Detecting Lack of Identification in GMM

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 674 July 2000 DETECTING LACK OF IDENTIFICATION IN GMM Jonathan H. Wright 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publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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 IFDPs are available on the Web at www.bog.frb.fed.us.

DETECTING LACK OF IDENTIFICATION IN GMM Jonathan H. Wright* Abstract: In the standard linear instrumental variables regression model, it must be assumed that the instruments are correlated with the endogenous variables in order to ensure the consistency and asymptotic normality of the usual instrumental variables estimator. Indeed, if the instruments are only slightly correlated with the endogenous variables, the conventional Gaussian asymptotic theory may still provide a very poor approximation to the finite sample distribution of the usual instrumental variables estimator. Because of the crucial role of this identification condition, it is common to test for instrument relevance by a first-stage F-test. Identification issues also arise in the generalized method of moments model, of which the linear instrumental variables model is a special case. But I know of no means of testing for identification in this model, in the existing literature. This paper proposes a test of the null of underidentification in the generalized method of moments model. KEYWORDS: Generalized Method of Moments, Identification, Asset Pricing, Instrumental Variables. * Wright is an economist in the International Finance Division of the Federal Reserve Board. I am grateful to Jon Faust, John Fernald and Jim Stock for their helpful comments. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any person associated with the Federal Reserve System.

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vdpsolqj glvwulexwlrq ri wkh dvvrfldwhg w0vwdwlvwlfv lv idu iurp ehlqj vwdqgdug qrupdo1 Djdlq wkh sureohpv jhw ohvv vhyhuh dv wkh vdpsoh vl}h lqfuhdvhv1 Wkh sursrvhg whvw kdv yhu| olwwoh srzhu lq wkh vdpsoh ri vl}h 4331 Lwv srzhu lqfuhdvhv zlwk wkh vdpsoh vl}h/ exw +dssursuldwho|, grhv vr pruh vorzo| wkdq lq prgho P61 Lq prgho P8/ L (cid:31)qg +olnh Wdxfkhq +4<;9,, wkdw wkh frqyhqwlrqdo dv|pswrwlf wkhru| zrunv zhoo lq doo vdpsoh vl}hv1 Fruuhvsrqglqjo|/ wkh sursrvhg whvw kdv d yhu| kljk uhmhfwlrq udwh lq doo vdpsoh vl}hv1 Lq vxppdu|/ wkh sursrvhg whvw lv frqvhuydwlyh xqghu wkh qxoo zkloh/ lq wkh vlp0 xodwlrqv zkhuh wkh lghqwl(cid:31)fdwlrq frqglwlrq lv vdwlv(cid:31)hg +prghov P60P8,/ wkh lwv srzhu lv vwurqjo| dvvrfldwhg zlwk wkh txdolw| ri wkh frqyhqwlrqdo dv|pswrwlf wkhru|1 Wkh uhodwlrqvkls lv qrw d shuihfw rqh> qr pruh wkdq lw lv zlwk wkh (cid:31)uvw0vwdjh I0whvw lq wkh olqhdu LY prgho +Vwdljhu dqg Vwrfn +4<<:,,471 Uhwxuqv rq d ulvniuhh dvvhw fdq dovr eh jhqhudwhg e| wkh dojrulwkp ri Wdxfkhq dqgKxvvh| +4<<4,1 L gr qrw uxq vlpxodwlrqv lq zklfk erwk vwrfnv dqg d ulvniuhh dvvhw duh lq wkh Hxohu htxdwlrq +C ’ 2,1 Wklv lv ehfdxvh lq vxfk d prgho/ wkh pdwul{ (cid:18) zloo dozd|v kdyh udqn 5/ zkhqhyhu wkhuh lv dq lqwhufhsw lq wkh vhw ri lqvwuxphqwv +jlyhq wkdw frqvxpswlrq lv qrw frqvwdqw,1 Wklv lv wuxh hyhq li doo wkh rwkhu lqvwuxphqwv duh udqgrp qxpehuv1 Lq wklv vhqvh/ wkh qxoo k|srwkhvlv ri xqghulghqwl(cid:31)fdwlrq lv qrw 47Wkh (cid:31)uvw0vwdjh I0whvw lv dq lpshuihfw phdvxuh ri wkh txdolw| ri wkh frqyhqwlrqdo dv|pswrwlf wkhru|lqwkholqhduLYprgho1 Wklvlvwuxhhyhqdevwudfwlqjiurplvvxhvrisduwldolghqwl(cid:31)fdwlrq+h1j1 lq d prgho zlwk d vlqjoh hqgrjhqrxv uhjuhvvru,1 55

zhoo gh(cid:31)qhg zkhq C ’ 21 Ri frxuvh/ vxfk d prgho lv olnho| wr eh rqo| yhu| zhdno| lghqwl(cid:31)hg1 81 Frqfoxvlrq1 Lq wkh olqhdu LY prgho/ wkh (cid:31)uvw0vwdjh I0whvw lv dq lpsruwdqw gldjqrvwlf iru fkhfnlqj wkh txdolw| ri wkh lqvwuxphqwv1 Lq wkh h{lvwlqj olwhudwxuh/ wkhuh lv qr dqdorj ri wklv whvw lq wkh JPP prgho1 Wklv sdshu kdv sursrvhg d whvw ri wkh qxoo ri sduwldo ru frpsohwh xqghulghqwl(cid:31)fdwlrq lq wkh jhqhudo JPP prgho dqg kdv dujxhg wkdw lw lv d xvhixo gldjqrvwlf iru lghqwl(cid:31)fdwlrq gl!fxowlhv lq wklv prgho1 Uhihuhqfhv1 Dqghuvrq/ W1Z1 +4<84,= HvwlpdwlqjOlqhdu Uhvwulfwlrqv rq Uhjuhvvlrq Frh!flhqwv iru wkh Pxowlyduldwh Qrupdo Glvwulexwlrq/ Dqqdov ri Pdwkhpdwlfdo Vwdwlvwlfv/ 55/ ss165:0 6841 Dqghuvrq/ W1Z1 dqg K1 Uxelq +4<7<,= Hvwlpdwlrq ri wkh Sdudphwhuv ri d Vlqjoh Htxdwlrq lq d Frpsohwh V|vwhp ri Vwrfkdvwlf Htxdwlrqv/ Dqqdov ri Pdwkhpdwlfdo Vwdwlvwlfv/ 53/ ss1790961 Edvpdqq/U1O1+4<93,=RqIlqlwhVdpsohGlvwulexwlrqvriJhqhudol}hgFodvvlfdoOlqhdu Lghqwl(cid:31)delolw| Whvw Vwdwlvwlfv/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ 88/ ss1983098<1 56

Ehnnhu/ S1D1 +4<<7,=DowhuqdwlyhDssur{lpdwlrqvwrwkhGlvwulexwlrqvriLqvwuxphqwdo Yduldeoh Hvwlpdwruv/ Hfrqrphwulfd/ 95/ ss198:09;41 Erxqg/ M1/ G1D1 Mdhjhu dqg U1 Ednhu +4<<8,= Sureohpv zlwk Lqvwuxphqwdo Yduldeohv Hvwlpdwlrq zkhq wkh Fruuhodwlrq Ehwzhhq wkh Lqvwuxphqwv dqg wkh Hqgrjhqrxv H{0 sodqdwru| Yduldeoh lv Zhdn/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ <3/ ss177607831 Fkrl/ L1 dqg S1F1E1 Skloolsv +4<<5,= Dv|pswrwlf dqg Ilqlwh Vdpsoh Glvwulexwlrq Wkh0 ru| iru LY Hvwlpdwruv dqg Whvwv lq Sduwldoo| Lghqwl(cid:31)hg Vwuxfwxudo Htxdwlrqv/ Mrxuqdo ri Hfrqrphwulfv/ 84/ ss144604831 Fudjj/ M1J1 dqg V1J1 Grqdog +4<<6,= Whvwlqj Lghqwl(cid:31)delolw| dqg Vshfl(cid:31)fdwlrq lq Lq0 vwuxphqwdo Yduldeoh Prghov/ Hfrqrphwulf Wkhru|/ </ ss155505731 Fudjj/ M1J1 dqg V1J1 Grqdog +4<<:,= Lqihuulqj wkh Udqn ri d Pdwul{/ Mrxuqdo ri Hfrqrphwulfv/ :9/ ss155605831 Gxirxu/ M1P1+4<<:,=VrphLpsrvvlelolw|WkhruhpvlqHfrqrphwulfvzlwkDssolfdwlrqv wr Vwuxfwxudo dqg G|qdplf Prghov/ Hfrqrphwulfd/ 98/ ss14698046;:1 Kdqvhq/ O1S1 +4<;5,= Odujh Vdpsoh Surshuwlhv ri Jhqhudol}hg Phwkrg ri Prphqwv Hvwlpdwruv/ Hfrqrphwulfd/ 83/ ss1435<043871 Kdqvhq/ O1S1/ M1 Khdwrq dqg D1 \durq +4<<9,= Ilqlwh Vdpsoh Surshuwlhv ri Vrph Do0 whuqdwlyh JPPHvwlpdwruv/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 47/ ss15950 5;31 57

Kdqvhq/ O1S1 dqg N1 Vlqjohwrq +4<;5,= Jhqhudol}hg Lqvwuxphqwdo Yduldeoh Hvwlpdwlrq ri Qrqolqhdu Udwlrqdo H{shfwdwlrqv Prghov/ Hfrqrphwulfd/ 83/ ss1459<045;91 Kvldr/ F1 +4<;6,= (cid:19)Lghqwl(cid:31)fdwlrq(cid:20)/ lq Kdqgerrn ri Hfrqrphwulfv/ Yro1 4/ hgv1 ]1 Julolfkhv dqg P1G1 Lqwuloljdwru/ Qruwk0Kroodqg/ Dpvwhugdp1 Nrfkhuodnrwd/ Q1 +4<<3,=RqWhvwvriUhsuhvhqwdwlyhFrqvxphuDvvhwSulflqj Prghov/ Mrxuqdo ri Prqhwdu| Hfrqrplfv/ 59/ ss15;806371 Pdggdod/ J1V1 dqg M1 Mhrqj +4<<5,= Rq wkh H{dfw Vpdoo Vdpsoh Glvwulexwlrq ri wkh Lqvwuxphqwdo Yduldeoh Hvwlpdwru/ Hfrqrphwulfd/ 93/ ss14;404;61 Qhovrq/ F1U1 dqgU1 Vwduw}+4<<3d,=VrphIxuwkhuUhvxowvrqwkh H{dfwVpdoo Vdpsoh Surshuwlhv ri wkh Lqvwuxphqwdo Yduldeohv Hvwlpdwru/ Hfrqrphwulfd/ 8;/ ss1<9:0<:91 Qhovrq/ F1U1 dqg U1 Vwduw} +4<<3e,= Wkh Glvwulexwlrq ri wkh Lqvwuxphqwdo Yduldeoh Hvwlpdwru dqg Lwv w0udwlr Zkhq wkh Lqvwuxphqw lv d Srru Rqh/ Mrxuqdo ri Exvlqhvv/ 96/ ss18458084731 Skloolsv/ S1F1E1 +4<;3,= Wkh H{dfw Ilqlwh Vdpsoh Ghqvlw| ri Lqvwuxphqwdo Ydul0 deohv Hvwlpdwruv lq dq Htxdwlrq zlwk q.4 Hqgrjhqrxv Yduldeohv/ Hfrqrphwulfd/ 7;/ ss1;940;:;1 Skloolsv/ S1F1E1 +4<;6,= (cid:19)H{dfw Vpdoo Vdpsoh Wkhru| lq wkh Vlpxowdqhrxv Htxdwlrqv Prgho(cid:20)/ lq Kdqgerrn ri Hfrqrphwulfv/ Yro1 4/ hgv1 ]1 Julolfkhv dqgP1G1 Lqwuloljdwru/ Qruwk0Kroodqg/ Dpvwhugdp1 Ulfkdugvrq/ G1K1 +4<9;,= Wkh H{dfw Glvwulexwlrq ri d Vwuxfwxudo Frh!flhqw Hvwlpd0 58

wru/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ 96/ ss14547045591 Urelq/ M1P1 dqg U1M1 Vplwk +5333,= Whvwv ri Udqn/ Hfrqrphwulf Wkhru|/ 49/ ss14840 4:81 Vdzd/ W1 +4<9<,= Wkh H{dfw Vdpsolqj Glvwulexwlrq ri Ruglqdu| Ohdvw Vtxduhv dqg WzrVwdjhOhdvwVtxduhvHvwlpdwruv/Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ 97/ ss1<560<691 Vkhd/ M1 +4<<:,= Lqvwuxphqw Uhohydqfh lq Pxowlyduldwh Olqhdu Prghov= D Vlpsoh Phd0 vxuh/ Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ :</ ss167;06851 Vwdljhu/ G1 dqg M1K1 Vwrfn +4<<:,= Lqvwuxphqwdo Yduldeohv Uhjuhvvlrq zlwk Zhdn Lqvwuxphqwv/ Hfrqrphwulfd/ 98/ ss188:08;91 Vwrfn/ M1K1 dqg M1K1 Zuljkw +5333,= JPP zlwk Zhdn Lghqwl(cid:31)fdwlrq/ Hfrqrphwulfd/ 9;/ ss133303331 Wdxfkhq/ J1 +4<;9,= Vwdwlvwlfdo Surshuwlhv ri Jhqhudol}hg Phwkrg ri Prphqwv Hvwl0 pdwruv ri Vwuxfwxudo Sdudphwhuv Rewdlqhg iurp Ilqdqfldo Pdunhw Gdwd/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 7/ ss16<:07581 Wdxfkhq/J1dqgU1Kxvvh|+4<<4,=TxdgudwxuhEdvhgPhwkrgviruRewdlqlqjDssur{0 lpdwh Vroxwlrqv wr Qrqolqhdu Dvvhw Sulflqj Prghov/ Hfrqrphwulfd/ 8</ ss16:406<91 ]lyrw/ H1 dqg M1 Zdqj +4<<;,= Lqihuhqfh rq Vwuxfwxudo Sdudphwhuv lq Lqvwuxphqwdo Yduldeohv Uhjuhvvlrq zlwk Zhdn Lqvwuxphqwv/ Hfrqrphwulfd/ 99/ ss146;<047371 59

Wdeoh 4= Sdudphwhu Ydoxhv lq wkh Prghov Prgho (cid:25) (cid:11) (cid:6) (cid:17) (cid:16) (cid:21) (cid:22) (cid:21) (cid:22) (cid:21) (cid:22) 3=34; 3 3 3=3345 3=334: P4 31<: 416 3=346 3 3 3=334: 3=3479 (cid:21) (cid:22) (cid:21) (cid:22) (cid:21) (cid:22) 3=34; 3 3 3=3345 3=334: P5 4146< 461: 3=346 3 3 3=334: 3=3479 (cid:21) (cid:22) (cid:21) (cid:22) (cid:21) (cid:22) 3=354 (cid:3)3=494 3=34: 3=3345 3=334:: P6 31<: 416 3=337 3=747 3=44: 3=334:: 3=347 (cid:21) (cid:22) (cid:21) (cid:22) (cid:21) (cid:22) 3=354 (cid:3)3=494 3=34: 3=3345 3=334:: P7 4146< 461: 3=337 3=747 3=44: 3=334:: 3=347 (cid:21) (cid:22) (cid:21) (cid:22) (cid:21) (cid:22) 3 (cid:3)3=8 3 3=34 3 P8 31<: 416 3 3 (cid:3)3=8 3 3=34 Qrwh= Prghov P6 dqg P7 zhuh frqvlghuhg e| Nrfkhuodnrwd +4<<3,1 Prghov P4 dqg P5 vhw (cid:11) wr d pdwul{ ri }hurv dqg dgmxvw (cid:25) dqg (cid:6) vr wkdw wkh jurzwk udwhv ri frqvxpswlrq dqg glylghqgv duh wkh vdph dv lq prghov P6 dqg P71 Prgho P8 lv h{shulphqw 4E ri Wdxfkhq +4<<9,1 Wkh prghov duh glvfxvvhg ixuwkhu lq wkh wh{w1

Wdeoh 5= Vlpxodwlrq uhvxowv lq prgho P41 W@433 W@833 W@4333 43wk (wloh ri (cid:17)a 31;;9 31;;7 31;<7 WV Phgldq ri (cid:17)a 31<:4 31<:4 31<:5 WV <3wk (wloh ri (cid:17)a 41369 41368 41358 WV 43wk (wloh ri (cid:16)a 051<9; 061444 051954 WV Phgldq ri (cid:16)a 41597 41633 41757 WV <3wk (wloh ri (cid:16)a 81664 81748 71:48 WV 43wk (wloh ri (cid:17)a 31:<7 31:98 31:<3 FX Phgldq ri (cid:17)a 31<9: 31<98 31<9: FX <3wk (wloh ri (cid:17)a 4139; 4139; 41398 FX 43wk (wloh ri (cid:16)a 0919:7 0:1:86 09199; FX Phgldq ri (cid:16)a 415;7 4153: 415;4 FX <3wk (wloh ri (cid:16)a 43169: 4318:; <1<36 FX 43wk (wloh ri wa 0416:< 041763 0416:< (cid:17)WV Phgldq ri wa 31358 31345 31358 (cid:17)WV <3wk (wloh ri wa 41455 41464 413<5 (cid:17)WV 43wk (wloh ri wa 041569 04158; 0415<5 (cid:16)WV Phgldq ri wa 031345 31333 31363 (cid:16)WV <3wk (wloh ri wa 4158; 4163; 4154; (cid:16)WV 43wk (wloh ri wa 051776 051858 05176< (cid:17)FX Phgldq ri wa 0313:< 031467 0313:3 (cid:17)FX <3wk (wloh ri wa 417;8 41846 417;7 (cid:17)FX 43wk (wloh ri wa 0513:8 051354 05135< (cid:16)FX Phgldq ri wa 031344 031383 03133; (cid:16)FX <3wk (wloh ri wa 514;6 5146; 5155; (cid:16)FX NV+wa , 3136: 31365 313;5 (cid:17)WV NV+wa , 3134: 31353 313:5 (cid:16)WV NV+wa , 3145: 31483 31485 (cid:17)FX NV+wa , 31447 3145< 3144: (cid:16)FX Uhm Udwh ri M whvw 419 419 41: WV Uhm Udwh ri M whvw 319 315 317 FX Uhm Udwh ri Sursrvhg whvw 31: 31< 413 Qrwhv= Lq wklv prgho/ wkh uhmhfwlrq udwh ri wkh sursrvhg whvw uhsuhvhqwv lwv vl}h1 NV+1, uhihuv wr wkh Nroprjrury0Vpluqryvwdwlvwlffrpsdulqjwkhvdpsolqjglvwulexwlrqriwkhdujxphqwzlwkdvwdqgdug qrupdo glvwulexwlrq1 Doo whvwv kdyh 8( qrplqdo vl}h1 4/333 uhsolfdwlrqv zhuh frqgxfwhg lq hdfk vlpxodwlrq1

Wdeoh 6= Vlpxodwlrq uhvxowv lq prgho P51 W@433 W@833 W@4333 43wk (wloh ri (cid:17)a 31<4; 31<55 31<4< WV Phgldq ri (cid:17)a 41335 41338 41334 WV <3wk (wloh ri (cid:17)a 413:9 413;5 413:3 WV 43wk (wloh ri (cid:16)a 051986 051:67 051963 WV Phgldq ri (cid:16)a 417:7 419:3 417<9 WV <3wk (wloh ri (cid:16)a 91778 91<;< 91487 WV 43wk (wloh ri (cid:17)a 31686 31664 315<7 FX Phgldq ri (cid:17)a 41376 41369 4135< FX <3wk (wloh ri (cid:17)a 414<4 41477 41467 FX 43wk (wloh ri (cid:16)a 419;8 41975 419:8 FX Phgldq ri (cid:16)a 461485 47134; 461;85 FX <3wk (wloh ri (cid:16)a :719<; 9418;6 971<34 FX 43wk (wloh ri wa 061553 081;43 0:13;6 (cid:17)WV Phgldq ri wa 041;<7 0614:6 061977 (cid:17)WV <3wk (wloh ri wa 031875 031987 031<34 (cid:17)WV 43wk (wloh ri wa 0516:4 051669 05175: (cid:16)WV Phgldq ri wa 0415;< 041577 04164; (cid:16)WV <3wk (wloh ri wa 03169; 03165: 0316<7 (cid:16)WV 43wk (wloh ri wa 0441869 05315;3 0551<99 (cid:17)FX Phgldq ri wa 04167; 05174< 061357 (cid:17)FX <3wk (wloh ri wa 31743 3137: 0313;8 (cid:17)FX 43wk (wloh ri wa 041;66 051353 051378 (cid:16)FX Phgldq ri wa 03135: 31353 31344 (cid:16)FX <3wk (wloh ri wa :1644 81844 81:98 (cid:16)FX NV+wa , 31989 31:68 31:;3 (cid:17)WV NV+wa , 3187< 3186< 3188: (cid:16)WV NV+wa , 3175: 31884 318;6 (cid:17)FX NV+wa , 31543 314:6 31536 (cid:16)FX Uhm Udwh ri M whvw 414 413 31< WV Uhm Udwh ri M whvw 31< 415 513 FX Uhm Udwh ri Sursrvhg whvw 315 315 319 Qrwhv= Dv iru Wdeoh 51

Wdeoh 7= Vlpxodwlrq uhvxowv lq Prgho P61 W@433 W@833 W@4333 43wk (wloh ri (cid:17)a 31<4: 31<74 31<7< WV Phgldq ri (cid:17)a 31<:; 31<:5 31<:3 WV <3wk (wloh ri (cid:17)a 41359 31<<8 31<;< WV 43wk (wloh ri (cid:16)a 041648 0314;3 3155: WV Phgldq ri (cid:16)a 419<< 416;8 41654 WV <3wk (wloh ri (cid:16)a 71546 51959 51595 WV 43wk (wloh ri (cid:17)a 31;7: 31<67 31<7: FX Phgldq ri (cid:17)a 31<:5 31<:3 31<9< FX <3wk (wloh ri (cid:17)a 41368 31<<9 31<;< FX 43wk (wloh ri (cid:16)a 071587 031834 31477 FX Phgldq ri (cid:16)a 416<7 415<; 4158; FX <3wk (wloh ri (cid:16)a 71;76 51995 5158< FX 43wk (wloh ri wa 041433 04156; 0415:5 (cid:17)WV Phgldq ri wa 3154: 313:< 031344 (cid:17)WV <3wk (wloh ri wa 41593 41635 4164< (cid:17)WV 43wk (wloh ri wa 0413<4 04149: 04159< (cid:16)WV Phgldq ri wa 31536 313;4 31365 (cid:16)WV <3wk (wloh ri wa 4176: 41643 41673 (cid:16)WV 43wk (wloh ri wa 051337 0417;; 04173; (cid:17)FX Phgldq ri wa 3139: 31333 031385 (cid:17)FX <3wk (wloh ri wa 41774 41687 41665 (cid:17)FX 43wk (wloh ri wa 041;7: 041795 0416:: (cid:16)FX Phgldq ri wa 31394 031336 031389 (cid:16)FX <3wk (wloh ri wa 41:86 41678 4169; (cid:16)FX NV+wa , 313<5 31378 3135: (cid:17)WV NV+wa , 313;9 31377 31357 (cid:16)WV NV+wa , 313;: 3136: 31368 (cid:17)FX NV+wa , 313;7 3136; 3136: (cid:16)FX ( Uhm Udwh ri M whvw 416 41; 615 WV ( Uhm Udwh ri M whvw 414 51< 71: FX ( Uhm Udwh ri Sursrvhg whvw 915 8513 <319 Qrwhv=Lqwklvprgho/wkhuhmhfwlrqudwhriwkhsursrvhgwhvwuhsuhvhqwvlwvsrzhu1 NV+1, uhihuvwrwkh Nroprjrury0Vpluqryvwdwlvwlffrpsdulqjwkhvdpsolqjglvwulexwlrqriwkhdujxphqwzlwkdvwdqgdug qrupdo glvwulexwlrq1 Doo whvwv kdyh 8( qrplqdo vl}h1 4/333 uhsolfdwlrqv zhuh frqgxfwhg lq hdfk vlpxodwlrq1

Wdeoh 8= Vlpxodwlrq uhvxowv lq Prgho P71 W@433 W@833 W@4333 43wk (wloh ri (cid:17)a 41359 413<9 4143; WV Phgldq ri (cid:17)a 413<7 41459 41466 WV <3wk (wloh ri (cid:17)a 41498 41496 4148; WV 43wk (wloh ri (cid:16)a 8149: <1<6; 431<44 WV Phgldq ri (cid:16)a <18<; 451835 461483 WV <3wk (wloh ri (cid:16)a 4918:: 4:1557 4:1393 WV 43wk (wloh ri (cid:17)a 31<49 413<6 41443 FX Phgldq ri (cid:17)a 41444 41463 41468 FX <3wk (wloh ri (cid:17)a 41535 414:3 41496 FX 43wk (wloh ri (cid:16)a ;1789 431945 4415<5 FX Phgldq ri (cid:16)a 461499 461785 461965 FX <3wk (wloh ri (cid:16)a 741<83 551445 4;1656 FX 43wk (wloh ri wa 05134; 041:84 041:43 (cid:17)WV Phgldq ri wa 031:9; 031799 031636 (cid:17)WV <3wk (wloh ri wa 315:6 318;6 31:6< (cid:17)WV 43wk (wloh ri wa 051344 04195: 041883 (cid:16)WV Phgldq ri wa 031:85 0316<4 03156; (cid:16)WV <3wk (wloh ri wa 315:; 31:5: 4135; (cid:16)WV 43wk (wloh ri wa 051;:< 041;7< 041934 (cid:17)FX Phgldq ri wa 0317:6 031657 031544 (cid:17)FX <3wk (wloh ri wa 319;9 31;56 31;;9 (cid:17)FX 43wk (wloh ri wa 041846 0416:8 041674 (cid:16)FX Phgldq ri wa 0313;: 0313:9 031364 (cid:16)FX <3wk (wloh ri wa 51<57 41878 41747 (cid:16)FX NV+wa , 31647 314;; 31477 (cid:17)WV NV+wa , 31663 314:3 3143: (cid:16)WV NV+wa , 314;; 3145< 313<4 (cid:17)FX NV+wa , 31435 31376 31358 (cid:16)FX ( Uhm Udwh ri M whvw 4<14 471; 4316 WV ( Uhm Udwh ri M whvw 51; 718 719 FX ( Uhm Udwh ri Sursrvhg whvw 913 5:16 8514 Qrwhv= Dv iru Wdeoh 71

Wdeoh 9= Vlpxodwlrq uhvxowv lq Prgho P81 W@433 W@833 W@4333 43wk (wloh ri (cid:17)a 31<88 31<96 31<98 WV Phgldq ri (cid:17)a 31<:3 31<:3 31<:3 WV <3wk (wloh ri (cid:17)a 31<;7 31<:9 31<:7 WV 43wk (wloh ri (cid:16)a 413;7 41533 41559 WV Phgldq ri (cid:16)a 4159< 415<< 41635 WV <3wk (wloh ri (cid:16)a 418;: 41765 416;9 WV 43wk (wloh ri (cid:17)a 31<88 31<96 31<98 FX Phgldq ri (cid:17)a 31<:3 31<:3 31<:3 FX <3wk (wloh ri (cid:17)a 31<;7 31<:9 31<:9 FX 43wk (wloh ri (cid:16)a 413<< 41536 4155< FX Phgldq ri (cid:16)a 41639 41637 41637 FX <3wk (wloh ri (cid:16)a 4196< 4176< 416<3 FX 43wk (wloh ri wa 04167< 0416;4 041675 (cid:17)WV Phgldq ri wa 031345 31336 03134: (cid:17)WV <3wk (wloh ri wa 41648 41665 41659 (cid:17)WV 43wk (wloh ri wa 041697 041655 0415;< (cid:16)WV Phgldq ri wa 03147< 031339 3135: (cid:16)WV <3wk (wloh ri wa 414<7 4169; 415;8 (cid:16)WV 43wk (wloh ri wa 04174: 0416<5 041675 (cid:17)FX Phgldq ri wa 031363 031336 031373 (cid:17)FX <3wk (wloh ri wa 41634 41668 4165; (cid:17)FX 43wk (wloh ri wa 041593 0415<4 041547 (cid:16)FX Phgldq ri wa 31363 31377 313:5 (cid:16)FX <3wk (wloh ri wa 4167: 41739 4167< (cid:16)FX NV+wa , 31348 3135< 31358 (cid:17)WV NV+wa , 313:9 31357 31359 (cid:16)WV NV+wa , 31357 31363 31357 (cid:17)FX NV+wa , 31368 31368 31373 (cid:16)FX ( Uhm Udwh ri M whvw 815 715 71; WV ( Uhm Udwh ri M whvw 818 716 813 FX ( Uhm Udwh ri Sursrvhg whvw ;618 43313 43313 Qrwhv= Dv iru Wdeoh 71