42
tti| hU?} ? hL_U|L? ,UL?L4it NhM@? a aih4@?? ‘@h|L? 5ULL* N?iht|) Lu i??t)*@?@ 6ht| _h@u|G Li4Mih bb At ihtL?G @) bbe W?|hL_U|L? Ai Mt?itt U)U*i Mi@Lh Lu @tti| hi|h?t @t hiUi?|*) @||h@U|i_ @ }hi@| _i@* Lu @||i?|L?c ML| uhL4 ?@?U@* iUL?L4t|t @?_ uhL4 4@UhLiUL?L4t|t

tti| ˘h U ?} ? ˘hL U| L? ,UL?L4 itfinance.wharton.upenn.edu/~jermann/appapold.pdf · tti| ˘h U ?} ? ˘hL_U| L? ,UL?L4 it NhM@?a aih4@?? ‘@h|L?5ULL* N? ... Li@h* ih* ?itLuhiti@hU

  • Upload
    hakien

  • View
    221

  • Download
    0

Embed Size (px)

Citation preview

�tti| �h�U�?} �? �hL_�U|�L? ,UL?L4�it

NhM@? a� aih4@??�

`�@h|L? 5U�LL*N?��iht�|) Lu �i??t)*�@?�@

6�ht| _h@u|G �L�i4Mih �bb�A��t �iht�L?G �@) �bbe

Devwudfw

Wklv sdshu vwxglhv wkh lqwhudfwlrq ehwzhhq dvvhw uhwxuqv dqg exvl0

qhvv f|fohv lq gl�huhqw yhuvlrqv ri wkh rqh0vhfwru vwrfkdvwlf jurzwk

prgho1 Zh vkrz wkdw d prgho zlwk fdslwdo dgmxvwphqw frvwv/ kdelw

irupdwlrq suhihuhqfhv dqg �qdqfldo ohyhudjh suhglfwv htxlw| ulvn suh0

pld ri vhyhudo shufhqwdjh srlqwv1 Lq ghprqvwudwlqj wklv uhvxow wkh

sdshu dovr suhvhqwv d phwkrg wkdw doorzv rqh wr vroyh iru dvvhw uh0

wxuqv lq d odujh fodvv ri pdfurhfrqrplf prghov1 Nh|zrugv= Htxlw|

suhplxp> uhdo exvlqhvv f|fohv> orjqrupdo glvwulexwlrq1

� W?|hL_�U|�L?

A�i M�t�?itt U)U*i Mi�@��Lh Lu @tti| hi|�h?t �@t hiUi?|*) @||h@U|i_ @ }hi@|_i@* Lu @||i?|�L?c ML|� uhL4 �?@?U�@* iUL?L4�t|t @?_ uhL4 4@UhLiUL?L4�t|t�

�Fruuhvsrqghqfh wr= Xuedq M1 Mhupdqq/ Zkduwrq Vfkrro/ Xqlyhuvlw| ri Shqqv|oydqld/Ilqdqfh Ghsduwphqw/ Vwhlqehuj Kdoo 0 Glhwulfk Kdoo/ Vxlwh 558;/ Sklodghoskld/ SD 4<4370969:1 Wklv surmhfw kdv ehqh�wwhg iurp wkh lqwhoohfwxdo vxssruw ri Pduldqqh Ed{whu/ KdqvJhqehuj/ Urehuw J1 Nlqj dqg Plfkdho Nrxsdulwvdv/ dqg iurp wkh frpphqwv ri vhplqdusduwlflsdqwv dw wkh Ihghudo Uhvhuyh lq Zdvklqjwrq/ wkh Judgxdwh Lqvwlwxwh ri LqwhuqdwlrqdoVwxglhv lq Jhqhyd dqg wkh QEHU dvvhw sulflqj phhwlqj lq Ervwrq1 Ilqdqfldo vxssruwiurp wkh Irqgv qdwlrqdo gh od uhfkhufkh vflhqwl�txh/ wkh Irqgdwlrq Kdqv Zlovgrui dqg wkhVrfl�hw�h dfdg�hpltxh gh o*Xqlyhuvlw�h gh Jhq�hyh lv judwhixoo| dfnqrzohgjhg1 Doo uhpdlqlqjhuuruv duh p| rzq1

W? �?@?U�@* iUL?L4�Utc ti�ih@* i4T�h�U@* t|�_�it �@�i _LU�4i?|i_ �4TLh|@?|U)U*�U@* �@h�@|�L?t �? �@h�L�t tiU�h�|) hi|�h?t @?_ h�t! Thi4�@c M�| *�||*i �t!?L�? |L _@|i @ML�| |�i Lh�}�?t Lu |�iti �@h�@|�L?t�� W? 4@UhLiUL?L4�Utc @t�ti| hi|�h?t �@�i *L?} T*@)i_ @? �4TLh|@?| hL*i @t *i@_�?} iUL?L4�U �?_�U@|LhtchiUi?| i4T�h�U@* t|�_�it i4T�@t�3i |�iti hi*@|�L?t��Tt�2

A�i _L4�?@?| @?@*)|�U@* uh@4i�Lh! uLh t|�_)�?} |�i hi*@|�L?t��Tt Mi�|�ii? @tti| hi|�h?t @?_ iUL?L4�U ��U|�@|�L?t �t M@ti_ L? |�i i?_L�4i?|4L_i* Lu w�U@t E�b.H�� A��t 4L_i* �t @ U*i�ih |�iLhi|�U@* @Mt|h@U|�L?c t�?Ui�| Tih4�|t |�i t|�_) Lu @tti| hi|�h?t �? @ T@ht�4L?�L�t �?|ih|i4TLh@* uh@4i��Lh!� A��t uh@4i�Lh! ?i�ih|�i*itt �@t �|t *�4�|@|�L?t� 6�ht|c |�i 4L_i* *@U!thi@*�t4c �? |�@| _���_i?_t @?_ UL?t�4T|�L? @hi i^�@* |L i?_L�4i?|c |�i *@|ihMi�?} tTiU��i_ i L}i?L�t*)� 5iUL?_c MiU@�ti T@)L�|t @?_ UL?t�4T|�L? @hii L}i?L�tc @? i?_L�4i?| 4L_i* Lgiht ?L i T*@?@|�L? uLh ��@| @U|�@**) _i�|ih4�?it |�iti ^�@?|�|�it� 5|�_)�?} |�i igiU|t Lu iUL?L4�U t�LU!t EThL_�U�|���|)c �tU@* Lh 4L?i|@h)� L? @tti| hi|�h?t hi^��hit @ 4L_i* ��ihi UL?t�4T�|�L? @?_ ThL_�U|�L? �t _i|ih4�?i_ i?_L}i?L�t*)� A��h_c i?_L�4i?| 4L_i*tLgih ?L Thi_�U|�L?t @ML�| �L� @tti| hi|�h?t @hi hi*@|i_ |L _�gihi?| 4@UhL�iUL?L4�U ^�@?|�|�it� N?_iht|@?_�?} ��@| |�i 4@UhLiUL?L4�U h�t! u@U|Lht @hihi^��hit 4L_i*t |�@| }i?ih@|i @ h�U� ti| Lu Thi_�U|�L?t uLh |�i hi*@|�L?t��TtLu @tti| hi|�h?t ��|� �@h�L�t 4@UhLiUL?L4�U ^�@?|�|�it� AL UL?|h�M�|i |L @Mi||ih �?_iht|@?_�?} Lu |�i _i|ih4�?@?|t Lu @tti| hi|�h?tc |��t T@Tih �?_ih�|@!it @ ^�@?|�|@|��i t|�_) Lu @tti| hi|�h?t �? iUL?L4�it ��ihi ThL_�U|�L?�t i T*�U�|*) 4L_i*i_� W? T@h|�U�*@hc �i uLU�t L? ��i|�ih _�gihi?| �iht�L?tLu |�i L?i tiU|Lh hi@* M�t�?itt U)U*i 4L_i*c _h��i? M) ThL_�U|���|) t�LU!tcU@? i T*@�? ��t|Lh�U@* hi|�h? Thi4�@� �L4T@hi_ ��|� i?_L�4i?| 4L_i*tc_���_i?_ �L�t @hi _ih��i_ uhL4 4Lhi hi@*�t|�U @tt�4T|�L?t @ML�| |�i ?@|�hiLu ThL_�U|�L? @?_ �?�it|4i?| @U|���|) M) �h4tc @?_ M) UL?t�_ih�?} �?@?U�@**i�ih@}i� W? @__�|�L?c |�i tTiU��U@|�L? Lu ThL_�U|�L? @*L?} t|@?_@h_ ?iLU*@t�t�U@* *�?it Tih4�|t |�i t|�_) Lu �L� UL?t�4T|�L? ThL�*it hitTL?_ |L U�@?}it�? Thiuihi?Uit�� �@|�h@**)c t�U� }i?ih@* i^��*�Mh��4 ThL_�U|�L? 4L_i*t U@??i�ih _L Mi||ih |�@? 4L_i*t |�@| tTiU�u) UL?t�4T|�L? @?_ T@)L�| ThLUittit

4D ihz h{dpsohv ri wkhvh vwxglhv duh= Idpd dqg Iuhqfk +4<;<,/ Idpd +4<<3, dqgVfkzhuw +4<;</ 4<<3,1

5Vrph ri wkhvh vwxglhv duh= Fkhq +4<<4,/ Hvwuhood dqg Kdugrxyholv +4<<4, dqg Vwrfndqg Zdwvrq +4<;<,1

6Frfkudqh +4<<4/ 4<<5d, suhvhqwv dqrwkhu dssurdfk iru lqwhuwhpsrudo dvvhw sulflqj1 Khhydoxdwhv dvvhw sulflqj uhodwlrqvklsv ghulyhg iurp surgxfhuv* �uvw rughu frqglwlrqv1

2

i L}i?L�t*)( |�i ^�it|�L? Lu L�h t|�_) �t |�ihiuLhi �u L?i U@? LM|@�? i?_L}i�?L�t ThLUittit |�@| i T*@�? |�i t|)*�3i_ u@U|t Lu @tti| hi|�h?t�

�h�Lh hiti@hU� M@ti_ L? i?_L�4i?| 4L_i*t �@t 4@�?*) uLU�ti_ L? 4L_���U@|�L?t Lu |�i t|@?_@h_ 4L_i* |�@| U@? tL*�i �i�h@ @?_ �hitUL||<t E�bHD�Ri^��|) Thi4��4 T�33*i�� � *@h}i ML_) Lu *�|ih@|�hi �@t _i��ti_ ti�ih@* 4L_���U@|�L?t Lu Thiuihi?Uit @?_ T@)L�| t|h�U|�hi |�@| tL*�i |�i i^��|) Thi4��4T�33*i�e OL�i�ihc i |i?t�L?t |L 4L_i*t ��|� ?L?|h���@* ThL_�U|�L? tiU|Lht�ihi *itt t�UUittu�* @*L?} |��t *�?i Ei�}�c #@?|��?ic #L?@*_tL? @?_ �i�h@E�bb2�c +L��i?�Lht| E�bb���� W?_ii_c +L��i?�Lht| E�bb�� �?_t |�@| �| �t4Lhi _��U�*| |L i T*@�? t�Mt|@?|�@* h�t! Thi4�@ MiU@�ti i?_L}i?L�t UL?�t�4T|�L? MiUL4it i�i? t4LL|�ih @t h�t! @�iht�L? �t �?Uhi@ti_� A�i hi@tL?Mi��?_ |��t �t |�@| �? |�i t|@?_@h_ L?i�tiU|Lh 4L_i* @}i?|t U@? i@t�*) @*|ih|�i�h ThL_�U|�L? T*@?t |L hi_�Ui ��U|�@|�L?t �? UL?t�4T|�L?� A��t t�}}it|t|�@| |�i uh�U|�L?*itt @?_ �?t|@?|@?iL�t @_��t|4i?| Lu |�i U@T�|@* t|LU! �t @4@�Lh �i@!?itt �? |��t uh@4i�Lh!� �?i �@) |L L�ihUL4i |��t �t |L �?|hL_�UiU@T�|@* @_��t|4i?| ULt|t� �@T�|@* @_��t|4i?| ULt|t �@�i @ *L?} |h@_�|�L?�? |�i �?�it|4i?| *�|ih@|�hic |�i) @*tL ThL��_i @ uLh4@* uh@4i�Lh! uLh |�iTLT�*@h R^� |�iLh) E^ �t _i�?i_ @t |�i �@*�i Lu |�i U@T�|@* t|LU! _���_i_M) �|t hiT*@Ui4i?| ULt|�� W| |�ihiuLhi tii4t ?@|�h@* |L �?|hL_�Ui U@T�|@*@_��t|4i?| ULt|t �?|L |��t t|@?_@h_ uh@4i�Lh!� W? u@U|c ��|�L�| U@T�|@* @_���t|4i?| ULt|tc @t 4Lt| U�hhi?| M�t�?itt U)U*i 4L_i*t @hic |�iti 4L_i*t @hiT*@}�i_ M) @ UL�?|ihu@U|�@* UL?t|@?| ^� B��i? �|t Thi��L�t t�UUitt �? tL*��?}|�i i^��|) Thi4��4 T�33*i �? 4L_i*t ��|� |h���@* ThL_�U|�L? tiU|Lht Ei�}��Mi* E�bbf�c �L?t|@?|�?�_it E�bbf�� L�h @?@*)t�t @*tL �?U*�_it �@M�| uLh4@�|�L? Thiuihi?Uitc �? @__�|�L? |L |�i t|@?_@h_ |�4i�tiT@h@M*i tTiU��U@|�L?� i�?_ |�@| @? L|�ih��ti t|@?_@h_ 4L_i* ��|� U@T�|@* @_��t|4i?| ULt|tc |�@|@hi UL?t�t|i?| ��|� hi@*�t|�U �?�it|4i?| �L*@|�*�|) @?_ �? |�i h@?}i Lu i4T�h��U@**) T*@�t�M*i �@*�itc @?_ �@M�| uLh4@|�L? Thiuihi?Uit U@? }i?ih@|i i^��|)Thi4�@ Lu ti�ih@* TihUi?|@}i TL�?|t� �LhiL�ihc L�h t|�_) _i4L?t|h@|it |�@|�?@?U�@* *i�ih@}i _Lit @*tL �i*T i T*@�? |�i ��t|Lh�U i Uitt hi|�h?t Lu t|LU!tL�ih *L?} |ih4 ML?_t�

AL t|�_) |�iti TL�?|tc |�i T@Tih _i�i*LTt @ uh@4i�Lh! uLh UL4T�|�?}@tti| hi|�h?t @?_ uLh |��?!�?} @ML�| |�i U)U*�U@* �@h�@|�L? Lu @tti| hi|�h?t

7Dq lqfrpsohwh olvw ri vwxglhv wkdw sursrvh vroxwlrqv wr wkh htxlw| suhplxp sx}}oh lvEhqqlqjd dqg Surwrsdsdgdnlv +4<<3,/ Deho +4<<3,/ Frqvwdqwlqlghv +4<<3,/ Ulhw} +4<;;,dqg Pdqnlz +4<;9,1

|�@| �t @TT*�U@M*i |L @ MhL@_ h@?}i Lu 4@UhLiUL?L4�U |�iLh�it� A��t �t _L?iM) UL4M�?�?} hit�*|t uhL4 |�L i@h*�ih *�?it Lu hiti@hU� �? �?@?Ui @?_ 4@UhL�iUL?L4�Ut� 6�ht|c @tti| Th�U�?} uLh4�*@i M@ti_ L? |�i UL?_�|�L?@* *L}?Lh4@*_�t|h�M�|�L? �@�i *L?} Mii? �ti_ �? �?@?Ui� �Lhi hiUi?|*)c �@4TMi** E�bHS��tit t�U� uLh4�*@i |L �@*�i tiU�h�|�it ��|� t�?}*i�Tih�L_ T@)L�|t Et�4T*i ti�U�h�|�it� �? @ }i?ih@* i^��*�Mh��4 UL?|i |� � !i) ��h|�i Lu |�iti uLh4�*@i �t|�@| L?i U@? hi@_�*) �?_iht|@?_ |�i _i|ih4�?@?|t Lu h�t! Thi4�@ �? |ih4tLu |�i UL�@h�@|�L? Lu @ tiU�h�|)<t T@)L�|t ��|� @ M@t�U �@*�@|�L?� 5iUL?_c4@?) _)?@4�U h@|�L?@* i TiU|@|�L?t 4@UhLiUL?L4�U 4L_i*t �@�i @ *L}*�?i@hhi_�Ui_ uLh4�D �L4M�?�?} |�iti |�L |�iLhi|�U@* uh@4i�Lh!t _i*��iht Th�U�?}hi*@|�L?t |�@| ��}�*�}�| |�i 4@UhLiUL?L4�U _i|ih4�?@?|t Lu @tti| hi|�h?t�OL�i�ihc *L}?Lh4@* uLh4�*@i @?_ *L}*�?i@h 4L_i*t @*tL �4T*) |�@| t�4T*itiU�h�|�it E��|� @ t�?}*i�Tih�L_ T@)L�|� �@�i h�t! Thi4�@ ���U� _L ?L| �@h)��|� |�i t|@}it Lu |�i M�t�?itt U)U*i� vi|c @t |�i @?@*)t�t Mi*L� 4@!it U*i@hc4Lt| t|@?_@h_ tiU�h�|�itc t�U� @t UL44L? t|LU!t @?_ UL�TL? ML?_tc @hiUL4T*i tiU�h�|�itc ��i�c |�i) U@? Mi ��i�i_ @t TLh|uL*�Lt Lu t�4T*i tiU�h�|�it��L?ti^�i?|*)c �i @hi @M*i |L t�L� |�@| i TiU|i_ hi|�h?t @?_ h�t! Thi4�@ LuUL4T*i tiU�h�|�it �@h) @t @ u�?U|�L? Lu 4@UhLiUL?L4�U u@U|Lht�

A�i Lh}@?�3@|�L? Lu |�i T@Tih �t @t uL**L�t� 5iU|�L? 2 Thiti?|t }i?ih@*@?@*)|�U@* hit�*|t LM|@�?i_ �? |�i *L}*�?i@h @tti| Th�U�?} uh@4i�Lh!� 5iU|�L? �_�tU�ttit UL?t�4T|�L?�M@ti_ @tti| Th�U�?}c M) UL4T@h�?} �@4TMi**<t E�bHS�4L_i* ��|� |�4i�tiT@h@M*i Thiuihi?Uit |L @ �iht�L? Lu |�i �L?t|@?|�?�_itE�bbf� 4L_i* ��|� ?L?�|�4i�tiT@h@M*i Thiuihi?Uit� 5iU|�L? e t|�_�it h�t!Thi4�@ Lu @tti| hi|�h?t �? @ L?i�tiU|Lh hi@* M�t�?itt U)U*i 4L_i* ��|� _�gihi?|Thiuihi?Ui tTiU��U@|�L?t� 5iU|�L? D UL?|@�?t UL?U*�t�L?t @?_ _�hiU|�L?t uLhu�|�hi �Lh!�

2 wL}*�?i@h @tti| Th�U�?}c @?@*)|�U@* hit�*|t

A�i *L}?Lh4@* _�t|h�M�|�L? �@t i?�L)i_ UL?t�_ih@M*i TLT�*@h�|) �? |�i �?�|ih|i4TLh@* @tti| Th�U�?} *�|ih@|�hi� ,�i? |�L�}� |��t _�t|h�M�|�L?@* @tt�4T�|�L? 4@) Mi |LL hit|h�U|��ic �| �t @||h@U|��i MiU@�ti �| Tih4�|t @? @?@*)|�U@*tL*�|�L? |L |�i �?|ih|i4TLh@* i�U�i?U) UL?_�|�L?� 5�U� U*Lti_ uLh4 tL*�|�L?t

8Uhdo exvlqhvv f|foh prghov dorqj wkh olqhv ri Nlqj/ Sorvvhu dqg Uhehor +4<;;, kdyhwkh uhtxluhg orjolqhdu uhgxfhg irup> pdq| rwkhu h{dpsohv ri prghov duh glvfxvvhg odwhu lqwkh sdshu1

e

@hi _it�h@M*i MiU@�ti |�i) ThL��_i �?t�}�|t ?L| TLtt�M*i ��|� |�i @*|ih?@|��i@TThL@U� Lu ?�4ih�U@* @TThL �4@|�L? 4i|�L_t� �*Lti_ uLh4 tL*�|�L?t @hi@*tL i@t�ih @?_ u@t|ih |L �ti( @?_ |��t @**L�t L?i |L tL*�i 4L_i*t ��|� ti��ih@* t|@|i �@h�@M*it �? 4�U� *itt |�4i |�@? ��|� @*|ih?@|��i 4i|�L_t |�@| �ti�|ih@|��i ThLUi_�hit�

�L|@M*ic hiUi?| t|�_�it |�@| �ti *L}?Lh4@*�|) �?U*�_i O@?ti? @?_ 5�?�}*i|L? E�bH�� @?_ �@4TMi** E�bHS�� A�i uh@4i�Lh! Thiti?|i_ �ihi i |i?_t�@4TMi** E�bHS� @*L?} |�L _�4i?t�L?t� 6�ht|c �i �ti @ 4�*|��@h�@|i ti||�?}��ihi |�i @tti|<t T@)L�|t @?_ �|t �@*�@|�L? @hi U*i@h*) _�t|�?U|c @t LTTLti_|L i?_L�4i?| 4L_i*t ��ihi _���_i?_t @hi i^�@* |L i?_L�4i?| @?_ |�i �@*��@|�L? �t tL*i*) _i|ih4�?i_ M) i?_L�4i?| @?_ h�t! Thiuihi?Uit� 5iUL?_c �i��** �?|hL_�Ui UL4TLt�|i tiU�h�|�it ��|� 4�*|�T*i T@)L�|t� W? @__�|�L? |L Mi��?} 4Lhi }i?ih@*c |��t *@t| i |i?t�L? �t t�L�? |L @**L� uLh |�4i �@h�@|�L? �?UL?_�|�L?@* i Uitt hi|�h?t @?_ �@h�@?Uit� #itT�|i |�iti i |i?t�L?t |�i �?�|��|��i hi*@|�L?t��Tt Mi|�ii? @tti| hi|�h?t @?_ M�t�?itt U)U*i @hi }i?ih@**)Thitih�i_�S

2�� +i|�h?t uLh @tti|t ��|� @ t�?}*i T@)L�|

W?|ih|i4TLh@* @tti| Th�U�?} �tit |�i u@U| |�@| @?) U*@�4 |L @ TL|i?|�@**)h@?_L4 u�|�hi T@)L�| (|n& U@? Mi �@*�i_ M) |�i Thiti?| �@*�i hi*@|�L?t��TG

T|d(|n&o 'q&.|d\|n&(|n&o

\|

c E��

��ihi q �t |�i T�hi |�4i _�tUL�?| u@U|Lhc @?_ \|n& |�i 4@h}�?@* �@*�@|�L? Lu|�i ?�4ih@�hi @| |n &�

A�i t|h�U|�hi Lu L�h 4L_i* iUL?L4) �t @t uL**L�t� A�i *L}@h�|�4 Lu |�i_���_i?_ T@)L�| _| ' ,J}E(|�c @?_ |�i *L}@h�|�4 Lu @ �@*�@|�L? b| ' *L}E\|�@hi @tt�4i_ |L Mi *�?i@h UL4M�?@|�L?t Lu |�i *L}@h�|�4 Lu |�i t|@|i �iU|Lhr|� A�i t|@|i �iU|Lh �t @tt�4i_ |L uL**L� @ �ht| Lh_ih @�|Lhi}hitt��i ThLUitt��|� 4�*|��@h�@|i ?Lh4@* ����_� �4T�*titG

b| ' ,br|_| ' ,_r|r| ' �r|3� n "|

E2�

9Sduwv ri wklv vhfwlrq duh edvhg rq vrph uhvhdufk qrwhv ri U1 J1 Nlqj dqg J1 N1

Urxzhqkruvw1

D

��ihi |�i t^�@hi 4@|h� � }L�ih?t |�i _)?@4�Ut Lu |�i t)t|i4� i hi^��hi|�i t)t|i4 |L Mi t|@|�L?@h) Lh UE�� ?L?t|@|�L?@h)� A��tc |�i U�@h@U|ih�t|�UhLL|t Lu � �@�i 4L_�*�t *itt |�@? Lh i^�@* |L L?i� A�i u@U|Lh *L@_�?}t ,b@?_ ,_ @hi hL� �iU|Lht� B��i? ?Lh4@*�|) Lu |�i �4T�*titc |�i _���_i?_ @?_ �|t�@*�@|�L? @hi UL?_�|�L?@**) *L}?Lh4@*� A�i *�?i@h �L4Lt!i_@t|�U ?@|�hi Lu|�i t)t|i4 �4T*�it |�@| UL?_�|�L?@* tiUL?_ 4L4i?|t Lu _| @?_ b| @hi UL?t|@?|c@ hit�*| |�@| �t �ti_ hiTi@|i_*) Mi*L��

, TiU|i_ hi|�h?t

i ��** �ht| UL?t�_ih |�i U@ti Lu @tti|t ��|� @ t�?}*i T@)L�|c ���U� �i U@**Rt|h�Tt�� A��t |ih4 hiuiht |L |�i @U|�@* Th@U|�Ui �? tiU�h�|) �h4t Lu t|h�TT�?}ML?_t M) tiT@h@|�?} UL�TL? @?_ Th�?U�T@* @?_ ti**�?} |�i4 tiT@h@|i*) @t3ihL�UL�TL? ML?_t� �?i hi@tL? uLh t|�_)�?} t|h�Tt �t |�@| |�i) @hi i@t�ih |L|��?! @ML�|( 4Lhi UL4T*i tiU�h�|�it @hi UL?t|h�U|i_ @t M�?_*it Lu t|h�Tt�6Lh @ !�Tih�L_ t|h�Tc �i _i�?i |�i L?i Tih�L_ �L*_�?} hi|�h? @tG

-|c|n�d(|n&o 'T|n�d(|n&o

T|d(|n&oE��

W? Lh_ih |L tL*�i uLh |�i UL?_�|�L?@* i TiU|i_ hi|�h? .|E-|c|n�d(|n&o� �i�ht| |@!i |�i i TiU|@|�L? Lu T|n�d(|n&o @| |�4i |� N?_ih |�i @tt�4T|�L? Lu*L}?Lh4@*�|)c |��t }��itG

.|ET|n�d(|n&o� ' q&3�.| i TE.|n�E_|n& n b|n& � b|n�� n�

2�@h|n�E_|n& n b|n&��

' q&3� i TE.|E_|n& n b|n& � b|n���� i TE�

2�@h|E.|n�E_|n& n b|n& � b|n��� n

2�@h|n�E_|n& n b|n&��

Ee��L4M�?�?} |��t ��|� |�i �@*�@|�L? Lu T|d(|n&oc �i }i| @u|ih tL4i 4@?�T�*@�|�L? |�@|G

.|E-|c|n�d(|n&o� ' -|c|n�d�|n�o� i TE� UL�|Eb|n�c .|n�b|n& � b|n���� i TE� UL�|Eb|n�c .|n�_|n&���

ED�

,^�@|�L? ED� t�L�t |�@| |�i UL?_�|�L?@* i TiU|i_ hi|�h? Lu @ U*@�4 |L (|n&

U@? �tiu�**) Mi _���_i_ �?|L |�hii UL4TL?i?|tc ���U� �i _�tU�tt �? |�h?Mi*L��

S

#i|ih4�?@?|t Lu i TiU|i_ hi|�h?t

+�t! uhii h@|iG A�i �ht| |ih4 �? i^�@|�L? ED�c -|c|n�d�|n�o ' �*T|d�|n�ochiThiti?|t |�i hi|�h? |L �L*_�?} @ L?i�Tih�L_ ML?_ �?|�* 4@|�h�|)c ��i�c |�ih�t! uhii h@|i� `��*i |��t �?�it|4i?| �t h�t!*itt ��|� hitTiU| |L �|t i TiU|i_hi|�h?c �?Uih|@�?|) ?i�ih|�i*itt @giU|t |�i *i�i* Lu |��t hi|�h?� AL tii |��tchi�h�|i |�i h�t! uhii h@|i @tG

-|c|n�d�|n�o ' q3� i TEb| � .|b|n� ��

2�@h|Eb|n���� ES�

A�i �ht| |�L UL4TL?i?|t �? |�i i TL?i?|�@* u�?U|�L? U@T|�hi |�i t|@?_@h_igiU| Lu |�i �?|ih|i4TLh@* 4@h}�?@* h@|i Lu t�Mt|�|�|�L? L? i^��*�Mh��4 �?�|ihit| h@|it� W? T@h|�U�*@hc |�i *itt u�|�hi T@)L�|t @hi �@*�i_ ��|� hitTiU||L Thiti?| T@)L�|tc .|b|n� b|c |�i ��}�ih �t |�i i^��*�Mh��4 �?|ihit| h@|i�A�i �@h�@?Ui |ih4 �? ES� t|@?_t uLh ThiU@�|�L?@h) igiU|tc �? |�i ti?ti |�@| �|hi�iU|t �L� �?Uih|@�?|) @giU|t |�i LT|�4@* _iU�t�L? @?_ �i?Ui |�i i^��*�M�h��4 �?|ihit| h@|i� W?|��|��i*)c |�i ��}�ih �t �?Uih|@�?|)c |�i *itt @}i?|t ?ii_|L Mi UL4Ti?t@|i_ uLh TLt|TL?�?} |�i�h UL?t�4T|�L?�.

Aih4 @?_ T@)L�| �?Uih|@�?|) Thi4�@G A�i tiUL?_ |ih4 Lu i^�@�|�L? ED�c� UL�|Eb|n�c .|n�b|n& � b|n��c U@? Mi |�L�}�| Lu @t @ �L*_�?} Lh |ih4 Thi�4��4 uLh @ !�Tih�L_ _�tUL�?| ML?_ |�@| _iTi?_t L? |�i |ih4 t|h�U|�hi Lu�?|ihit| h@|it� W?_ii_c �u L?i i TiU|t U@T�|@* }@�?t @t @ UL?ti^�i?Ui Lu *L�ih�?|ihit| h@|it E|��t �t |�i U@ti ��i? .|n�b|n& i Uii_t b|n�� |L Mi UL?|i4�TLh@?iL�t ��|� *L� �@*�@|�L?c |�i? |��t �?u@�Lh@M*i ULhhi*@|�L? �@t |L MiUL4Ti?t@|i_ M) @ TLt�|��i h�t! Thi4��4� 6�?@**)c |�i |��h_ i*i4i?| Lu ED�c� UL�|Eb|n�c .|n�_|n&�c �t @}@�? *�?!i_ |L @ TLtt�M*i U@T�|@* }@�? Lh *Ltt @| |�4i|n�� Wu U@T�|@* }@�?t E��}�ih |�@? @�ih@}i i TiU|i_ T@)L�|t @| |�4i |n&� @hi?i}@|��i*) ULhhi*@|i_ ��|� |�i �@*�@|�L?c |�i? @}@�? @ h�t! Thi4��4 �t ?ii_i_|L UL4Ti?t@|i |�i �?�it|Lh uLh |�i �?_it�h@M*i U)U*�U@* ThLTih|) Lu |��t @tti|�W? L�h t�Mti^�i?| _�tU�tt�L? �i ��** U@** |�iti |�L UL�@h�@?Ui |ih4t hitTiU�|��i*) |�i |ih4 Thi4��4c #|E&�c @?_ |�i T@)L�| �?Uih|@�?|) Thi4��4c #RE&��

:Wklv lv uhodwhg wr wkh suhfdxwlrqdu| vdylqjv h�hfw glvfxvvhg lq wkh olwhudwxuh/ iru lq0

vwdqfh Nlpedoo +4<<3,1 Lq jhqhudo/ wklv uhvxow lv olqnhg wr wkh dvvxpswlrq ri frqyh{ pdu0

jlqdo xwlolw| ri frqvxpswlrq1 Li zh dvvxph wkdw pdujlqdo xwlolw| lv htxdo wr wkh h{srqhqwldo

ri d olqhdu frpelqdwlrq ri wkh vwdwhv/ pdujlqdo xwlolw| ehfrphv d frqyh{ ixqfwlrq ri wkh

orj ri wkh vwdwh lwvhoi1

.

A�i t�4 Lu |�iti |�L �t _i�?i_ @t |�i _���_i?_ Thi4��4c #_E&�� OL�i�ihc�| t�L�*_ Mi U*i@h |�@| ��|�L�| @__�|�L?@* �?uLh4@|�L? @ML�| |�i t|LU�@t|�UThLUittit Lu _���_i?_t @?_ 4@h}�?@* �@*�@|�L?t ?L|��?} U@? Mi t@�_ @ML�||�i t�}? Lh |�i 4@}?�|�_i Lu |�iti Thi4�@�

�| |��t t|@}ic �| �t �tiu�* |L t�44@h�3i tL4i hit�*|t |�@| U�@h@U|ih�3i i �TiU|i_ hi|�h?t uLh t|h�Tt� 6�ht|c t�?Ui |�i h�t! uhii h@|i �@h�it L�ih |�i M�t�?ittU)U*ic UL?_�|�L?@* i TiU|i_ hi|�h?t @*tL �@h) L�ih |�i M�t�?itt U)U*i� 5iUL?_ci Uitt hi|�h?t L? ML?_ @?_ _���_i?_ t|h�Ttc .|E-|c|n�d(|n&o�*.|E-|c|n�d�|n�o���c @hi UL?t|@?|� A��t uL**L�t _�hiU|*) uhL4 |�i u@U| |�@| UL?_�|�L?@* tiUL?_4L4i?|t �? |�i t|@|i tT@Ui t)t|i4 @hi UL?t|@?|� A�iti |�L hit�*|t |L}i|�ih4@!i |�@| |�i Thi_�U|@M*i UL4TL?i?|t Lu ML?_ @?_ _���_i?_ t|h�T hi|�h?t@hi @** ThLTLh|�L?@* |L |�i h�t! uhii h@|i�

�L?_�|�L?@* �@h�@?Ui

A�i |h@U|@M�*�|) Lu |�i *L}?Lh4@* _�t|h�M�|�L? Tih4�|t t�@hT �?t�}�|t �?|L|�i hi*@|�L?t��T Mi|�ii? |�i �L*@|�*�|) Lu @tti| hi|�h?t @?_ |�i ThLTih|�itLu M�t�?itt U)U*it� �L4T�|�?} |�i UL?_�|�L?@* �@h�@?Ui Lu hi|�h?t U@? Mi@UUL4T*�t�i_ �t�?} |�i t|@?_@h_ uLh4�*@ uLh |�i �@h�@?Ui Lu @ *L}?Lh4@*�@h�@M*i� A�@| �tc �u *L}E~� �t �E>c j� |�i? �@hE~� ' i TE2>nj2�Ei TEj2����� � 4Lhi _�hiU| U@*U�*@|�L? �tit |�i u@U| |�@| |�i L?i�Tih�L_ hi|�h? U@? Mi_iUL4TLti_ �?|L |�L T@h|t �? |�i uL**L��?} �@)G

-|c|n�d(|n&o ' .|E-|c|n�d(|n&o�T|n�d(|n&o

.|ET|n�d(|n&o�� E.�

A�i tiUL?_ T@h| Lu |�i h�}�| �@?_ t�_ic |�i hi��t�L? Lu |�i �?�|�@* Th�Ui uLhi�U@t|c U@? Mi �h�||i? @tG

i TE.|n�E_|n&nb|n&�b|n���.|E_|n&nb|n&�b|n����

2�@h|E.|n�E_|n&nb|n&�b|n�����

EH�W| |�i? uL**L�t _�hiU|*) |�@|G

�@h|E-|c|n�d(|n&o� ' .|E-|c|n�d(|n&o�2 Ei TE�@h|d.|n�E_|n& n b|n& � b|n��o�� �� �

Eb�,^�@|�L? Eb� t�L�t �L� |�i �L*@|�*�|) Lu hi��t�L?t Lu i TiU|@|�L?t �? |�i�?_ih*)�?} t)t|i4 _�hiU|*) |h@?t*@|it �?|L UL?_�|�L?@* �@h�@M�*�|) uLh hi|�h?t�

H

2�2 +i|�h?t uLh @tti|t ��|� 4�*|�T*i T@)L�|t

�i |c �i UL?t�_ih @? @tti| ���U� hiThiti?|t @ U*@�4 |L @? �?�?�|i ti^�i?UiLu TLtt�M*) h@?_L4 _���_i?_tG

T|di(|n&j"

&'�o '"[&'�

T|d(|n&o� E�f�

A��t _i�?�|�L? ULhhitTL?_t |L @ UL44L? t|LU! Lhc uLh UL?t|@?| T@)L�|tc |L @TihTi|�@* ML?_� �tti|t ��|� @ �?�|i ?�4Mih Lu T@)L�|tc uLh �?t|@?Ui UL�TL?ML?_tc U@? Mi @?@*)3i_ �? |�i t@4i �@)� A�i L?i�Tih�L_ �L*_�?} hi|�h? U@?Mi �h�||i? @tG

-|c|n�di(|n&j"

&'�o 'T|n�di(|n&j

"

&'�o

T|di(|n&j"

&'�o'

"[&'�

�|d(|n&o-|c|n�d(|n&o E���

��|� �|d(|n&o ' T|d(|n&o*T|di(|n&j"

&'�o Mi�?} |�i TLh|uL*�L �i�}�| @||@U�i_|L |�i _@|i |n & _���_i?_ t|h�T hi|�h?�

, TiU|i_ hi|�h?tG ,^�@|�L? E��� t@)t |�@| �L*_�?} @ UL44L? t|LU!U@? Mi ��i�i_ @t �L*_�?} @ TLh|uL*�L Lu _���_i?_ t|h�Tt� A��t hiThiti?|@|�L? �t�tiu�* MiU@�ti |�i TLh|uL*�L �i�}�|t @hi !?L�? @| |�4i |c @?_ uLh @ L?i�Tih�L_�@�i@_ UL?_�|�L?@* i TiU|@|�L?c |�i) U@? Mi T@tti_ |�hL�}� |�i i TiU|@|�L?LTih@|Lh� A@!�?} |�i UL?_�|�L?@* i TiU|@|�L? �i LM|@�? |�@|G

.|E-|c|n�di(|n&j"

&'�o� ' -|c|n�d�|n�o"[&'�

�|d(|n&o i TE#_E&�� E�2�

���U� t�L�t |�@| |�i i TiU|i_ hi|�h? Lu @ UL44L? t|LU! �t i^�@* |L |�ih�t! uhii h@|i |�4it @ �i�}�|i_ t�4 Lu |�i i TL?i?|�@*t Lu |�i _���_i?_ t|h�TThi4�@ #_E&�� `��*i |�i t|h�T Thi4�@ _L ?L| �@h) L�ih |�i M�t�?itt U)U*ic|�i U)U*�U �@h�@|�L? �? |�i �i�}�|t *i@_t |L |�4i��@h)�?} UL?_�|�L?@* i Uitthi|�h?tc tL *L?} @t |�i Thi4�@ t|h�U|�hi L�ih _�gihi?| |�4i �Lh�3L?t �t ?L|�Lh�3L?|@* E��i�c #_E&� 9' #_ uLh @** &�� ,^�@|�L? E�2� @*tL ��}�*�}�|t |�i u@U||�@| |�i t�3i Lu |�i i^��|) Thi4��4 �t _�hiU|*) hi*@|i_ |L |�i t�3i Lu |�i�?_���_�@* t|h�T Thi4�@� �*tLc �i�}�|t }i?ih@**) _iUhi@ti @t @ u�?U|�L? Lu|�i |�4i �Lh�3L?c ���U� 4i@?t |�@| @ t�3i@M*i i^��|) Thi4��4 hi^��hit *@h}it|h�T Thi4�@ uLh _@|it �? |�i ?i@h u�|�hi�

b

�L?_�|�L?@* �@h�@?UiG A�i UL?_�|�L?@* �@h�@?Ui Lu |�i UL44L? t|LU!hi|�h? �t @TThL �4@|i*) i^�@* |LG

�@h|E-|c|n�di(|n&j"

&'�o� � �@h|

#"[&'�

�|d(|n&o-|c|n�d(|n&o,eE&�"|n�

$E���

��ihi ,eE&�"|n� �t i^�@* |L .|n�E_|n& n b|n& � b|n���.|E_|n& n b|n& � b|n��c@t t�L�? �? i^�@|�L? EH��H 5�?Ui "|n� �t |�i L?*) �?Uih|@�? i*i4i?| �?t�_i |�iMh@U!i|tc �i U@? i@t�*) hi�h�|i |�i UL?_�|�L?@* �@h�@?Ui @tG

�@h|E-|c|n�di(|n&j"

&'�o� � -|c|n�d�|n&o2 dZE|�o

[""dZE|�o�

��|� ZE|� '"[&'�

�|d(|n&o i TE#_E&��,eE&�� E�e�

A��t i Thitt�L? ��}�*�}�|t |�L �4TLh|@?| TL�?|t� 6�ht|c t��u|t Lu |�i �i�}�|t�@�i |�i TL|i?|�@* |L }i?ih@|i |�4i �@h�@|�L? �? |�i UL?_�|�L?@* �@h�@?Ui� 5iU�L?_c |�i �@h�@?Ui�UL�@h�@?Ui 4@|h� Lu |�i �4T�*tit Lu |�i *�?i@h t)t|i4c

S""

c �t _�hiU|*) hi*@|i_ |L |�i UL?_�|�L?@* hi|�h? �L*@|�*�|)�

� �TT*�U@|�L?t Lu *L}*�?i@h @tti| Th�U�?}

A��t tiU|�L? Mi}�?t ��|� @ hi��i� Lu Th�Lh �Lh! M@ti_ L? |�i @tt�4T|�L?Lu *L}?Lh4@*�|)c @?_ _�tU�ttit �L� �| hi*@|it |L L�h @tti| Th�U�?} uh@4i�Lh!��i |c �i _i�i*LT @ 4L_i* ���U� �?ULhTLh@|it ?L?�|�4i�tiT@h@M*i Thiuihi?Uit�6�?@**)c �i UL4T@hi |�i t�3i Lu Thi4�@ uLh |�4i�tiT@h@M*i @?_ �@M�| uLh4@|�L?Thiuihi?Uit �? @ *L}*�?i@h i?_L�4i?| 4L_i*�

��� �L?t�4T|�L? M@ti_ @tti| Th�U�?}

A�i t|@?_@h_ @TThL@U� |L �?|ih|i4TLh@* @tti| Th�U�?} uL**L�t w�U@t E�b.H�M) @tt�4�?} @? i?_L�4i?| iUL?L4)� �@4TMi** E�bHS� @?@*)3it @ �iht�L?Lu |��t uh@4i�Lh! ��|� |�4i�tiT@h@M*ic �tLi*@t|�U Tih�L_ �|�*�|) Lu UL?t�4T�|�L?� Oi @*tL @tt�4it |�@| |�i i?_L�4i?| �t UL?_�|�L?@**) *L}?Lh4@*c @?_

;Wkh dssur{lpdwlrq xvhv h{s+{, � 4.{1 Iru lqvwdqfh/ li { lv qrupdo dqg kdv d vwdqgdug

ghyldwlrq ri 314858 +dssur{lpdwho| wkh vwdqgdug ghyldwlrq ri |hduo| vwrfn uhwxuqv, wkhq

wklv dssur{lpdwlrq zrxog jlyh 31481

�f

|�@| �|t *L}@h�|�4 uL**L�t @ �?��@h�@|i *�?i@h ThLUitt ��|� ����_� ?Lh4@* �4�T�*tit� O�t t|�_) uLU�tit L? |�i _i|ih4�?@?|t Lu h�t! Thi4�@c @?_ ThL��_it@ t|@h|�?} TL�?| uLh L�h �Lh!� W? L�h ?L|@|�L? |��t 4L_i* t|h�U|�hi @4L�?|t|L b| ' ��S|c ��|� � Mi�?} |�i ULi�U�i?| Lu hi*@|��i h�t! @�iht�L?c ��|� |�ii^��*�Mh��4 UL?_�|�L? |�@| _| ' S|� ,^�@|�L? ED� U@? |�i? Mi �h�||i? @tG

.|E-|c|n�d(|n&o� ' q3� i TE��ES| �.|S|n����2

2�@h|ES|n���

� i TE�� 2 UL�|ES|n�c .|n�S|n& � S|n���� i TE� UL�|ES|n�c .|n�S|n&���

E�D�

A��t hi*@|�L?t��T Mi|�ii? t|h�T Thi4�@ @?_ UL?t�4T|�L? _)?@4�Ut �t L?i Lu|�i 4@�? hit�*|t Lu �@4TMi**<t T@Tih� ,^�@|�L? E�D� 4@!it �| U*i@h |�@||ih4 Thi4�@ E|�i �ht| UL�@h�@?Ui |ih4� _iTi?_ L? |�i UL�@h�@?Ui Mi|�ii?UL?t�4T|�L? @?_ i TiU|i_ UL?t�4T|�L? }hL�|�c ��ihi@t T@)L�| �?Uih|@�?|)Thi4�@ E|�i tiUL?_ UL�@h�@?Ui |ih4� _iTi?_ L? |�i UL�@h�@?Ui Mi|�ii? UL?�t�4T|�L? @?_ |�i *i�i* Lu i TiU|i_ u�|�hi UL?t�4T|�L?� W| @*tL t�L�t |�@|h�t! @�iht�L?c � c i?|iht |ih4 Thi4�@ M) �|t t^�@hi_ �@*�i M�| @giU|t |�i T@)�L�| Thi4�@ L?*) ThLTLh|�L?@**)c @ hit�*| |�@| �t u�h|�ih _�tU�tti_ Mi*L��

A�i @_�@?|@}i Lu t�4T*i U*Lti_�uLh4 tL*�|�L?t �t Lu UL�hti i�i? 4Lhi@TThiU�@M*i ��i? 4L_i*t @hi |L Mi it|�4@|i_� 6Lh �?t|@?Uic O@?ti? @?_ 5�?�}*i|L? E�bH�� @?_ 5�?}*i|L? E�bbf� UL4M�?i |�4i�tiT@h@M*ic �tLi*@t|�U Tih�L_�|�*�|) Lu UL?t�4T|�L? ��|� |�i @tt�4T|�L? |�@| UL?t�4T|�L? }hL�|� h@|it@?_ @tti| hi|�h?t @hi �L�?|*) *L}?Lh4@**) _�t|h�M�|i_( |��t �4T*�it UL?t|@?|UL?_�|�L?@* �@h�@?Uit @?_ UL?_�|�L?@* 4i@?t |�@| @hi *�?i@h u�?U|�L?t Lu T@t|hi@*�3@|�L?t� AL |h@?t*@|i |��t uh@4i�Lh! �?|L L�h ?L|@|�L?c �i U@? |��?!@ML�| @tti| hi|�h?t @t L?i�Tih�L_ _���_i?_ t|h�Ttc @TThLTh�@|i*) tU@*i_ t�U�|�@| T|d(|n&o ' �� ,^�@|�L? ED� uLh UL?_�|�L?@* i TiU|i_ 4i@? hi|�h?t |�i?MiUL4itG

.|E-|c|n�� ' q3� i TE�ES| �.|S|n����2

2�@h|ES|n���

� i TE� UL�|ES|n�c *L}-|c|n����E�S�

,^�@|�L? E�S� t�L�t |�@|c }��i? UL?t|@?| UL?_�|�L?@* UL�@h�@?Uitc |�i h@|�L Lu@?) |�L @tti| hi|�h?t E@?_ |�ihiuLhi i Uitt hi|�h?t� @hi UL?t|@?|� ,4T�h�U@*i��_i?Ui U*i@h*) hi�iU|t |��t hit|h�U|�L?� 6Lh �?t|@?Uic 5�?}*i|L? E�bbf� t�L�t|�@| @ t�UUittu�* 4L_i* ?ii_t |L Mi @M*i |L @**L� uLh UL?t�_ih@M*i _�gihi?Uit�? @�|LULhhi*@|�L? ThLTih|�it @UhLtt _�gihi?| @tti|t� OL�i�ihc @t �i t�L�i_@ML�ic 4�*|�T*i�T@)L�| @tti|t @hi TL|i?|�@**) UL?t�t|i?| ��|� |�iti �?_�?}t�

��

��2 �L?tiT@h@M*i Thiuihi?Uit

�Lhi hiUi?|*)c ?L?tiT@h@M*i Thiuihi?Uit �@�i @||h@U|i_ UL?t�_ih@M*i @||i?�|�L? @t @ TLtt�M*i 4i@?t Lu hiUL?U�*�?} �?|ih|i4TLh@* @tti| Th�U�?} 4L_i*t��|� i4T�h�U@* i��_i?Ui� �L?|i4TLh@?iL�t ?L?�tiT@h@M�*�|�it U@? i@t�*) Mi�@?_*i_ �? L�h uh@4i�Lh!� 6Lh �?t|@?Uic ��i? *i�t�hi i?|iht |�i Tih�L_ �|�*��|) u�?U|�L? @*L?} ��|� UL?t�4T|�L?c |�i �@*�@|�L? \| �t t�4T*) |�i 4@h}�?@*�|�*�|) Lu UL?t�4T|�L? ���U� ?L� @*tL _iTi?_t L? *i�t�hi� �|�ih ?L?tiT@h@�M�*�|�it t�U� @t ?L?|h@_i_ }LL_t Lh �L�ti�L*_ ThL_�U|�L? U@? Mi |hi@|i_ �?|�i t@4i �@)�

�L?�|�4i�tiT@h@M*i Thiuihi?Uit @hi i�i? 4Lhi TLT�*@h �? |�i @tti| Th�U�?}*�|ih@|�hi( |�iti @*tL tii4 @ Th�Lh� |L Mi 4Lhi U�@**i?}�?}�b W?_ii_c |�i Th�Lhuh@4i�Lh! _Lit ?L| @TTi@h |L Mi _�hiU|*) @TT*�U@M*i MiU@�ti |�i 4@h}�?@*�@*�@|�L? Lu |�4i | UL?t�4T|�L? i Ti?_�|�hi �t |)T�U@**) @ h@?_L4 �@h�@M*i@| |�4i |� 6Lh |��t hi@tL?c @__�|�L?@* �@h�@?Ui |ih4t �? |�i _i?L4�?@|LhLu @? @tti| Th�U�?} uLh4�*@ UL�*_ UL4T*�U@|i |�i ti|�T� 6Lh|�?@|i*)c |�i*L}*�?i@h�*L}?Lh4@* t|h�U|�hi hi?_iht |�iti UL?t�_ih@|�L?t �hhi*i�@?|�

AL tii |��tc _i�?i *�ui|�4i 4@h}�?@* �|�*�|) Lu |�4i | UL?t�4T|�L? i Ti?_��|�hi @t M|c|nr� A��t ?L|@|�L? t�}}it|t |�@| UL?t�4T|�L? i Ti?_�|�hi @| | �@tigiU|t ?L| L?*) @| |�4i |c M�| @*tL @| |n�c |n2c���c ���U� �t |)T�U@**) |�i U@tiuLh @ �@M�| uLh4@|�L? tTiU��U@|�L?� �tt�4ic |�i?c |�@| �|c|nr ' *L}EM|c|nr��t i^�@* |L @ _�t|h�M�|i_ *i@_ Lu |�i *L} Lu |�i t|@|i �iU|LhG

�|c|nr 'r[

�'f

,�E��r|n�� E�.�

6Lh @tti| Th�U�?} �i ?ii_ |L i�@*�@|i

.|EM|c|nr� ' .| i TE�|c|nr�' i TE.|�|c|nr n

2�@h|E�|c|nr��

E�H�

���U� �t �4T*�i_ M) |�i *L}?Lh4@*�|) @tt�4T|�L?� B��i? |�@| @? @__�|�L?@*�@h�@?Ui |ih4 �t @*tL �? |�i ?�4ih@|Lh Lu @?) Th�U�?} uLh4�*@ *�!i i^�@|�L? E��c@?_ }��i? |�@| |�iti �@h�@?Uit @hi |�4i��?_iTi?_i?|c |�iti �@h�@?Ui |ih4tU@?Ui* L�|c @t �i t�L� �? |�i @TTi?_� � A��t �i U@? �ti \| ' i TE.|�|c|nr�@t |�i �@*�@|�L?c @?_ @** |�i Thi��L�t*) LM|@�?i_ hit�*|t @TT*) _�hiU|*)�

<H{dpsohv lqfoxgh= Deho +4<<3,/ Frfkudqh dqg Kdqvhq +4<<5,/ Frqvwdqwlqlghv +4<<3,/

Ihuvrq dqg Frqvwdqwlqlghv +4<<4,/ Khdwrq +4<<6, dqg Vxqgduhvhq +4<;<,1

�2

O@M�| uLh4@|�L? @?_ |�i �@*�@|�L?

V@h�L�t @�|�Lht �@�i _LU�4i?|i_ |�i @M�*�|) Lu �@M�| uLh4@|�L? Thiuihi?Uit|L }i?ih@|i ��}� Thi4�@ Etii uLL|?L|i b�� i U@? i@t�*) hiT*�U@|i |��t @h}��4i?| �? L�h uh@4i�Lh!c �**�t|h@|�?} |�i hi*@|�L?t��T Mi|�ii? �@M�| uLh4@|�L?c�@*�@|�L? @?_ t|h�T Thi4�@� A@!�?} @ t�4T*i �@M�| uLh4@|�L? tTiU��U@|�L?c�E�| � k�|3��c �| U@? Mi @TThL �4@|i_ *LU@**) M)

k�

E�� k�E�� kq�S|3� �

E� n k2q��

E�� k�E�� kq�S| n

kq�

E�� k�E�� kq�S|n� E�b�

��ihi S| �t |�i *L} Lu UL?t�4T|�L? i Ti?_�|�hi��f ,^�@|�L? E�b� hi�i@*t |�@|4@h}�?@* �|�*�|) Lu U�hhi?| UL?t�4T|�L? i Ti?_�|�hi _iTi?_t L? T@t| @?_u�|�hi i Ti?_�|�hi @t �i** @t L? U�hhi?| UL?t�4T|�L? i Ti?_�|�hi� 6Lh @?i?_L�4i?| 4L_i* �i U@? _i�?i |�i t|@|i r| |L Mi i^�@* |L dS|c S|3�o

�c ���U�T�|t |�i ThLM*i4 �?|L |�i uLh4 Lu i^�@|�L? E�.��

A�ihi @hi ^�@?|�|@|��i*) �4TLh|@?| �4T*�U@|�L?t Lu E�b� uLh |�i hi*@|�L?�t��T Mi|�ii? UL?t�4T|�L? @?_ hi@*�3i_ 4@h}�?@* �|�*�|) �| @?_c �i?Uic uLh|�i *�?!t Mi|�ii? UL?t�4T|�L? @?_ |�i 4@h}�?@* �@*�@|�L?c \|�

��@?}it �? UL?t�4T|�L? @| @** _@|itG Wu UL?t�4T|�L? U�@?}it M) @?i^�@* @4L�?| @| @** _@|itc |�i? �| uL**L�t |�@| |�i i*@t|�U�|) Y�*YS �t t�4T*)�� � A�@| �tc @t @h}�i_ M) 6ihtL? @?_ �L?t|@?|�?�_it E�bb��c � �t @TThL ��4@|i*) i^�@* |L hi*@|��i h�t! @�iht�L? ��|� hitTiU| |L @|i4TLh@* �i@*|� Mi|tc�? ���U� UL?t�4T|�L? @| @** u�|�hi _@|it �t @ U�L�Ui �@h�@M*i� W? L|�ih �Lh_tc�� �t |�i *L?}�h�? i*@t|�U�|) Lu 4@h}�?@* �|�*�|) ��|� hitTiU| |L Tih4@?i?|U�@?}it �? UL?t�4T|�L?�

��@?}it �? UL?t�4T|�L? ��t| @| _@|i |G Wu UL?t�4T|�L? U�@?}it��t| @| _@|i |c |�i? uLh @ �@M�| uLh4@|�L? T@h@4i|ih Lu k ' f�Sc @ �@*�i_�tU�tti_ *@|ih �? |�i T@Tihc @?_ uLh q ' f�bSc |�i i*@t|�U�|) �t ?L�

Y�|

YS|' �

� n k2q

E�� k�E�� kq�� � �H��

43Htxdwlrq +4<, lv rewdlqhg iurp wkh �uvw rughu frqglwlrq zlwk uhvshfw wr frqvxps0

wlrq h{shqglwxuh lq dq lq�qlwh krul}rq prgho xqghu fhuwdlqw|= Kw @ Gx+Fw � �Fw�4, �

��Gx+Fw.4 � �Fw,1 Zh wkhq wdnh d �uvw0rughu Wd|oru vhulhv dssur{lpdwlrq ri wkh orj ri

wklv h{suhvvlrq/ dqg xvh wkh idfw wkdw zkhq x+Fw � �Fw�4, @ +4 � �,�4+Fw � �Fw�4,4��

wkhq �G5x+=,+4� �,F@Gx+=, @ �=

��

�?i U@? |��?! @ML�| |��t i*@t|�U�|) @t t�Lh| |ih4 h�t! @�iht�L? ��|� hitTiU| |L|i4TLh@h) UL?t�4T|�L? U�@?}it� A��tc ��|� hitTiU| |L |i4TLh@h) U�@?}it�? U�hhi?| UL?t�4T|�L?c h�t! @�iht�L? �t igiU|��i*) H |�4it *@h}ih |�@? �| �t��|� hitTiU| |L �i@*|� U�@?}it�

��@?}it �? UL?t�4T|�L? @| | @?_ |n�G 5�TTLti |�@| UL?t�4T|�L?U�@?}it @| |�4i | @?_ | n � @hi *�?!i_ M) _S|n� ' %_S|� A�i? |�i i*@t|�U�|)Lu 4@h}�?@* �|�*�|) ��|� hitTiU| |L UL?t�4T|�L? �t

Y�|

YS|n %

Y�|

YS|n�' �

� n k2q � %kq

E�� k�E�� kq���

6Lh U�@?}it |�@| @hi i TiU|i_ |L Mi Tih4@?i?| E% ' ��c �| |�i? uL**L�t |�@||�i i*@t|�U�|) �t Y�|*YS| � �e�D� � Oi?Uic M) �@h)�?} |�i i |i?| |L ���U�U�@?}it @hi TihUi��i_ |L Mi Tih4@?i?|c �i U@? @*|ih |�i i |i?| Lu igiU|��ih�t! @�iht�L? ��|� hitTiU| |L UL?t�4T|�L? U�@?}it uhL4 H� E��|� % ' f�|L e�D� E��|� % ' ��� W?|��|��i*)c |��t hit�*| hi�iU|t |�i �_i@ |�@| ��|�UL?t�4T|�L? �@M�|t @? @}i?| �t ��**�?} |L T@) 4Lhi Ui|ih�t T@h�M�t |L @�L�_@ h�t! |�@| _�t|�hMt |�iti �@M�|t�

O@M�| uLh4@|�L? @?_ t|h�T Thi4�@

A�i t|h�T Th�U�?} uLh4�*@ �?_�U@|i_ |�@| |�ihi @hi |�L _i|ih4�?@?|t Lu |�ii^��|) Thi4��4 ���U� �i hiThL_�Ui �ihi uLh UL?�i?�i?Ui� 6�ht|c |�ihi @hi|�i �L*_�?} Lh |ih4 Thi4�@G

#|E&� ' � UL�|Eb|n�c .|n�b|n& � b|n���

5iUL?_c |�ihi @hi |�i T@)L�| �?Uih|@�?|) Thi4�@G

#RE&� ' � UL�|Eb|n�c .|n�_|n&��

6Lh i TLt�|Lh) T�hTLti �| �t �tiu�* |L uLU�t L? |�i U@ti �? ���U� E�� UL?�t�4T|�L? �t @ h@?_L4 �@*! @?_ E��� UL?t�4T|�L? @?_ _���_i?_t @hi i^�@*c_|n& ' S|n&�

+�t! Thi4�@ ��|� |�4i�tiT@h@M*i Thiuihi?UitG 5�?Ui UL?t�4T|�L?�t @ h@?_L4 �@*! |�ihi @hi ?L i TiU|i_ U�@?}it( |��t �4T*�it |�@| |ih4

�e

Thi4�@ @hi i^�@* |L 3ihL� A�i h@?_L4 �@*! @tt�4T|�L? @*tL 4i@?t |�iT@)L�| Thi4�@ @hi UL?t|@?| @UhLtt �Lh�3L?tc t�?Ui .|n�_|n& ' .|n�S|n& 'S|n�� 6�h|�ihc |�i *i�i* Lu |�i T@)L�| Thi4��4 �t ��t| �j2c ��ihi j2 �t |�i�@h�@?Ui Lu |�i UL?t�4T|�L? }hL�|� h@|i� Wu �i �ti |�i �i�h@ @?_ �hitUL||E�bHD� �@*�i Lu j ' �f�Sc |�i? |�i �@h�@?Ui �t j2 ' �ff��� Oi?Uic |�i T@)L�|Thi4��4 �t t4@** i�i? uLh *@h}i �@*�it Lu � � 6Lh i @4T*ic �u � ' 2 |�i?R ' 2 � �ff�� ' �ff2Sc ��i�c @ML�| L?i�^�@h|ih Lu @ TihUi?|� 5i||�?} � ' 2ft|�** 4@!it |�i i^��|) Thi4��4 L?*) 2�SI�

+�t! Thi4�@ ��|� �@M�| uLh4@|�L?G `�|� ?L?tiT@h@M*i Thiuihi?Uit�i �@�i i TiU|i_ U�@?}it �? 4@h}�?@* �|�*�|) @t t�}}it|i_ M) |�i Th�Lh @?@*)�t�t� �L?|�?��?} |L @tt�4i |�@| UL?t�4T|�L? uL**L�t @ h@?_L4 �@*!c �i �?_|�@| EuLh & � 2�

YE.|n�b|n& � b|n��

YS|n�' �� n

� n k2q � kq

E�� k�E�� kq�� � ��D��

A�@| �tc t@) @u|ih @ TLt�|��i t�LU!c 4@h}�?@* �|�*�|) ��** Mi i TiU|i_ |L �?�Uhi@ti @}@�? @u|ih �|t �?�|�@* _iU*�?i @| |n �� Oi?Uic �i !?L� |�@| |�ihi ��**Mi |ih4 Thi4�@c i�i? |�L�}� ?L?i �ihi Thiti?| ��|� tiT@h@M*i Thiuihi?Uit�A�i *i�i* Lu |�iti Thi4�@ �t @ML�|

#|E&� ' �E�e�D��E��D��j2�

A��t UL4T@h�?} |�i |ih4 Thi4�@ ��|� |�i T@)L�| Thi4��4 @ML�i �i �?_|�@| �| �t @ML�| �S� |�4it @t *@h}ic Lh @ML�| H��I uLh � ' 2� O@M�| uLh4@|�L?�t |�ihiuLhi U@T@M*i Lu }i?ih@|�?} *@h}i |ih4 Thi4�@ �? |��t ti||�?}� A�iT@)L�| Thi4�@ @hi

#RE&� ' � UL�|Eb|n�c .|n�_|n&� ' � UL�|Eb|n�c S|n��� e�D�j2I� ��2I

A��t |�i �?Uhi@ti �? T@)L�| Thi4�@ �t @ML�| �I ��i? �i t��u| |L |�i �@M�|uLh4@|�L? 4L_i*�

6�}�hi � t�L�t �L� |�iti UL?t�_ih@|�L?t LTih@|i �? @ �iht�L? Lu |�i �i�h@@?_ �hitUL|| E�bHD� i ihU�ti� +@|�ih |�@? @tt�4�?} |�@| UL?t�4T|�L? uL*�*L�t @ h@?_L4 �@*!c UL?t�4T|�L? }hL�|� h@|it uL**L� @ �ht| Lh_ih @�|Lhi�

�D

}hitt��i ThLUitt ��|� T@h@4i|ih ���e��� i Mi}�? M) t|�_)�?} |�i �4T�*tihitTL?ti u�?U|�L?tc ���U� @hi �? |�i h�}�|��@?_ T*L| �? i@U� hL�� #���_i?_t@hi |�i t@4i �? ML|� U@titc @t |�i) @hi ��t| i^�@* |L UL?t�4T|�L?� OL�i�ihc|�i _�gihi?Ui �? |�i hitTL?ti Lu 4@h}�?@* �|�*�|) �t _h@4@|�U� 6Lh |�i |�4i�tiT@h@M*i U@tic |�i ?i}@|��i tih�@* ULhhi*@|�L? �? UL?t�4T|�L? }hL�|�c Uhi@|itThi_�U|@M*i 4L�i4i?|t Lu UL?t�4T|�L? @?_ �i?Ui |�i �@*�@|�L?� A�i _iU*�?i�? �@*�@|�L? @| t�LU!��4T@U| �t uL**L�i_ M) @? �?Uhi@ti M@U! |L�@h_t |�i �?��|�@* *i�i*� A��t |�4i T@|� *i@_t |L @ _iUhi@ti �? �?|ihit| h@|itc @?_ |L TLt�|��i|ih4 Thi4�@� 6Lh �@M�| uLh4@|�L?c ?L| L?*) �t |��t _iUhi@ti �? �?|ihit| h@|it4�U� 4Lhi ThL?L�?Ui_c M�| |�i �@*�@|�L? @| | n �Q��i? |�i U@T�|@* }@�?tLUU�hQ�t 4�U� *L�ih� A��t }��it |ih4 Thi4�@ Lu L�ih |i? TihUi?| uLh �@M�|uLh4@|�L?� A�i Thi4�@ t|h�U|�hit �? |�i *iu|��@?_�t�_i �? �}�hi � @hi ��}�ih|�@? �? L�h Thi��L�t i @4T*i ��|� h@?_L4 �@*! UL?t�4T|�L? _�i |L |�i|i4TLh@h) UL4TL?i?|t �? |�i UL?t�4T|�L? T@|�� Ai4TLh@h) UL4TL?i?|t�?Uhi@ti |�i i TiU|i_ u�|�hi U�@?}i @u|ih |�i �?�|�@* t�LU!c @?_ |�ihiuLhi@4T*�u) �?|ihit| h@|i 4L�i4i?|t�

W? t�44@h)c L�h UL4T@h�tL? Lu �@M�| uLh4@|�L? @?_ |�4i�tiT@h@M*i Thiu�ihi?Uit �t UL?t�t|i?| ��|� |�i hit�*|t LM|@�?i_ �? |�i *�|ih@|�hi �? t�4�*@h4L_i*tG �@M�| uLh4@|�L? }i?ih@|it @ 4�U� ��}�ih i^��|) Thi4��4� W? u@U|c@t �i t�L�c �@M�| uLh4@|�L? �@t |�i @M�*�|) |L _h��i @ �i_}i Mi|�ii? h�t!@�iht�L? ��|� hitTiU| |L �i@*|� @?_ ��|� hitTiU| |L t�Lh| |ih4 UL?t�4T|�L?U�@?}itc @?_ |��t }i?ih@|it *@h}i Thi4�@� OL�i�ihc |�iti Thi4�@ @hi 4@�?*)|ih4 Thi4�@c T�| @?L|�ih �@)c �?|ihit| h@|it MiUL4i 4�U� 4Lhi �L*@|�*i�O�t|Lh�U@* 4i@? hi|�h?t uLh *L?} |ih4 ML?_t @?_ t|LU!t _�tT*@)i_ �? |@M*i �t�L� @ @?L|�ih T�U|�hiG |�i i^��|) Thi4��4 �t 4@�?*) @ Thi4��4 uLh T@)L�|�?Uih|@�?|) @?_ ?L| uLh �?|ihit| h@|i h�t!� A��t �t |L t@) |�@| |�i M@t�U �@M�|uLh4@|�L? 4L_i* �t ?L| i?|�hi*) t@|�tu@U|Lh) �? �|t �@) Lu tL*��?} |�i i^��|)Thi4��4 T�33*i� i hi|�h? |L |�i @?@*)t�t Lu �@M�| uLh4@|�L? Thiuihi?Uit�? |�i ?i | tiU|�L? M) �?�it|�}@|�?} �L� |�iti hit�*|t U�@?}i �? ThL_�U|�L?iUL?L4�it ��ihi UL?t�4T|�L? @?_ _���_i?_t @hi _i|ih4�?i_ i?_L}i?L�t*)�

44Phkud dqg Suhvfrww vshfli| d wzr0vwdwh/ glvfuhwh Pdunry surfhvv zlwk dxwrfruuhodwlrq

ri �=471

�S

e �tti| hi|�h?t �? ThL_�U|�L? iUL?L4�itc ^�@?�

|�|@|��i Thi_�U|�L?t

�| |��t TL�?|c �i _iT@h| uhL4 L�h @tt�4T|�L? |�@| |�i *L}*�?i@h t)t|i4 uLh_���_i?_t @?_ �|t �@*�@|�L? �t }��i? i L}i?L�t*)� AL _L tLc �i *�?! L�huLh4�*@i uLh @tti| Th�U�?} |L |�i *L}*�?i@h t|h�U|�hit LM|@�?i_ @t @TThL �4@|itL*�|�L?t |L t|LU�@t|�U i^��*�Mh��4 4L_i*t� k�?}c �*Lttih @?_ +iMi*L E�bHH�Thiti?| @? @TThL �4@|�L? 4i|�L_ uLh �?�?�|i �Lh�3L? ThLM*i4t |�@| }��it |�itL*�|�L? �? i @U|*) |�i *L}*�?i@h uLh4 hi^��hi_ M) L�h @tti| Th�U�?} uh@4i�Lh!�

A��t tiU|�L? i T*Lhit |�i ^�@?|�|@|��i Thi_�U|�L?t uLh @tti| hi|�h?t Lu @L?i�tiU|Lhc hi@* ThL_�U|�L? 4L_i* _h��i? M) i L}i?L�t t�LU!t |L ThL_�U�|���|)� �t �? |�i Th�Lh tiU|�L?c �i @*tL UL?t�_ih _�gihi?| tTiU��U@|�L?t Lu�?�it|Lht< Thiuihi?Uit� OL�i�ihc �| �t �4TLh|@?| |L ?L|i |�@| |�i Thiti?|uh@4i�Lh! �t ?L| *�4�|i_ |L |�i t|�_) Lu |��t U*@tt Lu hi@* M�t�?itt U)U*i4L_i*t� 6Lh i @4T*ic |�iti 4i|�L_t UL�*_ Mi �ti_ |L t|�_) @tti| Th�U��?} �? 4L_i*t ��|� @__�|�L?@* ui@|�hit t�U� @t L*�}LTL*�t|�U Th�U�?} E+L|i4�Mih} @?_ LL_uLh_ E�bb2��c |�4i�|L�M��*| �?�it|4i?| |iU�?L*L}) Ek)_*@?_@?_ �hitUL|| E�bH2��c ?L?|h@_i_ }LL_t E5|LU!4@? @?_ Ait@h E�bbf��c �L�ti��L*_ ThL_�U|�L? EBhii?�LL_c +L}ihtL? @?_ h�}�| E�bb���c *�^��_�|) igiU|tE��h�t|�@?L @?_ ,�U�i?M@�4 E�bb���c t|�U!) Th�Uit Ek�?} E�bb��� @?_ t|L�U�@t|�U �tU@* TL*�U) E�@ |ih @?_ k�?} E�bb���� �@ |ih @?_ aih4@?? E�bb��@TT*�i_ |��t uh@4i�Lh! |L @ 4L_i* ��|� �?UL4T*i|i @tti| 4@h!i|t�

e�� A�i 4L_i*

�L?t�_ih |�i t|@?_@h_ t|LU�@t|�U ?iLU*@tt�U@* }hL�|� 4L_i* ��|� @ *@h}i?�4Mih Lu �?�?�|i*)�*��i_ �h4t @?_ �?�it|Lht%�L�ti�L*_t� A�ihi �t @ t�?}*iUL?t�4T|�L?��?�it|4i?| }LL_ |�@| �t ThL_�Ui_ ��|� @ UL?t|@?|�hi|�h?t�|L�tU@*i ThL_�U|�L? |iU�?L*L}) ���U� �t t�M�iU| |L h@?_L4 t�LU!t �? ThL_�U|����|)�

6�h4t

W? i@U� Tih�L_c @ hiThiti?|@|��i �h4 �@t |L _iU�_i �L� 4�U� *@MLh |L ��hi@?_ �L� 4�U� U@T�|@* |L �?�it|� �@?@}iht 4@ �4�3i |�i �@*�i Lu |�i �h4 |L�|t L�?ihtc ���U� �t i^�@* |L |�i Thiti?| _�tUL�?|i_ �@*�i Lu @** U�hhi?| @?_

�.

u�|�hi i TiU|i_ U@t� �L�tG

.|

"[&'f

q&\|n&

\|

E�|n&8 Eg|n&cf|n&�|n&��`|n&�|n& � U|n&� E2f�

��ihi � �t |�i t|LU�@t|�U ThL_�U|���|) *i�i*c g �t |�i U@T�|@* t|LU!c ` �t |�i�@}i h@|ic � �t |�i ^�@?|�|) Lu *@MLh �?T�|c f �t |�i _i|ih4�?�t|�U |hi?_ �?*@MLh @�}4i?|�?} |iU�?�U@* U�@?}i ���U� }hL�t @| |�i h@|i � ' f|n�*f| @?_U �t �?�it|4i?| i Ti?_�|�hi� A�i �h4<t U@T�|@* t|LU! LMi)t @? �?|ih|i4TLh@*@UU�4�*@|�L? i^�@|�L? ��|� @_��t|4i?| ULt|tG

g|n� ' E�� B�g| n ��U|g|

�g| E2��

��ihi B �t |�i _iThiU�@|�L? h@|i @?_ �E�� @ TLt�|��ic UL?U@�i u�?U|�L?� A�iUL?U@�i u�?U|�L? U@T|�hit |�i �_i@ |�@| U�@?}�?} |�i U@T�|@* t|LU! h@T�_*)�t 4Lhi ULt|*) |�@? U�@?}�?} �| t*L�*)� A��t tTiU��U@|�L? @*tL @**L�t |�it�@_L� Th�Ui Lu �?t|@**i_ U@T�|@* |L _��ih}i uhL4 |�i Th�Ui Lu @? @__�|�L?@*�?�| Lu U@T�|@*c ��i�c �| Tih4�|t �@h�@|�L? �? ALM�?<t ^��2

A�i �h4 _Lit ?L| �tt�i ?i� t�@hitc M�| �?@?Uit �|t U@T�|@* t|LU! |�hL�}�hi|@�?i_ i@h?�?}t @?_ _�tUL�?| ML?_t� ,@U� Tih�L_c |�i �h4 �tt�it ��Tih�L__�tUL�?| ML?_t uLh @ � i_ uh@U|�L? D*� Lu �|t U@T�|@* t|LU!c @?_ T@)t M@U!�|t _iM| |�@| UL4it |L 4@|�h�|)� A�i _���_i?_t |L t�@hi�L*_iht @hi |�ihiuLhii^�@* |LG

(| ' �|8 Eg|c f|�|��`|�| � U| �D

�Eg|3E�3�� � T S

| d�|c|n�og|n�� E22�

��|� T S |�i Th�Ui Lu @ ULhTLh@|i ML?_� i U�LLti |��t �?@?U�@* TL*�U) MiU@�ti�| @**L�t |�i �h4 |L @_��t| �|t _iM| *i�i* t4LL|�*) |�hL�}� |�4i @t �| }hL�t�A�i T@h@4i|ih D _i|ih4�?it |�i L�ih@** *i�i* Lu _iM| @t @ uh@U|�L? Lu |�iU@T�|@* t|LU!�

45Fdslwdo dgmxvwphqw frvwv kdyh ehhq vwxglhg e| Hlvqhu dqg Vwurw} +4<96,/ Oxfdv +4<9:,/Oxfdv dqg Suhvfrww +4<:4, dqg Kd|dvkl +4<;5,1 Ed{whu dqg Fuxflql +4<<6, kdyh dssolhgwklv vshfl�fdwlrq wr dq rshq hfrqrp| uhdo exvlqhvv f|foh prgho1

�H

W?�it|Lht%OL�ti�L*_t

+iThiti?|@|��i �?�it|Lht 4@ �4�3i i TiU|i_ *�ui|�4i �|�*�|) Lu UL?t�4T|�L?ct�M�iU| |L @ ti^�i?|�@* M�_}i| UL?t|h@�?|G

4@ .|

"[&'f

q&�E�|n&�

r�|� `|�r| n @|ET

@| n(@

| � ' �| n @|n�T@| � E2��

Oihi @| �t @ �iU|Lh Lu �?@?U�@* @tti|t �i*_ @| | @?_ U�Lti? @| | � �c T @

@?_ (@ @hi �iU|Lht Lu @tti| Th�Uit @?_ U�hhi?| Tih�L_ T@)L�|t� A�i @tti|�iU|Lh @ UL?|@�?t t�@hit @?_ L?i�Tih�L_ ML?_t |L |�i hiThiti?|@|��i �h4@?_ TLtt�M*) L|�ih @tti|t� W? @__�|�L?c �?�it|Lht u@Ui @ E?Lh4@*�3i_� |�4iUL?t|h@�?| � ' � r

| nu|c ��|� u hiThiti?|�?} *i�t�hi @?_ �r ThL_�U|��i �Lh!�B��i? |�@| *i�t�hi _Lit ?L| i?|ih |�i �|�*�|) u�?U|�L?c @}i?|t ��** @**LU@|i |�i�hi?|�hi |�4i i?_L�4i?| |L ThL_�U|��i �Lh!� i ��** U@** |��t U@ti |�i � i_*@MLh iUL?L4)c 6w� A�L @__�|�L?@* U@tit @hi UL?t�_ihi_G |�i �@h�@M*i�*@MLhiUL?L4)c Vwc ��ihi �E�� ' �E�|c u|�c @?_ |�i �@M�|�uLh4@|�L? iUL?L4)c O6c��|� Tih�L_ �|�*�|) u�?U|�L? _i�?i_ @t �E�| � k�|3���

�@h!i| i^��*�Mh��4c _i�?�|�L? Lu �?@?U�@* @tti|t

W? i^��*�Mh��4c @** ThL_�Ui_ }LL_t @hi i�|�ih UL?t�4i_ Lh �?�it|i_( *@MLht�TT*) @*tL i^�@*t *@MLh _i4@?_� 6�?@?U�@* 4@h!i| i^��*�Mh��4 hi^��hit |�@||�i �?�it|Lht �L*_ @** L�|t|@?_�?} i^��|) t�@hit @?_ ULhTLh@|i ML?_tc @?_|�@| @** L|�ih @tti|t @hi �? 3ihL ?i| t�TT*)�

W? L�h ?�4ih�U@* @?@*)t�t �i ��** *LL! @| |�i i^��|) hi|�h?c -e|c|n� '

-|c|n�di(|n&j"

&'�oc |�i hi|�h? Lu @ Tih�L_ h�t!*itt ML?_c -s|c|n� ' -|c|n�d�|c|n�oc

@?_ |�i hi|�h? Lu @ TihTi|�@* ML?_c -K|c|n� ' -|c|n�di�|n&j

"

&'�o���

e�2 �@*�Mh@|�L?

AL _i�i*LT |�i ^�@?|�|@|��i Thi_�U|�L?t Lu |�i 4L_i*c �i U�LLti T@h@4i|iht��|��? |�i h@?}i Lu �@*�it }i?ih@**) UL?t�_ihi_ @t hi@tL?@M*i� `�i?i�ih

46Jlyhq wkdw zh h{foxgh wkh srvvlelolw| ri edqnuxswf|/ frusrudwh dqg ulvnohvv erqgv duhshuihfw vxevwlwxwhv1 Lq idfw/ lq rxu vlpxodwlrqv/ wkh suredelolw| ri ghidxow +�up ydoxh ehorzghew, lv qhjoljleoh iru wkh fdvhv ri lqwhuhvw1

�b

TLtt�M*ic �i �ti �?uLh4@|�L? uhL4 L�|t�_i |�i 4L_i* |L �_i?|�u) T@h@4i|ih�@*�it� `�ihi |��t �t ?L| TLtt�M*ic Lh ��ihi T@h@4i|iht t�Mt|@?|�@**) @giU||�i hit�*|tc �i ��** UL?t�_ih ti�ih@* �@*�it�

wL?} h�? Mi�@��LhG 5i�ih@* T@h@4i|iht @hi U�Lti? |L 4@|U� *L?}�h�? 4L_i* Mi�@��Lhc @t �| �t U�t|L4@h) �? |�i *�|ih@|�hi� A�iti T@h@4i|iht_L ?L| t�}?��U@?|*) @giU| 4L_i* _)?@4�Utc @?_ �i �ti t|@?_@h_ �@*�it� A�i^�@h|ih*) |hi?_ }hL�|� h@|i � �t ��ffec |�i U@T�|@* _iThiU�@|�L? h@|i B �t f�f2Dc|�i UL?t|@?| *@MLh t�@hi �? @ �LMM�#L�}*@t ThL_�U|�L? u�?U|�L? �t f�S�c |�iuh@U|�L? Lu |�4i @**LU@|i_ |L ThL_�U|��i �Lh! �t f�2fc @?_ |�i �?�it|4i?|t�@hi Lu L�|T�| �t f�2S� A��t T@h@4i|ih�3@|�L? � it |�i t|i@_) t|@|i h@|iLu hi|�h? �?_ih Uih|@�?|) @| S�DI @??�@**)� W4T*�U�|*)c |��t @*tL � it |�i}hL�|��@_��t|i_ _�tUL�?| u@U|Lhc qWc |�@| �t i^�@* |L q��3� ��e

O@M�| uLh4@|�L?G �L?t|@?|�?�_it E�bbf� hi^��hit @ �@M�| uLh4@|�L?*i�i* Lu k ' f�Hc �LU�h@?i @?_ O@?ti? E�bb2� �ti f�D @?_ f�S� i �ti f�S�A��t �@*�i @*tL }�@h@?|iit |�@| 4@h}�?@* �|�*�|) Lu UL?t�4T|�L? i Ti?_�|�hi�t @*�@)t TLt�|��i�

�@T�|@* @_��t|4i?| ULt|tG AL tTiU�u) |�i U@T�|@* @_��t|4i?| ULt||iU�?L*L})c �i L?*) ?ii_ |L !?L� |�i i*@t|�U�|) Lu |�i �?�it|4i?| U@T�|@*h@|�L ��|� hitTiU| |L ALM�?<t ^� A��t T@h@4i|ih Th�4@h�*) @giU|t �?�it|4i?|�L*@|�*�|)� W? |�i @Mti?Ui Lu t|hL?} @ Th�Lh� !?L�*i_}ic �?�it|4i?| �L*@|�*�|)U@? Mi �ti_ |L �4TLti ML�?_t L? |��t Uh�|�U@* @_��t|4i?| ULt| T@h@4i|ih� it|�_) |�hii U@titG *L�c 4L_ih@|i @?_ ��}� U@T�|@* @_��t|4i?| ULt|t� A��tULhhitTL?_t |L i*@t|�U�|�it Lu ��c ���c @?_ f���� �Mi* E�bHf� it|�4@|i_ |��tT@h@4i|ih �? @ tL4i��@| _�gihi?| 4L_i*c @?_ LM|@�?i_ �@*�it Mi|�ii? f�2.@?_ f�D2� A��t t�}}it|t |�@| L�h ��}� @_��t|4i?| ULt| i*@t|�U�|) Lu f��� �t �?|�i h@?}i Lu i4T�h�U@* T*@�t�M*i �@*�it�

47Wklv uhodwlrq looxvwudwhv krz lq d jurzlqj hfrqrp| lw lv ��> wkh glvfrxqw idfwru riwkh prgho zkhuh doo jurzlqj yduldeohv kdyh ehhq glylghg e| wkh olqhdu jurzwk wuhqg/ wkdwqhhgv wr eh vpdoohu wkdq rqh dqg qrw wkh ruljlqdo �= Iru xwlolw| wr eh �qlwh/ dqg wkh prghohtxloleulxp wr eh zhoo gh�qhg/ wkhuh lv dq dgglwlrqdo frqvwudlqw wkdw olplwv wkh sdwk iruwkh h{rjhqrxv surgxfwlylw| surfhvv1 D pruh ghwdloohg glvfxvvlrq ri wkhvh lvvxhv fdq ehirxqg/ iru lqvwdqfh/ lq Ehqqlqjd dqg Surwrsdsdgdnlv +4<<3,1

2f

+�t! @�iht�L?G A�i ULi�U�i?| Lu hi*@|��i h�t! @�iht�L? �@t T*@)i_ @4@�Lh hL*i �? |�i �?|ih|i4TLh@* @tti| Th�U�?} *�|ih@|�hi� ,@U� L?i Lu L�h|�hii 4L_i*t �tit |�i Tih�L_ �|�*�|) u�?U|�L? E� � ��3�[�3�

| c ��ihi [| �t|�i *i�i* Lu UL?t�4T|�L? tih��Uit� OL�i�ihc |�i |�hii 4L_i*t _�gih �? |�i�htTiU��U@|�L? Lu [| @t uL**L�tG

6� i_ *@MLh E6w�c [| ' �|(

V@h�@M*i *@MLh EVw�c [| ' �w|u

�3w| ( @?_

O@M�| uLh4@|�L? EO6�c [| ' �| � k�|3��

�UhLtt @** |�hii 4L_i*tc �i �@?| |L !iiT UL?t|@?| @}i?|t< Mi�@��Lh |L��@h_t @|i4TLh@* �i@*|� Mi|t� W| �t �i** !?L�? |�@|c uLh |�i 6w 4L_i*c h�t!@�iht�L? �t |��t i^�@* |L |�i T@h@4i|ih � � 6ihtL? @?_ �L?t|@?|�?�_it E�bb��@?_ L�h Thi��L�t _�tU�tt�L? t�L� |�@| � �t @*tL U*Lti |L h�t! @�iht�L? uLh|�i O6 4L_i*� 6�?@**)c uLh |�i Vw U@tic }��i? |�@| [ �t �L4L}i?iL�t Lu_i}hii L?ic @? �?Uhi@ti �? �i@*|� uLh @ UL?t|@?| hi@* �@}i ��** *i@�i |�iUL?t�4T|�L?�*i�t�hi h@|�L UL?t|@?|c ���U� @*tL 4@!it |�i T@h@4i|ih � |�ih�t! @�iht�L? ��|� hitTiU| |L @|i4TLh@* �i@*|� Mi|t� ,t|�4@|it Lu h�t! @�ih�t�L? M@ti_ L? 4@h!i| hi|�h?t *�!i 6h�i?_ @?_ �*�4i E�b.D� @hi @hL�?_ 2��@4TMi** E�bb��c M) �?U*�_�?} hi|�h?t |L ��4@? U@T�|@* }i|t �@*�it Mi|�ii?D @?_ H� A@!�?} �?|L @UUL�?| 4i@? hi�iht�L? �? @tti| Th�Uit U@? �?Uhi@ti|�iti it|�4@|it M) �T |L |�hii |�4it E�*@U! E�bbf�c �@4TMi** E�bb���� �L?�ti^�i?|*)c �i UL?t�_ih �@*�it uLh � Lu 2 @?_ �f�

6�?@?U�@* *i�ih@}iG �@t�*�t E�bHH� hiTLh|t *i�ih@}i h@|�LtQ_iM| @t @uh@U|�L? Lu |L|@* �h4 �@*�iQuLh |�i N�5� L�ih |�i *@t| t� |) )i@ht |L h@?}iuhL4 f��� |L f�ee uLh 4@h!i| �@*�it @?_ uhL4 f�D� |L f�.D uLh MLL! �@*�it�i ��** UL?t�_ih *i�ih@}i h@|�Lt Lu @ML�| f�D�

�hL_�U|���|) t�LU!t 6�?@**)c �i ?ii_ |L tTiU�u) |�i i L}i?L�t ThLUittuLh ThL_�U|���|) �|� ,t|�4@|it Lu 5L*L� hit�_�@*t |)T�U@**) )�i*_ @ ��}�*)Tiht�t|i?| �+E�� ThLUitt ��|� TLtt�M*) @ �?�| hLL|��D ��h it|�4@|itc M@ti_L? |�i _@|@ uhL4 �@U!�tc ki�Li @?_ k)_*@?_ E�bb2� }��i f�bH @?_ f�ffHD uLh|�i @�|Lhi}hitt��i ULi�U�i?| @?_ |�i �4T�*ti t|@?_@h_ _i��@|�L?c @?_ �i @hi

48Vhh Suhvfrww +4<;9, iru d glvfxvvlrq ri Vrorz uhvlgxdov* hvwlpdwhv1

2�

�?@M*i |L hi�iU| @ h@?_L4 �@*!� i ��** �ti |�L �@*�it uLh |�i Tiht�t|i?UiT@h@4i|ihc f�bD @?_ �c uLh @ t|@|�L?@h) @?_ @ _�gihi?Ui t|@|�L?@h) ThLUittc��|� t|@?_@h_ _i��@|�L?t Lu |�i t�LU! �4T�*ti Lu f�ffHD�

e�� "�@?|�|@|��i 4L_i* Thi_�U|�L?t

5i�ih@* Lu |�i t|�_�it Lu �?|ih|i4TLh@* @tti| Th�U�?} �? i?_L�4i?| 4L_i*tuL**L� �i�h@ @?_ �hitUL|| E�bHD�G 4L_i*t @hi i�@*�@|i_ �? |ih4t Lu |�i�h@M�*�|) |L }i?ih@|i @ ��}� i^��|) Thi4��4� AL UL4T@hi ThL_�U|�L? 4L_i*t|L |�iti Th�Lh hit�*|t �i uL**L� |�i t@4i t|h@|i})� OL�i�ihc �i ��** @*tL MiU@hiu�* |L _�t|�?}��t� Mi|�ii? T@)L�| �?Uih|@�?|) h�t! @?_ �?|ihit| h@|i h�t!�W?_ii_c @t t�}}it|i_ �? |�i *L?}�|ih4 _@|@ �? A@M*i �c |�i i^��|) Thi4��4�t 4@�?*) @ Thi4��4 uLh h�t!�?itt Lu |�i T@)L�|t h@|�ih |�@? uLh �?|ihit| h@|ih�t!�

5�44@h) Lu ?�4ih�U@* hit�*|t

A�i 4L_i*t< Thi_�U|�L?t uLh 4i@? hi|�h?t @?_ M�t�?itt U)U*i t|@|�t|�Ut @hi_�tT*@)i_ �? |@M*i 2 |L D� �iuLhi i @4�?�?} |�iti hit�*|t 4Lhi �? _i|@�*c �|tii4t �tiu�* |L Mh�i�) t|@|i |�i 4@�? hit�*|t� A�i 4@�Lh hit�*| �t |�@| UL4M��?@|�L?t Lu ��}� U@T�|@* @_��t|4i?| ULt|t @?_ �@M�| uLh4@|�L? Thiuihi?Uit U@?i T*@�? i^��|) Thi4�@ Lu ti�ih@* TihUi?|@}i TL�?|t��S A@M*i 2 @*tL 4@!it �|U*i@h ��) t�Mt|@?|�@* i^��|) Thi4�@ �ihi ?L| uL�?_ M) Th�Lh hiti@hU�iht Et�U�@t +L��i?�Lht| E�bb��� ��L t|�_�i_ ThL_�U|�L? iUL?L4�it ��|�L�| U@T�|@*@_��t|4i?| ULt|t� A@M*i 2 t�L�t |�@|c uLh *L� U@T�|@* @_��t|4i?| ULt|tc ?L4L_i* �@h�@|�L? U@? }i?ih@|i @? i^��|) Thi4��4 |�@| i Uii_t f��I� �__�?}�?@?U�@* *i�ih@}i _Lit u�h|�ih �?Uhi@ti |�i i^��|) Thi4��4 @?_ @*tL |�i Thi�4��4 Lu hi|�h?t L? i^��|) L�ih TihTi|�@* ML?_t� A�iti 4L_i* �iht�L?t ��|���}� U@T�|@* @_��t|4i?| ULt|t @?_ �@M�| uLh4@|�L? @hi u�h|�ih @M*i |L }i?ih�@|i �?�it|4i?| @?_ UL?t�4T|�L? �L*@|�*�|) MhL@_*) �? *�?i ��|� N�5� @}}hi}@|i_@|@� �?L|�ih hit�*| �t |�@| |�i �@h�@M*i *@MLh t�TT*) 4L_i* }i?ih@|it Thi�4�@ |�@| @hi UL?t�t|i?|*) t4@**ihQ�? @MtL*�|i �@*�itQ|�@? |�i � i_ *@MLh4L_i*� , T*@�?�?} |�i i^��|) Thi4��4 ��|� �@h�@M*i *@MLh t�TT*) hiThiti?|t|�ihiuLhi @? @__�|�L?@* U�@**i?}i uLh |�i hiThiti?|@|��i @}i?| 4L_i*�

49Frpsduhg wr wkh srvwzdu gdwd zh fdoleudwhg rxu prgho wr/ wkh yduldqfh ri hqgrzphqwlq wkh Phkud dqg Suhvfrww gdwd lv derxw irxu wlphv kljkhu1 Wklv lqfuhdvhv wkh ohyho suhpldurxjko| irxu wlphv iru wkhlu gdwd vhw1

22

W? |�i hi4@�?_ih Lu |��t tiU|�L?c �i |@!i @ U*Ltih *LL! @| |�i _i|ih4�?@?|tLu Thi4�@ �? ThL_�U|�L? 4L_i*t� i uL**L� |�i 4i|�L_ Lu tiU|�L? �c @?_i T*Lhi �L� |�i _)?@4�U hitTL?tit Lu _���_i?_t @?_ �@*�@|�L? i T*@�? h�t!Thi4�@� i |�i? _�tU�tt �L� UL4M�?@|�L?t Lu U@T�|@* @_��t|4i?| ULt|t @?_�@M�| uLh4@|�L? }i?ih@|i @ ��}� i^��|) Thi4��4� 6�?@**)c �i t�L� �L��?@?U�@* *i�ih@}i U@? u�h|�ih �?Uhi@ti |�i i^��|) Thi4��4�

�hi4�@ �? ThL_�U|�L? 4L_i*t

AL t�L� �L� ThL_�U|�L? 4L_i*t �Lh!c �}�hi 2 _�tT*@)t �@h�L�t t|h�T Thi4�@@?_ �4T�*ti hitTL?ti u�?U|�L?t uLh |�i M@t�U t|@|�L?@h) 4L_i* U@ti ��|� *L�h�t! @�iht�L? @?_ *L� U@T�|@* @_��t|4i?| ULt|t� �L|@M*)c t|h�T Thi4�@ @hi ?L�?L *L?}ih @*�@)t TLt�|��i �? UL?|h@t| |L |�i �?_�?}t �? |�i _�gihi?| i?_L��4i?| 4L_i*t �i t|�_�i_ MiuLhi� 6Lh �?t|@?Uic T@)L�| �?Uih|@�?|) Thi4�@ @hi?L� ?i}@|��i uLh t�Lh| 4@|�h�|�it� AL �?_iht|@?_ |��t tii4�?}*) UL�?|ih�?|���|��i hit�*|c hiU@** |�@| �i _i�?i_ |�i _���_i?_ @t L�|T�| 4�?�t *@MLh �?UL4i4�?�t �?�it|4i?|� A�ihiuLhic @u|ih @ TLt�|��i ThL_�U|���|) t�LU!c |�i t�@hT�?Uhi@ti �? �?�it|4i?| t�4T*) L�|�i�}�t |�i �?Uhi@ti �? |�i U@T�|@* �?UL4i�W? L|�ih |ih4tc |�i �h4<t _iU�t�L? �t |L �?Uhi@ti �|t hi|@�?i_ i@h?�?}t �? Lh�_ih |L |@!i @_�@?|@}i Lu |�i |i4TLh@h�*) ��}�ih ThL_�U|���|)G |��t i@h?�?}tThLUitt U@�tit ?i}@|��i T@)L�| Thi4�@� A�i i^��|) Thi4��4 �t UL4TLti_ LuML|� |�i |ih4 @?_ |�i T@)L�| �?Uih|@�?|) Thi4�@c ��ihi@t |�i ML?_ �@t L?*)|�i |ih4 Thi4�@� Oi?Uic �i U@? ?L� �?_iht|@?_ |�i @TT@hi?|*) @?L4@*L�thit�*| �? |@M*i 2G |�@|c �? |��t U@tic |�i i^��|) Thi4��4 E�ffS� �t *L�ih |�@?|�i ML?_ Thi4��4 E�ffH�� �|�ih hit�*|t �? |@M*i 2 U@? Mi @?@*)3i_ |�i t@4i�@)�

`�) _L U@T�|@* @_��t|4i?| ULt|t �?Uhi@ti Thi4�@q A�i tiUL?_hL� Lu �}�hi 2 �**�t|h@|it �L� U@T�|@* @_��t|4i?| ULt|t U@? �4ThL�i hit�*|tuLh |�i i^��|) Thi4��4� 6�ht|c M) hi_�U�?} |�i TL|i?|�@* uLh �?|ih|i4TLh@*t�Mt|�|�|�L? L? |�i ThL_�U|�L? t�_ic |�i |�4i T@|� uLh 4@h}�?@* �|�*�|) �t4Lhi �@h�@M*i� W| �t @*tL �?�@h�@M*) �?Uhi@t�?}c ���U� *i@_t |L TLt�|��i |ih4Thi4�@� 5iUL?_c }��i? |�@| �?�it|4i?| �L*@|�*�|) �t hi_�Ui_c _���_i?_t ?L�?L *L?}ih �@�i @ *@h}i �?�|�@* _L�?|�h?c ���U� Mi?i�|t |�i T@)L�| Thi4�@��t hiTLh|i_ �? |@M*i 2c |�i i^��|) Thi4��4c �? |��t 4L_i* ��|� 4L_ih@|i@_��t|4i?| ULt|tc �t �?Uhi@ti_ @ML�| |i? |�4it ��|� hitTiU| |L �|t �@*�i ��|�*L� U@T�|@* @_��t|4i?| ULt|t( �? @__�|�L?c �| �t *@h}ih |�@? |�i ML?_ Thi4��4�

2�

`�) �t ��}� h�t! @�iht�L? ?L| i?L�}�q 6�}�hi � i T*@�?t ��) h�t!@�iht�L? @*L?i U@??L| }��i ��}� i^��|) Thi4�@ �? ThL_�U|�L? 4L_i*t� W?_ii_c��}� h�t! @�iht�L? @U|�@**) hi_�Uit _���_i?_ hitTL?tit L�ih @** �Lh�3L?t� W?|��t UL?|i |c |�i u@U| |�@| |�i h�t! @�iht�L? ULi�U�i?| �t i^�@* |L |�i �?�ihtiLu |�i i*@t|�U�|) Lu �?|ih|i4TLh@* t�Mt|�|�|�L? �@t t|hL?} �4T*�U@|�L?t� A�i}hi@|ih _it�hi |L t4LL|� UL?t�4T|�L? *i@_t _���_i?_t |L @U|�@**) _iU*�?i L�ih@** �Lh�3L?t �? hitTL?ti |L @ TLt�|��i ThL_�U|���|) t�LU!�

`�@| �@TTi?t ��|� h@?_L4 �@*! ThL_�U|���|)q +@?_L4 �@*!ThL_�U|���|) uLh |�4i�tiT@h@M*i �|�*�|)c �? �}�hi �c Uhi@|it i�ih _iU*�?�?} i �TiU|i_ 4@h}�?@* �|�*�|)c |�i UL�?|ihT@h| Lu @? i�ih �?Uhi@t�?} UL?t�4T|�L?T@|�� A��t �?Uhi@tit �?|ihit| h@|it L�ih @** �Lh�3L?tc |��t *i@_�?} |L ?i}@|��i|ih4 Thi4�@� W?Uhi@t�?} h�t! @�iht�L? E?L| t�L�?� ��** �ihi �?Uhi@ti |�i �L*_��?} Thi4�@ M) @ ��}�ih h@|i |�@? |�i T@)L�| �?Uih|@�?|) Thi4�@c @t t�}}it|i_M) i^�@|�L? E�D�� A��t 4i@?t @ *L�ih i^��|) Thi4��4 uLh |�i 6w @?_ O64L_i*t ��|� *L� U@T�|@* @_��t|4i?| ULt|t� �L|ic �L�i�ihc |�@| |�i T@)L�|Thi4�@ @hi UL?t�t|i?|*) TLt�|��i @?_ UL?t�_ih@M*) *@h}ih |�@? uLh |�i t|@�|�L?@h) U@tit Lu �}�hi 2� �) 4@!�?} |�i |hi?_ *i�i* Lu _���_i?_t t|LU�@t|�Uch@?_L4 �@*! ThL_�U|���|) �?Uhi@tit |�i�h h�t!�?itt�

`�@| _i|ih4�?it |�i *i�i* Lu |�i h�t!�uhii h@|iq B��i? L�h T@h�|�U�*@h t|LU�@t|�U t|h�U|�hi |�i �?UL?_�|�L?@* 4i@? Lu |�i h�t!�uhii h@|i �@t|�i uL**L��?} U*Lti_ uLh4 tL*�|�L?G

.E-|c|n�d�|c|n�o� '�

qW

i T��

2E�@hE.|b|n� � b|�� �@hEb|n� � .|b|n���

�E2e�

��ihi |�i �ht| h@|�L �? |�i h�}�| �@?_ t�_i �t t�4T*) |�i t|i@_) t|@|i h@|i Luhi|�h? �?_ih Uih|@�?|)c @ u�?U|�L? Lu |�i |hi?_ }hL�|� h@|i @?_ |�i }hL�|�ULhhiU|i_ _�tUL�?| u@U|Lh� N?Thi_�U|@M*i �L*@|�*�|) Lu |�i �@*�@|�L? hi_�Uit|��t h@|ic ��@| �i �?|ihThi|i_ i@h*�ih @t ThiU@�|�L?@h) igiU|t( @?_ Thi_�U|@M*i�L*@|�*�|)c @ ai?ti?<t �?i^�@*�|) igiU|c �?Uhi@tit �|� 6Lh �4T�*ti hitTL?titc*L� h�t!�uhii h@|it @hi *�?!i_ |L *@h}i ��4Tt @| �4T@U| uL**L�i_ M) *�||*iThi_�U|@M*i U�@?}i� A��t �t |�i }i?ih@* T@||ih? uLh ?L?t|@|�L?@h) 4L_i*tc���U� @*tL U*i@h*) t�L�t �T �? |�i hit�*|t �? |@M*i 2�

2e

A�i �?|ih@U|�L? Mi|�ii? U@T�|@* @_��t|4i?| ULt|t @?_ �@M�| uLh4@�|�L?

��h Thi��L�t _�tU�tt�L? �? tiU|�L?t ��2 @?_ e�� i T*@�?i_ ��) U@T�|@* @_��t|�4i?| ULt|t @?_ �@M�| uLh4@|�L? U@? tiT@h@|i*) *i@_ |L ��}� i^��|) Thi4�@�A�i ?�4ih�U@* hit�*|tc �L�i�ihc 4@!i �| U*i@h |�@| �| �t |�i UL4M�?@|�L? Lu|�iti |�L i*i4i?|t |�@| @UUL�?| uLh @? i^��|) Thi4��4 Lu ti�ih@* TihUi?|@}iTL�?|t� A@M*i � @?_ e hiTLh| TLT�*@|�L? 4L4i?|t uLh M�t�?itt U)U*i t|@|�t|�Ut|�@| U*@h�u) |�i 4L_i* 4iU�@?�t4t @| �Lh!�

�@T�|@* @_��t|4i?| ULt|t hi_�Ui �?|ih|i4TLh@* t�Mt|�|�|�L? �? ThL_�U|�L?�W? |�h?c |��t 4@!it UL?t�4T|�L? 4Lhi �L*@|�*i @?_ �|t }hL�|� h@|i *itt Thi�_�U|@M*i� OL�i�ihc U@T�|@* @_��t|4i?| ULt|t @*L?i _L ?L| �?Uhi@ti h�t!�?itti?L�}� |L }i?ih@|i *@h}i Thi4�@� 6�h|�ihc U@T�|@* @_��t|4i?| ULt|t t|hL?}*)hi_�Ui �?�it|4i?| �L*@|�*�|) uLh |�4i�tiT@h@M*i 4L_i*t Mi*L� @?) i4T�h�U@**)T*@�t�M*i �@*�i� O@M�| uLh4@|�L? �?Uhi@tit h�t! @�iht�L? �? UL?t�4T|�L? �?|�i t�Lh| |ih4 �iht�t |�i *L?} |ih4c ���U� U@? Uhi@|i *@h}i Thi4�@� OL��i�ihc �@M�| uLh4@|�L? *L�iht �?|ih|i4TLh@* t�Mt|�|�|�L? �? Thiuihi?Uitc tL|�@| UL?t�4T|�L? MiUL4it @*tL 4�U� t4LL|�ih E��i�c *itt �L*@|�*i @?_ 4Lhi@�|LULhhi*@|i_�c ���U� hi_�Uit |�i h�t!�?itt Lu |�i i?_L}i?L�t UL?t�4T|�L?T@|�� EA��t *@||ih u@U| _Lit Lu UL�hti ?L| UL4i �?|L T*@) �? i?_L�4i?|4L_i*t�� �L4M�?i_ ��}� U@T�|@* @_��t|4i?| ULt|t @?_ �@M�| uLh4@|�L? !iiT�?|ih|i4TLh@* t�Mt|�|�|�L? �? UL?t�4T|�L? @?_ �? ThL_�U|�L? @| *L� *i�i*tc@?_ |��t }i?ih@|i Thi4�@ �? |�i Lh_ih Lu 4@}?�|�_i Lu i?_L�4i?| 4L_i*t�

#itT�|i |�i u@U| |�@| U@T�|@* @_��t|4i?| ULt|t _L hi_�Ui |�i @�|LULhhi�*@|�L? ULi�U�i?|t Lu UL?t�4T|�L? }hL�|� h@|itc �ht| Lh_ih ULi�U�i?|t Lu �e.@?_ �D tii4 t|�** h@|�ih ��}� Etii |@M*i e�� Oi@|L? E�bb�� hiTLh|t |�i �ht| ��i@�|LULhhi*@|�L? ULi�U�i?|t uLh }hL�|� h@|it Lu ti@tL?@**)�@_��t|i_ ^�@h|ih*)N�5� UL?t�4T|�L? i Ti?_�|�hi L? ?L?_�h@M*it @?_ tih��Uit @| �2.SE�fSH�c��fHE�fS��c �2f�E�fHf�c �fD.E�fH.� @?_ ��2f2E��fH� Et|@?_@h_ ihhLht �? T@hi?�|�itit�� Oi @h}�itc �L�i�ihc |�@| |�i ��}� �ht| Lh_ih tih�@* ULhhi*@|�L? UL�i�U�i?| �t _�i |L |�4i�@�ih@}�?} Lu |�i UL?t�4T|�L? _@|@� �L_i**�?} |�it@4T*i ThLTih|�it Lu @}}hi}@|i _@|@ �t Mi)L?_ |�i tULTi Lu L�h T@Tih�

6�?@?U�@* *i�ih@}i @?_ _���_i?_ �L*@|�*�|)

+it�*|t �? |@M*i 2 _LU�4i?| |�@| 4L_i* �iht�L?t ��|� U@T�|@* @_��t|4i?|ULt|t @?_ �@M�| uLh4@|�L? @hi @M*i |L }i?ih@|i i^��|) Thi4�@ U*Lti |L �I�

2D

#itT�|i |��tc |�i 4L_i* U@??L| i T*@�? 4Lhi |�@? @ �I i Uitt hi|�h? Lui^��|) L�ih *L?} ML?_tc ��ihi@t |@M*i � t�}}it|t |�@| |�i i^��|) Thi4��4 �@t@ *@h}i T@)L�| �?Uih|@�?|) UL4TL?i?|� 6�?@?U�@* *i�ih@}ic ��|�L�| @giU|�?}|ih4 Thi4�@c _Lit �?Uhi@ti |�i h�t!�?itt Lu _���_i?_tc @?_ |�ihiuLhi �@t |�iTL|i?|�@* |L tL*�i |��t ThLM*i4�

W? L�h uh@4i�Lh!c �?@?U�@* *i�ih@}i @U|t |�hL�}� |�L |h@?t4�tt�L? U�@?�?i*t� 6�ht|c }��i? |�@| �h4t *�?! |�i�h _iM| *i�i* |L |�i�h U�hhi?| U@T�|@*t|LU!c @ TLt�|��i t�LU! M) *i@_�?} |L }hL�|� �? |�i U@T�|@* t|LU! �?Uhi@tit|�i ^�@?|�|) Lu �tt�i_ ML?_t� A��t �i@!i?t |�i �?�|�@* _L�?|�h? �? _���_i?_thi*@|i_ |L �?Uhi@ti_ �?�it|4i?| |�@| �i �@�i tii? �? �}�hi 2c @?_ *i@_t |L��}�ih T@)L�| Thi4�@ uLh t�Lh| �Lh�3L?t� 5iUL?_c �u �?|ihit| h@|it _iUhi@ti@u|ih @ TLt�|��i t�LU!c |�i? |�i �h4 LM|@�?t @ ��}�ih Th�Ui uLh |�i t@*i Lu�|t _�tUL�?| ML?_t� 6�}�hi e t�L�t �L� |�iti |�L i*i4i?|t U@? UL?t�_ih@M*)�?Uhi@ti |�i T@)L�| �?Uih|@�?|) Thi4�@ uLh |�i U@ti ��i? |�i �h4 �tt�it L?*)L?i Tih�L_ ML?_t�

�@?i* � �? |@M*i D hiTLh|t i^��|) Thi4�@ uLh _�gihi?| *i�ih@}i T@h@4i�|ihtc Dc @?_ _iM| 4@|�h�|�it� W? Mh@U!i|t �i �@�i |�i 4i@?t @?_ t|@?_@h__i��@|�L?t Lu *i�ih@}i h@|�LtQ_i�?i_ @t _iM| L�ih |L|@* �h4 �@*�i� �@?i*� Thiti?| _���_i?_ �L*@|�*�|)� i hi|@�? |�L hit�*|tG i^��|) Thi4�@ _L �?��uLh4*) �?Uhi@ti ��|� *i�ih@}ic @?_ ML?_ 4@|�h�|�it @hi �4TLh|@?| uLh _����_i?_ �L*@|�*�|)��. ��ih@**c �u �i i U*�_i 4L_i* �iht�L?t ��|� i Uitt��i _����_i?_ �L*@|�*�|)c �?@?U�@* *i�ih@}i U@? @__ �T |L �@*u @ TihUi?|@}i TL�?| |L|�i i^��|) Thi4��4� W| �t �?|ihit|�?} |L ?L|i |�@| |�i *L� hiTLh|i_ t|@?�_@h_ _i��@|�L?t uLh *i�ih@}i h@|�Lt U*i@h*) t�}}it| |�@|c i UiT| uLh |�i |�hiiU@tit ��|� 4i@? *i�ih@}it h@|�Lt Lu �H @?_ ��}�ihc |�i @tt�4T|�L? Lu h�t!*ittULhTLh@|i MLhhL��?} �t �ihi ��t|��i_�

AL i T*@�? |�i _h@4@|�U _���_i?_ �L*@|�*�|) uLh U@tit ��ihi |�i �h4 hi��?@?Uit �|t i?|�hi _iM| �? i�ih) Tih�L_c ��i�c _iM| 4@|�h�|) �t i^�@* |L L?ic�i ?ii_ |L *LL! @| �?|ihit| h@|i �L*@|�*�|)� �t �i ?L|�Ui_ �? tiU|�L? � @?_@t _�tU�tti_ �? |�i *�|ih@|�hic �@M�| uLh4@|�L? Thiuihi?Uit 4@!i hi@* �?|ihit|h@|it |LL �L*@|�*ic tii uLh �?t|@?Ui �Mi* E�bb��� ,�i? |�L�}� |��t ThLM*i4�t *itt ThL?L�?Ui_ �? L�h 4L_i*c �?|ihit| h@|it _L MiUL4i 4Lhi �L*@|�*i uLh|�i 4L_i* U@tit UL?t�_ihi_ �? |@M*i D� W? T@h|�U�*@hc uLh |�i 4L_i* ��|�

4:Fhffkhwwl/ Odp dqg Pdun +4<<3, uhsruw d vwdqgdug ghyldwlrq ri dqqxdo glylghqgjurzwk udwhv lq wkh X1V1 iru wkh shulrg 4<:4 wr 4<;8 ri 4619(1 Dvvxplqj d udqgrpzdon/ wklv lv 91;( iru txduwhuo| jurzwk udwhv1

2S

h@?_L4 �@*! ThL_�U|���|)c ��}� h�t! @�iht�L? @?_ ��}� U@T�|@* @_��t|4i?|ULt|tc |�i ^�@h|ih*) t|@?_@h_ _i��@|�L? Lu �?|ihit| h@|it �t ��}�it| UL4T@hi_|L @** L|�ih 4L_i* U@tit @| @ML�| 2�DI� B��i? |�@| |�i �?*i�ihi_ _���_i?_�t @ML�| ��2DI Lu |�i U@T�|@* t|LU!c @ 2�DI U�@?}i �? �?|ihit| h@|itc ��|� @*i�ih@}i h@|�L Lu �Dc ��** |h�T*i |�i _���_i?_� �**L��?} uLh *L?}ih _iM| 4@�|�h�|�it _Lit UL?t�_ih@M*) hi_�Ui |��t �4T@U| L? _���_i?_t� A��t �t MiU@�ti*L?} |ih4 )�i*_t �? |�i 4L_i* @hi UL?t�_ih@M*) *itt �L*@|�*i |�@? t�Lh| |ih4)�i*_tc ���U� �t @*tL ��@| �i LMtih�i �? hi@* �Lh*_�

D �L?U*�t�L?t

i �@�i Thiti?|i_ @ 4i|�L_L*L}) |�@| @**L�t L?i |L i�@*�@|i @?_ |��?!@ML�| @tti| Th�Uit �? @ *@h}i U*@tt Lu 4@UhLiUL?L4�U 4L_i*t� �L4M�?�?} |�iUL?�i?�i?| ThLTih|�it Lu |�i *L}?Lh4@* _�t|h�M�|�L? ��|� @ *L}*�?i@h t)t|i4uLh iUL?L4�U �@h�@M*itc �i _ih��i i Thitt�L?t uLh UL?_�|�L?@* i TiU|i_ hi�|�h?t @?_ �@h�@?Uit uLh tiU�h�|�it ��|� t�?}*i @?_ 4�*|�T*i T@)L�|t� i t�L��L� |��t uh@4i�Lh! @**L�t L?i |L ThL��_i �4TLh|@?| �?|��|�L? @ML�| |�i *�?!Mi|�ii? @tti| hi|�h? Thi4�@ @?_ |�i ?@|�hi Lu |�i M�t�?itt U)U*i� i @*tLt�L� �L� |��t 4i|�L_ U@? Mi _�hiU|*) �ti_ |L t|�_) ?L?�|�4i�tiT@h@M*i Thiu�ihi?Uit�

A��t 4i|�L_ �t |�i? @TT*�i_ |L |�i @TThL �4@|i 4L_i* tL*�|�L?t Lu |�i L?itiU|Lh hi@* M�t�?itt U)U*i 4L_i*� W? |��t ti||�?}c ��|� i?_L}i?L�t ThL_�U|�L?_iU�t�L?tc �i *LL! @| �L� 4L_i* i*i4i?|t @?_ T@h@4i|ih �@*�it @giU| @tti|hi|�h? Thi4�@c uLU�t�?} L? |�i �?��i?Ui Lu M�t�?itt U)U*i _)?@4�Ut� i�?_ |�@| U@T�|@* @_��t|4i?| ULt|t @hi Ui?|h@* |L }i?ih@|�?} *@h}i h�t! Thi4�@�? @ ThL_�U|�L? 4L_i*( 4L_i* �iht�L?t ��|� U@T�|@* @_��t|4i?| ULt|tc �@M�|uLh4@|�L? �? Thiuihi?Uit @?_ �?@?U�@* *i�ih@}i @hi @M*i |L ThL_�Ui @? i^��|)Thi4��4 Lu ti�ih@* TihUi?|@}i TL�?|t�

A�i ^�@?|�|@|��i @TT*�U@|�L? TihuLh4i_ �? |��t T@Tih �t L?*) @ �?�|�@* t|iT�5�?Ui �i �@�i uL�?_ |�@| @ t4@**�tU@*i i^��*�Mh��4 4L_i* ��|� @ ?L?|h���@*ThL_�U|�L? tiU|Lh U@? }i?ih@|i h�t! Thi4�@ �? |�i Lh_ih Lu 4@}?�|�_i Lu��t|Lh�U@**) LMtih�i_ *i�i*tc |��t 4L_i* @?_ i |i?t�L?t Lu �| t�L�*_ Mi �tiu�*�? t�i__�?} @__�|�L?@* *�}�| L? |�i �?|ih@U|�L? Mi|�ii? @tti| hi|�h?t @?_ |�i?@|�hi Lu |�i M�t�?itt U)U*i�

2.

�TTi?_�

A��t @TTi?_� t�L�t |�@| |�i @tti| Th�U�?} uLh4�*@i U@? Mi _�hiU|*) @TT*�i_|L ?L?�|�4i�tiT@h@M*i �@*�@|�L?t�

Nt�?} |�i ?L|@|�L? _i�?i_ �? |�i |i |c UL?t�_ih |�i �@*�@|�L? Lu @ TLtt�M*)h@?_L4 T@)L�| (|n&G

T|d(|n&o 'q&.|EM|n&c|n&nr(|n&�

.|EM|c|nr��

�TT*)�?} |�i *@� Lu �|ih@|��i i TiU|@|�L?tc |�i ?�4ih@|Lh U@? |�i? Mi �h�||i?@tG

.|E.|n&EM|n&c|n&nr(|n&��c

@?_ |��t �t i^�@* |L.|E.|n&EM|n&c|n&nr�(|n&�

MiU@�ti (|n& �t _i|ih4�?�t|�U @| |�4i |n &� �TT*)�?} *L}?Lh4@*�|)c �i |�i?LM|@�? |�@|G

T|d(|n&o 'q&.|

�EEi T.|n&�|n&c|n&nr�(|n&� i TE

2�@h|n&E�|n&c|n&nr��

i TE.|�|c|nr� i TE�

2�@h|E�|c|nr��

i !?L� |�@| �@h|n&E�|n&c|n&nr� �t i^�@* |L �@h|E�|c|nr�c MiU@�ti |�i UL?_��|�L?@* tiUL?_ 4L4i?|t _L ?L| _iTi?_ L? |�i t|@|i Lu |�i t)t|i4� `�|� |��t*@t| t|iTc �i LM|@�? L�h @??L�?Ui_ hit�*| |�@|G

T|d(|n&o 'q&.|EEi T.|n&�|n&c|n&nr�(|n&�

i TE.|�|c|nr��

2H

+iuihi?Uit

�Mi*c �?_hi� �� E�bHf�c R,4T�h�U@* �?�it|4i?| i^�@|�L?tG @? �?|i}h@|��iuh@4i�Lh!c� �@h?i}�i�+LU�it|ih �L?uihi?Ui 5ih�it L? ��M*�U �L*�U) �2c�b� b��

�Mi*c �?_hi� �� E�bbf�c R�tti| Th�U�?} �?_ih �@M�| uLh4@|�L? @?_ U@|U��?}�T ��|� |�i aL?ititc� �,� �@Tiht @?_ �hLUii_�?}t Hfc �H�e2�

�@U!�tc #@��_c ki�Lic �@|h�U! @?_ k)_*@?_c 6�?? E�bb2�c RW?|ih?@|�L?@*hi@* M�t�?itt U)U*itc� aL�h?@* Lu �L*�|�U@* ,UL?L4) �ffc .eD�..D�

�@ |ihc �@h�@??i @?_ aih4@??c NhM@? a� E�bb��c RA�i �?|ih?@|�L?@* _��ih�t��U@|�L? T�33*i �t �Lhti |�@? )L� |��?!c� +LU�it|ih �i?|ih uLh ,UL�?L4�U +iti@hU�c Lh!�?} �@Tih r�Df�

�@ |ihc �@h�@??i @?_ �h�U�?� �@h�L a� E�bb��c R, T*@�?�?} t@��?}��?�it|4i?|ULhhi*@|�L?tc� �4ih�U@? ,UL?L4�U +i��i� H�c e�S�e�S�

�@ |ihc �@h�@??i @?_ k�?}c +LMih| B� E�bb��c R6�tU@* TL*�U) �? }i?ih@*i^��*�Mh��4c� �4ih�U@? ,UL?L4�U +i��i� H�c ��D���e�

�@t�c �@h@?|@T E�bH.�c R�? @_��t|4i?| ULt| 4L_i* Lu @tti| Th�U�?}c� W?|ih�?@|�L?@* ,UL?L4�U +i��i� 2Hc Sfb�S2��

�*@U!c 6�tU�ih E�bbf�c R�i@? hi�iht�L? @?_ UL?t�4T|�L? t4LL|��?}c� +i���i� Lu 6�?@?U�@* 5|�_�it �c �f.���e�

�i??�?}@c 5�4L? @?_ �hL|LT@T@_@!�tc �h�t E�bbf�c Rwi�ih@}ic |�4i Thiu�ihi?Uic @?_ |�i �i^��|) Thi4��4 T�33*i<c� aL�h?@* Lu �L?i|@h) ,UL�?L4�Ut 2Dc eb�DH�

�@4TMi**c aL�? v� E�bHS�c R�L?_ @?_ t|LU! hi|�h?t �? @ t�4T*i i U�@?}i4L_i*c� "�@h|ih*) aL�h?@* Lu ,UL?L4�Utc .HD�Hf��

�@4TMi**c aL�? v� E�bb��c RN?_iht|@?_�?} h�t! @?_ hi|�h?c� �?T�M*�t�i_T@Tihc �h�?Ui|L? N?��iht�|)�

2b

�iUU�i||� 5|iT�i? B�c w@4c �L!�t@?} @?_ �@h!c �i*tL? �� E�bbf�c R�i@?hi�iht�L? �? i^��*�Mh��4 @tti| Th�Uitc� �4ih�U@? ,UL?L4�U +i��i� Hfc�bH�e�H�

�iUU�i||�c 5|iT�i? B�c w@4c �L!�t@?} @?_ �@h!c �i*tL? �� E�bb��c RA�ii^��|) Thi4��4 @?_ |�i h�t! uhii h@|ic 4@|U��?} |�i 4L4i?|tc� aL�h?@*Lu �L?i|@h) ,UL?L4�Ut ��c 2��eD�

��i?c �@��6� E�bb��c R6�?@?U�@* �?�it|4i?| LTTLh|�?�|�it @?_ |�i 4@UhL�iUL?L4)c� aL�h?@* Lu 6�?@?Ui eSc D2b�DDe�

��h�t|�@?Lc w@�hi?Ui a� E�bb��c Rw�^��_�|) igiU|tc 4L?i|@h) TL*�U) @?_ |�iM�t�?itt U)U*ic� �?T�M*�t�i_ T@Tihc �Lh|��it|ih? N?��iht�|)�

��h�t|�@?Lc w@�hi?Ui a� E�bbf�c Rw�?i@h�^�@_h@|�U @TThL �4@|�L? @?_ �@*�i�u�?U|�L? �|ih@|�L?G � UL4T@h�tL?c� aL�h?@* Lu ��t�?itt : ,UL?L4�Ut5|@|�t|�Ut Hc bb�����

��h�t|�@?Lc w@�hi?Ui a� @?_ ,�U�i?M@�4c �@h|�? E�bbf�c RN?�| hLL|t �? hi@*}?TG #L �i !?L� @?_ _L �i U@hiqc� �@h?i}�i�+LU�it|ih �L?uihi?Ui5ih�it L? ��M*�U �L*�U) �2c .�S2�

�LU�h@?ic aL�? O� E�bb��c R�hL_�U|�L?�M@ti_ @tti| Th�U�?} @?_ |�i *�?!Mi|�ii? t|LU! hi|�h?t @?_ iUL?L4�U ��U|�@|�L?tc� aL�h?@* Lu 6�?@?UieSc 2fb�2�.�

�LU�h@?ic aL�? O� E�bb2@�c R� UhLtt�tiU|�L?@* |it| Lu @ ThL_�U|�L?�M@ti_@tti| Th�U�?} 4L_i*c� ��,+ Lh!�?} �@Tih �L� ef2D�

�LU�h@?ic aL�? O� @?_ O@?ti?c w@ht �� E�bb2M�c R�tti| Th�U�?} i T*Lh@|�L?tuLh 4@UhLiUL?L4�Utc� ��,+ �@UhLiUL?L4�Ut �??�@* �bb2c ��D��SD�

�L?t|@?|�?�_itc BiLh}i �� E�bbf�c RO@M�| uLh4@|�L?G � hitL*�|�L? Lu |�ii^��|) Thi4��4 T�33*ic� aL�h?@* Lu �L*�|�U@* ,UL?L4) bHc D�b�De��

#@?|��?ic ai@?���ihhic #L?@*_tL?c aL�? �� @?_ �i�h@c +@�?�t� E�bb2�cRA�i i^��|) Thi4��4 @?_ |�i @**LU@|�L? Lu �?UL4i h�t!c� aL�h?@* Lu,UL?L4�U #)?@4�Ut : �L?|hL* �.c Dfb�D�2�

�f

#@?|��?ic ai@?���ihhic #L?@*_tL?c aL�? �� @?_ �i�h@c +@�?�t� E�bHH�cR�? tL4i UL4T�|@|�L?@* @tTiU|t Lu i^��*�Mh��4 M�t�?itt U)U*i |�iLh)c�aL�h?@* Lu ,UL?L4�U #)?@4�Ut @?_ �L?|hL* ��c eeb�e.f�

,�t?ihc +LMih| @?_ 5|hL|3c +LMih|� O� E�bS��c R#i|ih4�?@?|t Lu M�t�?itt�?�it|4i?|c� W4T@U|t Lu 4L?i|@h) TL*�U)c UL4T�*i_ M) |�i �L44�tt�L?L? �L?i) @?_ �hi_�|� ,?}*i�LL_ �*�gtG �hi?|�Ui�O@**�

,t|hi**@c �h|�hL @?_ O@h_L��i*�tc B�!@t �� E�bb��c RA�i |ih4 t|h�U|�hi @t@ Thi_�U|Lh Lu hi@* iUL?L4�U @U|���|)c� aL�h?@* Lu 6�?@?Ui eSc DDD�D..�

6@4@c ,�}i?i 6� E�bbf�c R5|LU! hi|�h?tc i TiU|i_ hi|�h?tc @?_ hi@* @U|����|)c� aL�h?@* Lu 6�?@?Ui eDc �fH����fH�

6@4@c ,�}i?i 6� @?_ 6hi?U�c ki??i|� +� E�bHb�c R��t�?itt UL?_�|�L?t @?_i TiU|i_ hi|�h?t L? t|LU!t @?_ ML?_tc� aL�h?@* Lu 6�?@?U�@* ,UL?L4�Ut2Dc 2��eb�

6ihtL?c `@)?i ,� @?_ �L?t|@?|�?�_itc BiLh}i �� E�bb��c RO@M�| Tiht�t�|i?Ui @?_ _�h@M�*�|) �? @}}hi}@|i UL?t�4T|�L?c� aL�h?@* Lu 6�?@?U�@*,UL?L4�Ut 2bc �bb�2ef�

6h�i?_c Wh��? @?_ �*�4ic �@ht�@** E�b.D�c RA�i _i4@?_ Lu h�t!) @tti|tc��4ih�U@? ,UL?L4�U +i��i� SDc bff�b22�

Bhii?�LL_c aihi4)c +L}ihtL?c +�U�@h_ @?_ h�}�|c +@?_@** E�bb��c ROL�ti��L*_ ThL_�U|�L? �? hi@* M�t�?itt U)U*i |�iLh)c� +LU�it|ih �i?|ih uLh,UL?L4�U +iti@hU�c Lh!�?} T@Tih r�e.�

O@?ti?c w@ht �� @?_ 5�?}*i|L?c ki??i|� a� E�bH��c R5|LU�@t|�U UL?t�4T|�L?ch�t! @�iht�L?c @?_ |�i |i4TLh@* Mi�@��Lh Lu @tti| hi|�h?tc� aL�h?@* Lu�L*�|�U@* ,UL?L4) b�c 2eb�2SD�

O@)@t��c 6�4�L E�bH2�c RALM�?<t 4@h}�?@* @?_ @�ih@}i ^G � ?iLU*@tt�U@*�?|ihThi|@|�L?c� ,UL?L4i|h�U@ Dfc 2���22e�

Oi@|L?c aL�? E�bb��c RA�i �?|ih@U|�L? Mi|�ii? |�4i�?L?tiT@h@M*i Thiuih�i?Uit @?_ |�4i @}}hi}@|�L?c� ,UL?L4i|h�U@ S�c �D���HD�

k�4M@**c ��*it 5� E�bbf�c R�hiU@�|�L?@h) t@��?} �? |�i t4@** @?_ �? |�i*@h}ic� ,UL?L4i|h�U@ DHc D��.��

��

k�?}c +LMih| B� E�bb��c R�L?i) @?_ M�t�?itt U)U*itc� �?T�M*�t�i_ T@TihcN?��iht�|) Lu +LU�it|ih�

k�?}c +LMih| B�c �*Lttihc ��@h*it W� @?_ +iMi*Lc 5ih}�L A� E�bHH�c R�hL�_�U|�L?c }hL�|� @?_ M�t�?itt U)U*itc� aL�h?@* Lu �L?i|@h) ,UL?L4�Ut2�c �bD�2�2c �fb��e��

k)_*@?_c 6�?? ,� @?_ �hitUL||c ,_�@h_ �� E�bH2�c RA�4i |L M��*_ @?_@}}hi}@|i ��U|�@|�L?tc� ,UL?L4i|h�U@ Dfc ��eD���.f�

w�U@tc +LMih| ,�c ah� E�b.H�c R�tti| Th�Uit �? @? i U�@?}i iUL?L4)c�,UL?L4i|h�U@ eSc �e2b��eeD�

w�U@tc +LMih| ,�c ah� @?_ �hitUL|| ,_�@h_ �� E�b.��c RW?�it|4i?| �?_ih�?Uih|@�?|)c� ,UL?L4i|h�U@ �bc SDb�SH��

�@?!��c Bhi}Lh) �� E�bHS�c RA�i i^��|) Thi4��4 @?_ |�i UL?Ui?|h@|�L?Lu @}}hi}@|i t�LU!tc� aL�h?@* Lu 6�?@?U�@* ,UL?L4�Ut �.c 2���2�b�

�@t�*�tc +L?@*_ `� E�bHH�c A�i _iM|%i^��|) U�L�Uic �@**�?}ihc �@4Mh�_}i���

�i�h@c +@�?�t� @?_ �hitUL||c ,_�@h_ �� E�bHD�c RA�i i^��|) Thi4��4G �T�33*ic� aL�h?@* Lu �L?i|@h) ,UL?L4�Ut �Dc �eD��S��

�hitUL||c ,_�@h_ �� E�bHS�c RA�iLh) @�i@_ Lu M�t�?itt U)U*i 4i@t�hi4i?|c��@h?i}�i�+LU�it|ih �L?uihi?Ui 5ih�it L? ��M*�U �L*�U) 2Dc ���SS�

+�i|3c A�L4@t �� E�bHH�c RA�i i^��|) h�t! Thi4��4G � tL*�|�L?c� aL�h?@*Lu �L?i|@h) ,UL?L4�Ut 22c ��.���2�

+L|i4Mih}c a�*�L a� @?_ LL_uLh_c ��U�@i* E�bb2�c R�*�}LTL*�t|�U Th�U�?}@?_ |�i igiU|t Lu @}}hi}@|i _i4@?_ L? iUL?L4�U @U|���|)c� aL�h?@* Lu�L*�|�U@* ,UL?L4) �ffc ��D���2f.�

+L��i?�Lht|c Biih| k� E�bb��c R�tti| hi|�h?t @?_ M�t�?itt U)U*itc� �?T�M�*�t�i_ T@Tihc N?��iht�|) Lu +LU�it|ih�

5U��ih|c `�**�@4 B� E�bbf�c R5|LU! hi|�h?t @?_ hi@* @U|���|)G � Ui?|�h) Lui��_i?Uic� aL�h?@* Lu 6�?@?Ui eDc �2�.��2D.�

�2

5U��ih|c `�**�@4 B� E�bHb�c R`�) _Lit t|LU! 4@h!i| �L*@|�*�|) U�@?}i L�ih|�4iqc� aL�h?@* Lu 6�?@?Ui eec ���D���Df�

5�i}i*c aihi4) a� E�bb2�c RA�i hi@* h@|i Lu �?|ihit| uLh4 �Hff��bbfc� aL�h?@*Lu �L?i|@h) ,UL?L4�Ut 2bc 22.�2D2�

5�?}*i|L?c ki??i|� a� E�bbf�c R�tti| Th�U�?} 4L_i*tc� O@?_MLL! Lu �L?i�|@h) ,UL?L4�Ut �c ,*ti��ih 5U�i?Ui ��M*�t�ih �� V�c DHe�S2S�

5|LU!c a@4it O� @?_ @|tL? �@h! `� E�bHb�c R�i� �?_i it Lu UL�?U��_i?| @?_ *i@_�?} iUL?L4�U �?_�U@|Lhtc� ��,+ �@UhLiUL?L4�Ut �??�@*�bHbc �D���be�

5|LU!4@?c �*@? �� @?_ Ait@hc w�?_@ E�bb��c RA@t|it @?_ |iU�?L*L}) �?@ |�L�UL�?|h) 4L_i* Lu |�i M�t�?itt U)U*iG i T*@�?�?} �?|ih?@|�L?@*UL4L�i4i?|tc� �?T�M*�t�i_ T@Tihc N?��iht�|) Lu +LU�it|ih�

5�?_@hit@?c 5�hit� �� E�bHb�c RW?|ih|i4TLh@**) _iTi?_i?| Thiuihi?Uit @?_|�i �L*@|�*�|) Lu UL?t�4T|�L? @?_ �i@*|�c� +i��i� Lu 6�?@?U�@* 5|�_�it2c .��Hb�

��

Table 1Means of U.S. asset returns

A. Returns for the period 1948:1-1987:4

Asset Mean*

Short-term bond return: T-bills

0.80

Long-term bond return: long-term U.S. gov't debt

0.78

Stock return: S&P 500 8.90

*Annualized quarterly returns, percent per year. Source: SBBI

B. Returns for the period 1800 - 1990

Asset Mean*

Short-term bond return: 3.13

Long-term bond return: 3.71

Stock return: 7.77

*Returns measured as percent per year. Source: Siegel (1992)

Table 2Model predictions for mean returns

A. Stationary process for productivity

riskaversion

adjustmentcosts

Rf-1 (Rb/Rf)-1 (Re/Rf)-1

fixedlabor

variablelabor

habitformat'

fixedlabor

variablelabor

habitformat'

fixedlabor

variablelabor

habitformat'

τ=2 low 6.48 6.49 6.48 0.008 0.005 0.011 0.006 0.006 0.008

mod 6.46 6.48 6.41 0.048 0.025 0.140 0.055 0.034 0.148

high 6.43 6.47 6.15 0.103 0.038 0.750 0.130 0.055 0.806

τ=10 low 6.29 6.47 6.27 0.092 0.015 0.109 0.028 0.010 0.043

mod 6.11 6.42 5.98 0.331 0.088 0.498 0.275 0.094 0.425

high 5.61 6.35 4.67 1.091 0.201 2.749 1.096 0.234 2.744

B. Random-walk process for productivity

riskaversion

adjustmentcosts

Rf-1 (Rb/Rf )-1 (Re/Rf)-1

fixedlabor

variablelabor

habitformat'

fixedlabor

variablelabor

habitformat'

fixedlabor

variablelabor

habitformat'

τ=2 low 6.46 6.49 6.45 -0.044 -0.020 -0.040 0.007 0.006 0.014

mod 6.44 6.48 6.36 -0.035 -0.014 0.041 0.043 0.025 0.158

high 6.42 6.47 6.12 -0.021 -0.008 0.456 0.105 0.059 0.750

τ=10 low 4.50 6.37 4.31 -0.751 -0.091 -0.669 -0.272 0.010 -0.187

mod 4.43 6.35 3.77 -0.679 -0.072 -0.158 -0.158 0.057 0.421

high 4.28 6.32 2.00 -0.530 -0.045 1.950 0.104 0.136 2.850

Notes: All entries are quarterly returns, expressed as annualized percentage points.Mnemonics for the returns are: Rf = Risk-free rate of return; Rb = Bond return;Re= Equity return.

Table 3: Business cycle statisticsCCmodel and US data

Preferencespecification

Business-cyclestatistic

US data:1960-1991

low adj. costs;ττ=2

mod. adj. costs;ττ=10

high adj. costs;ττ=2

high adj. costs;ττ=10

Std(y) 0.0098 0.0086 0.0085 0.0086 0.0085

Fixed labor Std(c)/Std(y) 0.74 0.46 0.51 1.12 1.23

Std(i)/Std(y) 2.65 2.54 2.37 0.65 0.34

STATIONARY Std(y) 0.0098 0.0116 0.0097 0.079 0.0084

SHOCKS Variable labor Std(c)/Std(y) 0.74 0.48 0.78 1.18 1.05

Std(i)/Std(y) 2.65 2.47 1.63 0.50 0.86

Std(y) 0.0098 0.0086 0.0085 0.0086 0.0086

Habit formation Std(c)/Std(y) 0.74 0.26 0.27 0.79 0.44

Std(i)/Std(y) 2.65 3.28 3.23 1.85 2.82

Std(y) 0.0098 0.0085 0.0085 0.0085 0.0085

Fixed labor Std(c)/Std(y) 0.74 0.87 1.19 1.17 1.23

Std(i)/Std(y) 2.65 1.36 0.46 0.51 0.34

RANDOM Std(y) 0.0098 .0099 .0082 .0079 .0078

WALK Variable labor Std(c)/Std(y) 0.74 0.72 1.07 1.16 1.18

SHOCKS Std(i)/Std(y) 2.65 1.80 0.82 0.54 0.48

Std(y) 0.0098 0.0085 0.0085 0.0085 0.0085

Habit formation Std(c)/Std(y) 0.74 0.49 0.64 0.85 0.73

Std(i)/Std(y) 2.65 2.80 2.51 1.71 2.26

Notes: U.S. data is from the OECD. Data and model were filtered with the first-difference filter.

Table 4Habit formation model

Autocorrelation coefficients of consumption growth rates

adjustmentcosts

shockprocess

riskaversion

Autocorrelation coefficients at lag

1 2 3 4 5

stationary τ=2 .63 .40 .27 .19 .14

low τ=10 .61 .38 .24 .15 .11

randomwalk

τ=2 .61 .38 .25 .17 .13

τ=10 .59 .36 .21 .13 .08

stationary τ=2 .29 .06 .00 -.03 -.04

high τ=10 .47 .20 .07 .01 -.02

randomwalk

τ=2 .33 .11 .04 .01 .01

τ=10 .50 .25 .13 .06 .03

Table 5Financial leverage and dividend volatility

Habit formation model with high capital adjustment costs

A. The equity premium

shockprocess

riskaversion

noleverage

leverage parameter ν= 0.6 ν = 0.8 ν = 1.2

maturity (in quarters)

20 40 40 40

stat. τ=2 0.81 1.02 0.91 0.98 1.36

[-] [.50(.02)] [.41(.01)] [.54(.02)] [.82(.03)]

τ=10 2.74 3.67 3.13 3.39 4.53

[-] [.48(.04)] [.40(.03)] [.53(.04)] [.80(.06)]

random τ=2 0.75 1.01 0.94 1.06 1.79

walk [-] [.50(.05)] [.42(.05)] [.56(.06)] [.84(.10)]

τ=10 2.85 3.05 3.01 3.02 3.20

[-] [.29(.01)] [.25(.01)] [.33(.02)] [.50(.03)]

Figures in brackets denote mean leverage ratios defined as debt divided by total firm value with standarddeviations in parentheses.

B. Standard deviation of quarterly dividend growth rates

shockprocess

riskaversion

noleverage

leverage parameter, ν = 0.6 ν = 0.8 ν = 1.2

maturity (in quarters)

1 20 40 40 40

stat. τ=2 1.53 249.01 13.10 3.75 6.86 26.08

τ=10 2.96 147.97 16.18 3.92 8.37 31.17

random τ=2 1.52 238.32 9.35 2.34 4.15 15.49

walk τ=10 2.33 129.44 10.49 2.54 4.48 10.09