Applied Econometrics and International Development Vol.9-1 (2009)

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1 Applied Economerics and Inernaional Developmen Vol.9- (2009) THE BILATERAL RELATIONSHIP BETWEEN CONSUMPTION AND IN MEXICO AND THE US: A COMMENT GOMEZ-ZALDIVAR, Manuel * VENTOSA-SANTAULARIA, Daniel Absrac This aricle presens a criical appraisal of hree differen economeric echniques commonl emploed o analze causal relaionships among economic series. Our resuls indicae ha he empirical applicaion of he Granger causali es, he Engle-Granger coinegraion es and he Hausman es for causali performed wih small samples suffers severe size disorions, and herefore ha he resuls should be aken wih cauion. Furhermore, we show ha hese ess produce beer resuls if he series are differeniaed. Our resuls are applied o he series for consumpion and in Meico and he US and sugges ha hese series are coinegraed in he case of he US onl (causali and coinegraion are differen). We commen upon hese resuls in relaion o he conclusions of Guisan (2004), and oher relaed sudies, in which several mehods are used o analze he bilaeral causali beween consumpion and in Meico and he US and where i was found ha coinegraion and Granger causali ess ma fail o deec he rue causal relaionships. JEL classificaion numbers: C5, C52, E2, O5, O57 Kewords: Granger causali es, coinegraion, Meico, he US, consumpion and Gross Domesic Produc.. Inroducion Guisan (2004) analzed he resuls of several ess o deec he causal relaionship eising beween real consumpion and real in Meico and he Unied Saes: (i) he Granger causali es, (ii) he modified Granger causali es, (iii) he Engle-Granger coinegraion es, and (iv) he Hausman es for causali. The main conclusions are:. Granger Causali: a. There is no evidence of Granger causali beween consumpion and in Meico. Hence, he Granger es failed o deec causali in his counr. b. There is evidence of bilaeral Granger causali beween consumpion and in he US. Hence, he Granger es did no fail o deec causali in his counr. 2. Modified Granger Causali: a. There is evidence of bilaeral Granger causali beween consumpion and in boh counries. Therefore, he modified version of he Granger es leads o beer resuls han he former es. 3. Coinegraion: a. The resuls of he coinegraion es are ambiguous and did no allow us o rejec ssemaicall he null hpohesis of no coinegraion, alhough here is more evidence in favor of coinegraion han here is agains i. * Manuel Gome Universidad de Guanajuao, Escuela de Economía. manuel.gomez@ugo.org. Corresponding auhor: Daniel Venosa.Universidad de Guanajuao, Escuela de Economía. daniel@venosa-sanaularia.com. UCEA Campus Marfil, Col. El Esablo, Guanajuao, Go. CP

2 Applied Economerics and Inernaional Developmen Vol.9- (2009) b. There is evidence of a coinegraed relaionship beween consumpion and in he US. 4. Hausman Tes for Causali: a. There is mied evidence of causali à la Hausman in boh counries. In his paper, we discuss differen feaures of Guisan s work. In paricular, we analze and eend her resuls in several direcions: firsl, we appl a se of well-known uni-roo ess o he variables under eaminaion o deermine which Daa Generaing Process (DGP), if an, bes suis hem. We do his because he performance and reliabili of he ess emploed depend upon he saisical properies of each variable. Secondl, we show b means of Mone Carlo eperimens ha he reliabili of he ess emploed decreases significanl when a shor sample is used. Thirdl, we propose addiional es procedures ha srenghen he inference o be drawn from such ess. In paricular, we perform Granger Causali (GC) ess wih series in firs differences [causali] and esimae an Error-Correcion Model [Coinegraion] for boh counries. Our resuls sugges ha here is a coinegraed relaionship beween consumpion and in he US as well as an adjusmen of is when he variables deviae from heir long-erm equilibrium relaionship. The res of he paper is organized as follows: In Secion, we deermine which DGP bes fis he series for consumpion and in Meico and he US. In Secion 2, we presen he resuls of he Mone Carlo eperimens o show ha he Granger causali es, Engle- Granger coinegraion es (EG) and he Hausman es for causali suffer from severe size disorions when he series have a rending mechanism, wheher he laer is sochasic or deerminisic. Secion 3 presens he resuls of he causali ess for he series for consumpion and in Meico and he US in firs differences. Secion 4 shows he resuls of an Error-Correcion Model (ECM) applied o hese series. Conclusions are drawn in Secion 5.. DGP-ificaion of he Consumpion and Series. In his secion we perform a well-known se of uni-roo ess o deermine which DGP, if an of hose radiionall used in his lieraure, bes suis he series for Meico and he US. Equaions 5 show he DGPs ha are poenial represenaions for consumpion and in he US and Meico. + i = = Y0 u i () + i = = Y0 + µ u i (2) 78 + i = = Y0 + µ + θ DT u i (3) = µ + β + u (4) = µ + β + γ DT + u (5) where DT is a dumm variable allowing changes in he slope, ha is, DT = ( Tb )( > Tb ), where ( ) is he indicaor funcion, and T b is he unknown dae of he break in. We assume ha he innovaions, 2 u, are i. d. N ( 0, ) i σ..

3 GomeM.,Venosa, D. Bilaeral Relaionship Beween Consumpion and in Meico and he US DGP () represens a random-walk process, DGP (2) a process wih sochasic and deerminisic rends, DGP (3) a process wih boh sochasic and deerminisic rends, and a break in he deerminisic rend, DGP (4) a rend-saionar process and DGP (5) is a broken rend-saionar process... Uni-Roo Tess Table shows he resuls of appling he Augmened Dicke-Fuller ess (ADF), Dicke- Fuller GLS (DF-GLS), Phillips-Perron es (PP) and he Ng-Perron es. In all cases, he number of lags used o conrol for auocorrelaion were auomaicall seleced b he Schwarz Informaion Crierion (SIC). On he one hand, he resuls in columns 2, 3 and 4 show ha i is no possible o rejec he null of uni roo for all he series. On he oher, he Ng-Perron es finds mied evidence regarding he saionari of consumpion in Meico and in US; furhermore, i shows ha consumpion in he US could be considered saionar. Finall, as in he previous hree ess, i is no possible o rejec he null of uni roo for Meican. The inference drawn from hese ess is no conclusive for he series ecep ha of Meican, which seems o conain a uni roo. Table : Uni-Roo Tess Tes ADF Variable DF- Ng-Perron 2 GLS 2 PP 2 MZa MZ MSB MPT Consumpion Meico * -2.64* * Consumpion US 8.57** -2.90* 0.5** 5.76* Meico US * * 6.2* Specificaion of he DF es: No drif; 2 Wih drif and rend. *,** and *** denoe rejecion of he null hpohesis a 0%, 5%, and %, respecivel..2. Uni-Roo Tess allowing for Srucural Breaks. In his secion, we emplo uni-roo ess ha allow for srucural breaks eiher under he null hpohesis (DGP 3) or under he alernaive (DGP 5). Table 2 presens he resuls of appling he Zivo and Andrews es o our series; srucural breaks are allowed in he inercep, he deerminisic rend or boh. This is a popular es ha discriminaes beween he null of uni roo and he alernaive of saionari wih srucural breaks. The las column of his able shows he resuls of he Gómez and Venosa-Sanaulària es (GVS). 2 Zivo and Andrews es fails o rejec he null hpohesis of uni roo for all he variables; herefore, we can conclude ha he series are no being generaed b DGPs 4 and 5. The 2 This formal saisical procedure disinguishes beween he null hpohesis of uni roo and ha of uni roo wih drif (wih a poenial break). This procedure is asmpoicall robus wih regard o auocorrelaion and akes ino accoun a poenial single srucural break. See Gómez and Venosa- Sanaulària (2008). 79

4 Applied Economerics and Inernaional Developmen Vol.9- (2009) GVS es idenifies he presence of a drif for US consumpion and US : his suggess ha DGP 2 could be generaing boh series. Finall, he series of consumpion and for Meico do no have a deerminisic rend; consequenl, he seem o be beer represened b DGP. Table 2: Uni-Roo Tess allowing for Srucural Breaks Tes Zivo and Andrews Variable Inercep 2 Trend 2 Boh 2 GVS 2 (R 2 ) Consumpion Meico Consumpion US *** Meico US *** -raio associaed o he auoregressive erm; Criical Values provided b Zivo and Andrews (992). 2 *** and *** denoe rejecion of he null hpohesis a 0%, 5%, and %, respecivel. 2. Mone Carlo Simulaions The previous secion showed ha Meican variables can be seen as drifless uni roos whils he US series behave more like uni roos wih drif. These resuls are used in he presen secion o design Mone Carlo eperimens o analze he accurac of he ess emploed b Guisan (2004) when he empirical applicaion is performed in small samples. The ables presened below assume differen DGPs for he series; hese DGPs were chosen according o he findings of he previous secion as well as o previous resuls in his lieraure. 3 There is evidence ha he GC es, EG coinegraion es and Hausman es for causali ma suffer from severe size disorions when applied in small samples. 2.. Mone Carlo Evidence wih Trended Series. Table 3 shows he resuls of appling he GC es using he DGPs found in secion one. According o he previous secion, he Meican variables behave as uni roos, whils he US series appear o be uni roo wih drif. Performing his es wih such DGPs generaes severe size disorions, especiall in small samples (T=30). We should epec he rejecion raes o be around 5%, bu he Mone Carlo simulaion ehibis rejecion raes of beween 2% and 7%. 3 The parameer values of he DGPs emploed in all he Mone Carlo eperimens as well as he number of replicaions can be found in he appendi of his aricle. 80

5 GomeM.,Venosa, D. Bilaeral Relaionship Beween Consumpion and in Meico and he US Table 3: Granger Causali Tes* DGP less Uni Roo less Uni Roo less Uni Roo Sample Size, T=00 less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no Granger causali; Level: 0.05 When he adequae DGP is a deerminisic rend wih a break, his es suffers from similar size disorions. In fac, when he sample size is larger, using one (or boh) of he variables generaed b DGPs (4) or (5) would aggravae such size disorions. These simulaions are in line wih he findings of Venosa-Sanaulària and Vera-Valdés (2008). The auhors sudied he asmpoic properies of he GC es for similar specificaions when he variables are mean-saionar wih level breaks and rend-saionar wih rend breaks processes; he found ha he GC es ma lead o erroneous inference and rejec (asmpoicall) he null hpohesis of no Granger causali beween oherwise independen variables. 8

6 Applied Economerics and Inernaional Developmen Vol.9- (2009) A poenial soluion for his problem as will be proposed in he ne secion is o perform he GC ess wih variables in firs differences. Table 4 shows he Mone Carlo resuls of performing he Modified Granger Causali (MGC) es using similar DGPs. The size disorions ha occur wih he MGC es are even more significan han he are wih he GC es. In his case, rejecion raes are 6% and 9%, and do no decrease, even for samples as large as T=50. Size disorions are even more imporan when he variables are rend-saionar or/and broken rend-saionar processes. In his case, rejecion raes reach 00%. Table 4: Modified Granger Causali Tes* DGP less Uni Roo less Uni Roo less Uni Roo Sample Size, T=00 less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no Granger causali; Level: 0.05 Tables 5, 6 and 7 show he Mone Carlo resuls of performing he EG coinegraion es wih and wihou one lag and he Hausman es for causali, respecivel. The Mone 82

7 GomeM.,Venosa, D. Bilaeral Relaionship Beween Consumpion and in Meico and he US Carlo eperimens confirm ha hese ess draw correc inference when he variables are uni roo and/or uni roo wih drif, even when he sample size is small, for eample, 30 observaions. Neverheless, here are severe disorions whenever one or boh variables include a deerminisic rend. Such size disorions worsen he larger he sample size. Table 5: Engle-Granger Coinegraion Tes, No Lags* DGP less Uni Roo less Uni Roo less Uni Roo Sample Size, T=00 less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no coinegraion; Level: As saed in Noriega and Venosa-Sanaulària (2007), we should bear in mind ha he EG coinegraion es beween variables ha include deerminisic rends and/or breaks ma provide spurious resuls, ha is, here ma be considerable size and power disorions. In his case, we should furher bear in mind ha he concep of coinegraion refers o a longrun equilibrium relaionship beween he variables. There is no eviden link beween causali and coinegraion. 83

8 Applied Economerics and Inernaional Developmen Vol.9- (2009) We would herefore sugges he esimaion of an Error-Correcion Model (ECM). Wih he ECM, we should be able o draw inference concerning which variables adjus whenever here is a shor-run disequilibrium. Alhough his could no be formall regarded as causali, we would a leas know which variable moves firs afer a shock occurs. Table 6: Engle-Granger Coinegraion Tes, One Lag* DGP less Uni Roo less Uni Roo less Uni Roo Sample Size, T=00 less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no coinegraion; Level:

9 GomeM.,Venosa, D. Bilaeral Relaionship Beween Consumpion and in Meico and he US Table 7: Hausman Tes for Causali* DGP less Uni Roo less Uni Roo less Uni Roo Sample Size, T=00 less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no Hausman causali; Level: Mone Carlo Evidence wih Variables in Firs Differences I is no surprising ha causali ess when applied o inegraed variables ield poor resuls; however, in pracice, in he case of variables inegraed of order one, such ess applied o saionar firs differences, ma also fail o accep rue causal relaionships and rejec unrue ones, as is he case in he following resuls presened b Guisan (200): Percenages of coinegraion accepaion for models in levels and firs differences beween real consumpion and real in 25 OECD counries for he period

10 Applied Economerics and Inernaional Developmen Vol.9- (2009) Table 7 bis.*,** Summar of resuls** Levels Firs Differences % of Own Coinegraion McKinnon EG 0% 88% % of Own Coinegraion 84% McKinnon ADF 00% % of Cross Coinegraion 9% McKinnon EG 23% % of Cross Coinegraion 66% McKinnon ADF 96% * Source: Guisan (200). ** The auhor noes ha boh EG and ADF ess perform beer wih variables in firs differences compared o levels in deecing rue causali beween he consumpion and of he own counr (i.e. he percenages of accepance of he rue hpohesis are higher), bu performs worse in firs differences han in levels o rejec he unrue hpohesis of a causal relaionship beween he crossed variables of differen counries (i.e. he percenages of accepance of he unrue hpohesis are higher). Tables 8, 9 and 0 show he Mone Carlo resuls for each of he ess; he variables have been firs-differenced. These resuls show ha size disorions are considerabl reduced for he GC and MGC ess for all DGP combinaions. There is no relevan improvemen in working wih differenced variables when he Hausman es for causali es is used. Table 8: Granger Causali Tes, Variables in Firs Differences* DGP less Uni Roo less Uni Roo less Uni Roo Number of replicaions: 0,000; rejecion rae of he null hpohesis of no Granger causali; Level:

11 GomeM.,Venosa, D. Bilaeral Relaionship Beween Consumpion and in Meico and he US Table 9: Modified Granger Causali Tes, Variables in Firs Differences* DGP less Uni Roo less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no Granger causali; Level: Table 0: Hausman Causali Tes, Variables in Firs Differences* DGP less Uni Roo less Uni Roo less Uni Roo * Number of replicaions: 0,000; rejecion rae of he null hpohesis of no Hausman causali; Level: Causali Tess wih Variables in Firs Differences We now use Guisan s (2004) daa se o draw inference concerning causali. The sraeg was advanced earlier in his work: differencing he series is appropriae when dealing wih non-saionari. 87

12 Applied Economerics and Inernaional Developmen Vol.9- (2009) Table : Causali Tess, Variables in Firs Differences [Guisan daa se] Hausman Granger Causali Causali Counr Meico US Independen - Dependen Consumpion- - Consumpion Consumpion- - Consumpion 88 Modified Granger Causali -sa. p-value F-sa. p-value F-sa. p-value The resuls in Table show ha he ess, using variables in firs differences, fail o deec causali: here is no evidence of Granger causali or Hausman causali beween he Meican variables a he 5% level. In he case of he US variables, all he ess reveal evidence in favor of causali from consumpion o, bu no vice-versa. 4. Error-Correcion Model wih Variables in Firs Differences To formall implemen he ECM, consider equaion (6), which represens he long-run equilibrium relaionship beween consumpion and, c, and, respecivel, where If c z, z = m, usa, c c ECM = α + β z = c z + ε z α β z, are CI(,), he variables have an error-correcion form = γ = γ 2 + θ + θ 2 ECM ECM + + m i s= m i 3 s= δ zs δ z2s c s s + + m i 2 m z s= i 4 s= z φ where θ and θ 2 are inerpreed as speeds of adjusmen o a shor-run u z u 2 disequilibrium ;, and z, are whie noise disurbances. The ECM allows us o verif ha changes in consumpion and a period depend upon he deviaion from heir long-run equilibrium relaionship in period. For insance, if he level of consumpion a is above he level deermined b (6), hen we would epec ha a + is level would decrease or would increase o reurn o he long-run level. The las wo erms ha appear in boh equaions in (7) are included o ake ino accoun he poenial problem of auocorrelaion. In order o be coinegraed, a leas one parameer, eiher θ or θ 2 should be saisicall significan. If boh were zero, he long-run equilibrium relaionship would no eis and consumpion and would no be coinegraed. Table 2 shows he resuls of esimaing an ECM for Meico and he US. zs φ z2s s c s z + u + u 2 (6) (7)

13 GomeM.,Venosa, D. Bilaeral Relaionship Beween Consumpion and in Meico and he US The number of lags included was seleced in each case b opimizing he Akaike Informaion Crierion (AIC). Table 2: Error-Correcion Model Independen - Counr ˆ θ Consan Dependen i ˆ θ Q z, i and Lags 6, d. f. LM 2, lags Consumpion NO/ Meico NO/ Consumpion Consumpion YES/m= U.S NO/m4= Consumpion The ECM suggess ha consumpion and in Meico are no coinegraed. In hese cases, boh speed of adjusmen parameers, θ, are saisicall equal o zero. This implies ha eiher consumpion or is unresponsive o he previous period s deviaions from he long-run equilibrium beween hese wo variables. Furhermore, he resuls impl ha consumpion and in he US are coinegraed. Whenever consumpion a ime, us i c,, eceeds he long-run equilibrium value, α + β us us us, ( ε us, > 0 ), he income, us, + is correced (augmened) in he following period a a speed of Conclusions We show b means of Mone Carlo eperimens ha severe size disorions arise when working wih small sample-size series in he case of he Granger causali es, he modified version of he Granger causali es, he Engle-Granger coinegraion es, and he Hausman es for causali. Furhermore, he resuls obained from hese ess are unreliable if he series are no saionar, for which reason we chose o work wih he series in firs differences. Our empirical resuls reveal ha he mehodological improvemens did no lead o he deecion of a causal relaionship beween consumpion and : here is no evidence of eiher causali or coinegraion beween he Meican series for consumpion and [his ma be due o he small sample used; furher research, wih larger samples, should be carried ou]. These resuls are similar o hose in Guisan (2004). In he case of he US series, we find evidence of causali from consumpion o. We also find evidence of coinegraion beween hese variables. The esimaed ECM model saes ha he variable is ha which adjuss o shor-run disequilibria. Nowihsanding hese findings, i should be clear ha coinegraion does no impl causali (i is raher a long-run equilibrium relaionship beween he variables) and ha causali in small samples is difficul o deec wih he available ess. Bibliograph Brown, R., J. Durbin, and J. Evans (975). Techniques for Tesing he Consanc of Regression Relaionships Over Time, Journal of he Roal Saisical Socie, 37,

14 Applied Economerics and Inernaional Developmen Vol.9- (2009) Dicke, D., and W. Fuller (979). Disribuion of he Esimaors for Auoregressive Time Series wih a Uni Roo, Journal of he American Saisical Associaion, 74(366), Enders, W. (2004). Applied Economeric Time Series. Wile, Second Ediion. Engle, R., and C. Granger (987). Coinegraion and Error Correcion: Represenaion, Esimaion, and Tesing, Economerica, 55, Ellio, Grahwa, Rohenberg, Thomas J., and Sock, James H., (996). Efficien ess for an auoregressive uni roo, Economerica 64 (4), pp Góme M. and Venosa-Sanaulària D (2008). Tesing for a deerminisic rend when here is evidence of Uni-Roo. Guanajuao School of Economics Working Paper Series No EC Guisan, M.C. (200). Causali and coinegraion beween consumpion and in 25 OECD counries: limiaions of he coinegraion approach, Applied Economerics and Inernaional Developmen, vol. pp Guisan, M.C. (2003). Causali ess, inerdependence and model selecion: applicaion o OECD counries, Working Paper Series of Economic Developmen, No. 63. Guisan, M.C. (2004). A comparison of causali ess applied o he bilaeral relaionship beween consumpion and in he USA and Meico, Inernaional Journal of Applied Economerics and Quaniaive Sudies, Vol., pp Guisan, M.C., Malacon, C., and Eposio, P. (2003). Effecs of he inegraion of Meico ino NAFTA on Trade, Indusr, Emplomen and Economic Growh. Working Paper Series of Economic Developmen, No. 63. Kwiakowski, Denis, Phillips, Peer and Schmid, Peer (992). Tesing he null hpohesis of saionari agains he alernaive of a uni roo, Journal of Economerics 54 (), pp Ng, Serena and Perron, Pierre, (200). Lag Lengh Selecion and he Consrucion of Uni Roo ess wih Good Size and Power, Economerica 69(6), pp Noriega A. and Venosa-Sanaulària D. (997). Spurious Regression and Trending Variables, Oford Bullein of Economics and Saisics, Vol. 69 (3), pp Phillips, P.C.B. and Perron, P. (988). Tesing for a uni roo in ime series regression, Biomerica, vol. 75 (2), pp Phillips, P. C. B. (986) Undersanding spurious regressions in economerics, Journal of Economerics, vol. 33, pp Venosa-Sanaulària D. and Vera-Valdés, J.E. (2008). Granger-Causali in he presence of srucural breaks, Economics Bullein, Vol. 3, No 6 pp. -4 Zivo, E., and D. Andrews (992). Furher Evidence on he Grea Crash, he Oil-Price Shock, and he Uni-Roo Hpohesis, Journal of Business and Economic Saisics, vol. 0, Appendi: Daa Generaing Processes of he Simulaions The parameer values used for all he simulaions included in his aricle are as follows: DGP Parameers [var. ] Parameers [var. ] [less Uni Roo] σ 2 = σ 2 = 2 [ ] 2 = 4 [] 5 [ ] σ ; µ = 7 σ 2 = ; µ = 2 σ 2 = ; = 7 µ ; β = σ ; µ = 7 ; β = ; γ 2 = = = σ ; µ = 2 = 7 β = 0.03 µ ; σ 2 = ; µ = 2 µ = 7 ; β = 0.03 ; γ = Noes: Innovaions an iid normall disribued wih zero mean and consan variance. The number of replicaions is 0,000. Aricles on line a he EAAEDS Web sie: hp://