NPTEL Project. Econometric Modelling. Module23: Granger Causality Test. Lecture35: Granger Causality Test. Vinod Gupta School of Management

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1 P age NPTEL Proec Economerc Modellng Vnod Gua School of Managemen Module23: Granger Causaly Tes Lecure35: Granger Causaly Tes Rudra P. Pradhan Vnod Gua School of Managemen Indan Insue of Technology Kharagur, Inda Emal:

2 2 P age MODULE OBJECTIVE Ths module aems o exlore he drecon of causaly among he me seres varable. The usual regresson echnque usually works ou he naure of causaly and s sgnfcance level. However, does no exlan he drecon of causaly. In fac, s very moran n he me seres seng. In hs secon, we hghlgh he followngs:. Wha s Granger causaly es? 2. Tes Procedure for Granger causaly es 3. Choce of lag lengh n he Granger causaly es WHAT IS GRANGER CAUSALIT TEST? Afer examnng, n he earler secon, he un roo and conegraon n he me seres seng, he nex se s o know he drecon of causaly. And for hs, we aly Granger Causaly es. The es reresens ha for a wo varables (say and ); f s nfluenced by boh lagged values of and lagged values of, hen s called as Granger causes ( ). Smlarly f s nfluenced by s lag and he lagged values of, hen we call Granger causes ( ). However beween and, f Granger causes and Granger causes, we call b-dreconal causaly. If only one exss, hen s he case of un-dreconal causaly. If boh do no exs, hen he varables are ndeenden o each oher. 2

3 3 P age 3 THE TEST PROCEDURE OF GRANGER CAUSALIT TEST If he wo seres and are ndvdually I () and conegraed, hen Granger Causaly es may use I () daa because of suer conssency roeres of esmaon. In hs case, he followng regresson model has o be esmaed: q b a s r d c Where, ε and η are random dsurbances, whch are serally uncorrelaed wh zero mean and un varance. And α, β, a, a 2,.., a, b, b 2,, b are he arameers o be esmaed. Here, Granger causes, f he null hyohess H 0 : b = b 2 = = b q = 0 s reeced agans he alernave hyohess H A : A leas one b 0, =, 2, 3. q. And Granger causes, f H 0 : d = d 2 = = d s = 0 s reeced agans he alernave hyohess H A : A leas one d 0, =, 2, 3. s. If Granger causaly es wh conegraed varables may ulze he I (0) daa wh an error correcon erm, hen he earler model has o be modfed as: q ECT b a s r ECT d c

4 4 P age Where, ECT sands for Error Correcon Term, whch combnes he long run conegraon relaonsh and shor run correcons/adusmens of conegraed varables owards he long run equlbrum. Here, Granger causes, f he null hyohess H 0 : b = b 2 = = b q = 0 s reeced agans he alernave hyohess H A : A leas one b 0, =, 2, 3. q. And Granger causes, f H 0 : d = d 2 = = d s = 0 s reeced agans he alernave hyohess H A : A leas one d 0, =, 2, 3. s. If daa are I () bu no conegraed, Granger Causaly es requres ransformaon of he daa o make hem I (0). And n hs case, he regresson model becomes: a q b r c s d In all he cases, he omal lags have been chosen by Akake Informaon Creron (AIC) and Schwarz Bayesan Creron (SBC). Here, Granger causes, f he null hyohess H 0 : b = b 2 = = b q = 0 s reeced agans he alernave hyohess H A : A leas one b 0, =, 2, 3. q. And Granger causes, f H 0 : d = d 2 = = d s = 0 s reeced agans he alernave hyohess H A : A leas one d 0, =, 2, 3. s. In all hese cases, he es has been underaken by F-sascs, whose value deends uon he resrced resdual sum squares (RSS R ) and unresrced resdual sum squares (RSS UR ). If he 4

5 5 P age comued F-value exceeds he crcal F-value, we reec he null hyohess and conclude ha here exss causaly beween he wo varables. ERROR CORRELATION MECHANISM The error correcon mechansm (ECM) develoed by Engle and Granger s a means of reconclng he shor-run behavor of an economc varable wh s long-run behavor. Whle he conce of conegaron s clearly an moran heorecal undernnng of he error correcon model here are sll a number of roblems surroundng s raccal alcaon. For esmaon rocess, we use he followng model. 0 l l 2l l 3ECT l l u () 0 l l 2l l 3ECT l l v (2) Where, ECT s error correcon, caured from he conegraon regresson; u and v are muually uncorrelaed whe nose resduals. The error correcon model has an neresng emoral causal nerreaon n he sense ha a bvarae conegraed sysem mus have a causal orderng n a leas one drecon. Alhough conegraon ndcaes he resence of Granger causaly, a leas n one drecon, does no ndcae he drecon of causaly beween varables. The drecon of he Granger causaly n hs case can only be deeced hrough he error correcon model (ECM) derved from he long run conegrang vecors. In addon o ndcang he drecon of causaly amongs varables, he ECM also enables us o dsngush beween he shor run and he long run Granger causaly. The F-es and he exlanaory varables ndcae he shor run causaly, whereas he long run causaly s mled hrough he sgnfcance of he -es of he lagged error 5

6 6 P age correcon erm. For nsance, he fnance develomen s sad o Granger cause economc growh n he long run, f α 2 0 and α 3 0. Smlarly, economc growh s sad o Granger cause fnance develomen, f β 0 and β