How do Agglomeration Economies and Migration explain the Change of Interregional Income Disparities?

Transcription

1 Paper presented at 48 th Congress of the ERSA How do Agglomeraton Economes and Mgraton explan the Change of Interregonal Income Dspares? Ryohe Nakamura Department of Economcs Okayama Unversy Japan August, 2008 Ths paper nvestgates the causes of changng ncome dspares across regons by the extenson of β convergence model. Increasng returns to scale n presence of agglomeraton economes and of nterregonal populaton mgraton are ncluded n the model. Agglomeraton economes nduce populaton n-mgraton due to hgher productvy. The regon experencng populaton n-mgraton wll decreases s productvy n a sense of neoclasscal economc theory,.e., the exstence of decreasng returns to scale. At the same tme, however, populaton n-mgraton has a possbly of enhancng agglomeraton economes. If margnal effect of agglomeraton economes s greater than decreasng margnal productvy of labour, then regonal dspares may expand. Ths suggests a knd of the Verdoorn effect. Of course the dfferences of ndustral composon across regons are another mportant cause of dspares. In ths paper I present a consstent model whch explans changng regonal dspares and try to estmate the magnudes of IRS by consderng the exstence of human capal. The model s a knd of the ntegraton of Kaldoran model and endogenous growth model. The estmatons are carred out by usng Japanese regonal data. Keywords: agglomeraton economes, mgraton, ncome transfer, convergence/dvergence, regonal ncome dspary E-mal ubbz0252@cc.okayama-u.ac.jp

2 1. Introducton Convergence or dvergence of per-capa ncome n an nter-regonal economc system s an essental topc to polcy maker as well as scholars. In the long run, whch mples more than thrty years, nterregonal ncome dspares tend to show marked convergence. Ths s confrmed n several countres ncludng Japans by Barro and Sala--Martn (2004), and others. However, the rate of declne n regonal per-capa ncome dspares s not constant over the perod. Furthermore, n the course of economc progress we have often experenced dvergence of per-capa ncome across regons. There are two competng theores whch explan convergence/dvergence of regonal dspares. The one s neoclasscal growth theory ncludng endogenous growth theory whch states convergence to the steady state soluton. The other s cumulatve growth theory whch suggests dfferental growth among regons. Ths s nally advocated by Kalor and subsequently ntegrated to Verdoorn Law by Dxon and Thrlwall (1975). 1 A number of papers have appled convergence model by Barro and Sala--Martn and also structural convergence model proposed by Mankw, Romer and Wel (1992) to regonal dspares n many countres. 2 Although some earler studes found regonal convergence n the long-run by applyng β-convergence model, recent research s drected to explan non-convergence trend or even dvergence trend n regonal dspares and to extend the condonal convergence model. Ths s because of recent detecton of ncreasng regonal dspares shown n several countres. For examples, Funke and Strulk (1999) found ncreasng dspares of per-capa ncome snce 1990 for Länder (states) n West Germany, and Terras (1999) also verfed dvergence across Italan regons snce 1975, and more recently Longh and Musoles (2007) found the convergence process of the natonal economes of the EU coexsts wh dvergence process between regons n EU countres. In order to overcome a shortcomng of the cross-sectonal approach whch neglects the dynamc effects of growth and ncorporate dvergence effect nto condonal convergence model, several efforts have been done. Funke and Strulk propose an estmaton model 1 Targett and Fot (1999) estmated convergence equaton and cumulatve growth equaton smultaneously for cross-country pooled data. 2 Crhfeld and Panggabean (1995), Crhfeld et al. (1955), Lall and Ylmaz (2001), Mller and Genc (2004) for US regons (states or metropolan areas); Terras (1999) for Italan regons; de la Fuente (2002) for Spansh regons; Badnger et al (2004) for NUT 2 regons; Chrstopouls and Tsonas (2004) for Greece; Carluer and Gaule (2005) for French regons; Armstrong (1955) for EU regons; and Henley (2003) for regons n the UK. 1

3 allowng for dfferent convergence rate as well as dfferent steady-states across regons and estmate by panel data. 3 Hammond (2006) suggests dvergence of regonal dspares due to the exstence agglomeraton economes created by knowledge spllovers and resultng ncreasng returns to scale regonal producton functon. Tme varant model wh a data generatng process s estmated by usng tme seres of the US metropolan data and shows dvergence between metropolan and non-metropolan ncomes. In a hstorcal vew the perod when the naton s experencng hgh economc growth, ncome dspares across regons tend to ncrease, and then the relatvely hgher ncome regons often accomplsh hgher growth rate of per-capa ncome than lower ncome regons n such a perod. The large metropolan regons, whch often exhb relatvely hgher ncome, are lkely to generate endogenous growth and attract human capals due to ther agglomeraton economes. Ths cumulatve causaton mples the tradeoff between aggregate effcency and nterregonal equaly. When we observe decreasng regonal dspares, economc dspares across regons converge to a steady state level. On the contrary, n case of ncreasng or expandng regonal dspares, the economy s n transon to another steady state due to changng ndustral structure. There are many sources whch could change nter-regonal ncome dspares. In a dynamc context, mgraton s an mportant factor whch can be the cause and/or result of regonal dspares as well as regonal dfference of technologcal progress. Many emprcal studes fnd agglomeraton economes arsng from populaton and ndustral concentraton wll rase regonal productvy. A regonal ncome transfer by the natonal government s another mportant factor affectng ncome dspares. Income transfer usually s mplemented to poor regons n order to adjust dfferences n local publc fnance. The total amount of transfer, n case of Japan, s determned by the natonal tax revenue and polcal judgement. In ths paper I wll focus on three man factors, whch have been neglected n the convergence model but mportant for changng regonal ncome dspares,.e., agglomeraton, mgraton, and ncome transfers. Startng by the fndngs the contrbutons of those factors to ncome dspares graphcally, I provde the base of specfcaton of the 3 Wang and Ge (2004) appled ther model to Chnese provnces. 2

4 model. Ths s presented n the followng secton. The trends of regonal per-capa ncome dspares measured by the CV (Coeffcent of Varaton) are depcted wh/whout ncome transfers and wh excludng Tokyo. The graphcal relatonshps between per-capa ncome growth and agglomeraton, ncome transfers, mgraton are also exhbed. Secton 3 provde neoclasscal convergence model ncludng agglomeraton and regonal mgraton. Specfcaton of the model presented n Secton 3 s estmated and results are nterpreted n Secton 4 by usng Japanese regonal data. Concludng remarks are gven n Secton Fact Fndngs on Regonal Convergence/Dvergence In ths secton we wll focus on the trend of regonal dspares and examne some factors whch are seemed to be related to the change n regonal ncome dspares. The canddates for factors are agglomeraton and mgraton, and ncome transfers. After graphcally examnng such factors, I proceed to construct the model explanng regonal convergence/dvergence. 2.1 Trend of Coeffcent of Varaton Fgure 1 dsplays the tme trend of per-capa ncome dspares across 47 prefectural regons measured by the CV (Coeffcent of Varaton). There are two lnes; the lower blue lne means the CV calculated by usual per-capa ncome of each regon, and the upper red lne s the CV n whch the amount of governmental ncome transfers to each regon s subtracted from regonal ncome. The nterpretaton of ths measure s presented n the followng subsecton. By takng a look at Fgure 1 we can notce there were at least three perods when Japanese economes have experenced the expanson of nterregonal per-capa ncome dspares. The frst one s the perod of ; ths perod, ten years after the WWII, the modern ndustralsaton n Japanese economy had started by accompanyng locally weghted publc nvestment. Ths mght cause the expanson of dspares as well as the hgh economc growth as a naton. The second ncreasng perod s the 1980s. In partcular, the late n 1980s, Japanese economy experenced sharp ncrease n land prce n large metropolan areas as well as n stock prces. Later we call bubble economy. After the bubble economy Japan had been sufferng from s negatve herage. The thrd s the most recent trend of the CV from 3

5 2000 to C.V Fgure 1 Trend of per-capa ncome dspares measure by the CV: per-capa ncome wh and whout the governmental ncome transfer ' ' After Transfer Before Transfer It s lkely sad that the behavor of regons wh large economc sze wll domnate the change of the CV. Partcularly, Tokyo whch s the capal regon n Japan, would have a sgnfcant role on the level and change of the CV as Tokyo occupes approxmately 16 % of total ncome of 47 prefectural regons. In order to capture the effect of Tokyo on the regonal dspares, two lnes of the CV are depcted n Fgure 2; the one s the lne of the CV calculated by 47 prefectural regons, the other s the lne calculated whout Tokyo. In Fgure 2 the trend of the CV excludng Tokyo shfts downward, however does not substantally change the general behavor of the CV trend except for the late 90s. It also shows that n the perod of ncreasng CV the effect of Tokyo s greater than other decreasng perods of regonal dspares. From these fndngs we can conjecture that n the ncreasng perod of regonal dspares Tokyo relatvely grew hgher than other less rch regons and ths wll be due to some specfc factors whch are nternal or external to ncome producng actves n Tokyo. The representatve factor n whch Tokyo domnates over s agglomeraton economes. 4

6 Fgure 2 Trend of per-capa ncome dspares measure by the CV: 47 regons and 46 regons excludng Tokyo C.V ' ' Prefectures Excludng Tokyo 2.2 Convergence/Dvergence The followng four fgures n Fgure 4 are typcal examples for the perods n growng regonal dspares and shrnkng regonal dspares, respectvely. In the early 70s the graph shows a clear convergence, and smple correlaton coeffcent between per-capa ncome of nal year 1970 and s growth rate to 1975 s Relatvely hgher ncome regons lke Tokyo, Osaka, and Ach were damaged by the ol-crss occurred n In the late 80s, we can fnd that the relatvely hgher ncome regons, partcularly Tokyo, have pulled the natonal economc growth. The correlaton coeffcent between nal ncome level 1984 and growth rate to 1989 s 0.490, ths s a que contrastng the fgure of After 1990, the Japanese economy had been sufferng from the after-effects of remarkable ncrease n asset prces by the excessve speculaton and has experenced a low economc growth, and even a deflatonary recesson n the late 1990s. Ths s one of the reasons for the decrease n regonal dspares. In recent years, , regonal dspares have a tendency to ncrease due to the effect of an economc recovery whch has been led by the Tokyo metropolan regon. From four representatve graphs we can also magne that agglomeraton economes would substantal to dvergence of regonal per-capa ncome and some polcy nstrument mght be effectve durng convergence perod. Accordng to prevous emprcal studes on 5

7 convergence of regonal dspares, the man reasons for decreasng ncome dspares across Japanese regons after 1955 are regonal ncome redstrbuton through governmental transfer and drect publc nvestment whch attracts factory frms wh ndustral dsperson polcy for local (non metropolan) regons. Fgure 3 Typcal Examples of Covergence/Dvergence n per-capa Income Relatve Growth Rate to Regonal Average: Ach Relatve Growth Rete to Regonal Average: Tokyo Osaka log of Relatve per-capa Income Dfference n Osaka Ach log of per-capa Income Dfference n 1989 Tokyo 13 Relatve Growth Rate to Regonal Average: Reatve Growth Rate to Regonal Average: Ach log of per Capa Income Dfference n Ach 23 Osaka 13 Tokyo log of per-capa Income Dfference n 2000 Tokyo Agglomeraton Economes Agglomeraton s an mportant factor to explan dynamc change n regonal dspares as well as cross sectonal vewpont of nterregonal dspares. The most popular measurement of agglomeraton s populaton, n partcular populaton at workplace. Thus, I choose top three largest regons n terms of daytme populaton, whch are Tokyo, Ach, and Osaka. These prefectural regons have been also top three hghest per-capa ncome levels. Fgure 4 shows the trend of regonal share of populaton at workplace for those three regons. In the perods when regonal dspares are expandng ( , , ) Tokyo s share s also ncreasng whle the share of Osaka s declnng after 1975 and that of Ach s constantly ncreasng. As a result per-capa ncome of Osaka s lower than that of 6

8 Ach n recent years. Fgure 4 Regonal Share of Populaton at Workplace Regonal Share of Populaton at Workplace (%) Tokyo Ach Osaka Fgure 5 shows another measure of agglomeraton counted by regonal share of the number of manufacturng workers. It s often sad that n the ndustralsng perod agglomeraton of manufacturng actvy could become the drvng force of regonal economc growth. In the early expandng perod of regonal dspares rapd concentraton of manufacturng works n Tokyo was found from ths fgure. Ths feature concdes wh the trend of CV n Fgure 1. After 1965, the share of manufacturng workers n Tokyo s contnung to decrease. The trend of Osaka s smlar to that of Tokyo. On the contrary, for Ach regon manufacturng share s ncreasng snce 1975 and n recent years s ncrease comes from the growng export of car of Toyota because the headquarter and man factores of Toyota are located n Ach Prefecture. Interestngly, as a result, the share of manufacturng workers n each regon became equal n Therefore, we can magne that agglomeraton of manufacturng ndustres whch would be reflected n regonal scale economes n producton was effectve n the early stage of regonal development. 4 4 Ths wll be true for other developed countres as well as currently developng countres. 7

9 Fgure 5 Regonal Shares of Manufacturng Workers Regonal Share of Manufacturng Workers (%) Tokyo Ach Osaka In order to understand the role of agglomeraton effects on ncome dvergence, I check for the exstence of scale economes (ncreasng returns to scale) n large regons. A smple relatonshp s assumed between the populaton (P) and ncome (Y), whch s expressed as ( ) lny = β0 + β1+ βtdtokyo + βadach + βodosaka ln P, (1) where β, β, and β are, respectvely, Tokyo, Ach, and Osaka regonal dummes, and TD AD OD β0 and β 1 are parameters to be estmated. Equaton (1) also nterpreted as a regonal aggregate producton functon wh one factor of producton (populaton). In a regonal level, agglomeraton economes are nternalsed and appeared n the parameters of β + β Tokyo + β Ach + β Osaka OD. The regresson equaton s rewrten n the form of 1 TD AD per-capa ncome: Y ln = β0 + ( β1 + βtdtokyo + βad Ach + βodosaka 1) ln P. (2) P In Fgure 6, the lne shows estmated values of be a posve correlaton between the trend of CV and that of of Tokyo was ncreasng and also n 2000s s ncreasng. 8 β DT s. At frst consderaton, there seems to β DT ; n the 80s scale parameter

10 Addonal Scale Parameter of Tokyo Fgure 6 Trend of Scale Parameter of Tokyo Income Transfers In general, factor mobly s not free between regons and also there certanly exst agglomeraton economes both n producton and consumpton. These are oppose factors to convergence n the neoclasscal growth theory. If s not easy for some factor n producton to move among regons, then regonal dspares wll be sustaned. If agglomeraton economes are substantal, then regonal dspares may be expand. Therefore, n order to converge dspares across regons, ncome transfers by the natonal government are mplemented as a polcy tool, so that the growth rates of poorer regons can catch up to the rcher regons. Concernng the above four perods we examne how governmental transfers contrbute to reduce per-capa ncome dspares across regons. In each fgure horzontal lne ndcates total amount of per-capa transfers durng the perod, measured as mllon yen per capa. It s obvous that n the perod of contractng dspares the amount of (per-capa) ncome transfers by the central government exhb hgh correlaton wh per-capa ncome growth. In the perod of expandng regonal dspares ( , ), transfers of lower per-capa ncome regons are not effectve to ncrease ncome level. 9

11 Fgure 7 The relaton between Income Transfers and Regonal Growth Rate Relatve Growth Rate to Regonal Average: Cumulatve per-capa Income Transfers: Relatve Growth Rate to Regonal Average: Cumulatve per-capa Income Transfers: Relatve Growth Rate to Regonal Average: Cumulatve per-capa Income Transfers: Relatve Growth Rate to Regonal Average: Cumulatve per-capa Income Transfers: Mgraton Mgraton causes a change of nter-regonal ncome dspares whereas nter-regonal ncome dspary s also a reason of mgraton. In a neoclasscal regonal growth model nterregonal populaton mgraton s assumed to respond to regonal dfferences n factor prces, so that regons wh relatvely hgher labour productvy attracts populaton and then margnal productvy wll decrease due to dmnshng returns. In ths case regonal ncome dspares wll converge. However, mgraton followed by human capal such as hgh sklled labour may rase the average ncome n n-mgraton regon. Ths s another type of agglomeraton n terms of human capal. In ths case regonal ncome dspares could dverge. The causaly between mgraton and ncome dfferental are stll now ambguous. Fgure 5 depcts lne exhbng per-capa ncome level relatve to the average over 47 prefectural regons and draws bar showng net mgraton. By takng a glance at fgures, we can realze 10

12 that there exst strong correlaton between net mgraton n a regon and relatve per-capa ncome dfference. Regardng to Tokyo, mgraton seems to lead relatve change of per-capa ncome n most of the perod. Mgraton causes n the late 50s Tokyo has accepted much mgraton and followed by decreasng relatve pre-capa ncome. In a neoclasscal theory out-mgraton nduces to rase margnal productvy of labour, so that per-capa regonal ncome wll ncrease. Ths s well traced n the fgure of Kagoshma n Fgure 8. Tokyo Fgure 8 Mgraton and Relatve per-capa Income Osaka Relatve per-capa Income Net Mgraton (Thousand) Relatve per-capa Income Net Mgraton (Thousand) 0.3 ' ' ' ' log of relatve per-capa Income Net Mgraton n Tokyo log of relatve per-capa Income Net Mgraton n Osaka Aomor Kagoshma Relatve per-capa Income Net Mgraton (Thousand) Relatve per-capa Income Net Mgraton (Thousand) ' ' ' ' log of relatve per-capa Income Net Mgraton n Aomor log of relatve per-capa Income Net Mgraton n Kagoshma 3. Convergence Model n presence of Agglomeraton Economes and Mgraton In ths secton I try to formulate convergence model n presence of agglomeraton and mgraton. Frst, we defne per capa ncome producng functon as ( ) ( ; ) y = A P f k Y, (1) where y and k are respectvely per-capa ncome and per-capa capal stock n regon at tme t. These varables are defned as y = Y / P and k = K / P, n whch Y, K, and P are total ncome, capal stock, and populaton n regon, respectvely. The exstence of Y as 11

13 an argument n functon f mples the possbly of ncreasng returns to scale due to nternalsed agglomeraton economes n a regonal aggregated level. neutral shft factor of producton. The change n capal stock, K, s gven by K = I d K ( ) A P denotes Hcks, (2) where I s nvestment n regon and d s deprecaton rate whch s assumed to be constant over the perod and regon. By dvdng both sde of equaton (2) by P the change n per capa capal, k, s derved as P P k = I d + k = sk, y d + k, (3) P P where s K, s the proporton of nvestment n regonal ncome. In equaton (3), unlke standard convergence model, populaton growth rate s varable over the perod. The reason for ths s that there s hgh frequency of nterregonal mgraton compared to nternatonal mgraton due to regonal openness. 5 Populaton change s dvded nto natural change and socal one. The separaton of two factors s wrten as P = n P + M. (4) The mgraton rate s defned by M m =, (5) P whch s also dependent of regonal characterstcs such as relatve per-capa ncome level. Thus, m s rewrten as ( / ) m = m y y, (6) t where s the average value of y over regons, and equaton (6) s dm / d ( / ) y y y > 0. t t At ths pont the causaly between mgraton and per-capa ncome level s ambguous. In a neoclasscal world, for regons experencng posve net mgraton per-capa ncome wll decrease due to dmnshng returns to scale wh respect to labor. On the other hand, for regons recevng n-mgraton of sklled-labor may ncrease per-capa ncome. 5 In ther perspectves on regonal economc growth, Nkamp and Poot (1998) formulate the endogenous growth model by consderng labour mgraton. 12

14 Thus steady-state of capal ntensy level s gven by the equaton: ( ) ( ) dln k K,, k s A P f k Y = = ( n + d + m ) = 0. (7) dt k k Let denote ( ) = ( ) ( ) G k s A P f k, Y / k K (8a) and ( ) ( ) H k = d+ n + m k, (8b) where tme subscrpt s added, and y k s assumed. In equatons (8a) and (8b), H(k ) s ncreasng functon of k whle G(k ) s decreasng functon of k. The per-capa capal at steady state k s gven by the soluton of G( k ) = H( k ). Ths steady state at tme t s characterzed by E n Fgure 9. Now that we suppose the functon G ( k ) shfts upward due to agglomeraton effect such as Y < Y. If ths occurs n regons whch are relatvely ' hgher per-capa ncome, then ncome dspares wll dverge. Then a temporary steady state pont s gven by E ' n the fgure. Although regons move to new steady state pont, regon wll experence populaton n-mgraton because of hgher capal/labour rato. Ths wll shft H ( k ) curve upward. Ths n turn generates convergence process of nterregonal dspares. ( ), H( k ) G k E Fgure 9 Shft of Steady-state Pont E ' E ' ( ) H = d + n + m y ' ' ( ) H = d + n + m y ( ) G = s A f k, Y / k K ' ' ' ' ' ( ) G = s A f k, Y / k K k k ' k ' k 13

15 Even f regon s not on the steady state path at tme t, per-capa ncome of regon E approaches to the steady state under the condons that G exhbs negatve slope and H does posve slope, wh respect to k, respectvely. Snce there s no reason that at tme t regon s on the steady-state path, the approachng to steady-state n terms of per-capa ncome of regon s usually descrbed by the partal adjustment equaton as y y y y = yt yt yt yt, (9) ln ' ln b ln ln where y s per-capa ncome at perod t n regon and y s s equlbrum soluton at t. The convergence equaton whch has been tested n many regona and countres s derved from ths equaton and the coeffcent whch s derved from solvng dfference-equaton (9), as a functon of b, denotes a speed of convergence. The rght hand sde of equaton s approxmately equal to the growth rate of per-capa ncome n regon measured by the devaton from the regonal average. The convergence equaton s y ln y ' y = a +β ln y. (10) t In convergence model β s assumed to be constant over the perod. If β takes the negatve value, then regons devatng from the steady state n terms of per-capa ncome would converge. However, regons wh relatvely hgher per-capa ncome may grow faster than the regons wh relatvely lower per-capa ncome due to agglomeraton effects, and furthermore hgher ncome level wll attract human capal from lower regons, whch n turn nduces n-mgraton. Therefore, we cannot deny the non-negatvy of β as well as s constancy over the perod. 6 As shown n Fgure 9, the transon of steady-state may occur durng [t, t ]. In ths case parameter β wll depend upon the dfference of two equlbrum levels of per-capa ncome, ln y e ' ln y (superscrpt e means expectaton of equlbrum value at current perod), and mgraton rate explanng the shft of equaton (8b). Therefore, constant parameter β can be 6 There are some papers whch try to specfy and estmate the changng convergence parameters n order to capture regonal dvergence. 14

16 wrten by the functonal form lke e y ' β = β ln, m,( t, t'). (11) y In equaton (11), s expected that the effect of mgraton on β wll be posve because mgraton promotes to converge nter-regonal per-capa ncome dspares by dmnshng returns to labour n neoclasscal model. On the other hand, the speed of convergence to new steady-state wll declne due to the addonal change of steady-state or hgh expectaton of new steady-state may causes dvergence. 4. Specfcaton of the Model Frst, I wll defne the Cobb-Douglas producton functon for frms wh agglomeraton economes. In a specfcaton of a frm-level producton functon agglomeraton economes are external to ndvdual frms, and then the producton functon s expressed as y = α PY k l, (12) η γ α 1 α j 0 and Y K y =, k, l E = E = L E, where E s the number of frms, y s produced ncome per frm, k s capal stock per j frm, and l s labour whch s measured as employees per frm. s the total produced j ncome n regon, and external to ndvdual frms. In aggregatng nto a regonal level the producton functon s rewrten as Y = AP K L Y η α 1 α γ ( ) η α 1 α κ γ = AP K P Y, (13) Y j where labour s assumed to be the constant rato of populaton, κ. Rewrng Equaton (13) n terms of per-capa ncome gves the estmaton form as where L Y = A κ P K, (14) 1/(1 γ ) (1 α)/(1 γ ) (1 α+ η)/(1 γ ) α/(1 γ ) = κ P. Thus per-capa ncome s expressed as y = A κ P k (15a) 1/(1 γ ) (1 α)/(1 γ ) ( η+ γ )/(1 γ ) α/(1 γ ) 15

17 or where y = A k Y P, (15b) 1 κ α α γ η k = K / P, and y = Y / P. Equaton (15a) ndcates the ndustry-level producton functon n whch agglomeraton economes presented by regonal aggregate ncome are nternalsed. Thus, the regonal aggregate producton functon exhbs ncreasng to returns to scale when γ s posve, even gven constant returns to scale at the frm level. Substutng equaton (15a) nto (8a) gves 1/(1 γ ) (1 α)/(1 γ ) ( γ + η)/(1 γ ) ( α+ γ 1 ( ) = κ G k s A P k K, )/(1 γ ) (16) The soluton of steady state, k, s obtaned by equatng (16) and (8b): (1 γ)/(1 α γ) 1/(1 ) (1 )/( 1 ) s α γ α γ K, ( γ η)/(1 α γ) κ α = + δ + n + m k A P (17a) Therefore, per-capa ncome at the steady-state s expressed as α/(1 α γ) 1/(1 α γ) (1 α)/(1 α γ) sk, ( γ+ η)/(1 α γ) κ δ + n + m y = A P. (18a) Ths equaton mples that regonal populaton has a role of shftng per-capa ncome upward f agglomeraton parameter γ s posve. By applyng equaton (15b) to equaton (8a) nstead of (15a), we can drve another specfcaton of steady-state lke 1/(1 α ) 1/(1 α ) sk, γ/(1 α) η/(1 α) = κ δ + n + m k A Y P (17b) and α/(1 α) 1/(1 α ) sk, γ/(1 α) η/(1 α) = κ δ + n + m y A Y P. (18b) Ths specfcaton explcly presents agglomeraton sources by aggregate ncome and regonal populaton sze and shows posve effect of agglomeraton on per-capa ncome whle mgratons s negatve effect on per-capa ncome. By combnng equatons (9) to (11) and (18a)/(18b), we can construct the estmaton model. 16

18 5. Estmaton of the Model 5.1 Data Wh regard to regonal classfcaton, the most relevant Japanese regonal counterpart of NUTS 2 regons s prefectures n Japan. There are 47 prefectures ncludng the Tokyo Metropols, whch has 23 specal wards, smlar to nner London. Each prefecture s a local government and has s own governor. The average area over the 47 prefectural regons s approxmately 7,930 km 2, whch s slghtly larger than the average of 36 NUTS 2 regons n the UK, whch s 6,773 km 2. The data on ncome are from the Cabnet Offce n Japan, Annual Report on Prefectural Income (varous ssues) and data on populaton and job occupaton by regon are from Census of Populaton whch s ssued by each fve year. In terms of statstcal avalably we can use data on the Regonal System of Accounts (Annual Report on Prefectural Income) as for back as The data on ncome transfers by the natonal government are also avalable snce Income transfer s called grant-n-ad from tax revenue; s redstrbuted to local muncpales (ces, towns, vllages, and prefectures) for whch the amount of local fnancal demand exceeds local tax revenue. 5.2 Estmaton Model In specfyng convergence parameter functon β we add two varables whch wll be sgnfcant to explan per-capa ncome level by the nvestgaton of graphs n secton 2. The one s the ncome transfers conducted by the natonal government, whch would help to converge ncome dspares across regons, denoted by S. The other s the number of sklled workers whch acts as human capal n a regonal economy. Mgraton brngs sklled labour force whch wll be affect posvely per-capa ncome growth. Hence, the varyng parameter model of convergence parameter β s wrten as β = bβ + b + b + b + b e t' t' P ' H ' M S Pln H0 H1ln S H t P t P P. (19) The estmaton equaton s obtaned by substutng equaton (19) nto equaton (10) as 17

19 t' t' y ' P ' H ' M S y ln = a+ b bpln bh0 bh1ln + bs ln, (20) y β P H t P t P yt where the expected sgns of parameters are b β < 0, b > 0, b 0 < 0, P H b > H1 0, and b S > 0. The posve sgn of parameter b P means agglomeraton economes have negatve mpact on convergence. Mgraton n general tends to conver ge regonal dspares,.e., 0 < 0 because of dmnshng returns to labour, whle parameter b H1 b H may be posve as human capal represented by sklled labour can be brought wh populaton n-mgraton and contrbutes to ncrease regonal per-capa ncome. Fnally, the sgn of ncome transfers s expected to be posve snce the role of transfers s contract to regonal dspares 5.3 Estmaton Results In the estmaton some varables have endogenous characterstcs whch means a correlaton to the error term, so that we use the two-stage least squares method wh nstrumental varables n order to deal ths endogeney problem. The canddates of nstruments are lagged dependent varables. By consderng fgures 1 to 5 I select fve typcal sub-perods whch shows ncreasng n terms of the CV; , , , and decreasng n the CV; , The reason I do not use the whole perod s that the purpose of ths paper s to nvestgate how agglomeraton and mgraton economes affect change n regonal dspares. If we try to estmate agglomeraton effect on regonal dspares n the long-run, wll be faled to capture correctly. The estmatons are carred out by two types of specfcaton of agglomeraton economes n addon to smple β -convergence model. The one s equaton (19) n whch the parameter of regonal populaton change reflect agglomeraton effect, and the other s regonal aggregate ncome s adopted as the agglomeraton varable nstead of regonal populaton, n whch the parameter of change n regonal aggregate ncome, coeffcent n Kaldoran cumulatve growth model. ( ) ln Y / Y, mples so-called Verdoorn ' 18

20 In Table 1 the frst row n each perod shows estmates of absolute convergence model. In the early 70s and 90s smple regresson model well capture convergence, partcularly for the perod the adjusted R 2 s que hgh. On the contrary, the late 50s n whch Japanese economy started hgh growth and the late 80 s n whch Japan experenced an excessve economy n real estate market, show non-convergence estmated values. Table 1 Estmated Parameters Dvergence Convergence Dvergence OLS 2SLS 2SLS OLS 2SLS 2SLS OLS 2SLS 2SLS b β (2.45) (-0.08) (3.08) (-11.70) -(3.69) (-2.15) (3.69) (2.98) (0.62) α P (-0.96) (2.88) (2.31) α Y (16.88) (11.93) (12.19) α M (2.06) (1.94) (-2.77) (-2.87) (1.82) (2.23) α H (2.25) (2.48) (2.57) (1.83) α S (-1.65) (2.71) (2.52) (2.18) (2.92) (3.25) R Table 1 (Contnued) Convergence Dvergence OLS 2SLS 2SLS OLS 2SLS 2SLS b β (6.78) (-2.64) (-3.94) (2.46) (2.47) (1.96) α P (-0.86) (-0.92) α Y (13.32) (14.62) α M (-2.60) (-2.55) (2.05) (4.83) α H (1.81) (2.19) (-1.23) (1.40) α S (3.19) (3.63) (2.03) (3.98) 2 R Estmated parameters of populaton change, α P, whch s a proxy of agglomeraton effect are found to be nsgnfcant and even negatve n most of the perods. The reason of ths s 19

21 that populaton change and net mgraton rate are often hghly correlated. Concernng the estmated parameters α Y s show sgnfcant contrbuton to the posve change of per-capa ncome rather n the perod of ncreasng dspares than decreasng dspares across regons. The parameter also ndcates Verdoorn effect mplyng the elastcy of per-capa ncome growth, and seems to be stronger n the earler perod such as the begnnng age of ndustral development n Japan. Mgraton effects on the convergence provde posve sgn for the perods, and , whch are decreasng n dspares of regonal per-capa ncome. However, the perods for the ncreasng dspares show posve sgn whch mply populaton net mgraton may nduce dvergence. Although the causaly between mgraton and ncome dspary has been ambguous, can be sad from our estmaton results that populaton mgraton could support convergence for the perod of decreasng dspares whle contrbutes to dvergence due to transon to the new steady-state for the perod n ncreasng dspares. In recent years, after 2000, Japanese regonal economes are experencng ncrease n nterregonal ncome dspares, n partcular compared to Tokyo metropolan regon. The estmated results for mply that populaton mgraton nto farly hgher ncome regons represented by Tokyo would ncrease regonal dspares accompaned by agglomeraton economes. We also add a varable for human capal to account for mgraton parameter estmates. Human capal s represented by the number of sklled labour whch comes from Census of Populaton by occupaton. It well controls the parameter of mgraton because of s posve sgn n most of the cases. From Fgure 1 s lkely sad that ncome transfers by the natonal government have a role of decreasng ncome dspares across regons. 7 Fgure 7 also shows transfers to lower ncome regons help catch up hgher ncome regons n the perod of decreasng regonal dspares. The parameter of ncome transfers, α S, would reflect the magnude of convergence n case of posve sgn. Table 1 shows posve estmates and t-values are greater than 2.0 n most of the perods. Income transfers are effectve for lower ncome regons n order to catch up hgher per-capa ncome regons. 7 Barro and Sala--Martn (1996) states that nterstate transfers are not responsble for the long-run declne n ncome n spe of admtng transfers help reduce per-capa ncome dsperson. 20

22 6. Concludng Remarks In ths paper I have focused on the role of agglomeraton and mgraton n regonal convergence/dvergence n terms of per-capa ncome. Although numerous studes are conducted about regonal convergence as well as nternatonal comparson, there are few studes sheddng lght on the role of agglomeraton and mgraton n framework of neoclasscal (new) growth theory. I extended the beta-convergence model nto varyng parameter verson whch allows dvergence feature due to agglomeraton as well as sources of convergence such as ncome transfers. Mgraton effect also s ncorporated nto the extended model wh human capal varable. The emprcal mplementaton was conducted wh Japanese regonal data whch cover from 1955 to Whle s avalable to estmate long-run convergence, I have chosen typcal perods whch respectvely show ncreasng and decreasng dspares. For the developed countres lke ths case wll be natural to converge n the long-run. The summary of the results are as follows. Agglomeraton economes measured by regonal aggregate ncome have sgnfcant mpact on regonal dspares n dvergence whle ncome transfers contrbute to regonal convergence. Ths ndcates the exstence of so-called Verdoorn effect n dvergence of regonal dspares. Concernng another agglomeraton varable, regonal populaton, whch s alternately used to aggregate ncome, estmated parameters also ndcate dvergence though the degree of dvergence s decreasng. Mgraton n general contrbute regonal convergence, but n the perod of ncreasng dspares s attracted to hgher ncome regons due to agglomeraton economes. These estmated results report mportant mplcatons for regonal polcy. In the medum term (not long-run) agglomeraton economes rase per-capa ncome. It may be effectve for convergence, partcularly n low growth years of GDP, to redstrbute tax revenues to relatvely poorer regons by means of ncome transfer. However, does not mean regonal sustanably. As shown n Fgure 9 the share of ncome transfers n GDP s declnng n recent years and thus ths may generate non-convergence. In order to get out of dependency on transfers regonal polcy should be headed for fosterng ndustral clusters whch most lkely exhb agglomeraton economes. 21

23 6 Fgure 10 Regonal Dspares and Income Transfers 6 Dfference of CV wh and whoud Transfers ' ' ' % of Transfers n GDP Dfference of CV Share of Total Transfers n GDP In ths analyss I dropped mportant feature, whch s a spatal nterdependency between neghborng regons. Recent papers ncorporate spatal correlatons nto regonal convergence models and confrm the mportance of spatal effects. For examples, Lall and Ylmaz (2001), Badnger et al. (2004), Henley (2005), and Batts and Vao (2008) etc.. Although spatal nterdependency affects the change of regonal per-capa problem of estmatng convergence equaton s to know how convergence or ncome, most mportant dvergence occurs. Ths paper provded some lght on. 22

24 References Allngton N.F.B. and McCombe J.S.L. (2007) Economc growth and beta-convergence n the east European transon economes, n Arests eds. Economc Growth: New Drecton n Theory and Polcy, Edward Elgar, Massachusetts. Armstrong H.W. (1995) Convergence among regons of the European Unon, , Papers n Reg. Sc., 74, Badnger, H et al., (2003) Regonal convergence n the European Unon, : A Spatal Dynamc Panel Analyss, Regonal Studes, 38, 3, , 2004(2003). Barro R. and Sala--Martn X. (1996) Regonal coheson: Evdence and theores of regonal growth and convergence, European Econ. Rev., 40, Barro R. and Sala--Martn X. (2004) Economc Growth, 2 nd Edn. MIT Press, Cambrdge, MA. Batts M. and D Vao G. (2008) A spatally fltered mxture of β convergence regresson for EU regons, , Emp. Econ., 34, Carluer F. and Gauler G. (2005) The mpact of convergence n the ndustral mx on regonal comparatve groth: Emprcal evdence from the French case, Ann. Reg. Sc., 39, Crhfeld J.B., J.F.Gertz, and S.Mehta (1995) Economc growth n the Amercan States: the end of convergence? The Quart. Rev. of Econ. and Fnance, 35, Chrhfeld J. B. and Panggbean M.P.H. (1955) Growth and convergence n U.S. ces, J. Urban Econ., 38, Chrstopoulos, D.K. and Tsonas, E. (2004) Convergence and regonal productvy dfferences: evdence from Greek prefectures, Ann. Reg. Sc., 38(3), Coulombe S. (2007) Globalzaton and Regonal Dspary: A Canadan case study, Reg. Studes, 41, de la Fuente A. (2002) On the source of convergence: A close look at the Spansh regons, European Econ. Rev., 46, Desmet K. and Fafchamps M. (2006) Employment concentraton across U.S. countes, Reg. Sc. Urban. Econ., 36, Dxon, R. and Thrlwall, A.P. (1975) A model of regonal growth rate dfferences on Kaldoran lnes, Oxford Econ. Papers, 27, Funke M. and Strulk H. (1999) Regonal growth n West Germany: convergence or dvergence? Econo. Modellng, 16, Hammond G.W. (2006) A tme seres analyss of U.S. metropolan and non-metropolan ncome dvergence, Ann. Reg. Sc., 40, Hellwell, J. F., Convergence and Mgraton among Provnces, Canadan Journal of Economcs, 29, S324-S330, Henley A. (2005) On regonal growth convergence n Great Bran, Reg. Studes, 39, Kosfeld R. et al. (2006) Regonal productvy and ncome convergence n the Uned 23

25 Germany, , Reg. Studes, 40, Lall S.V. and Ylmaz S. (2001) Regonal economc convergence: Do polcy nstruments make a dfference? Ann. Reg. Sc., 35, Mller J.R. and Genc I. (2005) Alternatve regonal specfcaton and convergence of U.S. regonal growth rates, Ann. Reg. Sc., 39, Njkamp P. and Poot J. (1998) Spatal perspectves on new theores of economc growth, Ann. Reg. Sc., 32, Terras M. (1999) Convergence and dvergence across Italan regons, Ann. Reg. Sc., 33, Wang Z. and Z. Ge (2004) Convergence and transon auspce of Chnese regonal growth, Ann. Reg. Sc., 38, Webber D.J. and Whe P. (2003) Regonal Factor prce convergence across four major European countres, Reg. Studes, 37,