a)ANLISIS DEL PBI Y CONSUMO DE FORMA CONJUNTA:Al haber analizado por separado cada serie: PBI y CONSUMO, al utilizar el Test de ic!ey"#uller a$bas son no estacionarias% este proble$a se solucion& $ediante la aplicaci&n de una pri$era di'erencia( )s as* +ue a$bas son Inte,radas de Orden Uno, I-./, lo cual abre la posibilidad a la e0istencia de cointe,raci&n de dichas series(0100,000200,000300,000400,000500,00050 55 60 65 70 75 80 85 90 95 00 05 10CONSUMO PBISe plantea el $odelo si,uiente, para ir esbozando al,una relaci&n e0istente entre a$bas 1ariables, y descartar la e0istencia de una relaci&n espuria entre las 1ariables% es decir, +ue sea una re,resi&n +ue a pesar de cu$plir con la si,ni'icancia del $odelo, sea 'icticia en la relaci&n real(Dependent Varia!e" PBIMet#$d" %ea&t S'(are&Date" 12)03)14 *i+e" 17"02Sa+p!e" 1950 2013In,!(ded $&er-ati$n&" 64Varia!e C$e..i,ient Std/ 0rr$r t1Stati&ti, Pr$/C 118439/52 2348/908 17/850255 0/0000CONSUMO 1/689206 0/018666 90/49407 0/000021&'(ared 0/992486Mean dependent -ar 170786/63d4(&ted 21&'(ared 0/992365S/D/ dependent -ar 97964/74S/0/ $. re5re&&i$n 8560/16536ai6e in.$ ,riteri$n 20/97838S(+ &'(ared re&id 4/540709S,#8ar9 ,riteri$n 21/04584%$5 !i6e!i#$$d 1669/3081:annan1;(inn ,riter/ 21/004963(t$+ati, 1 a&ed $n SIC, +aA!a5B10?t1Stati&ti, Pr$/C3(5+ented Di,6e@120SID01?Met#$d" %ea&t S'(are&Date" 12)03)14 *i+e" 09"19Sa+p!e >ad4(&ted?" 1953 2013In,!(ded $&er-ati$n&" 61 a.ter ad4(&t+ent&Varia!e C$e..i,ient Std/ 0rr$r t1Stati&ti, Pr$/20SID01>11? 11/005954 0/130222 17/724893 0/000021&'(ared 0/498532Mean dependent -ar 173/39453d4(&ted 21&'(ared 0/498532S/D/ dependent -ar 12039/63S/0/ $. re5re&&i$n 8525/79036ai6e in.$ ,riteri$n 20/95584S(+ &'(ared re&id 4/360709S,#8ar9 ,riteri$n 20/99044%$5 !i6e!i#$$d 1638/1530:annan1;(inn ,riter/ 20/96940D(rin1=at&$n &tat 1/982688)l Test de ic!ey"#uller rechaza la e0istencia de 3a*z unitaria, es decir, la serie de 3esiduos es estacionaria o I-4/(c)PRUEBA DE COINTEGRACIN: 5abiendo cu$plido los re+ueri$ientos necesarios: )stacionariedad de los residuos y series I-./ para las 1ariables% pode$os ubicar al,6n ,rado de cointe,raci&n entre las series PBI y CONSUMO()s as* +ue utiliza$os el M7todo de 8ohansen para deter$inar el n6$ero de 1ectores de cointe,raci&n(Date" 12)03)14 *i+e" 11"22Sa+p!e" 1950 2013In,!(ded $&er-ati$n&" 61Serie&" PBI CONSUMO %a5& inter-a!" 1 t$ 2 Se!e,ted >0/05 !e-e!C? N(+er $. C$inte5ratin5 2e!ati$n& @ M$de!Data *rend" N$ne N$ne %inear %inear ;(adrati,*e&t *@pe N$ Inter,ept Inter,ept Inter,ept Inter,ept Inter,eptN$ *rend N$ *rend N$ *rend *rend *rend*ra,e 1 0 0 0 0MaA10i5 1 0 0 0 0 CCriti,a! -a!(e& a&ed $n Ma,Einn$n1:a(51Mi,#e!i& >1999? In.$r+ati$n Criteria @ 2an6 and M$de!Data *rend" N$ne N$ne %inear %inear ;(adrati,2an6 $r N$ Inter,ept Inter,ept Inter,ept Inter,ept Inter,eptN$/ $. C0& N$ *rend N$ *rend N$ *rend *rend *rend %$5 %i6e!i#$$d @2an6 >r$8&? and M$de! >,$!(+n&?0 11192/103 11192/103 11189/557 11189/557 11187/0551 11186/018 11185/821 11185/719 11185/589 11183/4462 11185/509 11183/240 11183/240 11182/993 11182/993 36ai6e In.$r+ati$n Criteria @ 2an6 >r$8&? and M$de! >,$!(+n&?039/3476439/3476439/3297339/3297339/313291 39/27927C39/3056139/3350539/3635839/32610239/3937539/3849239/3849239/4424039/44240 S,#8ar9 Criteria @ 2an6 >r$8&? and M$de! >,$!(+n&?039/62448C39/62448C39/6757739/6757739/72855139/6945239/7554639/8195139/8826439/87977239/9474240/0078040/0078040/1344940/13449Se identi'ica la e0istencia de una ecuaci&n de cointe,raci&n, dado el supuesto de Intercepto sin tendencia en la C) y 9A3(As* el testeo indica +ue e0iste una ecuaci&n de cointe,raci&n cuando no se considera intercepto y tendencia(Date" 12)03)14 *i+e" 11"26Sa+p!e >ad4(&ted?" 1953 2013In,!(ded $&er-ati$n&" 61 a.ter ad4(&t+ent&*rend a&&(+pti$n" N$ deter+ini&ti, trendSerie&" PBI CONSUMO %a5& inter-a! >in .ir&t di..eren,e&?" 1 t$ 2Unre&tri,ted C$inte5rati$n 2an6 *e&t >*ra,e?:@p$t#e&i9ed *ra,e 0/05N$/ $. C0>&? 0i5en-a!(e Stati&ti, Criti,a! Va!(e Pr$/CCN$ne C0/18087913/1873812/320900/03573t +$&t 10/0165251/0164714/1299060/3638 *ra,e te&t indi,ate& 1 ,$inte5ratin5 e'n>&? at t#e 0/05 !e-e! C den$te& re4e,ti$n $. t#e #@p$t#e&i& at t#e 0/05 !e-e! CCMa,Einn$n1:a(51Mi,#e!i& >1999? p1-a!(e&Unre&tri,ted C$inte5rati$n 2an6 *e&t >MaAi+(+ 0i5en-a!(e?:@p$t#e&i9ed MaA10i5en 0/05N$/ $. C0>&? 0i5en-a!(e Stati&ti, Criti,a! Va!(e Pr$/CCN$ne C0/18087912/1709111/224800/03403t +$&t 10/0165251/0164714/1299060/3638 MaA1ei5en-a!(e te&t indi,ate& 1 ,$inte5ratin5 e'n>&? at t#e 0/05 !e-e! C den$te& re4e,ti$n $. t#e #@p$t#e&i& at t#e 0/05 !e-e! CCMa,Einn$n1:a(51Mi,#e!i& >1999? p1-a!(e& Unre&tri,ted C$inte5ratin5 C$e..i,ient& >n$r+a!i9ed @ FCS11CBI?" PBI CONSUMO14/6701055/900105 9/130105 10/000143 Unre&tri,ted 3d4(&t+ent C$e..i,ient& >a!p#a?" D>PBI? 13339/55448/40742D>CONSUMO? 11967/082322/87531 C$inte5ratin5 0'(ati$n>&?"%$5 !i6e!i#$$d 11186/018N$r+a!i9ed ,$inte5ratin5 ,$e..i,ient& >&tandard err$r in parent#e&e&?PBI CONSUMO 1/000000 11/263292 >0/07565?3d4(&t+ent ,$e..i,ient& >&tandard err$r in parent#e&e&?D>PBI?0/155959 >0/04441?D>CONSUMO?0/091864 >0/03046?1 Tanto para los Test de Traza y M20i$o 9alor, se identi'ica la e0istencia de un 1ectorde cointe,raci&n para la $*ni$a probabilidad de 4(4:( Sin e$bar,o, es necesario co$probar los si,nos de los Coe'icientes Al'a, para as* notar si los residuos a'ectar2n en la relaci&n de lar,o plazo -o ta$bi7n lla$ada ;Nor$alized cointe,ratin, coe''icients(.?@>? A .B(>B4C4)ntonces la hip&tesis nula se rechaza a 'a1or de la alterna, co$probando la e0istencia de un 1ector de inte,raci&n(1 At Most .:.(4.DE@. A E(.BCC4DA+u*, en ca$bio, la hip&tesis nula es aceptada, indicando la e0istencia de cuanto $2s un 1ector de cointe,raci&n(-Test del Mximo autovalor:Se di1ide en dos subtests: None y At Most ., la se,unda es la co$probaci&n de la pri$era(o Para None, se $ane=a el si,uiente criterio de decisi&n, donde:Ho: rangodecointegracin r=0H1: r=1, rangodecointegracin esigual ar+1o Para At $ost ., se $ane=a el si,uiente criterio de decisi&n, donde:Ho: el rangodecointegracines r 1H1: el rango decointegracin es r+21 Para None : .B(.@4C. A ..(BBE?4Se rechaza la hip&tesis nula, es decir el ran,o de cointe,raci&n es i,ual a rF.1 Para At Most .: .(4.DE@. AE(.BCC4DSe acepta la hip&tesis nula, indicando +ue el ran,o de cointe,raci&n es r .)ntonces, lue,o de analizar los Test de Traza y M20i$o auto1alor, a$bos indican la e0istencia de cointe,raci&n de por lo $enos se,undo orden( )s as* +ue se co$prueba la e0istencia de una relaci&n razonable entre el PBI y el CONSUMO()CUACIGN ) COINT)H3ACIGNN$r+a!i9ed ,$inte5ratin5 ,$e..i,ient& >&tandard err$r in parent#e&e&?PBI CONSUMO 1/000000 11/263292 >0/07565?3d4(&t+ent ,$e..i,ient& >&tandard err$r in parent#e&e&?D>PBI?0/155959 >0/04441?D>CONSUMO?0/091864 >0/03046?PBI1.263292CONSUMO=0PBI=1.263292CONSUMOSe ha especi'icado la relaci&n de lar,o plazo -ecuaci&n anterior/, sin e$bar,o, al analizar los coe'icientes al'a de correcci&n, sus 1alores son positi1os, lo cual a'ecta ne,ati1a$ente la relaci&n de lar,o plazo -e+uilibrio/( Por lo tanto, este $odelo no es pertinente, al $enos co$o se calcula, es decir, sin haber sido trans'or$ado(Por lo tanto, para recobrar la estacionariedad en los residuos, es necesaria la trans'or$aci&nen di'erencias, y as* esti$ar el $odelo 9A3(MODELO VAR PARA LAS SERIES EN DIFERENCIA: PBI Y CONSUMO.Ia especi'icaci&n del $odelo 9A3, no es te&rica, pero es un re'le=o de ecuaciones si$ult2neas para series de tie$po, es por ello +ue la esti$aci&n se basa en criterios l&,icos basados sobre el A!!ai!e y SchJarz, para nu$erosos $odelos para 1arios retrasos, para as*1eri'icar cu2l es el $e=or()$peza$os esti$ando un 9A3-B/: Ve,t$r 3(t$re5re&&i$n 0&ti+ate& Date" 12)03)14 *i+e" 16"53 Sa+p!e >ad4(&ted?" 1953 2013 In,!(ded $&er-ati$n&" 61 a.ter ad4(&t+ent& Standard err$r& in > ? G t1&tati&ti,& in H IDCONSUMO DPBIDCONSUMO>11?0/3743290/295675 >0/28762?>0/42578?H 1/30147I H 0/69444IDCONSUMO>12? 11/039537 11/561879 >0/28595?>0/42330?H13/63544I H13/68979IDPBI>11?0/1719480/377685 >0/19543?>0/28931?H 0/87984I H 1/30549IDPBI>12?0/5904170/999886 >0/19745?>0/29230?H 2/99020I H 3/42081IC1651/9722771/713 >848/183?>1255/60?H 1/94766I H 2/20748I 21&'(ared0/4344080/441748 3d4/ 21&'(ared0/3940090/401873 S(+ &'/ re&id&1/5807093/470709 S/0/ e'(ati$n5315/9847869/484 d$. ad4/?3/530714 Deter+inant re&id ,$-arian,e2/970714 %$5 !i6e!i#$$d 11189/557 36ai6e in.$r+ati$n ,riteri$n39/32973 S,#8ar9 ,riteri$n39/67577%(e5$ (n V32>3?" Ve,t$r 3(t$re5re&&i$n 0&ti+ate& Date" 12)03)14 *i+e" 16"53 Sa+p!e >ad4(&ted?" 1954 2013 In,!(ded $&er-ati$n&" 60 a.ter ad4(&t+ent& Standard err$r& in > ? G t1&tati&ti,& in H IDCONSUMO DPBIDCONSUMO>11?0/4341070/437978 >0/30370?>0/44706?H 1/42937I H 0/97968IDCONSUMO>12? 11/107630 11/663523 >0/30036?>0/44213?H13/68771I H13/76248IDCONSUMO>13?0/2625080/201607 >0/32641?>0/48048?H 0/80423I H 0/41959IDPBI>11?0/1679660/314510 >0/20574?>0/30285?H 0/81641I H 1/03850IDPBI>12?0/5900840/971282 >0/20300?>0/29882?H 2/90682I H 3/25037IDPBI>13? 10/1194420/026841 >0/22205?>0/32687?H10/53790I H 0/08212IC1472/0222328/876 >905/353?>1332/70?H 1/62591I H 1/74748I 21&'(ared0/4429330/455848 3d4/ 21&'(ared0/3798690/394246 S(+ &'/ re&id&1/5607093/370709 S/0/ e'(ati$n5418/4187976/062 d$. ad4/?3/660714 Deter+inant re&id ,$-arian,e2/850714 %$5 !i6e!i#$$d 11168/827 36ai6e in.$r+ati$n ,riteri$n39/42756 S,#8ar9 ,riteri$n39/91624V32>4?" Ve,t$r 3(t$re5re&&i$n 0&ti+ate& Date" 12)03)14 *i+e" 16"53 Sa+p!e >ad4(&ted?" 1955 2013 In,!(ded $&er-ati$n&" 59 a.ter ad4(&t+ent& Standard err$r& in > ? G t1&tati&ti,& in H IDCONSUMO DPBIDCONSUMO>11?0/3850410/342945 >0/31711?>0/46431?H 1/21421I H 0/73860IDCONSUMO>12? 11/126515 11/695949 >0/31834?>0/46611?H13/53872I H13/63851IDCONSUMO>13?0/2562220/184342 >0/34809?>0/50967?H 0/73608I H 0/36169IDCONSUMO>14?0/2127450/419334 >0/33816?>0/49514?H 0/62912I H 0/84690IDPBI>11?0/2015620/379049 >0/21558?>0/31565?H 0/93497I H 1/20085IDPBI>12?0/6273281/042392 >0/21244?>0/31106?H 2/95292I H 3/35111IDPBI>13? 10/1123440/041822 >0/22789?>0/33367?H10/49298I H 0/12534IDPBI>14? 10/182682 10/355283 >0/23100?>0/33823?H10/79083I H11/05043IC1594/8892550/282 >962/714?>1409/60?H 1/65666I H 1/80922I 21&'(ared0/4506600/468499 3d4/ 21&'(ared0/3627660/383459 S(+ &'/ re&id&1/5307093/280709 S/0/ e'(ati$n5535/2588104/689 d$. ad4/?4/000714 Deter+inant re&id ,$-arian,e2/870714 %$5 !i6e!i#$$d 11149/496 36ai6e in.$r+ati$n ,riteri$n39/57614 S,#8ar9 ,riteri$n40/209979A3-D/: Ve,t$r 3(t$re5re&&i$n 0&ti+ate& Date" 12)03)14 *i+e" 16"54 Sa+p!e >ad4(&ted?" 1957 2013 In,!(ded $&er-ati$n&" 57 a.ter ad4(&t+ent& Standard err$r& in > ? G t1&tati&ti,& in H IDCONSUMO DPBIDCONSUMO>11?0/3479690/289917 >0/30196?>0/44887?H 1/15237I H 0/64588IDCONSUMO>12? 10/980205 11/458888 >0/30444?>0/45256?H13/21969I H13/22364IDCONSUMO>13?0/3265020/356177 >0/34238?>0/50896?H 0/95362I H 0/69981IDCONSUMO>14?0/4683890/670725 >0/35556?>0/52854?H 1/31734I H 1/26900IDCONSUMO>15? 10/781198 11/136013 >0/34048?>0/50613?H12/29442I H12/24452IDCONSUMO>16? 10/462779 10/437793 >0/35520?>0/52802?H11/30286I H10/82913IDPBI>11?0/1781960/383753 >0/20869?>0/31023?H 0/85387I H 1/23701IDPBI>12?0/5861830/917739 >0/21098?>0/31363?H 2/77838I H 2/92621IDPBI>13? 10/300919 10/252756 >0/22491?>0/33433?H11/33796I H10/75601IDPBI>14? 10/384766 10/590238 >0/23054?>0/34270?H11/66900I H11/72233IDPBI>15?0/5388210/877162 >0/24289?>0/36107?H 2/21836I H 2/42937IDPBI>16?0/4811550/474845 >0/25757?>0/38288?H 1/86808I H 1/24020IC1253/1262004/421 >984/374?>1463/29?H 1/27302I H 1/36980I 21&'(ared0/5708720/571284 3d4/ 21&'(ared0/4538360/454361 S(+ &'/ re&id&1/1907092/640709 S/0/ e'(ati$n5205/9467738/762 d$. ad4/?3/800714 Deter+inant re&id ,$-arian,e2/260714 %$5 !i6e!i#$$d 11103/785 36ai6e in.$r+ati$n ,riteri$n39/64159 S,#8ar9 ,riteri$n40/57350Se #a e&ti+ad$ +$de!$& V32 de&ded$& #a&ta &ei& re9a5$&, e! ,riteri$ de e!e,,iJn &erKa a'(e! +$de!$ '(e pre&enta e! 366ai6e @ S,#8ar9 +en$re&/ Sin e+ar5$, eAi&te (n *e&t de 2e9a5$& Lpti+$& en 0-ie8&, '(e pr$-ee (na &erie de e&tadK&ti,$& a&ad$& &$re !a ra9Jn de -er$&i+i!it(d"V32 %a5 Order Se!e,ti$n Criteria0nd$5en$(& -aria!e&" DCONSUMO DPBI 0A$5en$(& -aria!e&" C Date" 12)03)14 *i+e" 16"55Sa+p!e" 1950 2013In,!(ded $&er-ati$n&" 58 %a5 %$5% %2