Convergence of Income Among Provinces in Canada An Application of GMM Estimation

Transcription

1 Economerics Working Paper EWP0502 Deparmen of Economics ISSN Convergence of Income Among Provinces in Canada An Applicaion of GMM Esimaion Mukesh Ralhan Deparmen of Economics, Universiy of Vicoria Vicoria, B.C., Canada & Aji Dayanandan Deparmen of Economics, Universiy of Norhern Briish Columbia Prince George, B.C., Canada March, 2005 Absrac This paper ess for uncondiional and condiional income convergence among provinces in Canada during he period We apply he firs-differenced GMM esimaion echnique o he dynamic Solow growh model and compare he resuls wih he oher panel daa approaches such as fixed and random effecs. The mehod used in his paper accouns for no only province-specific iniial echnology levels bu also for he heerogeneiy of he echnological progress rae beween he richer and no so richer provinces of Canada. One of he findings of he paper is ha he Canadian provinces do no share a common echnology progress rae and a homogeneous producion funcion. The findings of he sudy sugges a convergence rae of around 6% o 6.5% p.a. whereas he previous sudies using OLS and oher echniques repored a convergence rae of around.05 % for per capia GDP and 2.89% p.a. for personal disposable income among Canadian provinces. Keywords: JEL Classificaions: Provincial convergence, Canada, Panel daa, GMM O40, O4, O53, C4, H4 Auhor Conac: Mukesh Ralhan, Dep. of Economics, Universiy of Vicoria, P.O. Box 700, STN CSC, Vicoria, B.C., Canada, V8W 2Y2; mralhan@uvic.ca; FAX:

2 . INTRODUCTION In recen years, he issue of per capia income convergence has been an area of inense research and invesigaion. The idea of convergence is based on he neoclassical growh model Solow, 956, Swan, 956. Neoclassical heory predics ha if differen counries or provinces are a differen poins relaive o heir balanced growh pahs, poorer counries or regions will grow faser han he rich ones, he so-called β bea convergence. Evidence of his cach-up effec is inerpreed as suppor for he neo-classical growh model. Various sudies have examined he convergence hypohesis in differen pars of he world wih varying resuls. The empirical lieraure disinguishes hree disinc, hough relaed, conceps of convergence, see Hossain 2000: sigma σ convergence, bea β convergence and condiional bea β c convergence. Anoher ype of convergence, called sochasic convergence, focuses on he ime series properies of he disribuion of per capia income. We explain hese erms in he following secions. Sigma convergence is concerned wih cross-secional dispersion of per capia income or produciviy levels; ha is, here exiss a convergence if he cross-secional dispersion of per capia income or produciviy levels decrease over ime. The sandard deviaion of he log of per capia oupu is commonly used o es for sigma convergence. Thus he presence of sigma convergence suggess a endency o equalizaion of per capia income or produciviy levels across regions or economies. The presence of sigma convergence, however, does no necessarily imply he presence of bea convergence, which suggess ha poorer counries or regions grow a faser raes han richer counries or regions given ha hey all have he same seady-sae growh pah for per capia oupu. Wheher he convergence of per capia oupu levels, measured by sigma convergence, is due o higher growh raes of poorer regions han he richer ones can be examined by esing for he presence of bea or condiional bea convergence. Bea convergence, as defined in he empirical lieraure is concerned wih cross-secion regression of he ime averaged income growh rae on he iniial per capia income level; ha is, here exiss a bea convergence if he coefficien of he iniial per capia income level in a cross-secion regression for per capia oupu growh bears a negaive sign. This suggess ha counries or regions wih higher iniial income levels grow slowly han counries or regions wih lower iniial income levels. The concep of condiional bea convergence concerns wih cross-secion regression of he ime averaged oupu growh rae on he iniial per capia oupu level and a se of addiional explanaory variables ha define he seady-sae growh pah for per capia oupu Barro and Sala-i-Marin, 99. Wihin such augmened growh regression, here exiss a condiional bea convergence if 2

3 he coefficien of he iniial per capia oupu level bears a negaive sign. One of he mos generally acceped resuls is ha while here is no evidence of uncondiional convergence among a broad sample of counries; he condiional convergence hypohesis holds when examining more homogeneous group of counries or regions or when condiioning for addiional explanaory variables Baumol, 986, Barro and Salai-i-Marin, 992, and Mankiw e al., 992 hereafer MRW. For exposiional purposes, his paper is divided ino five secions: secion 2 briefly reviews he mehodological framework; secion 3 ouches upon he daa issue; secion 4 is devoed o empirical invesigaion and secion 5 summarizes he conclusions emanaing from he sudy. 2. METHODOLOGY The issue of he presence and persisence of regional dispariies in income and oupu per capia in Canada has been a horny issue and has concerned boh economiss and poliicians. Esimaes of convergence β convergence over a wide range of daa sugges a convergence rae ha ranges from.05% p.a. for gross provincial produc per capia o 2.89 % p.a. for personal disposable income per capia see, for example, Coulombe and Lee 995 and Lee and Coulombe 995. Lee and Coulombe 995 have applied he OLS mehod in a pooled regression for heir esimaes. Kaufman e al recenly sudied he differenial impac of federal ransfer programs on oupu convergence in provinces in Canada using hree sages leas squares mehod. They found ha while he employmen insurance EI sysem seems o have had a significan negaive effec on oupu convergence by discouraging migraion wihin Canada, he equalizaion ransfers migh have acually helped spur convergence. In ye anoher sudy Wakerly 2002, using daa on provinces and indusries found ha he process of economic growh in Canada has resuled in poor provinces saying poor and he rich provinces saying rich. These conrasing conclusions raise quesions abou he divergen mehodologies used by researchers in analyzing his issue in he Canadian conex. One of he major limiaions of sudies on convergence of income in Canadian provinces is he absence of any sudies ha addresses his issue using panel daa mehods or echniques. The main usefulness of he panel approach lies in is abiliy o allow for differences in he aggregae producion funcion across economies. This leads o resuls ha are significanly differen from hose obained from single cross-counry regressions Islam,

4 Thus, he main aim of his paper is firs, o examine he issue of income convergence in Canada using sound mehodologies such as panel daa mehods and/or Generalized Mehod of Momens GMM esimaion echniques, and o see how he resuls hus obained differ from oher esimaions. If he findings do sugges widening gap or slow regional income convergence, anoher objecive is o simulae he debae on policy formulaions in regard o balanced regional developmen in Canada. We apply he Fixed Effec FE and Random Effec RE echniques and compare our resuls wih firs-differenced GMM as he Solow growh model ha we esimae in our sudy is a dynamic model and hence he endogeneiy issue has o be addressed. Anoher mehod ha could be applied is he sysem GMM esimaor developed by Blundell and Bond 998 ha presens a significan improvemen over he oher panel esimaion mehods such as he firs-difference GMM esimaor see Arellano and Bond 99. Using Mone Carlo simulaions, hey demonsrae ha he weak insrumens problem in firs-difference GMM could resul in large finie-sample biases. Also he biases can be dramaically reduced by incorporaing more informaive momen condiions ha are valid under quie reasonable saionariy resricions on he iniial condiion process. Essenially he sysem GMM esimaor represens he use of lagged firs-differences as insrumens for equaions in levels, in addiion o he usual lagged levels as insrumens for equaions in firs-differences. In addiion, he finie-sample performance of he sysem GMM can be esed by he idenificaion of an esimaion range for he convergence speed provided by he OLS and oher esimaors like wihin-group esimaor. In his paper, however, we confine our sudy o he applicaion of he Fixed and Random Effecs and he firsdifferenced GMM esimaors. The applicaion of sysem GMM could be considered for fuure research work. Wih a view o conserving space, our inenion is no o review he basic Solow growh model in deail here. See sudies by MRW 992 and Islam 995 ha give a deailed descripion of he basic Solow growh model and augmened Solow growh model. In he following secions, we succincly explain he usefulness of a panel daa approach on he basis of he work by Islam 995. The basic Solow model is discussed briefly below MRW, 992: The raes of saving, populaion growh and echnological progress are reaed as exogenous. There are wo inpus, capial and labor, which are paid heir marginal producs. Solow assumes a Cobb-Douglas producion funcion, so producion a ime is given by: Y = K A L ; 0 < <, 4

5 where Y is oupu, K is capial, L is labor, and A is he level of echnology. L and A are assumed o grow exogenously a he raes n and g: L = L 0 e n A = A 0 e g. Assuming ha s is he consan fracion of oupu ha is saved and invesed, and defining oupu and sock of capial per uni of effecive labor as y ˆ = Y / AL and k ˆ = K / AL, respecively, he dynamic equaion for kˆ is given by: kˆ = s yˆ n g δ kˆ = s kˆ n g δ kˆ where δ is he consan rae of depreciaion. I is eviden ha kˆ converges o is seady sae value: / s ˆ* k =. n g δ Upon subsiuion his gives he following expression for seady sae per capia income: Y ln ln 0 ln ln δ = A g s n g L Assuming ha he counries are currenly in heir seady sae, MRW 992 used equaion o see how differing saving and labor force growh raes can explain he differences in he curren per capia incomes across counries. They found he model o be quie successful excep ha he esimaes of he elasiciy of oupu wih respec o capial,, were found o be unusually high. In order o overcome his problem, hey suggesed augmened Solow growh model wih human capial as anoher inpu of he producion and hence as a variable in he regression equaion. MRW assumed ha g and δ are consan across counries. Bu he A0 erm in equaion 5

6 6 reflecs no jus echnology bu resource endowmens, climae, insiuions, ec.. I may herefore differ across counries. So hey assumed ha Ln A0 = a ε, where a is a consan and ε is a counry-specific shock. Thus log income per capia a a given ime ime 0 for simpliciy is: ε δ = ln ln ln g n s a L Y 2 A his sage, however, MRW made he assumpion ha ε is independen of he explanaory variables, s and n. This was heir idenifying assumpion, and i allowed hem o proceed wih he Ordinary Leas Squares OLS esimaion of he equaion. Anoher specificaion used by MRW is o include human capial in he producion funcion in view of he imporance of human capial o he process of growh. Therefore, he producion funcion now becomes: β β = L A H K Y, where H is he sock of human capial, and all oher variables are defined as before. Le s k be he fracion of income invesed in physical capial and s h be he fracion of income invesed in human capial. The evoluion of he economy is now deermined by:. k g n y s k k δ =. h g n y s h h δ = where y = Y/AL, k = K/AL, and h = H/AL are quaniies per effecive uni of labor, and β <, which implies ha here are decreasing reurns o all capial. The economy converges o a seady sae defined by: / * β δ β β = g n s s k h k ; / * β δ = g n s s h h k

7 Subsiuing k* and h* ino he producion funcion and aking logarihms gives an equaion for income per capia similar o equaion : Y β β ln = ln A0 g ln n g δ ln s k ln sh 3 L β β β MRW esimaed equaion 3 using he OLS mehod. While esimaing equaion 2, MRW assumed ha ε is independen of he explanaory variables, s and n. However, Islam 995 argues ha in general, he counry-specific echnology shif erm ε is likely o be correlaed wih he saving and populaion growh raes experienced by ha counry. A a heurisic level, as A0 is defined no only in he narrow sense of producion echnology, bu also o include resource endowmens, insiuions, ec., i is no enirely convincing o argue ha saving and feriliy behavior will no be affeced by all ha is included in A0. Wha is imporan o noe here is ha in he framework of a single cross-secion regression, his assumpion of independence becomes an economeric necessiy. OLS esimaion is valid only under his assumpion. For he above reasons, Islam 995 proposes ha a panel daa framework provides a beer and more naural seing o conrol for his echnology shif erm ε. Islam 995 has derived he seady sae behavior in he following manner: Le ŷ * be he seady sae level of income per effecive worker, and le yˆ be is acual value a any ime. Approximaing around he seady sae, he rae of convergence is given by: where λ = ngδ-. d ln yˆ d = λ [ln yˆ * ln yˆ ], This equaion implies ha: λτ λτ ln yˆ 2 = e ln yˆ* e ln yˆ, ˆ where y is income per effecive worker a some iniial poin of ime and τ = 2 -. ˆ Subracing y from boh sides yields λτ λτ ln yˆ 2 ln yˆ = e ln yˆ* e ln yˆ. 7

8 This equaion represens a parial adjusmen process ha becomes more apparen from he following rearrangemen. λτ ln yˆ 2 ln yˆ = e ln yˆ* ln yˆ. In he sandard parial adjusmen model, he opimal or arge value of he dependen variable is deermined by he explanaory variables of he curren period. In he presen case, ŷ * is deermined by s and n, which are assumed o be consan for he enire inervening ime period beween and 2 and hence represen he values for he curren year as well. Subsiuing for ŷ * gives: λτ ln yˆ 2 ln yˆ = e ln s λτ e ln n g δ e λτ ln yˆ. 4 MRW used his equaion o sudy he process of convergence across differen samples of counries. Islam 995 reformulaed he equaion in erms of income per capia. Noe ha income per effecive labor is: Y Y yˆ = =, g A L L A e so ha Y yˆ = ln ln A0 g L = ln y ln A0 g where y is he per capia income, [Y/L]. Subsiuing for ŷ ino he above equaion, we ge he usual growh-iniial level equaion: 8

9 λτ ln y 2 ln y = e ln s λτ e ln n g δ e λτ ln y e λτ ln A0 g 2 e λτ 2 However, if we collec erms wih ln y on he righ-hand side, we can wrie he equaion in he following alernaive form: λτ ln y 2 ln y = e ln s λτ λτ e ln n g δ e ln y e λτ ln A0 g 2 e λτ 2 5 I can now be seen ha he above represens a dynamic panel daa model wih -e λτ ln A0 as he ime-invarian individual counry-effec erm. We may use he following convenional noaion of he panel daa lieraure: 2 i = γyi j= y, β x η u v, 6 j j i i i where y i = ln y 2 y i, = ln y γ λτ = e, x i = ln s λτ β = e, β = λτ 2 e 2 x i u i = ln n g δ λτ = e ln A0 η = g. i λτ 2 e Panel daa esimaion of his equaion now allows us o conrol for he individual counry effecs. Islam 995 applied Leas Squares wih Dummy Variable LSDV and Minimum Disance MD esimaion echniques for he esimaion of equaion 6. We sar our empirical invesigaions in Secion 3, using Fixed and Random Effecs echniques and proceed o he firs-difference GMM esimaor see Arellano and Bond 99. Some of he 9

10 advanages of using he panel daa approach are: availabiliy of large number of daa poins help in reducing problem of limied degrees of freedom and enhance he efficiency of he esimaors; problem of mulicollineariy is less likely since explanaory variables vary in wo dimensions; enables researches o address quesions by sudying ineremporal behavior of cross-secions, which is oherwise no possible o answer; problem of omied variables can be reduced by explicily modeling unobserved variables as a uni-specific effec or ime-specific effec or boh. In addiion o he fixed and random effecs and firs-differenced GMM esimaors ha we discuss in he nex secion, anoher approach for dynamic panel daa models is he sysem GMM as suggesed by Blundell and Bond 998. Weeks and Yao 2002 have recenly applied he sysem GMM esimaion echnique for esing condiional income convergence in provinces of China. They have examined he issue of income convergence in he basic Solow Growh framework. Using a differen noaion, Weeks and Yao 2002 esimae he equaion 6 in he following form: y = by η i ' j i, θ xi, T i vi 7 where and x i = ln s i ',ln ηi g δ, θ = ς η = ς ln A0, T = g 2 ζ, i b = β = ς.., ς, ' They inerpre he effecs η i as a composie of unobservable province-specific facors, which includes iniial echnology differences. Similarly, T capures he ime-specific effecs, which includes he rae of echnological change. In order o es ha he echnology progress rae of coasal provinces is differen from ha of he inerior provinces in China, Weeks and Yao 2002 include a composie dummy consruced by aking he produc of a ime and coasal dummy D i. So, hey re-wrie equaion 7 as: y i, = byi, θxi, DiT T η vi, 8 0

11 Following reforms in China, he coasal regions aained a faser rae of growh compared o he inerior regions. In order o differeniae beween he wo regions, Weeks and Yao 2002 have used he coas dummy variable. If he provinces belong o he coasal regions, he dummy variable is equal o, and 0 oherwise. In his paper, however, we repor resuls from he fixed effecs, random effecs and firs-differenced GMM esimaion echniques and applicaion of Sysem GMM approach will be underaken for fuure research work. 3. DATA ISSUES We have used he annual per capia real ne provincial domesic produc NPDP for he period for 0 provinces viz., Newfoundland NF, Prince Edward Island PEI, Nova Scoia NS, New Brunswick NB, Quebec QB, Onario ON, Manioba MB, Saskaoon SK, Albera AB and Briish Columbia BC. Our main source of daa is he online daabase of Saisics Canada: CANSIM II. The variables for which we colleced daa include: NPDP, labor force growh rae for working age populaion in he age group 5-64 years and Real Invesmen. Our empirical sudy is confined o esimaion of he basic Solow growh model and endogenous growh model a his sage. Daa sources and exac definiions of variables are available from he auhors on reques. Following Islam 995, we use five-year ime inervals for averaging he daa. By adoping his approach our resuls are less likely o be influenced by business cycle flucuaions. In his empirical invesigaion, we have classified he provinces ino a Below Average Provinces Nova Scoia, New Brunswick, Prince Edward Island and Newfoundland, Quebec, Saskachewan and Manioba and c Above Average Provinces Albera, Briish Columbia and Onario based on heir relaive performance. By such classificaion, we would like o es ha convergence hypohesis holds more srongly for a homogenous group of counries or regions Barro and Salai-i-Marin, 992, and Mankiw e al., 992.

12 Figure : GDP Per Capia by Province, Relaive o Canada, 98 & Per Cen NF PEI NB NS Sas Qb Canada On BC Al Figure 2: GDP Per Capia by Province, Relaive o Canada, 990 & Per Cen NF PEI NB NS Sas Qb Canada On BC Al

13 Figure shows he GDP per capia by province relaive o he Canadian average in 98 and 990. There are wo sriking conclusions: firs, here is considerable difference beween he average income of he riches province and ha of he poores. Per capia real provincial gross domesic produc in Newfoundland in 990 is only 62 per cen of he naional average, while in Onario i was 6 per cen, more han wice as grea. By 200, his picure has marginally changed wih he posiion of provinces like BC showing a marginal deerioraion and ha of Albera showing subsanial improvemen over he naional average. Second, hese dispariies have no changed much in he 990 s as is eviden from Figure EMPIRICAL INVESTIGATION In his secion, we sar our empirical invesigaion wih he endogenous growh model Barro, 99 and Barro and Sala-i-Marin, 99, 992 used by Coloumbe and Lee 995. They examined six differen conceps of per capia income and oupu convergence using OLS in a pooled regression. Coulombe and Lee 995 have used he following model in heir esimaion approach: 0 Y.ln i, 0 Y i / Y / Y 0 e = B 0 β0 Yi.ln u _ Y where i =,.,0 regional unis for en provinces; = 96, 97, 98, and where i, 9 Y _ refers o he Canadian average weighed by populaion income, Y is oupu or income per capia, B is a consan erm, u is an error erm, and and T are he iniial and he final year of comparison. So, T- is he observaion period. Thus Coulombe and Lee 995 divided he 96 o 99 observaion period ino hree sub periods: 96-7, 97-8 and Our endeavor would be o apply panel esimaion approach o esimaing equaion 9, which is a es for uncondiional convergence hypohesis. We also es for condiional bea convergence as in equaion 6 above: 2 j i. β j xi η ui vi, 0 j= y i = γy These esimaors are called by various names like Leas Squares Dummy Variable LSDV or fixed effecs esimaors. βˆ is unbiased. I is also consisen when eiher N or T or boh end o 3

14 infiniy. In our case, he number of unis, i.e. provinces. is equal o en. However, when he number of unis is large, he fixed effecs model has oo many parameers. The loss of degrees of freedom could be avoided by assuming u i o be random. Equaion 0 could herefore, be rewrien in he following form: where i i i 2 j i, β j xi η vi, j= y i = µ γy v = u. This model is called he random effecs RE model or error-componens model. When he sample size is large, RE or FGLS will have he same asympoic efficiency as GLS. Even for moderae sample size e.g., T 3, N- K 9; for T = 2, N- K 0, he FGLS or RE is more efficien han FE esimaor. However, if we are ineresed in provincespecific effec, FE is appropriae. We esimae our model using boh he esimaors and hen apply he Hausman es o deermine as o which esimaor we should prefer. Anoher relaed bu imporan issue is ha he model we esimae is a dynamic model and sandard esimaors like OLS, FE and RE are biased or inconsisen because regressors are correlaed wih he error erm. The consisency of he FE esimaor depends on T being large. For RE, he ransformed regressors will be correlaed wih he ransformed errors. In order o overcome his problem, Arellano and Bond 99 sugges ha addiional insrumens can be obained. They derive a consisen esimaor when N goes o infiniy wih T fixed. Arellano and Bond s preliminary onesep consisen esimaor is given by he GLS esimaor and hen hey obain he opimal GMM esimaor. The ulimae resuling esimaor is he wo-sep esimaor, which is consisen. This paper conribues o he exising sudies on convergence in Canadian provinces in many ways. Firs of all, we use more recen ime horizon compared o 96 o 99 used by Coulombe and Lee 995. Second, Coulombe and Lee 995 have used he OLS mehod ha does no ake ino accoun variables ha are unobservable and specific o he uni bu are ime-invarian. Third, he assumpion in previous sudies is ha all he provinces in Canada share a homogenous producion funcion. This is because OLS canno be applied if he producion funcion is heerogeneous. This paper also conribues in erms of beer mehodological framework like fixed or random effecs and firs-differenced GMM. One of he common mehods of measuring persisence is o calculae he half-life of income deviaions; i.e., he amoun of ime i akes a shock o a series o rever half-way back o is mean value. The approximae half-life of a shock o Y i is compued as ln 2 / ln ρ, where β ρ i i. The persisence parameers i ρ s capure he speed of relaive income convergence i 4

15 across provinces. Our primary focus is on he β is, he coefficiens on he lagged log of he gross domesic produc Y i ; he nearer β i is o zero, he longer is he esimaed half-life of a shock. The OLS esimaes of ρˆ are downward biased in small samples Kendall, 98. In order o correc for he small sample bias, we follow he popular mehod of adjusmen recommended by Nickel 98 for adjusmen of he ρˆ values. The esimaed bias-adjused ρ, along wih he approximae half-life calculaions 2 are repored in Tables 2 and 3. The esimaed half-life values give us an idea abou he ime required in years for a province o reach he seady sae income level based on he esimaed speed of convergence. We compare our resuls wih he speed of convergence esimaes obained by Coulombe and Lee 995. Table shows he speed of convergence for OECD counries including Canada. The convergence rae for Canada based on Coulombe and Lee esimaion varies from.05% p.a. o 2.89% p.a. wih esimaed half-life from 29 years o 66 years. For oher developed counries, i ranges from a low of 0.2% for Denmark o a high of 4.96% p.a. for he Neherlands. The lower he speed of convergence, he more ime i akes for an economy or province o converge o is seady sae equilibrium measured in half-life. Our objecive in he paper is o ascerain wheher speed of convergence has undergone a significan change among Canadian provinces ever since Coulombe and Lee 995 derived heir esimaes. Our esimaion work is based on wo samples. We used he original panel daa for he period 98 o 200 and he 5-year averaged daa for he same period and ha resuled in T = 4 viz. 985, 990, 995 and 2000 for he en provinces included in our analysis. We hen applied leas squares, fixed and random effecs and firs-differenced GMM esimaors o boh he samples. Our esimaion resuls are abulaed below in Table 2 and Table 3. We used a number of specificaions o es for he convergence hypohesis. However, our basic model coninued o be Solow Growh model. In order o compare our resuls wih he Coulombe and Lee 995 specificaion, we also esed for uncondiional convergence Table 2. We applied boh leas squares and panel esimaion echniques o see how our resuls differ from Coulombe and Lee 995. As menioned earlier, we classified he provinces ino wo caegories: Above average and below average. For his purpose, we included province-specific dummies o capure he speed of convergence for he respecive caegories. If he provinces belong o above average caegory like Albera, Briish Columbia and Onario, he dummy is equal o and 0 oherwise. Table 3 presens resuls from his specificaion. Also included are esimaion resuls from he specificaion which included boh ime dummies and province-specific dummies. 5

16 Table Convergence in OECD counries Uncondiional convergence in Canada, 96-9 Coulombe and Lee, 995 Variables β Rae of Convergence GPP PRO.05% GPP NAT.84% EI % PIT % PI % PDI % Source: Coulombe and Lee 995 Half-life years U.S. Uncondiional U.S. Condiional R 2 Uncondiional convergence in oher counries Barro e al, 99, 992 Counry Rae of Convergence.8% 2.22% Neherlands 4.96% U.K. 3.37% Belgium 2.37% Germany Ialy France Denmark 2.30%.8%.0% 0.2% 6

17 Table 2 Esimaes of convergence among provinces in Canada year average 985, 990, 995,2000 β R 2 Halflife years β 2 R 2 Halflife years Uncondiional convergence Leas *** 0. 0 Leas * 0.2 Squares Squares 2.32 FE *** FE *** RE ** 0. 0 RE * GMM FD *** GMM FD ** Condiional convergence Solow Growh Model Wih ngδ and Real Savings as addiional independen variables Leas *** 0. Leas * 0.5 Squares 4.70 Squares 2.23 FE *** FE *** RE *** 0. RE * GMM FD *** GMM FD Condiional convergence Solow Growh Model Wih ngδ and Real Savings and province dummy as addiional independen variables β Dummy R 2 Halflife years β 2 Dummy R 2 Halflife years Leas -0.37*** Squares FE -0.23*** 9.82 RE *** GMM FD 0.005*** Leas Squares Dropped FE *** Near singular marix Noes: Figures in he parenheses are -raios *** Significan a % level of significance ** Significan a 5% level of significance *Significan a 0% level of significance -0.35** RE ** 3.53 GMM FD 0.005* Dropped * Near singular marix - 7

18 Table 3: 5-year average - Condiional convergence Solow Growh Model Wih ngδ and real ravings, ime dummies and province-specific dummy as addiional independen variables Variables Leas Squares Fixed Effec Random Effec Firsdifferenced GMM LogGDP- -0.4* *** ** Dummy DT.004* *** D *** D *** D *** Logngd * *** Logreal saving Consan *** R Half-life years Noe: Figures in he parenhesis are -raios *** Significan a % level of significance ** Significan a 5% level of significance *Significan a 0% level of significance 8

19 The null hypohesis of all province-specific effec being he same is srongly rejeced in our fixed effecs model for he period 98 o 200. However, he same is no rue for he 5-year average sample. So we don ge suppor for he use of fixed effecs model for he laer. For he random effecs model, our null hypohesis is ha he regressors and he error erm are no correlaed. Again, we fail o srongly rejec he null hypohesis for he 5-year average sample. In oher words, i jusifies he use of random effecs mehod for his sample. We also conduced he Hausman specificaion es o see which model we should prefer. The es is based on he idea ha under he hypohesis of no correlaion, boh OLS in he LSDV model and GLS are consisen, bu OLS is inefficien, whereas under he alernaive, OLS is consisen, bu GLS is no. Therefore, under he null hypohesis, he wo esimaes should no differ sysemaically, and a es can be based on he difference. For he firs sample size i.e. 98 o 200, he es saisic is greaer han he criical value a any level of significance. The hypohesis ha he individual effecs are uncorrelaed wih he oher regressors in he model, is herefore, srongly rejeced. So he use of random effecs for his sample is no appropriae. Ineresingly, he resuls from Hausman es for he second sample i.e. 5-year average, also provides suppor for he fixed effecs model. However, he problem wih he fixed effecs model is ha i sweeps ou he effec of province-specific dummy variable. In order o deermine hese effecs, we will have o use he random effecs esimaor. Some of he imporan highlighs of our resuls are as follow: Rae of convergence urns ou o be much higher han hose repored by previous sudies. On an average i ranges from 6%% o 6.5% wih half-life esimaes of around year o 3 years. Our resuls are consisen wih hose obained by Islam 995. Their findings sugges ha panel daa esimaion echniques give us a higher rae of convergence compared o Leas Squares. The empirical resuls from he leas squares and random effecs esimaors are quie close o each oher. Fixed Effecs and Firs-differenced GMM esimaors sugges a much higher rae of convergence. Province-specific dummy urns ou o be significan in boh he specificaions. In oher words, i suggess ha if he province belongs o he above average caegory, i aains a faser rae of convergence. 9

20 Time-dummies urn ou o be insignifican. So he role of ime variable owards convergence can be ruled ou. We also esimaed equaion 8 above by including boh T and DiT Table 3. To recapiulae, T capures he ime-specific effecs, which includes he rae of echnological change. DiT is a composie dummy consruced by aking he produc of a ime and province dummy. In paricular, if we are ineresed in knowing if he echnology progress rae of above average provinces is differen from ha of he below average provinces, we can es his hypohesis by including composie dummy. This equaion gives us a rae of 9.85% wih esimaed half-life of around 7 years. 4. CONCLUSIONS Under he Consiuion Ac of 982, boh federal governmen and provincial governmens are commied o balanced regional developmen in Canada. The faser rae of convergence of around 6.5% is probably an indicaion ha he programs like federal equalizaion ransfers o provinces and oher measures are paying off. If he esimaion of convergence rae of around 6.5% among Canadian provinces urns ou o be rue, hen i surpasses he rae repored for U.S. saes by a wide margin which is beween.8% o 2.22% p.a.. The esimaed rae of convergence by Coulombe and Lee 995 relaed o he ime period from 96 o 99 whereas he sample period used in our sudy is more recen i.e. 98 o 200. Moreover, he Canadian economy has undergone a significan ransformaion since he 980 s and i is no surprising o ge such resuls. Ever since he referendum in Quebec, Canadian economy has become more coheren wih federal governmen ransferring more and more resources o he provinces. The impac of hese programs a he provincial level is more visible in he sample period chosen by our sudy han in Coulombe and Lee 995. In shor, he increase in convergence rae for his period makes some sense. Moreover, Coulombe and Lee 995 applied OLS in a pooled regression whereas we have applied a beer mehodological framework of panel daa esimaion echniques. This could be anoher reason for such a divergence in he rae of convergence esimaes. I would, however, be ineresing o examine as o wha are he driving facors for a faser rae of convergence. Federal equalizaion program is definiely one of he facors responsible for poorer provinces caching up wih he richer ones as some of he sudies have already demonsraed See, for example, Kaufman e al Our inenion is o use sysems GMM esimaor as well o ge more robus resuls. Anoher imporan issue may be o divide he sample size used by us ino 20

21 wo samples like 98 o 990 and 99 o 200 and hen examine he rae of convergence. One of he mos generally acceped resuls is ha he condiional convergence hypohesis holds more srongly when examining more homogeneous group of counries or regions Baumol, 986, Barro and Salai-i-Marin, 992, and Mankiw e al., 992 hereafer MRW. Using our classificaion of above average and below averages provinces; we could es he hypohesis of condiional convergence and expec even a higher rae of convergence. Acknowledgemens: We would like o express our sincere hanks o Dr David Giles and Dr. Nilanjana Roy for heir invaluable commens on he paper. The usual disclaimer in regard o misakes applies and hese remain he sole responsibiliy of he auhors. 2

22 Foonoes: Given S = ρ S ρ 2S 2... ρk S k ε, he approximae measure for he ime needed o eliminae half of any shock o ε is - ln 2 / ln ρ. The approximae measure is always a real number for our discree models and so he half-life mus be he rounded-up value. To compue he exac half-life, noe ha any k h order difference equaion can be wrien as s order k h vecor difference equaion of he form S = As e, where { S, S,... S } S = k and he marix A and e are defined accordingly. Then, EsT = ATs. Seing S 0 o 0 and hen allowing S =ε >0, we can deermine he value of T ha makes ES T = ε /2. 2 Half-life calculaions are based on bias-adjused ρ esimaes, applying Nickel s 98 formula, which is given by: ˆ p lim ρ ρ = ATBT / n C T ; where A T = ρ / T, B T = / T ρ T / ρ, and CT = 2ρ BT / BT / ρ T. This bias arises in any AR fixed effecs model and is always negaive for posiive ρ. As wih he Kendall bias adjusmen, we recognize ha i is a firs order approximaion of he bias for an AR k process, and ha all k coefficiens will suffer from bias. 22

23 Appendix A Log of Per Capia GDP - Provinces - Canada Bea Convergence Canada NF PEI NS NB Qb On Mb Sas Al BC Yukon Sandard Deviaion of Per Capia GDP Logs Sigma Convergence Sandard Deviaion of Per Capia GDP Sigma Convergence

24 References: Arenallo, M. and Bond, S. 99, Some ess of specificaion for panel daa: Mone Carlo evidence and an applicaion o employmen equaions, Review of Economic Sudies, 58, Barro, R.J. 99, Economic growh in a cross-secion of counries, Quarerly Journal of Economics, 06, Barro, R.J and Salai-i-Marin, X. 99, Convergence across saes and regions, Brookings Papers on Economic Aciviy,, Barro, R.J and Salai-i-Marin, X. 992a Convergence, Journal of Poliical Economy, 00, Barro, R.J and Salai-i-Marin, X. 992b Regional Growh and Migraion: A Japan-US Comparison, NBER Working paper No. 4308, Cambridge, Mass. Baumol, W.J. 986, Produciviy growh, convergence and welfare: wha he long run daa show, American Economic Review, 76, Blundell, R. and Bond, S. 998, Iniial condiions and momen resricions in dynamic panel daa models, Journal of Economerics, 87, Coulombe S. and Lee, F.C. 995, Convergence across Canadian provinces, 96 o 99, Canadian Journal of Economics, 28, Hossain, Akhar 2000, Convergence of per capia oupu levels across regions of Bangladesh, , IMF Working Paper No. 2. Islam, N. 995, Growh empirics: A panel daa approach, Quarerly Journal of Economics, 0, Kendall, M.G. 954 Noe on bias in he esimaion of auocorrelaion, Biomerika, 5,

25 Lee, F.C. and Coulombe S. 995, Regional produciviy convergence in Canada, Canadian Journal of Regional Science, 8, Mankiw, N., Romer, D., and Weil, D.N. 992, A conribuion o he empirics of economic growh, Quarerly Journal of Economics, 07, Nickell, S. 98 Biases in dynamic models wih fixed effecs, Economerica, 49, Solow, R.M. 956, A conribuion o he heory of economic growh, Quarerly Journal of Economics, 70, Swan, T.W. 956, Economic growh and capial accumulaion, Economic Record, 32, Wakerley, E.C. 2002, Disaggregae dynamics and economic growh in Canada, Economic Modelling, 9, Weeks, M. and Yao, Y. 2003, Provincial condiional income convergence in China, : A panel daa approach, Economeric Reviews, 22,