@|i |G

Sc| ' Y ES|_YS KS|3

|  K.|

Y ES|n KS|

YS|  E2

,^@|L? E22 4T*it |@| ? |i @Mti?Ui Lu ?Uih|@?|)c | L*_ Mi |i 4@h}?@* |*|)

Lu UL?t4T|L?

Ai €ht| Lh_ih UL?_|L? uLh |n t }i? M)G

|' q.||n-_Z|n

|nc Z|n'

|n

|  E2e

At i^@|L? 4T*it |@| |i @*i Lu L?i _L**@h ? |i Uhhi?| TihL_ t i^@* |L |i Thiti?| _tUL?|i_ @*i Lu |i _L**@ht L?i LM|@?t M) _iTLt|?} @ _L**@h ? ?i | TihL_<t €?@?U@* 4@h!i|

 Ai `@}i #iUtL?

t ? ,hUi}c Oi?_ihtL? @?_ wi? E2fffc i @tt4i |@| |i LtiL*_ t @ 4L?LTL*) tT

T*ih Lu @ _gihi?|@|i_ *@MLh tihUic | W| ti**t |t tihUi |L @ hiThiti?|@|ic UL4Ti||i

€h4 U |h@?tuLh4t | ?|L @? @}}hi}@|i *@MLh ?T|c u|c t?} |i uL**L?} |iU?L*L})G

u| ' ] _ f   b | _ b 

53_{Iru erwk wkhvh hhfwv wr eh rshudwlyh/ x}

w pxvw ulvh lq wkh shulrg diwhu dq h{sdqvlrqdu|

prqhwdu| srolf| vkrfn1 Wr khos jhqhudwh wklv uhvxow/ lw lv xvhixo wr dvvxph wkdw wkh frvw ri ydu|lqj fdslwdo xwlol}dwlrq wdnhv wkh irup ri orvw frqvxpswlrq jrrgv1 Li/ iru h{dpsoh/ wkh frvw zhuh d

kljkhu fdslwdo ghsuhfldwlrq udwh/ wkhq xw frxog dfwxdoo| idoo diwhu dq h{sdqvlrqdu| prqhwdu|

srolf| vkrfn1 Wklv lv ehfdxvh lq wkh suhvhqfh ri lqyhvwphqw dgmxvwphqw frvwv wkh vkdgrz ydoxh ri lqvwdoohg fdslwdo ulvhv diwhu d srvlwlyh prqhwdu| vkrfn1 Wklv zrxog lqfuhdvh wkh frvw ri xwlol}lqj fdslwdo1

Ai _i4@?_ Uhi uLh | t }i? M)G | '  `| `|  b b3 u|c   b 4c E2D

ihi `| t |i @}}hi}@|i @}i h@|ic ic |i ThUi Lu u|c U t hi*@|i_ |L ?__@*

LtiL*_ @}itc `|c @ |i hi*@|L?tTG

`| ' ]  f E`|  3b _ 3b  E2S

Ai LtiL*_ |@!it u| @?_ `| @t }i?

OLtiL*_t ti| |ih @}i h@|i @UULh_?} |L @ @h@?| Lu |i 4iU@?t4 ti_ |L 4L_i*

ThUi ti||?} M) €h4t W? i@U TihL_c @ LtiL*_ u@Uit @ UL?t|@?| ThLM@M*|)c   1c Lu

Mi?} @M*i |L hiLT|43i |t ?L4?@* @}i Ai @M*|) |L hiLT|43i t ?_iTi?_i?| @UhLtt LtiL*_t @?_ |4i `i UL?t_ih |L tTiU€U@|L?t Lu @| @TTi?t u @ LtiL*_ U@??L| hiLT|43i |t @}i Ai €ht| tTiU€U@|L? ULhhitTL?_t |L |i t|@?_@h_ L?i ti_ ? |i *|ih@|hic @UULh_?} |L U

`|' 7Z`c|3 E2.

W? |i tiUL?_ tTiU€U@|L?c |i | _{LtiL*_ 4t| ti| |t @}i @UULh_?} |LG}

`c| ' Z|3`c|3 E2H

hLUii_?} @t ? Lh _tUttL? Lu ?|ih4i_@|i }LL_ €h4tc i uLUt L? tTiU€U@|L?

E2H wi| `| _i?L|i |i @*i Lu `| ti| M) @ LtiL*_ |@| U@? hiLT|43i |t @}i h@|i

@| |4i | h ?L|@|L? _Lit ?L| @**L `| |L _iTi?_ L?  At t MiU@ti @** LtiL*_t

|@| U@? hiLT|43i |ih @}i ULLti |i t@4i @}i2 _{Ai €ht| Lh_ih UL?_|L? @ttLU@|i_}

| `| tG .|3 " [ ,'f E1q,c|n,|n, %  `|f|, |n,  b 5c|n, |n, & ' fc E2b

ihic f|c, t _i€?i_ ? Eb AL ?_iht|@?_ E2bc ?L|i |@| `| ?i?Uit LtiL*_

|*|) L?*) @t *L?} @t | U@??L| hiLT|43i |t @}i h@|i Ai ThLM@M*|) |@| |t @TTi?t

uLh , TihL_t t E1,c ? U U@ti |i LtiL*_<t @U|@* @}i h@|i t `|f|, Ai Thiti?Ui

Lu E1, ? E2b @t |i igiU| Lu tL*@|?} u|hi hi@*3@|L?t Lu _Lt)?Uh@|U ?Uih|@?|)

ihi `| UL?|?it |L @giU| |i LtiL*_<t |*|)

54_{Vhh wkh Dsshqgl{ iru d surri1 Wklv uhvxow pluuruv uhvxowv lq Hufhj/ Khqghuvrq/ dqg Ohylq}

+5333, dqg Zrrgirug +4<<9,1

L|i |@| i? 1 ' fc E2b hi_Uit |LG  `| |  b 5c| .|3Sc| ' f Ef

Oihic i @i |@!i? ?|L @UUL?| E22c @?_ |i u@U| |@| `|c c|c 5c|c | @hi ?L| u?U|L?t

Lu |i TihL_ | hi@*3@|L? Lu 4L?i) }hL| UULh_?} |L Efc |i LtiL*_ ti|t |t

hi@* @}i i^@* |L @ UL?t|@?| 4@h!Tc bc Lih |i i TiU|i_ 4@h}?@* h@|i Lu tMt|||L?

Mi|ii? UL?t4T|L? @?_ *ithi +L}*) tTi@!?}c E2b 4T*it |@| i? 1 : fc |i

LtiL*_ ti|t @ i}|i_ @ih@}i Lu Ef Lih |4i |L 3ihL 2 +i@* @*@?Uit

Ai LtiL*_<t €ht| Lh_ih UL?_|L? uLh '| tG

_E^

| n |' |-| E

At i ThittL? L*_t uLh i@U TLttM*i hi@*3@|L? Lu |i Uhhi?| TihL_ 4L?i) }hL| h@|i MiU@ti |i U@t M@*@?Ui _iUtL? t 4@_i @u|ih |i Uhhi?| TihL_ 4L?i) }hL| h@|i t hi@*3i_ UULh_?} |L E |i 4@h}?@* |*|) Lu @ _L**@h @**LU@|i_ |L U@t M@*@?Uit 4t| i^@* |i 4@h}?@* |*|) Lu @ _L**@h @**LU@|i_ |L |i €?@?U@* ?|ih4i_@h) +i*@|L? E t |i 4L?i) _i4@?_ i^@|L? ? Lh 4L_i*

 W?it|4i?|

Ai €ht| Lh_ih UL?_|L?t uLh 7&|n @?_ | 4T*)

.|3|' q.|3|n



|no&|n @E|n n &_c|nE  B

&_c|



c E2

@?_G

.|3| ' .|3d|&_c|8_c|n q_|n_&c|n8_2c|no  E

Oihic 8c| t |i T@h|@* _ih@|i Lu 8E|c |3 | hitTiU| |L |t | @h}4i?|c  ' c 2

*tLc &_c| t |i t@_L @*ic ? UL?t4T|L? ?|tc Lu @ ?| Lu 7&_|n @t Lu |i |4i |@|

|i TihL_ | ?it|4i?| @?_ U@T|@* |*3@|L? _iUtL?t @hi 4@_i W| t @| |i ThUi Lu

?t|@**i_ U@T|@* L*_ Mi u |ihi ihi @ 4@h!i| uLh 7&|n @| |i Mi}???} Lu TihL_ |

AL ?_iht|@?_ |i ,*ih i^@|L? uLh 7&|nc ?L|i |@| |i *iu| t_i Lu E2 t |i 4@h}?@*

ULt| Lu tTi?_?} L?i ?| Lu UL?t4T|L? L? 7&|n Ai h}| t_i t |i hi|h? |L |t ?it|

4i?| Ai LMiU| ? t^@hi Mh@U!i|t t |i h@|i Lu hi|h? L? U@T|@*c ? ?|t Lu UL?t4T|L? }LL_t Ai L|ih |ih4 UL?ih|t |i hi|h? ?|L 4@h}?@* |*|) ?|t

AL ?_iht|@?_ |i ,*ih i^@|L? uLh |c ?L|i |@| |i *iu| t_i Lu E t |i 4@h}?@*

ULt| Lu @ ?| Lu ?it|4i?| }LL_t Oihi i ti |i u@U| |@| |i ThUi Lu ?it|4i?| }LL_t ? |ih4t Lu UL?t4T|L? t ?|) AL ?_iht|@?_ |i h}| t_i Lu Ec ?L|i |@| @? i |h@

?| Lu ?it|4i?| }LL_t ThL_Uit 8c| i |h@ ?|t Lu 7&|n Ai @*i Lu |iti }LL_tc ?

|*|) |ih4tc t &_c|8_c|._|3_| ? ?Uhi@ti ? _|@*tL @giU|t |i ^@?||) Lu ?t|@**i_ U@T|@*

ThL_Ui_ ? |i ?i | TihL_ M) 82c|n Ai *@t| |ih4 ? E 4i@thit |i |*|) @*i Lu

|iti @__|L?@* U@T|@* }LL_t

`i ?L Mhi) _tUtt |i 4L|@|L? uLh ?ULhTLh@|?} @_t|4i?| ULt|t ?|L |i @?@* )tt UULh_?} |L Lh it|4@|it ? tiU|L? 2c @u|ih @ TLt|i 4L?i|@h) tLU! |i hi@* h@|i

Lu ?|ihit|c -|*Z|nc _hLTt uLh tiih@* ^@h|iht ? i4ThU@**) T*@tM*i 4L?i|@h) 4L_i*

tL*_ hiThL_Ui |t LMtih@|L? 5U @ 4L_i* t @*tL *!i*) |L 4T*) |@| |i h@|i Lu

hi|h? L? U@T|@* u@**t | -|*Z|n Lc tTTLti |ihi ihi ?L @_t|4i?| ULt|tc ic

&_c| ' _&c|n '  wi@?} @t_i 4Li4i?|t ? |i 4@h!T @?_ ? _|c |t UL*_ L?*) Mi

@UUL4T*ti_ M) @ u@** ? |i 4@h}?@* ThL_U| Lu U@T|@* At ? |h? hi^hit @ th}i ?

?it|4i?| At t @| i uL?_ ? Th@U|Uic ii? |L} |i 4@h!T @?_ | @hi uhii |L

@h) W? Lh ?4ihU@* t4*@|L?tc i uL?_ |@| |i th}i ? ?it|4i?| @?_ L|T| t UL?|ihu@U|@**) *@h}i Etii @*tL @hc UBh@||@? @?_ kiLic 2fff

Ai u?U|L?@* uLh4 uLh 8 ? E2 |@| i @_LT| t 4L|@|i_ M) Lh i4ThU@* €?_?} |@| ?it|4i?| i M|t @ 4Tt@Ti_ hitTL?ti |L @ 4L?i|@h) TL*U) tLU! h tTiU

€U@|L? uLh 8c U Ti?@*3it |i U@?}i ? |c t @ t|h@}|uLh@h_ @) |L @UUL44L_@|i

|t22

55_{Rwkhu dxwkruv/ vxfk dv Fkdul/ Nhkrh dqg PfJudwwdq +5333, dqg PfFdooxp dqg Qhovrq}

+4<<;, dgrsw vshflfdwlrqv zklfk shqdol}h wkh ohyho ri lqyhvwphqw1 Lq sudfwlfh zh irxqg wkdw lw lv glfxow wr dffrxqw iru wkh kxps0vkdsh uhvsrqvh ri lqyhvwphqw zlwk wkh odwwhu vshflfdwlrq1 Wklv qglqj lv wkh rxwfrph ri qxphulfdo h{shulphqwv lq zklfk zh dgrswhg wkh iroorzlqj vshflfdwlrq iru wkh fdslwdo dffxpxodwlrq whfkqrorj|=

nw.4 T+4  ,nw> lw>

zkhuh

T+|> }, @d4|#. d5}#4@#>

iru #  41 Khuh/ | ghqrwhv suhylrxvo| lqvwdoohg fdslwdo diwhu ghsuhfldwlrq dqg } ghqrwhv qhz

lqyhvwphqw jrrgv1 Wkh vfdoduv d4> d5 A 3 zhuh fkrvhq wr jxdudqwhh wkdw T| @ T} @ 4 lq

qrqvwrfkdvwlf vwhdg| vwdwh1 Zkhq # @ 4> wkh deryh whfkqrorj| fruuhvsrqgv wr wkh frqyhqwlrqdo olqhdu fdslwdo dffxpxodwlrq htxdwlrq1 Lq wkh fdvh ri dgmxvwphqw frvwv/ # ? 4> wkh pdujlqdo surgxfw ri qhz lqyhvwphqw jrrgv lv ghfuhdvlqj lq wkh rz ri lqyhvwphqw1 Wklv whfkqrorj| kdv mxvw wkh rqh iuhh sdudphwhu/ #= Zh irxqg wkdw iru d odujh udqjh ri vhwwlqjv ri # rxu prgho kdv wkh lpsolfdwlrq wkdw wkh lqyhvwphqw lpsdfw ri d srvlwlyh prqhwdu| srolf| vkrfn lv juhdwhvw lq wkh shulrg zkhq lqyhvwphqw fdq uvw uhvsrqg +l1h1/ wkh shulrg diwhu wkh prqhwdu| srolf| vkrfn,1

e @T|@* N|*3@|L?

Ai ,*ih i^@|L? @ttLU@|i_ | LtiL*_<t U@T|@* |*3@|L? _iUtL? tG

.|3|o&|  @E|' f Ee

UULh_?} |L |t i ThittL?c |i i TiU|i_ 4@h}?@* Mi?i€| Lu h@t?} |*3@|L? 4t| i^@* |i @ttLU@|i_ i TiU|i_ 4@h}?@* ULt| u|ih *?i@h3?} |t i ThittL? @ML| ?L?t|LU@t|U t|i@_) t|@|i Etii |i TTi?_ c i LM|@?G

.|3 o|& j@ |' f ED

Oihic j@ _i?L|it @*@c @?_ @c @ _i?L|i |i €ht| @?_ tiUL?_ _ih@|it Lu @c i@*@|i_ ?

t|i@_) t|@|ic hitTiU|i*)2 _{6hL4 |t i U@? tii |@| uLh t4@** @*it Lu j}

@c .| o|n& ' f uLh

 :  +iU@** |@| r|n t @? ?Uhi@t?} u?U|L? Lu o|n& Etii ED 5Lc @**L?} uLh U@T|@*

|*3@|L? @?_ @ *L @*i Lu j@ i*Tt 4|i |i hitTL?ti Lu 4@h}?@* ULt| @?_ ?@|L? |L @

4L?i|@h) TL*U) tLU! Etii ES @?_ EH e L?i|@h) @?_ 6tU@* L*U)

+iU@** |@| ? Lh i4ThU@* Lh! i hiThiti?| 4L?i|@h) TL*U) M) E2 t i _tUtt

|ihic i ?|ihThi| |t h*i @t 4i@??} |@| |i 4L?i|@h) @|Lh|) @**Lt >| ' |n*|

|L @_t| ? @ @) U i?thit |@| E2 L*_t At ? |h? hi^hit |@| >|hitTL?_ ? @

T@h|U*@h @) |L |i Uhhi?| @?_ T@t| @*it Lu @** |i tLU!t ||?} |i iUL?L4) 5?Ui |i L?*) tLU! i @hi UL?t_ih?} t @ tLU! |L 4L?i|@h) TL*U)c |i hiThiti?|@|L? Lu 4L?i|@h) TL*U) |@| i @_LT| ? Lh 4L_i* t }i? M)G

>| ' > n wf0|n w0|3n w20|32n  ES

Oihic > _i?L|it |i 4i@? }hL| h@|i Lu 4L?i) @?_ w t |i hitTL?ti Lu .|>|n |L @ |4i

| 4L?i|@h) TL*U) tLU! 6?@**)c i @tt4i |@| |i }Lih?4i?| @t @UUitt |L *4T t4 |@ it @?_ Thtit @ +U@h_@? €tU@* TL*U) N?_ih |t |)Ti Lu TL*U)c |i _i|@*t Lu |@ TL*U) @i ?L 4T@U| L? ?@|L? @?_ L|ih @}}hi}@|i iUL?L4U @h@M*it t @ hit*|c i

?ii_ ?L| tTiUu) |i _i|@*t Lu €tU@* TL*U)2e

56_{Khuh/ zh kdyh xvhg wkh idfw wkdw zh lpsrvh u}n _{@ d}3_{/ zkhuh u}n _{ghqrwhv wkh uhqwdo udwh rq}

fdslwdo lq vwhdg| vwdwh1

57_{Vhh Vlpv +4<<7, ru Zrrgirug +4<<7, iru d ixuwkhu glvfxvvlrq1}

D wL@? @h!i| *i@h?}c |i +itLhUi L?t|h@?| @?_ ,^*Mh4

6?@?U@* ?|ih4i_@hit hiUii | '| uhL4 LtiL*_t @?_ @ |h@?tuihc E>|  | uhL4

|i 4L?i|@h) @|Lh|) h ?L|@|L? ihi hiiU|t |i i^*Mh4 UL?_|L?c @

| ' |

6?@?U@* ?|ih4i_@hit *i?_ @** Lu |ih 4L?i) |L ?|ih4i_@|i }LL_ €h4tc U ti |i

u?_t |L T@) uLh u| wL@? 4@h!i| U*i@h?} hi^hit

`|u|' >|| '| E.

`i U@? ti |t i^@|L?c |L}i|ih | |i LtiL*_<t 4L?i) _i4@?_ i^@|L?c Ec |L ?_iht|@?_ L Lh 4L_i* @UUL?|t uLh |i it|4@|i_ ?i}@|i hitTL?ti Lu |i ?|ihit| h@|i |L @ TLt|i 4L?i|@h) TL*U) tLU! W? Lh 4L_i*c @? ?Uhi@ti ? |i 4L?i) tTT*) 4t|

Mi @MtLhMi_ M) LtiL*_t At t MiU@ti |i _i4@?_ uLh 4L?i) M) €h4tc `|u|c _Lit

?L| hitTL?_ |L @ TL*U) tLU! At hiiU|t Lh @tt4T|L? |@| UL?t4T|L?c ?it|4i?|

@?_ U@T|@* |*3@|L? @hi ti| ThLh |L @ 4L?i|@h) tLU! tL |@| u| t Thi_i|ih4?i_ 5?Ui

|i `|<t _L ?L| hitTL?_ |L @ 4L?i|@h) TL*U) tLU!c | uL**Lt uhL4 E2S |@| `| t @*tL

Thi_i|ih4?i_ 6hL4 E. | uL**Lt |@| @ TihL_ | 4L?i) ?iU|L? 4t| Mi u**) @MtLhMi_

M) LtiL*_t ? |i uLh4 Lu @? ?Uhi@ti ? U@t L*_?}tc '|

AL ?_iht|@?_ |i 4T@U| Lu |i hti ? '| L? -|c tTTLti uLh |i 4L4i?| |@| | t

UL?t|@?| 5?Ui | t Thi_i|ih4?i_c |i hti ? '| ULhhitTL?_t |L @ hti ? hi@* M@*@?Uit

UULh_?} |L Ec |i L?*) @) |L ?_Ui LtiL*_t |L ?Uhi@ti '|*|t uLh -||L u@** W?

Th@U|Ui i uL?_ |@| @| |i it|4@|i_ @*it Lu |i 4L_i* T@h@4i|iht |hitTL?_t hi*@|i*)

*||*i |L @ 4L?i|@h) tLU! tL |i ThiLt @h}4i?| U@T|hit |i M@tU uLhUit @| Lh! t

? t|@?_@h_ *4|i_ T@h|UT@|L? 4L_i*tc |i _hLT ? -| @htit MiU@ti @ tMti| Lu @}i?|t

4t| @MtLhM |i u** @4L?| Lu @? ?Uhi@ti ? |i 4L?i) tTT*) N?*!i |Lti 4L_i*tc ihi | t LtiL*_t |@| @MtLhM |i U@t

6?@**)c i ?L|i |@|c L|ih |?}t i^@*c |i _iU*?i ? |i ?|ihit| h@|i hi_Uit 4@h}?@* ULt| At ? |h? i*Tt |i 4L_i* }i?ih@|i @? ?ih|@* hitTL?ti Lu ?@|L? |L @ TLt|i 4L?i|@h) TL*U) tLU!

`| hitTiU| |L |i @}}hi}@|i hitLhUi UL?t|h@?|c ? |i @TTi?_ i LM|@? @? i  ThittL? |@| hi*@|it @}}hi}@|i UL?t4T|L? @?_ ?it|4i?| |L @}}hi}@|i *@MLh @?_ U@T|@*

tihUit2D _{W? |i @TTi?_ i @*tL uLh4@**) _i€?i @? i^*Mh4 uLh Lh 4L_i* iUL?L4)}

t?} @ t|@?_@h_ ti^i?UiLu4@h!i|t UL?UiT| W? @__|L? i _tUtt Lh UL4T|@|L?@*

58_{H{dfw djjuhjdwlrq lv qrw srvvleoh/ vlqfh wkhuh lv dq dgglwlrqdo whup lq wklv uhodwlrqvkls}

kdylqj wr gr zlwk wkh glvwulexwlrq ri sulfhv dqg zdjhv1 Krzhyhu/ dv vkrzq e| \xq +4<<9, dqg Hufhj/ Khqghuvrq dqg Ohylq +5333,/ wkdw whup grhv qrw dsshdu lq wkh olqhdu dssur{lpdwlrq ri wkh uhvrxufh frqvwudlqw derxw vwhdg| vwdwh1 Wkdw lv/ wr d uvw rughu dssur{lpdwlrq wkh djjuhjdwh uhvrxufh frqvwudlqw lv h{suhvvhg dv d ixqfwlrq lqyroylqj rqo| djjuhjdwh frqvxpswlrq/ lqyhvwphqw/ oderu dqg fdslwdo vhuylfhv1

t|h@|i}) uLh @TThL 4@|?} |@| i^*Mh4 At ?L*it |@!?} @ *?i@h @TThL 4@|L? @ML| |i ?L?t|LU@t|U t|i@_) t|@|i Lu |i iUL?L4) @?_ t?} |i tL*|L? 4i|L_ _t Utti_ ? ht|@?L E2ff

S 6?U|L?@* 6Lh4 tt4T|L?t

`i @tt4i |@| |i u?U|L?t U@h@U|ih3?} |*|) @hi }i? M)G E ' *L} E

5E ' fE2

 E ' ^Eu_3j3j^_^

 EH

W? @__|L?c ?it|4i?| @_t|4i?| ULt|t @hi }i? M)G

8E|c |3 ' E  7  | |3  |

`i hit|hU| |i u?U|L?c 7c |L t@|tu) |i uL**L?} ThLTih|itG 7E ' 7_{E ' fc @?_}

y  7_{E : f N?_ih Lh @tt4T|L?tc ? @ ?L?t|LU@t|U t|i@_) t|@|i 8}

 ' c 82 ' fc tL

|@| E 4T*it &_c| ' _&c|n '  W| t i@t) |L ihu) |@| |i t|i@_) t|@|i Lu |i 4L_i*

_Lit ?L| _iTi?_ L? |i @_t|4i?| ULt| T@h@4i|ihc y u ULhtic |i _)?@4Ut Lu |i 4L_i* @hi ?i?Ui_ M) y Bi? Lh tL*|L? ThLUi_hic ?L L|ih ui@|hit Lu |i 7 u?U|L? ?ii_ |L Mi tTiU€i_ uLh Lh @?@*)tt

`i 4TLti |L hit|hU|L?t L? |i U@T|@* |*3@|L? u?U|L?c @E| 6ht|c i hi^hi

|@| | '  ? t|i@_) t|@|i ) Eec |t t i^@*i?| |L @ ' o& 5iUL?_c i @tt4i

@E ' f N?_ih Lh @tt4T|L?tc |i t|i@_) t|@|i Lu |i 4L_i* t ?_iTi?_i?| Lu j@c _i€?i_

@u|ih ED Ai _)?@4Ut _L _iTi?_ L? j@ Bi? Lh tL*|L? ThLUi_hic i _L ?L| ?ii_

|L tTiUu) @?) L|ih ui@|hit Lu |i u?U|L?c @

e ,UL?L4i|hU i|L_L*L})

W? |t tiU|L? i _tUtt Lh 4i|L_L*L}) uLh it|4@|?} @?_ i@*@|?} Lh 4L_i* `i

T@h||L? |i 4L_i* T@h@4i|iht ?|L |hii }hLTt Ai €ht| }hLT t UL4TLti_ Lu qc kc Bc fc

^c b @?_ > `i ti| q ' f3f2Dc U 4T*it @ t|i@_) t|@|i @??@*3i_ hi@* ?|ihit| h@|i

Lu  TihUi?| hLUii_?} @t ? ht|@?Lc ,Ui?M@4 @?_ ,@?t Ebb.c i ti| k ' fSc U ULhhitTL?_t |L @ t|i@_) t|@|i t@hi Lu U@T|@* ?UL4i i^@* |L hL}*) S TihUi?| `i ti| B ' ff2Dc U 4T*it @? @??@* h@|i Lu _iThiU@|L? L? U@T|@* i^@* |L f TihUi?| At t hL}*) i^@* |L |i it|4@|i hiTLh|i_ ? ht|@?L @?_ ,Ui?M@4 Ebb2 Ai

T@h@4i|ihc fc @t ULti? |L 4T*) @ t|i@_) t|@|i @*i Lu u i^@* |L ?|) 54*@h*)c |i

T@h@4i|ih ^ @t ti| |L i?thi '* ' fee ? t|i@_) t|@|i At t i^@* |L |i h@|L Lu

 |L 2 @| |i Mi}???} Lu Lh t@4T*i TihL_ W? u@U| |i h@|L Lu  |L 2 i M|t

@ _L?@h_ |hi?_ ? |i _@|@ `i hi__ Lh @?@*)tt t?} _gihi?| @*it Lu ^ @?_ uL?_

|@| |i L?*) t}?€U@?| 4T@U| @t L? |i it|4@|i_ @*i Lu j^ Ai *@h}ih |i @tt4i_

@*i Lu ^c |i t4@**ih |i i*@t|U|) Lu 4L?i) _i4@?_ hi^hi_ |L 4@|U |i _@|@c ic |i

*@h}ih |i 4T*i_ @*i Lu j^ Ai T@h@4i|ihc >c @t ti| |L f.c U i^@*t |i TLt|@h

^@h|ih*) @ih@}i }hLtt }hL| h@|i Lu 2 | Lh @tt4i_ T@h@4i|ih @*itc |i t|i@_) t|@|i i*LU|) Lu 4L?i) t }i? M)G

t

 ' E>  ^ E  k

q

> ' fS

At t t*}|*) Mi*L |i @ih@}i @*ic feec Lu 2 i*LU|) ? Lh t@4T*i

`i ti| |i T@h@4i|ihc bc |L fD W? ?4ihU@* t4*@|L?t i uL?_ |@| Lh hit*|t

@hi hLMt| |L Tih|hM@|L?t ? |t T@h@4i|ih2S _{h tTiU€U@|L? Lu 5E 4T*it @ 6htU}

*@MLh tTT*) i*@t|U|) i^@* |L ?|) At i*@t|U|) t *L M) UL4T@htL? | |i @*it

@tt4i_ ? |i hi@* Mt?itt U)U*i *|ih@|hi2. _{OLiihc | t i** |? |i h@?}i Lu TL?|}

it|4@|it hiTLh|i_ ? |i *@MLh *|ih@|hi Etii +L|i4Mih} @?_ `LL_uLh_c bbb

Ai tiUL?_ }hLT Lu T@h@4i|iht U@h@U|ih3i 4L?i|@h) TL*U) ? |i 4L_i* `i ULLti

|iti M) hi^h?} |@| |i w<t ? ES UL?U_i i @U|*) | Lh it|4@|i Lu |i _)?@4U

hitTL?ti Lu |i }hL| h@|i Lu 4L?i) |L @ 4L?i|@h) TL*U) tLU! `i ThLUii_ @t ? k?} @?_ `@|tL? EbbS W? T@h|U*@hc i ?ULhTLh@|i ?|L |i 4L_i* |i |4i tihit hiThiti?|@|L?

uLh >| 4T*U| ? |i V+c @Mt|h@U|?} uhL4 ?L?4L?i|@h) TL*U) tLU!t wi| S _i?L|i |i

.| UL*4? Lu |i 4@|h  ? E22 Ai?c ti||?} ?L?4L?i|@h) tLU!t |L 3ihLc |i V+ ? E22 U@? Mi h||i?

t| ' t|3n  n et|3en S0| Ee

wi|  _i?L|i @ hL iU|Lh | 3ihLt @?_ @ t?}*i i*i4i?| UL?|@??} ?|) ? |i *LU@|L? Lu

t|UL?|@??} 4L?i) }hL|c ec t|' >| Ai t|LU@t|U ThLUitt uLh 4L?i) }hL| |@| t

?ULhTLh@|i_ ?|L |i 4L_i* t Ee | |i ?_iht|@?_?} |@| t|t _@|i | 4L?i) }hL|c

@?_ |hi@|?} |i L|ih @h@M*it ? t| @t ?uLh4@|L? @h@M*it tiu* uLh uLhiU@t|?} u|hi

@*it Lu t| `| |t ThLUi_hic |i 4L?} @ih@}i hiThiti?|@|L?c ESc Lu 4L?i)

}hL| ?ULhTLh@|i_ ?|L |i 4L_i* ULhhitTL?_t i @U|*) |L |i 4L?} @ih@}i hiThiti?|@|L? it|4@|i_ ? |i _@|@ ht|@?Lc ,Ui?M@4 @?_ ,@?t EbbH _itUhMi @ 4i|L_ uLh

59_{Kroglqj {hg wkh rwkhu sdudphwhu ydoxhv dw wkhlu ehqfkpdun ydoxhv uhsruwhg ehorz/ zh}

irxqg wkdw wkh lpsxovh uhvsrqvh ixqfwlrqv lpsolhg e| wkh prgho duh lqvhqvlwlyh wr ydoxhv ri z=

5:_{Iru h{dpsoh/ wkh Iulvfk hodvwlflw| lpsolflw lq wkh cglylvleoh oderu* prgho lq Fkulvwldqr dqg}

Hlfkhqedxp +4<<5, lv urxjko| 5=8 shufhqw1

@TThL 4@|?} |t 4L?} @ih@}i hiThiti?|@|L? ? @ T@ht4L?Lt @) Ai) €?_ |@| | t ?L| t|@|t|U@**) t}?€U@?|*) _gihi?| uhL4 |i 4L?} @ih@}i hiThiti?|@|L? }i?ih@|i_ M) @ €ht| Lh_ih @|Lhi}hittL? | ULiUi?| hL}*) i^@* |L fD

Ai |h_ }hLT Lu 4L_i* T@h@4i|iht tG

  Ebsc 1c 1Rc j^c yc Kc j@

Aiti ihi it|4@|i_ M) 4?43?} @ 4i@thi Lu |i _t|@?Ui Mi|ii? |i 4L_i* @?_ i4ThU@* 4T*ti hitTL?ti u?U|L?t wi| [E _i?L|i |i 4@TT?} uhL4  |L |i 4L_i* 4T*ti hitTL?ti u?U|L?tc @?_ *i| [ _i?L|i |i ULhhitTL?_?} i4ThU@* it|4@|it `i ?U*_i |i €ht| 2D i*i4i?|t Lu i@U hitTL?ti u?U|L? h it|4@|Lh Lu  t |i tL*|L? |LG

a ' 4?

 E [  [E

_T3_{E [  [E Ee2}

Oihic T t @ _@}L?@* 4@|h | |i t@4T*i @h@?Uit Lu |i [<t @*L?} |i _@}L?@* Aiti @h@?Uit @hi |i M@tt uLh |i UL?€_i?Ui ?|ih@*t hiTLh|i_ ? 6}hi  5Lc | |t ULUi Lu Tc  t igiU|i*) ULti? tL |@| [E *it @t 4U @t TLttM*i ?t_i |iti UL?€_i?Ui ?|ih@*t

D ,4ThU@* +it*|t

W? |t tiU|L? i @UUL4T*t |hii |?}t 6ht|c i _tUtt |i it|4@|i_ T@h@4i|ih @*it 5iUL?_c i @ttitt |i @M*|) Lu |i it|4@|i_ 4L_i* |L @UUL?| uLh |i 4T*ti hitTL?ti u?U|L?t _tUtti_ ? tiU|L? 2 Ah_c i _LU4i?| L |i _gihi?| ui@|hit Lu |i 4L_i* UL?|hM|i |L |t i4ThU@* TihuLh4@?Ui

D @h@4i|ih ,t|4@|it

Ai hL *@Mi*i_ Mi?U4@h!< ? A@M*i  t44@h3it Lh TL?| it|4@|it Lu |i T@h@4i|iht

? |i iU|Lhc  `| |i i UiT|L? Lu j@c t|@?_@h_ ihhLht @hi hiTLh|i_ ? T@hi?|itit2H

5;_{Khuh/ zh eulh| ghvfuleh krz zh frpsxwhg wkh vwdqgdug huuruv1 Ohw j+a> a#, @ 3 ghqrwh wkh}

uvw rughu frqglwlrq dvvrfldwhg zlwk wkh vroxwlrq wr wkh plqlpl}dwlrq sureohp lq +715,1 Khuh/

+a> a#, duh wkh hvwlpdwruv fruuhvsrqglqj wr wkh wuxh ydoxhv ri wkh sdudphwhuv/ +3_{> #}3_{,1 Wkh}

ixqfwlrq/ j> lpsolflwo| ghqhv d pdsslqj iurp #3 _{wr }3_{= Wkh Wd|oru vhulhv h{sdqvlrq ri wklv}

pdsslqj derxw wkh wuxh ydoxhv ri wkh sdudphwhuv/ lv zulwwhq/ j4+a 3, .j5+ a#  #3, @ 3> zkhuh

j4dqg j5duh wkh sduwldo ghulydwlyhv ri j zlwk uhvshfw wr  dqg #/ hydoxdwhg dw 3> #3+lq sudfwlfh/

wkhvh duh hydoxdwhg dw wkh srlqw hvwlpdwhv,1 Ohw G @ j4

4 j5= Wkhq/sW+a3, _d Q+3> GZG3,>

`i _L ?L| hiTLh| @ t|@?_@h_ ihhLh uLh j@ MiU@ti Lh it|4@|L? ThLUi_hi _hit |@|

T@h@4i|ih |L@h_t 3ihLc @| U TL?| |i @*}Lh|4 Mhi@!t _L? t @ hit*|c i t4T*)

ti| j@ ' ff @?_ LT|43i_ |i it|4@|L? Uh|ihL? Lih |i hi4@??} i*i4i?|t ? 

5i||?} j@ |L @ t4@** @*i ULhhitTL?_t |L |i @tt4T|L? |@| |i @_t|4i?| ULt| u?U|L?

L? U@T|@* |*3@|L? t ih) ?i@h*) *?i@h W? tiU|L?  i i T*@?i_ L *L @*it Lu j@

_@4Ti? 4Li4i?|t ? |i hi?|@* h@|i Lu U@T|@*c 4@h}?@* ULt|t @?_ ThUit @u|ih @ 4L?i|@h) TL*U) tLU!

`i ?L _tUtt |i hi4@??} T@h@4i|iht ? A@M*i  6ht|c Lh TL?| it|4@|i Lu 1

4T*it |@| @}i UL?|h@U|t *@t| L? @ih@}i  ^@h|iht 5iUL?_c Lh TL?| it|4@|i Lu

1R 4T*it |@| ThUi UL?|h@U|t *@t| L? @ih@}i 2 ^@h|iht Ah_c Lh it|4@|i Lu 1 t

t|@|t|U@**) t}?€U@?|*) _gihi?| uhL4 3ihLc *i 1R t L?*) 4@h}?@**) tL At t}}it|t

|@| t|U!?itt ? ?L4?@* @}it T*@) @? 4TLh|@?| hL*i ? |i 4L_i*<t i4ThU@* TihuLh4@?Uic *i t|U!?itt ? ?L4?@* ThUit _Lit ?L| `i i T*Lhi |t uh|ih Mi*L 6Lh|c |L

?|ihThi| |i TL?| it|4@|i Lu j^c | t tiu* |L *L}*?i@h3i |i 4L?i) _i4@?_ u?U|L?c

Ec 4TLt?} EHG ^| ' _j ^  --  - |n |   ED

Ai 4T*i_ ?|ihit| ti4i*@t|U|) Lu 4L?i) _i4@?_ t Y *L} ^

Y- '



ej^E-  c

L*_?}  UL?t|@?| Oihic i @i |@!i? ?|L @UUL?| |@| |i |4i TihL_ Lu |i 4L_i*

t ^@h|ih*) @?_ |i i*@t|U|) t 4i@thi_ | hitTiU| |L |i @??@*3i_ h@|i Lu ?|ihit| h T@h@4i|ih it|4@|it 4T*) |@| |t i*@t|U|) t fDc ic @ L?i TihUi?|@}i TL?| hti ? |i @??@*3i_ h@|i Lu ?|ihit| *i@_t |L @ fD TihUi?| hi_U|L? ? hi@* M@*@?Uit At i*@t|U|) t UL?t_ih@M*) t4@**ih |@? t|@?_@h_ it|4@|it hiTLh|i_ uLh t|@|U 4L?i) _i4@?_ i^@|L?t Lu |t uLh4 6Lh i @4T*ic |i @?@*L}Lt ?4Mih ? wU@t EbHH t Hf `i

uL?_ |@| Lh it|4@|i Lu j^ t _hi? Th4@h*) M) |i 4L_i*<t @||i4T| |L hiT*U@|i |i

?|@* hitTL?tit Lu |i ?|ihit| h@|i |L @ 4L?i|@h) TL*U) tLU! Etii Mi*L L?ti^i?|*)c i ?|ihThi| Lh ?|ihit| ti4i*@t|U|) @t Tih|@??} |L |i tLh|h? hitTL?ti Lu 4L?i) _i4@?_ At i*@t|U|) t Lu|i? it|4@|i_ |L Mi ^|i t4@** Etii ht|@?Lc ,Ui?M@4 @?_ ,@?tc bbb

zkhuh Z lv wkh +dv|pswrwlf, yduldqfh fryduldqfh pdwul{ risW+ a#  #3_{,= Wkh vwdqgdug huuruv}

uhsruwhg lq Wdeoh 4 duh wkh uhohydqw gldjrqdo whupv lq GZG3_{> diwhu wdnlqj vtxduh urrwv dqg}

glylglqj e|sW=

6u|c |L ?|ihThi| |i TL?| it|4@|i Lu yc i *L}*?i@h3i |i LtiL*_<t ,*ih i^@|L? uLh ?it|4i?|c Ec @ML| t|i@_) t|@|i |L LM|@?G

&_c| ' y._|3i =_| =_|3 q d =_|n =_|oj c tL |@|G =|' =|3n_y " [ 'f q_. |3 &_c|n

UULh_?} |L |t i ThittL?c *y t |i i*@t|U|) Lu ?it|4i?| | hitTiU| |L @ L?i TihUi?|

?Uhi@ti ? |i Uhhi?| ThUi Lu ?t|@**i_ U@T|@*2b _{`*i | t 4ThiUti*) it|4@|i_c Lh TL?|}

it|4@|i 4T*it |@| |t i*@t|U|) t i^@* |L f2H  4Lhi Tihtt|i?| U@?}i ? |i ThUi Lu U@T|@* ?_Uit @ *@h}ih TihUi?|@}i U@?}i ? ?it|4i?| At t MiU@ti @_t|4i?| ULt|t ?_Ui @}i?|t |L Mi uLh@h_ *LL!?} 6Lh i @4T*ic @ Tih4@?i?| L?iTihUi?| U@?}i ? |i

ThUi Lu U@T|@* ?_Uit @ * dyE  qo ' H TihUi?| U@?}i ? ?it|4i?|f

5 |c Lh TL?| it|4@|i Lu |i @M| T@h@4i|ih K t fS At t U*Lti |L |i TL?| it|4@|i Lu f. hiTLh|i_ ? L*_h?c ht|@?L @?_ 6tih E2ff ALti @|Lht @h}i |@| |i @M*|) Lu t|@?_@h_ }i?ih@* i^*Mh4 4L_i*t |L @UUL?| uLh |i i^|) Thi44 @?_ L|ih @tti| 4@h!i| t|@|t|Ut t UL?t_ih@M*) i?@?Ui_ M) |i Thiti?Ui Lu @M| uLh4@|L? ?

Thiuihi?Uit 6?@**)c |i it|4@|i_ @*i Lu bsc eDc t U*Lti |L |i @*i ti_ ? +L|i4Mih}

@?_ `LL_uLh_ EbbD i*Lc i _tUtt @| ui@|hit Lu |i _@|@ _hi |i it|4@|L?

Uh|ihL? |L |t @*i `i tL |@| |i !i) hL*i Lu bs t |L @**L |i 4L_i* |L @UUL?|

uLh |i hitTL?ti Lu *@MLh ThL_U||) |L @ 4L?i|@h) TL*U) tLU! Ai 4T*ti hitTL?ti

u?U|L?t Lu |i L|ih @h@M*it ? |i 4L_i* @hi ?ti?t|i |L @*|ih?@|i @*it uLh bs ii?

@*it @t *L @t fD

D2 hLTih|it Lu |i ,t|4@|i_ L_i*

Ai 4T*ti hitTL?ti u?U|L?t Lu |i it|4@|i_ 4L_i* @hi hiThiti?|i_ M) |i tL*_ *?it ? 6}hi   ?4Mih Lu hit*|t @hi Lh| i4T@t3?} ihi 6ht|c |i 4L_i* _Lit i** @| @UUL?|?} uLh |i _)?@4U hitTL?ti Lu |i N5 iUL?L4) |L @ 4L?i|@h) TL*U) tLU! `| |L i UiT|L?tc |i 4L_i* 4T*ti hitTL?tit *i |? |i |Lt|@?_@h_ _i@|L?

5<_{Uhfdoo wkdw xqghu rxu wlplqj dvvxpswlrqv Hw4Sn3>w@ Sn3>w1}

63_{Wkh olwhudwxuh rq Wrelq*v t dovr uhsruwv hpslulfdo hvwlpdwhv ri lqyhvwphqw hodvwlflwlhv1 Lw lv}

glfxow wr frpsduh wkhvh hvwlpdwhv zlwk rxuv/ krzhyhu1 Wklv lv ehfdxvh wkh Wrelq*v t olwhudwxuh

irfxvhv rq vshflfdwlrqv lq zklfk rqo| wkh fxuuhqw ydoxh ri aSn3_>w hqwhuv lqwr a~_w1 Iurp rxu

shuvshfwlyh/ wkh hodvwlflwlhv uhsruwhg lq wklv olwhudwxuh uhsuhvhqw d frpelqdwlrq ri v dqg wkh ghjuhh ri shuvlvwhqfh lq aSn3_>w=

UL?€_i?Ui ?|ih@* UL4T|i_ uhL4 |i _@|@ Ai i UiT|L?t @hi |@| 4L_i* L|T| hitTL?_t tL4i@| |LL t|hL?}*) @?_ ThL€|t |LL i@!*) ? |i €ht| )i@h 5iUL?_c |i 4L_i* tUUii_t ? @UUL?|?} uLh |i ?ih|@* hitTL?ti Lu ?@|L? W?_ii_c |ihi t ?L ?L|Ui@M*i hti ? ?@|L? ?|* hL}*) |hii )i@ht @u|ih |i TL*U) tLU! Ah_c |i 4L_i* }i?ih@|it @ ih) Tihtt|i?| hitTL?ti ? L|T|c | |i Ti@! hitTL?ti LUUhh?} @u|ih L?i )i@h u|ih |hii )i@htc |i TL*U) tLU! ?_Uit @ U4*@|i hti ? L|T| Lu  TihUi?| ih @*u Lu |t ?Uhi@ti LUUht @u|ih |i €ht| )i@h

6}hi 2 ThL_it @ _gihi?| @) Lu **t|h@|?} |i *@t| |L LMtih@|L?t Aihic i _tT*@) |i hitTL?ti Lu |i ThUi *ii*c |i 4L?i) t|LU! @?_ L|T| ? |i 4L_i* ,@U t i Thitti_ @t @ TihUi?| Lu |t *ii* @*L?} |i ?tLU!i_ }hL| T@| L|Ui L |i 4L?i) t|LU! htit |L |t Ti@! *ii* M) |i |h_ ^@h|ih @u|ih |i tLU! @?_ t hL}*) M@U! |L ihi | t|@h|i_ M) |i 4__*i Lu |i |h_ )i@h #itT|i |i ThL*L?}i_ hti ? |i 4L?i) t|LU!c |ihi t itti?|@**) ?L U@?}i ? |i ThUi *ii* | |i t@4i |4ic |ihi t @ ThL*L?}i_ MLL4 ? L|T| |@| *@t|t ii? @u|ih |i MLL4 ? |i 4L?i) tTT*) t Lih Ai Ti@! ? L|T| t @*4Lt| |Ui @t M} @t |i Ti@! ? |i 4L?i) tTT*)c | |i uLh4ih LUUhh?} L?i@*u )i@h @u|ih |i *@||ih

+i|h??} |L 6}hi c ?L|Ui |@| |i 4L_i* t @M*i |L @UUL?| uLh |i _)?@4U hitTL?ti Lu |i ?|ihit| h@|i |L @ 4L?i|@h) TL*U) tLU! L?tt|i?| | |i _@|@c @? i T@?tL?@h) 4L?i|@h) TL*U) tLU! ?_Uit @ t@hT _iU*?i ? |i ?|ihit| h@|i U |i? hi|h?t |L |t ThitLU! *ii* |? @ )i@h W| t ?|ihit|?} |@| @ TL*U) tLU! ?_Uit @ 4Lhi Tihtt|i?| igiU| L? L|T| |@? L? |i ?|ihit| h@|i W?_ii_c |i Ti@! igiU| L? L|T| LUUht L?i ^@h|ih @u|ih |i TL*U) @h@M*i @t hi|h?i_ |L |t t|i@_) t|@|i @*i 5Lc hi}@h_*itt Lu i|ih i 4i@thi TL*U) M) |i 4L?i) t|LU! Lh |i ?|ihit| h@|ic |i igiU|t Lu @ TL*U) tLU! L? @}}hi}@|i @h@M*it Tihtt| Mi)L?_ |i igiU|t L? |i TL*U) @h@M*i |ti*u At hiiU|t |i t|hL?} ?|ih?@* ThLT@}@|L? ? |i 4L_i*

i | ?L|i |@|c @t ? |i _@|@c |i hi@* @}i htit M) @ t4@** TLt|i @4L?| ? hitTL?ti |L |i TL*U) tLU! 6?@**)c UL?t4T|L?c ?it|4i?| @?_ ThL_U||) @** i M| Tihtt|i?|c 4Tt@Ti_ htit |@| @hi UL?tt|i?| | Lh it|4@|it

`i ?L @?@*)3i L |i @hLt ui@|hit Lu |i 4L_i* UL?|hM|i |L |t TihuLh4@?Ui 6}hit  @?_ 2 ?_U@|i |@| |i 4L?i) tTT*) ThLUitt ? |i _@|@ @t |L _t|?}t?} ui@|hitG |i _)?@4U hitTL?ti |L @ TL*U) tLU! t ?L| t4LL| @?_ |i *ii* Lu |i 4L?i) t|LU! ii?|@**) hi|h?t |L |t ThitLU! *ii* AL ihu) |@| |i 4L_i* ThLTih|it @hi ?L| ti?t|i |L |iti ui@|hit Lu |i 4L?i) ThLUittc i tL*i_ |i 4L_i* @tt4?} |@|

|i hitTL?ti Lu |i }hL| h@|i Lu 4L?i)c >|c |L @ TL*U) tLU! t }Lih?i_ M) >|  > '

fD E>|3 > n 0|c ic

>| > ' 0|n fD0|3n fD20|32n  

t ?L|i_ @MLic ht|@?Lc ,Ui?M@4 @?_ ,@?t EbbH @h}i |@| |t t @ }LL_ t|@ 2S

|t|U@* @TThL 4@|L? |L |i it|4@|i_ 4T*ti hitTL?ti u?U|L? uLh 4L?i) }hL| Ai €ht| UL*4? Lu 6}hi  _tT*@)t |i ThLTih|it Lu |i 4L_i* M@ti_ L? |t hiThiti?|@|L? Lu 4L?i) }hL| L|Ui |@| |i _)?@4U Mi@Lh Lu |t ihtL? Lu |i 4L_i* t t4*@h |@| Lu |i Mi?U4@h! 4L_i*

5iUL?_c ? Lh 4L_i* |i U@??i* M) U @ TL*U) tLU! @giU|t @}}hi}@|i ^@?||it @?_ ThUit LTih@|it @ |t 4T@U| L? |i u|hi 4L?i) tTT*) W? T@h|U*@hc u |i TL*U)

tLU! @_ ?L 4T@U| L? |nrc r  2c |i? ThUitc @}itc L|T|c UL?t4T|L?c ?it|4i?|

@?_ ThL_U||) L*_ Mi ?@giU|i_ @| @** _@|it _{|c |i ?|ihit| h@|i L*_ _iU*?i ?}

|i TihL_ Lu @ TL*U) tLU! AhL} @ ti^i?Ui Lu ?4ihU@* i Tih4i?|tc i uL?_ |@|

|i 4@}?|_i Lu |i _hLT ? -| _iTi?_t Th4@h*) L? |i 4@}?|_i Lu |i ?Uhi@ti ? >|

@?_ hi*@|i*) *||*i L? |i Tihtt|i?Ui ThLTih|it Lu 4L?i) At hiiU|t |@| |i tLh||ih4

@?|UT@|i_ ?@|L? igiU|t Lu @ TL*U) tLU! @hi t4@** ? Lh 4L_i*2

Ah_c t|U!) ThUit _L ?L| T*@) @ UhU@* hL*i ? |i TihuLh4@?Ui Lu |i Mi?U4@h! 4L_i* L*4? 2 ? 6}hi  _tT*@)t |i 4T*ti hitTL?ti u?U|L?t uLh @ ihtL? Lu |i 4L_i* ?

U i ti| 1R ' f @?_ L*_ |i hi4@??} T@h@4i|iht @| |ih Mi?U4@h! @*it `|

|hii i UiT|L?tc |t ihtL? Lu |i 4L_i* _Lit ^|i i** Ai i UiT|L?t @hi |@| L|T| @?_ hi@* @}it hti |LL 4U ? hitTL?ti |L |i TL*U) tLU! W? @__|L?c ?@|L? _hLTt M) |LL 4U Ai *@||ih hit*| hiiU|t |i u@** ? 4@h}?@* ULt|t t|i44?} uhL4 |i _hLT ? |i ?|ihit| h@|i

 _gihi?| @) |L @ttitt |i 4T@U| Lu t|U!) ThUit t |L hiit|4@|i Lh 4L_i*c tMiU| |L

|i UL?t|h@?|c 1R ' f Ai hit*|?} TL?| it|4@|it @hi hiTLh|i_ ? A@M*i  Ai @ttLU@|i_

4T*ti hitTL?ti u?U|L?t @hi ?L| _tT*@)i_ MiU@ti |i) @hi tL t4*@h |L |i L?it ?

L*4? 2 L|i uhL4 A@M*i  |@| ?uihi?Ui @ML| 1 t hLMt| |L 4TLt?} |i hit|hU|L?c

1R ' f Ai Th4@h) 4T@U| Lu |t hit|hU|L? L? |i TL?| it|4@|i t |L hi_Ui |i it|4@|i

Lu bsc U u@**t uhL4 eS |L 2b W| t Lh| t|hitt?} |@| | 1R ' f |i 4L_i* t|**

64_{Wkh dujxphqw lv dv iroorzv1 Lw lv hdv| wr yhuli| wkdw wkh wlph w yduldeohv lq wkh htxdwlrqv}

fkdudfwhul}lqj wkh htxloleulxp rxwfrphv iurp shulrg w . 4 rq duh fw> lw> Sw> Zw dqg nw= Wkhvh

yduldeohv/ lq frqmxqfwlrq zlwk djhqwv* ylhzv derxw Pw.v> v  5> frpsohwho| ghwhuplqh wkh

htxloleulxp rxwfrphv iurp w . 4 rq1 +Wkh yduldeoh/ Pw.4> dsshduv lq wkhvh htxdwlrqv wrr/

krzhyhu/ rqo| dv d surgxfw/ w.4Pw.4 +vhh +6153, dqg +616:, iru shulrg w . 4,1 Wkh glvfxvvlrq

lq wkh wh{w uhhfwv wkdw w.4Pw.4@ Pw.51, Rxu wlplqj dvvxpswlrqv lpso| wkdw fw> lw> Sw> Zw

dqg nw duh lqyduldqw wr wkh uhdol}dwlrq ri d shulrg w srolf| vkrfn1 Wkh uhvxow iroorzv iurp wkh

dvvxpswlrq wkdw Pw.v> v  5 lv dovr xqdhfwhg e| d shulrg w srolf| vkrfn1

65_{Wr vhh wklv/ zh frqvlghuhg wzr yhu| glhuhqw uhsuhvhqwdwlrqv iru prqh| jurzwk1 Lq wkh uvw/}

d srolf| vkrfn kdv qr lpsdfw rq wkh ixwxuh prqh| vxsso|= w@  . %w %w4= Lq wkh vhfrqg/ wkh

orqj0uxq lpsdfw rq wkh prqh| vwrfn ri d srolf| vkrfn lv whq wlphv odujhu wkdq wkh lpsdfw hhfw=

w  @ 3=<+w4 , . %w= Zh vroyhg wkh prgho iru wkh wzr glhuhqw prqh| surfhvvhv dqg

frpsxwhg wkh lpsdfw hhfw rq Uw ri vhwwlqj %w@ 3=48= Lq wkh fdvh ri wkh uvw prqh| surfhvv/

Uwgursv 47 edvlv srlqwv/ zkloh lq wkh vhfrqg lw gursv 46 edvlv srlqwv1

}i?ih@|it *@h}ic Tihtt|i?| ?Uhi@tit ? L|T| @?_ @? ?ih|@* hitTL?ti ? ?@|L? Aiti LMtih@|L?t tMt|@?|@|i |i U*@4 ? |i ?|hL_U|L? |@| t|U!) ThUit T*@) @ *4|i_ hL*i ? @UUL?|?} uLh |i }LL_ €| Lu |i Mi?U4@h! 4L_i*

6Lh|c t|U!) @}it T*@) @ UhU@* hL*i ? |i 4L_i*<t TihuLh4@?Ui L*4?  ? 6}hi

 _tT*@)t |i 4T*ti hitTL?ti u?U|L?t uLh @ ihtL? Lu |i 4L_i* ? U i ti| 1 '

f @?_ L*_ |i hi4@??} T@h@4i|iht @| |ih Mi?U4@h! @*it L|i |@| |i 4L_i*<t TihuLh4@?Ui _i|ihLh@|it _h@4@|U@**) W?@|L? @?_ |i hi@* @}i th}i ? |i @u|ih4@| Lu |i tLU! |T| htit M) L?*) @ t4@** @4L?| ? |i €ht| TihL_ @u|ih |i tLU! @?_ |i? ^U!*) hi|h?t |L |t ThitLU! }hL| T@| At hit*| t hi4?tUi?| Lu @hc kiLi @?_ UBh@||@?<t E2fff €?_?} |@|c ? 4L_i*t ihi |i L?*) ?L4?@* h}_|) t t|U!) ThUitc 4L?i|@h) TL*U) tLU!t _L ?L| ThL_Ui *@h}ic Tihtt|i?| 4Li4i?|t ? L|T| *tL ?L|i |@| ? |t ihtL? Lu Lh 4L_i*c UL?t4T|L?c ?it|4i?|c ThL€|t @?_ ThL_U||) @hi

itti?|@**) ?@giU|i_ M) |i tLU! `i? i @||i4T|i_ |L it|4@|i |i 4L_i* | 1 ' fc

|i it|4@|i Lu 1R t _hi? |L ?|) ,_i?|*)c |i it|4@|L? Uh|ihL? Thiuiht i |hi4i

_i}hiit Lu ThUi t|U!?itt i? |ihi @hi ?L t|U!) @}it

6u|c i ?L |h? |L |i hL*i T*@)i_ M) |i ui@|hit Lu |iU?L*L}) @?_ Thiuihi?Uit |@| _t|?}t Lh 4L_i* uhL4 |i |i |MLL! L?itiU|Lh }hL| 4L_i* L*4?  ? 6}hi e _tT*@)t |i 4T*ti hitTL?ti u?U|L?t uLh @ ihtL? Lu |i 4L_i* ? U i t| _L? @h@M*|) ? U@T|@* |*3@|L?c @M| Tihtt|i?Ui ? Thiuihi?Uit @?_ @_t|4i?| ULt|t ?

?it|4i?| _{Ai hi4@??} T@h@4i|iht @hi ti| @| |ih Mi?U4@h! @*it L|Ui |i}

_h@4@|U _i|ihLh@|L? ? 4L_i* TihuLh4@?Ui Ai hitTL?ti Lu ?@|L? t 44i_@|i @?_ t|hL?}G _itT|i |i Thiti?Ui Lu t|U!) @}it @?_ ThUitc |i 4L_i* u@*t |L @UUL?| uLh |i t4@**c ?ih|@* hitTL?ti Lu ?@|L? |L @ TL*U) tLU! 54*@h*)c L|T| @?_ ?it|4i?| ?|@**) Lihhi@U| |L |i tLU! @?_ i M| *||*i Tihtt|i?Ui W? @__|L?c |i 4L_i* u@*t |L hiThL_Ui |i Tihtt|i?| _hLT ? |i ?|ihit| h@|ic @?_ Thi_U|t @ UL?|ihu@U|@* _hLT ? |i hi@* @}i 6?@**)c UL?t4T|L?c ThL_U||) @?_ ThL€|t i M| itti?|@**) ?L hitTL?ti |L |i TL*U) tLU! `i? i @||i4T|i_ |L hiit|4@|i |i T@h@4i|iht Lu |t ihtL? Lu |i

4L_i*c 1R @?_ 1 ihi _hi? |L ?|) At t @ _h@4@|U **t|h@|L? Lu |i U*@4 4@_i ?

|i ?|hL_U|L? |@| ?uihi?Ui @ML| ?L4?@* h}_|it t ti?t|i |L }i||?} |i hi@* t_i Lu |i 4L_i* h}|<

L*4?t 2c  @?_ e Lu 6}hi e @?_ A@M*i  @**L t |L tii L U@T@U|) |*3@|L?c @_t|4i?| ULt|t @?_ @M| uLh4@|L? i@U UL?|hM|i |L |i _)?@4Ut Lu Lh 4L_i* L*4? 2 ?_U@|it |@| t||?} _L? @h@M*|) ? U@T|@* |*3@|L? hi_Uit |i 4@}?|_i @?_ Tihtt|i?Ui ? |i hitTL?ti Lu |i 4L_i*<t hi@* @h@M*it 6hL4 L*4? c i tii |@| i? |ihi @hi ?L @_t|4i?| ULt|t ? ?it|4i?|c @ TL*U) tLU! *i@_t |L @ UL?|ihu@U|@* th}i ? ?it|4i?| @?_ L|T|c @?_ *i@it UL?t4T|L? @| L*4? e ?_U@|it |@|c ? |i @Mti?Ui

66_{Zh gr wklv e| vhwwlqj}

d@ 4333> e @ 3>~ @ 3=4=