Non Sationarity in the Consumption Income Ratio: Further Evidence from Panel and Assymetric Unit Root Tests. Abstract. Panteion University

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1 Non Saonary n he Conumpon Income Rao: Furher Evdence from Panel and Aymerc Un Roo e Efymo ona Ahen Unvery of Economc and Bune Dmr Chropoulo Deparmen of Economc and Regonal Developmen, Paneon Unvery Abrac In h paper we e he aonary propere of he conumpon ncome rao for a ample of 4 European Unon counre over he perod ulzng recen advance n panel un roo and aymmerc un roo e. We fnd ha a falure o ake accoun of aymmere, would mply I() conumpon ncome rao alhough un roo e baed on AR model ndcae aonary n a lea one regme. h reul provde more evdence n relaon o Saran and Sewar (Economc Leer, 999) who found ha he conumpon ncome rao I(). Caon: ona, Efymo and Dmr Chropoulo, (00) "Non Saonary n he Conumpon Income Rao: Furher Evdence from Panel and Aymerc Un Roo e." Economc Bullen, Vol. 3, No. pp. 5 Submed: June 0, 00. Acceped: July 6, 00. URL: hp:// 0C0004A.pdf

2 . Inroducon he me ere propere of he conumpon-ncome rao a conroveral ue n heorecal and emprcal macroeconomc. he relave ncome hypohe, he hab peren model, he permanen ncome hypohe and lfe cycle hypohe all predc ha a long run equlbrum relaonhp ex beween conumpon and ncome whch n urn mple ha he conumpon-ncome rao converge o a eady ae. Whn h framework, devaon n average propeny o conume from he eady ae hould be emporary. On he conrary, he Keynean abolue ncome hypohe, he Marxan underconumpon heory and Deaon (977) nvolunary avng heory all mply ha he average propeny o conume doe no converge oward a conan n he long run. he heore can be eed by nvegang he aonary propere of he conumpon-ncome rao. he fndng of a un roo n he conumpon-ncome rao would mply ha h ere doe no flucuae around a predcable level. Under h cenaro, all hock permanenly aler he average propeny o conume wh no endency o reurn o a conan value. In h cae, a rucural relaonhp beween conumpon and ncome canno be eablhed, o he average propeny o conume canno have a long run equlbrum. h reul ha far reachng mplcaon for modelng and forecang he economy and for underandng avng behavor and he bune cycle. On he emprcal de, Drobny and Hall (989), Hall and Paeron (99), and Horoka (997) produced evdence for a nonaonary average propeny o conume whle Ungern-Senberg (986) and Kng e al (99) reached he oppoe concluon. Accordng o Saran and Sewar (999) he lack of conenu can be arbued o he low power of un roo e. o h end, hey ued he Im, Pearan and Shn (997) (hereafer IPS) and aylor and Sarno (998) panel un roo e o draw harp nference. her reul led uppor o he conenon ha he average propeny o conume generaed by a non-aonary ochac proce. In h paper ung daa for 4 European unon counre over he perod we e for he exence of a un roo n he conumpon-ncome rao. More pecfcally:. We ue he IPS panel un roo e along wh Maddala and Wu (MW) (999) and Harr-zaval (999) (hereafer H) panel un roo e ha have conderable more power relave o he IPS e, ee Breung (999).. We acknowledge ha an aymmerc adjumen may have affeced he propere of our me ere. Ender and Granger (998) revewed many mporan example of aymmerc adjumen of economc varable uch a real GDP, unemploymen, and ndural producon. o ha end, we conder he Caner and Hanen (000) un roo

3 e n he conex of hrehold auoregreve model, and we provde an MW panel veron of h e. he layou of h paper a follow: Panel un roo e a well a he aymmerc un roo e are oulned n econ. he emprcal reul are conaned n econ 3 whle econ 4 conclude he paper.. Mehodology o e for a un roo n panel daa, Harr and zaval (999) conder he model y = z, + γ + u () ρ y where z are deermnc varable, u d (0, σ ) and ρ = ρ. he e ac a ac on ρ gven by N e (ρˆ ) ~ y, = = ρ = () where ~ y = y h(, ) y, u~ = u h(, ) u = = h(, ) = z ( z z ) z, = N e = N ) u ~ = = (, and ρˆ he OLS emae of ρ. I can be hown ha f here are fxed effec and a me rend n he model, hen ˆ 3 3( N ρ + ) N(0, ) (3) ( + 3 5( )( + ) A more popular approach for eng for un roo n a panel daa eng he IPS ac. h baed on averagng ndvdual Dckey-Fuller un roo e. Inead of averagng ndvdual Dckey-Fuller un roo e, Maddala and Wu (MW) (999) propoed a ac ha combne he p-value from ndvdual ADF e ( p ay for he h croecon, =,.., N ). he MW ac P = ln p, drbued a χ (N). Fnally, we allow he un roo hypohe o be eed agan an alernave of aonary wh aymmerc adjumen. Followng Caner and Hanen (000), he model gven by a AR( k ) of he form where N = y = θ + u (4) x ( z λ) + θx ( z λ) y he ere we conder, λ he hrehold parameer, x (,,,.., ) y r y y k, z y y m for ome m ( m = n h = applcaon), and r a vecor of exogenou varable, a conan n our cae. he

4 procedure can be ued o e mulaneouly for aonary a well a hrehold effec. Fr, model (4) emaed by OLS for a fxed λ [ λ, λ], and he redual varance ) uˆ( ) compued. he hrehold parameer emaed by ( λ = λ = λ ˆ = arg mn : ( λ ). For he emae λˆ, he redual û and he redual varance λ are compued. o e for un roo, we ue he one-ded formulaon of Caner and Hanen (000), namely H ρ = ρ 0 veru he alernave H ρ 0 or ρ < 0 0 : = : < where ρ denoe he fr elemen of θ. he e ac a wo-ded Wald e of he form R = + where gnfe he -rao for ρˆ from OLS regreon n he AR model. Exac p -value for h e can be compued ung he boorap. Snce exac p -value are avalable, a panel daa veron of he Caner and Hanen (000) e can be conruced by conderng an MW formulaon. h e combne he p -value from he ndvdual aymmerc Dckey-Fuller equaon accordng o he followng formula P = N = ln and drbued a χ (N). h wll be call he Maddala and Wu e under aymmerc adjumen (hereafer MWA). p 3. Emprcal Reul me ere ADF e are repored n able for all foureen counre. I evden ha we canno rejec he preence of a un roo n he conumpon-ncome rao a convenonal level of acally gnfcance. Panel un roo e (IPS, MW and H), repored n able, uppor he hypohe of a un roo n he conumpon-ncome rao acro counre, a well a he hypohe of I (0) n fr dfference. However, he reul are much dfferen when we accoun for he preence of an aymmerc adjumen n he conumpon-ncome rao. e for aonary are repored n la column of able. Accordng o hee fndng, we fnd aonary n a lea one regme n egh cae (Belgum, Greece, France, Ialy, Neherland, Porugal, Norway, and Sweden). Save for Belgum, we have aonary n he econd regme. Annual conumpon-ncome daa over he perod are from he European Unon AMECO daabae (Annual Macro Economc Daa Bae DG). Conumpon meaured by oal prvae conumer expendure, and ncome by GDP. Boh varable are expreed n conan prce euro. he reul remaned qualavely he ame when we condered a logc ranformaon of he rao.

5 able. Un Roo e for he Conumpon-Income Rao Counry e for aonary ADF Belgum (0.07) (0.78) Denmark (0.99) (0.8) Greece (0.38) (0.09) Span (0.85) (0.40) France (0.86) (0.009) Ireland (0.66) (0.78) Ialy (0.54) (0.04) Neherland (0.7) (0.0) Porugal (0.) (0.006) UK (0.53) (0.65) Aura (0.98) (0.4) Norway (0.65) (0.05) Sweden (0.54) (0.09) Fnland (0.) (0.5) Noe: ADF denoe he Augmened Dckey Fuller un roo e wh drf and rend erm n he fed equaon. Boldface value denoe amplng evdence n favour of un roo. Number n parenhee are boorap p-value. For boorappng 0,000 replcaon have been ued. wo-ded Wald e are ued for he aymmerc un roo e, and a gnfcance level of 0% o decde wheher here a un roo n eher regme. A panel veron of he aymmerc un roo e (MWA) provde addonal evdence ha aonary preval n a lea one regme. h mean ha a falure o ake accoun of aymmere would mply a rejecon of he hypohe ha he conumpon ncome rao overall I (0) alhough n egh ou of foureen counre h clearly unrue n he econd regme. In oher word, he aymmerc un roo e offer le evdence n favour of he un roo hypohe. 3

6 IPS H MW able. Panel Un Roo e for Conumpon-Income Rao Level Fr dfference IPS H MW MWA * -6.88*** -5.46*** 99.75*** Noe: IPS, H and MW are repecvely he Im, Pearan and Shn, Harr and zaval, and Maddala and Wu e for a un roo n he model. Bold face value denoe amplng evdence n favour of un roo. he crcal value for he MWA e are 48.8 and a he % and 5% acal level repecvely. (***) gnfe rejecon of he un roo hypohe a he % level. 4. Concluon h paper apple hree panel un roo procedure, and an aymmerc un roo ac o e he me ere propere on he conumpon-ncome rao for a ample of 4 European unon counre over he perod Alhough he IPS, Maddala and Wu (999) and Harr and zaval (999) panel un roo procedure fnd he average propeny o conume o be aonary, he aymmerc un roo e ugge ha a aonary ochac proce more plauble. herefore, reearcher ha ue andard un roo e hould be cauou abou he preence of an aymmerc adjumen. Reference Breung, L., 999, he Local Power of Some Un Roo e for Panel Daa, Dcuon Paper, Humbold Unvery, Berln. Caner, M., and B.E. Hanen, 000, hrehold auoregreon wh a un roo, dcuon paper, Unvery of Wconn. Deaon, A.S., 977, Involunary avng hrough unancpaed nflaon, Amercan Economc Revew 6, Drobny, A. and Hall, S.G., 989, An nvegaon of he long-run propere of aggregae non-durable conumer expendure n he Uned Kngdom, Economc Journal 99, Ender,W., and Granger, C.W.J.,998, Un roo e and aymmerc adjumen wh an example ung he erm rucure of nere rae, Journal of Bune of Economc and Sac 6, Hall, S.G. and Paeron, K.D., 99, A yem approach o he relaonhp beween conumpon and wealh, Appled Economc 4, Harr, R.D.F. and zaval, E., 999, Inference for Un roo n Dynamc Panel where he me Dmenon Fxed, Journal of Economerc, 9, 0-6. Horoka, C.Y., 997, A conegraon analy of he mpac of he age rucure of he populaon on he houehold avng rae n Japan, he Revew of Economc and Sac 79, Im, S.K., Pearan, H. M. and Shn, Y., 997, eng for Un Roo n Heerogeneou Panel, Deparmen of Appled Economerc, Unvery of Cambrdge. Kng, R.G., Ploer, C.I., Sock, J.H. and Waon, M.W., 99, Sochac rend and economc flucuaon, Amercan Economc Revew 8,

7 Maddala, G. S. and Wu, S., 999, A Comparave Sudy of Un Roo e wh Panel Daa and a New Smple e, Oxford Bullen of Economc and Sac, 6, Saran, N. and Sewar, C., 999, I he conumpon-ncome rao aonary? Evdence from panel un roo e, Economc Leer 64, aylor, M.P. and Sarno, L. and 998, Real exchange rae under he recen floa: unequvocal evdence of mean reveron, Economc Leer 60, Ungern-Sernberg,.V., 986, Inflaon and he conumpon funcon, Welwrchflche Archv,