Convergence and Regional Productivity Divide in Italy: Evidence from Panel Data

Transcription

1 MPRA Munich Personal RePEc Archive Convergence and Regional Produciviy Divide in Ialy: Evidence from Panel Daa Francesco Aiello and Vincenzo Scoppa Deparmen of Economics and Saisics, Universiy of Calabria (Ialy Augus 2008 Online a hp://mpra.ub.uni-muenchen.de/17343/ MPRA Paper No , posed 16. Sepember :02 UTC

2 Convergence and Regional Produciviy Divide in Ialy: Evidence from Panel Daa Francesco Aiello and Vincenzo Scoppa Universiy of Calabria Deparmen of Economics and Saisics I Rende (CS Ialy 1. Inroducion Absrac: Using a panel daa model o conrol for differences in regional echnological levels and o ake ino accoun endogeneiy, we find wo key resuls for he growh of Ialian regions. Firsly, we show ha he rae of condiional convergence of each region is much higher (from 12% o 18% according o specificaions han ha esimaed in sandard cross-secion regressions (2%. Secondly, a large par of produciviy gaps across regions canno be impued o differences in physical or human capial bu i is raher relaed o relevan differences in Toal Facor Produciviy (TFP. Keywords: economic growh, convergence, regional TFP heerogeneiy JEL Classificaion : O47; R11; O11. Many empirical sudies have examined he paern of growh of Ialian regions sysemaically showing wide differences in he level of oupu per worker (or per capia and a slow process of convergence beween poor and rich regions (in paricular afer he mid-sevenies. Analysing convergence across counries, hese works have mainly used cross-secion regressions assuming a homogenous aggregae producion funcion for all regions. The use of a common producion funcion is mainly due o he fac ha cerain variables, such as efficiency, echnology, organizaional capial, insiuions and so on, are hard o observe or measure and, hence, canno be considered in a cross-secions regression. As shown by Islam (1995, Casell Esquivel and Lefor (1996 and de la Fuene (2002, cross-secion esimaions are biased because he unobservable level of echnology is omied, or raher i is assumed common among counries. However, a hos of evidence shows ha echnology differs across counries and is correlaed o he explanaory variables normally included in growh regressions. As a way ou, hese auhors adop a panel daa approach, in view of he fac ha i allows hem o deal wih unobservable differences in he producion funcion of counries. Their resuls are remarkably differen from previous esimaes obained in cross-secions analysis, in paricular as regards he speed of convergence of counries o heir own seady sae, which is much more elevaed han in previous cross-secion analyses. Our aim is o apply he mehodology proposed in hese sudies o Ialian regions using a panel daa model wih regional fixed effecs and esimaing i wih Leas Square Dummy Variables (LSDV o avoid he omied variable bias. Preliminarly, since his approach has been criicized by Dowrick and Rogers (2002 we verify following hese auhors if he condiions are me for he The paper is he resul of a join work beween he wo auhors. However, Francesco Aiello is mainly responsible for secions 4, 5 and 6 and Vincenzo Scoppa for secions 1, 2 and 3. We would like o hank Mariarosaria Agosino, Paola Cardamone and Maria De Paola for useful commens on an earlier version. Usual disclaimers apply. Financial suppor from he MIUR (PRIN n is graefully acknowledged. 1

3 use of his mehodology. Moreover, since convergence esimaions are plagued by he problem of endogeneiy of explanaory variables, we also use he Generalized Mehod of Momens (GMM esimaors suggesed by Arellano and Bond (1991 and Arellano and Bover (1995 o deal wih boh heerogeneiy and endogeneiy issues. Besides overcoming he problems of omied variable and endogeneiy biases ypical in cross-secion regressions, panel daa esimaions also enable researchers o esimae a measure of he level of echnology or efficiency (TFP in each region (from individual fixed effecs and can help o shed some ligh on he characerisics of regional economies. Panel daa have been used for Ialian regions only recenly. Carmeci and Mauro (2002 use panel daa esimaors o explore he relaionship beween he convergence process and he characerisics of Ialian labour markes, finding ha he imperfecions in he working of labour markes (in paricular, he cenralized wage bargaining mechanism and he unemploymen rae lowers he rae of growh and slow down convergence of less-developed regions. Di Libero, Pigliaru and Mura (2007 use panel daa wih he aim o esimae he role of echnological convergence across Ialian regions beween he Sixies and Nineies. They find srong evidence ha a process of TFP convergence ook place among Ialian regions, in paricolar up o he mid-sevenies. The common denominaor beween our paper and hose by Carmeci and Mauro (2002 and Di Libero, Pigliaru and Mura (2007 is he similariy in resuls concerning he speed of convergence of Ialian regions when using analogous esimaions echniques. However, we use more recen daa (from 1980 up o 2004 while Di Libero, Pigliaru and Mura (2007 resric heir analysis o he period and Carmeci and Mauro (2002 use daa from he period 1963 o More imporanly, we focus on he analysis of heerogeneiy in TFP across regions, using regional fixed effecs o measure he echnological level of each region and o obain implicaions abou he long-run rend of regional income levels. We will use a new daa se (over he period recenly published by he Ialian Naional Saisical Insiue (ISTAT, 2005 buil using he new SEC95 mehodology. The enire period is spli ino 4-year ime periods. The use of panel daa mehodology reveals wo imporan findings. Firs of all, he rae of convergence o seady sae for Ialian regions is much higher (around 11-12% according o specificaions han he rae esimaed in cross-secions analysis, which reached a consensus on a rae of convergence as low as 1% or 2%. Therefore, he resuls show ha regions are close o heir own seady saes and are no definiely on differen poins of he same growh pah, which would lead, in he long-run, all he regions o he same equilibrium. Secondly, a large par of produciviy gaps across regions canno be impued o differences in he accumulaion of physical or human capial bu raher o differences in Toal Facor Produciviy (TFP. The index of TFP obained in our panel esimaions is in line wih he levels of TFP obained by Di Libero, Pigliaru and Mura (2007 using panel daa esimaions or by Aiello and Scoppa (2000 hrough growh accouning mehodology. This finding implies ha echnology is no a public good and regional efficiency depends on learning by doing, organizaional and social capial and so on. This, in urn has relevan policy implicaions: when one admis differences in regional producion funcions he scope for policy is amplified raher han being resriced. The paper is organized as follows. Secion 2 briefly reviews previous esimaes of he rae of convergence across Ialian regions. Secion 3 considers he omied variable bias arising in crosssecion regressions and esimaes he convergence regression wih panel daa, emphasizing he marked differences in he resuls wih respec o cross-secion esimaes. Secion 4 deals wih he endogeneiy bias. In Secion 5, we deermine regional TFP levels and discuss he implicaions of heerogeneiy of producion funcion across regions. Secion 6 repors some conclusions. 2

4 2. Exising sudies on he convergence rae of Ialian Regions Following he renewed ineres in growh heory and he empirical works on cross-counry growh paerns, a large number of papers has analyzed he process of growh of Ialian regions and he exisence of a endency o converge in erms of income levels. The empirical lieraure on convergence has aimed o deermine, among oher hings, if poor regions are growing faser han rich regions, ha is if hey are closing he considerable gap in erms of income per capia or labour produciviy, converging in he long-run o he same seady sae (absolue convergence, or if hey are converging o differen seady saes (condiional convergence. The common approach used for evaluaing he process of condiional convergence has been he esimaion, hrough Ordinary Leas Squares (OLS, of he following cross-region growh equaion: y ln y [1] ( i i T 0 = a + β ln y + φ X + ε 0 where y is he oupu per worker in region i a an iniial ime 0 0, y i, T is he same variable a he mos recen ime T, φ is a parameers vecor and X i a vecor of srucural variables (e.g. invesmen rae (s, human capial (h, growh of labour force (n, depreciaion rae (δ ec., ε i is an error erm. In pracice, he growh rae of oupu per worker is regressed on he iniial level of oupu and on a se of explanaory (srucural variables. The esimaion in regression [1] of a saisically significan parameer β < 0 implies ha poor regions are growing faser han rich ones, in line wih he predicions of he neoclassical growh model (condiional bea convergence. Some works have also sudied absolue convergence, saring from he assumpion ha differen regions converge o he same seady sae, ha is, by assuming ha he srucural variables X in eq. [1] are equal among regions and hus are no included in he regression. Even hough his assumpion seems, in general, plausible wihin a counry, i does no apply o Ialy where regions are so differen in geography, insiuions and local policies. Mos of he exising works show a weak condiional convergence process and almos no absolue convergence across Ialian regions. The esimaion of he speed of convergence ( λ, ha is he rae a which less developed regions are closing he gap, is abou 1-2% per year 1. In paricular, Barro and Sala-i-Marin (1991 have found ha Ialian regions (in he period end o converge a a rae of abou 1.18%, no dissimilar from oher European counries (around 2% 2. Sala-i-Marin s (1996 esimae of λ is even lower (ranging from 1% o 1.5% according o specificaions. Paci and Saba (1998 have obained a rae of condiional convergence equal o 2.37%, while from he esimaion of Paci and Pigliaru (1995 he rae is no far from zero. Similar esimaes of oher sudies on Ialy are repored in able However, when he pre-1975 period is considered he rae of convergence is considerably higher (see, Paci and Saba, The speed of convergence of 2% per year seems o be an ubiquious consan : mos of he exising sudies a he inernaional level show esimaes of λ around his value (Mankiw, Some of he Ialian sudies (Mauro and Podrecca, 1994; Paci and Pigliaru, 1995 have made an aemp o ake ino accoun differen producion funcions among regions including dummies for macro-regions. However, he crosssecion analysis does no allow he auhors o consider a sufficien number of variables as he number of regions is oo small. 3

5 Table 1. Resuls from main empirical works on convergence of Ialian regions Rae of convergence Barro and Sala-i-Marin ( %-1.55% Sala-i-Marin (1996 1% Bianchi and Menegai ( % Cosci and Maesini (1995; % (3.8%* Di Libero ( % (0.7% afer 1975 Fabiani and Pellegrini ( % (4.02%* Ferri and Maesini ( % Mauro and Podrecca ( Paci and Pigliaru ( % Paci and Saba ( %* Cellini and Scorcu ( % Carmeci and Mauro ( % * Condiional convergence The usual esimae of around 1.5-2% implies a very low process of convergence: a ha rae, i would ake abou years o eliminae only half of iniial gap in income per worker wih respec o he seady sae! 3. The speed of convergence: he new esimae hrough panel daa 3.1. Economeric problems in cross-secion analysis In his secion, we presen he srucural equaion which is esimaed in cross-secion regressions and poin ou he economeric problems plaguing hese esimaions. As is well known (see Romer, 2001 saring from he neoclassical growh model and aking a log-linear approximaion around he seady sae, i is possible o obain he following equaion: λ [2] ln( y ln( y = e [ ln( y0 ln( y ] where y 0 represens he oupu per worker a an iniial period 0 and y is he seady sae level and λ indicaes he speed of convergence. From he sandard Cobb-Douglas producion funcion α 1 Y = K AL, he seady sae level of income per worker is equal o: ( α Y s [3] y = = A δ L n + g + g In eq. [3] he level of echnology A grows a he exogenous rae g: A = A0e, as he sandard growh model saes; by aking he logs of eq. [3] and subsiuing hem in he eq. [2], one obains he following expression: λ λ α s λ [4] ln( y ln( y0 = ( 1 e ln( y0 + ( 1 e ln + ( 1 e ln A0 + g 1 α n + g + δ Following Mankiw, Romer and Weil (1992, a number of sudies has esimaed eq. [4] wih cross-secion daa. The invesmen raio (s and growh rae of labour force (n represen he observable independen variables (aken as averages over he enire sample period, δ is he depreciaion rae (assumed consan, while hese works assume ha he unobservable variable A 0 (which reflecs he sae of echnology a ime 0 or oher counry specific effecs such as insiuions, geography ec. is common among counries, apar from a sochasic specific shock: A 0 is herefore spli ino wo componens, one is included in he consan and he oher in he error α 1 α 4

6 erm. Esimaion of he speed of convergence λ are recovered from he coefficien of ( 0 β = 1 e λ, according o he formula: λ = ln ( 1+ β τ, where τ is he ime span. denoed wih ( ln y, This esimaion procedure would be correc if echnology were a public good and could be easily applied by all counries as neoclassical growh model assumes. However, a hos of sudies (see Hall and Jones, 1998; Klenow and Rodriguez-Clare, 1997; Presco, 1998, for cross-counries evidence; Aiello and Scoppa, 2000; Di Libero, Pigliaru and Mura, 2007, for Ialian regions shows ha TFP is no homogenous across counries or regions. More imporanly, as shown by Islam (1995 and Casell Esquivel and Lefor (1996, if A 0 differs across regions and is correlaed wih oher explanaory variables (physical capial, human capial, ec., esimaes of eq. [4] are biased and inconsisen. In oher words, in cross-secion regressions here is a problem of omied variables since i is no possible o ake ino accoun he unobservable differences in echnology. As a consequence, he convergence coefficien esimaed in previous cross-secion economeric sudies is unreliable. Since he correlaion beween he omied variable A and y 0 is reasonably posiive, he omission of A deermines an upward bias in he esimae of coefficien of ln( y 0 in eq. [4] and, as a consequence, he esimae of λ will be downward biased. In less echnical erms, in order o esimae he rae of convergence correcly, i is necessary o ake ino accoun he level of seady sae of each region: in cross-secion regressions his is parly done by inroducing he socks of physical and human capial, bu his ype of analysis canno also include he unobservable level of echnology, which is a fundamenal deerminan of long-run prosperiy A preliminary es of common echnological growh across regions Dowrick and Rogers (2002 criicise he recen esimaions of cross-counry convergence equaions ha follow he approach proposed by Mankiw, Romer and Weil (1992, because of heir assumpion of a common rae of echnology growh across counries and of he use of a log-linear approximaion of he Solow growh model which leads o biased esimaions. Alernaively, Dowrick and Rogers (2002 propose a procedure which allows o es rigorously if he rae of echnology growh is uniform across counries/regions using capial sock daa raher han invesmen daa, as in Mankiw, Romer and Weil (1992. We follow Dowrick and Rogers (2002 and es a he ouse if he rae of echnological progress is common across Ialian regions. Saring from a sandard producion funcion: α 1 Y = K ( AhL α, dividing by L and aking logs we obain: ln( Y L = α ln( K L + ( 1 α ln( h + ( 1 α ln( A. Taking he derivaive wih respec o ime, we arrive a: y& k& h& [5] = α + ( 1 α + ( 1 α g y k h Using regional daa on physical and human capial socks (ISTAT, 2005, his equaion allows us o esimae α and g, he rae of echnological progress and, more imporanly, o esimae if his rae differs across Ialian regions. In a panel model we esimae: k& h& [6] zi = α + ( 1 α + ( 1 α gi + ε i k h i i where zi represens he rae of growh of per worker income of region i during period, and g i represen he regional fixed effecs. 5

7 We deermine regional capial sock on he basis of he perpeual invenory mehod using daa on oal invesmen a consan prices, by seing he depreciaion rae a δ = 4.18%, he effecive depreciaion rae as calculaed by ISTAT along he considered period. We esimae he model firs wih only capial sock (o make easier comparisons wih Dowrick and Rogers esimaions and hen wih boh physical and human capial. Resuls are shown respecively in columns 1 and 2 of Table 2. The main resul we obain is ha regional fixed effecs are no significanly differen from zero a any convenional level (p-values are 0.17 and 0.52 in column 1 and 2, respecively. This implies ha here is no heerogeneiy across regions in he growh rae of echnology. Alhough regions are very heerogeneous in he level of per worker income, he resuls obained using he mehodology of Dowrick and Rogers (2002 reassure us ha Ialian regions have a common rae of echnological growh and herefore ha following Mankiw, Romer and Weil and using log-linearizaion does no lead o biased esimaions. As robusness exercise on capial sock daa, we also use Ialian regional daa from CRENOS which sar from 1960 in order o calculae he daa on he iniial capial sock (1980. Resuls are very similar and are no repored. Table 2. Panel esimaion of he producion funcion (Dowrick and Rogers, Dependen variables: regional growh of per worker income over he period (1 (2 Only Physical capial Physical and human capial k & k 0.578*** 0.305*** (0.076 (0.076 h & h 2.221*** (0.339 Consan 0.014** *** (0.006 (0.009 Regional Fixed Effecs YES YES Observaions Number of regions R-squared F es ha all g i =0 F(19, 99 = 1.35 F(19, 98 = 0.95 p-value ha fixed effecs are equal Source: ISTAT (2005, Coni Economici Regional Anni (available on-line. Sandard errors in parenheses. ** significan a 5%; *** significan a 1% 3.3. A panel daa model The use of panel daa allows us o solve he main problems of cross-secion regressions, by esimaing a growh regression which includes he regional dummy variables o conrol for unobservable regional echnological differences. The esimaed equaion, based on eq. [4] wih he addiion of a human capial variable h, is he following: [7] ln( yi ln( y = β ln( y τ + c1 ln( si + c2 ln( ni + g + δ + c3 ln( hi + µ i + η ε i i τ + 6

8 λτ where, in paricular, β = ( 1 e ; µ ( e λτ ln( A i = 1 0 is he regional fixed effec; η is a se of ime dummies o ake ino accoun exogenous shifs over ime of he producion funcion. Using SEC95 mehodology, he Ialian Naional Saisical Insiue (ISTAT has made available in 2005 a daase of Regional Economic Accouns for he period (ISTAT, Coni Economici Regional Anni We spli he whole period ino several sub-periods of span τ. The ime span we adop is four years. In he lieraure a 5-year ime inerval is frequenly used (see Islam 1995, Casell Esquivel and Lefor, 1996, bu some auhors (e.g. de la Fuene, 2002 choose hree or wo years inervals. The advanage of shorer ime periods is he availabiliy of a greaer number of daa, bu he cos is ha cyclical or shor-run effecs can bias he resuls hrough serial correlaion of he errors. The ime span we adop is four years and, hus, we obain 7 observaions for each region ( ; ; ; ; ; ; , and he firs observaion is devoed o deermine he level 0 The level of oupu per worker i y and he growh rae 4. y is obained as he raio beween he regional value added and he oal unis of labour, s i is he raio of privae and public invesmen o GDP and n i is he growh rae of employmen. y i, s i and n i are calculaed as he geomeric average over he years in each sub-period. Variables are expressed a consan 1995 prices. Variables g and δ are considered common for all regions and periods: g is assumed o be equal o 1.44%, which corresponds o he average growh rae of labour produciviy for Ialy over ; δ is equal o 4.18% and represens he Ialian average depreciaion rae in he considered period, calculaed as he raio beween capial depreciaion and he exising capial sock 5. In line wih Bils and Klenow (2000, he procedure o deermine human capial sock is based on he earnings funcions proposed by Mincer (1974. The sock of human capial per worker rsi for region h i, is assumed o be equal o: h i = e where S i refers o he regional average years of school (in he labor force and r represens he rae of reurn for each year of schooling. We assume r = 5.7%, based on he economeric analysis carried ou by Brunello and Miniaci (1999 on reurns o school of Ialian male workers. Alernaively, we have used he rae of reurn of human capial esimaed by Ciccone (2004 (see also Ciccone, Cingano, Cipollone, In order o ake ino accoun he fac ha regions may differ in heir raes of reurn on educaion, he sock of human capial has been calculaed using he r i funcion i S h i = e, where r i represens he specific rae of reurn on schooling for region i calculaed by Ciccone (2004. However, esimaion resuls regarding human capial conribuion are no very differen from hose obained using he uniform rae of reurn and we choose o no repor hese resuls o avoid cluering he ables. In order o ensure ha differences wih previous works do no depend on he daa se used, we firsly esimae wih OLS a cross-secion regression wih he new daa. Previous resuls showing slow convergence (see able 1 are largely confirmed, since in our esimaion λ = 2.36% ( λ = 2.72% when absolue convergence is esimaed (Table 3, columns 1 and 2. For a furher comparison wih he exising lieraure, we esimae a pooled regression ignoring differences in individual regions, ha is, imposing a common inercep across regions. From Table 3 (column 4 i is eviden ha he panel naure of he daa (ha is, when daa over he enire period are divided in shor periods per se does no change he resuls. From β = we can deermine he implied speed of convergence λ = 3.40% which is similar o he esimaion obained above in he single cross-secion regression and o many oher empirical sudies on Ialian 4 The resuls are robus o changes in he ime-span τ. We have obained very similar resuls wih boh five-year and hree-year ime inerval. 5 In cross-counries sudies, because of a lack of daa on depreciaion, i is assumed ha g + δ = 5 %. 7

9 regions. This also confirms ha he division ino shor sub-periods has no inroduced business cycle disorions. A his poin, we can properly exploi he naure of panel daa in order o conrol for unobservable regional characerisics. As for he esimaion mehod, since our main concern is he correlaion beween explanaory variables and he individual specific error componen, i is no appropriae o use he random effecs mehod, which requires he error o be uncorrelaed wih he explanaory variables. Therefore, we esimae a fixed effecs model using he Leas Squares Dummy Variables esimaor (LSDV, he resuls of which are repored in Table 3. We es he sandard assumpion ha he error erms of our panel daa growh model are independen across regions. If here is cross secional dependence, hen he esimaes obained using a fixed effec esimaor will be unreliable (Phillips and Sul, A his aim we employ he es proposed by Pesaran (2004, whose saisics follows a sandard normal disribuion. Resuls show ha Pesaran's es is and, herefore, we can conclude ha he process of β-condiional convergence of Ialian regions does no suffer from cross-secional dependence (Table 3. Table 3. Cross-secion, Pooled Regression and Fixed Effecs Esimaor. Dependen variable ln ( y i ln( y i, τ Cross-secion (absolue Cross-secion (condiional Cross-secion (condiional Pooled Regression Variables convergence convergence convergence ln( y i, τ ** 0.420** ** 0.127** (0.078 (0.096 [0.119] (0.028 ( s i, ln (0.085 ( s privae ln (0.121 ( s public ln * (0.025 ( + g + δ n i ln 0.317* (0.121 ( ** [0.121] ( ** (0.015 LSDV ** ( ** ( ** (0.015 ln h i, ** (0.787 [0.984] (0.081 (0.203 Consan 1.855** ( ( [0.816] ( ** (0.229 F-Fisher R-squared Pesaran Tes (p-value in parenhesis F es ( µ i = 0 : F(19, 96=2.78** ( Implied λ 2.72% 2.36% 1.87% 3.40% 13.01% Observaions Source: ISTAT (2005, Coni Economici Regional Anni (available on-line. Noes: sandard errors in parenheses. *significan a 5% level; ** significan a 1% level. 2 The value of R is quie high. The coefficien of he lagged oupu per worker variable is highly significan and, as expeced, negaive. 8

10 The variable ( + g + δ ln n i has he expeced negaive sign and is significan. Human capial is posiive and highly significan, in line wih he new growh heory. The coefficien of he invesmen rae resuls negaive, a odds wih growh heory, bu i is no significan a 5% level. The anomalous relaionship beween invesmen and growh is no new for Ialian regions (see Galli and Onado, Accumulaion of physical capial has been heavily subsidized by he Sae and is sysemaically higher in poorer Souhern regions. However, he expendiure in invesmen is no ypically ransformed ino producive capial, especially for he public secor (see Scoppa, 2007, for a similar analysis for Ialian regions. Because of agency problems plaguing governmens, public acors migh follow opporunisic behaviour, such as corrupion, paronage or simply provide low effor o reduce coss, which creae a divergence beween he cos of invesmen and is effecive efficiency. Souhern regions are paricularly affeced by hese problems (see Golden and Picc Furhermore, privae invesmens are also heavily subsidized by he Sae, especially in he Souh. These subsidies o firms could disor invesmen choice: firms may over-inves or inves in less efficien projecs or secors (i.e., he Sae migh help declining secors or he funds could simply be embezzled by enrepreneurs. On he whole, hese consideraions help o explain he negaive relaionship beween invesmen and produciviy. In order o invesigae furher his aspec, following Carmeci and Mauro (2004 we have splied he invesmen in physical capial beween public and privae invesmens. Consisenly wih our explanaions, we find ha he privae invesmen has a posiive effec on regional growh (alhough no significan, while public capial exers a srong negaive impac (see Table 3, column 3. The wo mos sriking resuls in he LSDV esimaions are he relevan differences exising across regional economies and he high speed of convergence λ, which is equal o 13.01%. Regional fixed effecs are significan (we rejec he null hypohesis ha all µ i = 0 a 1% level. Moreover, he imporan role played by regional dummies is confirmed by he high fracion of variance explained by µ i ( As regards he speed of convergence we find ha i is abou fourfold he previous esimae which ignored regional fixed effecs. This implies ha regional economies converge very rapidly owards heir own level of seady saes. In his case, i akes abou 10 years for regions o close half of heir gap. Using fixed effecs in panel daa model, analogous resuls are obained a cross-counries level by Islam (1995 (for OECD counries λ ranges from 6.7% o 10.7% according o he esimaion mehod; Casell Esquivel and Lefor (1996 (for non-oil counries λ = 12,8%, Canova and Marce (1995 ( λ = 23% for European regions and λ =11% for OECD counries; de la Fuene (2002 ( λ = 12.7% for Spanish regions. The correcion for he omied variable problem leads o dramaic changes in economeric esimaes. The exising consensus on a very slow condiional convergence process is compleely overurned by hese resuls. The considerable differences wih previous esimaes are o be aribued o he relevance of omied variable bias and o he correlaion beween unobservable and explanaory variables. In fac, because of he posiive correlaion beween y 0 and A 0, β was upward biased in cross-secion and, herefore, λ downward biased. However, as poined ou by Casell Esquivel and Lefor (1996, growh regressions can also be affliced by he problem of endogeneiy of explanaory variables ha we shall face in he nex Secion using GMM esimaors. 6 The correlaion among fixed effecs and explanaory variables is equal o -0.89, confirming ha he random effecs mehod is no adequae. 9

11 4. Dealing wih he endogeneiy issue The hypohesis of sric exogeneiy of he regressors of equaion (7 ensures he consisency of he resuls obained hrough he use of he LSDV esimaor (Hsiao, 2003; Casell Esquivel and Lefor, Bu his condiion is hard o verify in growh regressions where he usual explanaory variables are endogenous. For example, referring o eq. [7] i is likely ha he level of invesmens and he sock of human capial are simulaneously deermined wih he regional growh rae. The problem is widespread, as Casell Esquivel and Lefor (1996 noe, exending o he inerdependence of virually all of he relevan growh relaed variables he only excepion is perhaps he morphological srucure of a counry s geography (p In order o ackle he endogeneiy issue we use a Generalized Mehod of Momen (GMM esimaor (Arellano and Bond, 1991; Blundell and Bond, reaing all explanaory variables as poenially endogenous. To his aim, we rewrie eq. [5] in dynamics erms, as follows: ln y = γ ln y τ + c ln s + c ln n + g + δ + c3 ln h + µ + η + ε [8] ( i ( i 1 ( i 2 ( i ( i i i λτ where γ = 1 + β = e. Eq. [8] is a dynamic panel model wih fixed effecs and a lagged dependen variable. I can be properly esimaed hrough he firs differences GMM (GMM-DIFF esimaor proposed by Arellano and Bond (1991. We proceed as follows. Firs of all, we accoun for naionwide shocks due o he macroeconomic cycle, by expressing all he variables in each period 20 1 as deviaions from naional means, i.e., y = ln( y ln( y. This implies ha he yearspecific inercep (he erm η 20 i= 1 drops from regression [8]. Afer obaining he deviaion form of he model, we ake he firs differences of he variables in order o address he issue of unobserved region specific effecs (herefore, he erm µ i drops from regression [8]. The esimaed equaion is he following: [9] y y = γ ( y y + c ( s s + c ( n n + c ( h h + ( ε ε τ τ 2τ 1 τ where in every period he variables are expressed as deviaions from he Ialian average. The GMM in firs differences (eq. [9] uses all he available lags of each independen variable in levels as insrumens. However, he levels are poor insrumens in growh equaions, where variables generally exhibi srong persisence. For his reason, as a es of robusness, we employ a sysem esimaor ha rescues some of he cross-secional variance los in he differences of he GMM-DIFF esimaor. The esimaion of he sysem of equaions (GMM-SYS has been suggesed by Arellano and Bover (1995 and implemened by Blundell and Bond (1998. I combines he firs differenced regression used in GMM-DIFF and he eq. [8] in levels, whose insrumens are he lagged differences of he endogenous variables. 2 τ 3 τ τ 7 Casell Esquivel and Lefor (1996 discuss he use of LSDV o esimae a dynamic growh model in Islam (1995, Knigh, Loayza and Villanueva (1993 and Loayza (1994 and argue ha his procedure yields inconsisen resuls because i does no conrol for endogeneiy. Similar conclusions are in Hsiao (2003, who sresses he special case, as ours, when N is larger han T. I is worh noing ha LSDV and GMM are comparable (hey are asympoically equivalen when he residuals of a regression are homoscedasic when regressors are sricly exogenous. Under his circumsance all he leads and lags of each explanaory variable are valid insrumens in GMM esimaions. 8 I is worh noicing ha GMM esimaors perform well in large samples and ha in our case and in all he papers focusing on Ialian regions (see, i.e., Carmeci and Mauro 2002; Di Libero, Pigliaru and Mura 2007 he crosssecions are 20 and T is generally shor. Alhough daa limiaions imply ha GMM resuls ough o be inerpreed wih cauion, our evidence confirms he oucomes obained in his paper using oher esimaion echniques (see able 3 and hose obained in he oher above-menioned sudies on he Ialian regional economic divide. 10

12 Our esimaion resuls are displayed in able 4. The firs column (Model A refers o he GMM-DIFF esimaes, while he las wo columns summarize he GMM-SYS resuls. The insrumenal variables used in every regression are he lagged values of explanaory variables. To validae our models wo ypes of ess are considered. The Sargan ess on he overindenifying resricions is conduced o assess he appropriaeness of he insrumens. Failure o rejec Ho indicaes ha he exra insrumens are valid and suppor he model s specificaion. Moreover, we repor he p-values of he ess proposed by Arellano and Bond (1991 o deec firs and secondorder serial correlaion in he residuals. If ε i are no serially correlaed, he differenced residuals should show auocorrelaion of firs-order and absence of second-order serial correlaion. Finally, in order o es he hypohesis of cross secional dependence, we re-esimae he dynamic panel models hrough a fixed effec esimaor and using Pesaran s es. Alhough Nickell (1981 bias holds, Pesaran s es remains valid for he purposes of esing for cross secional dependence (Sarafidis and De Hoyos According o Pesaran s es resuls, which we repor in he las row of able 4, he hypohesis of cross secional independence canno be rejeced. An oucome of able 4 is ha GMM esimaors perform slighly well (he p-value of Sargan es does no rejec he model s overidenifying resricions. The diagnosic ess (in paricular he p-value of he second-order auocorrelaion make GMM-SYS figures more reliable han hose obained wih he GMM-DIFF. Furhermore, GMM-SYS procedure yields a direc esimaion of he regional fixed effecs (shown in able 5 which is he key variable for deecing TFP heerogeneiy across Ialian regions. 9 However, he resuls of able 4 are comparable in all specificaions and he parameers have similar values o LSDV esimaes (see able 3. Looking a he esimaed coefficiens we noe ha, afer conrolling for heerogeneiy and endogeneiy, human capial remains posiively and significanly relaed wih he oupu per worker. The coefficien of invesmen remains negaive, albei no significan, and ha associaed wih he variable ln( n i + g + δ has he expeced sign and is significan a 5% level. These resuls confirm, o a grea exen, much of he empirical evidence derived from Solow model o explain he difference of produciviy across Ialian regions and are qualiaively similar o hose obained hrough he LSDV esimaor (see Table 3. As for he main purpose of his paper i is worh noing ha GMM esimaions confirm he resuls obained hrough LSDV esimaors. Indeed, he saisical significance (no shown of fixed effecs is sill high: regional inerceps are always significan a 1% or 5% level. Furhermore, we rejec he null hypohesis (i.e. H o : all regional fixed effecs are zero when esing he join significance: he p-value of he Wald es in model C is This is an evidence of he heerogeneiy exising across Ialian regions in he efficiency of heir economic sysems. The second ineresing oucome regards he high significance of he one-period-lagged oupu per worker, whaever he mehod of esimaion used (GMM-DIFF or GMM-SYS. For insance, he esimaion of his coefficien in model C is which implies a speed of condiional convergence equal o 11.12% per year. This rae is lower han ha 13% obained wih he LSDV esimaor, bu is sill noably higher han ha obained in all regressions which failed o conrol for specific regional effecs. I is imporan o emphasise ha passing from pooled o GMM-SYS esimaions he speed of convergence increases more han fourfold, from 2.72% o 11.12% per year. To sum up, afer conrolling for heerogeneiy and endogeneiy biases, his secion of he paper confirms ha he speed of condiional convergence esimaed for Ialian regions using GMM esimaors is exremely high [on his poin see also he papers by Carmeci and Mauro (2002 and Di 9 Besides beer diagnosic ess, we choose he GMM-SYS esimaions because hey yield direc esimaes of he regional fixed effecs. On he conrary, in GMM-DIFF he regional fixed effecs can be rescued by aking he ime average of he residuals of he firs-differenced regression (see Casell Esquivel and Lefor, These residuals are a composie error because hey include he regional fixed effecs, which we are ineresed in, and he idiosyncraic disurbance which mus be lef ou of he TFP calculaions. 11

13 Libero, Pigliaru and Mura (2007]. This means ha each region converges o is own seady sae, which differs significanly from ohers, bu i akes a very shor ime o close he gap beween he observed income level and ha associaed wih is own seady sae equilibrium. Table 4 GMM esimaes of he exended Solow model for Ialy over GMM-DIFF GMM-SYS Variables Model A Model B Model C ln( y i τ (2.32 (4.21 (4.82 ln(s (-0.87 (-1.21 ln(n+g+d (-1.65 (-2.1 ln(h (1.76 (1.93 Regional Dummies -- yes yes Speed of Convergence 12.85% 11.47% 11.12% Sargan es (p-value AR(1 (p-value AR(2 (p-value Pesaran es* (pvalue ( ( (0.115 Obs Noes: The -values are repored in parenhesis and are robus o heeroskedaciy. All variable are expressed as deviaions from he naional means. In models A, all righ-hand side variables are endogenous and insrumened by all available lags. In model B and C, he regressors are all endogenous and he insrumens are he lagged values of explanaory variables from -2 back for equaion in levels and lags from -3 back for equaion in firs differences. * The values of Pesaran es are hose obained by esimaing models A-C wih a fixed effec esimaor. 5. Fixed Effecs and TFP differences across Ialian Regions The resuls presened above indicae ha he regional fixed effecs play a crucial role in he analysis of convergence across Ialian regions. If hey are lef ou, he speed of convergence is low and esimaions are affeced by omied variables problem. On he conrary, heir inclusion ino he growh equaion allows us o conrol for heerogeneiy bias and yields high speed of condiional convergence. The aim of his secion is o deermine he fixed effecs in order o show he heerogeneiy in regional TFP and o discuss he long run implicaions of he regional efficiency divide. A measure of regional TFP can be obained from he GMMS-SYS esimaions of he λτ regional fixed effecs (Model C, ha is, by using he relaionship µ i = ( 1 e ln( A o, where A o is he proxy of he TFP (see eq. 7 and 8. In such a way, a measure of regional economic efficiency λτ is given by Ao = exp [ µ i ( 1 e ]. The values of µ i esimaed hrough GMM-SYS and he resuling figures of A o are lised in he firs wo columns of able 5, while he hird column repors a measure of TFP dispersion, 12

14 expressed as he raio beween he index of efficiency of he i-h region and ha esimaed for Lombardia, he region wih he highes values of A o. Table 5 shows ha TFP differs markedly from one region o anoher: he highes value refers o Lombardia, while he lowes is ha esimaed for Calabria. TFP disance beween hese wo regions is, in relaive erms, abou 16%. Emilia Romagna, Friul Lazio, Lombardia, Piemone, Trenino Alo Adige, Valle d Aosa and Veneo appear o be he mos efficien regions, whereas Calabria, Puglia, Campania, Sicily, Sardegna are he leas. To pu i simply, i clearly emerges ha he group wih he lowes index of efficiency comprises all he Souhern regions, whereas he regions of he Cenre and he Norh of Ialy compose a more homogenous group wih higher indexes of efficiency (able 5. These oucomes sugges i may be rewarding o ake a closer look a he relaionship beween TFP and oupu per worker, because, if hese variables are srongly correlaed, hen he gap in he level of regional produciviy can be ascribed o differences in TFP. This line of invesigaion may provide meaningful insighs because, oher hings being equal, a region can achieve higher level of income in he long run by improving elemens incorporaed in A o. From eq. 3 we expec a posiive correlaion beween TFP and Y/L. Noe ha our measure of TFP is ime invarian, being based on he fixed effecs of panel daa esimaions. Therefore, he relaionship beween A 0 and Y/L is expeced o be insensiive o he year a which i is compued and, hus, i can be explored eiher by considering Y/L daa averaged over or using daa observed in each sub-period analysed. 13

15 Table 4 Regional fixed effecs and TFP in Ialy over Regions Regional Fixed Effecs µ i exp 1 e o = λτ A Y/L Y/L (LOMB=1 Piemone Valle d'aosa Lombardia Trenino-Alo Adige Veneo Friuli-Venezia Giulia Liguria Emilia-Romagna Toscana Umbria Marche Lazio Abruzzo Molise Campania Puglia Basilicaa Calabria Sicilia Sardegna Ialy S.Dev. of TFP (A S.Dev. of Y/L in S.Dev. of Y/L in Seady Sae 4.54 Correlaion beween Y/L in and Y/L in Correlaion beween Ao and Y/L in Correlaion beween Ao and Y/L in Correlaion beween Ao and Y/L (average Correlaion beween Ao and he growh rae of Y/L Correlaion beween Ao and Human capial ( A i A max Average

16 Figure 1 The posiive relaionship beween TFP and oupu per worker (Y/L over Y/L y = x R 2 = TFP Figure 1 plos A 0 in he horizonal axis and he oupu per worker regisered in he enire span period I shows a srong posiive relaionship beween oupu per worker and TFP: he proporion of he variabiliy of oupu per worker explained only by TFP is 0.75 (figure 1. Similarly, his proporion is 0.56 in he firs sub-period considered ( and 0.81 in he las period In he ligh of he above findings, i can be argued ha he differences across Ialian regions in oupu per worker are explained by he differences in TFP: norhern regions are rich because of he efficiency of heir regional economic sysem and no because of differences in he accumulaion of physical or human capial. This evidence is in line wih he resuls of many oher auhors in similar analyses of produciviy dispariies in Ialy (Aiello and Scoppa, 2000; Di Libero, Pigliaru and Mura, 2007; Maffezzol 2006 or across counries (Easerly and Levine, 2000; Hall and Jones, 1999; Islam, Alhough one mus be cauious in comparing resuls because of differences in mehods of analysis and in ime coverage, i is worh noing ha our measure of TFP is highly correlaed (ρ=0.89 wih ha obained by Aiello and Scoppa (2000 in a developmen accouning exercise aimed o decompose he regional oupu per worker in A similar high correlaion (ρ=0.81 exiss beween our index of TFP and ha obained by Di Libero, Pigliaru and Mura (2007 using GMM-DIFF o analyse echnological convergence in Ialy over he period We can, herefore, confidenly confirm ha he persisen differences in TFP play a crucial role in explaining he dispariies of income levels in Ialy. The regional differences in TFP are similar o hose exising in he levels of oupu per worker. In , he produc per worker in Calabria was 64% of Valle d Aosa and 68% of Lombardia figures. During he period a cerain degree of convergence ook place (see secions 2 and 3, even if a he end of he period he disance in oupu levels sill remained significan. Indeed, in he oupu per worker in Calabria was less han 70% of he value observed in Valle d Aosa and in Lombardia. This evidence is summarized in Figure 2, where he regional levels of oupu per worker in (Y/L is ploed agains he levels of Y/L in , boh relaive o Ialy (he correlaion beween Y/L and Y/L is 0.8, see able 4. There is a very high degree of persisence in differences in regional produciviy: regions below he naional average level a he beginning of he period, mainly in he Souh, are sill as far behind he oher regions a he end of he period. 15

17 Figure 2 The persisence in oupu per worker gaps in Ialy. Linear relaionship beween Y/L in and in Y/L Y/L Finally, we discuss he wo key oucomes of his paper. On he one hand we have shown ha he Ialian regions converge o heir own seady sae exremely rapidly; on he oher hand TFP has been found o play a significan role in explaining differences in he oupu per worker. These resuls can be properly used o derive he level of produciviy in seady sae. We know ha in his * equilibrium y = y τ y, where y * i is he level of oupu per worker in seady sae. From he specificaion C of eq. [8], i, = i y γy τ + µ i + ε =, y, where µˆ i is * * y i can be expressed as i = ˆ µ i ( 1 γ he regional fixed effecs and γˆ is he esimaed parameer of he one-period lagged dependen variable. We use GMM-SYS esimaions of eq. [8] considering as condiioning variables he regional dummies only (able 3, model C. * The derivaion of he level of Y/L in seady sae ( y enables us o measure he difference wih he level observed a he end of he period analyzed (y 2004 and o verify if in he long run he economic divide will sill persis among Ialian regions. Boh variables (y * and y 2004 are ploed in figure 3. Two resuls, which confirm previous ones, clearly emerge: he firs refers o he wide differences in seady sae levels across regions, whereas he second illusraes how close regions are o heir own seady sae equilibrium. Moreover, i is eviden ha Ialian regional gaps are likely o persis in he long run: in equilibrium, he produciviy of norhern and cenral regions will be sysemaically higher han ha esimaed for he Mezzogiorno. 10 Anoher ineresing resul is he acual relaive posiion of each region wih regard o he seady sae level of produciviy. We find a sharp difference in he behaviour of rich and poor Ialian regions. In fac, figure 3 illusraes ha many regions of he Norh and Cenre of Ialy are behind he equilibrium of seady sae (hey have sill o grow in order o fill heir gap of income, whereas he conrary holds for 5 Souhern regions (Molise, Basilicaa, Calabria, Sicily and Sardegna. In oher words, in equilibrium, he level of income of hese regions is even lower han ha measured in 2004 and his means, in he absence of any srucural shock, ha hese regions will face he risk in he near fuure of a furher process of impoverishmen. 10 This resul is parially confirmed by he sandard deviaion of labour produciviy which increases from 3.26 o 4.54 passing from he observed value of income per worker in 2004 o ha esimaed for seady sae (able 4. 16

18 Figure 3 A comparison beween he level of labour produciviy observed in 2004 and he seady sae esimaed level (daa in logs Y/L 2004 Y /L in Seady Sae Codes: 1=Piemone, 2=Valle d'aosa, 3=Lombardia, 4=Trenino-Alo Adige, 5=Veneo, 6=Friuli- Venezia Giulia, 7=Liguria, 8=Emilia-Romagna, 9=Toscana, 10=Umbria, 11=Marche, 12=Lazio, 13=Abruzzo, 14=Molise, 15=Campania, 16=Puglia, 17=Basilicaa, 18=Calabria, 19=Sicilia, 20=Sardegna 5. Concluding remarks In his paper we apply a panel daa approach o invesigae he neoclassical convergence and he exisence of echnological heerogeneiy across Ialian regions. By using a new daase from ISTAT covering he period , we show ha he esimaion of a sandard cross-region regression produces a speed of condiional convergence of 2,36% per year. From an economic poin of view, he slow convergence in cross-secion sudies depends on he fac ha here appears o be almos no negaive correlaion beween he iniial oupu level and he growh rae. Since he level of echnology is no conrolled for, he seady sae levels of rich and poor regions are quie similar. Therefore, i appears ha poor regions are growing a a very slow rae wih respec o heir disan arge, resuling in slow convergence. Our cross-secion resuls regarding slow convergence process are analogous o hose of he considerable body of lieraure explaining he economic divide in Ialy, bu, as in Casell Esquivel and Lefor (1996 and Islam (1995, we argue ha much of his work is affeced by a misspecificaion of he growh regression due o problems of omied variables and endogeneiy. By using differen panel daa mehods o conrol for echnological heerogeneiy and for endogeneiy, we find a noably higher speed of condiional convergence. Our chosen economeric specificaion of he growh model is obained by referring o he GMM-SYS esimaor proposed by Arellano and Bover (1995. In his specificaion, he speed of condiional convergence is 11.12% per year. The second key resul of his paper is he high significance of regional fixed effecs which we use o measure he echnological level observed in each region over he period under scruiny. The evidence of a high β-condiional convergence and of marked differences in he aggregae producion funcions a regional level sugges ha regions converge in a very rapid way o heir own seady sae. The differences observed in he daa are no due o he differen locaions of he regions along he same ransiional dynamic pah, bu raher o very differen seady saes. However, hese findings are disurbing from a policy perspecive because even if, on one hand, regions are converging speedily, on he oher hand hey predic ha, in he long run, regions will reach very differen income levels. I is confirmed ha he norhern and cenral areas of he 17

19 counry will converge o a much higher level of income han ha achievable by he souh of Ialy. In oher words, wihou srucural shocks which provoke shifs of he aggregae regional producion funcion, he Ialian economy will be characerised by a dualisic srucure also in he long-run equilibrium. If he gaps beween regions persis in he saionary level of income, hen he crucial quesion will be o invesigae he deerminans of such differences. This sudy clearly confirms ha facor accumulaion in Ialy does no play an imporan role in deermining regional developmen. On he conrary, i has been shown ha TFP no only significanly differs region-by-region, bu also ha i is he key variable in explaining regional divide in he seady sae equilibrium. The evidence is ha he income per capia is high in he norhern regions, which are hose recording he highes index of economic efficiency, and low in he Souhern regions wih he lowes values of TFP. Therefore, his paper suggess ha in order o foser regional growh in Ialy, improvemens of convenional variables (i.e., invesmens in physical and human capial should no be a prioriy in he policy agenda; effors mus raher be devoed o all he facors (economic, social and poliical which ener ino he regional TFP and deermine he efficiency of he local economic sysems. 18