Upload
others
View
0
Download
0
Embed Size (px)
Citation preview
CENTRE FOR ECONOMIC POLICY RESEARCH
Australian National University
DISCUSSION PAPERS
Sole Parents, Income Support and
Family Wellbeing
Garry Barrett
Department of EconomicsUniversity of New South Wales
andEconomics Program
Research School of Social SciencesAustralian National University
DISCUSSION PAPER NO. 411
October 1999
Revised version of the paper presented to theCentre for Economic Policy Research, ANU Conference
Labour Market Trends and Family Policies:Implications for Children14-15 July 1999 Canberra
ISSN: 1442-8636
ISBN: 0 7315 2275 3
CONTENTS
Page
Abstract 1
1 Introduction 2
2 Data and Methods 2
2.1 Characteristics of the Sole Parent Population (SPP) 2
2.2 Characteristics of Sole Parent Pensioners 3
2.3 Measuring Family Well-being 4
2.3.1 Measures of inequality and well-being 7
3 Empirical Results 9
3.1 Characteristics of the Sole Parent Population, 1996 9
3.2 Characteristics of the Sole Parent Population at a point in time 11
3.3 The Dynamics of Sole Parent Population Participation 13
3.3.1 Empirical hazard rate estimates 14
3.3.2 Duration model estimates 15
3.4 The Well-being of Sole Parent Families 1975-1993 19
3.4.1 The Distribution of Income 19
3.4.2 The distribution of consumption 20
4 Conclusion 23
References 24
Figures 1-10 26-35
Tables 1-8 36-43
5L*i �@hi?|tc W?UL4i 5�TTLh| @?_ 6@4�*) ì**Mi�?}
B@hh) 6� �@hhi||#iT@h|4i?| Lu ,UL?L4�Ut
N?��iht�|) Lu �i� 5L�|� @̀*it5)_?i)c �5`c 2fD2
@?_,UL?L4�Ut �hL}h@4
+iti@hU� 5U�LL* Lu 5LU�@* 5U�i?Uit��t|h@*�@? �@|�L?@* N?��iht�|)
�@?Mihh@c ��Ac f2ff
6�ht| Viht�L?G a�*)c bbbA��t Viht�L?G �U|LMihc bbb
�Mt|h@U|
A�i U�@h@U|ih�t|�Ut Lu |�i tL*i T@hi?| TLT�*@|�L? �? ��t|h@*�@ �t i @4�?i_ �t�?} |�ibbS �i?t�t OL�ti�L*_ 5@4T*i 6�*i� �i | |�i U�@h@U|ih�t|�Ut Lu tL*i T@hi?|t ��L hiUi��i_�?UL4i t�TTLh| |�hL�}� |�i 5L*i �@hi?| �i?t�L? E5��� ThL}h@4 @hi @?@*)ti_ �t�?} |�i6@�5 wL?}�|�_�?@* #@|@ 5@4T*i Ew#5�� �L|� |�i U�@h@U|ih�t|�Ut Lu |�i �t|LU!< Lu 5��iht@| @ TL�?| �? |�4ic @?_ |�i U�@h@U|ih�t|�Ut Lu |�i ��?�L�< �?|L 5�� @hi UL?t�_ihi_c @*L?}��|� |�i _)?@4�U @tTiU|t Lu 5�� T@h|�U�T@|�L?� W? |�i ?@* tiU|�L? Lu |�i T@Tih ��5OL�ti�L*_ , Ti?_�|�hi 5�h�i) _@|@ @hi @?@*)ti_ |L _i|ih4�?i ��i|�ih T�M*�U �?UL4it�TTLh| �@t 4@�?|@�?i_ |�i t|@?_@h_ Lu *���?} Lu tL*i T@hi?| u@4�*�it L�ih hiUi?| _iU@_it�
W?|hL_�U|�L?
A�i LM�iU|��i Lu |��t T@Tih �t |L ThL��_i @? L�ih��i� Lu |�i tL*i T@hi?| TLT�*@|�L? �?
��t|h@*�@ @?_ |L UL?t�_ih |�i hL*i Lu T�M*�U �?UL4i t�TTLh|c �? T@h|�U�*@h |�i 5L*i �@hi?|
�i?t�L? E5���c �? 4@�?|@�?�?} |�i t|@?_@h_ Lu *���?} Lu tL*i T@hi?|t @?_ |�i�h U��*_hi?�
AL u�*** |��t LM�iU|��i |�i bbS �i?t�t OL�ti�L*_ 5@4T*i 6�*i �t �ti_ |L _itUh�Mi |�i
U�@h@U|ih�t|�Ut Lu |�i tL*i T@hi?| TLT�*@|�L?� W? _itUh�M�?} |�i tL*i T@hi?| TLT�*@|�L?c
@tTiU|t Lu |�i�h *@ML�h 4@h!i| @||@U�4i?| @?_ TL|i?|�@* *@ML�h 4@h!i| _�t@_�@?|@}i @hi
i4T�@t�3i_� A��t _itUh�T|��i i ihU�ti �t @ ThiU�htLh |L @ 4Lhi �?�_iT|� @?@*)t�t Lu |�i
|�4i T@||ih? Lu T@h|�U�T@|�L? �? |�i 5��� 6Lh |��t UL4TL?i?| Lu |�i @?@*)t�t �t M@ti_ L?
|�i hiUi?|*) UL?t|h�U|i_ #iT@h|4i?| Lu 6@4�*) @?_ �L44�?�|) 5ih��Uit wL?}�|�_�?@*
#@|@ 5@4T*i Ew#5�� A�i U�@h@U|ih�t|�Ut Lu |�i �t|LU!< Lu tL*i T@hi?|t ��L hiUi��i_ |�i
5�� @hi UL?t�_ihc @t �i** @t |�i U�@h@U|ih�t|�Ut Lu |�i ��?�L�< �?|L |�i ThL}h@4 L�ih @
Tih�L_ Lu |�4i� A�i *L?}�|�_�?@* @tTiU| Lu |�i w#5 @hi i T*L�|i_ �? @?@*)t�?} |�i *i?}|�
Lu |�4i tL*i T@hi?|t tTi?_ L? |�i 5��� A�i ?@* tiU|�L?t Lu |�i T@Tih uLU�t L? |�i �i**�
Mi�?} Lu tL*i T@hi?| u@4�*�itc @?_ �L� |�i _�t|h�M�|�L? Lu �i**�Mi�?} �@t U�@?}i_ L�ih
|�4i� A�i ��5 OL�ti�L*_ , Ti?_�|�hi 5�h�i) EO,5� _@|@ UL�ih�?} |�i Tih�L_ b.D�
bb� @hi �ti_ |L UL?t|h�U| UL?t�t|i?| 4i@t�hit Lu u@4�*) UL?t�4T|�L?c ���U� ThL��_i
@ _�hiU| 4i@t�hi Lu |�i �i**�Mi�?} Lu tL*i T@hi?| u@4�*�it� W? |��t UL4TL?i?| Lu |�i
@?@*)t�tc |�i igiU|��i?itt Lu T�M*�U �?UL4i t�TTLh| �? 4@�?|@�?�?} |�i t|@?_@h_ Lu *���?}
Lu tL*i T@hi?| u@4�*�it �t UL?t�_ihi_�
2 #@|@ @?_ i|�L_t
2� ��@h@U|ih�t|�Ut Lu |�i 5L*i �@hi?| �LT�*@|�L?
A�i ht| UL4TL?i?| Lu |�i @?@*)t�t t�4T*) _itUh�Mit |�i UL4TLt�|�L? Lu |�i 5L*i �@hi?|
TLT�*@|�L? �? ��t|h@*�@� A��t UL4TL?i?| Lu |�i @?@*)t�t Thiti?|t @ tih�it Lu UhLtt�
|@M�*@|�L?t uhL4 |�i bbS �i?t�t OL�ti�L*_ 5@4T*i 6�*i� A�i ui@|�hit Lu |�i 5� TLT�
�*@|�L? uLU�ti_ L? �?U*�_i M@t�U _i4L}h@T��U @?_ tLU�L�iUL?L4�U U�@h@U|ih�t|�Utc *@ML�h
4@h!i| @||@U�4i?| @?_ i_�U@|�L?@* @||@�?4i?|� W? Thiti?|�?} |�i _itUh�T|��i t|@|�t|�Utc
2
|�hii |)Tit Lu u@4�*�it �? |�i ��t|h@*�@ TLT�*@|�L? @hi UL4T@hi_G tL*i 4L|�ihc T@h|?ihi_
�L4i? @?_ tL*i u@|�iht� W? Thiti?|�?} |��t UL4T@h�tL?c |�i _��iht�|) Lu |�i 5� TLT�*@�
|�L? �t ��}�*�}�|i_c ��|� |�i �i|ihL}i?i�|) Lu |�i tL*i T@hi?| TLT�*@|�L? U*i@h*) hi�iU|i_
@*L?} _�4i?t�L?t t�U� @t *@ML�h 4@h!i| @U|���|)c i_�U@|�L?@* @||@�?4i?| @?_ �?UL4i�
2�2 ��@h@U|ih�t|�Ut Lu 5L*i �@hi?| �i?t�L?iht
6Lh |�i tiUL?_ UL4TL?i?| Lu |�i @?@*)t�t |�i UL4TLt�|�L? Lu |�i 5�� U@ti*L@_ @| @ TL�?|
�? |�4i �t _itUh�Mi_ �t�?} |�i hiUi?|*) UL?t|h�U|i_ 6@�5 *L?}�|�_�?@* _@|@ t@4T*i Ew#5�
���U� �t _ih��i_ uhL4 @_4�?�t|h@|��i hiULh_t� A�i 6@�5 w#5 EThiti?|*)� UL�iht |�i
Tih�L_ 2?_ ��}�t| bbS � 2e|� �Th�* bbH� A�i ht| uLh|?�}�| Lu |�i _@|@ Tih�L_ @U|��
@**) �?U*�_it |�i _@|i |�@| |�i bbS �i?t�t �@t UL?_�U|i_c @?_ uLh UL4T@h@M�*�|) ��|�
|�i _itUh�T|��i t|@|�t|�Ut Thiti?|i_ �? |�i Thi��L�t tiU|�L?c |��t uLh|?�}�| �@t ti*iU|i_�
`��*i |��t i ihU�ti ��}�*�}�|t |�i U�@h@U|ih�t|�Ut Lu |�i 5�� @| @ TL�?| �? |�4ic �?U*�_�?}
@ 4i@t�hi Lu E�?UL4T*i|i� tTi** _�h@|�L?c |��t �t @ �t|LU! t@4T*i< ���U� _Lit ?L| ThL��_i
@? @UU�h@|i }��_i |L |�i |�4i T@||ih? Lu 5�� T@h|�U�T@|�L?� W? Lh_ih |L }@�? @? �?�
_iht|@?_�?} Lu |�i _)?@4�Ut Lu 5�� T@h|�U�T@|�L?c |�i *L?}�|�_�?@* @tTiU| Lu |�i w#5 �t
i T*L�|i_ M) UL?t|h�U|�?} �uhit�< tTi**t EUL?tiU�|��i uLh|?�}�|t� Lu Ti?t�L? hiUi�T| ���U�
Mi}@? _�h�?} |�i _@|@ Tih�L_� A�iti tTi**t @hi �ti_ |L @?@*)ti |�i *i?}|� Lu |�4i 5�
u@4�*�it hi4@�?i_ L? |�i ThL}h@4�
A�i t@4T*i Lu 5�� tTi**t @hi @?@*)ti_ �? @ �@3@h_ u�?U|�L? uh@4i�Lh!� A��t UL4�
TL?i?| Lu |�i @?@*)t�t ThLUii_t M) it|�4@|�?} |�i i4T�h�U@* �@3@h_ h@|i @?_ t�h���@*
ThLM@M�*�|) u�?U|�L?t� A�i i4T�h�U@* �@3@h_t @?_ t�h���@* ThLM@M�*�|�it @hi i^���@*i?|
�@)t |L t�44@h�ti |�i T@||ih? Lu 5�� i �|t @t @ u�?U|�L? Lu |�4i L? |�i ThL}h@4�
� *�4�|@|�L? Lu |�i i4T�h�U@* �@3@h_ h@|i it|�4@|Lh �t |�@| �| |hi@|t |�i TLT�*@|�L?
@t �L4L}i?iL�t� 5Ti** *i?}|�t ��** �@h) @UULh_�?} |L |�i U�@h@U|ih�t|�Ut Lu |�i tL*i
T@hi?| u@4�*) @?_ ��|� *@ML�h 4@h!i| UL?_�|�L?t @?_ ThL}h@4 T@h@4i|iht� AL UL?|hL*
uLh UL�@h�@|it |�i ThLTLh|�L?@* �@3@h_ _�h@|�L? 4L_i* �t �ti_ ��ihiM)
��E|� ' �JE|� i Ti5�E|��qj��ihi ��E|� �t |�i �@3@h_ uLh TihtL? � c �JE|� �t |�i M@ti*�?i �@3@h_ UL44L? |L @** �?_��
�
��_�@*tc 3�E|� �t @ �iU|Lh Lu LMtih�@M*i U�@h@U|ih�t|�Ut E���U� 4@) �@h) ��|� |� @?_ q �t @
T@h@4i|ih �iU|Lh |L Mi it|�4@|i_� 6Lh _�gihi?| �@*�it Lu 5�E|��qc |�i �@3@h_ u�?U|�L? uLh
�?_���_�@* � �t t��u|i_ ThLTLh|�L?@**) �T Lh _L�? hi*@|��i |L |�i M@ti*�?i�
A�i it|�4@|�L? @TThL@U� @_LT|i_ �? |��t T@Tih �t _i|@�*i_ �? i)ih EbHH( bbf�
@?_ w@?U@t|ih EbbfG.2�2fH�� A�i M@ti*�?i �@3@h_ �t it|�4@|i_ ?L?T@h@4i|h�U@**) @t @
T�iUi���ti UL?t|@?| u�?U|�L?� A�i |�4i @ �t �t _���_i_ �?|L @ ?�|i ?�4Mih Lu �?|ih�@*t
@?_ @ tiT@h@|i M@ti*�?i �@3@h_ T@h@4i|ih �t it|�4@|i_ uLh i@U� �?|ih�@*� A��t @TThL@U�
ThL��_it @ �ih) �i �M*i 4i|�L_ uLh it|�4@|�?} |�i M@ti*�?i �@3@h_ u�?U|�L? @?_ @�L�_t
|�i �4TLt�|�L? Lu @ T@h@4i|h�U u�?U|�L?@* uLh4 L? |�i M@ti*�?i�
2�� i@t�h�?} 6@4�*) ì**�Mi�?}
W? |�i ?@* UL4TL?i?| Lu |�i @?@*)t�tc |�i _�t|h�M�|�L? Lu �i**�Mi�?} @4L?} tL*i T@hi?|
u@4�*�it �t i @4�?i_� � 4i@t�hi Lu �i**�Mi�?} |�@| �@t |h@_�|�L?@**) Mii? �ti_ �t u@4�*)
�?UL4i� OL�i�ihc M@ti_ L? iUL?L4�U |�iLh)c @ 4Lhi _�hiU| 4i@t�hi Lu �i**�Mi�?} �t
u@4�*) UL?t�4T|�L?� �L|� 4i@t�hit Lu �i**�Mi�?} @hi i @4�?i_ �t�?} _@|@ uhL4 |�i
��t|h@*�@? ��hi@� Lu 5|@|�t|�Ut< OL�ti�L*_ , Ti?_�|�hi 5�h�i) EO,5� uLh |�i )i@ht b.D�
.Sc bHec bHH�Hb @?_ bb��be�
A�i O,5 ThL��_it �?uLh4@|�L? L? u@4�*) i Ti?_�|�hit ���*i |�i 4@�? LM�iU| Lu |�i
@?@*)t�t �t u@4�*) UL?t�4T|�L?� , Ti?_�|�hi @?_ UL?t�4T|�L? ��** _�gih @| @ TL�?| �?
|�4i �? |�i U@ti Lu _�h@M*i }LL_t t�?Ui M) _i?�|�L? _�h@M*it ThL��_i @ �L� Lu UL?�
t�4T|�L? tih��Uit L�ih @ ?�4Mih Lu Tih�L_t� W? |�i @?@*)t�t W uLU�t L? |�i _�t|h�M�|�L?
Lu ?L?�_�h@M*i UL?t�4T|�L?� AL ThLTih*) _i@* ��|� _�h@M*i }LL_t �| �t ?iUitt@h) |L
�4T�|i |�i �L� Lu UL?t�4T|�L?t tih��Uit u@4�*�it hiUi��i uhL4 |�i�h _�h@M*it� N?uLh|��
?@|i*)c |�i O,5 L?*) hiTLh|t |�i T�hU�@ti Lu _�h@M*it _�h�?} |�i t�h�i) Tih�L_ ��|�L�|
ThL��_�?} @?) �?uLh4@|�L? L? |�i t|LU! Lu _�h@M*it L�?i_ M) @ u@4�*)� #�h@M*it @hi @?
�4TLh|@?| 4i@?t M) ���U� u@4�*�it U@? t4LL|� |i4TLh@h) �?UL4i t�LU!t( T�hU�@tit Lu
_�h@M*it @hi _i*@)i_ E@?_ �i?Ui i �t|�?} t|LU!t @hi _�h@M*it @hi h�?_L�? u�h|�ih� ��i?
@? �?i TiU|i_ ?i}@|��i �?UL4i t�LU! �t hi@*�ti_ E@?_ ��Ui��iht@ ��i? TLt�|��i �?UL4i
t�LU!t @hi hi@*�ti_�� �L?ti^�i?|*)c |�i T�hU�@ti Lu _�h@M*it hiTLh|i_ �? |�i O,5 @hi
e
_�tThLTLh|�L?@|i*) 4@_i M) u@4�*�it ��L i Tih�i?Ui TLt�|��i �?UL4i t�LU!t� AL �4T�|i
|�i UL?t�4T|�L? �L�t L?*) |L |�iti u@4�*�itc ���*i _�thi}@h_�?} |�i UL?t�4T|�L? tih��Uit
Lu Thi��L�t*) T�hU�@ti_ _�h@M*itc �L�*_ t)t|i4@|�U@**) L�ih�it|�4@|i |�i �i**�Mi�?} Lu
u@4�*�it i Tih�i?U�?} TLt�|��i �?UL4i t�LU!tc �? @ }��i? UhLtt�tiU|�L?� 5�4�*@h*)c |��t ThL�
Ui_�hi @*tL hit�*|t �? @? �?_ih�it|�4@|i Lu |�i �i*u@hi Lu u@4�*�it i Tih�i?U�?} ?i}@|��i
t�LU!t�
6�h|�ihc �u |�i 4@}?�|�_i Lu E|h@?t�|Lh)� �?UL4i t�LU!t �@t Mii? U�@?}�?} L�ih |�4i
Etii �@hhi||c �hLtt*i) @?_ L̀ht��U!c bbb uLh i��_i?Ui L? |��t� |�i? @TT@hi?| |hi?_t �?
u@4�*) �i**�Mi�?} ELh �?i^�@*�|) �? �i**�Mi�?}� 4@) i�|�ih hi�iU| |h�i U�@?}it �? iUL?L4�U
t|@|�t Lh t�4T*) }hi@|ih t4LL|��?} M) u@4�*�it E��|� *�||*i U�@?}i �? �i**�Mi�?}�� AL
i?t�hi |�@| W �@�i @ 4i@t�hi Lu ?L?�_�h@M*i UL?t�4T|�L? |�@| �t UL?t�t|i?| @UhLtt |�i uL�h
t�h�i)tc W _i?i ?L?�_�h@M*it @t i Ti?_�|�hit L? uLL_c @*UL�L* @?_ |LM@UULc u�i*c U*L|��?}c
4i_�U@* U@hic |h@?tTLh|c hiUhi@|�L? @?_ U�hhi?| �L�t�?}�2 �) uLU�t�?} L? ?L?�_�h@M*i
UL?t�4T|�L?c @?_ �}?Lh�?} |�i UL?t�4T|�L? �L�t uhL4 _�h@M*itc W ��** �?_ihit|�4@|i
|�i |h�i *i�i* Lu �i**�Mi�?}� OL�i�ihc |�i uLU�t Lu ?L?�_�h@M*it t�L�*_ ThL��_i @ 4Lhi
hi*�@M*i }��_i |L U�@?}it �? |�i *i�i* Lu �i**�Mi�?} L�ih |�4i�
A�i _i?�|�L? Lu ?L?�_�h@M*it _Lit �?U*�_i U�hhi?| �L�t�?} ULt|t� 6Lh u@4�*�it hit�_�
�?} �? hi?|@* @UUL44L_@|�L?c |��t t�4T*) ULhhitTL?_t |L E@�ih@}i �ii!*)� hi?| T@)4i?|t�
6Lh u@4�*�it ��L L�?i_ Lh �ihi T�hU�@t�?} |�i�h @UUL44L_@|�L?c W �4T�|i @ UL?t�4T�
|�L? �L� M) @_LT|�?} |�i 4i|�L_ �ti_ M) �i?_@!�h EbbH�� 6Lh |�iti u@4�*�itc |�i
UL?t�4T|�L? �L� uhL4 �L�t�?} �@t �4T�|i_ @t |�i u@4�*)krzhyhu/ wklv lwhp lv frpelqhg zlwk gxudeohv lq wkh 4
6�ht|c W UL??i |�i t@4T*i |L t�?}*i u@4�*) �L�ti�L*_t� �*|�T*i u@4�*) �L�ti�L*_ @UUL�?|
uLh @ t4@** @?_ @TThL �4@|i*) UL?t|@?| TLh|�L? Lu |�i TLT�*@|�L? L�ih |�i t|�_) Tih�L_�
5iUL?_*)c |L 4�?�4�ti |�i TL|i?|�@* �?��i?Ui Lu 4i@t�hi4i?| ihhLh @?_ |L i?t�hi |�i
hit�*|t @hi hLM�t| |L L�|*�iht �? |�i _@|@c W uL**L� �*�?_i** @?_ �hit|L? Ebb.� M) |h�44�?}
|�i |LT @?_ ML||L4 � TihUi?| Lu LMtih�@|�L?t M@ti_ L? |�i _�t|h�M�|�L? Lu �?UL4i� 6�?@**)c
@ �ih) t4@** ?�4Mih Lu �L�ti�L*_t hiTLh|i_ ?i}@|��i i Ti?_�|�hit �? |�i UL4TL?i?|t Lu
?L?_�h@M*i UL?t�4T|�L? i @4�?i_ @?_ |�i) @hi _hLTTi_ uhL4 |�i @?@*)t�t�
A�i ?L4�?@* �@*�it Lu �?UL4i @?_ UL?t�4T|�L? @hi @_��t|i_ uLh U�@?}it �? Th�Uit
L�ih |�4i� W |@!i |�i ?@|�L?@* UL?t�4ih Th�Ui �?_i uLh i@U� t�h�i) )i@h @?_ �?�@|i |�i
�@*�it |L bbS _L**@ht� W_i@**)c @ t|@|i�tTiU�U ��W tih�it ���U� |@!it �?|L @UUL�?| |�i
hi}�L?@* _�gihi?Uit �? |�i ULt| Lu *���?} �L�*_ Mi �ti_( �L�i�ihc |��t �t ?L| ui@t�M*i t�?Ui
|�i T�M*�U hi*i@ti �iht�L? Lu |�i bHH O,5 _Lit ?L| hiTLh| t|@|i Lu hit�_i?Ui�
`�i? @?@*)t�?} UL?t�4T|�L? T@||ih?t �| �t ?@|�h@* |L |��?! Lu |�i u@4�*) @t |�i
M@t�U tTi?_�?} �?�| ���*i u@4�*) E@?_ tLU�@*� �i*u@hi �t �t�@**) |@!i? |L Mi @ u�?U|�L? Lu
|�i �i**�Mi�?} Lu UL?t|�|�i?| �?_���_�@*t� �? �?_���_�@*
2��� i@t�hit Lu W?i^�@*�|) @?_ ì**�Mi�?}
W?i^�@*�|) �? |�i _�t|h�M�|�L? Lu �i**�Mi�?} �t i @4�?i_ M) UL?t|h�U|�?} wLhi?3 U�h�it
uLh |�i _�t|h�M�|�L? Lu �?UL4i @?_ UL?t�4T|�L?� wLhi?3 U�h�i @hi |�i? UL4T@hi_ L�ih
|�4i� �?i _�t|h�M�|�L? �t UL?t�_ihi_ 4Lhi i^�@* |�@? @?L|�ih �u �|t ULhhitTL?_�?} wLhi?3
U�h�i *�it i�ih)��ihi @ML�i |�@| Lu |�i L|�ih� A��t h@?!�?} Lu _�t|h�M�|�L?t �t M@ti_
t�4T*) L? |�i wLhi?3 _L4�?@?Ui Uh�|ih�@c ���U� 4Lhi uLh4@**) �4T*�it |�@| _�t|h�M�|�L?
@ �t 4Lhi i^�@* |�@? _�t|h�M�|�L? M �u �| �t TLtt�M*i |L 4L�i uhL4 M |L @ M) @ ti^�i?Ui Lu
|h@?tuiht uhL4 h�U�ih |L TLLhih �L�ti�L*_t A��t ThLTih|) �t @*tL !?L�? @t |�i RTh�?U�T*i
Lu |h@?tuiht� @?_ �t ��_i*) @UUiT|i_ @t @ 4�?�4@* ThLTih|) uLh ?Lh4@|��i 4i@t�hit Lu
�?i^�@*�|)� AL U�iU! uLh wLhi?3 _L4�?@?Ui hi*@|�L?tc @?_ �?@4M�}�L�t _�gihi?Uit �?
�?i^�@*�|) L�ih |�4ic W it|�4@|i wLhi?3 U�h�it wET�c ���U� t�L�t |�i U�4�*@|��i t�@hi Lu
|L|@* �?UL4i ELh UL?t�4T|�L?� }L�?} |L |�i TLLhit| T TihUi?| Lu |�i TLT�*@|�L?c uLh i@U�
t�h�i) )i@h� wLhi?3 U�h�it @hi tU@*i�uhii @?_ ThL��_i @ T�U|�hi Lu |�i �?i^�@*�|) ���U� �t
@ u�?U|�L? Lu |�i t�@Tic @?_ �?_iTi?_i?| Lu |�i *LU@|�L?c Lu |�i _�t|h�M�|�L?�
W @*tL UL?t|h�U| |�i Bi?ih@*�ti_ wLhi?3 EBw� U�h�it uLh |�i _�t|h�M�|�L? Lu �i**�Mi�?}
@UhLtt tL*i T@hi?| u@4�*�it� 6Lh4@**)c BwET�'>wET�c ���U� �t U@*U�*@|i_ M) tU@*�?} |�i
wLhi?3 U�h�i M) |�i 4i@? *i�i* Lu �?UL4i �? |�i _�t|h�M�|�L?� A�i Bi?ih@*�ti_ wLhi?3
U�h�i }h@T�t U�4�*@|��i |L|@* �?UL4i M) U�4�*@|��i ThLTLh|�L? Lu |�i TLT�*@|�L? E��ihi
|�i TLT�*@|�L? �t h@?!i_ uhL4 TLLhit| |L h�U�it|�c �?ULhTLh@|�?} �?uLh4@|�L? hi}@h_�?}
ML|� i^��|) EwET�� @?_ i�U�i?U) E>�c |�ihiuLhi ThL��_�?} @ 4i@t�hi Lu |�i *i�i* Lu �i*u@hi
�? |�i _�t|h�M�|�L? E5�LhhLU!tc bH��
� *�4�|@|�L? Lu |�i wLhi?3 @?_ Bi?ih@*�ti_ wLhi?3 U�h�it uLh �?i^�@*�|) @?_ �i*u@hi
@?@*)t�t �t |�@| |�i) L?*) ThL��_i @ T@h|�@* h@?!�?} Lu _�t|h�M�|�L?t� Wu |�L U�h�it �?|ihtiU|
�| �t ?L| TLtt�M*i |L h@?! L?i _�t|h�M�|�L? @t 4Lhi i^�@* |�@? @?L|�ih _�t|h�M�|�L? M) |�i
_L4�?@?Ui Uh�|ih�L?� AL LM|@�? @ UL4T*i|i Lh_ih�?} Lu _�t|h�M�|�L?tc @?_ |L ^�@?|�u) |�i
_�gihi?Ui �? |�i *i�i* Lu �?i^�@*�|) Lh �i*u@hic �| �t ?iUitt@h) |L �ti @ t�44@h) �?_i
Lu �?i^�@*�|) @?_ �i*u@hi� 6Lh |��t @?@*)t�t W U@*U�*@|i |�i B�?� ULi�U�i?| @?_ ti�ih@*
Lu |�i �|!�?tL? �?_�Uit Lu �?i^�@*�|)� A�i �i*u@hi �?_�Uit �?_ih*)�?} |�iti �?i^�@*�|)
.
�?_�Uit @hi @*tL Thiti?|i_�
�L|� |�i B�?� ULi�U�i?| @?_ |�i �|!�?tL? �?_�Uit @hi 4i4Miht Lu |�i �|!�?tL?�
kL*4�5i? E�k5� U*@tt Lu ?Lh4@|��i �?i^�@*�|) �?_�Uit ���U� U@? Mi hiThiti?|i_ @t
U ' � 1>
��ihi > �t 4i@? �?UL4i @?_ 1 �t |�i Ri^�@**) _�t|h�M�|i_ i^���@*i?| E,#,� �?UL4i��
A�i ,#, �?UL4ic 1c �t |�@| *i�i* Lu �?UL4i ���U� �u }��i? |L i�ih) TihtL? �? |�i TLT��
*@|�L? �L�*_ }i?ih@|i |�i t@4i *i�i* Lu tLU�@* �i*u@hi @t |�i @U|�@* �?UL4i _�t|h�M�|�L?�
A�ihiuLhi |�i ,#, �?UL4i 1 �t @*tL |�i �i*u@hi �?_i �?_ih*)�?} |�iti �?i^�@*�|) �?_�Uit
Etii �*@U!LhM) @?_ #L?@*_tL?c b.H�� W?|��|��i*)c |�i �i*u@hi �?_i ULhhitTL?_t |L |�i
4i@? *i�i* Lu �?UL4i _�tUL�?|i_ M) |�i *i�i* Lu �?i^�@*�|) �? |�i _�t|h�M�|�L?�
6Lh4@**)c |�i B�?� ULi�U�i?| �t }��i? M)G
CE+� ' � >
?[�'
E2�� �+E��
��ihi )E� �����)E�� � ��� �)E?� �t |�i �?UL4i �iU|Lh @hh@?}i_ �?|L _itUi?_�?} Lh_ihc �ULhhitTL?_t |L |�i h@?! Lu |�i �?_���_�@* �? |�i Lh_ihi_ _�t|h�M�|�L? @?_ ? �t |�i t�3i Lu
|�i TLT�*@|�L?� BiL4i|h�U@**)c |�i B�?� ULi�U�i?| �t i^�@* |L |��Ui |�i @hi@ Mi|�ii? |�i
*�?i Lu i^�@*�|) @?_ |�i wLhi?3 ��h�ic @?_ |�i _�gihi?Ui Mi|�ii? |�L B�?� ULi�U�i?|t �t
t�4T*) |�i @hi@ Mi|�ii? |�i |�L ULhhitTL?_�?} wLhi?3 U�h�it�
A�i �|!�?tL? �?_�Uit @hi _i?i_ @tG
UkE+� '
;A?A=
� >
k?
S?�' +
3k�
l 3k k � fc k 9'
� >
T?�' +
?
� k '
��ihi k �t |�i �?i^�@*�|) @�iht�L?< T@h@4i|ih ��|� *@h}ih �@*�it Lu ULhhitTL?_�?} |L
}hi@|ih �?i^�@*�|) @�iht�L?�
A�i B�?� ULi�U�i?| @?_ �|!�?tL? W?_�Uit t@|�tu) |�i wLhi?3 _L4�?@?Ui Uh�|ih�L?�
�L|� t�44@h) 4i@t�hit Lu �?i^�@*�|) @*tL �4TLti @__�|�L?@* t|h�U|�hi L? |�i �?_ih*)�?}
5`6� A�i 4@�? _�gihi?Ui Mi|�ii? |�i B�?� ULi�U�i?| @?_ |�i �|!�?tL? �?_�Uit �t �? |�i�h
ti?t�|���|) |L |h@?tuih Mi|�ii? _�gihi?| TL�?|t �? |�i _�t|h�M�|�L?� A�i B�?� ULi�U�i?|
H
�i�}�|t |h@?tuiht @UULh_�?} |L |�i _�gihi?Uit �? |�i h@?! Lh_ih Lu |�i �?_���_�@*t �?�L*�i_�
W? UL?|h@t|c |�i �|!�?tL? �?_�Uit �i�}�| @ }��i? |h@?tuih @UULh_�?} |L |�i h@|�L Lu |�i
�?UL4i t�@hit Lu |�i �?_���_�@*t �?�L*�i_� W? @__�|�L?c |�i �?_�Uit ULhhitTL?_�?} |L *@h}ih
�@*�it Lu k T*@Ui @ ThL}hitt��i*) *@h}ih tLU�@* �i�}�| L? |h@?tuiht �?�L*��?} �?_���_�@*t
��|� |�i t4@**it| �?UL4i t�@hit� W? |�i *�4�| @t @TThL@U�it k $ 4c |�i �?_i T*@Uit @**|�i tLU�@* �i�}�| L? |�i �?UL4i t�@hi Lu |�i TLLhit| �?_���_�@*�
� ,4T�h�U@* +it�*|t
�� ��@h@U|ih�t|�Ut Lu |�i 5L*i �@hi?| �LT�*@|�L?c bbS�
A�i U�@h@U|ih�t|�Ut Lu |�i ��t|h@*�@? tL*i T@hi?| TLT�*@|�L?c M@ti_ L? |�i bbS �i?t�tc
@hi Thiti?|i_ �? A@M*i � �u @TThL �4@|i*) ecDfHcbff u@4�*�itc @*4Lt| e�.I �ihi tL*i
T@hi?| u@4�*�it ELu ���U� 2�DI �ihi �i@_i_ M) tL*i 4L|�iht @?_ 2��I M) tL*i u@|�iht��
A�i ht| UL*�4? Lu ?�4Miht �? A@M*i Thiti?|t |�i t@4T*i 4i@?t uLh |�i ti| Lu tL*i
4L|�iht� �L*�4? 2 Thiti?|t |�i _itUh�T|��i t|@|�t|�Ut uLh T@h|?ihi_ �L4i? @?_ UL*�4?
� UL?|@�?t |�i ULhhitTL?_�?} _itUh�T|��i t|@|�t|�Ut uLh tL*i u@|�iht� W? |ih4t Lu M@t�U
_i4L}h@T��U U�@h@U|ih�t|�Utc tL*i 4L|�iht �ihi t�Mt|@?|�@**) )L�?}ih L? @�ih@}i E�e )i@ht
Lu @}i� |�@? i�|�ih T@h|?ihi_ �L4i? Ee. )i@ht� Lh tL*i u@|�iht Eeb )i@ht�� 5L*i 4L|�iht
�ihi @*tL 4Lhi *�!i*) |L Mi ��t|h@*�@? MLh?c @?_ �@�i ��t|h@*�@? MLh? T@hi?|tc UL4T@hi_
|L |�i L|�ih 2 }hL�Tt�
A�h?�?} |L 4@h�|@* t|@|�tc @TThL �4@|i*) 2�I Lu tL*i 4L|�iht �ihi ?i�ih 4@hh�i_c
hi*@|��i |L ��eI uLh tL*i u@|�iht� A�i �?U�_i?Ui Lu ��_L��LL_ �@t t�4�*@h @4L?} tL*i
4L|�iht @?_ u@|�ihtc ���*i tL*i 4L|�iht �ihi *itt *�!i*) |L Mi tiT@h@|i_ Lh _��LhUi_
ED.�DI� UL4T@hi_ |L tL*i u@|�iht ESS�HI�� �*|�L�}� ?L| Thiti?|i_ �? |��t |@M*ic M)
i @4�?�?} 4@h�|@* t|@|�t M) @}i UL�Lh|c �| �t uL�?_ E�?t�hTh�t�?}*)� |�@| �?i�ih 4@h�
h�i_< tL*i T@hi?|t @hi 4Lhi UL44L? @4L?} |�i )L�?}ih @}i }hL�Tt� A�i �?U�_i?Ui Lu
|�i �?i�ih 4@hh�i_< U*@tt�U@|�L? _iU*�?itc @?_ |�@| uLh �tiT@h@|i_ Lh _��LhUi_< �?Uhi@tit
@4L?} |�i L*_ih @}i }hL�Tt� A��t hi�iU|t ML|� @ *�ui�U)U*i T�i?L4i?@c @?_ M�h|��
UL�Lh|%}i?ih@|�L?@* |hi?_t� ,�i? tLc |�iti }�hit t�}}it| |�@| 4@h�|@* _�ttL*�|�L? �t
b
|�i 4Lt| UL44L? hi@tL? ��) �L4i? @?_ 4i? MiUL4i tL*i T@hi?|tc h@|�ih |�@? |�hL�}�
�L�|�Lu��i_*LU!< M�h|�t�
A�i ?i | tih�it Lu UhLtt�|@M�*@|�L?t hi*@|i |L i_�U@|�L?@* @||@�?4i?|c ���U� �t @?
�4TLh|@?| UL4TL?i?| Lu ��4@? U@T�|@* @?_ �i?Ui @ Uh�|�U@* i*i4i?| Lu @? �?_���_�@*
u@|�iht �@t meSD E�.I ��}�ih��
��ih@**c |�i Mhi@!_L�? M) }i?_ih t�L�t |�@| |�ihi �t UL?t�_ih@M*i _��iht�|) �? |�i
tL*i T@hi?| TLT�*@|�L? �? |ih4t Lu @}ic 4@h�|@* ��t|Lh)c ��4@? U@T�|@* U�@h@U|ih�t|�Ut @?_
*@ML�h 4@h!i| �?|i}h@|�L?� ,�i? ��|��? i@U� }i?_ih }hL�T |�ihi �t UL?t�_ih �i|ihL}i?i�
�|)�
��2 ��@h@U|ih�t|�Ut Lu |�i 5�� TLT�*@|�L? @| @ TL�?| �? |�4i
5�44@h) t|@|�t|�Ut uLh |�i t@4T*i Lu 5� ��L hiUi��i_ |�i 5�� �? |�i uLh|?�}�| Mi}�??�?}
��}�t| 2 bbSc M@ti_ L? |�i w#5c @hi Thiti?|i_ A@M*i 2� A�i t@4T*i 4i@?t uLh |��t
�t|LU!< Lu hiU�T�i?|t @| @ TL�?| �? |�4i t�L� |�@| �@t| 4@�Lh�|) Lu 5��iht @hi tL*i 4L|�iht�
A�i @�ih@}i @}i Lu 5��ih �? @ }��i? uLh|?�}�| �@t @TThL �4@|i*) �e )i@htc H TihUi?|
Lu |�i 5��iht �ihi MLh? �? ��t|h@*�@ @?_ ��H TihUi?| �_i?|�u) @t @MLh�}�?@* Lh @ ALhhit
5|h@�| Wt*@?_ih� A�i @�ih@}i ?�4Mih Lu _iTi?_i?| U��*_hi? �@t �DD E��|� �� @}i_
�?_ih � )i@ht�c ���*i |�i @�ih@}i @}i Lu |�i )L�?}it| U��*_ �@t D�D )i@ht� W? |ih4t
Lu �L4i�L�?iht��T t|@|�tc @*4Lt| 2 TihUi?| �ihi �L4i�L�?ih ���*i @ u�h|�ih H TihUi?|
�ihi i�|�ih T@)�?} Lg @ �L4i Lh �i*_ tL4i uLh4 Lu �L�?|�L�?iht��T Lu @ �L4i� A�i
*@h}i 4@�Lh�|) Lu 5��iht �ihi hi?|iht( @*4Lt| ee TihUi?| Lu |�i 5��iht @| @ TL�?| �?
|�4i hi?|i_ Th��@|i*) ���*i 2f TihUi?| hi?|i_ uhL4 @ }L�ih?4i?| @�|�Lh�|)c . TihUi?|
�@_ tL4i L|�ih hi?|@* @hh@?}i4i?| Et�U� @t ML@h_ @?_ *L_}�?}� ���*i ��t| L�ih e TihUi?|
T@�_ ?L hi?|� �UhLtt |�i t@4T*ic |�i @�ih@}i @4L�?| Lu hi?| T@�_ �@t me2 TihUi?|
uLh|?�}�| EmH. @�ih@}i_ @UhLtt |�Lti ��L T@) tL4i uLh4 Lu hi?|�� A�i _�t|h�M�|�L? Lu
5��iht @UhLtt |�i t|@|it @?_ |ihh�|Lh�it t�L�t |�@| �5`%��A @UUL�?|t uLh |�i *@h}it|
uh@U|�L? ��|� L?i�|��h_ Lu |�i U@ti*L@_ ���*i |�i �Lh|�ih? Aihh�|Lh) �@t |�i t4@**it|
uh@U|�L? ��|� �S TihUi?|�
A�h?�?} |L |�i ?@?U�@* �@h�@M*itc @TThL �4@|i*) eb TihUi?| Lu |�i 5��iht hiUi��i_
tL4i U��*_ t�TTLh|� A�i @�ih@}i uLh|?�}�|*) @4L�?| Lu U��*_ t�TTLh| �@t mfe E m2f�
@4L?} |�Lti ��L hiUi��i_ U��*_ t�TTLh|�� a�t| L�ih @ ^�@h|ih Lu 5��iht hiUi��i_ i@h?i_
�?UL4ic ���U� @�ih@}i_ mb� Em�D� uLh |�Lti ��|� TLt�|��i i@h?�?}t�� �?*) � TihUi?| Lu
5�� |)T�U@**) hiUi��i_ tL4i �?i@h?i_ �?UL4ic ���U� @�ih@}i_ mH Tih 5��ih Tih uLh|?�}�|
EmSS uLh |�Lti ��|� �?i@h?i_ �?UL4i�� W? |ih4t Lu ThL}h@4 T@)4i?|tc |�i @�ih@}i 5��
M@t�U T@)4i?| �@t m�� @?_ |�i @�ih@}i 6@4�*) �@)4i?| |L @ 5��ih �@t m.f� �TThL �
�4@|i*) ef TihUi?| Lu 5��iht _�h�?} |��t uLh|?�}�| @*tL hiUi��i_ hi?| @tt�t|@?Ui E|�i *@h}i
4@�Lh�|) Lu 5��iht T@)�?} hi?| |L @ Th��@|i *@?_*Lh_� ��|� @? @�ih@}i hi?| @tt�t|@?Ui
T@)4i?| Lu @*4Lt| m2b Em. @�ih@}i_ @UhLtt |�Lti hiUi���?} hi?| @tt�t|@?Ui�� 6�?@**)c
|�ihi �@t �ih) *L� �?U�_i?Ui Lu hi4L|i @hi@ @**L�@?Ui T@)4i?|t @?_ L|�ih @__�|�L?@*
T@)4i?|tc ���U� @UUL�?|t uLh |�i t4@** @�ih@}i @4L�?|t uLh |�iti T@)4i?| |)Tit�
A�i t@4T*i Lu uLh|?�}�|*) hiULh_t uhL4 |�i eS uLh|?�}�|t UL�ihi_ M) |�i w#5 �ihi
|�i? @}}hi}@|i_ M) �?_���_�@* tL*i T@hi?|� A�i ti| Lu D2Df 5��iht �? |�i w#5c ��L
@UUL�?|i_ uLh SecH�f uLh|?�}�| T@)4i?|tc �@t }hL�Ti_ M) *i?}|� Lu |L|@* |�4i tTi?| L?
5�� T@)4i?| _�h�?} |�i _@|@ Tih�L_c @?_ t�44@h) t|@|�t|�Ut @hi Thiti?|i_ �? A@M*i ��
�L*�4? E2� Thiti?|t |�i @�ih@}i U�@h@U|ih�t|�Ut Lu |�Lti tL*i T@hi?|t ��L hiUi��i_ |�i
5�� uLh @ |L|@* Lu S Lh ui�ih uLh|?�}�|t _�h�?} |�i t@4T*i Tih�L_� �L*�4?t E���ES� t�L�
|�i @�ih@}i U�@h@U|ih�t|�Ut uLh |�i ti| Lu 5��iht ��|� ThL}hitt��i*) }hi@|ih |L|@* |�4i
L? 5��c ��|� UL*�4? ES� t�44@h�t�?} |�i U�@h@U|ih�t|�Ut Lu |�Lti ��|� |�i 4@ �4�4
TLtt�M*i LMtih�i_ *i?}|� L? |�4i L? |�i ThL}h@4 Lu eS uLh|?�}�|t� 6hL4 �L*�4? E2�
�| �t @TT@hi?| |�@| |�Lti ��L tTi?| *itt |L|@* |�4i L? |�i ThL}h@4 �ihic L? @�ih@}ic
4@h}�?@**) L*_ih @?_ t�Mt|@?|�@**) 4Lhi *�!i*) |L Mi @ tL*i u@|�ihc UL4T@hi_ |L |�i @�ih@}i
Lu @** 5��iht� W? @__�|�L?c |�i) �ihi 4Lhi *�!i*) |L �@�i tL4i uLh4 Lu �L4i L�?iht��T
@?_ *itt *�!i*) |L Mi hi?|�?}c @?_ 4�U� *itt *�!i*) |L Mi �? T�M*�U �L�t�?} EitTiU�@**) �?
�5`%��A�� A�iti 5��iht �@_ @ *L�ih �?U�_i?Ui Lu U��*_ t�TTLh| hiUi�T| @?_ *L�ih
�?U�_i?Ui Lu i4T*L)4i?| �?UL4i E|�L�}�| |�i @�ih@}i @4L�?| Lu i@h?�?}t �@t }hi@|ih
|�@? uLh |�i t@4T*i Lu @** 5��iht�� �__�|�L?@**)c |�i �@h�L�t UL4TL?i?|t Lu ThL}h@4
T@)4i?|t �ihi L? @�ih@}i *itt uLh |��t }hL�T�e 5L*i T@hi?|t ��L �ihi L? |�i ThL}h@4
uLh @| 4Lt| S uLh|?�}�|t _�h�?} |�i t@4T*i Tih�L_ @UUL�?|i_ uLh @TThL �4@|i*) f TihUi?|
Lu @** 5��iht LMtih�i_ _�h�?} |�i t@4T*i Tih�L_c @?_ @t @ }hL�T |�i) @UUL�?|i_ uLh �2
7Qrwh wkdw wklv lv sxuho| d fruuhodwlrq/ dqg zrxog eh huurqhrxv wr lqihu iurp wklv lqirupdwlrq wkdworzhu sd|phqw ohdg wr vkruwhu shulrgv ri wlph rq wkh surjudp1 Wklv fruuhodwlrq frxog vlpso| uh�hfwwkh d�hfw ri d wklug idfwru/ vxfk dv qxpehu ri fkloguhq ru hduqhg lqfrph/ rq erwk wkh wlph vshqw rq wkhsurjudp dqg wkh dfwxdo dprxqw ri sd|phqwv1
2
TihUi?| Lu |�i |L|@* |�4i tTi?| L? |�i ThL}h@4 @?_ � TihUi?| Lu |L|@* 5�� ThL}h@4
i Ti?_�|�hit _�h�?} |��t Tih�L_�
6Lh Mhi��|)c UL*�4? ES�c ���U� t�44@h�tit |�i U�@h@U|ih�t|�Ut Lu |�Lti ��L �ihi 4Lt|
_iTi?_i?| L? |�i ThL}h@4 _�h�?} |�i _@|@ Tih�L_c �t UL4T@hi_ ��|� UL*�4? E2�� ��ih
�. TihUi?| Lu |�i 5��iht LMtih�i_ �? |�i _@|@ Tih�L_ hi4@�?i_ L? |�i ThL}h@4 uLh |�i
u�** eS uLh|?�}�|t� A��t }hL�T Lu 5��iht @UUL�?|i_ uLh @TThL �4@|i*) DD TihUi?| Lu
ML|� |�i |L|@* |�4i tTi?_ L? |�i ThL}h@4 @?_ |L|@* ThL}h@4 i Ti?_�|�hit L�ih |�i _@|@
Tih�L_� +i*@|��i |L UL*�4? E2�c |��t }hL�T Lu 5��iht �t 4Lhi *�!i*) |L Mi UL4TLti_ Lu
tL*i 4L|�ihtc |�Lti MLh? �? ��t|h@*�@ @?_ ?L| �_i?|�u)�?} @t @MLh�}�?@* Lh ALhhit 5|h@�|
Wt*@?_ih� A�i �*L?}�|ih4iht
4�*|�T*i tTi**t�� 5�44@h) t|@|�t|�Ut uLh |�i t@4T*i Lu 5�� tTi**t @hi Thiti?|i_ �? A@M*i e�
A�i �@3@h_ 4L_i* �ihi it|�4@|i_ �t�?} Ruhit�� tTi**t ���U� Mi}@? _�h�?} |�i _@|@ Tih�L_
UL�ihi_ M) |�i w#5� 6Lh |��t t@4T*i Lu 5�� tTi**tc @�ih@}i _�h@|�L? �@t S uLh|?�}�|tc
Hb TihUi?| �ihi i Tih�i?Ui_ M) tL*i 4L|�ihtc |�i @�ih@}i @}i @| tTi** UL44i?Ui4i?| �@t
�2)i@htc Hf TihUi?| �ihi i Tih�i?Ui_ M) tL*i T@hi?|t ��L �ihi MLh? �? ��t|h@*�@? @?_ D�D
TihUi?| �ihi M) �?_���_�@*t ��L �_i?|�u) @t �A5W� A�i @�ih@}i ?�4Mih Lu U��*_hi? �@t�S
E��|� �� �?_ih @}i ��c @?_ |�i @�ih@}i @}i Lu |�i )L�?}it| U��*_ �? |�i u@4�*) �@t e�D
)i@ht� W? |ih4t Lu @UUL44L_@|�L? @hh@?}i4i?|tc @TThL �4@|i*) e TihUi?| Lu |�i tTi**t
�ihi i Tih�i?Ui_ M) tL*i T@hi?|t ��L �ihi �L4i L�?ihtc S TihUi?| �ihi T@)�?} Lg |�i�h
�L4i ���*i ee TihUi?| hi?|i_ uhL4 @ Th��@|i *@?_*Lh_c f TihUi?| �ihi �? T�M*�U �L�t�?}c
@?L|�ih f TihUi?| T@�_ uLh ML@h_ Lh *L_}�?} @?_ @ u�h|�ih f TihUi?| ?i�|�ih L�?i_ @
�L4i ?Lh T@�_ hi?|� A�ihi �@t @ hi*@|��i*) *L� �?U�_i?Ui Lu U��*_ t�TTLh| �?UL4ic L?*)
H TihUi?| hiUi��i_ tL4i i4T*L)4i?| �?UL4i E|�i @�ih@}i i@h?�?}t uLh |�Lti ��L �Lh!i_
�@t mH2�D�%f�He'meeH Tih uLh|?�}�|� ���*i S TihUi?| hiUi��i_ tL4i �?i@h?i_ �?UL4i�
A�i @�ih@}i 5�� T@)4i?| @| |�i UL44i?Ui4i?| Lu |�iti tTi** �@t m� Tih uLh|?�}�|c
@?_ |�i @�ih@}i 6� �@t mHb Tih uLh|?�}�|� �TThL �4@|i*) �b TihUi?| @*tL hiUi��i_ hi?|
@tt�t|@?Ui� W? |L|@* |�ihi �ihi 2eb. �uhit�< tTi**tc Lu ���U� 2b TihUi?| ULhhitTL?_i_ |L @
hiTi@| tTi** M) @ tL*i T@hi?|c @?_ S2 TihUi?| hi4@�?i_ �? ThL}hitt @| |�i i?_ Lu |�i _@|@
Tih�L_�
���� ,4T�h�U@* O@3@h_ +@|i ,t|�4@|it
A�i i4T�h�U@* �@3@h_ h@|i u�?U|�L? uLh |�i t@4T*i Lu uhit� tTi**t �t Thiti?|i_ �? A@M*i
D� A�i i �| h@|it }i?ih@**) _iU*�?i_ ��|� tTi** _�h@|�L?c @*|�L�}� |�i �@3@h_t h@|it @|
|�i *L?}it| tTi** _�h@|�L?t @hi tL4i��@| ihh@|�U _�i |L |�i t4@** ?�4Mih Lu LMtih�@|�L?
i?_�?} @| |�iti _�h@|�L?t� A�i i �| h@|i uhL4 5�� t|@h|t @| 2�S TihUi?| �? |�i ht|
uLh|?�}�| Lu @ tTi**c �?Uhi@tit |L �� @?_ ��2 TihUi?| M) |�i uL�h|� @?_ u|� uLh|?�}�|t Lu
@ tTi**tc hi4@�?t @| @ t�4�*@h *i�i* L�ih uLh|?�}�|t S�.c @?_ |�i? t|@h|t 4L��?} @hL�?_
tL4i��@| ihh@|�U@**)� �u|ih uLh|?�}�| Hc |�i i �| h@|it i ��M�|t @ }i?ih@* |i?_i?U) |L
u@**� A�i �?i�i? _iU*�?i �? |�i i �| h@|i ��|� tTi** _�h@|�L? t�L�t |�@| �| �L�*_ Mi
e
�?@TThLTh�@|i |L �4TLti @ t4LL|�c T@h@4i|h�U u�?U|�L?@* uLh4 L? |�i �@3@h_t�
�? @*|ih?@|��i _itUh�T|�L? Lu |�i tTi** _@|@ �t ThL��_i_ M) |�i t�h���@* u�?U|�L? it|��
4@|it �? A@M*i D� A�i t�h���@* u�?U|�L?t t�L�t |�i ThLTLh|�L? Lu tTi**t |�@| @hi @| *i@t|
4L?|�t *L?}� 6hL4 |�i |@M*ic �| �t @TT@hi?| |�@| 2D TihUi?| Lu @** tTi**t i?_ ��|��?
uLh|?�}�|tc �� TihUi?| �@�i i?_i_ M) D uLh|?�}�|t ���*i Df TihUi?| �@�i i?_i_ @u|ih
�e uLh|?�}�|t Lu Mi?i| hiUi�T| E|�i 4i_�@? tTi** *i?}|��� � |L|@* Lu eS TihUi?| Lu tTi**t
@hi t|�** �? ThL}hitt @u|ih ef uLh|?�}�|t E@TThL �4@|i*) H 4L?|�t��
A�i ti| Lu 5�� tTi**t �ihi |�i? _���_i_ �?|L t�M}hL�Ttc @UULh_�?} |L L?i ti| Lu
U�@h@U|ih�t|�Ut @| @ |�4i� A�i i4T�h�U@* t�h���@* u�?U|�L? uLh |�i �@h�L�t _���t�L?t Lu |�i
tTi** t@4T*i @hi Thiti?|i_ �?|L A@M*i S� �) t|h@|�u)�?} |�i t@4T*i @*L?} L?i _�4i?t�L?c @|
@ |�4ic �| �t TLtt�M*i |L LM|@�? @ Mi||ih ti?ti Lu |�i hi*@|�L?t��T Mi|�ii? |�@| U�@h@U|ih�t|�U
@?_ tTi** _�h@|�L?�
A�i t�@Ti Lu |�i i4T�h�U@* �@3@h_ @?_ t�h���@* u�?U|�L?t �?_�U@|i @ _i}hii Lu ?i}@|��i
_�h@|�L? _iTi?_i?Ui( |�i *L?}ih @ tL*i T@hi?| u@4�*) hi4@�?t L? |�i 5��c |�i E4@h}�?@**)�
*itt *�!i*) �| �t |�i) ��** i �|� OL�i�ih |�i _iU*�?i �? |�i i �| h@|it �t hi*@|��i*) 4�?Lhc
T*�t |��t @TT@hi?| _�h@|�L? _iTi?_i?Ui 4@) Mi @ hi�iU|�L? Lu _�gihi?Uit �? �?_���_�@*
U�@h@U|ih�t|�Ut h@|�ih |�@? |h�i t|@|i _iTi?_i?Ui�
����2 #�h@|�L? L_i* ,t|�4@|it
,giU|t Lu #i4L}h@T��U @?_ ,UL?L4�U ��@h@U|ih�t|�Ut
A�i it|�4@|it Lu |�i T�iUi���ti UL?t|@?| ThLTLh|�L?@* �@3@h_ 4L_i*t @hi Thiti?|i_ �?
A@M*it .� 5TiU�U@|�L? E� L?*) �?U*�_it UL?|hL*t uLh M@t�U _i4L}h@T��U U�@h@U|ih�t|�Ut� W|
�t U*i@h |�@| |�i hi*@|��i*) t4@** ?�4Mih Lu tL*i u@|�iht �@�i @ t�Mt|@?|�@*c @?_ t|@|�t|�U@**)
t�}?�U@?|c ��}�ih i �| h@|i uhL4 5�� UL4T@hi_ |L t�?}*i 4L|�iht� �*_ih tL*i T@hi?|
|i?_ |L �@�i ��}�ih i �| h@|itc |�L�}� |��t igiU| �t ?L| t�}?�U@?|� W| �t @TT@hi?| |�@|
|�i |L|@* ?�4Mih Lu U��*_hi? �t ?L| �4TLh|@?| �? i T*@�?�?} |�i *i?}|� Lu |�4i tL*i T@hi?|t
hiUi��i |�i 5��( �L�i�ihc |�i @}i Lu |�i )L�?}it| U��*_ �t �ih) �4TLh|@?|� �? �?Uhi@ti
�? |�i @}i Lu |�i )L�?}it| U��*_ M) L?i )i@h �t @ttLU�@|i_ ��|� @? �?Uhi@ti �? |�i i �|
h@|i M) 2 TihUi?| ��}�ih� 6�h|�ihc |�i TL�?| it|�4@|it �?_�U@|i |�@| tL*i T@hi?|t ��L @hi
D
i�|�ih �44�}h@?|t Lh �_i?|�u) @t @MLh�}�?@* Lh ALhhit 5|h@�| Wt*@?_ih |i?_ |L �@�i ��}�ih
i �| h@|ic |�L�}� |��t _�gihi?Ui �t t|@|�t|�U@**) �?t�}?�U@?|�
5TiU�U@|�L? E2� �?U*�_it �@h�@M*it �?_�U@|�?} |�i �L�t�?} t�|�@|�L? Lu |�i tL*i T@hi?|
u@4�*)� A�i hiuihi?Ui U@|i}Lh) ELh L4�||i_ }hL�T� @hi |�Lti ��L hi?| uhL4 @ Th��@|i *@?_�
*Lh_� +i*@|��i |L |��t hiuihi?Ui }hL�Tc |�i it|�4@|it t�}}it| |�@| |�Lti �? T�M*�U �L�t�?}
@?_ |�Lti ��L L�? |�i�h L�? �L4i |i?_ |L �@�i *L�ih i �| h@|i� ,�i? tLc |�i _�gihi?Ui
�? |�i i �| h@|i uhL4 5�� M) @UUL44L_@|�L? t|@|�t @hi t|@|�t|�U@**) �?t�}?�U@?| E@T@h|
uhL4 |�Lti uLh ��L |�i �L�t�?} �?uLh4@|�L? �t 4�tt�?}��
A�i ?i | 4L_i* �?U*�_it |�i ti| Lu �@h�@M*it ���U� �?_�U@|i t|@|i Lu hit�_i?Ui� A�i
hiuihi?Ui U@|i}Lh) �t �5`%��A� A�ihi @hi *@h}i @?_ t�}?�U@?| _�gihi?Uit �? |�i i �|
h@|i M) *LU@|�L?� 5L*i T@hi?| ��L hit�_i �? "�ii?t*@?_c ìt|ih? ��t|h@*�@ @?_ A@t4@?�@
�@�i t�Mt|@?|�@**) ��}�ih i �| h@|it uhL4 |�i 5��� A�i _�gihi?Uit �? |�i i �| T@||ih? M)
*LU@|�L? 4@) hi�iU| _�gihi?Uit �? hi}�L?@* *@ML�h 4@h!i|tc ULt| Lu *���?} Lh *LU@* tLU�@*
t�TTLh| ?i|�Lh!� 6�|�hi hiti@hU� uLh |��t ThL�iU| ��** �?�it|�}@|i |�i TL|i?|�@* hi@tL?t
uLh |�iti *@h}i _�gihi?Uit �? i �| h@|i M) *LU@|�L?c M) 4@|U��?} �? �?uLh4@|�L? L? |�i
tLU�L�iUL?L4�U U�@h@U|ih�t|�Ut Lu 5��ih
�?U*�_i_ �? tTiU�U@|�L? ED�� A�i hit�*|t t�L� |�@| tL*i T@hi?|t ��|� tL4i @||@U�4i?|
|L |�i �LM 4@h!i| _L i �| |�i 5�� @| @ t�}?�U@?| @?_ t�Mt|@?|�@**) ��}�ih h@|i� A�Lti
��|� @?) uLh4 Lu T@�_ i4T*L)4i?| �@�i @ . TihUi?| ��}�ih i �| h@|i |�@? |�Lti ��|�
?L i4T*L)4i?| �?UL4i� A�i hiUi�T| Lu �?i@h?i_ �?UL4i �@t ?L| t�}?�U@?|*) hi*@|i_ |L
|�i i �| h@|ic ��ihi@t tL*i T@hi?|t ��L hiUi��i_ tL4i U��*_ t�TTLh| T@)4i?|t |i?_i_ |L
�@�i @ ��}�ih i �| h@|i uhL4 5�� E|��t igiU| �@t 4@h}�?@**) �?t�}?�U@?|��
L_i* ES� |�i? �?U*�_it |�i @U|�@* @4L�?| Lu �?UL4i hiUi��i_ uhL4 |�i |�hii Th��@|i
tL�hUit� A�i it|�4@|it t�L� |�@| tL*i T@hi?|t ��|� tL4i i@h?�?}t �ihi t�}?�U@?|*) 4Lhi
*�!i*) |L i �|c @?_ |�i ThLM@M�*�|) Lu i �| �?Uhi@ti_ M) @ u�h|�ih S TihUi?| ��|� i�ih) mff
Lu uLh|?�}�|*) i@h?�?}t� �*|�L�}� �| �t U*i@h |�@| �LM @||@U�4i?| �t @ttLU�@|i_ ��|�
��}�ih i �|t uhL4 5��c �| �t _��U�*| |L T�?TL�?| |�i �?_ih*)�?} U@�ti Lu |��t @ttLU�@|�L?�
6Lh i @4T*ic |��t @ttLU�@|�L? Mi|�ii? i@h?�?} @?_ 5�� i �|t 4@) hi�iU| |�i �4TLh|@?|
igiU|t Lu �Lh! i Tih�i?Ui �? }i?ih@|�?} Mi||ih �LM LTTLh|�?�|�it ���U� �*|�4@|i*) *i@_
|L iUL?L4�U ti*u�t��U�i?U)� �*|ih?@|i*)c |��t @ttLU�@|�L? 4@) t�4T*) Mi |�i hi�iU|�L? Lu
L|�ih �?_ih*)�?} u@U|Lhtc t�U� @t |�i tL*i T@hi?|
|�i 5�� i �| h@|i� 5TiU�U@|�L? EH� Lu A@M*i H �?U*�_it |�L �@h�@M*it ���U� �?_�U@|i
��i|�ih |�i tL*i T@hi?| Ti?t�L?ih hiUi��i_ |�i hi4L|i @hi@ @**L�@?Ui Lh hi?| @tt�t|@?Ui�
A�i it|�4@|it t�L� |�@| |�i hi*@|��i*) t4@** ?�4Mih Lu tL*i T@hi?|t �? |�i _it�}?@|i_
hi4L|i @hi@t �@_ t�Mt|@?|�@**) ��}�ih i �| h@|it EM) UL4T@h�tL?c |�i�h UL�?|ihT@h|t �?
L|�ih hi}�L?t Lu `� @?_ |�i �A �@_ *L�ih i �| h@|it�� �__�|�L?@**)c tL*i T@hi?|t ��L
hiUi��i_ hi?| @tt�t|@?Ui �@_ @ 2f TihUi?| *L�ih i �| h@|i |�@? UL4T@h@M*i tL*i T@hi?| �?
Th��@|i hi?|@* @UUL44L_@|�L? ��L _�_ ?L| hiUi��i hi?| @tt�t|@?Ui� �}@�?c U@�|�L? ?ii_t
|L Mi i ihU�ti_ �? �?|ihThi|�?} |��t hit�*|� �?i i T*@?@|�L? uLh |��t hit�*| �t |�@| |�i
hiUi�T| Lu hi?| @tt�t|@?Ui �?_�Uit *L?}ih t|@)t L? |�i 5��� OL�i�ihc @? i^�@**) T*@�t�M*i
i T*@?@|�L? �t |�@| |�i TLLhit| tL*i T@hi?| u@4�*�it �? Th��@|i hi?|@* hiUi��i hi?| @tt�t|@?Ui
@?_ |�i ULi�U�i?| it|�4@|i t�4T*) t�L�t |�@| |�i TLLhit| u@4�*�it hi4@�? L? |�i 5��
*L?}ih� A�i _@|@ @hi �?@M*i |L _�t|�?}��t� Mi|�ii? |�iti UL4Ti|�?} �?|ihThi|@|�L?t�
� ^�it|�L? Lu ��_i TL*�U) �?|ihit| �t |�i �4T@U| L? 5�� T@)4i?| *i�i*t L? |�i ThL�
}h@4 i �| h@|i� L_i* Eb� �?U*�_it |�i 4@ �4�4 TL|i?|�@* *i�i* Lu |L|@* T@)4i?|t |�@|
|�i tL*i T@hi?| u@4�*) 4@) hiUi��i�D A�i ULi�U�i?| L? |��t �@h�@M*i �t ?i}@|��i @?_
t�}?�U@?|c �?_�U@|�?} |�@| @? i |h@ mff uLh uLh|?�}�| Lu TL|i?|�@* T@)4i?|t �?_ih |�i
5�� hi_�Uit |�i i �| h@|i M) E@ t|@|�t|�U@**) t�}?�U@?|� e TihUi?|� OL�i�ih |L|@* TL�
|i?|�@* T@)4i?|t EtTiU�U@**) u@4�*) T@)4i?|t� @hi @ u�?U|�L? Lu |�i ?�4Mihc @?_ @}i
Lu _iTi?_i?| U��*_hi?� A�i �?U*�t�L? Lu |��t T@)4i?| �@h�@M*i �? |�i 4L_i* *i@_t |L @
_h@4@|�U U�@?}i �? |�i it|�4@|i_ igiU| Lu |�i ?�4Mih Lu U��*_hi?c ��|� i@U� @__�|�L?@*
U��*_ @ttLU�@|i_ ��|� @ S TihUi?| ��}�ih i �| h@|i uhL4 5��� A��t ULi�U�i?| it|�4@|i �t
UL�?|ih��?|��|��i t�?Ui @__�|�L?@* U��*_hi? hiThiti?| @ ��}�ih ETih Tih�L_� ULt| Lu i4T*L)�
4i?| t�U� @t U��*_�U@hi i Ti?tit E��|�L�| @ UL?UL4�|@?| �?Uhi@ti �? TL|i?|�@* i@h?�?}t�
���U� @ Th�Lh� �4T*�it @ ?i}@|��i ULi�U�i?|� A�i it|�4@|i_ igiU| Lu |�i @}i Lu |�i
)L�?}it| U��*_ �t @*tL tL4i��@| ti?t�|��i |L |�i �?U*�t�L? Lu |�i T@)4i?| �@h�@M*i� �
4Lhi hi@tL?@M*i i T*@?@|�L? Lu |�i ULi�U�i?| it|�4@|i_ uLh 4L_i* Eb� �t |�@| TL|i?|�@*
8Pd{lpxp srwhqwldo sd|phqwv xqghu wkh VSS lv gh�qhg khuh dv wkh vxp ri wkh pd{lpxp edvlfudwh ri VSS sd|phqw/ pd{lpxp idplo| sd|phqw/ skduphdxwlfdo doorzdqfh/ uhqw dvvlvwdqfh +iru sulydwhuhqwhuv, dqg uhprwh duhd doorzdqfh +iru wkrvh lq wkh uhprwh duhdv,1 Lw lv wkh srwhqwldo dprxqw vlqfh wkhlqfrph dqg dvvhwv whvwv uhgxfwlrqv duh qrw wdnhq lqwr dffrxqw1
H
5�� T@)4i?|t @hi @? �?Uhi@t�?} u�?U|�L? Lu |�i ?�4Mihc @?_ @}ic Lu _iTi?_i?| U��*_hi?
@?_ |��t ULhhi*@|�L? �? U@T|�hi_ �? |�i ULi�U�i?| it|�4@|it uLh |�iti � �@h�@M*it� A�ihi�
uLhi �| �t @TT@hi?| |�@| |�i �4T@U| Lu |L|@* TL|i?|�@* T@)4i?|t L? |�i i �| h@|i U@??L| Mi
tiT@h@|i*) �_i?|�i_ uhL4 |�i ?�4Mih Lu _iTi?_i?| U��*_hi? @?_ |�i�h @}i UL4TLt�|�L?�
��e A�i ì**�Mi�?} Lu 5L*i �@hi?| 6@4�*�itc b.D�bb��
��e� A�i _�t|h�M�|�L? Lu �?UL4i
W? @?@*)t�?} U�@?}it �? |�i *i�i* Lu �i**�Mi�?} Lu tL*i T@hi?| u@4�*�it L�ih |�4ic |�i
_�t|h�M�|�L? Lu }hLtt E�?_���_�@*�i^���@*i?|� �t UL?t�_ihi_ ht|� 6�}�hi Thiti?|t |�i
wLhi?3 U�h�it uLh |�i uL�h t�h�i) )i@ht� 5�?Ui �| �t _��U�*| |L ��t�@**) _�t|�?}��t� |�i
tiT@h@|i wLhi?3 U�h�itc |�i �ih|�U@* _�t|@?Ui Mi|�ii? i@U� wLhi?3 U�h�i @?_ |�i EeDL�
*�?i Lu i^�@*�|) @hi T*L||i_ �? 6�}�hi 2 Etii #i@|L? Ebb.� @?_ �@hhi|| i|�@*� Ebbb�
uLh @ _�tU�tt�L? Lu |��t |h@?tuLh4i_ wLhi?3 U�h�i�� A��t }h@T� U*i@h*) t�L�t |�@| |�i
wLhi?3 U�h�it �?|ihtiU| i@U� L|�ihc @?_ �i?Ui |�i wLhi?3 _L4�?@?Ui Uh�|ih�L? _Lit ?L|
ThL��_i @ h@?!�?} Lu |�i _�t|h�M�|�L?t� OL�i�ihc |�i }h@T� t�L�t |�@| |�i ThLTLh|�L?
Lu |L|@* �?UL4i hiUi��i_ M) |�i ML||L4 �@*u Lu |�i tL*i T@hi?| TLT�*@|�L? �@t Mii?
ThL}hitt��i*) �?Uhi@t�?} L�ih |�4i� A�ihiuLhi �?i^�@*�|) �?_�Uit |�@| @hi 4Lt| ti?t�|��i
|L |h@?tuiht |L�@h_t |�i ML||L4 Lu |�i _�t|h�M�|�L? ��** |i?_ |L t�L� @ _iUhi@ti �? �?UL4i
�?i^�@*�|) L�ih |�4i� |�@| �?i^�@*�|) �? �?UL4i @4L?} tL*i T@hi?| u@4�*�it �@t �?Uhi@ti_
ThL}hitt��i*) L�ih |�4i�
W?i^�@*�|) �?_�Uit uLh |�i _�t|h�M�|�L? Lu �?UL4i @hi Thiti?|i_ �? |�i |LT T@?i* Lu
A@M*i b� A�i B�?� ULi�U�i?| @?_ |�i ti| Lu �|!�?tL? �?_�Uit @** t�L� @ t�Mt|@?|�@*
_iUhi@ti �? �?i^�@*�|) Mi|�ii? b.D @?_ bb�G L�ih |�i |�L _iU@_it �?UL4i �?i^�@*�|)
ui** M) �� TihUi?|� A��t �t �? UL?|h@t| |L |�i TLT�*@|�L? ��_i |hi?_ Lu �?Uhi@t�?}
�?UL4i �?i^�@*�|) hiTLh|i_ �? �@hhi|| i|�@*� Ebbb��
�i | |�i *i�i* Lu �i*u@hi @4L?} tL*i T@hi?| u@4�*�it �t i @4�?i_� 6�}�hi � Thiti?|t
|�i Bi?ih@*�ti_ wLhi?3 U�h�it uLh |�i _�t|h�M�|�L? Lu �?UL4i �? b.D @?_ bb�� A�i
}�hi t�L�t |�@| |�i Bi?ih@*�ti_ wLhi?3 U�h�i uLh b.D @?_ bb� UhLttc ��|� |�i ML||L4
�@*u Lu |�i _�t|h�M�|�L? u@h�?} t*�}�|*) Mi||ih �? bb� |�@? |�i i@h*�ih Tih�L_� OL�i�ihc
b
|�ihi �t @ 4Lhi t�Mt|@?|�@* _iU*�?i �? @�ih@}i �?UL4i @hL�?_ |�i 4�__*i @?_ |LT Lu
|�i �?UL4i _�t|h�M�|�L?� AL u�h|�ih i T*Lhi |�iti U�@?}itc 6�}�hi e t�L�t |�i }hL�|�
�? �?UL4i M) TihUi?|�*i Lu |�i �?UL4i _�t|h�M�|�L? uLh i@U� Lu |�i t�h�i) )i@ht� A��t
}h@T� ��}�*�}�|t |�i u@U| |�@| |�ihi �@t Mii? @ t�Mt|@?|�@* �4ThL�i4i?| �? �?UL4i *i�i*t
@4L?} |�i TLLhit| tL*i T@hi?| u@4�*�it� 6�h|�ih4Lhic u@4�*�it �? |�i ML||L4 ^��?|�*i
i Tih�i?Ui_ �?UL4i }hL�|� Mi|�ii? b.D @?_ bb� E��|� 4Lt| Lu |�i }hL�|� UL?Ui?|h@|i_
�? |�i Tih�L_ bHH�b��� OL�i�ihc |�ihi �@t Mii? @ ThL}hitt��i _i|ih�Lh@|�L? �? |�i *i�i* Lu
hi@* �?UL4it @UhLtt |�i hit| Lu |�i _�t|h�M�|�L?c T@h|�U�*@h*) @4L?} |�i 4�__*i Df TihUi?|
Lu u@4�*�it� �}@�?c |�i T@||ih? Lu �?UL4i }hL�|� @4L?} tL*i T@hi?| u@4�*�it UL?|h@t|t
|�@| ��|?itti_ uLh |�i ��t|h@*�@? TLT�*@|�L? @t @ ��L*iG �@hhi|| i|�@*� Ebbb� hiTLh|i_
*@h}ih ETLt�|��i� �?UL4i }hL�|� h@|it ��}�ih �T |�i �?UL4i _�t|h�M�|�L?�
A�i t�44@h) 4i@t�hit Lu �i*u@hi uLh tL*i T@hi?| u@4�*�it @hi hiTLh|i_ �? |�i |LT
T@?i* Lu A@M*i f� A�iti }�hit t�L� |�@| @�ih@}i hi@* �?UL4i _iU*�?i_ M) @*4Lt| b
TihUi?| L�ih |�i Tih�L_ b.D�b�� #itT�|i |�i _iUhi@ti �? �?UL4i �?i^�@*�|)c |�ihi �@t
@? L�ih@** _iU*�?i �? |�i *i�i* Lu �i*u@hi @4L?} tL*i T@hi?| u@4�*�it� OL�i�ihc |�i 4Lt|
�?i^�@*�|)�ti?t�|��i �i*u@hi �?_�Uit �?_�U@|i |�i t4@**it| _iU*�?i �? @}}hi}@|i �i**�Mi�?}�
��e�2 A�i _�t|h�M�|�L? Lu UL?t�4T|�L?
A�i �4T*�U@|�L?t Lu U�@?}it �? |�i �?UL4i _�t|h�M�|�L? uLh U�@?}it �? u@4�*) �i**�Mi�?}
?ii_ |L Mi |i4Tihi_ M) |�i u@U| |�@| |�i TL�?|��?�|�4i t?@Tt�L|t Lu |�i �?UL4i _�t�
|h�M�|�L?t hi�iU| ML|� �?UL4i �?t|@M�*�|) @?_ �?UL4i �?i^�@*�|)� BL�ih?4i?|t t4LL|�
��U|�@|�L?t �? �?UL4it |�hL�}� |�i |@ �|h@?tuih t)t|i4� BL�ih?4i?| @*tL hi_�t|h�M�|it
hitL�hUit Mi|�ii? �?_���_�@*t @?_ u@4�*�it |�hL�}� |�i |@ �|h@?tuih t)t|i4� W? @__�|�L?c
Th��@|i �L�ti�L*_ @hi @M*i |L hi_�Ui |�i �4T@U| Lu �?UL4i �?t|@M�*�|) L? u@4�*) �i**�Mi�?}
M) MLhhL��?} @?_ t@��?}� A�ihiuLhic UL?t�4T|�L? *i�i*t t�L�*_ ThL��_i @ 4Lhi @UU�h@|i
}��_i |L �?i^�@*�|) �? u@4�*) �i**�Mi�?} E@?_ �? Tih4@?i?| �?UL4i� |�@? }hLtt �?UL4i
hiUi��i_ �? @ �ih) t�Lh| Tih�L_� A��t TL�?| �t �**�t|h@|i_ �? 6�}�hi Dc ���U� t�L�t |�i
U�4�*@|��i ThLTLh|�L? Lu Th��@|i E4@h!i|� �?UL4ic ?i| �?UL4i E'Th��@|i �?UL4i n }L�|
|h@?tuiht � _�hiU| |@ it� @?_ ?@* UL?t�4T|�L? M) U�4�*@|��i ThLTLh|�L? Lu |�i TLT�*@�
2f
|�L? ELh_ihi_ M) Th��@|i �?UL4i� �? bb�� A�i 4Lt| t�}?�U@?| ui@|�hi Lu |��t }h@T� �t
|�i ��}i _�gihi?Ui Mi|�ii? |�i wLhi?3 U�h�i uLh Th��@|i �?UL4i @?_ ?i| �?UL4i� A�i
}L�ih?4i?| |@ �|h@?tuih t)t|i4 hi_�Uit |�i @TT@hi?| *i�i* Lu �?UL4i �?i^�@*�|) M) @ t�M�
t|@?|�@* @4L�?|� �h��@|i E}hLtt� �?UL4ic ���U� �t |�i L?*) �?UL4i UL?UiT| UL?t�t|i?|
@UhLtt |�i e _@|@ ti|t i @4�?i_ �? |��t tiU|�L?c �@t|*) L�ih�it|�4@|it |�i *i�i* Lu �?UL4i
�?i^�@*�|) M) ?L| |@!�?} �?|L @UUL�?| |�i �4T@U| Lu |@ it @?_ |h@?tuiht�S A�i UL?t�4T�
|�L? UL?Ui?|h@|�L? U�h�i *�it @ML�i |�i ?i| �?UL4i U�h�ic hi�iU|�?} |�i u�h|�ih hi_�U|�L?
�? iUL?L4�U �?i^�@*�|) @U��i�i_ |�hL�}� Th��@|i t4LL|��?} Mi�@��L�h� A�i t4LL|��?}
|�hL�}� Th��@|i 4i@?tc ?L| t�hTh�t�?}*)c �t }hi@|it| |L�@h_ |�i |LT Lu |�i �?UL4i _�t|h�M��
|�L?� OL�i�ihc |�i �tt�i Lu Th��@|i t4LL|��?} �t Lu *ittih �4TLh|@?Ui �? UL4T@h�tL? |�i
t�Mt|@?|�@* igiU|t Lu |�i |@ �|h@?tuih t)t|i4 L? |�i _�t|h�M�|�L? Lu iUL?L4�U �i**�Mi�?}�
A�i ?i | tih�it Lu }h@T�t uLU�t L? U�@?}it �? |�i _�t|h�M�|�L? Lu ?L?�_�h@M*i UL?t�4T�
|�L?� A�i _�t|h�M�|�L? Lu UL?t�4T|�L? �@t |�i @_�@?|@}i Lu �?ULhTLh@|�?} |�i igiU|t Lu
T�M*�U t4LL|��?} @?_ hi_�t|h�M�|�L? T*�t Th��@|i t4LL|��?} L? |�i _�t|h�M�|�L? Lu u@4�*)
�i**�Mi�?}� 6�}�hi S Thiti?|t |�i wLhi?3 U�h�it uLh |�i _�t|h�M�|�L? Lu UL?t�4T|�L?
�? i@U� t�h�i) )i@h� AL ThL��_i @ U*i@hih tiT@h@|�L? Lu |�i wLhi?3 U�h�itc |�i �ih|�U@*
_�t|@?Ui Mi|�ii? |�i U�h�it @?_ |�i *�?i Lu i^�@*�|) @hi T*L||i_ �? 6�}�hi .� A�i wLhi?3
U�h�itc @?_ |h@?tuLh4i_ wLhi?3 U�h�itc uLh UL?t�4T|�L? @hi U*Ltih |L}i|�ih |�@? |�i
ULhhitTL?_ U�h�it uLh �?UL4i� OL�i�ihc |�i wLhi?3 U�h�it @}@�? UhLtt @?_ �i?Ui |�i
wLhi?3 _L4�?@?Ui Uh�|ih�L? U@??L| ThL��_i @ h@?!�?} Lu |�i UL?t�4T|�L? _�t|h�M�|�L?t�
A�i u@U| |�@| |�i TLLhit| SD TihUi?| Lu tL*i T@hi?| u@4�*�it hiUi��i_ @ }hi@|ih ThLTLh|�L?
Lu |L|@* E?L?�_�h@M*i� UL?t�4T|�L? �? bb� |�@? b.D t�}}it|t |�i �?i^�@*�|) �?_�Uit
4Lt| ti?t�|��i |L U�@?}it @| |�i ML||L4 Lu |�i _�t|h�M�|�L? ��** �?_�U@|i @? �4ThL�i4i?|
�? UL?t�4T|�L? �?i^�@*�|)�
A�i *L�ih T@?i* Lu A@M*i b Thiti?|t |�i �?i^�@*�|) �?_�Uit uLh |�i _�t|h�M�|�L? Lu
UL?t�4T|�L?� A�iti ?�4Miht UL?h4 |�@| |�i *i�i* Lu �?i^�@*�|) �? |�i _�t|h�M�|�L? Lu
UL?t�4T|�L? �t 4�U� *itt |�@? |�@| uLh �?UL4i� 6Lh �?t|@?Uic |�i B�?� ULi�U�i?| uLh
9Dv glvfxvvhg ehorz/ wkh vxevwdqwldo gl�huhqfh ehwzhhq wkh fxuyhv iru sulydwh dqg qhw lqfrph lv gxh wrwkh idfw wkdw idplolhv lq wkh erwwrp kdoi ri wkh glvwulexwlrq zhuh doprvw frpsohwho| uholdqw rq jryhuqphqwwudqvihuv iru lqfrph1 Wklv lqfrph vrxufh lv gh�qhg dv sduw ri qhw lqfrph exw qrw sulydwh lqfrph1
2
|�i _�t|h�M�|�L? Lu UL?t�4T|�L? �? bb� �@t f�2f�H UL4T@hi_ |L |�i B�?� ULi�U�i?| uLh
�?UL4i Lu f�2e�� A�i �?i^�@*�|) �?_�Uit @*tL t�L� @ _iU*�?i �? UL?t�4T|�L? �?i^�@*�|)
L�ih |�i Tih�L_ Lu |�i t|�_)( �L�i�ihc |�i _iU*�?i �@t *itt |�@? |�@| uL�?_ uLh |�i �?UL4i�
A�h?�?} |L |�i *i�i* Lu u@4�*) �i**�Mi�?}c 6�}�hi H Thiti?|t |�i Bi?ih@*�ti_ wLhi?3
U�h�it uLh UL?t�4T|�L? �? b.D @?_ bb�� W? UL?|h@t| |L |�i �?UL4i _�t|h�M�|�L?c �| �t
@TT@hi?| |�@| u@4�*) �i*u@hi @t 4i@t�hi_ M) ?L?�_�h@M*i UL?t�4T|�L? �?@4M�}�L�t*)
�4ThL�i_ L�ih |�4i� A�i �i*u@hi �?_�Uit Thiti?|i_ �? |�i *L�ih T@?i* Lu A@M*i f hi�iU|
|��t t��u| �T Lu |�i UL?t�4T|�L? Bi?ih@*�ti_ wLhi?3 U�h�it L�ih |�i t|�_) Tih�L_� A�i
�?Uhi@ti �? |�i 4i@? *i�i* Lu UL?t�4T|�L?c UL�T*i_ ��|� |�i _iU*�?i �? �?i^�@*�|)c *i@_ |L
@ h�ti �? |�i UL?t�4T|�L? �i*u@hi �?_�Uit M) H� TihUi?| Mi|�ii? b.D @?_ bb��
A�i }hL�|� �? UL?t�4T|�L? *i�i*t @UhLtt |�i _�t|h�M�|�L? �t t�L�? �? 6�}�hi b� W|
�t @TT@hi?| |�@| |�ihi �@t t�Mt|@?|�@* }@�?t �? |�i hi@* UL?t�4T|�L? *i�i*t @4L?} |�i
TLLhit| D�f TihUi?| tL*i T@hi?| u@4�*�it� 5�}?�U@?|c M�| 4Lhi 4L_it|c }@�?t ��ihi
i Tih�i?Ui_ @4L?} |�i f�2D|� TihUi?|�*itc @?_ �?�uLh4 M�| t4@**ih }@�?t ��ihi @U��i�i_
@UhLtt |�i hi4@�?_ih Lu |�i _�t|h�M�|�L?� �? �4TLh|@?| UL4TL?i?| Lu |�i �4ThL�i4i?|
�? |�i �i**�Mi�?} Lu tL*i T@hi?| u@4�*�it L�ih |�i t|�_) Tih�L_ �ihi |�i }@�?t 4@_i _�h�?}
bHH�b��
�t @ ?@* i*i4i?| �? |�i @?@*)t�tc W i @4�?i |�i �4TLh|@?Ui Lu _�gihi?| �?UL4i
tL�hUit @UhLtt |�i _�t|h�M�|�L? @?_ L�ih |�4i� W UL?t�_ih uL�h �?UL4i tL�hUitG �@}it
@?_ t@*@h�itc ti*u�i4T*L)4i?| �?UL4ic }L�ih?4i?| |h@?tuiht @?_ �L|�ih< hit�_�@* �?UL4i
Et�U� @t U@T�|@* �?UL4i @?_ Th��@|i |h@?tuiht�� A�i hi*@|��i �4TLh|@?Ui Lu |�iti �?UL4i
tL�hUit L�ih |�4i @hi T*L||i_ uLh i@U� ^��?|�*i Lu |�i �?UL4i _�t|h�M�|�L? �? 6�}�hi f�
A�i uL�h tL�hUit @hi UL?t�_ihi_ ti^�i?|@**)c @?_ U�4�*@|i_c tL |�@| |�i �ih|�U@* _�t|@?Ui
Mi|�ii? |�i *�?i uLh �@}i @?_ t@*@h) �?UL4i T*�t ti*u�i4T*L)4i?| �?UL4ic @?_ uLh |�@|
4@h!i| �?UL4i ��|� }L�ih?4i?| |h@?tuihtc ULhhitTL?_t |L |�i ThLTLh|�L? Lu |L|@* �?UL4i
uhL4 T�M*�U |h@?tuiht� 6hL4 |�i }h@T�t �| �t U*i@h |�@| }L�ih?4i?| |h@?tuiht @UUL�?|
uLh |�i Thi_L4�?@|i tL�hUi Lu �?UL4i EL�ih bf TihUi?|� @4L?} u@4�*�it �? |�i ML||L4
^��?|�*i E2fI� Lu |�i _�t|h�M�|�L?� ��ih |�4ic }L�ih?4i?| |h@tuiht �@�i MiUL4i @?
�?Uhi@t�?}*) �4TLh|@?| tL�hUi Lu �?UL4i �? |�i L|�ih ti}4i?|t Lu |�i _�t|h�M�|�L? @t �i**�
22
6Lh �?t|@?Uic }L�ih?4i?| |h@?tuiht @UUL�?|i_ uLh ��t| L�ih �@*u Lu @** �?UL4i �? |�i 2?_
^��?|�*i �? b.D @?_ M) bb� �| @UUL�?|i_ uLh L�ih bf TihUi?| Lu @** �?UL4i� W? |�i |��h_
^��?|�*i }L�ih?4i?| |h@?tuiht �?Uhi@ti_ uhL4 2 TihUi?| Lu |L|@* �?UL4i �? b.D |L L�ih
.D TihUi?| �? bb�� W? |�i e|� ^�@h|�*ic }L�ih?4i?| |h@?tuiht �i?| uhL4 @ hi*@|��i*)
4�?Lh f TihUi?| Lu �?UL4i �? b.D |L L�ih �@*u Lu @** �?UL4i �? bb��. A�i }hL��?}
�4TLh|@?Ui Lu |h@?tuih �?UL4i �@t Mii? 4�hhLhi_ M) @? i^�@* _iU*�?i �? |�i �4TLh|@?Ui Lu
*@ML�h 4@h!i| �?UL4i� A�ihiuLhi |�i }@�?t �? |�i iUL?L4�U i^�@*�|) @4L?} tL*i T@hi?|
u@4�*�itc @?_ �4ThL�i4i?|t �? |�i�h iUL?L4�U �i**�Mi�?}c �@�i UL�?U�_i_ ��|� }hL��?}
hi*�@?Ui L? T�M*�U @tt�t|@?Ui @UhLtt 4Lt| Lu |�i _�t|h�M�|�L?�
e �L?U*�t�L?
A��t T@Tih ti| L�| |L _itUh�Mi |�i U�@h@U|ih�t|�Ut Lu |�i tL*i T@hi?| TLT�*@|�L?c @?_ |�i
t�Mti| Lu |�@| TLT�*@|�L? �? hiUi�T| Lu T�M*�U �?UL4i t�TTLh|� A�i *i?}|� Lu |�4i tL*i
T@hi?|t hi4@�?i_ L? �?UL4i t�TTLh| �@t @*tL UL?t�_ihi_� A�i ?@* tiU|�L? Lu |�i T@Tih
i @4�?i_ ��i|�ih |�i �i**�Mi�?} Lu tL*i T@hi?| u@4�*�it �@_ U�@?}i_ L�ih |�4i�
W| �@t uL�?_ |�@| |�ihi �@_ Mii? UL?t�_ih@M*i �4ThL�i4i?|t �? |�i *i�i* Lu iUL?L4�U
�i**�Mi�?} Lu tL*i T@hi?| u@4�*�it L�ih |�i T@t| |�L _iU@_it� LhiL�ihc |�i }hi@|it| }@�?t
�@_ Mii? i Tih�i?Ui_ M) |�i *i@t| �i** Lg tL*i T@hi?| u@4�*�it� �L�?U�_�?} ��|� |�i }@�?t
�? |�i @}}hi}@|i �i*u@hi Lu tL*i T@hi?| u@4�*�it �@t @ _iUhi@ti �? |�i *i�i* Lu iUL?L4�U
�?i^�@*�|)� �? �4TLh|@?| u@U|Lh �?_ih*)�?} |�iti }@�?t �t |�i hL*i Lu }L�ih?4i?| |h@?tuih
�?UL4i� ��M*�U @tt�t|@?Ui �@t ThL�i? |L Mi Ui?|h@* |L |�i h�t�?} *���?} t|@?_@h_ Lu |�i
TLLhit| tL*i T@hi?| u@4�*�it� OL�i�ihc |�ihi �@t Mii? @ }i?ih@* h�ti �? hi*�@?Ui L? T�M*�U
�?UL4i t�TTLh| @UhLtt |�i tL*i T@hi?| u@4�*) �?UL4i _�t|h�M�|�L?� A�i }hL��?} hi*�@?Ui
L? T�M*�U �?UL4i t�TTLh| �@t *i@_ |L @ UL?UL4�|@?| _iU*�?i �? *@ML�h 4@h!i| �?UL4i� �?
�4TLh|@?| |LT�U uLh u�|�hi hiti@hU� �t |L �?_iht|@?_ |�i hi@tL?t �?_ih*)�?} |�i �?Uhi@t�?}
hi*�@?Ui L? |h@?tuih �?UL4ic @?_ |�i hi_�U|�L? �? T@h|�U�T@|�L? �? |�i �Lh!uLhUic M) tL*i
T@hi?|t�
:Lq wkh wrs txlqwloh/ zdjhv dqg vdodulhv zhuh frqvlvwhqwo| wkh suhgrplqdwh lqfrph vrxufh ryhu wkhvwxg| shulrg +dsduw iurp d whpsrudu| idoo lq 4
+iuihi?Uit
do �|!�?tL?c���� Eb.f� ��? |�i 4i@t�hi4i?| Lu �?i^�@*�|)< aL�h?@* Lu ,UL?L4�U A�i�
Lh)c 2c 2ee�S��
d2o �@hhi||c B�6�c A� �hLtt*i) @?_ �� L̀ht��U! Ebbb�� #i4L}h@T��U Ahi?_t @?_ �L?�
t�4T|�L? W?i^�@*�|) �? ��t|h@*�@ Mi|�ii? b.D @?_ bb�c �4iLc ��t|h@*�@? �@|�L?@*
N?��iht�|)�
d�o �*�?_i**c +� @?_ �hit|L?c W� EbbH�c �L?t�4T|�L? W?i^�@*�|) @?_ W?UL4i N?Uih�
|@�?|)c "�@h|ih*) aL�h?@* Lu ,UL?L4�Utc @) bbH�Sf��Sef�
deo �i?|hi*�?!c EbbH�� �i?|hi*�?! W?uLh4@|�L?G � B��_i |L �@)4i?|t @?_ 5ih��Uitc
�i?|hi*�?!c �@?Mihh@�
dDo #i@|L?c ��c Ebb.�� A�i �?@*)t�t Lu OL�ti�L*_ 5�h�i)tG � �UhLiUL?L4i|h�U �T�
ThL@U� |L #i�i*LT4i?| �L*�U)� �@*�|4Lhic aL�? OLT!�?t N?��iht�|) �hitt�
dSo OiU!4@?c a�a� @?_ ��5�?}ih EbHD�� 5LU�@* tU�i?Ui _�h@|�L? @?@*)t�tc �? a�a�OiU!4@?
@?_ ��5�?}ih Ei_t��c wL?}�|�_�?@* �?@*)t�t Lu w@MLh @h!i| #@|@c �@4Mh�_}iG �@4�
Mh�_}i N?��iht�|) �hittc �b�f�
d.o w@4Mih|c ��a� Ebb�� A�i #�t|h�M�|�L? @?_ +i_�t|h�M�|�L? Lu W?UL4iG � @|�i4@|�
�U@* �?@*)t�tc @?U�it|ih N?��iht�|) �hittc @?U�it|ihc 2?_ i_�|�L?�
dHo w@?U@t|ihc A� Ebbf�� A�i ,UL?L4i|h�U �?@*)t�t Lu Ah@?t�|�L? #@|@c �@4Mh�_}iG
�@4Mh�_}i N?��iht�|) �hitt�
dbo i)ihc ��#� EbHH�� 5i4�T@h@4i|h�U it|�4@|�L? Lu �@3@h_ 4L_i*tc �4iLc WA�
dfo i)ihc ��#� Ebbf�� �? N?i4T*L)4i?| W?t�h@?Ui @?_ N?i4T*L)4i?| 5Ti**tc ,UL?L�
4i|h�U@c �DHEe�c TT�.D.�.H2�
do L�||c +� Ebb2�� W?Ui?|��i ,giU|t Lu |�i N�5� ì*u@hi 5)t|i4G � +i��i�c aL�h?@*
Lu ,UL?L4�U w�|ih@|�hic ��fE�c TT��S�
2e
d2o �i?_@!�hc k�c EbbH�� ��@?}it �? �@?@_�@? 6@4�*) W?UL4i @?_ 6@4�*) �L?t�4T|�L?
W?i^�@*�|) �i|�ii? b.H @?_ bb2c +i��i� Lu W?UL4i @?_ `i@*|�c eeE2�G2Db�2H��
d�o �hi?|�Uic +� @?_ w�B*LiU!*ih Eb.H�� +i}hitt�L? @?@*)t�t Lu }hL�Ti_ t�h���@* _@|@
��|� @? @TT*�U@|�L? |L Mhi@t| U@?Uih _@|@c ��L4i|h�Utc �ec D.�S.�
2D
Cu
mu
lative
Sh
are
Eq
uiv
ale
nt G
ross In
co
me
Cum. Pop. Prop.
1975 1984 1988 1993
0 .5 1
0
.5
1
6�}�hi G wLhi?3 ��h�it uLh W?UL4i
2S
Lin
e o
f E
qu
alit
y -
Cu
mu
lative
In
co
me
Sh
are
Eq
uiv
ale
nt G
ross In
co
me
Cum. Pop. Prop.
1975 1984 1988 1993
0 .5 1
0
.05
.1
.15
.2
6�}�hi 2G Ah@?tuLh4i_ wLhi?3 ��h�it uLh W?UL4i
2.
Cu
mu
lative
Co
nd
itio
na
l M
ea
nE
qu
iva
len
t G
ross In
co
me
Cum. Pop. Prop.
1975 1993
0 .5 1
0
100
200
300
6�}�hi �G Bi?ih@*�ti_ wLhi?3 ��h�it uLh W?UL4i
2H
Ra
tio
to
19
75
Income percentile
93 88 84
10 25 50 75 90 100
.7
.8
.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
6�}�hi eG +i@* ,^���@*i?| W?UL4i BhL�|�
2b
Cu
mu
lative
Sh
are
19
93
Ho
use
ho
ld E
xp
en
ditu
re S
urv
ey
Cumulative Population Proportion
priv inc net inc consumption Cum. Pop. Prop.
0 .5 1
0
.5
1
6�}�hi DG �L?Ui?|h@|�L? Lu �L?t�4T|�L? hi*@|��i |L W?UL4i
�f
Cu
mu
lative
Sh
are
Eq
uiv
ale
nt N
on
du
rab
le C
on
su
mp
tio
n
Cum. Pop. Prop.
1975 1984 1988 1993
0 .5 1
0
.5
1
6�}�hi SG wLhi?3 ��h�it uLh �L?t�4T|�L?
�
Lin
e o
f E
qu
alit
y -
Cu
mu
lative
Co
nsu
mp
tio
n S
ha
reE
qu
iva
len
t N
on
du
rab
le C
on
su
mp
tio
n
Cum. Pop. Prop.
1975 1984 1988 1993
0 .5 1
0
.05
.1
.15
.2
6�}�hi .G Ah@?tuLh4i_ wLhi?3 ��h�it uLh �L?t�4T|�L?
�2
Cu
mu
lative
Co
nd
itio
na
l M
ea
nE
qu
iva
len
t N
on
du
rab
le C
on
su
mp
tio
n
Cum. Pop. Prop.
1975 1993
0 .5 1
0
100
200
300
6�}�hi HG Bi?ih@*�ti_ wLhi?3 ��h�it uLh �L?t�4T|�L?
��
Ra
tio
to
19
75
Expenditure percentile
93 88 84
10 25 50 75 90 100
.7
.8
.9
1
1.1
1.2
1.3
1.4
1.5
1.6
6�}�hi bG +i@* ,^���@*i?| �L?�_�h@M*i , Ti?_�|�hi BhL�|�
�e
Income Sourceyear
wages and salary self employment govt. transfers
1st quintile
.25
.5
.75
1
2nd quintile
3rd quintile
75 84 88 95
.25
.5
.75
1
4rth quintile
75 84 88 95
6�}�hi fG W?UL4i 5L�hUi M) vi@h @?_ W?UL4i "��?|�*i
�D
Table 1. Characteristics of Sole Parent Population, 1996Sole Mothers Partnered Women Sole Fathers
DemographicsAge (yrs) 33.98 47.13 49.05Australian Born 73.04 68.31 69.26Mother Austn. Born 65.53 59.59 63.46Father Austn. Born 61.27 56.28 57.05Identifies as ATSI 4.00 2.98 7.09
Marital Statusnever married 22.77 - 13.4widowed 19.76 - 19.8divorced 30.70 - 33.69separated 26.77 - 33.1married - 100 -
Age Left Schoolstill attending 0.91 0.51 1.08never attended 1.26 0.74 0.7914 years 14.91 13.6 18.9215 years 25.99 24.2 24.3316 years 23.09 22.58 19.917 years 16.82 20.14 13.418 years 8.53 10.77 9.0619 years 4.04 3.42 4.73not stated 4.44 4.04 7.78
Post School QualificationDegree 7.2 11.07 8.77Diploma 6.29 7.88 4.63Vocational Qualfn. 6.38 7.4 22.57Part/Complete High School 70.35 63.41 52.32not stated 9.78 10.14 11.73
Labour Force Statusemployee 39.75 47.06 47.39self employed 2.08 5.6 7.48unemployed: looking for ft 4.03 1.87 6.31unemployed: looking for pt 3.71 1.18 1.58not in labour force 49.19 43.27 35.76not stated 1.25 1.02 1.48
Hours Worked (last wek)Part-time 20.74 24.92 12.02Full-time 20.31 26.55 41.87Not Work 58.17 47.34 45.12not stated 0.78 1.19 0.99
Average Wekly Income 339.498 298.11 464.92
Observation 5613 38461 1015(%Families) 12.45% 85.30% 2.25%
Table 2. Population of Sole Parent Pensioners, August 2 1996.Stock Sample Means
Demographic CharacteristicsSole Mother 0.9338Sole Father 0.0662Age (yrs) 33.6617Australian Born 0.8079Identifies as ATSI 0.0379Number children under 13years 1.3022Number children over 13 years 0.2546Age of youngest child 5.5442
Home ownershipNot home-owner 0.7944Home owner 0.1230Purchasing home 0.0361Other home-owner 0.0465
Rental TypeNot renting 0.2411Private rent 0.4372Govt. rent 0.2024Board and lodging 0.0709No rent paid 0.0439Other rental 0.0045Rent paid ($) 141.765
State of residenceNSW/ACT 0.3323Vic 0.2213Qld 0.2053SA 0.0872WA 0.1069Tas 0.0307NT 0.0163
Financial VariablesWhether Received Child Support 0.4903Amount Child Support 104.2093Whether Earnings>0 0.2629Earned Income 92.9776Whether Unearned Income >0 0.1256Unearned Income 8.3701
Program VariablesFamily Payment Amount 169.7683Basic Payment Entitlement 313.4039Pharmaceutical Allowance 5.3783Whether Received Rent Assist. 0.4223Rent Assistance Entitlement 29.4401Remote Area Allowance 0.7034Share Total Income Private 0.2329Duration on Payment (Years) 3.3100
Total Observations 3488
Table 3. Sample of Sole Parent Pensioners.Characteristics All SPPers Time 1-6 Time 7-13 Time 14-29 Time 30-45 Time 46
(1) (2) (3) (4) (5) (6)Total Time on SPP 31.396 3.550 9.846 21.176 38.707 46.000Age 33.047 33.261 33.187 32.330 31.901 34.015Sole mother 0.9145 0.8665 0.8729 0.8972 0.9156 0.9475Total children 1.567 1.497 1.499 1.568 1.542 1.619Age of youngest child 5.120 4.984 5.433 4.986 4.786 5.345Australian Born 0.8040 0.7971 0.7875 0.7954 0.8065 0.8135Foreign Born 0.1960 0.2029 0.2125 0.2046 0.1935 0.1865Identifies as ATSI 0.0438 0.0512 0.0740 0.0442 0.0409 0.0352
Not home-owner 0.7817 0.7203 0.7761 0.7733 0.8005 0.7936Home owner 0.1331 0.1590 0.1480 0.1460 0.1236 0.1208Purchasing home 0.0478 0.0804 0.0645 0.0519 0.0443 0.0341Other home-owner 0.0373 0.0402 0.0114 0.0288 0.0315 0.0515
Not renting 0.2568 0.3236 0.2808 0.2690 0.2404 0.2350Private rent 0.4314 0.4186 0.4345 0.4198 0.4535 0.4271Govt. rent 0.1640 0.0987 0.1063 0.1239 0.1569 0.2232Board and lodging 0.0838 0.0878 0.1006 0.0932 0.0878 0.0708No rent paid 0.0594 0.0676 0.0759 0.0855 0.0563 0.0408Other rental 0.0042 0.0037 0.0019 0.0086 0.0043 0.0025NSW*Govt. rental 0.0655 0.0384 0.0417 0.0500 0.0656 0.0877Rent paid ($) 138.41 133.30 131.21 138.22 143.46 138.85
NSW-ACT 0.3290 0.2998 0.3112 0.3343 0.3666 0.3165VIC 0.2170 0.2029 0.1670 0.2181 0.2106 0.2375QLD 0.2164 0.2395 0.2694 0.2181 0.2063 0.2008SA 0.0823 0.0768 0.0930 0.0807 0.0691 0.0897WA 0.1067 0.1225 0.1006 0.0999 0.1032 0.1096TAS 0.0328 0.0384 0.0361 0.0327 0.0307 0.0316NT 0.0126 0.0146 0.0209 0.0144 0.0119 0.0092
Whether Child Support>0 0.4086 0.2943 0.3169 0.3622 0.4007 0.4944Amount Child Support 85.48 53.08 67.56 72.46 88.06 104.68Whether Earnings>0 0.2291 0.1865 0.2353 0.2257 0.2370 0.2365Earned Income 85.53 92.31 109.23 90.07 89.66 72.40Whether Unearned Income >0 0.1410 0.1700 0.1765 0.1508 0.1304 0.1244Unearned Income 9.12 9.76 8.41 8.00 11.37 8.38
Family Payment Amount 175.66 172.13 176.06 180.89 172.10 175.90Basic Payment Entitlement 314.16 301.63 306.17 313.97 311.87 321.27Pharmaceutical Allowance 5.367 5.203 5.400 5.395 5.382 5.381Whether Rent Assist.>0 0.4091 0.3492 0.4175 0.4073 0.4186 0.4190Rent Assistance Entitlement 28.533 24.775 28.814 28.479 29.118 29.184Remote Area Allowance 0.6700 0.8702 0.9032 0.8036 0.4655 0.6030Add-ons 0.0468 0.0938 0.1152 0.0808 0.0423 0.0000
Share SPP Pop. 1.0000 0.1042 0.1000 0.1983 0.2234 0.3737Share Total Time 1.0000 0.0118 0.0314 0.1337 0.2755 0.5475Share SPP Exp. (excl.FA) 1.0000 0.0115 0.0303 0.1314 0.2726 0.5541Share SPP Exp. (incl.FA) 1.0000 0.0111 0.0292 0.1292 0.2715 0.5589
Table 4. Sample of SPP SpellsTotal Spells Fresh Spells
Demographic CharacteristicsSole Mother 0.9135 0.8851Sole Father 0.0865 0.1149Age (yrs) 32.2922 31.8879Identifies as ATSI 0.0451 0.0553Australian Born 0.8057 0.8026Foreign Born 0.1943 0.1974Number children under 13years 1.3352 1.3812Number children over 13 years 0.2441 0.2295Age of youngest child 5.1168 4.5198
State of residenceNSW/ACT 0.3288 0.3240Vic 0.2100 0.1942Qld 0.2234 0.2487SA 0.0822 0.0753WA 0.1043 0.1005Tas 0.0346 0.0400NT 0.0167 0.0172
Home ownershipNot home-owner 0.7866 0.7757Home owner 0.1293 0.1382Purchasing home 0.0471 0.0625Other home-owner 0.0370 0.0236
Rental TypeNot renting 0.2560 0.2767Private rent 0.4309 0.4221Govt. rent 0.1611 0.1033Board and lodging 0.0835 0.1013No rent paid 0.0633 0.0905Other rental 0.0052 0.0061Rent paid ($) 139.244 135.722
Financial VariablesWhether Received Child Support 0.4087 0.2948Amount Child Support 84.5407 57.0661Whether Earnings>0 0.2301 0.1842Earned Income 88.6187 82.5298Whether Unearned Income >0 0.1402 0.1606Unearned Income 8.6129 8.9519
Program VariablesFamily Payment Amount 177.9559 189.3930Basic Payment Entitlement 312.4836 311.1982Pharmaceutical Allowance 5.3549 5.3222Whether Received Rent Assist. 0.4079 0.3877Rent Assistance Entitlement 28.5912 27.4054Remote Area Allowance 0.6848 0.6588Add-ons 0.0650 0.1557
Repeat Spell 0.1228 0.2944Right censored 0.6156 0.6227Observed Duration (fortnights) 27.6147 16.0437Observations (Spells) 5985 2497
Table 5. Empirical Hazard and Survival Function EstimatesDuration Hazard Rates (Std.Err.) Survival Pr. (Std.Err.)
1 0.0264 (0.003) 1.0000 -2 0.0270 (0.003) 0.9736 (0.003)3 0.0296 (0.004) 0.9473 (0.005)4 0.0311 (0.004) 0.9192 (0.006)5 0.0321 (0.004) 0.8906 (0.006)6 0.0303 (0.004) 0.8620 (0.007)7 0.0335 (0.004) 0.8359 (0.008)8 0.0195 (0.003) 0.8079 (0.008)9 0.0308 (0.004) 0.7922 (0.009)
10 0.0237 (0.004) 0.7677 (0.009)11 0.0265 (0.004) 0.7495 (0.009)12 0.0302 (0.005) 0.7297 (0.010)13 0.0256 (0.005) 0.7076 (0.010)14 0.0185 (0.004) 0.6895 (0.010)15 0.0213 (0.004) 0.6768 (0.010)16 0.0187 (0.004) 0.6624 (0.011)17 0.0296 (0.005) 0.6500 (0.011)18 0.0221 (0.005) 0.6307 (0.011)19 0.0245 (0.005) 0.6168 (0.011)20 0.0142 (0.004) 0.6017 (0.011)21 0.0175 (0.005) 0.5931 (0.011)22 0.0159 (0.005) 0.5828 (0.012)23 0.0098 (0.004) 0.5735 (0.012)24 0.0178 (0.005) 0.5679 (0.012)25 0.0127 (0.005) 0.5578 (0.012)26 0.0067 (0.003) 0.5507 (0.012)27 0.0107 (0.004) 0.5470 (0.012)28 0.0189 (0.006) 0.5411 (0.012)29 0.0141 (0.005) 0.5309 (0.012)30 0.0065 (0.004) 0.5234 (0.013)31 0.0069 (0.004) 0.5200 (0.013)32 0.0197 (0.007) 0.5164 (0.013)33 0.0112 (0.006) 0.5063 (0.013)34 0.0095 (0.005) 0.5006 (0.013)35 0.0138 (0.007) 0.4958 (0.013)36 0.0111 (0.006) 0.4890 (0.014)37 0.0209 (0.009) 0.4835 (0.014)38 0.0192 (0.010) 0.4734 (0.014)39 0.0056 (0.006) 0.4643 (0.015)40 0.0196 (0.011) 0.4617 (0.015)41 0.0079 (0.008) 0.4527 (0.015)42 0.0100 (0.010) 0.4491 (0.016)
Table 6. Empirical Survival ProbabilitesCharacteristic 1 month 3 months 6 months 12 months 18 monthsPopulation 0.973 0.862 0.730 0.568 0.489Sole Mother 0.977 0.864 0.741 0.597 0.505Sole Father 0.948 0.846 0.643 0.481 0.363
Age31.88 years 0.973 0.850 0.704 0.535 0.470
Not identify as ATSI 0.973 0.863 0.734 0.572 0.491Identifies as ATSI 0.978 0.838 0.654 0.500 0.448
Australian Born 0.974 0.863 0.726 0.556 0.481Foreign Born 0.974 0.867 0.745 0.616 0.522
1 child13years 0.985 0.844 0.683 0.493 0.395Youngest child 5 years old 0.986 0.855 0.682 0.515 0.436
NSW/ACT 0.975 0.871 0.757 0.598 0.536Vic 0.977 0.887 0.765 0.604 0.530Qld 0.969 0.847 0.686 0.519 0.415SA 0.984 0.875 0.752 0.570 0.531WA 0.972 0.849 0.713 0.552 0.466Tas 0.950 0.809 0.630 0.483 0.378
Not home-owner 0.974 0.866 0.732 0.569 0.496Home owner 0.980 0.854 0.733 0.583 0.463Purchasing home 0.981 0.852 0.712 0.552 0.452
Not renting 0.968 0.837 0.703 0.545 0.456Private rent 0.973 0.868 0.732 0.577 0.487Govt. rent 0.973 0.902 0.781 0.595 0.537Board and lodging 0.989 0.870 0.736 0.584 0.532No rent paid 0.978 0.855 0.733 0.546 0.490
Not Receive Child Support 0.976 0.860 0.742 0.579 0.496Received Child Support 0.969 0.868 0.702 0.543 0.472
No Earnnigs 0.975 0.862 0.737 0.584 0.512Positive Earnings 0.970 0.862 0.696 0.498 0.384No Unearnt Income 0.972 0.862 0.733 0.570 0.490Positive Unearnt Income 0.983 0.864 0.713 0.558 0.480
Family Payment$189 per ft 0.983 0.852 0.735 0.566 0.502Basic Payment$311 per ft 0.973 0.864 0.738 0.577 0.502No Rent Assistance 0.963 0.850 0.719 0.556 0.479Received Rent Assistance 0.991 0.880 0.747 0.569 0.505
First Observed Spell 0.963 0.850 0.719 0.556 0.479Repeat Spell 0.970 0.816 0.676 0.518 0.423
Table 7. Duration Model Estimates, SPP SpellsVariable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7Sole Father 0.2411 0.2379 0.2418 0.2423 0.2772 0.2742 0.2790
(0.098) (0.099) (0.100) (0.100) (0.101) (0.101) (0.101)Age (10yrs) 0.0736 0.0849 0.0962 0.0979 0.0964 0.1006 0.1031
(0.055) (0.057) (0.057) (0.057) (0.059) (0.059) (0.059)Children 0.0089 0.0125 0.0083 0.0085 0.0049 0.0136 0.0071
(0.036) (0.037) (0.037) (0.037) (0.037) (0.037) (0.037)Age of Youngest 0.2137 0.2101 0.2043 0.2022 0.1764 0.1779 0.1625
(0.097) (0.097) (0.097) (0.097) (0.098) (0.098) (0.098)Foreign Born 0.1116 0.1085 0.0777 0.0799 0.0650 0.0638 0.0568
(0.085) (0.085) (0.086) (0.086) (0.087) (0.087) (0.087)Identifies as ATSI 0.1777 0.1930 0.1738 0.1719 0.1750 0.1665 0.1728
(0.140) (0.142) (0.150) (0.150) (0.150) (0.149) (0.149)Rent - Govt. -0.1673 -0.1430 -0.1042 -0.1145 -0.1336 -0.1428
(0.124) (0.125) (0.149) (0.150) (0.149) (0.150)Rent- Other 0.0004 0.0092 0.0102 0.0155 0.0169 0.0210
(0.118) (0.118) (0.118) (0.118) (0.118) (0.118)Rent - Paid 0 -0.0110 0.0147 0.0148 0.0325 0.0345 0.0442
(0.125) (0.125) (0.125) (0.124) (0.124) (0.125)Own home -0.0770 -0.0570 -0.0571 -0.0707 -0.0611 -0.0400
(0.108) (0.108) (0.108) (0.109) (0.110) (0.109)Purch. Home 0.0379 0.0386 0.0398 0.0267 0.0435 0.0722
(0.142) (0.142) (0.142) (0.142) (0.144) (0.144)Other Home Owner 0.0445 0.0912 0.0911 0.0841 0.0923 0.0937
(0.203) (0.205) (0.205) (0.210) (0.210) (0.208)Rent/Own Missing 0.3196 0.3043 0.3066 0.3138 0.2950 0.2490
(0.131) (0.132) (0.132) (0.133) (0.133) (0.132)
Vic -0.0295 -0.0407 -0.0364 -0.0405 -0.0298(0.099) (0.101) (0.101) (0.102) (0.102)
Qld 0.2531 0.2431 0.2472 0.2498 0.2453(0.087) (0.089) (0.090) (0.090) (0.090)
SA -0.0001 -0.0142 -0.0143 -0.0102 0.0005(0.145) (0.148) (0.149) (0.148) (0.149)
WA 0.2108 0.1995 0.1926 0.1966 0.2104(0.118) (0.121) (0.121) (0.121) (0.121)
Tas 0.4474 0.4324 0.4325 0.4369 0.4378(0.157) (0.160) (0.160) (0.160) (0.161)
NT 0.2339 0.2261 0.2230 0.3234 0.2952(0.254) (0.255) (0.259) (0.260) (0.256)
NSW*Rent-Govt. -0.11523 -0.11250 -0.11340 -0.12770(0.253) (0.253) (0.253) (0.252)
Earnings>0 0.1744 0.1716 0.1516(0.085) (0.086) (0.086)
Unearnt Inc.>0 -0.0726 -0.0631 -0.0524(0.096) (0.097) (0.097)
ChildSp.>0 0.1103 0.0946 0.0587(0.073) (0.073) (0.074)
Earnings ($100) 0.0585 0.0565(0.033) (0.032)
Unearnt Inc($100) -0.1303 -0.1239(0.074) (0.074)
ChildSp.($100) -0.0368 -0.0395(0.030) (0.030)
Repeat Spell 0.2593(0.076)
Table 8. Duration Model Estimates, SPP SpellsVariable Model 8 Model 9
Sole Father 0.2727 0.2590(0.101) (0.102)
Age (10yrs) 0.0962 0.0800(0.060) (0.060)
Children 0.0187 0.1661(0.037) (0.069)
Age of Youngest 0.1887 0.2474(0.099) (0.102)
Foreign Born 0.0471 0.0407(0.087) (0.087)
Identifies as ATSI 0.0827 0.0977(0.152) (0.152)
Rent - Govt. -0.2962 -0.2698(0.163) (0.163)
Rent- Other -0.0493 -0.0557(0.122) (0.121)
Rent - Paid 0 -0.1138 -0.0949(0.141) (0.141)
Own home -0.2016 -0.1824(0.129) (0.129)
Purch. Home -0.0934 -0.0949(0.158) (0.158)
Other Home Owner -0.0300 -0.0148(0.216) (0.216)
Rent/Own Missing 0.1969 0.1984(0.142) (0.142)
NSW*Rent-Govt. -0.0883 -0.0706(0.252) (0.252)
Earnings>0 0.1671 0.1473(0.086) (0.086)
Unearnt Inc.>0 -0.0570 -0.0573(0.097) (0.097)
ChildSp.>0 0.0937 0.0345(0.073) (0.077)
Earnings ($100) 0.0599 0.0608(0.033) (0.033)
Unearnt Inc($100) -0.1169 -0.1252(0.074) (0.074)
ChildSp.($100) -0.0396 -0.0602(0.030) (0.031)
Received Rem.AA 0.8211 0.8608(0.266) (0.266)
Received Rent Ass. -0.1927 -0.0485(0.094) (0.111)
Max. Total Payments ($100) -0.1381(0.054)
Table 9. Summary Measures of Inequality, 1975-19931975 1984 1988 1993 Change 93-75
Distribution of Gross (Adult-Equivalent) IncomeGini Index 0.2725 0.2685 0.2584 0.2413 -11.45%Atkinson Indices:
=0.5 0.0585 0.0555 0.0508 0.0459 -21.54%=1.0 0.1155 0.1055 0.0988 0.0866 -25.02%=2.0 0.2229 0.1866 0.1819 0.1528 -31.45%
Distribution of (Adult-Equivalent) Non-Durable ExpenditureGini Index 0.2129 0.2289 0.2217 0.2038 -4.27%Atkinson Indices:
=0.5 0.0361 0.0412 0.0376 0.0330 -8.59%=1.0 0.0723 0.0806 0.0743 0.0637 -11.89%=2.0 0.1440 0.1529 0.1425 0.1194 -17.08%
Table 10. Summary Measures of Family Wellbeing, 1975-19931975 1984 1988 1993 Change 93-75
Average (AE) Income 300.95 275.07 275.84 273.94 -8.97%Gini Welfare Index 218.94 201.21 204.56 207.84 -5.07%Atkinson Welfare Indices:
=0.5 283.34 259.80 261.83 261.37 -7.76%=1.0 266.19 246.05 248.59 250.22 -6.00%=2.0 233.87 223.74 225.66 232.08 -0.76%
Average (AE) Non-Dur.Exp. 228.34 246.97 234.59 247.69 8.47%Gini Welfare Index 179.73 190.44 182.58 197.21 9.73%Atkinson Welfare Indices:
=0.5 220.10 236.79 225.77 239.52 8.82%=1.0 211.83 227.06 217.16 231.91 9.48%=2.0 195.46 209.21 201.16 218.12 11.59%
α
α
α
α