A revisit on the role of macro imbalances in the US recession of Aviral Kumar Tiwari # ICFAI University Tripura, India

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1 A revisi on he role of acro ibalances in he US recession of Aviral Kuar Tiwari # ICFAI Universiy Tripura, India Absrac The presen sudy is an aep o revisi he evidences of a very recen sudy of Paul (2010) on he role of acro ibalances in he US recession of Conrary o Paul (2010) who finds ha grea recession was due o, paricularly, win deficis, I found cenral cause of he proble was prolonged fiscal defici. Key words: acro ibalances, US recession, nonlinear Granger causaliy. JEL Classificaion: E3, E56, E6. # Research scholar and Faculy of Applied Econoics, Faculy of Manageen, ICFAI Universiy Tripura, Kaalgha, Sadar, Wes Tripura, Pin , India, Eail-Id: aviral.eco@gail.co 1

2 1. Inroducion The discussion of he US grea recession of has brough considerable ineres of boh researchers and policy akers. Nuber of aeps has been ade o idenify reasons of his grea depression. In a very recen sudy, Paul (2010) show ha, using vecor Auoregressive (VAR) odel, rade deficis and fiscal deficis has conribued o he low ineres rae and decreasing he oupu over he period of He also shows ha low ineres rae is caused by low privae saving which grealy conribued o he housing bubble. And hence, Paul (2010) concluded ha low saving and win deficis have been he ain reason for he grea recession eperienced. 1 However, I have ade an aep in his sudy o revisi he findings and conclusions drawn by Paul (2010). Since, Paul (2010) has used VAR odel o analyze he proble and if here is evidence of nonlineariy in he daa series conclusion drawn fro he sudy will be biased. Therefore, in he presen sudy I ade and aep o analyze he proble by using he nonlinear Granger causaliy analysis in he fraework of Hiesra and Jones (1994) which was iproved upon Baek and Brock (1992) proposed es. 2. Nonlinear Granger causaliy I is iporan o enion ha he linear approach o causaliy esing can have he low power deecing cerain kinds of nonlinear causal relaion. In his regard Baek and Brock (1992) is he firs sudy o he bes of our knowledge which proposed a es based on a nonparaeric saisical ehod for uncovering nonlinear causal relaions ha canno be deeced by radiional liner Granger causaliy es. Baek and Brock s (1992) proposed es was based on an approach ha uilizes he correlaion inegrals, which is an esiaor of spaial probabiliies across ie based upon he closeness of he poins in hyperspace o deec he relaion beween wo ie series. The disribuion of he es saisic is one ailed and hence, rejecions of he hypohesis are resriced o one ail of he disribuion. Hiesra and Jones (1994) odified he saisic of Baek and Brock (1992) and show ha heir es saisics has beer sall-saple properies and i can be applied o he series ha relaes he assupion ha he series are i.i.d. Hiesra and Jones (1993) show in heir Mone Carlo siulaions ha heir odified es is robus o he presence of srucural breaks in he series and coneporaneous correlaions in he errors of he VAR odel used o filer ou linear cross- and auo-dependence. Baek and Brock (1992) developed a nonparaeric saisical echnique for deecing nonlinear causal relaionships fro he residuals of linear Granger causaliy odels. Following Hiesra and Jones (1994), we le F ( I 1) denoe he condiional probabiliy disribuion of consiss of an L -lengh lagged vecor of given he inforaion se I 1, which, say (, +1,..., 1), and an LY - 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. 2

3 lengh lagged vecor ofy, say Y ( Y, Y +1,..., Y 1). Hiesra and Jones (1994) consider esing, for a given pair of lags L and L Y, he following relaionship: H : F I ) = F( ( I Y )) (1) 0 ( 1 1 Tha is, he null hypohesis of ineres 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 Hiesra and Jones (1994), we denoe he -lengh lead vecor of suarize he vecors defined so far, for Z, as:,,..., ), = 1, 2, = ( by, so ha we can,,..., ), = 1, 2, (2) = ( +1 1 Y Y, Y,..., Y ), = 1, 2, = ( +1 1 A crucial clai ade by Hiesra and Jones (1994) wihou proof, saes ha he null hypohesis given in equaion (1) iplies, for all ε > 0: ( < ε < ε Y Y < ε ) P, s s s ( < ε < ε ) = s s P, (3) where P(A B) denoes he condiional probabiliy of A given B, and he aiu nors-a disance easure (in his case supreu nor), which for a d-diensional vecor T d = ( 1,..., d 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 are wihin a disance ε for each oher (or ε -close), given he corresponding vecor of { } (i.e., and s ) and Y L -lengh lag vecor Y }(i.e., { s ) L -lengh lag and s 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 ) are wihin a disance ε for each oher (or ε -close), given ha he corresponding lagged -lengh lag vecors of { } (i.e., and s ) are wihin a disance of ε of each oher (orε -close). Hence, non-granger causaliy iplies ha he probabiliy ha 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; and condiional upon he lag vecors of { } only being wihin a disance ε of each oher. In oher words, no Granger causaliy eans ha he probabiliy ha lead vecors are wihin disance ε is he sae wheher we have inforaion abou he disance beween { Y } lag vecors or no. 3

4 We can wrie he condiional probabiliy epressed in equaion (3) as raios of join probabiliies. Assuing ha C 1( + L, L, ε ) / C2( L, L, ε ) and C 3( + L, ε ) / C4( L, ε ) denoe he raio of y y join probabiliies corresponding o he Lef Hand Side (LHS) and RHS of equaion (3), he join probabiliies can be wrien as: + + ( < ε Y Y ε ) C 1 ( L, L, ε ) = P, <, + y s s ( < ε Y Y ε ) C 2 ( L, L, ε ) P, <, y = s s + + ( ) C 3 ( + L, ε ) = P < ε, s ( ) C 4 ( L, ε ) P < ε (4) = s Furher, we can wrie he sric Granger non-causaliy condiion in equaion (3) 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. Now, assuing ha { } and { Y } denoe he acual realizaion of he process and I ( A, B, ε ) denoing an indicaor funcion ha akes he value one if he vecor A and B are wihin a disance ε of each oher and zero oherwise and considering ha he properies of he supreu nor + + allow us o inscribe P ( < ε, < ε ) as P ( < ε ) s s esiaes of he correlaions inegrals in equaion (5) can be epressed as: C1( +,, ε, n) I (, s, ε ) I( Y, Ys, ε ), n( n 1) (,, ε ) I( Y, Y ε ) 2 C2(,, ε, n) I s s, n( n 1) + + (, ) 2 C3( +, ε, n) I s,ε n( n 1) (, ) 2 C4(, ε, n) I s,ε n( n 1) For s = a( L, L ) + 1,..., T + 1; n = T + 1 a( L, L )., y y s, hen he 4

5 Assuing ha and specified in Denker and Keller (1983), under he null hypohesis ha Granger cause Y are sricly saionary and ee he required iing condiions as, he es saisic T is asypoically norally disribued. Tha is, Y does no sricly 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 where, n = T + a( L, L ) and σ 2 ( ) is he asypoic variance of he odified Baek 1 y and Brock (1992) es saisic. 2 One sided criical values are used, based upon his asypoic resuls, rejecing when he observed value of 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 ha { 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 for 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 significanly 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 Before esing for nonlinear Granger causaliy, i is iporan o firs deerine if he daa are characerized by nonlineariies. 3 Therefore, I perfor a foral nonlinear dependence es known as he Brock, Decher, and Scheinkan (BDS) es. The BDS approach essenially ess for deviaions fro idenically and independenly disribued (i.i.d.) behavior in ie series. Resuls of he BDS es reveal ha he vas ajoriy of he esiaes of he BDS saisics are saisically significan, indicaing significan nonlineariies in he univariae ie series. 4 To conduc ess for nonlinear causaliy we use he residuals fro he linear VAR odel, fro which any linear 2 The asypoic variance is esiaed using he heory of U-saisic for weakly dependen processes (Denker and Keller, 1983). For a coplee and deailed derivaion of he variance see he appendi in Hiesra and Jones (1994). 3 I a hankful for Prof. Paul for sharing he daa which he used in he analysis in his paper. Daa source for relaed variables can be found in his paper. I a also hankful o Panchenko for providing e he codes for his analysis. 4 Resuls of correlaion and descripive saisics are presened in he appendi of he paper and resuls of he BDS es are available upon reques o he auhor. Resuls of correlaion has been presened jus o ach wih he resuls of Paul (2010) presened in Table 1. 5

6 predicive relaionship has already been reoved. Values for he lead lengh, he lag lenghs and L Y, and he disance easure ε us be seleced in order o ipleen he Baek and Brock (1992) es. In conras o linear causaliy esing, we do no have any well developed ehods for choosing opial values for lag lenghs and disance easure. Therefore, I followed Hiesra and Jones (1994) and se he lead lengh a = 1 and se L = LY for all cases. In he presen sudy I use coon lag lenghs of one o five lags and a coon disance easure of ε =1.5σ, where σ denoes he sandard deviaion of he ie series. 5 In he resuls of his paper I focus on p-values for he odified Baek and Brock (1992) es as his enables us o copare he 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 Baek and Brock (1992) es, hereby, aking hese resuls ore reliable. 6 Diks and DeGoede (2001) have conduced a nuber of eperiens in order o deerine he bes randoizaion procedure for obaining epirical p-values. There, finding show ha he bes finie saple properies of he ess are obained when only he causing series were boosrapped in he analysis. Hence, I adop his ehodology in his analysis. I used he Saionary boosrap of Poliis and Roano (1994) o preserve poenial serial dependence in he causing series. The resapling schee which is robus wih respec o paraeer esiaion uncerainy is ipleened as follows: 1. Firs, esiae a paraeric odel and obain he fied values of he condiional ean and he esiaed residuals Ne, resaple he residuals in such a way ha saisfies he null hypohesis. 8 5 In he esiaion we also considered ε = 0.5σ and 1.0σ. There were no qualiaive differences in our resuls. 6 Baek and Brock (1992) sugges ha a weakness of heir es is ha i could spuriously rejec he null hypohesis of Granger noncausaliy due o he presence of non-saionariy induced by srucural breaks in he daa and heeroskedasiciy (recen finding by Diks and Panchenko (2005, 2006) also suggess ha he rejecion of he null in his case ay also indicae he presence of condiional heeroskedasiciy in he daa). Furher, Granger non-causaliy es does no idenify he underlying source of causaliy which ay be due o due o srucural breaks in he daa (Baek and Brock, 1992; Andersen, 1996) or o a differenial reacion o inforaion flow as proied by volailiy (Ross, 1989) or soe cobinaion of he wo. To es wheher resuls are period sensiive we can conduc an eperien for sub periods however, we have avoided his esing because if we conduc his kind of es are lef wih a very sall saple in boh periods which again ay provide us isleading resuls. Furher, since odified Baek and Brock (1992) es for Granger non-causaliy is applied o he residuals of he VAR odel, raher han o original unreaed observaions. This ay also lead o erroneous inferences because of an unaccouned esiaion uncerainy. The reason for his is he poenial difference of he null disribuion when he es is applied o residuals raher han o original observaions (Randles, 1984). This difference arises because he paraeer esiaion uncerainy is no refleced in he es saisics. To eliinae any erroneous inference we use a re-sapling schee ha incorporaes paraeer esiaion uncerainy. We coninue o use he es saisics of he odified Baek and Brock (1992) es and odify he re-sapling procedure of Diks and DeGoede (2001) o deerine epirical p-values of he nonlinear Granger causaliy ess. The es saisics T i is given in equaion (6). 7 The esiaion uncerainy of he calendar effecs is accouned by saring wih he unadjused reurns and eplicily including he calendar duies in he condiional ean equaion. 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 ineres, ha is, 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. 6

7 3. In he ne sep, creae arificial daa 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. Finally, 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 0 wih he es saisics under he null T i : N #( T0 Ti ) i = 0 p =, N + 1 where, #( ) denoes he nuber of evens in he brackes. The es rejecs he null hypohesis in he direcion of nonlinear Granger causaliy whenever T 0 is large. For he boosrapping I se he nuber of boosraps 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. 9 B=99 is he salles coonly suggesed nuber of boosrap replicaions (see Davidson and MacKinnon, 2000 for deails). Because of copuaional liiaions we were unable o increase N, which ay possibly resul in soe loss of power for our ess. 7

8 Table 1: Resuls of nonlinear Granger causaliy Null hypohesis Lag1 Lag2 Lag3 Lag4 Lag5 1. Fiscal defici does no Granger cause Fed rae Trade defici does no Granger cause Fed rae Fed rae does no Granger cause saving rae Fiscal defici does no Granger cause GDP growh Trade defici does no Granger cause GDP growh Trade defici does no Granger cause fiscal defici Fiscal defici does no Granger cause Trade defici Trade defici does no Granger cause saving rae Fed rae does no Granger cause Fiscal defici Saving rae does no Granger cause rade defici Fiscal defici does no Granger cause saving rae Saving rae does no Granger cause fiscal defici Fed rae does no Granger cause rade defici Saving rae does no Granger cause Fed rae GDP growh does no Granger cause fiscal defici GDP growh does no Granger cause rade defici Noe: This able repors paraeric boosrap p-values for he sandard Baek and Brock (1992) nonlinear Granger causaliy es given in equaion (6). The nuber of lags on he residuals series used in he es is one. In all cases, he ess are applied o he uncondiional unsandardized residuals. The lead lengh,, is se o uniy, and he disance easure, ε, is se o 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. Therefore, we have conrary findings o Paul (2010). He found ha fiscal and rade defici Granger cause Fed rae and argued ha high fiscal and rade defici lowered he fed rae ha iplies ha acroeconoic ibalances indirecly conribued o he cheap oneary policy and hence he housing bubble before he financial crises. However, I argue here igh be any oher reason for chap oneary policy of US bu a leas hese wo ibalances were no. Furher, Paul (2010) found ha fed rae Granger cause saving rae and hence he concluded ha fed rae called falling saving raes which lower down he payens for hoe buying, lower equiy, higher leverage, higher risk and a bigger bubble in he housing arke. However, again, y findings do no provide any suppor o his arguen. Furher, Paul (2010) finds ha win defici Granger cause GDP growh and hence, win defici suppored in oupu decline however, I find ha i he 8

9 rade defici which is he causing phenoenon for 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, conrary o Paul (2010) who found ha win defici are augening (reinforcing each oher) i.e., Granger causaliy runs in boh direcions y sudy finds ha rade defici Granger cause fiscal defici while fiscal defici does no. Furher, sudy shows ha fiscal defici and saving rae Granger cause each oher i.e., fiscal defici and savings rae appeared o have reinforcing each oher. I also find ha fed rae Granger cause fiscal defici i.e., cheap oneary policy has been he cause of high fiscal defici. Conrary o Paul (2010), I did no find evidence ha rade defici appeared o have lowered he saving raes or savings appeared o have increased he rade defici. 4. Conclusions This sudy is an aep o revisi he evidences of a very recen sudy by Paul (2010) on he finding ou he causing facors of recen winessed he grea recession of in he US, he wors one, since he Grea Depression. Paul (2010) in his sudy finds ha, wihou checking he saionariy propery of he daa series and applying he Granger causaliy, boh he rade defici and fiscal defici have conribued in lowering he ineres rae and oupu decline over he period of However, his sudy reveals a differen sory. I do no find any evidence o suppor for his evidence ha his is he win defici, which is conribued o cheap oneary policy. Furher, i is he rade defici which has lowered he GDP growh no he win defici (fiscal defici and rade defici). 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 and ha conribued o he housing bubble. The cenral cause of housing bubble is relaed o fiscal defici. Low rae of fed rae (ineres rae), GDP growh rae and high saving rae and rade defici have conribued o high fiscal defici and high fiscal defici have increased he saving rae and increased savings have lowered he ineres rae (i.e., cheap oneary policy) and ha has been he cause of housing bubble. 9

10 References Andersen, T.G., Reurn volailiy and rading volue: an inforaion flow inerpreaion of sochasic volailiy. Journal of Finance. 51, Baek, E., Brock, W., A general es for nonlinear granger causaliy: bivariae odel. Working Paper. Iowa Sae Universiy. Davidson, R., MacKinnon, J., Boosrap ess: how any boosrap? Econoeric Reviews. 19, Denker, M., Keller, G., On u-saisics and von-ises saisics for weakly dependen processes. Zeischrif fur Wahrscheinlichkeisheorie und Verwande Gebiee. 64, Diks, C., DeGoede, J., 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. Diks, C., Panchenko, V., A noe on he hiesra-jones es for granger non-causaliy. Sudies in Nonlinear Dynaics and Econoerics. 9(2), ar. 4. Diks, C., Panchenko, V., A new saisics and pracical guidelines for nonparaeric Granger causaliy esing. Journal of Econoic Dynaics and Conrol. 30, Hiesra, C., Jones, J.D., 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. Hiesra, C., Jones, J.D., Tesing for linear and nonlinear granger causaliy in he sock price-volue relaion. Journal of Finance. 49, Paul, B. P., The role of acro ibalances in he US recession of Inernaional Journal of Business and Econoics. 9(3), Poliis, D.N., Roano, J.P., The saionary boosrap. Journal of he Aerican Saisical Associaion. 89, Ross, S., Inforaion and volailiy: he no-arbirage aringale approach o iing and resoluion irrelevancy. Journal of Finance. 44,

11 Appendi 1: Table of correlaion and descripive saisics Correlaion FEDRATE FISCALDEFICIT GDPGROWTH SAVINGRATE TRADEDEFICIT FEDRATE 1 FISCALDEFICIT GDPGROWTH SAVINGRATE TRADEDEFICIT Descripive saisics Mean Median Maiu Miniu Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy Su Su Sq. Dev Observaions