Propensity Score Estimates of the Effects of Fertility on Marital Dissolution
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(9) shqghqw rq wkh sduwlflsdwlrq lqwr wuhdwphqw Fl > rqfh rqh frqwurov iru wkh revhuydeoh yduldeohv [l 1 Lq v|perov=. Gl +3, B Fl m[l. +7,. Lw lpsolhv wkdw/ jlyhq [l / wkh qrq0wuhdwhg rxwfrphv duh zkdw wkh wuhdwhg rxwfrphv zrxog kdyh ehhq kdg wkh| qrw ehhq wuhdwhg1 Wklv uxohv rxw wkh srvvlelolw| wkdw yduldeohv rwkhu wkdq [l / rq zklfk wkh dqdo|vw fdqqrw frqglwlrq/ d hfw erwk Gl +3, dqg Fl > l1h1 wkhuh lv qr vhohfwlrq rq xqrevhuydeohv144 Pruhryhu/ lw dvvxphv wkdw S u+Fl @ 3 m [l @ {, A 3 iru doo { zklfk jxdudqwhhv wkdw/ zlwk srvlwlyh suredelolw|/ wkhuh duh xqwuhdwhg frxsohv iru hdfk {145 Iurp wkh suhylrxv wzr dvvxpswlrqv/ lw iroorzv wkdw H +Gl +3, m [l > Fl @ 4, @ H +Gl +3, m [l > Fl @ 3, +vhh Urvhqedxp dqg Uxelq 4<;6 iru pruh ghwdlov,1 Wkh frqglwlrqdo phdq uhvsrqvh ri wkh wuhdwhg xqghu qr wuhdwphqw iru d jlyhq [ fdq wkxv eh hvwlpdwhg e| wkh frqglwlrqdo phdq uhvsrqvh ri wkh xqwuhdwhg xqghu qr wuhdwphqw +wkh whfkqltxh lv vlpso| wr uhsodfh wkh xqrevhuyhg rxwfrphv ri wkh wuhdwhg kdg wkh| qrw ehhq wuhdwhg zlwk wkh rxwfrph ri qrq0sduwlflsdqwv zlwk wkh vdph [l fkdudfwhulvwlfv/ vlqfh wkh| duh vwdwlvwlfdoo| htxlydohqw,1 Lq rwkhu zrugv/ wkh pdwfkhg qrq0wuhdwhg frxsohv duh xvhg wr phdvxuh krz wuhdwhg zrxog kdyh ehkdyhg/ rq dyhudjh/ kdg wkh| qrw ehhq wuhdwhg146. 715. 47. Wkh dyhudjh wuhdwphqw h hfw iru wkh wuhdwhg. Xqghu wkh FLD/ wkh dyhudjh h hfw ri wuhdwphqw rq wkh wuhdwhg fdq eh frpsxwhg dv iroorzv=. Krzhyhu/ vlqfh p| remhfwlyh lv rqo| wkh frqvwuxfwlrq ri wkh frxqwhuidfwxdo . E( Ef f c ' lq htxdwlrq 6c wkh zhdnhu yhuvlrq ri wkh FLD vx!flhv wr lghqwli| wkh DWW1 4 4 Lq rwkhu zrugv/ wkh FLD dvvxphv wkdw rqfh wzr frxsohv zlwk wkh vdph klvwru| lq whupv ri wkhlu revhuydeoh fkdudfwhulvwlfv kdyh ehhq irxqg/ lw lv olnho| wkdw wkh| kdyh wkh vdph klvwru| dovr lq whupv ri wkhlu xqrevhuydeohv1 Frqvhtxhqwo|/ ehlqj fruuhodwhg/ frqwuroolqj iru wkh revhuydeohv lw lv srvvleoh wr frqwuro iru wkh xqrevhuydeohv dw wkh vdph wlph1 4 5 Wklv lpsolhv wr pdwfk frxsohv rqo| ryhu wkh frpprq vxssruw uhjlrq ri [ zkhuh wkh wuhdwhg dqg qrq0wuhdwhg jurxs ryhuods1 Frqvhtxhqwo|/ wkh DWW lv frpsxwhg rqo| iru wkrvh wuhdwhg frxsohv idoolqj zlwklq wkh frpprq vxssruw1 Wkh gudzedfn ri wklv vhohfwlrq lv wkdw li wkh wuhdwphqw h hfw lv khwhurjhqhrxv dfurvv frxsohv/ uhvwulfwlqj wkh vdpsoh ri wuhdwhg wr wkh frpprq vxssruw fdq fkdqjh wkh sdudphwhu hvwlpdwhg1 4 6 Qrwh wkdw xqghu wkh frqglwlrqdo dvvxpswlrq/ lw lv qrw qhfhvvdu| wr pdnh dvvxpswlrqv derxw vshfl f ixqf0 wlrqdo irupv ri rxwfrph htxdwlrqv/ ghflvlrq surfhvv ru glvwulexwlrq ri xqrevhuydeohv1 4 7 Qrwh wkdw wkh FLD lv frqwuryhuvldo ehfdxvh lw lv edvhg rq wkh dvvxpswlrq wkdw wkh frqglwlrqlqj yduldeohv dydlodeoh wr wkh hfrqrphwulfldqv duh vx!flhqwo| ulfk wr mxvwli| dssolfdwlrq ri pdwfklqj1 Lq sduwlfxodu/ wkh FLD uhtxluhv wkdw wkh vhw ri wkh [ *v vkrxog frqwdlq doo wkh yduldeohv wkdw mrlqwo| lq xhqfh wkh rxwfrph zlwk qr0 wuhdwphqw ( Ef dv zhoo dv wkh vhohfwlrq lqwr wkh wuhdwphqw +lw lv fdoohg d gdwd kxqju| lghqwl fdwlrq vwudwhj| e| Khfnpdq hw do1/ 4<<;,1 Wr mxvwli| wkh dvvxpswlrq/ hfrqrphwulfldqv lpsolflwo| pdnh frqmhfwxuhv derxw zkdw yduldeohv hqwhu lq wkh ghflvlrq vhw ri frxsohv/ dqg krz xqrevhuyhg +e| wkh dqdo|vwv, uhohydqw yduldeohv duh uhodwhg wr revhuydeohv1. :.
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(11) phwkrgv ri pdwfklqj, rq wkh edvlv ri wkh hvwlpdwhg surshqvlw| vfruh kdyh ehhq sursrvhg lq wkh olwhudwxuh wr vroyh wklv sureohp +L uhihu wkh uhdghu wr wkh Dsshqgl{ iru d ghwdlohg ghvfulswlrq ri wkh phwkrgv,1 Lq wkh qh{w vhfwlrq/ wkh h{whqvlrq ri wkh pdwfklqj phwkrgrorj| wr wkh pxowlydoxhg wuhdwphqw fdvh lv ghvfulehg1. 8. Hvwlpdwlrq ri wkh dyhudjh fdxvdo h hfw zlwk pxowl0ydoxhg wuhdwphqw. Lpehqv +5333, dqg Ohfkqhu +4<<<, kdyh sursrvhg dq h{whqvlrq ri wkh surshqvlw| vfruh phwkrg0 rorj| wkdw doorzv iru hvwlpdwlrq ri dyhudjh fdxvdo h hfwv zlwk pxowl0ydoxhg wuhdwphqwv1 Wkh nh| lqvljkw ri wklv phwkrg lv wkdw iru hvwlpdwlrq ri dyhudjh fdxvdo h hfwv lw lv qrw qhfhvvdu| wr glylgh wkh srsxodwlrq lqwr vxesrsxodwlrqv zkhuh fdxvdo frpsdulvrqv duh ydolg/ dv wkh surshqvlw| vfruh grhv> lw lv vx!flhqw wr glylgh wkh srsxodwlrq lqwr vxesrsxodwlrqv zkhuh dyhudjh srwhqwldo rxwfrphv fdq eh hvwlpdwhg +Lpehqv/ 5333= :39,1 Khuh lw lv dvvxphg wkdw wkh wuhdwphqw Fl fdq wdnh ydoxhv ehwzhhq 3 dqg N/ l1h1 n @ 3> 4> ===> N1 L dp lqwhuhvwhg lq dyhudjh rxwfrphv/ H iGl +n,j/ iru doo ydoxhv ri n/ dqg lq sduwlfxodu lq gl huhqfhv ri wkh irup H iGl +n, Gl +v,j/ l1h1 wkh dyhudjh fdxvdo h hfw ri h{srvlqj doo xqlwv wr wuhdwphqw n udwkhu wkdq wr wuhdwphqw v1 Wkh nh| dvvxpswlrq/ olnh lq wkh elqdu| fdvh/ lv wkdw dgmxvwlqj iru fryduldwhv vroyhv wkh sureohp ri gudzlqj fdxvdo lqihuhqfhv1 Wklv lv irupdol}hg e| xvlqj d zhdn yhuvlrq ri FLD lq wkh pxowlydoxhg wuhdwphqw fdvh1 Ohw Wl +n, eh wkh lqglfdwru ri uhfhlylqj wkh wuhdwphqw n= Wl +n, @ 4 li Fl @ n @ 3 rwkhuzlvh Wkh zhdn yhuvlrq ri FLD +dovr zhdn xqfrqirxqghgqhvv, vwdwhv wkdw wkh dvvljqphqw wr wuhdw0 phqw Fl lv zhdno| xqfrqirxqghg/ jlyhq wkh fryduldwhv [l li=. Wl +n, B Gl +n, m [l iru doo n @ 3> ===N Zhdn xqfrqirxghgqhvv uhtxluhv rqo| sdluzlvh lqghshqghqfh ri wkh wuhdwphqw zlwk hdfk ri wkh srwhqwldo rxwfrphv1 Ixuwkhupruh/ wkh lqghshqghqfh ri wkh srwhqwldo rxwfrph Gl +n, zlwk wkh wuhdwphqw kdv wr eh rqo| orfdo dw wkh wuhdwphqw ohyho ri lqwhuhvw/ l1h1 zlwk wkh lqglfd0 wru Wl +n, udwkhu wkdq zlwk wkh wuhdwphqw ohyho Fl 1 Wkh lpsruwdqw uhvxow lv wkdw xqghu zhdn xqfrqirxqghgqhvv wkh h{shfwhg ydoxh ri Gl +n, fdq eh hvwlpdwhg/ e| dgmxvwlqj iru [l =. H iGl +n, m [l j @ H iGl +n, m Wl +n, @ 4> [l j @ H iGl m Fl @ n> [l j Wkhq/ wkh dyhudjh rxwfrphv fdq eh hvwlpdwhg e| dyhudjlqj wkh frqglwlrqdo phdqv= H iGl +n,j @ H ^H iGl +n, m [l j` = Vlploduo| wr wkh elqdu| fdvh/ lw fdq eh gl!fxow wr hvwlpdwh H iGl +n,j zkhq wkh glphqvlrq ri [l lv odujh1 Wr vroyh wkh sureohp/ Lpehqv sursrvhv wkh pxowlydoxhg yhuvlrq ri wkh surshqvlw| <.
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(19) Ehfnhu J1V1/ Odqghv H1P1 dqg Plfkdho U1W/ +4<::,/ Dq hfrqrplf dqdo|vlv ri pdulwdo lqvwdelolw|/ Mrxuqdo ri Srolwlfdo Hfrqrp| ;8+4,= 4474044;:1 Ehfnhu J1V1/ +4<<4,> D Wuhdwlvh rq wkh Idplo|> Kduydug Xqlyhuvlw| Suhvv1 Eoxqghoo U1 dqg Frvwd Gldv P1 +5333,/ Hydoxdwlrq Phwkrgv iru Qrq0H{shulphqwdo Gdwd/ plphr XFO Eulhq P1M1/ Oloodug O1D1 dqg Vwhuq V1/ +4<<<,/ Frkdelwdwlrq/ Pduuldjh/ dqg Glyrufh lq d Prgho ri Pdwfk Txdolw|/ plphr/ Xqlyhuvlw| ri Ylujlqld1 Ghkhmld U dqg Zdked V1 +4<<;,/ Surshqvlw| Vfruh Pdwfklqj Phwkrgv iru Qrq0 H{shulphqwdo Fdxvdo Vwxglhv/ QEHU Zrunlqj Sdshu q 9;5< Ghkhmld U dqg Zdked V1 +4<<<,/ Fdxvdo H hfwv lq Qrqh{shulphqwdo Vwxglhv= Uhhydoxdwlqj wkh Hydoxdwlrq ri Wudlqlqj Surjudpv/ MDVD= 438604395 Huplvk M1 dqg Iudqfhvfrql P1 +4<<9,/ Shuwqhuvkls Irupdwlrq dqg Glvvroxwlrq lq Juhdw Eulwdlq/ ZS <9043 ri wkh HVUF/ Frofkhvwhu/ Xqlyhuvlw| ri Hvvh{1 Juhhq Z1K1/ +4<;:,/ Hfrqrphwulf Dqdo|vlv/ 6ug1 hglwlrq/ Suhqwlfh Kdoo1 Khfnpdq M1 dqg Krw} Y1M1 +4<;<,/ Fkrrvlqj Dprqj Dowhuqdwlyh Qrqh{shulphqwdo Phwkrgv iru Hvwlpdwlqj wkh Lpsdfw ri Vrfldo Surjudpv= wkh Fdvh ri Pdqsrzhu Wudlqlqj/ MDVD Ghfhpehu= ;950;;31 Khfnpdq M1/ Lfklpxud K/ dqg Wrgg S1 +4<<;,/ Pdwfklqj dv dq Hfrqrphwulf Hydoxdwlrq Hvwlpdwru / Uhylhz ri Hfrqrplf Vwxglhv 98= 59405<7 Khfnpdq M1/ Lfklpxud K/ dqg Wrgg S1 +4<<:,/ Pdwfklqj dv dq Hfrqrphwulf Hydoxdwlrq Hvwlpdwru= Hylghqfh iurp Hydoxdwlqj d Mre Wudlqlqj Surjudpph/ Uhylhz ri Hfrqrplf Vwxglhv 97= 9380987 Khfnpdq M1/ Lfklpxud K/ Vplwk M1D1/ dqg Wrgg S1 +4<<;,/ Fkdudfwhulvlqj Vhohfwlrq Eldv Xvlqj H{shulphqwdo Gdwd/ Hfrqrphwulfd 991 Nrr K dqg Mdqrzlw} E1/ +4<;6,/ Lqwhuuhodwlrqvkls ehwzhhq ihuwlolw| dqg pdulwdo glvvroxwlrq= uhvxowv ri d vlpxowdqhrxv orjlw prgho / Ghprjudsk| 53 +5,= 45<04781 Lpehqv J1/ +5333,/ Wkh Uroh ri Surshqvlw| Vfruh lq Hvwlpdwlqj Grvh Uhvsrqvh Ixqf0 wlrqv/ Elrphwulnd ;:1 Lpehqv J1/ Uxelq G1E1/ dqg Vdfhugrwh E/ +4<<<,/ Hvwlpdwlqj wkh H hfw ri Xqhduqhg Lqfrph rq Oderu Vxsso|/ Hduqlqjv/ Vdylqjv dqg Frqvxpswlrq= Hylghqfh iurp d Vxuyh| ri Orwwhu| Sod|huv/ QEHU Whfkqlfdo Zrunlqj Sdshu Vhulhv q :3341 Ohfkqhu P1 +5334,/ Surjudp Khwhurjhqhlw| dqg Surshqvlw| Vfruh Pdwfklqj= Dq Dssolfd0 wlrq wr wkh Hydoxdwlrq ri Dfwlyh Oderu Pdunhw Srolflhv/ Xqlyhuvlw| ri Vw Jdoohq/ plphr1. 4:.
(20) Oloodug O1D1 dqg Zdlwh O1M1 +4<<6,/ D Mrlqw Prgho ri Pdulwdo Fklogehdulqj dqg Pdulwdo Glvuxswlrq/ Ghprjudsk| 63= 98609;41 Pdqvnl F1I1/ Vdqghixu J1G1/ PfOdqdkdq V1 dqg Srzhuv G1/ +4<<5,/ Dowhuqdwlyh Hvwlpdwhv ri wkh H hfw ri Idplo| Vwuxfwxuh Gxulqj Dgrohvfhqfh rq Kljk Vfkrro Judgxdwlrq/ MDVD ;:= 5806:1 Rqr K1/ +4<<;,/ Kxvedqgv* dqg Zlyhv* Uhvrxufhv dqg Pdulwdo Glvvroxwlrq/ Mrxuqdo ri Pduuldjh dqg wkh Idplo| 93= 9:709;<1 Shwhuv H1/ +4<;9,/ Pduuldjh dqg Glyrufh= Lqirupdwlrqdo Frqvwudlqwv dqg Sulydwh Frq0 wudfwlqj/ Wkh Dphulfdq Hfrqrplf Uhylhz :9= 76:07871 Urvhqedxp S1U1 dqg Uxelq G1E1/ +4<;6,/ Wkh fhqwudo uroh ri wkh surshqvlw| vfruh lq revhuydwlrqdo vwxglhv iru fdxvdo h hfwv/ Elrphwulnd :3= 740881 / +4<;8d,/ Uhgxflqj Eldv lq Revhuydwlrqdo Vwxglhv Xvlqj wkh Vxefodvvl fdwlrq rq wkh Surshqvlw| Vfruhv/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ yro1:<= 84908571 / +4<;8e,/ Frqvwuxfwlqj d Frqwuro Jurxs Xvlqj Pxowlyduldwh Pdwfkhg Vdpsolqj Phwkrgv wkdw Lqfrusrudwh wkh Surshqvlw|/ Dphulfdq Vwdwlvwlfldq/ yro16<+4,= 6606;1 Uxelq G1 +4<:<,/ Xvlqj Pxowlyduldwh Pdwfkhg Vdpsolqj dqg Uhjuhvvlrq Dgmxvwphqw wr Frqwuro Eldv lq Revhuydwlrq Vwxglhv/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ yro1 :7= 64;065;1 Vldqhvl E1 +5334,/ Dq Hydoxdwlrq ri wkh Dfwlyh Oderu Pdunhw Surjudpv lq Vzhghq/ plphr XFO Wkruqwrq D/ +4<::,/ Fkloguhq dqg pdulwdo vwdelolw|/ Mrxuqdo ri Pduuldjh dqg wkh Idplo| 6<= 86408731 Yxul G1 +5334,/ Ihuwlolw| dqg Glyrufh/ Hxurshdq Xqlyhuvlw| Lqvwlwxwh Zrunlqj Sdshu q 8= Zdlwh O1 dqg Oloodug O1/ +4<<4,/ Fkloguhq dqg pdulwdo glvuxswlrq/ Dphulfdq Mrxuqdo ri Vrflrorj| <9= <630861 Zdlwh O1/ Kdjjvwurp J1 dqg Ndqrxvh G1/ +4<;8,/ Sduhqwkrrg dqg pdulwdo vwdelolw|/ Dphulfdq Vrflrorjlfdo Uhylhz 83= ;8308:1 Zhlvv/ \ dqg Zloolv/ M1U1/ +4<;8,/ Pdwfk Txdolw|/ Qhz Lqirupdwlrq dqg Pdulwdo Glvvrox0 wlrq/ Mrxuqdo ri Oderu Hfrqrplfv 48= V5<60V65<1. < <14. Vwdwlvwlfdo Dsshqgl{ Wkh eorfnlqj hvwlpdwruv. Wkh vwudwd duh fkrvhq vr wkdw wkh edodqflqj surshuw| lv vdwlv hg1 Wkhq/ zlwklq wkhvh eorfnv lqgh{hg e| t/ wkh dyhudjh gl huhqfh lq pdulwdo vwdwxv ehwzhhq wkh wuhdwphqw dqg wkh frqwuro xqlwv lv frpsxwhg= 4;.
(21) S et @ . S. S. Gl Gl l L +t ,>Fl @3 S + , @4 @ S Fl +4 Fl , l L +t , l L +t ,. l5L t >Fl. 5. 5. 5. + , @4 Gl W. S. l5L t >Fl. + , @3 Gl. l5L t >Fl. Qt. QtF. zkhuh QtW dqg QtF duh wkh qxpehuv ri wuhdwhg dqg frqwurov lq eorfn t/ dqg L +t, lv wkh lqglfdwru ixqfwlrq iru wkh zrpdq l ehlqj lq wkh eorfn t> wkhq/ lq rughu wr h{whqg wklv uhvxow wr wkh hqwluh srsxodwlrq ri wuhdwhg/ wkh zhljkwhg dyhudjh ri wkhvh gl huhqfhv lv frpsxwhg=. e @ mFl @4. S T [ Fl l5L +t , e t S Fl ;l t @4. zkhuh wkh zhljkwv lq hdfk vwudwxp duh wkh iudfwlrq ri wuhdwhg xqlwv lq hdfk eorfn1 Wkh vwdqgdug huuruv iru wklv hvwlpdwru uhsruwhg lq wdeohv 90; kdyh ehhq frpsxwhg e| errw0vwudsslqj zlwk 533 uhshwlwlrqv1 Dq dowhuqdwlyh lv d olqhdu uhjuhvvlrq ru fryduldqfh dgmxvwphqw whfkqltxhv zlwklq hdfk eorfn1 Lq wklv fdvh/ wkh wuhdwphqw h hfw t lv rewdlqhg e| uhjuhvvlqj Gl rq wkh wuhdwphqw lqglfdwru ri ihuwlolw| dqg rwkhu fryduldwhv zlwklq hdfk eorfn/ dqg wkhq frpsxwlqj d zhljkwhg dyhudjh h{dfwo| dv rxwolqhg ehiruh +wkh zhljkwv duh lghqwlfdo,=Wkh dgydqwdjh ri wkh uhjuhvvlrq lq pdwfklqj lv wkdw frqwuroolqj djdlq rq wkh fryduldwhv [l vkrxog khos wr holplqdwh wkh uhpdlqlqj zlwklq eorfn0gl huhqfhv/ dowkrxjk wkh uhvxowv vkrxog qr fkdqjh zkhq wkh fryduldwhv duh zhoo edodqfhg1. <15. Wkh pdwfklqj hvwlpdwru. Lq wkh qhduhvw0pdwfk phwkrg/ hdfk wuhdwhg xqlw lv pdwfkhg wr wkh frqwuro xqlw+v, zlwk wkh forvhvw surshqvlw| vfruh1 Lq v|perov/ wkh wuhdwhg zrpdq l lv pdwfkhg wr wkdw qrq0wuhdwhg zrpdq m vxfk wkdw=. s +[l , s +[m , @. plq. n5iFl. @3. j. im s +[l , s +[n , mj. Qrqh ri wkh wuhdwhg zrphq lv glvfdughg lq wkh qhduhvw0pdwfk phwkrg ehfdxvh lw lv dozd|v srvvleoh wr qg d pdwfkhg frqwuro hyhq li lw lv idu dzd| iurp wkh wuhdwhg zrpdq1 Wkh udglxv phwkrg ri pdwfklqj frqvlvwv lq pdwfklqj hdfk wuhdwhg wr wkh frqwuro zrphq zkrvh surshqvlw| vfruh lv zlwklq d udglxv fkrvhq e| wkh uhvhdufkhu1 Lq v|perov=. A s +[l , s +[m , @. plq. n5iFl. @3. j. im s +[l , s +[n , mj. Li d wuhdwhg xqlw kdv qr frqwuro frxsohv zlwklq d udglxv/ wklv xqlw lv glvfdughg1 Khqfh/ vzlwfklqj iurp wkh qhduhvw0pdwfk wr wkh udglxv pdwfk rqh lpsuryhv wkh txdolw| ri wkh pdwfkhv exw hqgv xs xvlqj ohvv revhuydwlrqv dqg wkxv jhqhudwh ohvv suhflvh hvwlpdwhv1 Wkh dyhudjh gl huhqfh lq pdulwdo rxwfrphv ri wkh vxe0jurxs ri wuhdwhg dqg wkh vxe0jurxs ri pdwfkhg frpsdulvrqv lv xvhg wr fdofxodwh wkh h hfw ri kdylqj fkloguhq yhuvxv qrw kdylqj fkloguhq. 4<.
(22) rq pdulwdo glvvroxwlrq1 Irupdoo|/ wkh pdwfklqj hvwlpdwru lv= % & [ [ P 4 e @ W Gl $F mFl @4 l Gl Q l5 W. +:,. l5 F. zkhuh W dqg F ghqrwh wkh vhwv ri wuhdwhg dqg pdwfkhg frqwuro xqlwv uhvshfwlyho| dqg $ F l lv wkh qxpehu ri wlphv d sduwlfxodu frqwuro l 5 F lv xvhg lq wkh pdwfklqj zlwk d wuhdwhg xqlw= Wkhuhiruh/ wkh dyhudjh wuhdwphqw h hfw lv vlpso| jlyhq e| wkh dyhudjh ri wkh rxwfrph lq fdvh ri wuhdwphqw plqxv wkh zhljkwhg dyhudjh ri wkh rxwfrph lq fdvh ri qr wuhdwphqw/ zlwk dssursuldwh zhljkwv iru uhshdwhg revhuydwlrqv158 Wkh vwdqgdug huuru iru wklv hvwlpdwru uhsruwhg lq wdeohv 90; kdyh ehhq frpsxwhg e| errw0vwudsslqj zlwk 533 uhshwlwlrqv1 Dv iru wkh vwudwl fdwlrq hvwlpdwru/ dq dowhuqdwlyh lv wr uhjuhvv/ ryhu wkh vdpsoh ri sdluv/ wkh glyrufh rxwfrph rq wkh wuhdwphqw lqglfdwru ri ihuwlolw| dqg wkh fryduldwhv/ zlwk dssursuldwh zhljkwv iru uhshdwhg xqlwv +wkh orjlf iru frpsxwlqj wkh zhljkwv lv wkh vdph dv ghvfulehg deryh,1 Qrwh wkdw/ zkloh lq wkh vwudwl fdwlrq phwkrg wkh uhjuhvvlrq zdv vlpso| dq ROV hvwlpdwlrq zlwklq eorfnv/ lq wkh pdwfklqj phwkrg d zhljkwhg ohdvw vtxduh uhjuhvvlrq +ZOV, lv shuiruphg/ zkhuh wkh zhljkwv duh rqh iru wkh wuhdwhg dqg wkh qxpehu ri wlphv hdfk frqwuro xqlwv lv xvhg lq wkh pdwfklqj iru wkh frqwurov +vhh htxdwlrq +:,,1. Qrwh wkdw A lv htxdo wr wkh qxpehu ri doo wuhdwhg xqlwv lq wkh qhduhvw pdwfk phwkrgv/ dqg wr wkh qxpehu ri wkh wuhdwhg xqlwv iru zkrp dw ohdvw rqh pdwfkhg frqwuro frxog eh irxqg lq wkh udglxv phwkrg1 58. 53.
(23) Wdeoh 4= Ghvfulswlyh vwdwlvwlfv ri revhuydeoh fryduldwhv iru doo wkh zrphq+vdpsoh vl}h 58<47, Yduldeoh. Doo zrphq phdq. vw1ghy. glyrufh udwh. 314;. 316;. & fkloguhq 304;. 4144. 4154. & fkloguhq 309. 3175. 31:9. & fkloguhq 904;. 418<. 417:. kdylqj fkloguhq 304;. 3188. 317<. kdylqj fkloguhq 309. 315:. 3177. kdylqj fkloguhq 904;. 315;. 3178. Gxudwlrq ri pduuldjh. 4:18. 4516. Qr Glsorpd. 3145. 3166. Vrph Vfkrrolqj. 3196. 317;. Ghjuhh ru pruh. 3157. 3176. Rxw ri Zhgorfn eluwk. 3155. 3174. Djh dw pduuldjh. 5514. 713;. Zklwh. 31;7. 3169. Eodfn. 313<. 315;. Rwkhuv. 313:. 3159. Klvsdqlf ruljlq. 313;. 315:. Gdwd ohjhqg= Wkh wkuhh yduldeohv %Qxpehu ri fkloguhq ehwzhhq 304;/ 309 dqg 904;% udqjh iurp 3 wr 8 zkhuh 8 phdqv kdylqj yh ru pruh wkdq yh fkloguhq> Gxudwlrq= gxudwlrq ri wkh pduuldjh> Kljkhvw ohyho ri hgxfdwlrq udqjlqj iurp 64 +ohvv wkdq 4vw judgh, wr 79 +Grfwrudwh ghjuhh, kdv ehhq glylghg lqwr wkuhh gxpplhv= Qr Glsorpd +iurp 64 %Ohvv wkdq 4vw Judgh% wr 6;, %45wk Judgh Qr Glsorpd%/ Vrph Vfkrrolqj +iurp 6< %JHG% wr 75 %Dvvrfldwh Ghj%, dqg Ghjuhh ru pruh+iurp 76 %Edfkhoru% wr 79 %SkG%, > Zklwh= 4 li zrpdq ri zklwh udfh> Eodfn= 4 li zrpdq ri eodfn udfh> Rwkhuv= 4 iru doo rwkhuv udfh> Rxw ri Zhgorfn eluwk@4 li uvw fklog zdv eruq ehiruh pduuldjh> klvsdqlf= 4 li Klvsdqlf ruljlq1. 54.
(24) Wdeoh 5= Ghvfulswlyh vwdwlvwlfv ri revhuydeoh fryduldwhv e| fkloguhq djhg 304;/ 309 dqg 904;1 Yduldeoh. nlgv 304;. qr nlgv304;. nlgv 309. qr nlgv 309. nlgv 904;. qr nlgv 904;. glyrufh udwh. 3153 +317,. 3149+316:,. 3153+317,. 314:+316:,. 314<+316<,. 314;+316;,. ^:16;` Gxudwlrq. 46157+:1:,. 551<9+471:,. ^91;` ;16+813,. ^9;17` Ghjuhh ru pruh. 3157+3176,. 3156+3175,. 3197+318,. 3196+318,. 315:+3177,. 3144+3165,. 3146+3167,. 3195+317;,. 5514+816,. 5515+816,. 3144+3165,. 315:+317,. 3147+316,. 5517+715,. 31;6+317,. 31;8+316,. 315:+3177,. 313<+316,. 313;+316,. 31;6+316:,. 313;+3159,. 3139+3157,. 313;+315:,. 313<+316,. 3139+315,. 5513+813, 314<+316<, 31;9+3169, 313<+315;,. 313;+315:,. 3139+3157,. 541;+717,. ^4419`. 3139+3158, ^451<`. 551;+71<, ^91:`. 3159+177,. 314<+317, ^4419`. 31;6+16:,. 31;7+3169, ^519`. 313<+315<,. 313;+315;, ^51<`. 313:+3158,. ^81:` 3144+3164,. 3146+3166, ^618`. ^419`. ^819` Klvsdqlf. 3144+3164,. ^51:`. ^414` Rwkhu. 3145+3166,. 3195+317;, ^71;`. ^4814`. ^71;` Eodfn. 3198+17:,. ^917`. ^5717` Zklwh. 3197+317;,. 3157+3176, ^51:;`. ^415`. ^315<` Rxw ri Zhgorfn. 3156+3175,. ^613:`. ^716` Djh dw pduuldjh. 3156+3175,. 4:15+4:14, ^71<`. ^717`. ^419` Qr Glsorpd. 4;14+4:1<,. ^;716`. ^417;` Vrph vfkrrolqj. 541;+4517,. ^416`. 313:+3159, ^318`. 313;+315:,. 313;+315:, ^3137`. Qrwhv= Vwdqgdug ghyldwlrq lq sduhqwkhvhv1 Lq vtxduh eudnhwv/ wkh w0vwdwlvwlfv ri wkh gl huhqfh lq phdqv ehwzhhq zrphq zlwk dqg zlwkrxw fkloguhq lq wkh wkuhh udqjh jurxsv= 304;/ 309 dqg 904;. 55.
(25) Wdeoh 6= Sdudphwulf Hvwlpdwhv ri wkh h hfw ri gl huhqw phdvxuhv ri ihuwlolw| rq pdulwdo glvvroxwlrq. kdylqj fkloguhq 304; +4,elqdu| wuhdwphqw. kdylqj fkloguhq 309. d. kdylqj fkloguhq 904; & fkloguhq 304; +5, pxowl0ydoxhg wuhdwphqw. e. & fkloguhq 309 & fkloguhq 904;. ROV. Surelw. +4,. +5,. 031457. 0313;;. +3133:,. +3133:,. 03145<. 031456. +31339,. +31339,. 31344. 31374. +31338,. +31338,. 031348. 031338. +31335,. +31335,. 03136;. 031373. +31336,. +31336,. 31358. 31366. +31335,. +31335,. Qrwhv= Lq froxpq 5 +surelw, pdujlqdo h hfwv duh uhsruwhg 1 d Ohdvw vtxduh uhjuhvvlrq= pdulwdo glvvroxwlrq gxpp| rq d frvwdqw/ d ihuwlolw| wuhdwphqw lqglfdwru/ gxudwlrq ri pduuldjh/ djh dw pduuldjh/ wzr gxpplhv iru hgxfdwlrq/ eodfn gxpp|/ rwkhu udfh gxpp|/ klvsdqlf ruljlq gxpp|/ rxw ri zhgorfn gxpp|1 e Ohdvw vtxduh uhjuhvvlrq= glyrufh gxpp| rq d ihuwlolw| pxowl0ydoxhg wuhdwphqw lqglfdwru dqg rq wkh vdph fryduldwhv dv lq d 1. 56.
(26) Wdeoh 7= Surshqvlw| vfruh hvwlpdwhv ri wkh h hfw ri wkh suhvhqfh ri fkloguhq ehwzhhq 3 dqg 4; |hduv rog/ ehwzhhq 3 dqg 9 |hduv rog/ dqg ehwzhhq 9 dqg 4; |hduv rog rq pdulwdo glvvroxwlrq +DWW, Kdylqj fkloguhq. Kdylqj fkloguhq. Kdylqj fkloguhq. 304;. 309. 904;. 0313;;. 031435. 31339. +31366,. +3137,. +31337,. 031466. 031488. 3134:. +3133;,. +3133:,. +31339,. 03136<. 0313<6. 0313348. +31338,. +3133:,. +3133:,. 03137;. 0313;8. 0313353. +31337,. +3133:,. +31339,. 031398. 0313;6. 0313344. +31338,. +3133;,. +3133:,. Vwudwl fdwlrq= edvhg rq txlqwlohv Pdwfklqj= Qhduhvw Pdwfk Udglxv= ?313334 Udglxv= ?313338 Udglxv= ?31334. Qrwhv= Frh!flhqwv rq wkh elqdu| yduldeohv Kdylqj fkloguhq ehwzhhq 3 dqg 4; |hduv rog/ Kdylqj fkloguhq ehwzhhq 3 dqg 9 |hduv rogdqg Kdylqj fkloguhq ehwzhhq 9 dqg 4; |hduv rog duh uhsruwhg1 Errw0vwudsshg vwdqgdug huuruv lq sduhqwkhvhv1 Surshqvlw| vfruhv duh hvwlpdwhg xvlqj wkh surelw prgho/ zlwk wkh iroorzlqj vshfl fdwlrq= Su+Fl @4,@I+pdulwdo gxudwlrq/ djh dw pduuldjh/ 5 gxpplhv iru hgxfdwlrq/ eodfn udfh gxpp| /rwkhu udfh gxpp|/ klvsdqlf ruljlq gxpp|/ rxw ri zhgorfn eluwk. 57.
(27) Wdeoh 8= Surshqvlw| vfruh hvwlpdwhv ri wkh h hfw ri qxpehu ri fkloguhq djhg 304;/ djhg 309 dqg djhg 904; rq pdulwdo glvvroxwlrq Iurp 3 wr 4 fklog Iurp 4 wr 5 fkloguhq Iurp 5 wr 6 fkloguhq Iurp 6 wr 7 fkloguhq Iurp 7 wr 8+., fkloguhq Dyhudjh h hfw. & fkloguhq 304;. & fkloguhq 309d. & fkloguhq 904;. 3136. 31457. 31335. +31338,. +31339,. +31339,. 031335. 031389. 31344. +31334,. +31334,. +31339,. 31346. 03139:. 31336. +313335,. +31336,. +31338,. 31337. 0313;;. 31339. +31334,. +31336,. +31335,. 031334. 0. 3133<. +31334,. 0. +31336,. 31345. 3138. 3133:. +31335,. +31336,. +31335,. Qrwh= Errwvwudsshg vwdqgdug huuruv lq sduhqwkhvhv1 Wkh fryduldwhv [ lqfoxghg lq wkh uhjuhvvlrq duh wkh vdph olvwhg lq wdeoh 61 @ Iru wkh wuhdwphqw %qxpehu ri fkloguhq djhg 309%/ wkh pd{lpxp qxpehu ri fkloguhq frqvlghuhg lv 7 ru pruh wkdq 71 Iru wkh wuhdwphqwv %qxpehu ri fkloguhq djhg 304;% dqg %qxpehu ri fkloguhq djhg 904;%/ wkh pd{lpxp qxpehu ri fkloguhq frqvlghuhg lv 8 ru pruh wkdq 81. 58.
(28) Histogram of the Estimated Propensity Score for the Treated and the Controls (having children aged 0-18) 2500. 2000. 1500. 1000. 500. 0. 81. 40 0. 40. 5 0. 50. 6 0. 60. 7 0. 70. 8. 35 0. 35. -0 .. 30 0. 30. -0 .. 20 0. 20. -0 .. 15. -0 .. -0 .. 0. 15. 0. 00. 0. 10. 00. 00. 5 50. 10. 0. TREATED CONTROLS. Estimated p(x). Histogram of the Estimated Propensity Score for the Treated and the Controls (having the youngest children aged between 0-6 years) 3000 2500 2000 1500 1000 500. 00. 0.0 00 05 50. 0.1 10 0 0. 0.2 20 0 0. 0.3 30 0 0. 0.4 40 0 -0 .5 0. 0 50 0. .6 50 0. .6 60 0. .8 80. 0.9 90. 9 0. 5 95 -1. 0 TREATED CONTROLS. Estimated p(x). Histogram of the Estimated Propensity Score for the Treated and the Controls (having the youngest child aged 6-18) 4500 4000 3500 3000 2500 2000 1500 1000 500. 6. 8. 9. 0. 60.. 0. 80.. 0. 91. 5 -0 .. 0. 50.. 0. 45. 45 0. 40.. 4 -0 . 0. 35. 35 -0 .. 30 0. 30. 0. 20. -0 .. 20. 0. 15. -0 .. 15 -0 .. 0. 10. 5 00. 00. 0. 00. 50. 10. 0 TREATED CONTROLS. Estimated p(x).
(29)
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