A Revisit on the Role of Macro Imbalances in. the US Recession of : Nonlinear Causality Approach

Transcription

1 Applied Maheaical Sciences, Vol. 7, 2013, no. 47, HIKARI Ld, A Revisi on he Role of Macro Ibalances in he US Recession of : Nonlinear Causaliy Approach Aviral Kuar Tiwari Research scholar and Faculy of Applied Econoics Faculy of Manageen, ICFAI Universiy Tripura Kaalgha, Sadar, Wes Tripura, Pin , India aviral.eco@gail.co Bhari Pandey Reader and Head, Deparen of Econoics J.N.P.G. College, Universiy of Lucknow, Lucknow, India dr.bharipandey06@gail.co Copyrigh 2013 Aviral Kuar Tiwari and Bhari Pandey. This is an open access aricle disribued under he Creaive Coons Aribuion License, which peris unresriced use, disribuion, and reproducion in any ediu, provided he original work is properly cied. Absrac This sudy reeaines evidences fro a recen sudy by Paul (2010) on he role of acro ibalances in he US recession of Paul (2010) ascribes he prolonged recession o he win deficis; while we idenify fiscal defici as he proble. Keywords: Macro ibalances, US recession, nonlinear Granger causaliy

2 2322 Aviral Kuar Tiwari and Bhari Pandey 1. Inroducion The US recession of has drawn considerable ineres aong researchers and policyakers. Aeps have been ade o idenify cause of his recession. Using vecor Auoregressive (VAR) odel, Paul (2010) has shown ha rade deficis fiscal deficis have conribued o he lower ineres rae and declining oupu during He also shows ha low ineres raes caused low privae saving, which conribued o he housing bubble. So, Paul (2010) concludes: low saving and win deficis have caused he recession. 1 Paul s (2010) resuls are based on VAR odel which can produce biased resul in he presence of nonlineariy in he series. This paper is revisis Paul s (2010) conclusions by ipleening he nonlinear Granger causaliy a la Hiesra and Jones (1994) (HJ henceforh), which is an iproveen over Baek and Brock (1992) (BB henceforh). 2. Nonlinear Granger causaliy Linear approach o causaliy es can have low power in he presence of nonlineariy. BB firs proposed a nonparaeric es o capure nonlinear causaliy ha is no deeced by sandard Granger es. The es uilizes he correlaion inegrals, which is an esiaor of spaial probabiliies across ie, based on he closeness of he poins in hyperspace ha deecs he relaion beween wo ie series. Because he disribuion of he es saisic is one-ailed, rejecions of he null hypohesis are resriced o one-ail. HJ odified he BB es which has beer sall-saple properies and does no require he assupion of i.i.d. HJ in heir Mone Carlo siulaions show ha he odified es is robus o srucural breaks in he series and coneporaneous correlaions in he errors of he VAR odel used o filer ou linear cross- and auo-dependence. Following HJ, le F ( I 1) denoe he condiional probabiliy disribuion of given he inforaion se I 1, which consiss of an L - lengh lagged vecor of, say (, +1,..., 1), and an L Y -lengh lagged vecor ofy, say Y ( Y, Y +1,..., Y 1). In he es, a given pair of lags L and L Y holds wihin he following relaionship: H 0 : F( I 1) = F( ( I 1 Y )) (1) The null hypohesis of ineres hus saes ha aking he vecor of pas Y-values ou of he inforaion se does no affec he disribuion of curren -values. Adoping he noaion used by HJ, we denoe he -lengh lead vecor of suarize he vecors defined so far, for Z, as: by. We 1 More coprehensive review on his aspec can be referred in Paul (2010) as his sudy is jus a revisi of he evidence of Paul (2010) herefore, review has been avoided.

3 A revisi on he role of acro ibalances in he US recession 2323,,..., ), = 1, 2, = ( = (, +1,..., 1 = ( Y, Y +1,..., Y 1), ), = 1, 2, (2) Y = 1, 2, A crucial clai ade by Hiesra and Jones (1994) wihou proof, saes ha he null hypohesis in equaion (1) iplies, for all ε > 0: ( s < ε s < ε Y Ys < ε ) ( < ε < ε ) P, = s s P, (3) where P(A B) denoes he condiional probabiliy of A given B, and he aiu nors-a disance easure (here supreu nor), which for a d-diensional vecor T d = ( 1,..., d ) and is given by = supi= 1 i. The probabiliy on he lef-hand side of equaion (3) is he condiional probabiliy ha wo arbirary -lengh lead vecors { } (i.e., and s ) are wihin a disance ε of each oher (ε -close), given he corresponding L -lengh lag vecor of { } (i.e., and s ) and LY -lengh lag vecor { Y }(i.e., and s ) are wihin ε of each oher (or ε -close). The probabiliy on he righ hand Side (RHS) of equaion (3) is he condiional probabiliy ha wo arbirary -lengh lead/lag vecors of { }(i.e., and s ) are wihin a disance ε for each oher, given ha he corresponding lagged -lengh lag vecors of { } (i.e., and s ) are wihin a disance,ε of each oher. Hence, non- Granger causaliy iplies ha he probabiliy of wo arbirary lead vecors of lengh are wihin a disance of ε of each oher is he sae, condiional upon he wo lag vecors of { } being wihin a disance ε of each oher; and wo lag vecors of { Y } being wihin a disance ε of each oher. In oher words, no Granger causaliy eans ha he probabiliy of he lead vecors are wihin disance ε is he sae wheher we have inforaion abou he disance beween { Y } lag vecors or no. We can wrie he condiional probabiliy epressed in equaion (3) as raios of join probabiliies. Assuing ha C 1( +,, ε)/ C2(,, ε) and C 3( +, ε)/ C4(, ε) denoe he raio of join probabiliies corresponding o he lef hand side (LHS) and RHS of equaion (3), he join probabiliies is wrien as: + + = P( s < ε Y Ys ε ) ( < ε Y Y ε ) C 1 ( L, L, ε ), <, + y C 2 ( L, L, ε ) P, <, y = s s

4 2324 Aviral Kuar Tiwari and Bhari Pandey + + = P( s ) ( ) C 3 ( + L, ε ) < ε, C 4 ( L, ε ) P < ε (4) = s The sric Granger non-causaliy condiion in equaion (3) can be wrien as follows: C 1( +,, ε ) C3( +, ε ) = C2( L, L, ε ) C4( L, ε ) y (5) For given values of, L, L Y 1 and ε > 0. Le { } and { Y } be he acual realizaion of he process and I ( A, B, ε ), an indicaor funcion ha akes he value 1 if he vecor A and B are wihin a disance ε of each oher; and zero oherwise. Also consider ha he properies of he supreu nor + + allow us o inscribe P ( s < ε, s < ε ) as P ( s < ε ), so ha he esiaes of he correlaions inegrals in equaion (5) can be epressed as: + + (,, ε ) I ( Y, Y ε ) 2 C1( +,, ε, n) I s s,, n( n 1) 2 C2(,, ε, n) I(, s, ε ) I( Y, Ys, ε ) n( n 1) C3( +, ε, n) I(, s,ε ) n( n 1) 2 C4(, ε, n) I(, s,ε ) n( n 1) For, s = a(, ) + 1,..., T + 1; n = T + 1 a(, ). Assuing ha and Y are sricly saionary and ee he required iing condiions as specified in Denker and Keller (1983); and under he null hypohesis Y does no sricly Granger cause, he es saisic T is asypoically norally disribued. Tha is, C1( + L,,, ) 3(,, ) ε n C + ε n 1 2 T = ~ N 0, σ (, L,, ε ), 2(,,, ) 4(,, ) (6) C ε n C ε n n

5 A revisi on he role of acro ibalances in he US recession 2325 where, n = T + 1 a( L, L y ), and σ 2 ( ) is he asypoic variance of he odified BB es saisic. 2 Based on his asypoic resuls and one-sided criical values, he null is rejeced if he es saisic in equaion (6) is oo large. To es for nonlinear Granger causaliy beween { } and { Y }; es saisic in equaion (6) is applied o he esiaed residual series fro he bivariae VAR odel. In his case, he null hypohesis is: { Y } does no nonlinearly sricly Granger cause { }, and equaion (6) holds for all, L, L Y 1 and ε > 0. By reoving a linear predicive power fro a linear VAR odel, any reaining increenal predicive power of one residual series for anoher can be considered nonlinear predicive power (see Baek and Brock, 1992). A significan es saisics in equaion (6) suggess ha lagged values of Y help o predic, whereas a significan negaive value sugges knowledge of he lagged value of Y confounds he predicion of. For his reason, he es saisic in equaion (6) should be evaluaed wih righ-ailed criical values when esing for he presence of Granger causaliy. Using Mone Carlo siulaions Hiesra and Jones (1993) find ha he odified Baek and Brock (1992) es has rearkably good finie saple size and power properies agains a variey of nonlinear Granger causal and non-causal relaions. 3. Daa analysis and resuls inerpreaion Prior o forally checking for nonlinear Granger causaliy, he Brock, Decher, and Scheinkan (BDS) es forally ess if he daa are characerized by nonlineariies. 3 The BDS approach essenially ess for deviaions fro idenically and independenly disribued (i.i.d.) behavior in ie series. Resuls show ha he vas ajoriy of he BDS saisics are saisically significan, suggesing significan nonlineariies in he univariae ie series. 4 Values for he lead lengh, he lag lenghs and L Y, and he disance easure ε us be seleced in prior o ipleening he Baek and Brock (1992) es. This is sharp conras wih he linear causaliy es where we do no have any well developed ehods for choosing opial lag lenghs and disance easure. Following Hiesra and Jones (1994) we se he lead lengh a = 1 and se L = L Y for all cases. The coon lenghs of (1 5) lags and a coon disance easure of ε =1.5σ, (σ denoes he sandard deviaion of he series) 5 is used. In he resuls focus on p-values for he odified BB es as his enables us o copare he 2 The asypoic variance is esiaed using he heory of U-saisic for weakly dependen processes (Denker and Keller, 1983). For deailed derivaion of he variance see he appendi in Hiesra and Jones (1994). 3 We are hankful for Prof. Paul for sharing he daa used in his paper. Daa source for relaed variables can be found in his paper, and o Mr. Panchenko for providing e he codes for he analysis. 4 Correlaion and descripive saisics are presened in he working paper version of he sudy and can be found in Tiwari (2011). Resuls of he BDS es are available upon reques. 5 In esiaion we also considered ε = 0.5σ and 1.0σ; bu wihou any qualiaive differences.

6 2326 Aviral Kuar Tiwari and Bhari Pandey wih he epirical p-values obained using he re-sapling procedure. The epirical p-values accoun for esiaion uncerainy in he residuals of he VAR odel used in he odified BB es which akes he resuls ore reliable. 6 Diks and DeGoede (2001) conduced several eperiens o deerine he bes randoizaion procedure for obaining epirical p-values. They found ha he bes finie saple properies of he ess are obained when only he causing series are boosrapped in he analysis. As such his ehodology has been adoped in his paper. Specifically, we used he saionary boosrap of Poliis and Roano (1994) o preserve poenial serial dependence in he causing series. The re-sapling schee 7 which is robus wih respec o paraeer esiaion uncerainy is ipleened as follows: 1. Esiae a paraeric odel and obain he fied values of he condiional ean and he esiaed residuals. 2. Resaple he residuals in such a way ha saisfies he null hypohesis Creae arificial series using he fied values and he re-sapled residuals. 4. Furher, re-esiae he odel using he arificial daa and obain new series of he residuals. 5. Copue es saisics T i for he arificial residuals. By repeaing he boosrap N-ies and calculaing es saisic T i for each boosrap i=1 N, we obain epirical disribuion of he es saisics under he null. Furher, o obain he epirical p-values of he es we copare he es saisics copued fro he iniial daa T o wih he es saisics under he null T i : p = N i = 0 #( T0 Ti ), N Baek and Brock (1992) (BB) sugges ha heir es could spuriously rejec he null hypohesis of Granger noncausaliy fro he presence of non-saionariy due o srucural breaks in he daa and heeroskedasiciy [see Diks and Panchenko (2005, 2006) for he effec of condiional heeroskedasiciy]. Granger non-causaliy es does no idenify he underlying source of causaliy which ay be due o srucural breaks in he daa (BB; Andersen, 1996), differenial reacion o inforaion flow, proied by volailiy (Ross, 1989), or soe cobinaion. To es if resuls are period-sensiive, eperien wih sub-periods is possible leaves very sall saple in boh periods which can isleading. Since odified BB es uses residuals of he VAR odel, no he original unreaed observaions, inference ay be erroneous due o unaccouned esiaion uncerainy. Randles (1984) poins ou ha in he above noed siuaion he poenial difference in oucoe is no refleced in he es saisics. To avoid his, we use a re-sapling schee by incorporaing paraeer esiaion uncerainy. We use he es saisics of he odified BB, bu using he re-sapling procedure of Diks and DeGoede (2001) o deerine he epirical p- values of nonlinear Granger causaliy ess. The es saisics T i is given in equaion (6). 7 The re-sapling schee is heavily drawn fro Francis e al. (2010). 8 The re-sapling procedure iposes a ore resricive null hypohesis of condiional independence. However, he es deecs he deviaions fro he null in he direcion of Granger causaliy. Le N denoe he lengh of he series and PS is he saionary boosrap swiching probabiliy. We sar a new boosrapped sequence fro a rando posiion in he iniial series seleced fro he unifor disribuion beween 1 and N. Wih probabiliy 1 PS, he ne eleen in he boosrapped sequence corresponds o he ne eleen in he iniial series. Wih probabiliy PS we randoly selec an eleen fro he iniial sequence and pu i as he ne eleen in he boosrapped sequence. The procedure coninues unil we obain a boosrapped sequence of lengh N. To ensure saionariy of he boosrapped sequence, we connec he beginning and he end of he iniial sequence.

7 A revisi on he role of acro ibalances in he US recession 2327 where, #( ) denoes he nuber of evens in he brackes. The es rejecs he null hypohesis in he direcion of nonlinear Granger causaliy whenever T o is large. For he boosrapping he nuber of boosraps is se a N=99. 9 The boosrap swiching probabiliy PS is se o The resuls based on he boosrapped epirical p-values of non-linear Granger causaliy analysis are repored in he following Table 1. Table 1: Resuls of nonlinear Granger causaliy Null hypohesis abou Granger causaliy Lag1 Lag2 Lag3 Lag4 Lag5 Fiscal defici does no cause Fed rae Trade defici does no cause Fed rae Fed rae does no cause saving rae Fiscal defici does no cause GDP growh Trade defici does no cause GDP growh Trade defici does no cause fiscal defici Fiscal defici does no cause Trade defici Trade defici does no cause saving rae Fed rae does no cause Fiscal defici Saving rae does no cause rade defici Fiscal defici does no cause saving rae Saving rae does no cause fiscal defici Fed rae does no cause rade defici Saving rae does no cause Fed rae GDP growh does no cause fiscal defici GDP growh does no cause rade defici Noe: This able repors paraeric boosrap p-values for he sandard Baek and Brock (1992) nonlinear Granger causaliy es (equaion-6). The nuber of lags on residuals used is one. All ess are applied o he uncondiional unsandardized residuals. The lead lengh, =1, and disance easure, ε =1.5. Bold are significan. I is eviden fro Table 1 ha fiscal defici and rade defici do no Granger-cause Fed rae; fiscal defici does no Granger cause GDP growh and rade defici; Fed rae does no Granger cause saving rae and rade defici. However, rade defici Granger case GDP growh and fiscal defici; fiscal defici Granger cause saving rae and saving rae Granger fiscal defici and fed rae and GDP growh Granger cause boh rade defici and fiscal defici. The findings conras wih hose of Paul (2010). He found ha fiscal and rade defici Granger-cause Fed rae and argued ha high fiscal and rade defici lowers he Fed rae. This iplies ha acroeconoic ibalances indirecly conribued o he cheap 9 B=99 is he salles coonly suggesed nuber of boosrap replicaions (see Davidson and MacKinnon, 2000). Due o copuaional liiaions we were unable o increase N, which ay cause low power for our ess.

8 2328 Aviral Kuar Tiwari and Bhari Pandey oneary policy which led o he housing bubble and uliaely caused he financial crisis. We argue ha here igh be any nuber of reasons working owards a cheap oneary policy in he US; he leas of which is he wo ibalances Paul (2010) cies. Furher, Paul (2010) found ha Fed rae Granger-cause saving rae. So, he concluded ha Fed rae was responsible for he falling saving raes and hus he failure o pay for he hoe, leading o lower equiy, higher leverage, higher risk and an ever growing bubble in he housing arke. The findings of his paper do no lend any suppor o Paul. Paul s (2010) finds ha he win defici Granger-cause GDP growh and o oupu decline. We find ha he rade defici is he facor causing oupu decline, no he fiscal defici. In addiion o ha I also find ha GDP growh is also causing win defici ha iplies ha GDP growh has increased he burden of rade defici and fiscal defici. Furher, Paul (2010) found ha win deficis show bidirecional Granger causaliy. By conras, we find ha rade defici Granger-cause fiscal defici while fiscal defici does no. Alhough research shows ha fiscal defici and saving rae Granger cause each oher i.e., fiscal defici and savings rae reinforce each oher, we also found ha Fed rae Granger cause fiscal defici i.e., cheap oneary policy has been he cause of high fiscal defici. We did no find evidence rade defici o lower saving raes or ha savings were helped by increased rade defici. 4. Conclusions This paper revisis he findings by Paul (2010) who idenifies rade and fiscal defici as he facors behind he cause of he grea recession of in he US, he wors since he Grea Depression. By applying he Granger causaliy, Paul (2010) argues ha he win deficis have conribued o lowering he ineres rae and oupu decline over he period of Paul (2010) resuls are suspec as he did no check he saionariy propery of he series in applying Granger causaliy. Using ore refined ehods appropriae o he cone, we did no find any evidence o suppor for he win defici hypohesis, raher i is he rade defici which has lowered he GDP growh. Furher, i is no he low ineres rae which caused low savings bu i is low rae of savings which caused he low rae of ineres rae which caused boo and ha conribued o he housing bubble. Low saving led o he failure by he borrowers o cushion he deb. The housing bubble is relaed o fiscal defici. Low fed rae (ineres rae) and GDP growh rae, and high saving rae and rade defici have conribued o high fiscal defici, whereas high fiscal deficis has increased he saving rae. Finally, increased savings has lowered he ineres rae (i.e., cheap oneary policy) which has been he cause of housing bubble.

9 A revisi on he role of acro ibalances in he US recession 2329 References [1] A. K. Tiwari, A revisi on he role of acro ibalances in he US recession of , Research paper, (2011), available a: hp:// [2] B.B. Francis, M. Mougoué, V. Panchenko, Is here a syeric nonlinear causal relaionship beween large and sall firs?, Journal of Epirical Finance, 17 (2010), [3] B.P. Paul, The role of acro ibalances in he US recession of , Inernaional Journal of Business and Econoics, 9(2010), [4] C. Diks, J. DeGoede, A general nonparaeric boosrap es for Granger causaliy, in: Broer, H.W., Krauskopf, W., Veger, G. (Eds.), Global analysis of dynaical syses, Insiue of Physics Publishing, Brisol, UK, (2001). [5] C. Diks, V. Panchenko, A new saisics and pracical guidelines for nonparaeric Granger causaliy esing, Journal of Econoic Dynaics and Conrol, 30(2006), [6] C. Diks, V. Panchenko, A noe on he hiesra-jones es for granger noncausaliy, Sudies in Nonlinear Dynaics and Econoerics, 9(2005), ar. 4. [7] C. Hiesra, J.D. Jones, Soe inforaion relaing o he finie saple properies of odified baek, and brock nonlinear granger causaliy es, Working paper, Universiy of Srahclyde and Securies and Echange Coission, (1993). [8] C. Hiesra, J.D. Jones, Tesing for linear and nonlinear granger causaliy in he sock price-volue relaion, Journal of Finance, 49(1994), [9] D.N. Poliis, J.P. Roano, The saionary boosrap, Journal of he Aerican Saisical Associaion, 89(1994), [10] E. Baek, W. Brock, A general es for nonlinear granger causaliy: bivariae odel, Working paper, Iowa Sae Universiy, 1992.

10 2330 Aviral Kuar Tiwari and Bhari Pandey [11] M. Denker, G. Keller, On u-saisics and von ises saisics for weakly dependen processes, Z. Wahrscheinlichkeisheorie Verw, Geb, 64(1983), [12] R. Davidson, J. MacKinnon, Boosrap ess: how any boosrap?, Econoeric Reviews, 19(2000), [13] S. Ross, Inforaion and volailiy: he no-arbirage aringale approach o iing and resoluion irrelevancy, Journal of Finance, 44(1989), [14] T.G. Andersen, Reurn volailiy and rading volue: an inforaion flow inerpreaion of sochasic volailiy, Journal of Finance, 51(1996), Received: Deceber 4, 2012