Cahier 2001-07
RUGE-MURCIA, Francisco J.
Département de sciences économiques
Université de Montréal
Faculté des arts et des sciences C.P. 6128, succursale Centre-Ville Montréal (Québec) H3C 3J7 Canada http://www.sceco.umontreal.ca SCECO-information@UMontreal.CA Téléphone : (514) 343-6539 Télécopieur : (514) 343-7221
Ce cahier a également été publié par le Centre interuniversitaire de recherche en économie quantitative (CIREQ) sous le numéro 07-2001.
This working paper was also published by the Center for Interuniversity Research in Quantitative Economics (CIREQ), under number 07-2001.
CAHIER 2001-07
A PRUDENT CENTRAL BANKER
Francisco J. RUGE-MURCIA1
1
Centre de recherche et développement en économique (C.R.D.E) and Département de sciences économiques, Université de Montréal
March 2001
___________________
The author is indebted to Paul Evans, David Peel, and an anonymous referee for helpful suggestions and comments. An earlier version of this paper was circulated under the title "Deflation and Optimal Monetary Policy.'' Financial support from the Social Sciences and Humanities Research Council and the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche is gratefully acknowledged.
RÉSUMÉ
Ce mémoire étudie la politique monétaire dans une économie où les préférences de la Banque centrale sont asymétriques autour de l'inflation optimale. Plus précisément, les déviations positives de l'optimum peuvent avoir une plus grande ou une plus faible pondération dans la fonction de perte que les déviations négatives en ce qui concerne les preneurs de décisions des politiques. Sous des préférences asymétriques, il a été démontré que l'incertitude pouvait entraîner un comportement prudent de la part de la Banque centrale. Ainsi, les motifs de prudence peuvent être assez grands pour annuler le biais d'inflation, une politique monétaire optimale peut être réalisée même en l'absence de règles, de réputation ou de mécanismes contractuels. Pour certaines valeurs de paramètres, un biais de déflation peut survenir en équilibre.
Mots clés : délégation, préférences asymétriques, prudence, déflation
ABSTRACT
This paper studies monetary policy in an economy where the central banker's preferences are asymmetric around optimal inflation. In particular, positive deviations from the optimum can be weighted more, or less, severely than negative deviations in the policy maker's loss function. It is shown that under asymmetric preferences, uncertainty can induce a prudent behavior on the part of the central banker. Since the prudence motive can be large enough to override the inflation bias, optimal monetary policy could be implemented even in the absence of rules, reputation, or contractual mechanisms. For certain parameter values, a deflationary bias can arise in equilibrium.
W?|hL_U|L?
At T@Tih t|_it 4L?i|@h) TL*U) ? @? iUL?L4) ihi |i Ui?|h@* M@?!ih<t Thiuihi?Uit @hi @t)44i|hU @hL?_ |i LT|4@* h@|i Lu ThUi ?@|L? Ai Thiuihi?Ui tTiUU@|L? Tih4|t _gihi?| i}|t uLh TLt|i @?_ ?i}@|i ?@|L? _i@|L?t uhL4 |i LT|44c @?_ ?U*_it @t @ tTiU@* U@ti |i ^@_h@|U *Ltt u?U|L? i4T*L)i_ M) ThiLt *|ih@|hi W? UL?|h@t| |L |i
^@_h@|U 4L_i*c ihi |i *Ltt @ttLU@|i_ | @ _i@|L? _iTi?_t tL*i*) L? |t 4@}?|_ic ?_ih @t)44i|hU Thiuihi?Uit ML| 4@}?|_i @?_ t}? 4@||ih |L |i TL*U) 4@!ih At 4Lhi }i?ih@* Thiuihi?Ui tTiUU@|L? @t ?L?|h@* 4T*U@|L?t uLh |i _it}? Lu 4L?i|@h) TL*U) @?_ 4L_it tL4i Lu |i i@h*ih UL?U*tL?t _ihi_ ?_ih |i @tt4T|L? Lu t)44i|h) At TL?| t **t|h@|i_ ihi ? @ t4T*i }@4i|iLhi|U@* 4L_i* Lu 4L?i|@h) TL* U) ? |i tTh| Lu @hhL @?_ BLh_L? EbH W| t tL? |@| hi*@ ?} Uih|@?|) i^@*i?Ui ?_Uit @ Th_i?| Mi@Lh L? |i T@h| Lu |i Ui?|h@* M@?!ih |@| U@? hi_Ui Lh i*4?@|i |i ?@|L? M@t @ttLU@|i_ | _t Uhi|L?@h) 4L?i|@h) TL*U) LhiLihc |ihi i t|t @*it Lu |i Thiuihi?Ui T@h@4i|iht uLh U @ _i@|L?@h) M@t U@? @hti ? i^*Mh4
t |i RUL?tih@|i Ui?|h@* M@?!ih ? +L}Lg EbHDc |i RTh_i?| Ui? |h@* M@?!ih ihi t U@h@U|ih3i_ M) Thiuihi?Uit |@| U@? _gih uhL4 |i L?it Lu |i @ih@}i 4i4Mih Lu tLUi|) Ai uLh4ih @||@Uit @ *@h}ih hi*@|i i}| |L ?@|L? t|@M*3@|L? ? ih *Ltt u?U|L? |@? tLUi|) _Lit Ai *@||ih i}|t 4Lhic Lh *ittc tiihi*) TLt|i |@? ?i}@|i ?@|L? _i @|L?t uhL4 |i LT|4@* h@|i OLiihc *i |i RUL?tih@|i Ui?|h@* M@?!ih hi_Uitc M| _Lit ?L| hi4Lic |i ?@|L? M@tc |ihi i t| @*it Lu |i Thiuihi?Ui T@h@4i|iht uLh U @ RTh_i?| Ui?|h@* M@?!ih U@? i*4?@|i |i M@t @?_ 4@ 43i tLU@* i*u@hi Oi?Uic LT|4@* 4L?i|@h) TL*U) UL*_ Mi 4T*i4i?|i_ ii? |L| h*itc hiT|@|L?c Lh UL?|h@U|@* 4iU@?t4t W? Lh_ih |L tii |i ?||L? Lu |t hit*|c ?L|Ui |@| hi*@ ?} |i @t t4T|L? Lu ^@_h@|U Thiuihi?Uit 4i@?t |@| Uih|@?|) i^@*i?Ui ?L *L?}ih L*_t Ai?c |i i TiU|i_ 4@h}?@* ULt| Lu _iT@h|?} uhL4 LT|4@* ?@|L? t ?L?*?i@h ? ?@|L? W? T@h|U*@hc i? |i Ui?|h@* M@?!ih @ttLU@|it @ *@h}ih *Ltt |L TLt|i |@? ?i}@|L? ?@|L? _i@|L?t uhL4 |i LT|44c ?Uih|@?|) h@tit |i i TiU|i_ 4@h}?@* ULt| @?_ ?_Uit @ Th_i?| Mi@Lh
4Vhh/ dprqj rwkhuv/ N|godqg dqg Suhvfrww +4<::,/ Eduur dqg Jrugrq +4<;6,/ Urjr
+4<;8,/ Zdovk +4<<8,/ Vyhqvvrq +4<<:/ 4<<<,/ Ehhwvpd dqg Mhqvhq +4<<;,/ Fodulgd/ Jdol/ dqg Jhuwohu +4<<<,/ dqg Hlmqjhu/ Krhehulfkwv/ dqg Vfkdolqj +5333,1
L? |i T@h| Lu |i 4L?i|@h) @|Lh|) h_i?Ui |i? 4L_ih@|it |i TL*U) 4@!ih<t ?Ui?|i |L Uhi@|i thThti ?@|L?
6Lh Uih|@? Thiuihi?Ui T@h@4i|ih @*itc |t Th_i?Ui 4L|i t *@h}i i?L} |@| ?@|L? t L? @ih@}i Mi*L |t LT|4@* h@|i Oi?Uic @t)4 4i|hU Thiuihi?Uit U@? ThL_i @ |iLhi|U@* uL?_@|L? uLh 5|@?*i) 6tUih<t LMtih@|L? d6tUih Ebbeo |@| @ _i@|L?@h) M@t U@? Mi @ TLttM*i L| UL4i ? |i @U|@* Th@U|Ui Lu 4L?i|@h) TL*U)
t)44i|hU _t@TTL?|4i?|@ihtL? Thiuihi?Uit ihiM) ?__@*t |hi@| _gihi?|*) i TiU|i_ }@?t @?_ *Lttit @i Mii? ThLTLti_ ? |i *|ih@|hi M) ,Tt|i? @?_ ~? EbHb @?_ B* Ebb +i}@h_?} @ }Lih?4i?| Lh Ui?|h@* M@?!c |ih _gihi?| @|||_i t @ t MLL4t @?_ hiUittL?t @?_ |i 4Lhi _L?@h_|@? T@h_h}_|) ? ThUit 4}| T*@tM*) ?_Ui @t)44i |hit ? |ih *Ltt u?U|L? L?tt|i?| | |t _i@ @hi ?_?}t M) *@h_@ @?_ Bih|*ih Ebb.c BL*_u@? @?_ V@*_it Ebbb @?_ +}ihU@ E2fff *@h_@ @?_ Bih|*ih it|4@|i @ hi@U|L? u?U|L? uLh |i ?_itM@?! @?_ ?_ |@| |i Ui?|h@* M@?! h@tit |i _@)|L_@) ?|ihit| h@|i i? ?@ |L? t @MLi |t t|i@_)t|@|i |hi?_ @*i M| M@hi*) hitTL?_t i? | t Mi*L BL*_u@? @?_ V@*_it i @4?i 4Lhi |@? 2ff iTtL_it Lu Uhhi?U) Lih@*@|L?t @?_ ?_ih@*@|L?tc @?_ _LU4i?| |@| *i |i uLh4ih t@**) ?t | t__i? U@?}it ? |i ?L4?@* i U@?}i h@|ic |i *@||ih i?_ M) |i t4LL| @_t|4i?| Lu ThUit @?_ @}it +}ihU@ _ihit 4T*U| ML?_t uLh |i @?@_@? ?@|L? |@h}i| 3L?i t?} _@|@ L? 4@h!i| _i|ih4?i_ ?L4?@* ?|ihit| h@|it @?_ hiTLh|t |@| *i |i TM*U 4}| TihUii |i M@?_ |L Mi Lu @TThL 4@|i*) |i t@4i _| @t @??L?Ui_c | @TTi@ht @t)44i|hU@**) _t|hM|i_ @hL?_ |i LU@* 4_@*i Lu 2I Tih )i@h
iuLhi ThLUii_?}c | t 4TLh|@?| |L 4i?|L? U*Lti*) hi*@|i_ hiti@hU M) LM@) @?_ ii* EbbH L t|_) LT|4@* UL44|4i?| @?_ _tUhi|L? ? 4L?i|@h) TL*U) t?} |i t@4i *Ltt u?U|L? i4T*L)i_ ihi At ThLiU| i |i?_t @?_ UL4T*i4i?|t |ih @?@*)tt M) u**) U@h@U|ih3?} |i |iLhi| U@* @?_ i4ThU@* 4T*U@|L?t Lu |i 4L_i* | |i |iLhi|U@* *ii* |i ThLTih|it Lu |i Ui?|h@* M@?!ih<t hi@U|L? @hi _ihi_c UL?_|L?t uLh |i i t|i?Ui @?_ ?^i?itt Lu |i @t i^*Mh4 @hi it|@M*ti_c @?_ |i }Lih?4i?|<t ThLM*i4 Lu LT|4@* _i*i}@|L? t uLh4*@|i_ @?_ tL*i_ | |i i4ThU@* *ii*c | t tL? |@| @t)44i|hU Thiuihi?Uit E }i?ih@|i @ TLt |i ?L?*?i@h hi*@|L? Mi|ii? ?@|L? @?_ ?@|h@* h@|i Lu ?i4T*L)4i?|c @?_ E Thi_U| |@| |i UL?_|L?@* @h@?Ui Lu ?@|L? i*Tt uLhiU@t| |t
4i@?
Ai T@Tih t Lh}@?3i_ @t uL**LtG tiU|L? 2 Thiti?|t @?_ tL*it @ }@4i |iLhi|U@* 4L_i* Lu 4L?i|@h) TL*U) | @t)44i|hU Thiuihi?Uit( tiU|L? it|@M*tit |t |iLhi|U@* @?_ i4ThU@* 4T*U@|L?t( @?_ tiU|L? e UL?U*_it @?_ _tUttit u|hi hiti@hU
2 Ai L_i*
2 Ai ,UL?L4U ,?hL?4i?|
6L**L?} |i *|ih@|hic |i hi*@|L? Mi|ii? ?@|L? @?_ ?i4T*L)4i?| t _itUhMi_ M) @? i TiU|@|L?t@}4i?|i_ **Tt UhiG
' ? bEZ Ze n #c b : fc E
ihi t |i h@|i Lu ?i4T*L)4i?|c ?t |i ?@|h@* h@|i Lu ?i4T*L)4i?|c
Z t |i h@|i Lu ?@|L?c Ze t |i TM*U<t ThiLt*)UL?t|hU|i_ ?@|L?
uLhiU@t|c @?_ # t @ tTT*) tLU! Ai TM*U t @tt4i_ |L uLh4 |t i TiU |@|L?t h@|L?@**)G
Ze ' .EZmUc E2
ihi . t |i i TiU|@|L?t LTih@|Lh @?_ U t |i TM*U<t ?uLh4@|L? ti| iU@ti |ihi t ?L Th@|i ?uLh4@|L? ? |i 4L_i*c |i }Lih?4i?|<t @?_ Ui?|h@* M@?!ih<t ?uLh4@|L? ti|t UL?U_i | |i TM*U<t @?_ @hi @*tL }i? M) U
+@|ih |@? ULLt?} |i h@|i Lu ?@|L? _hiU|*)c |i TL*U) 4@!ih t @tt4i_ |L @giU| Z |hL} @ TL*U) ?t|h4i?| E@t ? `@*t EbbD @?_ Whi*@?_ Ebbb Ai ?t|h4i?|c i|ih @ 4L?i|@h) @}}hi}@|i Lh @ tLh| |ih4 ?L4?@* ?|ihit| h@|ic t 4TihuiU| ? |i ti?ti |@| ? @ t|LU@t|U Lh*_ | U@??L| _i|ih4?i ?@|L? UL4T*i|i*) @?_ |t igiU| |@!it T*@Ui | @ L?i TihL_ *@}G
Z ' sE n "c E
ihi sE t @ 4L?L|L?Uc UL?|?Ltc @?_ _gihi?|@M*i u?U|L?c t |i TL*U) ?t|h4i?|c @?_ " t @ UL?|hL* ihhLh |@| hiThiti?|t 4TihuiU|L?t ? |i UL?_U| Lu 4L?i|@h) TL*U) 5?Ui t @tt4i_ |L Mi ULti? ? |i ThiLt TihL_c | uL**Lt |@| 5 U
6?@**)c UL**iU| |i 4L_i*<t t|hU|h@* _t|hM@?Uit ? |i 2 iU|Lh W| t @tt4i_ |@| t tih@**) ?ULhhi*@|i_ @?_ ?Lh4@**) _t|hM|i_ | 3ihL 4i@?G mU ' % # " & U Efc lc
ihi l hiThiti?|t @ 2 2 TLt|i_i?|i @h@?UiUL@h@?Ui 4@|h k)_*@?_ @?_ hitUL|| Eb.. @?_ @hhL @?_ BLh_L? EbH tL |@| ? |i @MLi ti|T ihi thThti ?@|L? U@? ThL_Ui *ii*t Lu ?i4 T*L)4i?| @MLi |i ?@|h@* h@|i @ }Lih?4i?| | Thiuihi?Uit Lih ? @|L? @?_ ?i4T*L)4i?| 4}| Mi ?@M*i |L Uhi_M*) UL44| |L |i LT| 4@* 4L?i|@h) TL*U) W?t|i@_c |i t|h@|i}U ?|ih@U|L? Mi|ii? |i TM*U @?_ |i }Lih?4i?| )i*_t @ tMLT|4@* @t i^*Mh4 ihi ?i4T*L) 4i?| ULhhitTL?_t |L |i ?@|h@* h@|i M| ?@|L? t t|hU|*) }ih |@? |i tLU@**)LT|4@* h@|i i*u@hi4ThL?} tL*|L? ?L*it |i _i*i}@|L? Lu 4L?i|@h) TL*U) |L @ tiT@h@|i @}i?| Lh Ui?|h@* M@?!ih2 W| t i@t) |L
tL |@| u |i Ui?|h@* M@?!ih @t i @U|*) |i t@4i Thiuihi?Uit @t |i }L ih?4i?|c |i ?iUi?| L|UL4i hi4@?t ?U@?}i_ Oi?Uic |i _i@ |@| _i*i}@|L? tL*it Lh hi_Uit |i |i4TLh@* ?UL?tt|i?U) Lu 4L?i|@h) TL*U) t L?*) 4i@??}u* u |i @}i?|<t Thiuihi?Uit @hic i|ih M) ?@|hi Lh M) _it}?c _gihi?| uhL4 |i }Lih?4i?|<t U*@ttU i @4T*i Lu |i ht| U@ti t |i RUL?tih@|i Ui?|h@* M@?!ih ? +L}Lg EbHD ihi |i @}i?| @t ^@_h@|U Thiuihi?Uit E@t _Lit |i }Lih?4i?| M| @||@Uit @ ThLTLh|L?@**) t4@**ih i}| |L ?i4T*L)4i?| ? ih *Ltt u?U|L? |@? |i }Lih?4i?| 4L?} |i tiUL?_ U*@tt Lu 4L_i*tc ihttL? @?_ A@Mi**? Ebb @?_ `@*t EbbD ThLTLti |i ti Lu @ *?i@h UL?|h@U| |@| 4L_it |i @}i?|<t *Ltt u?U|L? M) @TTi?_?} @ Ti?@*|) |@| ?Uhi@tit @t ?@|L? _i@|it uhL4 |i LT| 4@* h@|i Bhii? EbbS @?_ 5i?ttL? Ebb. UL?t_ih @? i T*U| ?@|L? |@h}i| |@| tu|t |i Ui?|h@* M@?!ih<t *Ltt u?U|L? tU |@| |i 4@h}?@* Mi?i| @?_ ULt| Lu ?@|L? |L |i @}i?| @hi i^@*3i_ @| |i tLU@**)LT|4@* ?@|L? h@|i
5Mhqvhq +4<<:, dujxhv wkdw vlqfh ghohjdwlrq lwvhoi lv glvfuhwlrqdu|/ lw pljkw qrw vroyh
wkh whpsrudo lqfrqvlvwhqf| ri prqhwdu| srolf| xqohvv wkhuh duh uhdssrlqwphqw frvwv1 Pf0 Fdooxp +4<<8, dqg Eolqghu +4<<;/ s1 79, txhvwlrq wkh jryhuqphqw*v lqfhqwlyh wr hqirufh frqwudfwxdo duudqjhphqwv zlwk wkh fhqwudo edqnhu1
22 Ai i?|h@* @?!ih
W? |i tTh| Lu +L}Lg EbHDc |t T@Tih t|_it |i 4T*i4i?|@|L? Lu 4L? i|@h) TL*U) M) @? @}i?| i?_Li_ M) ?@|hi | _gihi?| Thiuihi?Uit |@? |i @ih@}i 4i4Mih Lu tLUi|) `|L| 4TLt?} hit|hU|L?t L? |i hi*@|i i}| @||@Ui_ |L ?i4T*L)4i?| t|@M*3@|L?c |i Ui?|h@* M@?!ih<t LMiU |i u?U|L? t }i?ih@*3i_ |L @**L _gihi?| *Lttit uLh TLt|i @?_ ?i}@|i ?@|L? _i@|L?t uhL4 |t LT|4@* h@|iG
uEZc ' Ei TEkEZ ZW kEZ ZW *k2n E*2E &?2c Ee
ihi t k t @ ?L?3ihL hi@* ?4Mihc ZW t |i tLU@**) LT|4@* ?@|L? h@|ic
&? t |i _ithi_ h@|i Lu ?i4T*L)4i?|c f & c @?_ t @ TLt|i
UL?t|@?| |@| 4i@thit |i hi*@|i 4TLh|@?Ui Lu ?i4T*L)4i?| t|@M*3@ |L? Ai TLttM*) ?L?3ihL @*i ZW U@? Mi ?|ihThi|i_c uLh i @4T*ic @t |i
L?i @ttLU@|i_ | |i LT|4@* ?@|L? |@ c |@| 4}| hi_Ui |i ?ii_ uLh _t|Lh|?} ?UL4i |@ it Lh L|ih |)Ti Lu ?L?*4Tt4 |@ it
Ai ?@|L? UL4TL?i?| ? Ee t _itUhMi_ M) |i *?i u?U|L? Lh} ?@**) ?|hL_Ui_ M) V@h@? Eb.e @?_ i @4?i_ M) ~i**?ih EbHSc Bh@?}ih @?_ it@h@? EbbSc @?_ ht|Lgihti? @?_ #iML*_ Ebb. ? |i UL?|i | Lu LT|4@* uLhiU@t|?} At u?U|L? t T*L||i_ ? }hi E@ uLh |i tTiU@* U@ti ihi k : f L|Ui |@| uLh ?@|L? h@|it @MLi ZWc |i i TL?i?|@*
|ih4 ii?|@**) _L4?@|it @?_ |i *Ltt @ttLU@|i_ | @ TLt|i _i@|L? htit i TL?i?|@**) 6Lh Z ZWc | t |i *?i@h |ih4 |@| MiUL4it ThL}hit
ti*) 4Lhi 4TLh|@?| @t ?@|L? _iUhi@tit @?_ |i *Ltt htit *?i@h*) At @t)44i|h) U@? Mi i@t*) tii? M) UL?t_ih?}c uLh i @4T*ic |i *Ltt @ttLU@|i_ | @ ?@|L? _i@|L? uhL4 ZW W| t @TT@hi?| |@| ii? |L} |ih
4@}?|_it @hi |i t@4ic |i _i@|L? _i*iht @ t4@**ih *Ltt |@? |i n _i@|L? L?ti^i?|*)c TLt|i _i@|L?t @hi i}|i_ 4Lhi i@*) |@? ?i}@|i L?it ? |i Ui?|h@* M@?!ih<t LMiU|i u?U|L? EL?ihti hit*|t @hi LM|@?i_ i? k f W? UL?|h@t| |L |i t@* ^@_h@|U *Ltt u?U|L?c ihi L?*) |i 4@}?|_i Lu |i _i@|L? 4@||iht |L |i TL*U) 4@!ih dtii }hi EMoc ?_ih @t)44i|hU Thiuihi?Uit ML| |i 4@}?|_i @?_ t}? @giU| |i Ui?|h@* M@?!ih<t *Ltt
W? |i tTiU@* U@ti ihi k |i?_t |L 3ihLc |i *?i UL4TL?i?| ? Ee hi_Uit |L |i ^@_h@|U uLh4 EZ ZW2*2 AL tii |tc |@!i |i *4| Lu
Ei TEkEZ ZW kEZ ZW *k2 @t k }Lit |L f @?_ ti w<O LT|@*<t
h*i |Ui At hit*| t 4TLh|@?| MiU@ti | uLh4@**) ThLit |@| |i dDo
^@_h@|U *Ltt u?U|L? i4T*L)i_ ? ThiLt *|ih@|hi t @ tTiU@* U@ti Lu |i L?i ThLTLti_ ihi W| @*tL t}}it|t |@| |i )TL|itt |@| |i Ui? |h@* M@?!ih<t Thiuihi?Uit @hi t)44i|hU Lih ?@|L? UL*_ Mi i@*@|i_ M) |it|?} i|ih k t t}?U@?|*) _gihi?| uhL4 3ihL
2 @t ,^*Mh4
Ai ThLM*i4 Lu |i Ui?|h@* M@?!ih t |L ULLti |i @*i Lu |i ?t|h4i?| |@| 4?43it ih i TiU|i_ *Ltt 6Lh4@**)c
? .du EZc mUoc ij
tMiU| |L |i i TiU|@|L?t@}4i?|i_ **Tt Uhi @?_ |@!?} Ze@t }i?
Ai ht|Lh_ih UL?_|L? t
.dEYu*YZEYZ*Y n EYu*YEY*YZEYZ*YmUo ' fc
@?_ t t@|ti_ M) |i @*i Lu |@| i^@|it |i 4@h}?@* ULt| Lu }ih ?i4T*L)4i?| | |i 4@h}?@* Mi?i| Lu *Lih ?@|L? 5?Ui |i *Ltt u?U|L? t }*LM@**) UL?i c |t @*i ULhhitTL?_t |L @ ?^i 4?44 L4T|?} |i T@h|@* _ih@|itG
.dEi TEkEZ ZW *k bE &?mUo ' f ED
W? Lh_ih |L ?_ |i UL?_|L?@* i TiU|@|L? Lu i TEkEZ ZWc |i uL**L?}
hit*| t tiu*G
hLTLt|L? Ai @tt4T|L? Lu ?Lh4@**) _t|hM|i_ _t|hM@?Uit 4T*it |@|c UL?_|L?@* L? |i ?uLh4@|L? ti|c ?@|L? t ?Lh4@**) _t|hM|i_ hLLu A@!?} UL?_|L?@* i TiU|@|L?t Lu ML| t_it Lu Ec ?L|?} |@| uLh4t T@h| Lu |i TM*U<t ?uLh4@|L? ti|c @?_ tMt|||?} M@U! ?|L E )i*_t
Z ' .EZmU n c ES
6Lq sulqflsoh/ rqh frxog dovr frqvlghu d pruh jhqhudo prgho zlwk dv|pphwulf suhihuhqfhv
ryhu erwk lqdwlrq dqg xqhpsor|phqw1 Krzhyhu/ wkh vroxwlrq lv rqo| voljkwo| glhuhqw iurp wkh rqh ghulyhg khuh/ dqg wkh edvlf suhglfwlrqv ri wkh prgho uhpdlq xqfkdqjhg1
ihi ' Efc Ai?c t?Ui .EZmU uLh4t T@h| Lu U @?_ 1 t L?|*) ?Lh4@**) _t|hM|i_ M) @tt4T|L?c | uL**Lt |@|
ZmU E.EZmUc l~
Ai @MLi hit*| 4T*it |@|c UL?_|L?@* L? Uc |i @h@M*i i TEkEZ ZW
t _t|hM|i_ *L} ?Lh4@* Ai?c .di TEkEZ ZWmUo ' i TEkE.EZmU
ZW n k2j2
Z*2 ihi jZ2 ' l t |i UL?_|L?@* @h@?Ui Lu ?@|L?
Ai UL?_|L?@* i TiU|@|L? Lu ?i4T*L)4i?| U@? Mi uL?_ M) |@!?} .dmUo ? ML| t_it Lu E |L LM|@?G
.EmU ' ? bE.EZmU Ze
`| |iti ?|ih4i_@|i hit*|tc |i ht|Lh_ih UL?_|L? U@? Mi h||i? @t Ei TEkE.EZmU ZW nk2j2
Z*2 *k nb2E.EZmU Ze bE &? ' f
+iU@** |@| ? |i ^@_h@|U 4L_i*c |i ht|Lh_ih UL?_|L? Lu |i Ui?|h@* M@?!ih<t 4?43@|L? ThLM*i4 t *?i@h @?_ U@? Mi tL*i_ i T*U|*) |L LM |@? ih hi@U|L? u?U|L? ? |ih4t Lu |i TM*U<t ?@|L? uLhiU@t|c Zee W?
UL?|h@t|c ?_ih @t)44i|hU Thiuihi?Uitc |i ht|Lh_ih UL?_|L? L?*) _i?it |i hi@U|L? u?U|L? 4T*U|*)G
}E.EZmUc Ze
' Ei TEkE.EZmU ZW n k2j2
Z*2 *k n b2E.EZmU Ze bE &?c
' f
E. OLiihc t?} |i 4T*U| u?U|L? |iLhi4c | t TLttM*i |L tL |@|
Y.EZmU*YZe ' b2*Eb2 n i TEkE.EZmU ZW n k2j2
Z*2 5 Efc c
uLh @** @*it Lu k Oi?Uic @t ? |i ^@_h@|U 4L_i*c |i Ui?|h@* M@?!ih<t hi @U|L? t @ 4L?L|L?U@**) ?Uhi@t?} u?U|L? Lu |i TM*U<t ?@|L? uLhiU@t| *tL
Y2.EZmU*YEZe2 '
kbe2i TEkE.EZmU ZW n k2j2
Z*2*Eb2 n i TEkE.EZmU ZW n k2jZ2*2c
7Vwulfwo| vshdnlqj/ wkh uhdfwlrq ixqfwlrq uhodwhv wkh srolf| lqvwuxphqw/ l/ dqg h> erwk
ri zklfk duh ghwhuplqhg lq wkh suhylrxv shulrg1 Krzhyhu/ lq zkdw iroorzv lw zloo eh frqyhqlhqw wr zrun zlwk H+mL, udwkhu wkdq l= Vlqfh wkhvh wzr yduldeohv duh prqrwrqlfdoo| uhodwhg e| wkh ixqfwlrq i+,> wklv dssurdfk hqwdlov qr orvv ri jhqhudolw|1
|@| t *itt |@? 3ihL uLh k : fc i^@* |L 3ihL uLh k $ fc @?_ *@h}ih |@? 3ihL uLh k f Oi?Uic uLh k : f Ek f |i Ui?|h@* M@?!ih<t hi@U|L? t @ UL?U@i EUL?i u?U|L? Lu Ze
W? Lh_ih |L _ii*LT uh|ih |i hi@_ih<t ?||L? @?_ |L **t|h@|i u|hi |iLhi|U@* hit*|tc | t tiu* |L T*L| |i Ui?|h@* M@?!ih<t hi@U|L? u?U|L? uLh _gihi?| @*it Lu |i Thiuihi?Ui T@h@4i|ih k At t _L?i ? }hi 2 ?_ih |i @tt4T|L? |@| |i LT|4@* h@|i Lu ?@|L? t ZW ' fc @?_ hi4@??}
T@h@4i|iht @hi b ' 2c ' fDc & ' fHc ? ' Dc @?_ j2
Z ' 2D2 Ai }hi
@*tL ?U*_it |i hi@U|L? u?U|L? Lu |i ^@_h@|U Ui?|h@* M@?!ih |@| t LM|@?i_ i? k $ fc @?_ |i TM*U<t hi@U|L? u?U|L? |@| t t44@h3i_ M) |i h@|L?@* i TiU|@|L?t hi*@|L? E2 Bh@TU@**)c |i @t i^*Mh4 t |i TL?| ihi E. @?_ E2 ?|ihtiU| Ahi@|?} @** T@h@4i|iht @t i_c |i RTh_i?| Ui?|h@* M@?!ih<t hi@U|L? @t UL4T|i_ M) tL*?} ?4ihU@**) |i 4T*U| u?U|L? E. uLh Hf i^@**)tT@Ui_ @*it Lu Ze Mi|ii? H @?_
H
L|Ui |@| @*|L} ? @** U@tit |i Ui?|h@* M@?!ih<t hi@U|L? t @? ? Uhi@t?} u?U|L? Lu |i TM*U<t ?@|L? uLhiU@t|c ih **?}?itt |L @UUL4 4L_@|i |i TM*U<t i TiU|@|L?t _iTi?_t L? |i Thiuihi?Ui T@h@4i|ih k L?t_ih ht| |i U@ti ihi k f L|i |@| ? |t t|@|L? |i Ui?|h@* M@?!ih hitTL?_t |L Ze @| @? ?Uhi@t?} h@|i @?_ |i ?@|L? M@t t *@h}ih
|@? ?_ih ^@_h@|U Thiuihi?Uit 6Lh @*it Lu k *EbE &?c
|ihi t ?L ?|i h@|i Lu ?@|L? @| U E. @?_ E2 ?|ihtiU|c @?_ |i @t i^*Mh4 ** ?L| i t| dtii ThLTLt|L? 2 Mi*Lo
? |i L|ih @?_c i? k : f |i Ui?|h@* M@?!ih @UUL44L_@|it |i TM*U<t ?@|L? uLhiU@t| @| @ _iUhi@t?} h@|i @?_ |i ?@|L? M@t ** @*@)t Mi t4@**ih |@? ?_ih ^@_h@|U Thiuihi?Uit hLTLt|L? e Mi*L tLt |@| |ihi i t|t @ ?^ic TLt|i @*i Lu kc t@) kWc tU |@| |i
@t i^*Mh4 t LM|@?i_ @| |i LT|4@* h@|i Lu ?@|L? EAi hi@U|L? u?U|L? uLh |t U@ti t *@Mi*i_ @t RLT|4@* ? }hi 2 Oi?Uic @? LT|4@**) RTh_i?| Ui?|h@* M@?!ih U@? 4T*i4i?| LT|4@* 4L?i|@h) TL*U)c ii? ? |i @Mti?Ui Lu h*itc hiT|@|L? Lh UL?|h@U|@* @}hii4i?|t | |i }Lih?4i?|
6?@**)c uLh @*it Lu k : kWc @ _i@|L?@h)c h@|ih |@? @? ?@|L?@h)c
M@t U@? @hti ? i^*Mh4D Atc @t)44i|hU Thiuihi?Uit U@? ThL_i
@ |iLhi|U@* uL?_@|L? uLh 6tUih<t Ebbe LMtih@|L? |@| @ _i@|L?@h)
8Lq zkdw iroorzv/ ghdwlrq uhihuv qrw rqo| wr d qhjdwlyh udwh ri sulfh lqdwlrq/ exw/
pruh jhqhudoo|/ wr d udwh ri lqdwlrq ehorz wkh rswlpdo rqh1
M@t t @ TLttM*i L|UL4i ? |i Th@U|Ui Lu 4L?i|@h) TL*U)S
L?_|L?t uLh |i i t|i?Ui @?_ ?^i?itt Lu |i @t i^*Mh4 @hi Thiti?|i_ ? |i uL**L?} ThLTLt|L?G
hLTLt|L? 2 hL_i_ |@| n kbE &? : fc |ihi i t|t @ ?^i
Ze' .EZmUc tU |@| }E.EZmUc Ze ' f
hLLu AL ThLi i t|i?Uic UL?t|hU| @ Ze' .EZmU ' ZW kj2
Z*2 n E*k *?E n kbE &? EH
*}}?} EH ?|L E. @?_ t?} Ze ' .EZmU _i*iht }E.EZmUc Ze ' f AL
tL ?^i?ittc @tt4i |ihi i t|t @ tiUL?_ ?@|L? uLhiU@t|c t@) Ze '
ZW kj2
Z*2 n E*k *?E n kbE &? n %c |@| @*tL *it L? |i eD *?i L?
|i T*@?i EZec .EZmU @?_ t@|tit }E.EZmUc Ze ' f W| ** Mi tL? |@|
|i L?*) @) |t U@? @TTi? t u % ' f +iT*@Ui Ze ? E. Ai?c
EE n kbE &? i TEk% kbE &?*k ' f
54T*u)?}c
E n kbE &?Ei TEk% *k ' f
5?Ui n kbE &?: f @?_ k 9' fc |i? | 4t| Mi |i U@ti |@| % ' f~
L|Ui ? EH |@| _iTi?_?} L? |i t}? Lu |i Thiuihi?Ui T@h@4i|ih kc ?@|L? t @? ?Uhi@t?} Lh _iUhi@t?} u?U|L? Lu |t UL?_|L?@* @h@?Ui W? Lh_ih |L ?_iht|@?_ |t hit*|c | t tiu* |L hiU@** |@| i? |i *Ltt u?U|L? t ^@_h@|Uc Uih|@?|) i^@*i?Ui L*_t Oi?Uic |i 4L_i* tL*|L? t |i t@4i hi}@h_*itt Lu i|ih |ihi t ?Uih|@?|) Lh ?L| ? |i L|ih @?_c i? |i *Ltt u?U|L? t @t)44i|hU L? ?@|L?c |i 4@h}?@* ULt| Lu _iT@h|?} uhL4 ZW t ?L| *?i@h ? ?@|L?c M| UL?i Ei? k : f
Lh UL?U@i Ei? k f Atc i? k : fc @? ?Uhi@ti ? ?Uih|@?|) ?Uhi@tit |i i TiU|i_ 4@h}?@* ULt| Lu _i@|?} uhL4 ZW EAi UL?ihti
hit*| t LM|@?i_ i? k f UL4T@h@M*i hit*| U@? Mi uL?_ ? |i *|ih@|hi L? ThiU@|L?@h) t@?}t `i? |i @tt4T|L? Lu ^@_h@|U |*|) t hi*@ i_ @?_ *@MLh?UL4i ht! ? ?L?_iht@M*ic |i? ?Uih|@?|) ?Uhi@tit |i i TiU|i_ 4@h}?@* |*|) Lu u|hi UL?t4T|L? AL t@|tu) |i
9Wr p| nqrzohgjh wklv srlqw zdv uvw pdgh e| Qred| dqg Shho +4<<;,1
,*ih UL?_|L?c Th_i?| LtiL*_t _iUhi@ti Uhhi?| UL?t4T|L? UL4T@hi_ |L u|hi UL?t4T|L? @?_ ?Uhi@ti |ih t@?}t dtii @M@**ihL Ebbfo
6?@**)c ?L|i |@| @t t@* |i ?i4T*L)4i?| h@|i ? i^*Mh4 _Lit ?L| _gih t)t|i4@|U@**) uhL4 |i ?@|h@* h@|ic ?Lh _Lit | _iTi?_ L? |i Ui?|h@* M@?!ih<t Thiuihi?Uit AL tii |tc T*} ES ?|L E @?_ ti |i @tt4T|L? Lu h@|L?@* i TiU|@|L?t |L LM|@?G
' ?n c Eb
ihi ' Ec b
W4T*U@|L?t
At tiU|L? i @4?it @ ?4Mih Lu 4TLh|@?| ui@|hit Lu |i 4L_i* tL*|L? 6ht|c ?L|Ui |@| |i tL*|L? ?_ih @t)44i|hU Thiuihi?Uit U@? Mi tTiU@* 3i_ |L |i L?i LM|@?i_ t?} @ ^@_h@|U *Ltt u?U|L? AL tii |tc |@!i |i *4| Lu EH i? k $ f |L LM|@?
.EZmU ' ZW n bE &?
At i^@|L? ULhhitTL?_t |L |i L?i Lh}?@**) _ihi_ M) @hhL? @?_ BLh _L? EbHc T Db. W? |t U@ti |i ?@|L? M@tc bE &?c t t|hU|*)
TLt|i @?_c UL?ti^i?|*)c |i hi@*3i_ h@|i Lu ?@|L? t t)t|i4@|U@**) @MLi ZW iU@ti |i ?@|L? M@t t ?Uhi@t?} L? c @ RUL?tih@|i Ui?
|h@* M@?!ih |@| @||@Uit @ t4@**ih i}| |L ?i4T*L)4i?| t|@M*3@|L? ? ih *Ltt u?U|L? ?@4M}Lt*) hi_Uit |t 4@}?|_i OLiihc t?Ui |i LT|4@* @*i Lu 5 Efc 4 dtii +L}Lg EbHDc T .Hoc |i RUL?tih@|i Ui?|h@* M@?!ih hi_Uit M| U@??L| i*4?@|i |i ?@|L? M@t
L|i |@| ^@_h@|U Thiuihi?Uit Thi_U| @ *?i@h @?_ TLt|i hi*@|L?tT Mi|ii? ?@|L? @?_ |i ?@|h@* h@|i Lu ?i4T*L)4i?| W?t|i@_c |i 4L_i* | @t)44i|hU Thiuihi?Uit E }i?ih@|it @ TLt|i ?L?*?i@h hi*@|L? Mi |ii? Z @?_ ?c E Thi_U| |@| |i UL?_|L?@* @h@?Ui Lu ?@|L? i*Tt
uLhiU@t| |t 4i@?c @?_ E @**Lt i|ih @? ?@|L? Lh @ _i@|L?@h) M@t _iTi?_?} L? |i Ui?|h@* M@?!ih<t Thiuihi?Uit T@h@4i|iht AL tii |t *@|ih TL?|c ?L|i |@| |i ?L?*?i@h UL4TL?i?| E*k *?E n kbE &? t @*
@)t TLt|i OLiihc t?Ui |i |ih4 kj2
Z*2 ? EH U@? Mi TLt|i Lh
?i}@|i _iTi?_?} L? |i t}? Lu kc ?@|L? UL*_ Mi L? @ih@}i @MLi Lh Mi*L ZW
L?t_ih ht| |i U@ti ihi |i Thiuihi?Ui T@h@4i|ihc kc t ?i}@|i W? |t U@tic kj2
Z*2 : f @?_ |i 4L_i* Thi_U|t @? ii? *@h}ih TLt|i _iT@h
|hi Lu ?@|L? uhL4 ZW |@? |i tTiUU@|L? | ^@_h@|U Thiuihi?Uit
W? @__|L?c |i 4L_i* 4T*it @ TLt|i hi*@|L?tT Mi|ii? |i *ii* @?_ |i UL?_|L?@* @h@?Ui Lu ?@|L? At Thi_U|L? t ? *?i | i4Th U@* *|ih@|hi |@| hiTLh|t @ TLt|i hi*@|L? Mi|ii? |i ht| @?_ tiUL?_ ?@|L? 4L4i?|t ? 4L_ih@|i|L }?@|L? iTtL_it dtiic uLh i @4T*ic @**ic ?}c @?_ Ait*@ EbbSo
L?t_ih ?L |i 4Lhi T*@tM*i t|@|L? ihi k : f A@| tc TLt |i _i@|L?t uhL4 ZW @hi i}|i_ 4Lhi i@*) |@? ?i}@|i L?it ? |i
Ui?|h@* M@?!ih<t *Ltt u?U|L? Ai?c kj2
Z*2 f @?_ | 4}| Mi TLttM*i
uLh |t UL4TL?i?| |L Mi tUi?|*) *@h}i E? @MtL*|i @*i |L LihUL4i |i ?@|L? M@t At LMtih@|L? t}}it|t |@| |ihi i t|t @ @*i Lu kc uLh U @ RTh_i?| Ui?|h@* M@?!ih U@? i*4?@|i |i M@t @ttLU@|i_ | _tUhi|L?@h) TL*U)
At tti U@? Mi uLh4@**) i @4?i_ M) UL?t_ih?} |i ThLM*i4 Lu @ }L ih?4i?| UL?Uih?i_ | _i*i}@|?} 4L?i|@h) TL*U) |L @ RTh_i?| Ui?|h@* M@?!ih W? Lh_ih |L @**L @ _hiU| UL4T@htL? Mi|ii? |t 4L_i* @?_ Thi Lt *|ih@|hic @tt4i |@| |i }Lih?4i?|<t ELh ?|ihThi|i_ 4Lhi MhL@_*)c tLUi|)<t Thiuihi?Uit @hi _itUhMi_ M) |i t@* ^@_h@|U *Ltt u?U|L?G
CEZc ' E*2EZ ZW2n E*2E &?2 Ef
Ai?c }Lih?4i?|<t ThLM*i4 t
? .dCEZEkc mUoc ikj
uLh k 9' fc ihi |i 4?43@|L? |@!it EH @t }i?. +iU@**?} |@|
?i4T*L)4i?| _Lit ?L| _iTi?_ L? kc @?_ ?L|?} |@| YZ*Yk 9' fc |i ht|
:Dv lq suhfhglqj olwhudwxuh ^vhh/ iru h{dpsoh/ Urjr +4<;8, dqg Vyhqvvrq +4<<:,`/ wklv
sdshu suhvhuyhv wkh vlpsoli|lqj dvvxpswlrq wkdw wkh fhqwudo edqnhu*v suhihuhqfhv duh sxeolf lqirupdwlrq1 Wr prwlydwh wklv dvvxpswlrq/ lw frxog eh dujxhg wkdw wkh wudfn uhfrug dqg suhylrxvo|0h{suhvvhg rslqlrqv ri lqglylgxdov pljkw surylgh lqirupdwlrq derxw wkhlu suhihuhqfhv zkhq lq rfh1 Ehhvwpd dqg Mhqvhq +4<<;, dqg Pxvfdwhool +4<<<, h{dplqh wkh uhodwlyh phulwv ri lqdwlrq wdujhwv dqg olqhdu frqwudfwv lq d prgho zkhuh wkh fhqwudo edqnhu*v suhihuhqfhv duh xqrevhuyhg e| wkh jryhuqphqw dw wkh prphqw ri ghohjdwlrq1 Wkh xqfhuwdlqw| shuwdlqv rqo| wr wkh lqdwlrq2xqhpsor|phqw zhljkwv wkdw duh vwrfkdvwlf/ lq dq rwkhuzlvh vwdqgdug txdgudwlf orvv ixqfwlrq1
Lh_ih UL?_|L? t
.dEYC*YZEYZ*YkmUo ' .EZmU ZW ' f
Nt?} EHc | U@? Mi tii? |@| |i @*i kW |@| 4@ 43it tLU@* i*u@hi M)
_i*ih?} .EZmU ' ZW t |i L?i |@| tL*it
Ek ' kj2
Z*2 n E*k *?E n kbE &? ' f E
`*i |t i^@|L? @t ?L U*Lti_uLh4 tL*|L?c ThLTLt|L? e Mi*L tLt |@| @? kW _Lit i t| @?_ t ?^iH W? ThL?} ThLTLt|L? ec |i uL**L?}
hit*| t tiu*
hLTLt|L? Ek t 4L?L|L?U@**) _iUhi@t?} L? k 5 E*EbE &?c f ^ Efc 4
hLLu 5ii TTi?_ L?t_ih ?LG
hLTLt|L? e Aihi i t|t @ ?^i kW 5 Efc 4 tU |@| .EZmU ' ZW
hLLu +iU@** |@| |i ti| Lu @_4ttM*i @*it uLh k *@) ? |i ?|ih@* E*EbE &?c f ^ Efc 4 OLiihc t?Ui E*k *?E n kbE &?
@?_ j2
Z @hi t|hU|*) TLt|ic |i hLL| Lu Ek U@? L?*) *@) ? |i h@?}i Efc 4
L?t_ih |i *4|t
*4 Ek ' ZWn bE &? : f
k $ fn
@?_
*4 Ek ' ' 4c k $ n4
@?_ ?L|Ui Ek t UL?|?Lt L? k ? Efc 4 Oi?Uic |ihi i t|t @| *i@t| L?i @*i Lu k |@| tL*it E 5?Uic M) ThLTLt|L? c Ek t 4L?L|L?U@**) _iUhi@t?} L? kc |t @*i 4t| Mi ?^i~
;Wkh uhdfwlrq ixqfwlrq odehohg dv _rswlpdo% lq jxuh 5/ zdv lqghhg frqvwuxfwhg xvlqj
wkh ydoxh ri wkdw vroyhv +44, jlyhq wkh uhpdlqlqj vwuxfwxudo sdudphwhuv1 Wkh {hg srlqw zdv irxqg xvlqj wkh Qhzwrq phwkrg1
W| t 4TLh|@?| |L ?L|i |@| |i LT|4@**) RTh_i?| Ui?|h@* M@?!ih | Thiuihi?Ui T@h@4i|ih 4T*U|*) _i?i_ M) EkW ' fc 4T*i4i?|t |i LT|4@*
4L?i|@h) TL*U) ?_ih UL4T*i|i _tUhi|L?
Ai hi*@|L? Mi|ii? kW @?_ |i UL?_|L?@* @h@?Ui Lu ?@|L? @?_ |i
?@|h@* h@|i t L|*?i_ ? |i uL**L?} ThLTLt|L?G
hLTLt|L? D kW t ?Uhi@t?} L? ? @?_ _iUhi@t?} L? j2 Z
hLLu Nti |i 4T*U| u?U|L? |iLhi4 @?_ hLTLt|L? |L LM|@? YkW*Y?' EY*Y?*EY*YkW : fc
@?_
YkW*Yj2
Z ' EY*Yj2Z*EY*YkW f~
Aiti hit*|t ?_U@|i |@| @ 4Lhi Th_i?| Ui?|h@* M@?!ih tL*_ Mi @T TL?|i_ i? |i ?@|h@* h@|i Lu ?i4T*L)4i?| t }ih Lh ?@|L? t *itt L*@|*i W? |i ht| U@tic hiU@** |@| |i ?@|L? M@t t 4L?L|L?U@**) ?Uhi@t?} L? ? Ai?c |L 4L_ih@|i |i igiU| Lu ? L? |i i^*Mh4
|hL} |i UL4TL?i?| kj2
Z*2c @ *@h}ih _i}hii Lu Th_i?Ui t ?iUitt@h)
W? |i tiUL?_ U@tic ?L|i |@| i? j2
Z t *Lc @ UL4T@h@|i*) *@h}ih @*i Lu
k t hi^hi_ |L Lihh_i @ }i? ?@|L? M@t 6?@**)c uLh @*it Lu k : kWc |i |ih4 kj2
Z*2 t *@h}ih E? @MtL*|i
@*i |@? E*k *?EnkbE&? Atc kj2
Z*2nE*k *?EnkbE
&? f @?_ |i h@|i Lu ?@|L? t t)t|i4@|U@**) Mi*L |t tLU@**)LT|4@*
*ii* Oi?Ui @ _i@|L?@h) Eh@|ih |@? @? ?@|L?@h) M@t U@? @hti ? i^*Mh4
e L?U*tL?t @?_ 6|hi +iti@hU
At T@Tih Thiti?|t ?|@* hit*|t ? @ *@h}ih hiti@hU ThLiU| |@| i @4 ?it 4L?i|@h) TL*U) ?_ih @t)44i|hU Thiuihi?Uit Ai hi*i@?Ui Lu |t }i?ih@*3@|L? Lu |i Ui?|h@* M@?!ih<t *Ltt u?U|L? t **t|h@|i_ ihi ? |i t4T*it| TLttM*i ti|T Ai Ui?|h@* M@?!ih @?_ |i TM*U T*@) @ L?itL| }@4i |L| Th@|i ?uLh4@|L? W| t tL? |@| @*|L} |i Ui?|h@* M@?!ih<t hi@U|L? u?U|L? t ?L?*?i@h L? |i TM*U<t ?@|L? uLhiU@t|c |ihi
@hi UL?_|L?t ?_ih U |i @t i^*Mh4 i t|t @?_ t ?^i Lhi 4TLh|@?|*)c hi*@ ?} Uih|@?|) i^@*i?Ui 4i@?t |@| ?Uih|@?|) U@? ? _Ui Th_i?Ui 4L|i L? |i T@h| Lu |i 4L?i|@h) @|Lh|) h_i?Ui |i? 4L_ih@|it |i ?Ui?|i |L Uhi@|i thThti ?@|L? 6Lh Uih|@? T@h@4i|ih @*it LT|4@* ?@|L? U@? Mi LM|@?i_ 6h|ih4Lhic ? Uih|@? UhU4 t|@?Uitc @ _i@|L?@h) M@t U@? @hti ? i^*Mh4 At U@? i T*@?c uLh i @4T*ic ) |i ?_itM@?! h@tit |i _@)|L_@) ?|ihit| h@|i i? ? @|L? t @MLi |t t|i@_)t|@|i |hi?_ @*i M| M@hi*) hitTL?_t i? | t Mi*L dtii *@h_@ @?_ Bih|*ih Ebb.o
t T@h| Lu |i t@4i hiti@hU ThLiU|c +}ihU@ E2ff _ii*LTt @ _)?@4U 4L_i* Lu ?@|L? |@h}i|?} ihi |i ?@|h@* h@|i Lu ?i4T*L)4i?| t @**Li_ |L @h) Lih |4i Ai ?|i?|L? t |L i @4?i i|ih @t)44i|hU Thiuihi?Uit UL*_ @UUL?| uLh |i Tihtt|i?| ?_ihtLL|?} Lu ?@|L? |@h}i|t LMtihi_ ? tL4i UL?|hit hi*4?@h) it|4@|it Lu |i Ui?|h@* M@?!ih<t Thiuihi?Ui T@h@4i|iht uLh @?@_@c 5i_i?c @?_ |i N?|i_ k?}_L4 @hi t|@|t|U@**) _gihi?| uhL4 |i L?it 4T*i_ M) |i UL44L?*)ti_ ^@_h@|U *Ltt u?U|L? 6?@**)c t?Ui |i ?L|L? Lu @? @t)44i|hU Ui?|h@* M@?!<t *Ltt u?U|L? @t tL4i ?||i @TTi@* @?_ i4ThU@* tTTLh|c @? 4TLh|@?| UL4TL?i?| Lu |t hiti@hU @}i?_@ t |L ThL_i @_i^@|i 4UhLuL?_@|L?t uLh |t Thiuihi?Ui tTiUU@|L?
TTi?_ G hLLu Lu hLTLt|L?
+iU@** |@| k 9' f @?_ |@!i Y*Yk ' j2
Z*2nE*k2dkbE&?*EnkbE&?*?EnkbE&?o
5?Ui j2
Z*2 f @?_ E*k2 : fc @ tUi?| UL?_|L? uLh Y*Yk f t |@|
Ek ' kbE &?*E n kbE &? *?E n kbE &? f W **
tL |@| Ek $ f i? k $ f t @ }*LM@* 4@ 44 @?_c UL?ti^i?|*)c uLh @** L|ih @*it Lu k ? E*EbE&?c f^Efc 4c Ek f A@!?}
Y*Yk ' kbE &?*E n kbE &?2
L|i |@| Y*Yk $ f i? k $ f 6Lh @*it Lu k 5 E*EbE&?c fc
Ek t ?Uhi@t?} ? k 6Lh @*it Lu k 5 Efc 4c Ek t _iUhi@t?} ? k 5?Ui Ek $ f i? k $ fc |i? uLh @** @*it Lu k ? E*EbE &?c f ^ Efc 4c Ek f @?_ Y*Yk fc @t U*@4i_~
+iuihi?Uit
do @**ic + Ac ?}c 6c @?_ Ait*@c EbbSc R?@*)3?} W?@ |L? M) |i 6h@U|L?@**) W?|i}h@|i_ +6WB+O L_i*c aLh?@* Lu TT*i_ ,UL?L4i|hUtc G 2ef
d2o @hhLc + @?_ BLh_L?c # EbHc R Lt|i AiLh) Lu L?i|@h) L*U) ? @ @|h@* +@|i L_i*c aLh?@* Lu L*|U@* ,UL?L4)c bG DHbSf do ii|t4@c + @?_ ai?ti?c O EbbHc RW?@|L? A@h}i|t @?_ L?|h@U|t
| N?Uih|@? i?|h@* @?! hiuihi?Uitc aLh?@* Lu L?i)c hi_| @?_ @?!?}c fG HeGef
deo *?_ihc 5 EbbHc i?|h@* @?!?} ? AiLh) @?_ h@U|Uic Ai WA hittG @4Mh_}i
dDo @M@**ihLc + a Ebbfc RL?t4T|L? 33*it @?_ hiU@|L?@h) 5@ ?}tc aLh?@* Lu L?i|@h) ,UL?L4Utc 2DG S
dSo ht|Lgihti?c 6 @?_ #iML*_c 6 j Ebb.c RT|4@* hi_U|L? N?_ih t)44i|hU wLttc ,UL?L4i|hU AiLh)c G HfH H.
d.o *@h_@c + @?_ Bih|*ihc Ebb.c ROL |i ?_itM@?! L?_U|t L?i|@h) L*U)c ? +i_U?} W?@|L?c i_|i_ M) # +L4ih N?ih t|) Lu U@}L hittG U@}L
dHo *@h_@c +c B@*c ac @?_ Bih|*ihc Ebbbc RAi 5Ui?Ui Lu L?i|@h) L*U)G i ki)?it@? ihtTiU|ic aLh?@* Lu ,UL?L4U w|ih@|hic .G SS.f.
dbo ,?}ihc 5 `c OLiMihU|tc c @?_ 5U@*?}c , E2fffc R`) L?i) A@*!t @?_ `i@*| `tTihtG N?Uih|@?|) @?_ )t|^ic aLh ?@* Lu L?i)c hi_| @?_ @?!?} 2G 2H2D
dfo ,Tt|i?c w @?_ ~?c 5 EbHbc R5Mt|||L?c +t! ihtL?c @?_ |i Ai4TLh@* i@Lh Lu L?t4T|L? @?_ tti| +i|h?tG AiLhi|U@* 6h@4iLh!c ,UL?L4i|hU@ D.G b.bSb
do 6tUihc 5 Ebbec RL_ih? i?|h@* @?!?}c ? Ai @|hi Lu i?|h@* @?!?}c i_|i_ M) 6 @Tic BLL_@h|c 5 6tUihc @?_ 5U?@_| @4Mh_}i N?iht|) hittG @4Mh_}i
d2o BL*_u@?c W @?_ V@*_itc + Ebbbc RAi u|ih4@| Lu #iThiU@ |L?tc "@h|ih*) aLh?@* Lu ,UL?L4Utc eG 22b2S2
do Bh@?}ihc ` a @?_ it@h@?c O EbbSc R #iUtL? AiLhi|U T ThL@U |L 6LhiU@t| ,@*@|L?c N?iht|) Lu @4Mh_}ic #, `Lh!?} @Tih L bSH
deo Bhii?c a O EbbSc RW?@|L? A@h}i|?}G AiLh) @?_ W4T*U@|L?tc W6 5|@g @Tihtc eG ..b.bD
dDo B*c 6 Ebbc R AiLh) Lu #t@TTL?|4i?| ihtL?c ,UL?L4i|hU@ DbG SS.SHS
dSo Whi*@?_c Ebbbc R#Lit |i A4iL?tt|i?U) hLM*i4 , T*@? |i i@Lh Lu W?@|L? ? |i N?|i_ 5|@|itqc aLh?@* Lu L?i|@h) ,UL?L4Utc eeG 2.b2b
d.o ai?ti?c O Ebb.c Rhi_M*|) Lu T|4@* L?i|@h) #i*i}@|L?c 4ih U@? ,UL?L4U +iic H.G bb2f
dHo k)_*@?_c 6 @?_ hitUL||c , Eb..c R+*it +@|ih A@? #tUhi|L?G Ai W?UL?tt|i?U) Lu T|4@* *@?tc aLh?@* Lu L*|U@* ,UL?L4)c HDG e.ebf
dbo U@**4c A EbbDc RAL 6@**@Uit L?Uih??} i?|h@* @?! W? _iTi?_i?Uic 4ihU@? ,UL?L4U +ii @Tiht @?_ hLUii_?}tc HDG 2f2
d2fo LM@)c + @?_ ii*c # EbbHc RT|4@* L?i|@h) L*U) ? @ L_i* Lu t)44i|hU i?|h@* @?! hiuihi?Uitc wL?_L? 5ULL* Lu ,UL?L4Utc 4iL
d2o tU@|i**c V Ebbbc RW?@|L? L?|h@U|t @?_ W?@|L? A@h}i|t ? _ih N?Uih|@?|)G `) `i }| ii_ L?tih@|i i?|h@* @?!ihtc ,UL?L4U@c SSG 2e2De
d22o ihttL?c A @?_ A@Mi**?c B Ebbc R#it}??} W?t|||L?t uLh L?i |@h) 5|@M*|)c @h?i}i+LUit|ih L?uihi?Ui 5ihit L? M*U L*U)c bG DHe
d2o +L}Lgc k EbHDc RAi T|4@* #i}hii Lu L44|4i?| |L @ L?i|@h) A@h}i|c "@h|ih*) aLh?@* Lu ,UL?L4Utc ffG Sbbf
d2eo +}ihU@ E2fffc RN?ULih?} 6?@?U@* @h!i|<t i*iut @ML| W? @|L? A@h}i|tc aLh?@* Lu TT*i_ ,UL?L4i|hUtc DG eHD2
d2Do +}ihU@ E2ffc RW?@|L? A@h}i|?} ?_ih t)44i|hU hiuih i?Uitc N?iht|) Lu L?|hi@*c +#, `Lh!?} @Tih L fe2ff d2So 5i?ttL?c w , Ebb.c RT|4@* W?@|L? A@h}i|tc L?tih@|i
i?|h@* @?!tc @?_ w?i@h W?@|L? L?|h@U|tc 4ihU@? ,UL?L4U +iic H.G bHe
d2.o 5i?ttL?c w , Ebbbc RW?@|L? A@h}i|?} @t @ L?i|@h) L*U) +*ic aLh?@* Lu L?i|@h) ,UL?L4Utc eG Sf.SDe
d2Ho V@h@?c O Eb.ec R @)it@? TThL@U |L +i@* ,t|@|i ttitt4i?|c ? 5|_it ? @)it@? ,UL?L4Ut ? OL?Lh Lu w a 5@@}ic i_|i_ M) 5 , 6i?Mih} @?_ ~i**?ih Lh|OL**@?_G 4t|ih_@4
d2bo `@*tc EbbDc RT|4@* L?|h@U|t uLh W?_iTi?_i?| i?|h@* @?!ihtc 4ihU@? ,UL?L4U +iic HDG DfS.
dfo ~i**?ihc EbHSc R@)it@? ,t|4@|L? @?_ hi_U|L? Nt?} t)4 4i|hU wLtt 6?U|L?tc aLh?@* Lu |i 4ihU@? 5|@|t|U@* ttLU@|L?c HG eeSeD