The Analysis of Transitions in Economic Performance Using Covariate Dependent Statistical Models

Transcription

1 Th Analysis of Transitions in Economic Prformanc Using Covariat Dpndnt Statistical Modls Adam Baharum, M. Ataharul Islam Th Journal of Dvloping Aras, Volum 43, Numbr 2, Spring 2010, pp (Articl) Publishd by Tnnss Stat Univrsity Collg of Businss DOI: For additional information about this articl No institutional affiliation (23 Nov :01 GMT)

2 THE ANALYSIS OF TRANSITIONS IN ECONOMIC PERFORMANCE USING COVARIATE DEPENDENT STATISTICAL MODELS Adam Baharum M. Ataharul Islam Univrsiti Sains Malaysia, Malaysia ABSTRACT Th GDP or GNP as a masur of conomic prformanc of a country changs continuously. W can idntify th factors that prcd its ups and downs. For such forcasting, th us of Markov modls ar not nw, but in this papr, an attmpt is mad to propos a covariat-dpndnt Markov modl to idntify th factors that contribut to th stimation of transition probabilitis. Th proposd modl is mployd to stimat th transition probabilitis, th factors that contribut to transitions in conomic prformanc, and othr rlvant charactristics. Th cross-country data hav bn mployd for th priod for fitting th modl. This can provid a usful modl for forcasting th conomic prformanc in both dvloping and dvlopd countris. JEL Classifications: C35, O12, O40, O57 Kywords: GDP, Transition Probabilitis, Markov Modl, Logistic Rgrssion, Economic Prformanc Corrsponding Author s Addrss: adam@cs.usm.my INTRODUCTION Th masur of GDP dpnds on svral componnts such as privat consumption, invstmnt, govrnmnt consumption, changs in invntoris, total xports and total imports. It is obsrvd by Swamy and Fikkrt (2002) that th dtrminants of conomic growth which rly on cross-country growth rgrssions may b affctd by bias from two sourcs : (i) omittd variabls, and simultanity. Th first on is attributabl to country charactristics that affct growth but omittd by th conomtricians. Th scond on is du to th fact that th dtrminants of growth of GDP, such as invstmnt in physical capital, may also affctd by this growth. Currntly, thr is vidnc of rlationship btwn human capital accumulation and conomic growth. Astriou and Agiomirgianakis (2001) dmonstratd such rlationship btwn ducation variabls and GDP as wll as th causal dirction btwn thm for Grc. Similar rlationship was obsrvd in othr studis basd on cross-country data (Barro, 2001; Hanushk and Kimko, 2000). Th transition from agrarian to prdominantly industrial conomy had

3 290 bn succssful in raising th pac of conomic growth in som Asian countris during th rcnt past. In this papr, th growth of GDP has bn analyzd in ordr to idntify th factors that contribut to th chang in th conomic prformanc. For th purpos of this study, w hav mployd th cross-country data. Du to missing obsrvations for many variabls, w hav usd only som slctd variabls that ar associatd with th chang in th conomic prformanc in th cross-country stting. Th main objctiv of this papr is to dmonstrat th utility of Markov modls in idntifying th rol of th slctd charactristics in xplaining th growth in GDP ovr tim. Th advantag of such modl is that w can us rpatd obsrvations to idntify th factors that attribut to th chang in conomic prformanc. DATA AND METHODS W hav usd th cross-country data for th priod To dmonstrat a distinct trnd ovr tim, w hav takn into considration data aftr vry fiv yars from th World Dvlopmnt Rports for th yars 1980 through to Th gross domstic product (GDP) is considrd as th outcom variabl, which masurs th conomic prformanc of a country. Th slctd variabls ar: growth of industry (indgr), population growth (popgr), labor forc growth (lfgr), us of nrgy (nrus) W hav usd both linar rgrssion as wll as logistic rgrssion modls in this study for diffrnt tim priods. Thn a covariat dpndnt Markov modl is usd to xamin th chang in prformanc in conomic growth ovr tim. LINEAR REGRESSION MODEL FOR ECONOMIC GROWTH Th linar rgrssion modl for conomic growth is prsntd hr. Th outcom variabl is GDP and th xplanatory variabls ar: growth of industry (indgr), population growth (popgr), labor forc growth (lfgr), us of nrgy (nrus). W hav mployd two diffrnt sts of modls hr, on for ach slctd yar and th othr sts of modls includ th lag variabls. Th modls ar shown blow for th ith country in th jth yar: Modl 1a: GDP = β + β indgr + β popgr + β lfgr + β nrus +ε ij 0 j 1 j ij 2j ij 3j ij 4j ij ij Modl 1b: GDP = β + β indgr + β popgr + β lfgr + β nrus + ε ij 0 j 1 j j-5 2j j-5 3j j-5 4j j-5 ij Th first modl (Modl 1a) considrs both th outcom and xplanatory variabls during th sam yar for th slctd countris. Howvr th scond modl (Modl 1b) mploys xplanatory variabls obsrvd fiv yars bfor th outcom variabl. This modl is xpctd to tak account of th tim-lag in xplaining th outcom variabl, GDP. Th rsults for Modl 1a ar displayd in Tabl 1. It is vidnt from Tabl 1 that growth of industry is positivly associatd (p<0.01) during th priod with a stadily incrasing ffct on th growth of GDP. Population growth

4 291 dos not show any significant association with th growth of conomy. Growth in labor forc appars to hav no statistical association with growth in GDP. Howvr, us of nrgy appars to hav positiv association with conomic prformanc in 1985 (p<0.05). TABLE 1. ESTIMATES OF REGRESSION MODELS FOR GROWTH OF GDP FOR YEAR 1980, 1985, 1990, 1995 AND 2000 Variabl Intrcpt ( ) Growth of Industry *** ( ) Population Growth ( ) Labor Forc Growth Estimats (standard rror) ( ) ( ) *** ( ) ( ) ( ) *** ( ) *** ( ) ( ) ( ) ** ( ) *** ( ) ( ) ( ) ( ) *** ( ) ( ) * ( ) Enrgy in Us (pr capita) * ( ) ** ( ) ( ) ( ) * ( ) Nots: *** Significant at 1% lvl ** Significant at 5% lvl * Significant at 10% lvl Modl 1b uss th 5-yar lag btwn obsrvd GDP and xplanatory variabls. Tabl 2 shows that only growth of industry sms to hav positiv association with GDP for th yars and

5 292 TABLE 2. ESTIMATES OF REGRESSION MODELS FOR GROWTH OF GDP DURING THE PERIOD , , AND Estimats (standard rror) Variabl Intrcpt * *** *** *** ( ) ( ) ( ) ( ) Growth of Industry *** *** *** *** ( ) ( ) ( ) ( ) Population Growth ( ) ( ) ( ) ( ) Labor Forc Growth ( ) ( ) ( ) ( ) Enrgy in Us (pr capita) ( ) ( ) ** ( ) ( ) Nots: *** Significant at 1% lvl ** Significant at 5% lvl * Significant at 10% lvl LOGISTIC REGRESSION MODELS To xplor th undrlying association btwn growth in GDP and th slctd xplanatory variabls, two sts of logistic rgrssion modls ar fittd in this sction. Lt us dfin th following dichotomous variabls for th ith country in yar j: Yij = 0, if GDPij < 3.2 prcnt Y = 1, if GDP 3.2 prcnt ij ij

6 Thn lt us dfin th following modls: 293 Modl 2a: gx ( ij ) = β + β indgr + β popgr + β lfgr + β nrus. 0 j 1 j ij 2j ij 3j ij 4j ij Modl 2b: g( X ) = ij 5 β + β indgr + β popgr + β lfgr + β nrus. 0 j 1 j j-5 2j j-5 3j j-5 4j j-5 Thn th logistic rgrssion modls for both 2a and 2b ar: Modl 2a: ( ij 1 Xij ) PY = = 1+ Modl 2b: ( ij 1 Xij 5 ) g( Xij ) g( Xij ) g( Xij 5) PY = =. g( Xij 5) 1+ Tabl 3 shows th stimats for Modl 2a. It is clarly obsrvd from th rsults that growth of industry has bn positivly associatd with th growth of GDP for all th yars during (p<0.01). Th impact of growth on growth of GDP appars to xrt th largst impacts in th yars 1990 and Similarly, growth of labor forc shows statistically significant positiv association with growth in GDP for th yar 1990 (p<0.05). TABLE 3. ESTIMATES OF PARAMETERS OF LOGISTICS REGRESSION MODELS FOR GROWTH OF GDP IN 1980, 1985, 1990, 1996 AND 2000 Estimats ( standard rror ) Variabl Intrcpt *** *** * ** ( ) ( ) ( ) ( ) ( ) Growth of Industry *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) Population Growth ( ) ( ) ( ) ( ) ( ) Labor Forc Growth ( ) ( ) * ( ) ( ) ( ) Enrgy in Us (pr capita) ( ) ( ) * ( ) ( ) ( ) Nots: *** Significant at 1% lvl ** Significant at 5% lvl * Significant at 10% lvl

7 294 Modl 2b (Tabl 4) confirms th rsult that growth of industry incrass th growth of GDP during th priods , , and (p<0.01). Howvr, all othr slctd variabls do not show any statistically significant association with th outcom variabl xcpt population growth during TABLE 4. ESTIMATES FOR LAGGED LOGISTIC REGRESSION MODELS FOR BINARY OUTCOMES FOR THE PERIOD Variabl Intrcpt ** ** Growth of Industry *** *** *** *** Population Growth ** Labor Forc Growth Enrgy in Us (pr capita) * Nots: *** Significant at 1% lvl ** Significant at 5% lvl * Significant at 10% lvl MARKOV MODEL Th covariat dpndnt Markov modl was proposd by Munz and Rubinstin (1985) and thn Islam and Chowdhury (2006) xtndd th modl for highr ordr. Lt us giv a brif ovrviw of th modl hr from Munz and Rubinstin and Islam and Chowdhury. S ths paprs for mor dtails. Lt us considr a two stat Markov chain for a discrt tim binary squnc as follows: π00 π01 π = π10 π11 whr π 00 = 1 π 01 and π10 = 1 π11. Hr, 0 and 1 ar th two possibl outcoms of a dpndnt variabl, Y. Each row of th abov transition probability matrix provids a modl on th basis of conditional probabilitis. For instanc, th probability of a transition from 0 at tim t j 1 to 1 at tim t j is π 01 = PY ( j = 1 Yj 1 = 0) and similarly th probability of a transition from 1 at tim t j 1 to 1 at tim t j is π11 = PY ( j = 1 Yj 1 = 1). It is vidnt that π00 + π01 = 1 and similarly, π10 + π11 = 1. For covariat dpndnc, lt us dfin th following notations:

8 295 X i = 1, X i1,..., Xip = vctor of covariats for th ith prson; β0 = β00, β01,..., β0p = vctor of paramtrs for th transition from 0, β1 = β10, β11,..., β1p = vctor of paramtrs for th transition from 1. Thn th transition probabilitis can b dfind in trms of function of th covariats as follows: Modl for Incras in th Growth of GDP β0 X π01( Yj = 1 Yj 1 = 0, X) =, and β X Modl for Dcras in th Growth of GDP β1 X π11( Yj = 0 Yj 1 = 1, X) =. β X Tabl 5 shows th summary of th rsults for both incras and dcras in th growth of GDP for covariat dpndnt Markov modls. As xpctd, growth of industry is positivly associatd with incras in GDP growth (p-valu<0.01) and ngativly associatd with dcras in GDP growth during th priod Although thr is no association btwn growth in population and incras in GDP growth, whil thr is positiv association btwn population growth and dcras in GDP growth. Us of nrgy appars to hav no significant association with incras or dcras in GDP growth during th long duration from 1980 to TABLE 5. COVARIATE DEPENDENT MARKOV MODEL FOR INCREASING AND DECREASING IN THE GROWTH OF GDP FOR THE PERIOD Variabls Estimats (Standard Error) Incras Dcras Intrcpt *** *** ( ) ( ) Growth of Industry *** *** ( ) ( ) Population Growth * ( ) ( ) Labor Forc Growth ( ) ( ) Enrgy in Us (pr capita) ( ) ( ) Nots: *** Significant at 1% lvl ** Significant at 5% lvl * Significant at 10% lvl

9 SUMMARY AND CONCLUSION 296 This papr xamins th factors influncing th chang in conomic growth of countris. Th conomic prformanc of countris may dpnd on factors rlatd to capital invstmnt, invstmnt on human capital accumulation, xpnditur on halth, and many othr factors that ar associatd dirctly or indirctly with th conomic growth. This papr provids only a prliminary ovrviw of th problms associatd with th rlationship with growth in GDP. Th main purpos of this papr is to dmonstrat diffrnt tchniqus that can b mployd to xplain such rlationships. Du to data limitations, som of th important variabls could not b usd. In this papr, thr diffrnt mthods hav bn usd: (i) rgrssion modls, (ii) logistic rgrssion modls, and (iii) Markov modls with covariat dpndnc. First two modls tak account of both cross-sction data as wll as data with a lag of fiv yars. Th third modl uss th Markov modl for xplaining th transitions from low or modrat conomic prformanc to high prformanc as wll as transition from high conomic prformanc to modrat or low prformanc. It is surprising that in all ths modls, it appars that growth in industry is th most dominating factor in xplaining th growth in GDP. In som modls, th rol of growth in labor forc sms to hav statistically significant association. For th East Asian conomis, th transition to high prformanc was prcdd by th dmographic transitions that ld to high growth of labor forc during th priod of population momntum. Th Markov modls rvals th findings mor xplicitly du to us of rpatd masurs of conomic prformanc. It provids two sts of quations for incras in th growth of GDP as wll as dcras in th growth of GDP from th sam modl and thus th rol of variabls can b dtrmind for both dirctions in th chang of conomic prformanc. With mor dtaild data, th advantag of th covariat dpndnt Markov modl will b mor prcis and obvious. Kholodilin and Silvrstovs (2006) pointd out that th GDP rflcts th stat of th ovrall conomy. According to thm, in a dvlopd conomy lik Grmany, th shar of th componnts hav bn changd drastically, and th industrial production rprsnts lss than 50% of th contmporary Grman conomy. Thy notd that th srvic sctor plays an vr incrasing rol in th conomy. Th rgrssion modls basd on cross-national data displays a positiv association btwn growth in industry and growth of GDP. Ths rsults ar confirmd by both th logistic rgrssion modls with or without laggd variabls. Similarly, th rsults basd on th covariat dpndnt Markov modls show that during th longr duration from 1980 to 2000, thr is positiv association for incras in highr growth attributabl to growth in industry. Th short and long trm shifts in th growth of GDP can b of intrst in trms of changs in th growth of industry as compard to that of othr sctors such as srvic. Dawson (2006) includd th growth rat of th labor forc to xplain th cumulativ growth rat of th ral pr capita GDP on th basis of cross-country data and obsrvd that th labor forc growth is associatd ngativly with th growth in pr capita GDP. Howvr, it is obsrvd from th covariat dpndnt Markov modls that labor growth is not associatd with th incras or dcras in th growth of GDP for th priod Howvr, thr xists an opposit impact on th growth of GDP in dvloping and dvlopd countris. In th nar futur, it is xpctd that du to stagnation or dcras in labor supply driving from past low frtility will pos

10 297 difficultis in th most dvlopd countris (McDonald and Kippn, 2001). This will ncssitat adjustmnts in th major componnts of th GDP in ordr to minimiz th impact of such transition in th labor forc composition. In th prsnc of th labor forc growth in th modl, population growth dos not show any significant association with th growth in GDP. Barro (2001) showd that th quality of human capital accumulation is quantitativly much mor important for analyzing th growth in GDP. Hanushk and Kimko (2000) obsrvd that th dirct masurs of labor forc quality ar strongly rlatd to growth. Galor and Wil (2000) indicatd that th rlationship btwn incom and population growth has bn changd dramatically during th rcnt past and vn th poor countris ar xprincing rlativly highr population growth rat. Campos and Coriclli (2002) dscribd transition in conomy as th simultanous chang of conomic structurs and th dpndnc upon th cohrnt conomic rforms. Thy also pointd out th ncssity of futur rsarch with mphasis on conomically maningful contributions of labor. Thy furthr mphasizd on th mor rliabl stimats of physical and human capital and labor contributions to growth. This may provid us with th improvd undrstanding of th sourcs of this procss of transition and rlativ contributions of th undrlying dtrminants. REFERENCES Astriou, D. and Agiomirgianakis, G.M., Human Capital and Economic Growth Tim Sris Evidnc from Grc, Journal of Policy Modlling, 2001, Vol.23, pp Barro, R.J., Human Capital Growth, Th Amrican Economic Rviw, 2001, Vol. 91, pp Campos, N.F. and Coriclli, F., Growth in Transition: What W Know, What W Don t, and What W Should, Journal of Economic Litratur, 2002, Vol. 40, pp Dawson, J.W., Rgulation, Invstmnt and Growth Across Countris, Cato Journal, 2006, Vol. 26, pp Dincr, I., Enrgy and GDP Analysis of OECD Countris, Enrgy Convrsion Managmnt, 1997, Vol. 38, pp Galor, O. and Wil, D.N., Population, Tchnology, and Growth: From Malthusian Stagnation to th Dmographic Transition and byond, Th Amrican Economic Rviw, 2000, Vol. 90, pp Hanushk, E.A. and Kimko, D.D., Schooling, Labor-Forc Quality, and th Growth of Nations, Th Amrican Economic Rviw, 2000, Vol. 90, pp Kholodilin, K.A. and Silvrstovs, B., On th Forcasting Proprtis of th Altrnativ Lading Indicators for th Grman GDP: Rcnt Evidnc, Jahrbuchr fur Nationalokonomi und Statistik, 2006, Vol. 226, pp McDonald, P. and Kippn, R., Labor Supply Prospcts in 16 Dvlopd Countris, , Population and Dvlopmnt Rviw, 2001, Vol. 27, pp Munz, L.R. and Rubinstin, L.V., Markov Modls for Covariat Dpndnc of Binary Squncs, Biomtrics, 1985, Vol. 41, pp

11 298 Islam, M.A. and Chowdhury, R.I., A highr-ordr Markov modl for analyzing covariat dpndnc, Applid Mathmatical Modlling, 2006, Vol. 30, pp Swamy, A.V. and B. Fikkrt B., Estimating th Contributions of Capital and Labor to GDP: An Instrumntal Variabl Approach, Economic Dvlopmnt and Cultural Chang, 2002, Vol. 50, pp