Evidence Uncovered: Long-Term Interest Rates, Monetary Policy, and the Expectations Theory

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 712 October 2001 EVIDENCE UNCOVERED: LONG-TERM INTEREST RATES, MONETARY POLICY, AND THE EXPECTATIONS THEORY Jennifer E. Roush Note: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFPDs are available on the Web at www.federalreserve.gov/pubs/ifpd/.

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Wdeoh 4= Ghwhuplqlqj Odj Ohqjwk zkhq U? @6pr (cid:3) (cid:4) Prqhwdu| V|vwhp= | @ \ >S >SF >WU >UI >P5 >U(cid:12) | | | | | | | | & odjv DLF VF 4 0871<3 08716; 5 0881:4W 0871:6W 6 08819: 087157 7 088199 0861:9 8 088188 086153 9 088186 0851:6 : 088189 08515< ; 088195 0841;< < 088188 084168 43 088189 0831;< 44 08817; 083168 45 088183 07<1<3 46 088173 07<165 47 088175 07;1;: 48 088169 07;166 49 08816; 07:1;; Wdeoh 5= Iruhfdvw Huuru Yduldqfh Vkduhv Prqhwdu| V|vwhp= | @+\ >S >SF >WU >UI >P5 >U?, | | | | | | | | U? UI U? \ S UI U? \ S 6pr 6pr 6pr 6pr 7;pr 7;pr 7;pr 7;pr 5pr 169 187 1338 1335 156 15: 13: 13: 6pr 168 196 133; 1335 157 163 139 139 7pr 166 18; 133: 1334 156 15; 139 138 9pr 173 18: 1337 1335 157 15: 13; 138 <pr 193 185 13339 1338 163 159 143 144 45pr 149 183 1335 13335 147 158 138 135 57pr 13< 177 1334 13336 13; 153 137 137 69pr 13: 186 13338 13336 13: 155 136 137 5;

Wdeoh 6= Srlqw Hvwlpdwhv Prqhwdu| V|vwhp= | @+\ >S >SF >WU >UI >P5 >U?, | | | | | | | | Plq UPSG fdvh Uhfxuvlyh LGW U? F-(cid:14) UPSG Uhodwlyh Ydu1 UPSG Uhodwlyh Ydu1 5 pr D 136; 914( 13:7 5<19( 6 pr E 1365 61<( 1398 5818( 7 pr E 1357 515( 138< 5413( 9 pr E 1354 41;( 137< 461:( < pr F 1369 819( 1375 4318( 45 pr E 1383 441;( 1377 4619( 57 pr D 13;4 7616( 139: 7519( 69 pr D 1433 :313( 13;6 ;316( - Uhfxuvlyh Rughulqj = i\ >S >P5 >WU >UI >SF >U?j | | | | | | | Wdeoh 7= Fryhudjh Lqwhuydov iru Plq UPSG Fdvhv Prqhwdu| V|vwhp= | @+\ >S >SF >WU >UI >P5 >U?, | | | | | | | | U? F-(cid:14) s rggv UPSG Uhodwlyh Ydu1 58( 83( :8( 58( 83( :8( 5pr D 461:4 1344 1357 136< 514( 818( 4818( 6pr E 918; 1347 1357 1366 514( 61<( ;15( 7pr E 7159 1345 134; 1358 417( 517( 718( 9pr E 7154 133< 1348 1356 31:( 417( 613( <pr F 6196 1344 1353 1366 414( 613( :13( 45pr E 6179 1349 135; 1375 51:( ;1;( 5316( 57pr E 51;5 1358 136< 138: 4417( 761:( <714( 69pr D 719; 1359 1373 1393 561;( 9<17( 4581<( (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)0 S S UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)UI ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) D=S @\ @3>SF >P5 >WU 83>UI @3>\ 83> f f f f f f Sf S 8(cid:3)=358SF >P5 @=48WU = 2 2 f (cid:129)f E =D h{fhsw P5 @=43WU f (cid:129)f F =E zlwk WU 8=7\ f (cid:129)2 5<

Wdeoh 8= Srlqw Hvwlpdwhv Prqhwdu| V|vwhp= | @+\ >S >SF >P5 >U(cid:129)>U?, | | | | | | | Plq UPSG fdvh Uhfxuvlyh LGW U? F-(cid:14) UPSG Uhodwlyh Ydu1 UPSG Uhodwlyh Ydu1 5 pr G 1335< 13;5( 1345 168;( 6 pr G 13383 1595( 134< 1<:9( 7 pr G 13389 1687( 1357 41:( 9 pr G 13376 1558( 136; 61:( < pr G 13359 13<4( 1386 :15( 45 pr G 13363 1455( 1397 4418( 57 pr G 1338< 1674( 1433 6813( 69 pr G 13389 15<5( 144< 8<18( 7; pr G 1337< 1558( 1463 ;314( 93 pr G 13374 1488( 1466 <61;( 453 pr G 13433 1<:( 143; ;<1:( - Uhfxuvlyh Rughulqj= i\ >S >P5 >U(cid:129)>SF >U?j | | | | | | Wdeoh1 9= Fryhudjh Lqwhuydov (cid:3) (cid:4) Prqhwdu| V|vwhp= | @ \ >S >SF >P5 >U(cid:129)>U? | | | | | | | U? F-(cid:14) s rggv UPSG Uhodwlyh Ydu1 58( 83( :8( 58( 83( :8( 5pr G 4 1334: 13359 13368 1359( 1398( 1465( 6pr G 4 13363 13379 1338< 1344( 1546( 1759( 7pr G 4 13368 13385 133:3 1488( 1649( 18;6( 9pr G 4 13365 13383 133:5 145:( 1659( 1964( <pr G 4 13369 13386 133:8 1469( 168<( 1:49( 45pr G 4 1336; 1338: 133;4 149:( 167<( 1;4;( 57pr G 4 13383 133:: 13437 1547( 1839( 41485( 69pr G 4 1337; 133:6 13436 14;4( 17:8( 4174;( 7;pr G 4 1337< 133:7 13435 1468( 17:6( 418:8( 93pr G 4 1336: 13397 133<< 143:( 169;( 4185<( 453pr G 4 1336; 133:5 13468 147:( 1<68( 81566( (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:24) S S UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)U(cid:129) ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) G= S @\ @3>SF 83>P5 83>U(cid:129) @3 f f f f f 63

Wdeoh := Srlqw Hvwlpdwhv Prqhwdu| V|vwhp= | @+\ >S >SF >WU >UI >P5 >U?>U(cid:129), | | | | | | | | | Plq UPSG fdvh Uhfxuvlyh LGW U? F-(cid:14) UPSG Uhodwlyh Ydu1 UPSG Uhodwlyh Ydu1 5 pr D 13389 3149( 13455 4158( 6 pr E 1339< 3166( 134<5 614:( 7 pr E 1339; 3164( 1357: 816;( 9 pr D 13437 1384( 13667 <1;5( < pr D 1345; 319:( 13735 481<5( 45 pr D 3146< 31:<( 13788 56199( 57 pr D 13545 5165( 13989 971:5( 69 pr F 134;9 41:<( 13;34 43<137( 7; pr G 13573 615;( 13;74 46;1;:( 93 pr G 13598 7198( 13;63 4891:3( - Uhfxuvlyh Rughulqj= i\ >S >P5 >WU >UI >SF >U(cid:129)>U?j | | | | | | | | Wdeoh1 ;= Fryhudjh Lqwhuydov Prqhwdu| V|vwhp= | @+\ >S >SF >WU >UI >P5 >U?>U(cid:129), | | | | | | | | | U? F-(cid:14) s rggv UPSG Uhodwlyh Ydu1 58( 83( :8( 58( 83( :8( 5pr D 4 13387 1339: 133:; 134;( 163( 17;( 6pr E 4 133;5 133<8 13446 17:( 1:5( 4149( 7pr E 4 133;8 13433 13454 186( 1;4( 416:( 9pr D 4 13433 13458 13483 18;( 413;( 41<5( <pr D 4 13449 13477 134;9 1<6( 4196( 51<;( 45pr D 4 1345; 134:3 13555 414;( 5148( 7156( 57pr D 4 13496 1355: 13648 5174( 71:7( <1:9( 69pr F 4 134:6 13565 1365; 5165( 7199( 431:5( 7;pr G 4 134:5 13578 13668 518<( 9165( 48196( 93pr G 4 134;< 13589 13673 6149( :16;( 4:179( (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25) S S UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)U(cid:129) ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) D= S @\ @3>WU >SF >P5 83>UI @3>=:8UI 8U(cid:129) 84=58UI > f f f f f (cid:129) f (cid:129) WU 8\ >P5 @(cid:3)WU >UI @3 f (cid:129) f S 2 E= D zlwk WU 8\ lqvwhdg ri WU 8\ f 2e f (cid:129) F= D zlwkrxw UI @3 2 G= F zlwk WU 8\ lqvwhdg ri WU 8\ f (cid:12) f (cid:129) 64

Wdeoh <= Srlqw Hvwlpdwhv Prqhwdu| V|vwhp= | @+\ >S >P5 >UI >U?>U(cid:129), | | | | | | | Plq UPSG fdvh Uhfxuvlyh LGW U? F-(cid:14) UPSG Uhodwlyh Ydu1 UPSG Uhodwlyh Ydu1 5 pr D 133;< 4147( 13457 198( 6 pr D 13444 4148( 134;9 4188( 7 pr D 13449 4186( 13566 5188( 9 pr E 13463 4176( 135<< 714;( < pr F 1346: 4188( 13675 81;9( 45 pr G 13453 4194( 136:8 :199( 57 pr G 133<8 4186( 138<4 53156( 69 pr H 1339; 415;( 13:<; 6:1<;( 7; pr I 13396 414<( 13<73 89163( 93 pr J 13394 413:( 14364 :51;;( 453 pr K 1338< 61:4( 143:: 4351;8( -Uhfxuvlyh Rughulqj= i\ >S >P5 >UI >U(cid:129)>U?j | | | | | | (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)0 (cid:3) (cid:4) -Uhfxuvlyh rughulqj= \ >S >P5 >UI >U(cid:129)>U? S | |S | | | | UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)U(cid:129) ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uho1Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) D=S >\ >P5 83> UI @3> =:8UI 8U(cid:129) 84=58UI > \ @=8P5 > f f f f (cid:129) f (cid:129) f f S @=8P5 >S 83> UI @(cid:3)598P5 f f S f f E =D h{fhsw Ui @(cid:3)458P5 f f F = E h{fhsw Ui @(cid:3)443P5 f f G =S >\ >P5 83>UI @3>\ @=8P5 >=<8UI 8U(cid:129) 84=38UI >\ 8\ > f f f f f f (cid:129) f (cid:129) (cid:129) f H =G h{fhsw=;8UI 8U(cid:129) 84=48 (cid:129) f I =H h{fhsw =<8UI 8U(cid:129) 84=38UI dqg P5 @7\ (cid:129) f (cid:129) f f J=I h{fhsw P5 @5\ f f K =J h{fhsw =<;UI 8U(cid:129) 84=35UI (cid:129) f (cid:129) 65

Wdeoh1 43= Fryhudjh Lqwhuydov Prqhwdu| V|vwhp= | @+\ >S >P5 >UI >U?>U(cid:129), | | | | | | | UPSG Uhodwlyh Ydu1 U? F-(cid:14) s rggv 58( 83( :8( 58( 83( :8( 5pr D 63158 133;8 13434 13478 3193( 4147( 41<8( 6pr D 77178 13465 13489 1359; 4145( 514:( 61:;( 7pr D 49819: 13447 13475 134:6 31<<( 513<( 714<( 9pr E 4 13454 13493 134<; 4163( 5185( 8145( <pr E 4 13465 134:6 1354< 419<( 6146( 9198( 45pr F 457 1343< 13476 134;< 416<( 51:<( 9139:( 57pr G :3176 13433 13466 134:: 419;( 7194( 4818<( 69pr H 57< 133;8 13446 1348; 41:<( 813;( 4:197( 7;pr I 4 133:8 133<< 13455 41;3( 71:8( 481:7( 93pr J 4 133:; 133<< 13458 41;7( 819;( 5614;( 453pr K 4 1339: 133;6 1343: 51:;( <147( 641:4( (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25) S S UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)U(cid:129) ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0 (cid:127)(cid:27)(cid:28) D=S >\ >P5 83> UI @3> =:8UI 8U(cid:129) 84=58UI > \ @=8P5 > f f f f (cid:129) f (cid:129) f f S @=8P5 >S 83> UI @(cid:3)598P5 f f S f f E =D h{fhsw UI @(cid:3)458P5 f f F = E h{fhsw UI @(cid:3)443P5 f f G =S >\ >P5 83>Ui @3>\ @=8P5 >=<8UI 8U(cid:129) 84=38UI >\ 8\ > f f f f f f (cid:129) f (cid:129) (cid:129) f H =G h{fhsw=;8UI 8U(cid:129) 84=48 (cid:129) f I =H h{fhsw =<8UI 8U(cid:129) 84=38UI dqg P5 @7\ (cid:129) f (cid:129) f f J=I h{fhsw P5 @5\ f f K =J h{fhsw =<;UI 8U(cid:129) 84=35UI (cid:129) f (cid:129) 66

Wdeoh 44 Frqwhpsrudqhrxv Srolf| Sdudphwhu Hvwlpdwhv Prqhwdu| V|vwhp= | @+\ >S >P5 >UI >U?>4pr , | | | | | | | U? \ S P5 UI U? 4pr 5pr 06<17: 0;9176 05641<; 416< 061:5 61:6 6pr 058185 06:159 05451;< 417: 0614< 51:< 7pr 05718< 06<13; 05661;8 4173 0519< 5164 9pr 06;17< 03193 0735154 31;: 04179 4165 <pr 074169 04136 0758146 31:5 04138 31<8 45pr 074165 0<199 0766166 317: 031<8 4137 57pr 06819: 043185 074;165 315; 04143 4145 69pr 05517; 048139 077717< 3136 031;; 413< 7;pr 047188 0:1<8 077;1<5 3139 031<5 4134 93pr 06:1;8 0451:: 0764174 3137 031<6 4138 453pr 07;13; 04;3156 06791;4 3138 0319< 414< Wdeoh 45 Frqwhpsrudqhrxv Vwuxfwxuh ri wkh Ehqfkpdun Prgho bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb Prqh| Ghpdqg= d P5.d UI .d \ .d S @% (cid:129) 2 (cid:12) e (cid:127)( Prqhwdu| Srolf|= d P5.d UI @% D S (cid:127)(cid:27) Ilqdqfldo Vhfwru= d P5.d UI .d \ .d S .d U(cid:129) @% . b (cid:129)f (cid:129)(cid:129) (cid:129)2 -(cid:129) d P5.d UI .d \ .d S .d U(cid:129).d U? @% (cid:129)(cid:12) (cid:129)e (cid:129)D (cid:129)S (cid:129). (cid:129)H -? Surgxfwlrq Vhfwru= Orzhu wuldqjxodu lq rughu i\>Sj> Lqhuwldo zlwk uhvshfw wr Ilqdqfldo dqg Prqhwdu| Vhfwruv bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb 67

Wdeoh 46 Pd{lpxp Olnholkrrg Hvwlpdwhv ri Frqwhpsrudqhrxv Frh!flhqwv= Ehqfkpdun Prgho +U? @U(cid:12)S, +9;( htxdo wdlohg suredelolw| lqwhuydov, bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb Prqh| Ghpdqg= 587=44 P5. 4:4=34 UI (cid:3) 59=88 \ (cid:3) 4:=95 S @% (cid:127)( EDf(cid:23)eHc(cid:12)b.(cid:23)HD(cid:28) E(cid:129)f.(cid:23)b(cid:12)c(cid:129)Hb(cid:23)D.(cid:28) E3(cid:12)D(cid:23)2(cid:12)c3(cid:129)(cid:129)(cid:23)bf(cid:28) E3ef(cid:23)H2eDcb(cid:23)(cid:129)S(cid:28) Prqhwdu| Srolf|= (cid:3)6;4=;7 P5. <3=94 UI @% (cid:127)(cid:27) E3eeH(cid:23)bfc322.(cid:23)HD(cid:28) E2(cid:23)ebc(cid:129)D.(cid:23)Db(cid:28) Ilqdqfldo Vhfwru= (cid:3) 6;=39 P5(cid:3) 43:=3; UI (cid:3) 9=;4 \ (cid:3) 6<=76 S. E3Sf(cid:23)e.c3(cid:129)S(cid:23)Sb(cid:28) E3(cid:129)(cid:129).(cid:23)f.c3b.(cid:23)(cid:12)2(cid:28) E3(cid:129).(cid:23)HHc(cid:12)(cid:23).S(cid:28) E3S(cid:12)(cid:23)H(cid:129)c3(cid:129)S(cid:23)Sb(cid:28) 4;;=;< U(cid:129) @% -(cid:129) E(cid:129)H2(cid:23)D(cid:12)c(cid:129)bD(cid:23)2D(cid:28) (cid:3) 57=;3 P5(cid:3) 47=9; UI (cid:3) 5:=;3 \ (cid:3) 87=67 S(cid:3) E3e.(cid:23)(cid:129)bc32(cid:23)b(cid:12)(cid:28) E32D(cid:23)2.c3e(cid:23)(cid:12)e(cid:28) E3(cid:12)b(cid:23)f(cid:12)c3(cid:129).(cid:23)(cid:12)H(cid:28) E3.H(cid:23)2.c3(cid:12)(cid:129)(cid:23)D(cid:12)(cid:28) 436=<< U(cid:129). 5;4=54 U(cid:12)S @% -(cid:12)S E3(cid:129)(cid:129)(cid:12)(cid:23)b(cid:12)c3be(cid:23).e(cid:28) E2.(cid:129)(cid:23)DDc2bf(cid:23)e(cid:12)(cid:28) bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb 9;( htxdo wdlohg suredelolw| lqwhuydov edvhg rq 83/333 gudzv iurp wkh srvwhulru glvwulexwlrq ri prgho frh!flhqwv lq sduhqwkhvhv1 68

Wdeoh 47= Lqfrusrudwlqj Srolf| Uhvsrqvhv wr wkh Erqg Pdunhw= Lpsolfdwlrqv iru wkh Frqglwlrqdo H{shfwdwlrqv Wkhru| +8(/49(/;7(/<8(, iudfwlohv Ehqfkpdun (cid:25) @=38 (cid:25) @=58 -? -? U? UPSG Uho1 Ydu1 UPSG UY UPSG UY 5pr =335< =55( 1335; 153( 13357 149( E(cid:23)ffb(cid:12)c(cid:23)f(cid:129)2bc(cid:23)f(cid:12)f2c(cid:23)f(cid:12)fH(cid:28) E(cid:23)22Ic(cid:23)SSIc(cid:129)(cid:129)(cid:23)b(cid:129)Ic2(cid:12)(cid:23)eHI(cid:28) 6pr =33;5 4=<4( 133:< 41;4( 13396 416<( E(cid:23)ffb(cid:12)c(cid:23)f(cid:129)2bc(cid:23)f(cid:12)f2c(cid:23)f(cid:12).S(cid:28) E(cid:23)2DIc(cid:23).SIc(cid:129)(cid:12)(cid:23)2HIc2S(cid:23)(cid:129).I(cid:28) 7pr =3448 6=87( 13443 6173( 13443 6173( E(cid:23)ffb(cid:12)c(cid:23)f(cid:129)f(cid:12)c(cid:23)f(cid:12)fec(cid:23)f(cid:12).S(cid:28) E(cid:23)2SIc(cid:23)b2Ic(cid:129)(cid:12)(cid:23)HfIc2S(cid:23)2HI(cid:28) 9pr =3493 8=9<( 13484 8177( 1344< 716:( E(cid:23)ffbfc(cid:23)f(cid:129)2Sc(cid:23)f(cid:12)ffc(cid:23)f(cid:12)..(cid:28) E(cid:23)(cid:12)SIc(cid:23)H(cid:12)Ic(cid:129)2(cid:23)2fIc2(cid:12)(cid:23).fI(cid:28) <pr =3536 ;=7<( 134<3 :1<8( 13475 81:<( E(cid:23)ffHec(cid:23)f(cid:129)(cid:129)Sc(cid:23)f2Hfc(cid:23)f(cid:12)Sf(cid:28) E(cid:23)(cid:12)(cid:12)Ic(cid:23)H.Ic(cid:129)(cid:129)(cid:23)DeIc2e(cid:23)(cid:129)HI(cid:28) 4|u =3559 44=78( 1353; 4317<( 13476 919:( E(cid:23)ffHDc(cid:23)f(cid:129)(cid:129)Hc(cid:23)f2Hec(cid:23)f(cid:12)SD(cid:28) E(cid:23)e.Ic(cid:129)(cid:23)fDIc(cid:129)2(cid:23)f(cid:129)Ic2S(cid:23)(cid:12)SI(cid:28) 5|u =3583 6:=57( 1355: 67189( 13468 54163( E(cid:23)f(cid:129)fDc(cid:23)f(cid:129)D(cid:129)c(cid:23)fe(cid:129)f(cid:23)fD(cid:12)S(cid:28) E(cid:129)(cid:23)(cid:129)DIc2(cid:23).SIc(cid:12)2(cid:23)b(cid:12)Ic.e(cid:23)S(cid:129)I(cid:28) 6|u =358: 7;=97( 13567 79144( 13463 631<:( E(cid:23)f(cid:129)(cid:129)ec(cid:23)f(cid:129).fc(cid:23)febbc(cid:23)fSSf(cid:28) E(cid:129)(cid:23)DbIce(cid:23)2DIcDb(cid:23)bbIc(cid:129)(cid:12)2(cid:23).(cid:12)I(cid:28) 7|u =3586 84=64( 1355; 7;174( 13456 6417;( E(cid:23)f(cid:129)2.c(cid:23)f(cid:129)bfc(cid:23)fD.(cid:129)c(cid:23)f.DS(cid:28) E2(cid:23)D(cid:129)IcS(cid:23)(cid:129)eIcbf(cid:23)e.Ic(cid:129)(cid:12)b(cid:23)S(cid:129)I(cid:28) 8|u =356; 78=:8( 13545 75157( 1343< 56166( E(cid:23)f(cid:129)(cid:12)Dc(cid:23)f2fSc(cid:23)fS2(cid:129)c(cid:23)fH2(cid:129)(cid:28) E2(cid:23)HHIc.(cid:23)fDIc(cid:129)2(cid:129)(cid:23).fIc(cid:129)Sf(cid:23)(cid:129)(cid:12)I(cid:28) 43|u =34:; 65=87( 1347; 591:6( 1337< 8194( E(cid:23)f(cid:129)S2c(cid:23) S f2eSc(cid:23)f.(cid:12)(cid:129)c(cid:23)fb.(cid:129)(cid:28) SEe(cid:23)D2Ic(cid:129)2(cid:23)fDIc(cid:129)Df(cid:23)DHIc(cid:129)Df(cid:23)DHI(cid:28) UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) ?3(cid:129)U(cid:129) ,2‘(cid:129) eH |’f | ? (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1+UY, @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb Htxdo wdlohg suredelolw| lqwhuydov edvhg rq 83/333 gudzv iurp wkh srvwhulru glvwulexwlrq ri prgho frh!flhqwv lq sduhqwkhvhv1 69

Wdeoh 48 = Plqlpxp Suhplxp Ghyldwlrqv Frqglwlrqdo rq d Prqh| Ghpdqg Vkrfn Prqhwdu| V|vwhp= | @+\ >S >P5 >UI >U?>U(cid:129), | | | | | | | U? F-(cid:14) UPSG Uhodwlyh Ydu1 5 pr D 13358 3188( 6 pr D 13373 41;3( 7 pr D 13386 617;( 9 pr D 133:8 48138( < pr E 133;6 4<183( 45 pr E 133;; 571:9( 57 pr E 133;7 5:13<( 69 pr F 133;5 4:195( 7; pr F 133:; 59145( 93 pr F 133:7 69178( 453 pr F 1337< 7916:( (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:24) D= \ 83>S 83>P5 @3>UI @3>UI @3>\ 8S >S 8S >P5 @S >S 83 f f f f (cid:12) 2e 2e (cid:12) f f f (cid:12)S E= \ 83>S 83>P5 @3>UI @3>UI @3>\ 8S > S 8S f f f f (cid:12) 2e 2e (cid:12) f F=\ 83>S 83>P5 @3>UI @3>UI @3>\ 8S f f f f (cid:12) 2e 2e 6:

Wdeoh 49= Vhohfwhg Vxevdpsoh Uhvxowv Sdqho D= +Vdpsoh= 4<8<=4 0 4<:<=43, U? F-(cid:14) UPSG Uhodwlyh Ydu1 IHY+UI,W IHY+U?, IHY+\, IHY+S, 6pr H 1349 51;( 13< 148 1364 13338 9pr H 134: 61<( 13; 147 1358 1334 <pr H 134; <13( 13< 13; 1339 1335 (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)0 -IHY+{, @ iruhfdvw huuru yduldqfh ri yduldeoh { dw wkh 7;wk prqwk krul}rq S S UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)UI ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) H= S @\ @3>SF >P5 >WU 83>UI @3>\ 83> f f f f f f (cid:129)2 S 83>WU 8=58SF > 2e f (cid:129)2 Sdqho E= +Vdpsoh= 4<;5=43 0 4<<8=45, U? F-(cid:14) UPSG Uhodwlyh Ydu1 IHY+UI,W IHY+U?, IHY+\, IHY+S, 6pr I 1343 517( 14: 147 14< 1346 9pr I 1344 716( 147 13< 14: 1337 <pr J 1349 ;1:( 14: 143 147 133< (cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25)(cid:25) -IHY+{, @ iruhfdvw huuru yduldqfh ri yduldeoh { dw wkh 7;wk prqwk krul}rq S S UPSG @ ^ (cid:129) e. +U?(cid:3) (cid:129) &3(cid:129)UI ,2‘(cid:129) eH |’f | & (cid:26)’f |n(cid:26) 2 Uhodwlyh Ydu1 @ (cid:15)@oERoe6(cid:16)(cid:4)6(cid:131)0(cid:127)(cid:27)(cid:28) (cid:6)433( (cid:15)@oE-?(cid:131)0(cid:127)(cid:27)(cid:28) I=S @\ @3>SF >P5 >WU 83>UI @3>\ 83> f f f f f f Sf S 83>P5 @=43WU >P 83>WU 8\ (cid:129)2 f (cid:129)f (cid:129)2 f (cid:129)2 J= I zlwkrxw S 83 (cid:129)2 6;

Iljxuh 4= Lpsxovh Uhvsrqvhv wr d Frqwudfwlrqdu| Srolf| Vkrfn= shufhqwv ru (cid:4)orj ohyhov > (cid:3) (cid:4) | @ \ >S >SF >WU >UI >P5 >Ub > | | | | | | | | (cid:25)(cid:24)Plq UPSG 0 0 0 Uhfxuvlyh 6<

Iljxuh 5= Lpsxovh Uhvsrqvhv wr d Frqwudfwlrqdu| Srolf| Vkrfn= shufhqwv ru (cid:4)orj ohyhov > (cid:3) (cid:4) | @ \ >S >SF >P5 >U(cid:129)>USf > | | | | | | | (cid:25)(cid:24)Plq UPSG 0 0 0 Uhfxuvlyh 73

Iljxuh 6= Lpsxovh Uhvsrqvhv wr d Frqwudfwlrqdu| Srolf| Vkrfn= shufhqwv ru (cid:4)orj ohyhov > | @+\ >S >SF >WU >Ui >P5 >USf>U(cid:129), > | | | | | | | | | (cid:25)(cid:24)Plq UPSG 0 0 0 Uhfxuvlyh 74

Iljxuh 7= Lpsxovh Uhvsrqvhv wr d Frqwudfwlrqdu| Srolf| Vkrfn= shufhqwv ru (cid:4)orj ohyhov > | @+\ >S >P5 >Ui >U(cid:129)>USf, > | | | | | | | (cid:25)(cid:24)Plq UPSG 0 0 0 Uhfxuvlyh 75

0.018 2 M 0 -3 x 10 5 10 15 20 25 30 35 40 45 1.9442 0 f R -5.2322 -3 x 10 5 10 15 20 25 30 35 40 45 7.7313 Y 0 -3 x 10 5 10 15 20 25 30 35 40 45 11.0099 P 0 -2.9285 -3 x 10 5 10 15 20 25 30 35 40 45 1.5838 o 0 m 1 -2.8482 -3 x 10 5 10 15 20 25 30 35 40 45 1.4245 ) r y 3 0 ( R -1.1759 5 10 15 20 25 30 35 40 45 Iljxuh 8= Lpsxovh Uhvsrqvhv wr dq H{sdqvlrqdu| Srolf| Vkrfn lq wkh Ehqfkpdun Prgho +Uq@69pr, 76

Iljxuh 9= Lpsxovh Uhvsrqvhv wr d Frqwudfwlrqdu| Srolf| Vkrfn +gdwd vdpsoh=4<8<=404<:<=43,= (cid:3) (cid:4) shufhqwv ru (cid:4)orj ohyhov > | @ \ >S >SF >WU >UI >P5 >US > (cid:25)(cid:24)Plq UPSG 0 0 0 Uhfxuvlyh | | | | | | | | 77

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