Revisiting Wagner s Law for Selected African Countries: A Frequency Domain Causality Analysis

Transcription

1 Journal of Sascal and Economerc Mehods, vol.4, no.4, 015, ISSN: rn, onlne Scenress d, 015 Revsng Wagner s aw for Seleced Afrcan Counres: A Frequency Doman Causaly Analyss Yaya Keho 1 Absrac Ths sudy examnes he causal relaonsh beween governmen exendure and economc growh and ess he valdy of Wagner s aw for en Afrcan counres. Wagner s law hyoheszes ha here s a one-way causaly runnng from naonal ncome o governmen exendure. We emloy Granger causaly ess n he frequency doman whch allows us o dsngush shor, medum and long run causaly. The emrcal resuls show ha Wagner s law holds for Cameroon only n he medum erm, for Ghana n he shor, medum and long erms and for Ngera n he long-run. The oose vew s suored for Gabon and Senegal n he shor, medum and long run, and for Souh Afrca boh n he medum and shor run. There s bdreconal causaly beween governmen exendure and ncome for Burkna Faso over he shor, medum and long run. Mahemacs Subec Classfcaon: 6P0; 6H15; 6M10 1 Ecole Naonale Suéreure de Sasque e d Econome Alquée ENSEA Abdan. Côe d Ivore. Emal: yayakeho@yahoo.fr Arcle Info: Receved : Augus 5, 015. Revsed : Seember 1, 015. Publshed onlne : December 1, 015.

2 56 Revsng Wagner s aw for Seleced Afrcan Counres. Keywords: Wagner s law; governmen exendure; ncome; Frequency doman analyss 1. Inroducon The nexus beween governmen exendure and economc growh s one of he mos conroversal ssues n he macroeconomc leraure. Ths oc has moran olcy mlcaons. If governmen sendng causes economc growh, hen governmen exendure could be used o romoe economc growh and herefore reducng ublc sendng could lead o a fall n real ouu. On he oher hand, f he causaly runs n he oose drecon, hen budge defc-reducng olces may be mlemened whou dermenal effecs on economc growh. Theorecally, wo convenonal vews descrbe he relaonsh beween ublc sendng and economc growh. Frs, he Wagner s law sresses ha as er caa ncome ncreases he share of ublc sendng ends o rse o mee he ncreased roecve, admnsrave and educaonal funcons of he sae [1]. Ths vew suggess a undreconal causaly runnng from naonal ncome o governmen exendure. On he conrary, he Keynesan vew argues ha ublc sendng s an exogenous facor and a olcy nsrumen for ncreasng naonal ncome []. Ths lne of hough suggess ha causaly runs from governmen exendure o economc growh. An exensve emrcal research has examned he valdy of hese wo comeng vews. The emrcal evdence from hs leraure s however mxed and conroversal across counres, daa, model secfcaons and economerc echnques see [3], [4], [5], [6]. Regardng sudes on sub-saharan Afrcan counres, [7] nvesgaed he drecon of causaly beween governmen exendure and naonal ncome for Ghana, Kenya, and Souh Afrca. They found ha here s no long run relaonsh beween governmen exendure and

3 Yaya Keho 57 naonal ncome. In he shor-run, only Ghana shows evdence suorng Wagner s law. The resuls obaned by [8], [9], [10], [11] and [] for Ngera, [13] for Souh Afrca, [14] for Kenya, and [15] for Sudan are conssen wh Wagner s law. In conras, he sudes by [16], [17], [18] and [19] for Ngera, [0] for Sudan, and [1] for Souh Afrca rovded suor for he Keynesan vew. [] found suorve emrcal evdence for boh hyoheses boh n he shor run and long run for Ngera. Besdes, he resuls obaned by [3] suored neher Wagner s law nor Keynesan vew for Gamba, Ghana and Ngera. Mos of he revous sudes used he sandard aroach o Granger causaly, whch requres re-esng of un roo and conegraon. In he case of nonsaonary, varables are consdered n frs dfferences o make hem saonary whch cause loss of long-run nformaon. In addon, sandard aroach of Granger causaly gnores he ossbly ha he srengh and drecon of he causaly could vary over dfferen frequences. The new Keynesan aroach acces ha sze and drecon of neracon beween economc varables can change over me due o rgdes n an economy. In hs regard, he relaon beween wo varables mgh dsaear n he medum and long run, alhough s srong n he shor run. Ths sudy conrbues o he ublc exendure-growh leraure by emloyng he Granger causaly n he frequency doman o examne shor, medum and long run causaly and ams o ndcae wheher here s a change n causaly drecon over me. Frequency doman analyss allows analyzng he causal relaonsh beween economc varables n dfferen me erods shor, medum and long erms. To he bes of our knowledge, hs s he frs sudy nvesgang causaly beween governmen exendure and economc growh n hgh and low frequences. The emrcal analyss s based on a samle of nne Afrcan counres. The remander of he aer s organzed as follows. Secon descrbes he economerc mehodology. Secon 3 analyses he emrcal resuls and Secon 4 concludes he sudy.

4 58 Revsng Wagner s aw for Seleced Afrcan Counres.. Economerc Mehodology.1 Daa descron Ths sudy uses annual me seres daa for a samle of nne Afrcan counres, namely Burkna Faso, Cameroon, Coe d Ivore, Gabon, Ghana, Kenya, Ngera, Senegal and Souh Afrca. The varables under sudy are governmen exendures as share of GDP and real er caa GDP. The GDP deflaor was used o exress daa n consan 005 US dollars. Meanwhle, he effec of oulaon growh was removed by usng er caa values. Daa cover he erod from 1965 o 013, exce for Ngera for whch daa cover he erod All daa were obaned from he World Develomen Indcaors, avalable onlne. Table 1 reors sascs on he evoluon of he wo varables. The mos srkng feaure s he low levels of he sze of ublc secor as well as real ncome n mos counres. Also evden from he Table s he osve assocaon beween he wo varables. However, correlaon does no mean causaly. Our goal n hs sudy s o fnd ou wheher hs osve assocaon mles ha more governmen sendng causes hgher ncome or hgher ncome leads o more ublc sendng. I s ossble ha he assocaon beween he wo varables s no causal n any drecon, bu us concdenal.. Causaly es n he frequency doman Frequency doman descrbes he doman for analyss of mahemacal funcons wh resec o frequences, raher han me. In he frequency doman, a saonary rocess can be exressed as a weghed sum of snusodal comonens wh a frequency. Frequency doman causaly was develoed by [4], [5] and [6]. In hs sudy, we follow he descron n [6].

5 Yaya Keho 59 Table 1: Publc exendure and real er caa GDP over me Publc exendure % GDP Real er caa GDP Counres Burkna Faso Cameroon Côe d Ivore Gabon Ghana Kenya Ngera Senegal Souh Afrca Source: World Develomen Indcaors Onlne, World Bank

6 60 Revsng Wagner s aw for Seleced Afrcan Counres. e Z X, Y be a wo-dmensonal vecor of me seres. I has a fneorder VAR reresenaon of he form: Z I Z µ θ θ Θ where s he lag oeraor. The error vecor μ s whe nose wh Eμ 0 and Eμ μ Σ; where Σ s osve defne. e G be he lower rangular marx of he Cholesky decomoson, G G Σ -1 such ha η Gμ and Eη η I. If Z s saonary, he MA reresenaon s: Φ Φ Φ Φ Φ Z η η η µ µ ε where Фϴ -1 and ФG -1. Usng hs reresenaon he secral densy of X can be exressed as: π x e e f 3 Then, we can defne he measure of causaly suggesed by Geweke 198 as follows: log log π x x y e e e f M 4 To es he hyohess ha Y does no cause X a frequency, we consder he null hyohess: 0 0 x y e M 5 Breung and Candelon 006 show ha: e sn 0 cos 0 sn cos 0 θ θ θ θ 6

7 Yaya Keho 61 Breung and Candelon 006 roose a smle aroach o es hese lnear resrcons. They consder he VAR equaon for X secfes as follows: X α 1 X α X + β1y β Y + µ 1 7 The null hyohess M 0 y x s equvalen o he lnear resrcon: H : R β where R[β 1, β, β ] and cos cos... cos R 9 sn sn... sn The causaly measure for ϵ[0,π] can be esed usng he sandard F-es for lnear resrcons. The F-sasc follows an F dsrbuon wh, T- degrees of freedom. 3. Emrcal Resuls As a frs se of our emrcal analyss, we es for he order of negraon of he seres by means of un roo ess. To ha end, we aly wo well-known un roo ess he PP es of [7] and he KPSS es of [8]. These ess have been erformed under he models wh consan and rend for he level seres and wh consan for seres n frs dfference. The resuls dslayed n Table show ha he varables are non-saonary n her level bu acheve saonary saus afer akng he frs dfference. Before usng he frequency doman causaly es, we frs aly Granger causaly ess n he me doman o gan frs nsghs no he causal lnk beween governmen exendure and economc growh. To ha end, we aly he aroach roosed by [9]. Ths aroach does no requre esng for conegraon and esmang vecor error correcon model and s robus o he un roo and conegraon roeres of

8 6 Revsng Wagner s aw for Seleced Afrcan Counres. Table : Resuls of un roo ess Counry PP KPSS g y Δg Δy g y Δg Δy Burkna Faso Cameroon Coe d Ivore Gabon Ghana Kenya Ngera Senegal Souh Afrca Noes: Crcal values a he 5% level are: for PP es level and -.95 dfference, and for KPSS: level and dfference. he seres. Whle he sandard Granger causaly analyss requres esmang a level VAR, [9] rocedure requres esmang a level VAR+d where d s he maxmum negraon order of he varables. The null hyohess of Granger causaly s hen esed by mosng zero resrcon on he frs arameers usng a sandard Wald sasc. Accordng o he resuls of un roo ess, he maxmum negraon order of he varables s one. The lag lengh s deermned usng he Akake Informaon Creron AIC. The resuls are shown n Table 3. They ndcae ha here s a undreconal Granger causaly runnng from ncome o governmen exendure for only Ghana, and from governmen exendure o ncome for only Gabon, Senegal and Souh Afrca. There s bdreconal causaly beween he wo varables n he case of Burkna Faso.

9 Yaya Keho 63 Table 3: Resuls of lnear Toda and Yamamoo Granger-causaly es ag lengh Income does no cause governmen exendure Governmen exendure does no cause Income Burkna Faso * * Cameroon Coe d Ivore Gabon * Ghana * Kenya Ngera Senegal ** Souh Afrca * Noe: The lag lengh for he VAR+d models are deermned by AIC. Numbers n arenheses are he -values. * and ** denoe sascal sgnfcance a he 5% and 10% levels, resecvely. To measure shor, medum and long erms causal dynamcs, we calculae es sascs for frequences ϵ{0.5; 1; 1.5; ;.5; 3}. The frequency.5 corresonds o a erodcy of.5 years, he frequency 1.5 corresonds o a erodcy of 4. years, and he frequency 1 corresonds o a erodcy of 6.3 years. To elmnae he need for esng conegraon, we augmen he VAR model by one lag and es he resrcons by usng a VAR+1 model, so he frequency doman causaly es wll be robus o he conegraon roery of he varables as suggesed by [6]. Table 4 resens he causaly es resuls n frequency doman. The resuls sugges bdreconal causaly for Burkna Faso over he shor, medum and long erods. They also ndcae ha causaly from ncome o governmen sendng exss n medum erm for Cameroon, and n shor, medum and long erms for Ghana, and a ermanen long-erm causaly for Ngera. On he oher hand, he

10 64 Revsng Wagner s aw for Seleced Afrcan Counres. Burkna Faso * 0.07 Cameroon Table 4: Resuls of frequency doman Granger-causaly es Income does no cause governmen exendure Governmen exendure does no cause Income ong erm Medum erm Shor erm ong erm Medum erm Shor erm * * ** * * * * * * * * * Coe d Ivore Gabon * * * * * * 0.04 Ghana * * * * * * Kenya Ngera ** Senegal ** ** ** ** ** ** Souh Afrca * * * Noe: Numbers n arenheses are he -values. * and ** denoe sascal sgnfcance a he 5% and 10% levels, resecvely.

11 Yaya Keho 65 causaly from governmen sendng o ncome exss for Gabon and Senegal over he shor, medum and long erods, and for Souh Afrca boh n shor and medum erms. Causaly dsaears n he long run n Souh Afrca. There s no evdence of causal relaonsh beween governmen exendure and er caa GDP n Coe d Ivore and Kenya. Ths fndng suggess ha he movemens of governmen exendure and er caa ncome do no have sgnfcan macs uon each oher. In lgh of hese fndngs, we can conclude ha Wagner s law holds for Cameroon only n he medum erm, for Ghana n he shor, medum and long erms and for Ngera n he long-run. The Keynesan vew s suored for Gabon and Senegal n he shor, medum and long run, and for Souh Afrca boh n he medum and shor run. Governmen sendng n Burkna Faso follows Wagner s law and Keynesan vew over he shor, medum and long run. Conversely, evdence for Coe d Ivore and Kenya do suor neher Wagner s law nor Keynesan vew. 4. Concluson In hs arcle, we examned Wagner s aw for nne Afrcan counres usng me seres daa for he erod 1965 o 013. Wagner s law suggess undreconal causaly runnng from naonal ncome o governmen exendure. The resuls of radonal Granger causaly ess sugges ha Wagner s law s suored only for Ghana, whle he Keynesan vew holds for Gabon, Senegal and Souh Afrca. Burkna Faso has bdreconal causaly beween governmen exendure and ncome. Snce radonal causaly es does no consder me varyng naure of he relaonsh, we erform he frequency causaly es. The suerory of he frequency doman causaly aroach s ha decomoses me erods and examnes causaly n dfferen me frequences.

12 66 Revsng Wagner s aw for Seleced Afrcan Counres. The resuls ndcae ha Wagner s law holds for Cameroon n he medum erm, for Ghana n he shor, medum and long erms and for Ngera n he longrun. The Keynesan vew s suored for Gabon and Senegal n he shor, medum and long run, and for Souh Afrca boh n he medum and shor run. Therefore, hese hree counres can use ublc sendng o smulae her economes as conended by he Keynesan aradgm. Governmen sendng n Burkna Faso follows Wagner s law and Keynesan vew over he shor, medum and long run. Coe d Ivore and Kenya do suor neher Wagner s law nor Keynesan vew. As a resul, reducon n governmen fnal exendure would no negavely affec economc growh for hese wo counres. The resuls of hs sudy ndcae ha economss and olcymakers mus ake accoun of changng causales and desgn economc acons accordngly. In hs regard, fscal olces should ake no consderaon no only he causaly drecon beween governmen exendure and economc growh bu also wheher he drecon of causaly s emoral or ermanen. The fndngs of he sudy sugges ha governmen sendng s an exogenous nsrumen o smulae economc growh n Gabon and Senegal n he shor, medum and shor run and n Souh Afrca only n he shorer erods. References [1] A. Wagner, Three Exracs on Publc Fnance n R.A. Musgrave and A.T. Peacock eds, Classcs n he Theory of Publc Fnance, ondon, Macmllan, [] J.M. Keynes, The General Theory of Ineres, Emloymen and Money, ondon, McMllan, [3] P. Narayan, A. Prasad and B. Sngh, A es of he Wagner's hyohess for he F slands, Journal of Aled Economcs, 401, 008,

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