The Identification of Incentive Effects of Benefit Exhaustion in Unemployment Insurance Systems

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Socialforskningsinstituttet

The Identification of Incentive Effects of Benefit Exhaustion in Unemployment

Insurance Systems

Lars Pico Geerdsen

Social Integration and Marginalisation Working Paper 25:2002

Working Paper

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The Identification of

Incentive Effects of Benefit Exhaustion in

Unemployment Insurance Systems

Lars Pico Geerdsen

Social Integration and Marginalisation Working Paper 25:2002

The Working Paper Series of The Danish National Institute of Social Research contain interim results of research and preparatory studies. The Working Paper Series provide a basis for professional discussion as part of the research process.

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Escape Rate

Unemployment Duration No UI system

UI system, not eligible

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Hazard out of unemployment

Time on unemployment insurance UI running out Motivation

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zkhuh kf lv wkh edvholqh kd}dug dqg | lv d olqhdu ixqfwlrq ri [1 Lq wkh Fr{ sursruwlrqdo kd}dug wkh edvholqh kd}dug lv ohiw xqvshflhg1 Rqo| wkh sursruwlrqdo hhfwv rq wkh kd}dug ri[ lv hvwlpdwhg1 Wkh dgydqwdjh ri wklv prgho lv wkdw rqh grhv qrw kdyh wr lpsrvh dq dvvxpswlrq ri ixqfwlrqdo irup rq wkh gxudwlrq hhfw1 Li wkh yduldeoh frpsrqhqw ri wkh prgho +|+[|,, lv dvvxphg wr eh olqhdu/ wkhq wkh hhfw ri erwk revhuyhg dqg xqrevhuyhg

(14)

idfwruv rq wkh kd}dug lv frqvwdqw ryhu wkh orj ri wkh kd}dug1 Wklv fdq eh vhhq e| wdnlqj wkh ghulydwlyh ri wkh orj kd}dug/

orjk

{ @ +orjkf+w, .{,

{ @=

Lghqwlfdwlrq ri wkh prwlydwlrq hhfw lq wkhvh prghov lv grqh e| dvvxplqj wkdw dq| glhuhqfhv zh pd| qg lq oderxu pdunhw ehkdylrxu iru lqglylgxdov zkr duh lghqwlfdo rq doo rwkhu revhuydeohv lv doo gxh wr glhuhqfhv lq wlph wr ehqhwv h{kdxvwlrq/ ru lq rwkhu zrugv/ gxh wr wkh prwlydwlrq hhfw dqg qrlvh1 Wklv lv prghoohg e| lqfoxglqj d yduldeoh zklfk ghvfulehv lqglylgxdov* wlph wr ehqhwv h{kdxvwlrq1 Lq htxdwlrq 5 dqg 6 dq h{dpsoh lv jlyhq zlwk wkh orjlvwlf kd}dug prgho dvvxplqj d vlpsoh ixqfwlrqdo irup ri wkh yduldeohv1 Qrwlfh wkdw wkh prwlydwlrq hhfw khuh lv prghoohg e| wkh lqfoxvlrq ri wkh yduldeoh ehqhwv uhpdlqlqj +U, zkhuh wkh sdudphwhu fdswxuhv wkh prwlydwlrq hhfw lq wkh prgho1

k+w> U|> H|> [|, @ 4

4 . h{si|+w> U|> [|,j +5,

| @ .h{s+w, .U|.[|.y|> +6,

615 Lghqwlfdwlrq ri wkh prwlydwlrq hhfw

Lq doo hpslulfdo vwxglhv vr idu wkh prwlydwlrq hhfw lv hvwlpdwhg e| lqfoxglqj d yduldeoh vxfk dv uhpdlqlqj prqwkv2zhhnv ri ehqhwv +U, lq wkh kd}dug prgho1 Hvwlpdwlqj wkh prwlydwlrq hhfw lq wklv zd| srvhv vrph sureohpv zklfk kdv wr eh dgguhvvhg1 Uhpdlqlqj ehqhwv +U, fdq eh ghvfulehg zlwk wkh iroorzlqj dffrxqwlqj htxdwlrq=

U|@H|w.UM|= +7,

KhuhHlv ehqhwv hqwlwohphqw dw wkh ehjlqqlqj ri wkh vshoo/wlv wkh gxudwlrq ri wkh xqhpsor|phqw vshoo dqgUM lv dq| fkdqjhv lq wkh pd{lpxp ehqhwv

(15)

gxudwlrq zklfk lv uhdolvhg e| wkh xqhpsor|hg lqglylgxdo zkloh wkh vshoo jrhv rq1 Wkh yduldwlrq lq uhpdlqlqj ehqhwv +U, zloo doprvw dozd|v frph iurp rqh ru pruh ri wkhvh wkuhh uljkw kdqg vlgh yduldeohv1 D frqvhtxhqfh ri wklv lv wkdw lghqwlfdwlrq ri wkh prwlydwlrq hhfw qhfhvvlwdwhv wkdw dw ohdvw rqh ri wkh wkuhh uljkw kdqg vlgh yduldeohv ghvfulehg deryh kdyh wr eh h{foxghg iurp wkh kd}dug prgho +khqfhiruwk ghqrwhg wkh h{foxvlrq uhvwulfwlrq,1 Li zh gr qrw ohdyh dw ohdvw rqh ri wkh uljkw kdqg vlgh yduldeohv ri htxdwlrq +7, rxw ri wkh kd}dug prgho/ wkh yduldeoh uhpdlqlqj ehqhwv +U, zloo qrw frqwulexwh zlwk dq|wklqj wr wkh kd}dug prgho dqg zloo wkxv qrw eh lghqwlhg1 Krzhyhu/

li zh h{foxgh d yduldeoh iurp wkh kd}dug prgho zklfk grhv kdyh vrph hhfw rq wkh kd}dug rxw ri xqhpsor|phqw/ zh kdyh wkh fodvvlfdo rplwwhg yduldeoh sureohp dv ghvfulehg e| dprqj rwkhuv Khfnpdq dqg Uree +4<;8,1

Ohw ph jlyh d h{dpsoh1 Lq htxdwlrq +8, wkh yduldeoh frpsrqhqw ri wkh orjlvwlf kd}dug prgho +htxdwlrq +4,, lv ghvfulehg1 Qrwlfh wkdw zh kdyh dv0 vxphg wkdw gxudwlrq ri xqhpsor|phqw +w, grhv kdyh dq hhfw rq wkh kd}dug rxw ri xqhpsor|phqw exw lqglylgxdov* lqlwldo hqwlwohphqw +H, lv ohiw rxw1 Li hqwlwohphqw grhv srvvhv h{sodqdwru| srzhu/ wklv yduldeoh zloo dsshdu lq wkh huuru whup/ fi1 htxdwlrq 91 Zh nqrz iurp wkh dffrxqwlqj htxdwlrq +7, deryh wkdw uhpdlqlqj ehqhwv +U, lv d ixqfwlrq ri hqwlwohphqw +H,1 Hvwlpdwlqj wkh prwlydwlrq sdudphwhu zlwkrxw lqfoxglqj hqwlwohphqw zloo uhvxow lq lqfrq0 vlvwhqw hvwlpdwhv vlqfh wkh hvwlpdwru zloo lqfoxgh erwk wkh wuxh ydoxh ri dv zhoo dv wkh sduw ri wkh hhfw iurpH rq wkh kd}dug zklfk lv fruuhodwhg zlwk U1

| @ .h{s+w, .U|.[|.y|> +8,

y| @ orj+H|, .%| +9,

Lq rughu wr dyrlg wkh rplwwhg yduldeoh sureohp zh wkhuhiruh kdyh wr eh

(16)

vxuh wkdw wkh yduldwlrq lq wkh yduldeoh uhpdlqlqj ehqhwv +U, grhv qrw frph iurp vrph yduldeoh zklfk vkrxog kdyh ehhq lqfoxghg lq wkh prgho lq wkh uvw sodfh1 Lq vshfldo fdvhv/ krzhyhu/ lw pd| vwloo eh srvvleoh wr hvwlpdwh wkh prwlydwlrq hhfw hyhq wkrxjk doo wkh uljkw kdqg vlgh yduldeohv ri wkh dffrxqwlqj htxdwlrq +7, duh lqfoxghg lq wkh kd}dug prgho1 Wklv lv srvvleoh li wkh yduldeohv +H/w/ UM, duh prghoohg lq wkh kd}dug prgho zlwk d ixqfwlrqdo irup zklfk ohdyhv vrph h{sodqdwru| srzhu iru wkh uhpdlqlqj ehqhwv yduldeoh +U,1 Ohw ph h{sodlq wklv zlwk dq h{dpsoh1

Ohw xv dvvxph wkdw zh kdyh dffhvv wr sdqho gdwd zkhuh wkhuh lv qr yduld0 wlrq lq lqglylgxdov* hqwlwohphqw +H, ru uhdolvhg mxpsv ryhu wlph +UM,1 Rqo|

wkh gxudwlrq rq ehqhwv fkdqjhv ryhu wlph +w,1 Wklv phdqv wkdw wkh df0 frxqwlqj htxdwlrq iru wkh yduldeoh uhpdlqlqj ehqhwv +U, orrnv olnh

U|@Hw=

Lq rughu wr hqvxuh lghqwlfdwlrq ri wkh prwlydwlrq hhfw +iurp U, zh kdyh wr hlwkhu dvvxph wkdw wkh yduldwlrq wkurxjk wkh gxudwlrq ri xqhpsor|phqw vshoo +w, grhv qrw kdyh dq| vhsdudwh hhfw rq lqglylgxdov* kd}dug +h{foxvlrq uhvwulfwlrq, ru wkdw wklv hhfw iroorz d vshflf ixqfwlrqdo irup nqrzq wr xv sulru wr wkh hvwlpdwlrq1 Dvvxplqj qr vhsdudwh hhfw ri wkh gxudwlrq +w, zrxog lpso| wkdw zh gr qrw eholhyh wkdw wkhuh lv dq| gxudwlrq ghshqghqf|

lq wkh prgho1 D ohvv vwulfw dvvxpswlrq frxog eh wr dvvxph wkdw wkh gxudwlrq ghshqghqf| iroorzv dq h{srqhqwldo irup +h{s+w,, zklfk zh zloo gr lq wklv h{dpsoh1 Ohw xv qrz prgho wkh kd}dug rxw ri xqhpsor|phqw zlwk d glvfuhhw orjlvwlf irup=

k+w> U|> H|> [|, @ 4

4 . h{si|+w> U|> H|> [|,j= Zh fkrrvh wr zulwh wkh yduldeoh frpsrqhqw ri wkh prgho dv

|+w> U|> H|> [|, @.h{s+w, .U|.[|.%=

(17)

Qrwlfh wkh h{srqhqwldo irup ri wkh gxudwlrq frpsrqhqw1 Qh{w vwhs lv wr lqvhuw wkh htxdwlrq +7, iru uhpdlqlqj ehqhwv +U,>

|+w> U|> H|> [|, @.h{s+w, .+Hw, .[|.%=

Exw vlqfhH lv frqvwdqw iru doo lqglylgxdov/ wklv jlyhv=

|+w> U|> H|> [|, @ +.H, .h{s+w,w.[|.% zkhuh wkh prwlydwlrq hhfw lv lghqwlhg wkurxjkw1

7 H{foxvlrq uhvwulfwlrqv xvhg lq hpslulfdo vwxglhv ri wkh prwlydwlrq hhfw

Dv ghvfulehg lq wkh suhylrxv vhfwlrq yduldwlrq lq wkh uhpdlqlqj ehqhwv ydul0 deoh fdq frph iurp wkuhh glhuhqw yduldeohv/ hqwlwohphqw +H,/ gxudwlrq +w, dqg uhdolvhg vkrfnv +UM,1 Glhuhqw vrxufhv ri yduldwlrq lq wkh wkuhh ydul0 deohv kdyh ehhq xvhg lq wkh olwhudwxuh/ fi1 wdeoh 41 Wkh pdlq yduldeoh ri yduldwlrq lv hqwlwohphqw +H,1 Doprvw doo vwxglhv ri wkh prwlydwlrq hhfw⁴ kdyh xvhg yduldwlrq lq hqwlwohphqw lq vrph irup dv d vrxufh ri lghqwlfdwlrq1 Wkh yduldwlrq lq hqwlwohphqw fdq h{lvw iru pdq| glhuhqw uhdvrqv lq gdwd dqg qrw doo duh htxdoo| olnho| wr frpso| zlwk wkh h{foxvlrq uhvwulfwlrq1 D frpprq vrxufh ri yduldwlrq lv glhuhqw XL klvwru| dprqj lqglylgxdov1 Lql0 wldo hqwlwohphqw lv doprvw dozd|v d ixqfwlrq ri lqglylgxdov* hpsor|phqw dqg xqhpsor|phqw klvwru|1 Li gdwd lv vdpsohg zlwkrxw wkh uhtxluhphqw wkdw doo lqglylgxdov vkdoo kdyh jdlqhg ru uhjdlqhg wkh uljkw wr d ixoo ehqhw shulrg/

wkhq riwhq lqglylgxdov kdyh douhdg| xvhg vrph ri wkhlu doorwwhg ehqhwv lq suhylrxv vshoov uhvxowlqj lq glhuhqw hqwlwohphqwv1 Dqrwkhu vrxufh fdq eh uh0 jlrqdo glhuhqfhv lq wkh hqwlwohphqw uxohv1 Ru dv d yduldwlrq/ wkh uxohv fdq eh

4Doo vwxglhv wr p| nqrzohgjh h{fhsw Pr!w +4<;8,1

(18)

Wdeoh 4= Glhuhqw vrxufhv ri yduldwlrq1

Vrxufh ri yduldwlrq

Hqwlwohphqw H 41 Suhylrxv xqhpsor|phqw

51 Uhjlrqdo glhuhqfhv lq ohjlvodwlrq 61 Fkdqjhv lq ohjlvodwlrq ryhu wlph

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Yduldwlrq lq wkh yduldeoh uhdolvhg mxpsv +UM, fdq rffxu li XL ohjlvodwlrq lv fkdqjhg dqg lqglylgxdov ohduq derxw wkh fkdqjhv lq ehqhwv gxudwlrq zkloh wkh| duh xqhpsor|hg1 Li/ iru lqvwdqfh/ wkh ehqhwv gxudwlrq lv vkruwhqhg/

lqglylgxdov kdyh wr uh0hydoxdwh wkhlu h{shfwdwlrqv derxw krz orqj wlph wkh|

kdyh wr ehqhwv h{kdxvwlrq1

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Lq wkh iroorzlqj L zloo jr wkurxjk wkh gdwd xvhg lq prvw vwxglhv dv zhoo

(19)

dv wkh dssolhg h{foxvlrq uhvwulfwlrqv1

Wdeoh 5= Hpslulfdo vwxglhv ri prwlydwlrq hhfw

Vwxg| Gdwd Prgho Vrxufh ri ydu1 lq U H{foxvlrq uhvwulfw1

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suhy1 xqhpso1 suhy1 xqhpso1

w sdudp1gxu1prgho1

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Jhhugvhq +5335, Ghqpdun Orjlvwlf H shu1 vkruw1 shu1 vkruw1 UM shu1 vkruw1 shu1 vkruw1 w

Pr!w +4<;8, Pr!w lv rqh ri wkh uvw wr xvh dgplqlvwudwlyh sdqho gdwd wr dqdo|vh wkh hhfwv ri d XL v|vwhp rq lqglylgxdov* oderxu pdunhw ehkdylrxu1 Wkh gdwd kh xvhv lv XL dgplqlvwudwlyh uhfrugv dvvhpeohg lq d oh fdoohg Frqwlqxrxv Zdjh dqg Ehqhwv Klvwru| +FZEK, froohfwhg e| vwdwh XL r!fhv xqghu wkh vxshuylvlrq ri wkh Ghsduwphqw ri Oderxu lq wkh XV1 Wkh gdwd frqwdlqv lqirupdwlrq rq doo qhz pdoh XL uhflslhqwv lq wkluwhhq vwdwhv lq wkh XV iurp 4<:;04<;3 +ghshqglqj rq wkh vwdwh, wr Pdufk 64/ 4<;61 Vlqfh wkh

(20)

gdwd lv gudzq iurp dgplqlvwudwlyh uhfrugv/ h{dfw lqirupdwlrq lv dydlodeoh rq lqglylgxdov* ehqhwv/ wkhlu ehqhwv hqwlwohphqwv dqg wkh qxpehu ri zhhnv lqglylgxdov froohfw ehqhwv1 Wkh gdwd kdv rqh sureohp zlwk uhjdug wr dqdo|vlv ri prwlydwlrq hhfw1 lqglylgxdov duh qrw iroorzhg diwhu wkhlu ehqhwv uxq rxw1 Lw lv wkhuhiruh qrw srvvleoh wr vhh zkhwkhu lqglylgxdov diwhu ehqhwv h{kdxvwlrq vwd| xqhpsor|hg1

Lq wklv gdwd wkhuh duh vhyhudo vrxufhv ri yduldwlrq exw Pr!w rqo| wdnhv olplwhg xvh ri wkhp1 Iluvw ri doo/ hqwlwohphqw +H, ydulhv ehwzhhq vwdwhv1 Dovr/

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Pr!w qgv iurp Ndsodq0Ph|hu hvwlpdwhv fohdu hylghqfh ri prwlydwlrq hhfwv1 Kh grhv qrw kdyh vxffhvv/ krzhyhu/ wr lghqwli| wkh prwlydwlrq hhfw lq klv sursruwlrqdo kd}dug hvwlpdwhv1 Kh grhv qrw dsso| dq| ri wkh h{foxvlrq uhvwulfwlrqv dv ghvfulehg deryh1

Ph|hu +4<<3, Wkh gdwd xvhg e| Pr!w lv uhxvhg e| Ph|hu +4<<3,1 Ph|hu +4<<3, vwdwhv +rq s1 :96, wkdw wkhuh lv yduldelolw| lq pd{lpxp ehqhwv gx0 udwlrq dfurvv vwdwhv +H,1 Vhfrqg/ ehqhwv zhuh h{whqghg wkurxjk ihghudo surjudpphv lq wkh vdpsoh shulrg1 Wklv pd| erwk uhvxow lq mxpsv lq wkh gxudwlrq ri ehqhwv iru xqhpsor|phqw vshoov wkdw duh douhdg| surjuhvvlqj

(21)

+UM, dv zhoo fkdqjhv lq hqwlwohphqw +H, iru lqglylgxdov zkr ehjlq wkhlu xqhpsor|phqw vshoo diwhu wkh h{whqvlrq ri wkh ihghudo surjudpph1 Odvwo|/

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Urjhuv +4<<;, Urjhuv pdnhv xvh ri wkh vdph gdwd dv xvhg e| erwk Pr!w dqg Ph|hu1 Urjhu*v irfxv lv wr hvwlpdwh dqg whvw glhuhqw prghov iru xq0 hpsor|hg lqglylgxdov* h{shfwdwlrqv uhjduglqj pd{lpxp ehqhwv gxudwlrq1 Urjhu vwdwh wkdw lw pd| eh pruh fruuhfw wr prgho lqglylgxdov* h{shfwdwlrq dv shuihfw iruhvljkw wkdq qr iruhvljkw li lqglylgxdov duh fdsdeoh ri suhglfwlqj wkh fkdqjhv lq ehqhwv gxudwlrq gxh wr ihghudo h{whqvlrqv dqg vkruwhqlqjv ri wkh ehqhwv shulrg zklfk iroorzv wkh xfwxdwlrq ri wkh oderxu pdunhw1 Urjhuv rqo| xvhv iuhvk vshoov zklfk phdqv wkdw glhuhqfhv lq hqwlwohphqw +H, gxh wr suhylrxv xqhpsor|hg lv rplwwhg iurp gdwd1 Ixuwkhupruh/ Urjhuv rqo| xvhv gdwd iurp rqh vwdwh +Shqqv|oydqld, wkhuhe| rplwwlqj lqwhu vwdwh yduldwlrq1 Urjhuv xvhv d 4 shu fhqw vdpsoh ri doo lqglylgxdov ehjlqqlqj dq xqhpsor|phqw vshoo ehwzhhq Mxo| 4<;3 dqg Pdufk 4<;91 Doo wkh vshoov duh iroorzhg xqwlo wkh| hqg1 Urjhuv hqgv xs zlwk wzr vrxufhv ri yduldwlrq/ fi1 wdeoh 51 Wkh uvw lv uhdolvhg mxpsv +UM, lq wkh ehqhwv gxudwlrq gxh wr ihghudo h{whqvlrqv dqg vkruwhqlqjv ri wkh ehqhw shulrg1 Lq wkh shulrg eh0 wzhhq 4<;3 dqg 4<;9 wkh pd{lpxp ehqhw shulrg ydulhv ehwzhhq 59 dqg 98 zhhnv dqg wkhuh duh 44 mxpsv lq wkh pd{lpxp gxudwlrq iru wkh shulrg1 Vhf0 rqgo|/ wkhvh mxpsv lq wkh pd{lpxp gxudwlrq zloo dovr lq lfw rq lqglylgxdov hqwlwohphqw1 Lqghshqghqw ri h{shfwdwlrq prgho/ lqglylgxdov zkr ehjlq wkhlu

(22)

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(23)

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(24)

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(25)

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(26)

Wdeoh 6= Wkh h{foxvlrq uhvwulfwlrqv dssolhg lq wkh irxu glhuhqw prghov

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(27)

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815 Gdwd

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(28)

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(29)

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(30)

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Urjhuv +4<<;, dujxh wkdw wkh fkrlfh ri prgho xvhg wr ghvfuleh lqglylgx0 dov* h{shfwdwlrqv uhjduglqj wlph wr sdvvlyh ehqhwv h{kdxvwlrq pd| kdyh dq lpsdfw rq wkh uhvxowv zkhq wkh prwlydwlrq hhfw lv hvwlpdwhg1 Lq Jhhugvhq +5335, glhuhqw h{shfwdwlrq prghov kdyh ehhq whvwhg rq gdwd1 Wkh prgho zklfk vhhpv wr jlyh wkh ehvw ghvfulswlrq ri lqglylgxdov* h{shfwdwlrqv lv d vsh0 flf yduldqw ri qr iruhvljkw1 Wkh yduldqw lv fdoohg v|vwhp iruhvljkw LL1 Lq wklv prgho lqglylgxdov duh dvvxphg qrw wr nqrz derxw dq| ohjlvodwlyh fkdqjhv ehiruh wkh| duh lpsohphqwhg1 Lq rwkhu zrugv/ lqglylgxdov ljqruh dqqrxqfh0 phqwv ri ohjlvodwlyh fkdqjhv dqg gr rqo| uhdfw wr wkh dfwxdo lpsohphqwdwlrq ri ohjlvodwlyh fkdqjhv1 Lqglylgxdov* h{shfwdwlrqv uhjduglqj uhpdlqlqj sdvvlyh ehqhwv zloo eh prghoohg dffruglqj wr wklv h{shfwdwlrq prgho/ fi1 Jhhugvhq +5335, iru hvwlpdwlrq uhvxowv ri glhuhqw h{shfwdwlrq prghov1

9 Hpslulfdouhvxowv

Lq wdeoh 7 wkh hvwlpdwhg sdudphwhu ydoxhv ri wkh ghprjudsklf yduldeohv duh suhvhqwhg1 Wkh irxu glhuhqw h{foxvlrq uhvwulfwlrq prghov kdyh ehhq dssolhg1 Lw dsshduv wkdw wkh irxu prghov surgxfh uhodwlyho| vlplodu uhvxowv1 Wkh hvwl0 pdwlrq uhvxowv duh jhqhudoo| dv rqh zrxog h{shfw1 Wkh kd}dug rxw ri wkh XL v|vwhp lv orzhu iru vlqjoh lqglylgxdov wkdq iru lqglylgxdov zlwk idplolhv dqg

(31)

Wdeoh 7= Hvwlpdwlrq ydoxhv ri ghprjudsklfv xvlqj wkh irxu gl!huhqw h{fox0 vlrq uhvwulfwlrq prghov

Prgho L Prgho LL Prgho LLL Prgho LY

Vlqjoh qr nlgv 031453; 031453< 0313374 03144:3 +313444, +313444, +313486, +313444, Vlqjoh z1nlgv 031449: 031449; 314484 03144<<

+313488, +313488, +313488, +313488, Idp1z1nlgv 31388< 31388< 314:43 313856 +313433, +313433, +313473, +313433,

Pdoh 3139<3 3139<4 313:39 313:3:

+3133;3, +3133;3, +3133;3, +3133;3,

Sulpdu| 314;95 314;99 313473 314;53

+313536, +313536, +3134;;, +313536,

Yrfdwlrqdo 315856 315858 0314:53 31575:

+3134<<, +3134<<, +31358:, +3134<<, Vkruwhu xqly1 315837 315835 313:;: 3156<3 +313579, +313579, +3134;7, +313579,

Edfkhoru 315:33 315:34 313:95 3158:3

+31357;, +31357;, +313567, +31357<,

Pdvwhu 314:77 314:78 313<95 314958

+31358:, +31358:, +313569, +31358;, Qr hgxf1lqi1 3136<6 3136<; 0314649 3136<9 +31353;, +31353;, +3134<7, +31353<,

(32)

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Lq jxuh 7 wkh sdudphwhu ydoxhv ri wkh gxpplhv iru uhpdlqlqj ehqhwv +U, duh ghvfulehg iru wkh irxu h{foxvlrq uhvwulfwlrq prghov1 Wkh prwlydwlrq hhfw nlfnv lq dsur{lpdwho| 8 prqwkv sulru wr wkh hqg ri sdvvlyh shulrg dqg lqfuhdvhv iurp wkhuh rq1 Wkh shdn lq wkh prwlydwlrq hhfw lv irxqg ; prqwkv lqwr wkh dfwlydwlrq shulrg1 Wkh hhfwv vwduwv zlwk d kd}dug lqfuhdvh vrphzkhuh ehwzhhq 43 dqg 63 shu fhqw dqg shdnv zlwk d kd}dug lqfuhdvh ehwzhhq 443 dqg 473 shu fhqw1 Dw uvw vljkw lw pd| vhhp rgg wkdw wkh prwlydwlrq hhfw grhv qrw shdn ehiruh zhoo lqwr wkh dfwlydwlrq shulrg zklfk lv vxssrvhg wr wkh prwlydwlqj idfwru1 Wkh uhdvrq iru wklv lv wkdw lqglylgx0 dov/ zkhq wkh| hqwhu wkh dfwlydwlrq shulrg/ lq pdq| fdvhv gr qrw hqwhu dq dfwlydwlrq surjudp gluhfwo|1 Iluvw/ wkh| kdyh wr kdyh pdgh dq dfwlrq sodq zklfk lq ghwdlo ghvfulehv wkh dfwlydwlrq surjudpphv zklfk wkh| zloo sduwlf0 lsdwh lq1 Vhfrqgo|/ wkh fdvh zrunhu kdv wr qg dq rshqlqj iru wkh shuvrq1 Wkhvh wklqjv riwhq wdnhv wlph/ dqg lw lv wkhuhiruh prvw olnho| wkdw wkh odujh pdmrulw| ri lqglylgxdov gr qrw idfh frpsxovru| dfwlydwlrq ehiruh dw ohdvw ; prqwk lqwr wkh dfwlydwlrq shulrg1 Lq Jhhugvhq +5335, jxuhv lqglfdwh wkdw lw lv qrw ehiruh 43 prqwkv lqwr wkh dfwlydwlrq shulrg wkdw ixoo dfwlydwlrq kdv ehhq uhdfkhg1

Wkh irxu glhuhqw h{foxvlrq prghov lq jxuh 7 vhhp wr surgxfh uhvxowv zklfk sodfh wkh prghov lq wzr jurxsv1 Prgho L dqg LL surgxfh yhu| vlp0 lodu hvwlpdwlrq uhvxowv zklfk duh vpdoohu wkdq wkh hvwlpdwlrq ydoxhv iurp prgho LLL dqg LY1 Wkh glhuhqfh ehwzhhq prgho L dqg LL dqg prgho LLL dqg LY/ uhvshfwlyho|/ lv wkdw wkh wzr uvw prghov kdyh h{foxghg hqwlwohphqw +H,

(33)

Iljxuh 7= Hvwlpdwlrq uhvxowv ri uhpdlqlqj ehqhwv xvlqj irxu glhuhqw h{0 foxvlrq uhvwulfwlrqv

0,5 0,7 0,9 1,1 1,3 1,5 1,7 1,9 2,1 2,3 2,5

19>R>12 11 9 7 5 3 1 -1 -3 -5 -7 -9 -11 R<-12

Months of passive UI remaining

e(parameter values)

Model I Model II Model III Model IV

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frqvwuxfw lq prgho LY1 Lw lv lqwhuhvwlqj wr qrwh wkdw wkh prgho zlwk wkh

(34)

Iljxuh 8= Hvwlpdwlrq uhvxowv ri gxudwlrq yduldeohv xvlqj wkh irxu glhuhqw h{foxvlrq uhvwulfwlrq prghov1

0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6

2 6 10 14 18 22 26 30 34 38 42 46 50 54

Duration in months

e(parameter values)

Model I Model II Model III Model IV

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Lq jxuh 8 wkh hvwlpdwlrq uhvxowv ri wkh gxudwlrq yduldeoh +w, lv suhvhqwhg iru wkh irxu prghov1 Wkh sdudphwulf irup xvhg lq prgho L jlyhv d uhodwlyho|

jrrg w ri wkh gxudwlrq hhfw xs wr derxw 6; prqwkv lqwr wkh xqhpsor|phqw vshoo1 Wkhuh diwhu wkh hhfw ehfrphv yhu| yrodwloh1 Vwloo/ wkh sdudphwulf irup vhhpv wr fdwfk wkh wuhqg ri wkh gxudwlrq hhfw ryhudoo dqg iurp wkhvh uhvxowv lw grhv vhhp sodxvleoh wkdw d sdudphwulf prghoolqj ri wkh gxudwlrq hhfw lv qrw sureohpdwlf iru wkh hvwlpdwlrq ri wkh prwlydwlrq hhfw1

Lq jxuh 9 wkh hvwlpdwlrq ydoxhv ri wkh hqwlwohphqw yduldeoh +H, lv suh0 vhqwhg1 Wkh sdudphwulf irup ri wklv yduldeoh grhv qrw vhhp wr w dv zhoo dv zlwk wkh gxudwlrq yduldeoh1 Wkh gxpp| ydoxhv uhyhdo d orw ri xfwxdwlrq

(35)

Iljxuh 9= Hvwlpdwlrq uhvxowv ri hqwlwohphqw xvlqj wkh wzr h{foxvlrq uhvwulf0 wlrq prghov zklfk frqglwlrq rq wklv yduldeoh1

0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4

-10 -7 -4 -1 2 5 8 11 14 17 20 23 26 29 32 35 38 41 44

Remaining passive benefits in months

e(parameter values)

Model III Model IV

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: Frqfo xvlrq

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(36)

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41 Dvvxulqj lghqwlfdwlrq e| h{foxglqj hqwlwohphqw iurp wkh kd}dug prgho vhhpv wr eldv wkh hvwlpdwlrq uhvxowv wrzdugv }hur1 Wkhuhe| ulvnlqj wr glvplvv prwlydwlrq hhfwv zkhuh wkh| pljkw h{lvw1

51 Sro|qrpldov ru orj sro|qrpldov dsshdu wr jlyh d vx!flhqwo| h{leoh irup zkhq lw frphv wr prgho gxudwlrq dqg hqwlwohphqw1 Lq fdvhv zkhuh ghjuhhv ri iuhhgrp duh olplwhg lw pd| wkhuhiruh eh d ehwwhu vroxwlrq wr xvh wkhvh sdudphwulf irupv lqvwhdg ri prghoolqj wkh yduldeohv ixoo|

h{leoh zlwk gxpplhv1

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dqg Ph|hu +4<<3, Urjhuv +4<<;,1 Dffruglqj wr wkh hvwlpdwlrq uhvxowv suh0 vhqwhg deryh wklv pd| uhvxow lq xqghu hvwlpdwlrq ri wkh prwlydwlrq hhfw^;1 Lw lv wkhuhiruh qrw xqolnho| wkdw ehqhwv h{kdxvwlrq dfwxdoo| kdv dq hyhq vwurqjhu prwlydwlqj hhfw rq lqglylgxdov* kd}dug rxw ri xqhpsor|phqw wkdq irxqg lq wkhvh vwxglhv1

;Urjhuv +4<<;, rqo| xvhv iuhvk vshoov zklfk phdqv wkdw doo lqglylgxdov kdyh uhjdlqhg wkh uljkw wr d ixoo ehqhwv shulrg zkhq wkh| hqwhu xqhpsor|phqw1 Vwloo/ wkh hqwlwohphqw shulrg fkdqjhv lq wkh vdpsoh shulrg dqg pd| wkhuhiruh lq xhqfh lqglylgxdov* kd}dug rxw ri xqhpsor|phqw1

(37)

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^7` Ghylqh/ Wkhuhvd M1 dqg Qlfkrodv P1 Nlhihu +4<<4, Hpslulfdo Oderu Hfrqrplfv= Wkh Vhdufk Dssurdfk1 R{irug Xqlyhuvlw| Suhvv1 Fkdswhu 51

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\run= Fdpeulgjh Xqlyhuvlw| Suhvv1

(38)

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^43` Od|dug/ Ulfkdug/ Vwhskhq Qlfnhoo dqg Ulfkdug Mdfnpdq +4<<4, Xqhp0 sor|phqw= Pdfurhfrqrplf shuirupdqfh dqg wkh oderxu pdunhw R{irug Xqlyhuvlw| Suhvv/ R{irug1

^44` Pdnl/ G1 dqg ]1 D1 Vslqgohu +4<:8, Wkh hhfwv ri xqhpsor|phqw frp0 shqvdwlrq ri wkh udwh ri xqhpsor|phqw lq Juhdw Eulwdlq R{irug Hfr0 qrplf Sdshuv yro1 5: ss 773087

^45` Ph|hu Euxfh G1 +4<<3, Xqhpsor|phqw lqvxudqfh dqg xqhpsor|phqw vshoov Hfrqrphwulfd/ Yro 8;/ Qr1 7 +mxo|, ss1 :8:0:;51

^46` Pr!ww Urehuw +4<;8, Xqhpsor|phqw lqvxudqfh dqg wkh glvwulexwlrq ri xqhpsor|phqw vshoov Mrxuqdo ri Hfrqrphwulfv 5; ss1 ;804341

^47` Pr!ww/ Urehuw dqg Zdowhu Qlfkrovrq +4<;5, Wkh hhfw ri Xqhpsor|0 phqw Lqvxudqfh rq Xqhpsor|phqw= Wkh Fdvh ri Ihghudo Vxssohphqwdo Ehqhwv Wkh Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ Yro1 971 ss1 4044

^48` Pruwhqvhq/ Gdoh W1 +4<::, Xqhpsor|phqw Lqvxudqfh dqg Mre Vhdufk Ghflvlrqv Lqgxvwuldo dqg Oderu Uhodwlrqv Uhylhz/ Yro1 63/ Lvvxh 7/ ss1 838084:1

^49` Pruwhqvhq/ Gdoh W +4<;9, Mre Vhdufk dqg Oderu Pdunhw Dqdo|vlv lq R1 Dvkhqihowhu dqg U1 Od|dug Kdqgerrn ri Oderu Hfrqrplfv Yroxph LL1 Hovhylhz Vflhqfh Sxeolvkhuv

(39)

^4:` Qlfnhoo V1 M1 +4<:<, Wkh hhfw ri xqhpsor|phqw dqg uhodwhg ehqhwv rq wkh gxudwlrq ri xqhpsor|phqw Wkh hfrqrplf Mrxuqdo ;</ ss 6707<

^4;` Urjhuv/ F|qwkld O1 +4<<;, H{shfwdwlrqv ri Xqhpsor|phqw Lqvxudqfh dqg Xqhpsor|phqw Gxudwlrq Mrxuqdo ri Oderu Hfrqrplfv/ Yro1 49/

Qr1 6/ ss1 96309991

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^53` Wd|oru/ M1 +4<::, D qrwh rq wkh frpsdudwlyh ehkdylrxu ri pdoh dqg ih0 pdoh xqhpsor|phqw udwhv lq wkh Xqlwhg Nlqjgrp/ 4<840:9 Xqlyhuvlw|

ri Odqfdvwhu/ plphr1

(40)

D Hvwlpdwh uhvxowv iurp wkh 7 prghov

Wdeoh 8= Hvwlpdwlrq uhvxowv iurp Prgho L1

Yduldeohv Sdudphwhu Vw1huuru Sdudphwhu Vw1huuru

oq+w, 0416997 31376; U@4 314:97 31387;

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oq+w, 0317<36 3135<3 U@04 316699 31377<

oq+w,^e 3139<3 313376 U@05 315366 313849

4;AUA45 3138:; 3134:6 U@06 315<6: 313873

U@45 313<5< 313744 U@07 315;57 3138<5

U@44 03137:4 31376; U@08 315873 31397<

U@43 313787 313763 U@09 315;<5 3139;<

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U@9 313548 31379: U@043 316975 313<84

U@8 03134<9 3137<9 U@044 3144:9 314453

U@7 313;96 3137;< U@045 0316:;< 31485:

U@6 313897 313858 U?045 3133:6 313<69

U@5 31564; 313844 Frqvwdqw 0413;<< 313548

(41)

Wdeoh 9= Hvwlpdwlrq uhvxowv iurp Prgho LL1

Sdudphwhu Vw1huuru Sdudphwhu Vw1huuru

w5 031896: 31344; w77 041;965 314<<;

w6 03199:4 313464 w78 04199:5 3154<:

w7 031:;6: 313479 w79 0418;8; 315644

w8 031;77< 31348; w7: 04159;6 3157:6

w9 031<6;7 3134:9 w7; 031:79; 315:65

w: 031;;<; 3134;9 w7< 0417979 31645<

w; 04155<3 31354< w83 0416584 316486

w< 0413999 313567 w84 041:497 316;86

w43 041655: 3135:5 w85 041494: 316754

w44 04157<3 3135;4 w86 031;445 316698

w45 04157;8 3135<9 w87 04157:3 3174:;

w46 04165;< 313654 w88 0413<59 317863 w47 0416:86 31367; w89 041<568 31:6;<

w48 0417746 3136:: w8: 05173:9 413598

w49 0418935 313746 4;AUA45 3138;6 3134:6

w4: 041837: 313759 U@45 313<53 313745

w4; 0416;;6 313756 U@44 031383< 31376<

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