ah�jy8fRyy9 @ *H�bb N

P+iQ#2` Ry- kyRN

hQ/�vǶb *H�bb

! .2bB;M Q7 �M Q#b2`p�iBQM�H bim/v p2`bmb 2tT2`BK2Mi! J�BKQMB/2bǶ `mH2 U�M 2t�KTH2 Q7 � M�im`�H 2tT2`BK2MiV! AMi`Q/m+iBQM iQ i?2 T`QT2MbBiv b+Q`2

h?2 /2bB;M T?�b2 Q7 �M Q#b2`p�iBQM�H bim/v

:QQ/ Q#b2`p�iBQM�H bim/B2b �`2 /2bB;M2/X

�M Q#b2`p�iBQM�H bim/v b?QmH/ #2 +QM+2Tim�HBx2/ �b � #`QF2M`�M/QKBx2/ 2tT2`BK2Mi Ę BM �M Q#b2`p�iBQM�H bim/v r2 pB2r i?2Q#b2`p2/ /�i� �b ?�pBM; �`Bb2M 7`QK � ?vTQi?2iB+�H +QKTH2t`�M/QKBx2/ 2tT2`BK2Mi rBi? � HQbi `mH2 7Q` i?2 (�bbB;MK2MiK2+?�MBbK)- r?Qb2 p�Hm2b r2 rBHH i`v iQ `2+QMbi`m+iX _m#BM UkyydV

h?2 /2bB;M T?�b2 Q7 �M Q#b2`p�iBQM�H bim/v

P7 +`BiB+�H BKTQ`i�M+2- BM `�M/QKBx2/ 2tT2`BK2Mib i?2 /2bB;M T?�b2i�F2b TH�+2 T`BQ` iQ b22BM; �Mv Qmi+QK2 /�i�X �M/ i?Bb +`BiB+�H 72�im`2Q7 `�M/QKBx2/ 2tT2`BK2Mib +�M #2 /mTHB+�i2/ BM Q#b2`p�iBQM�H bim/B2b-7Q` 2t�KTH2- mbBM; T`QT2MbBiv b+Q`2 K2i?Q/b- �M/ r2 b?QmH/Q#D2+iBp2Hv �TT`QtBK�i2- Q` �ii2KTi iQ `2THB+�i2- � `�M/QKBx2/2tT2`BK2Mi r?2M /2bB;MBM; �M Q#b2`p�iBQM�H bim/vX _m#BM UkyydV

Reconstruct the assignment mechanism .

GQQFBM; 7Q` *�mb�H h`2�iK2Mi 1z2+ib

! *QKT�`2 bm`pBp�H BM T�iB2Mib r?Q �`2 i`2�i2/ rBi? � /`m; i?2`�Tv p2`bmbbm`;2`v BM � `�M/QKBx2/ +QMi`QH i`B�HX

! A7 T�iB2Mib i?�i mM/2`;Q bm`;2`v HBp2 3 v2�`b �M/ T�iB2Mib i?�i i�F2 /`m;i?2`�Tv HBp2 8 v2�`b i?2M i?2 i`2�iK2Mi 2z2+i Bb 3@84jX

P#b2`p�iBQM�H p2`bmb _�M/QKBx2/ aim/B2b

! AM Q#b2`p�iBQM�H bim/B2b i?2 `2b2�`+?2` /Q2b MQi `�M/QKHv �HHQ+�i2 i?2i`2�iK2MibX

! _�M/QKBx�iBQM 2Mbm`2b bm#D2+ib `2+2BpBM; /Bz2`2Mi i`2�iK2Mib �`2+QKT�`�#H2X

P#b2`p�iBQM�H aim/B2b

! amTTQb2 i?�i r2 ?�p2 �M Qmi+QK2 K2�bm`2/ QM irQ ;`QmTb Q7 bm#D2+ibUi`2�i2/ �M/ +QMi`QHVX

! q2 r�Mi iQ K�F2 � 7�B` +QKT�`BbQM #2ir22M i?2 i`2�i2/ ;`QmT �M/ i?2+QMi`QH ;`QmT BM i2`Kb Q7 i?2 Qmi+QK2X

! q2 +�M Q#i�BM +Qp�`B�i2b i?�i /2b+`B#2 i?2 bm#D2+ib #27Q`2 i?2v `2+2Bp2/i`2�iK2Mib- #mi r2 +�MǶi 2Mbm`2 i?�i i?2 ;`QmTb rBHH #2 +QKT�`�#H2 BMi2`Kb Q7 i?2 +Qp�`B�i2bX

AKTQ`i�M+2 Q7 _�M/QKBx�iBQM

! _�M/QKBx�iBQM i2M/b iQ T`Q/m+2 `2H�iBp2Hv +QKT�`�#H2 Q` dz#�H�M+2/Ǵi`2�iK2Mi ;`QmTb BM H�`;2 2tT2`BK2MibX

! h?2 +Qp�`B�i2b �`2MǶi mb2/ BM �bbB;MBM; i`2�iK2Mib BM �M 2tT2`BK2MiX! h?2`2Ƕb MQ /2HB#2`�i2 #�H�M+BM; Q7 i?2 +Qp�`B�i2b Ĝ BiǶb Dmbi � MB+2 72�im`2

Q7 `�M/QKBx�iBQMX! q2 ?�p2 bQK2 `2�bQM iQ ?QT2 �M/ 2tT2+i i?�i Qi?2` UmMK2�bm`2/V

p�`B�#H2b rBHH #2 #�H�M+2/- �b r2HHX

aKQFBM; +2bb�iBQM �M/ r2B;?i ;�BM

q?�i Bb i?2 2z2+i Q7 bKQFBM; QM r2B;?i ;�BM\

! .�i� r�b mb2/ 7`QK h?2 L�iBQM�H >2�Hi? �M/ Lmi`BiBQM 1t�KBM�iBQMam`p2v .�i� A 1TB/2KBQHQ;B+�H 6QHHQr@mT aim/v UL>1a6aV bm`p2v iQ�bb2bb i?Bb [m2biBQMX

! h?2 L>1a6a ?�b BM7Q`K�iBQM QM b2t- `�+2- r2B;?i- ?2B;?i- 2/m+�iBQM-�H+Q?QH mb2- �M/ BMi2MbBiv Q7 bKQFBM; �i #�b2HBM2 URNdR@d8V �M/ 7QHHQr@mTURN3kV pBbBibX

! h?2 bm`p2v r�b /2bB;M2/ iQ BMp2biB;�i2 i?2 `2H�iBQMb?BTb #2ir22M +HBMB+�H-Mmi`BiBQM�H- �M/ #2?�pBQ`�H 7�+iQ`bX

! � +Q?Q`i Q7 T2`bQMb k8@d9 r?Q +QKTH2i2/ � K2/B+�H 2t�K BM RNdR@d87QHHQr2/ #v � b2`B2b Q7 7QHHQr@mT bim/B2bX

! qQmH/ Bi #2 TQbbB#H2 iQ +QM/m+i � `�M/QKBx2/ bim/v iQ 2p�Hm�i2 i?2i`2�iK2Mi 2z2+i\

✓ [- r - r r

✓ I

Unethical to conduct a randomized study

of Smoking -

aKQFBM; +2bb�iBQM �M/ r2B;?i ;�BM

*2bb�iBQM U�4RV LQ +2bb�iBQM U�4yV�;2- v2�`b 9eXk 9kX3K2M- W 89Xe 9eXer?Bi2- W NRXR 38X9mMBp2`bBiv- W R8X9 NXNr2B;?i- F; dkX9 dyXj*B;�`2ii2bf/�v R3Xe kRXkv2�` bKQFBM; keXy k9XRHBiiH2fMQ 2t2`+Bb2- W 9yXd jdXNBM�+iBp2 /�BHv HB72- W RRXk 3XN

Baselinetable -

i .e

,at beginning of

{" " snareStoy .ae .

(Check

.myCov aviate balance .

Covariate.

Check to see if balanced .

J�BKQMB/2bǶ _mH2

! �M;`Bbi �M/ G�pv URNNNV Tm#HBb?2/ �M mMmbm�H bim/v Q7 i?2 2z2+ib Q7 +H�bbbBx2 QM �+�/2KB+ �+?B2p2K2MiX

! *�mb�H 2z2+ib Q7 +H�bb bBx2 QM TmTBH �+?B2p2K2Mi Bb /B{+mHi iQ K2�bm`2X! h?2 ir2H7i? +2Mim`v _�##BMB+ b+?QH�` J�BKQMB/2b BMi2`T`2i2/ i?2 i?2

h�HKm/Ƕb /Bb+mbbBQM Q7 +H�bb bBx2 �b,

dzhr2Miv@}p2 +?BH/`2M K�v #2 Tmi BM +?�`;2 Q7 QM2 i2�+?2`X A7 i?2MmK#2` BM i?2 +H�bb 2t+22/b ir2Miv@}p2 #mi Bb MQi KQ`2 i?�M 7Q`iv- ?2b?QmH/ ?�p2 �M �bbBbi�Mi iQ ?2HT rBi? BMbi`m+iBQMX A7 i?2`2 �`2 KQ`2i?�M 7Q`iv- irQ i2�+?2`b Kmbi #2 �TTQBMi2/XǴ

J�BKQMB/2bǶ _mH2

! aBM+2 RNeN Bi ?�b #22M mb2/ iQ /2i2`KBM2 i?2 /BpBbBQM Q7 2M`QHK2Mi +Q?Q`ibBMiQ +H�bb2b BM Ab`�2HB Tm#HB+ b+?QQHbX

! *H�bb bBx2 Bb mbm�HHv /2i2`KBM2/ #v �|m2M+2 Q` TQp2`iv Q7 � +QKKmMBiv-2Mi?mbB�bK Q` bF2TiB+BbK �#Qmi i?2 p�Hm2 Q7 2/m+�iBQM- bT2+B�H M22/b Q7bim/2Mib- 2i+X

! A7 �/?2`2M+2 iQ J�BKQMB/2bǶb `mH2 r2`2 T2`72+iHv `B;B/ i?2M rBi? � bBM;H2+H�bb bBx2 Q7 9y r?�i rQmH/ b2T�`�i2 i?2 b�K2 b+?QQH rBi? irQ +H�bb2br?Qb2 �p2`�;2 bBx2 Bb kyX8 Bb QM2 bim/2MiX

J�BKQMB/2bǶ _mH2

! J�BKQMB/2bǶ `mH2 ?�b i?2 H�`;2bi BKT�+i QM � b+?QQH rBi? �#Qmi 9ybim/2Mib BM � ;`�/2 +Q?Q`iX

! qBi? +Q?Q`ib Q7 bBx2 9y- 3y- �M/ Rky bim/2Mib- i?2 bi2Tb /QrM BM �p2`�;2+H�bb bBx2 `2[mB`2/ #v J�BKQMB/2bǶ `mH2 r?2M �M �//BiBQM�H bim/2Mi 2M`QHb�`2 b?QrM BM i?2 i�#H2X

P`B;BM�H *Q?Q`i aBx2 9y 3y Rky*H�bb bBx2 rBi? QM2 kyX8 kd jyXk8�//BiBQM�H bim/2Mi

Cohort : a groupof people with a

Common Statistical characteristic.

e - g ,the Root bi - th Cohort of

Children .

+1=7442--20.5= ) H 81/3=27

=3 tf ¥-30.gg

J�BKQMB/2bǶ _mH2

! �M;`Bbi �M/ G�pv HQQF2/ �i b+?QQHb rBi? }7i? ;`�/2 +Q?Q`ib BM RNNR rBi?#2ir22M jR �M/ 8y bim/2Mib- r?2`2 �p2`�;2 +H�bb bBx2b KB;?i #2 +mi BM ?�H7#v J�BKQMB/2bǶ `mH2X

! h?2`2 r2`2 kRR bm+? b+?QQHb- rBi? 3e Q7 i?2b2 b+?QQHb ?�pBM; #2ir22M jR�M/ 9y bim/2Mib BM }7i? ;`�/2- �M/ Rk8 b+?QQHb ?�pBM; #2ir22M 9R �M/ 8ybim/2Mib BM i?2 }7i? ;`�/2X

J�BKQMB/2bǶ _mH2

! �KQM; i?2 kRR b+?QQHb rBi? #2ir22M jR �M/ 8y bim/2Mib BM }7i? ;`�/2-i?2 T2`+2Mi�;2 /Bb�/p�Mi�;2/ ?�b � bHB;?iHv M2;�iBp2 E2M/�HHǶb +Q``2H�iBQMQ7 ƐyXRyX

! ai`QM; M2;�iBp2 +Q``2H�iBQMb Q7 ƐyX9k �M/ ƐyX88- `2bT2+iBp2Hv- rBi?T2`7Q`K�M+2 QM p2`#�H �M/ K�i?2K�iB+b i2bi b+Q`2bX

! 6Q` i?Bb `2�bQM- 3e K�i+?2/ T�B`b Q7 irQ b+?QQHb r2`2 7Q`K2/- K�i+?BM; iQKBMBKBx2 iQ iQi�H �#bQHmi2 /Bz2`2M+2 BM T2`+2Mi�;2 /Bb�/p�Mi�;2/X

J�BKQMB/2bǶ _mH2

0

J�BKQMB/2bǶ _mH2

3e T�B`b Q7 Ab`�2HB b+?QQHb i?�i �`2 K�i+?2/ �b 7QHHQrb,

RX PM2 b+?QQH rBi? #2ir22M jR �M/ 9y bim/2Mib BM i?2 }7i? ;`�/2 Uh = yV-kX PM2 rBi? #2ir22M 9R �M/ 8y bim/2Mib BM i?2 }7i? ;`�/2 Uh = RV- i?2 T�B`b

#2BM; K�i+?2/ 7Q` � +Qp�`B�i2 t 4 T2`+2Mi�;2 Q7 /Bb�/p�Mi�;2/ bim/2MibX

J�BKQMB/2bǶ _mH2

! ai`B+i �/?2`2M+2 iQ J�BKQMB/2bǶ `mH2 rQmH/ `2[mB`2 i?2 bHB;?iHv H�`;2` }7i?;`�/2 +Q?Q`ib iQ #2 i�m;?i BM irQ bK�HH +H�bb2b- �M/ i?2 bHB;?iHv bK�HH2`}7i? ;`�/2 +Q?Q`ib iQ #2 i�m;?i BM QM2 H�`;2 +H�bbX

! �/?2`2M+2 iQ J�BKQMB/2bǶ `mH2 r�b BKT2`72+i #mi bi`B+i 2MQm;? iQT`Q/m+2 � rB/2 b2T�`�iBQM BM ivTB+�H +H�bb bBx2X

J�BKQMB/2bǶ _mH2

! AM i?2B` bim/v- (u(R), u(y)) �`2 �p2`�;2 i2bi b+Q`2b BM }7i? ;`�/2 B7 i?2 }7i?;`�/2 +Q?Q`i r�b � HBiiH2 H�`;2` Uh = RV Q` � HBiiH2 bK�HH2` Uh = yVX

! q?�i b2T�`�i2b � b+?QQH rBi? � bHB;?iHv bK�HH2` }7i? ;`�/2 +Q?Q`i Uh = y-jRĜ9y bim/2MibV �M/ � b+?QQH rBi? � bHB;?iHv H�`;2` }7i? ;`�/2 +Q?Q`iUh = R- 9RĜ8y bim/2MibV\

! � ?�M/7mH Q7 ;`�/2 8 bim/2MibX

J�BKQMB/2bǶ _mH2

! a22Kb TH�mbB#H2 i?�i r?2i?2` Q` MQi � 72r KQ`2 bim/2Mib 2M`QH BM i?2 }7i?;`�/2 Bb � ?�T?�x�`/ 2p2MiX

! �M 2p2Mi MQi bi`QM;Hv `2H�i2/ iQ i?2 �p2`�;2 i2bi T2`7Q`K�M+2 (u(R), u(y))i?�i i?2 }7i? ;`�/2 rQmH/ 2t?B#Bi rBi? � H�`;2` Q` bK�HH2` +Q?Q`iX

! "mBH/BM; � bim/v BM i?2 r�v i?�i �M;`Bbi �M/ G�pv /B/- Bi b22Kb TH�mbB#H2i?�i i?2 T`QT2MbBiv Q7 � H�`;2`fbK�HH2` +H�bb �`2 7�B`Hv +HQb2 BM i?2 3eK�i+?2/ T�B`b Q7 irQ b+?QQHbX

J�BKQMB/2bǶ _mH2

� ǵM�im`�H 2tT2`BK2MiǶ Bb �M �ii2KTi iQ }M/ BM i?2 rQ`H/ bQK2 `�`2+B`+mKbi�M+2 bm+? i?�i � +QMb2[m2MiB�H i`2�iK2Mi r�b ?�M/2/ iQ bQK2 T2QTH2�M/ /2MB2/ iQ Qi?2`b 7Q` MQ T�`iB+mH�`Hv ;QQ/ `2�bQM �i �HH- i?�i Bb- ?�T?�x�`/HvX

An example of a natural experiment .

J�BKQMB/2bǶ _mH2

! Ai /Q2b b22K `2�bQM�#H2 iQ i?BMF i?�i T`Q#�#BHBiv Q7 � H�`;2` +H�bb �`2 7�B`Hv+HQb2 7Q` i?2 3e T�B`2/ Ab`�2HB b+?QQHbX

! h?Bb KB;?i #2 BKTH�mbB#H2 BM bQK2 Qi?2` +QMi2ti- b�v BM � M�iBQM�H bm`p2vBM *�M�/� r?2`2 b+?QQHb �`2 7mM/2/ #v HQ+�H ;Qp2`MK2Mib- bQ i?�i +H�bbbBx2 KB;?i #2 T`2/B+i2/ #v i?2 r2�Hi? Q` TQp2`iv Q7 i?2 HQ+�H +QKKmMBivX

J�BKQMB/2bǶ _mH2

h?2 };m`2 b?Qrb i?�i i`2�iK2Mi `2~2+ib i?2 ?�T?�x�`/ 2H2K2Mi- M�K2Hvbmb+2TiB#BHBiv iQ J�BKQMB/2bǶ `mH2 #�b2/ QM +Q?Q`i bBx2- `�i?2` i?�M `2�HBx2/+H�bb bBx2X .2}MBM; i`2�iK2Mi BM i?Bb r�v Bb �M�HQ;Qmb iQ �M ǵBMi2MiBQM@iQ@i`2�iǶ�M�HvbBb BM � `�M/QKBx2/ 2tT2`BK2MiX

0'a

h?2 T`QT2MbBiv b+Q`2

! *Qp�`B�i2b �`2 T`2@i`2�iK2Mi p�`B�#H2b �M/ i�F2 i?2 b�K2 p�Hm2 7Q` 2�+?mMBi MQ K�ii2` r?B+? i`2�iK2Mi Bb �TTHB2/X

! 6Q` 2t�KTH2- T`2@i`2�iK2Mi #HQQ/ T`2bbm`2 Q` T`2@i2bi `2�/BM; H2p2H �`2 MQiBM~m2M+2/ #v � i`2�iK2Mi i?�i rQmH/ �Hi2` #HQQ/ T`2bbm`2 Q` `2�/BM; H2p2HX

h?2 T`QT2MbBiv b+Q`2 Bb2(t) = S (h = R|t) ,

r?2`2 t �`2 Q#b2`p2/ +Qp�`B�i2bXh?2 Bi? T`QT2MbBiv b+Q`2 Bb i?2 T`Q#�#BHBiv i?�i � mMBi `2+2Bp2b i`2�iK2Mi ;Bp2M�HH i?2 BM7Q`K�iBQM- `2+Q`/2/ �b +Qp�`B�i2b- i?�i Bb Q#b2`p2/ #27Q`2 i?2i`2�iK2MiX

✓Vector of Co variates

I = ( 211 ,K2 ,

- - , ohh ) .

h?2 T`QT2MbBiv b+Q`2

! AM 2tT2`BK2Mib i?2 T`QT2MbBiv b+Q`2b �`2 FMQrMX! AM Q#b2`p�iBQM�H bim/B2b i?2v +�M #2 2biBK�i2/ mbBM; KQ/2Hb bm+? �b

HQ;BbiB+ `2;`2bbBQM r?2`2 i?2 Qmi+QK2 Bb i?2 i`2�iK2Mi BM/B+�iQ` �M/ i?2T`2/B+iQ`b �`2 �HH i?2 +QM7QmM/BM; +Qp�`B�i2bX

h?2 T`QT2MbBiv b+Q`2

*QMbB/2` � +QKTH2i2Hv `�M/QKBx2/ /2bB;M rBi? M = k 2tT2`BK2Mi�H mMBibX PM2mMBi Bb �bbB;M2/ i`2�iK2Mi QM2 Uh = RV �M/ QM2 mMBi Bb �bbB;M2/ iQ i`2�iK2MiirQ Uh = yVX h?2 TQbbB#H2 i`2�iK2Mi �bbB;MK2Mib 7Q` i?2 2tT2`BK2Mi�H mMBib�`2,

hR hk S(hR) S(hk)y y y yy R y yX8R y yX8 yR R y y

1�+? mMBiǶb T`QT2MbBiv b+Q`2 Bb \X

O = No treatment

1- -

Treatment'

- p

- a- A

- a

I

2

h?2 T`QT2MbBiv b+Q`2

*QMbB/2` � +QKTH2i2Hv `�M/QKBx2/ /2bB;M rBi? M = 3 mMBib �M/ i?`22 mMBib �`2�bbB;M2/ i`2�iK2Mi- �M/ 7Qm` mMBib �`2 �bbB;M2/ iQ +QMi`QH UBX2X- MQ i`2�iK2MiVX

! 1�+? mMBiǶb T`QT2MbBiv b+Q`2 Bb \X! h?2 T`Q#�#BHBiv Q7 �M T�`iB+mH�` i`2�iK2Mi �bbB;MK2Mi Bb \X

318

h?2 T`QT2MbBiv b+Q`2

B I@ +QK#MUR,3-jV+QHM�K2bUBV I@ T�bi2yUR,8e- +U]bi h`i �bbB;]- O `2M�K2 +QHmKMb

]M/ h`i �bbB;]-]`/ h`i �bbB;]- `2TU]i? h`i �bbB;]- 8jVVV

`QrXM�K2bUBV I@ T�bi2yU]lMBi ]- R,jV O `2M�K2 `QrbB(-R,9) OT`BMi 7B`bi 7Qm` +QHmKMb

Rbi h`i �bbB; kM/ h`i �bbB; j`/ h`i �bbB; 9i? h`i �bbB;lMBi R R R R RlMBi k k k k klMBi j j 9 8 e

1�+? +QHmKM +Q``2bTQM/b iQ i?2 mMBib i?�i rBHH #2 i`2�i2/c bQ i?2 mMBib i?�irBHH MQi #2 i`2�i2/ �`2 MQi BM+Hm/2/ BM i?2 +QHmKMX 6Q` 2t�KTH2 BM i?2 }`bii`2�iK2Mi �bbB;MK2Mi mMBib R- k- j rBHH #2 i`2�i2/ �M/ mMBib 9- 8- e- d- 3 rBHH #2;Bp2M +QMi`QHX

(11414156,7 ,

8)

←- a

→

h?2 T`QT2MbBiv b+Q`2

! *QMbB/2` � +QKTH2i2Hv `�M/QKBx2/ /2bB;M rBi? M mMBib �M/ K mMBib �`2�bbB;M2/ i`2�iK2MiX

! 1�+? mMBi ?�b T`Q#�#BHBiv KM Q7 `2+2BpBM; i`2�iK2Mi U�M/ R − K

M Q7 `2+2BpBM;+QMi`QHVX

! h?mb- 2�+? T2`bQMǶb T`QT2MbBiv b+Q`2 Bb K/MX! h?2 T`Q#�#BHBiv Q7 � T�`iB+mH�` i`2�iK2Mi �bbB;MK2Mi Bb R

(MK) X

¥