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Page 1: jqq - NBER

3J$I32 jqq DMDI$IOW 5HflM

HJflAWHT43$1 223DDA i4aqO HUA$IT UT4A HUASLT :2D5LUO3SI

JHUOM Y$1TWJOD-OWT A MI YDIJOI

13bnfifl .A ms io1T flo3 .M

4çt nbhoW

HD5LA35I DIMOMODH q UA[5IUfl JAMOITAM 3un3vA ud3aM OO1

8FJO AM bhdrnjD ô?QI disM

3ffnono3H Ia 1JB511Jfl IsnoiisM 3di i inqi31nq isnirn bnB jiET ulouD ,1in3&1 doSI [asrli W mon tIoqqu Iinniq .finb 13iha3 n no tnmmo3 IuIq14 iol 3flflJr1nI 1cnfnu2 Q1 i5I

iol 51inD D8IJ di bna £b&u3D lo !i3nuoD d3u51 iiinBrnuH briE 3ni3 IEi3o 3di '$1HflM lo flq i 1qEq idT .bbLwonA3E I1uI3iEI i ibui niufl IEnoiiErn3inI

1oriiuE di lo ocfi is btqx noiniqo '(nA .jnrnjvnI briE biT !.cnoiiEmiflI flu rnEio1q .dIa3$I imono3H lo usiufl lEnoiniM fIi lo oth ron brw

ix3i lo noii florf .b3v13i 3r1Fi hA .ioLsT iro .M briE ibn,nfl .A nB1, 'd ÔQQI © ilul lErti bbivoiq noiirm3q ii3i1qx iuodiiw bioup 3d vjm 1qrIiEq owi b3x3 01 ion

.o1uo di ol n3vi i ,33r1on © nthubni 31b313

Page 2: jqq - NBER

VtZ 13qE nbhoW $13 814 QQ! rbisM

3JflAW3J43$1 23DDA wino 3UA$IT UMA HUA$IT :3D$1UO23$1

JELUOM Y$ITMUOD-OWT A ML

TDAiITHA

31dswn3i nqo Isnoi3sn rttiw 1bom i1nijoo-owj boo-ow £ qo13v3b iqsq thIT

nuoi 31dw3n31 di iot noinoqoiq ioi1" lo o1&ts hqmqqa its vhb W .iuoi nuo c1T .noii3IJbolq biIivib lo boodil,Ail di 03 bits mflsq bsti ol ii lniI bits

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3ZXS nqo d b3rlirrri3bnu llsitnsi2du i noüqmuiq "3b51i moiu 2riis" 3isd 3rIi wilT

371110231 3f11 1fl3fl3d 2sw1s VL111U03 ninoqmi 3iU0i rli d bsoqrni 11hsT .iuoi .nivo1qmi-oi5tsq 3d '(Sm bits ,i33Ioqx3

io1sT flo .M l3bnslfl .A 23f1151

2*nonoH lo in3mflsq3U 37t3mfnoD lo 'iIuaJ sidmuloD d2iihfl lo '3i2i3vinU sidmuloD d2iihfl lo ii213vinU 11 TOy .D.fl 13vuoxtsV SI TOV .D.fl i3vuo3nsV

AUAT4AD AGAMAD $13M bits $I3flM bits

Page 3: jqq - NBER

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-how nood 2sf! II a1f1ii '13qo1q oioIqfflo3ni ai oiulisl 13*Ism oth ho oiusn ouT aoiulish lo*ism lsiinsladua

£ n,uIw 1U330 'sm noilzliolqxo-iovo tsth (.t1) nobioD ho how gniloonoiq offi 33(112 lasol Is booiaiobnu

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(Q1)

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o(11 ui aoasoiani ailsmsib d bosrnisb Isiovoa aEw Aola onIT .1 O I iso' orb ni nsod bola orb ho nir1ai1

\(13V0301 wolls 01 r1uono iovon oiow anoilauboi nialsa 1noupoadu .OVQ! bns 8QI noowiod gninuaao flalsa .)Iaoia orb ho

Page 4: jqq - NBER

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Page 5: jqq - NBER

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pCJcLOnUcJ v OL qJC LCUCMP1C LG2OITLCC cowbouGue onL bb prnjq OU pC C!C MOLJC O P&GCL

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LjJCOLGU.F p.i qqii0IJ1 /AG 0M 1JJ1 fIfflC1GU1 1111hJLi1A CL0 C0flU(LIG !U 1P! LS1!0 0I IC10L bLobot4Iou

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b'°P'"° iuq I1U1)IA

L iI COUC21iOU MCLC uCJiipJC Ui 1JC 2CLI2C 1J1 CLLA!U cbcA t/CLC 1LC LCpJIJAC 10 (JJC C1TLLCU 2OCj(

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21C OL JJC LC2OflLCC 2iOCJC II. 2 = K IJ1LJCL LOft4 CUTJO1 OCCIIU JJJC AL1pJC L 12 jJC ,TULUJ2JC OL

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pi2 IfiIJCfIOUf OLW OL 0(2)12 fC 1Oi2iC J1UC1JOW 2 MqcA n2C !U JJC U2!2 O LCUCMPIC

0(2) = L2(j-2\K) ()jc fI2C 2bCCIUC puCfiOuJ jOLUJ OL Q iACU pA

= 0(2) - W (I)

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Page 7: jqq - NBER

bni3 iuoi 3IdSw&131 3r11 lo lvisri 3111 i H .thoo owl rnimno bnE uboiq '(rlrIuo3 r13s

oi1w 3liEl3rrwn E a b3i11 ei M booD 1uiunEm a lo illguofIi 3d idim rI3idw booa idio mo i M

jloil3ubolq lo iols1 i3111o no '1no i 313d1 tiol 3oiuo1 3111 ol noilibbE nI .1 01 bi1srmon i hq 1inu 10 ior1o 8 .iocJ1 1no gnieu 3IE3 ol aniuii 1fli&1OQ rliiw b33ubolq 1u13s1IJnsM .J iodsI

1o 3111Ev 'iods1 i&fi wofLo1 Ii j i M lo oiiq 3rD A .M boos lo linu rio 3ubo1q lodEl lo iirni no

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.flOil3flhJl noiiouboiq ni1avisr1

(E) =

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linu 3rD in331q31 ()HJ grlifl3i .inslano3 3viiioq £ ai n bris nilvi&1 iuoi Iii bu iods[ lo inuoms

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.noil3ubolq lo 1203 linu all

() = HJSW = q

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311 dorn ai iod&I .

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= q bus ,

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muiidiliup3 vislogm3T nsibisoi5l £ .

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noh3nul li1i1u as1uoU-ddoD gniwollol 3111 d fl3vi ii1ilu

() = u

lo noilqrnuano3 Isubivibni ai rn , boog 331110231 3111 lo flOItqfIIIJanO3 Isubivibni 21n3231q31 rI 31311W

Page 8: jqq - NBER

i 'ii1i1u simixm imuano iIT I bns 0 nwd bifl i l3l3rnElEq i bni 31LJi3S1LJflEffi

b13i noiisimixsrn 2idT .w = m + flq iniii&io3 igbud uo3nE1ni&ri n ot 3331du 3mil ni ln3rnom

.bnfirn3b Isubivibni mit J twl i bnsrn3b 3ii23mob IsioT .(-I)w = m bns q\w = ri &ioii3niil bnsm3b

3vsfl w ,no qmuno in31q1 ot D iqi1313qu niu ur1T

() .J(q-I)w = ; q\Jw = DH

as 1133111w 3d ns boos iuoai (13 ioI bnsm3b e13vni 3113 ) ni noiaa1qx3 bns11 3131 3111 griinsiis5I

(V) DH\Jw = q

ai mono33 11 bns b3xi1 al bola iuoai 3111 3mit ni In3mom s is bia rIoit3ubOlq di nO

l3iinoll 1i1idiaaoq noii3ubolq nsibls3i$I vIsloqm3l 3111 anu13b noilibno3 in3rno1qm3 11th 31cr .nsibisoi5l

cf b3nirrni3b 3d 1153 lav-isr1 mundiliup3 1s1oqm33 1(1T .J = M + (2)s d nvi ai bns (1N)

Isup3 '1qqua griina d .3.i) (V) d nvig 33i1q brlsm3b 1i ot lsup3 (4) d f13v1 33fl 1qqua 3f13 fIiiI32

ab13i airiT .(bnsrrl3b 03

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Page 19: jqq - NBER

LX

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= L2(T-2\K) - xP12 = q2\ql = L*2*(!-2*\Ic) - (30)

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Page 20: jqq - NBER

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I = = w rhiW

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ai nslthwsi sd nsa (1) anoi1u1iiadjja sasril niAsM

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Page 23: jqq - NBER

+ x\f = \I mozd + *q = q noiiibno3 3111

() 0 = - - =

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Page 24: jqq - NBER

iqi rhiw U nhi1n313ThU Sr + J = I 31r1w qIy = U n3flilw 3d ns 'iilifli l33libfli i13moU

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Page 25: jqq - NBER

:mo3d rn3 noiisijp-owi iuO xci floqx3 ns iliiw b31ci3os IJfl3V1 rI1

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* 03 1oqa51 riliw mi' noiicup owl 2irh gnuisiin3111ib '11c1oT

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Page 26: jqq - NBER

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O 14 14 = - = - L(T-2\x) + L2\K)-

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UflWGUI(0L2 JU CXbLCOU2 (5) iiq (8) DGUUC 14 (pG IJ1'1UJGLtOL O G(bLC2iOU () uq 14* 82

MJ(P D > Oe MC CU JU cOwbLtiAc rcqA WtC CCC( q\q suq q\q pA GAJITPLJ tpc

(vs) to (va) MC 9AC fI2G CXbLC2!OU () 14OtC tpt 9 = 0 2 =

IU WOAJIJ LOUJ ((J) tO (V5) MG JJAC urnq 112G O tJJC Ct (P1 2 = 2* (=2J) t = 0 iu woiiu LOW

= (L + L)\cXK2 > 0 (vi)

= - L(J-2\K) + bFcX - L(j-2\K)]\c2 + (L + L*)\K2 (vs)

D = v2R -vi = (Lr'x - 'Q-2\K) + L2\K)\25 + (tir'*c - L*(J-2*\K) + L2\K)\x25 (vi)

2nP(!1I1t!U JJG UGCGLA bL(J1 qCLrAqAC cxbLc!ou 111(0 D 1C1Ci

= T\(c25Y uq j == - L(J-2\K) + L2\K V = - L*(J-2*\K) + L2*\K V = tX2IAI R = -J\(X2

i) I1LI MC CJCrqtC qJC on combouCu( lu cowb9LnAc 2tCqA W(C CxbLciou2 () uq (g)

bL00t O bLObO(JOU : (bLi2 ! uq !)

Page 31: jqq - NBER

) IoJJoMa JLOW (i).

pA x-2) uq qomic bLoqncou (iAcu pA L2(T-2\K))

br'c - L(T-2\J() = -\2 qomic !wbou2e drtj tpc LGUCC pcwcu qowcc cou2mubr!ou (Acu

L( -2\K) + '.\Ic] = u [(j + Lj] > y pi woiu 1o j ti pic n2cq rpc

J/ UOli 2JJOM q2,\q > 0 2!" (qq) = ij [v - v] = u E-c2\cx2 + brx -

0•

cxccGq iucc < j OL < prI2 4) urn p ucq1tc Mp!cp bLoAc2 qIIq2\q <

Page 32: jqq - NBER

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Page 33: jqq - NBER

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