1 Economic Convergence. Parametric Methods Regional Economic Policy Prof.ssa Cristina Brasili A. Y Regional Economic Policy Prof.ssa Cristina Brasili A. Y

2 1.Cohesion, integration and convergence 2.Theoretical model of convergence and divergence 3.Convergence measures 4. Beta and sigma convergence Economic Convergence. Parametric Methods - Cristina Brasili

3 Cohesion is a political object supported by the integration and convergence process and it stimulates the objectives of convergence and integration 1. Cohesion, integration and convergence Cohesion CONVERGENCE INTEGRATION Economic Convergence. Parametric Methods - Cristina Brasili

4 Cohesion is at the base of the first social (and second in the EU) policy of European Union Cohesion without convergence remains a theoretical concept The institutional cohesion has to be high to lead and to improve the cohesion 1. Cohesion, integration and convergence Economic Convergence. Parametric Methods - Cristina Brasili

5 The convergence is the process utilized to measure the cohesion It will be convergence when there is a significant reduction among regions and countries in the disparities of social and economic development We could speak of convergence only in the case of increasing development and wellbeing for all the regions/countries nor reducing the richness for the most developed regions. 1. Cohesion, integration and convergence Economic Convergence. Parametric Methods - Cristina Brasili

6 The theory of convergence showing the pattern towards the cohesion The regional/national economies converge if the less development economies growth at the higher rate than the more developed ones because of market mechanism and/or public policies 2. Theoretical model of convergence and divergence Economic Convergence. Parametric Methods - Cristina Brasili

7 -Fordism’s industrialization (Hoffmann 1958, Hamilton 1986) -«Light» industrialization (SMES’s enterprises) (Garofoli 1991, Piore e Sabel 1984, Putnam, Leonardi e Nanetti 1993) -Development’s poles and relevance of public sector (Perroux 1959, Carrello 1989, Saraceno 1977) -at the opposite the liberalization of the markets (Olson 1982, Hirsch 1976) -Fundamental role of the endogenous factors for the development by the local governments (Garofoli 1992, Nanetti 1987) 2. Theoretical model of convergence and divergence Economic Convergence. Parametric Methods - Cristina Brasili Convergence scenarios

8 -The regions could have some spillovers however it prevails the difficulties to have the convergence and it is born a vicious circle (by the economist Myrdal who studied the “cumulative circular causality”, 1957) - The Marxist economists support the hypothesis that in the capitalistic economies it is impossible to reach the convergence (Frank 1974, Holland 1976). -divergence model center-pherifery (Rokkan e Urwin 1982 e 1983, Tarrow 1977) 2. Theoretical model of convergence and divergence Economic Convergence. Parametric Methods - Cristina Brasili Divergence scenarios

9 How we can measure the convergence process? Theory of growth is the base of the measure of the economic convergence Neo-classical theory and endogenous theory are the theoretical frameworks for analysis of convergence 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical model

10 Neo-classical theory essentially argues that across regions with similar preferences and access to similar technologies, poorer regions will catch up wealthier regions and the marginal return from capital in the latter begins to diminish. Poorer regions, since they have less capital will attract mobile investment because of the relatively higher returns that they offer. Labour will migrate from regions where wages are low to those where wages are higher pushing up wages in the former and reducing them in the latter 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 1.

11 The standard neo-classical model of economic growth was formulated in 1956 by Solow and independently by Swan. The Solow-Swan model (1956) predicts that countries or regions with the same preferences and technology will converge to identical levels of per capita income reaching a steady state equilibrium. Constant marginal returns is one of the hypothesis 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 2.

12. The basic structure of the neo-classical model Aggregate production function: Yt =F(Kt,Lt ) where Yt : output, Kt : capital stock, Lt : labour force One sector Homogeneous output Infinitive mixture of the productive factors Interest rate does not condition the saving but it changes the ratio capital/output Initially there isn’t technological progress Neo-classical approach 3.

13 The Solow-Swan model (1956) predicts that countries or regions with the same structural parameters: saving rate, population growth rate (and then technology) will converge to the same steady state equilibrium. From that point the economies will growth at the same rate Neo-classical approach 4

14 The Solow-Swan model starting from a generic production function Y=F(L,K) It has to satisfy the three properties: Positive and diminishing marginal returns of factor inputs a. positive and diminishing marginal returns of capital and positive diminishing marginal returns of labour 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 5.

15 F() has constant returns to scale b. for every c. Inada conditions; 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 6.

16 THE NEOCLASSICAL SOLOW-SWAN GROWTH MODEL by Sarantis Kalyvitis Pp. 4-6 For the methodological details to derive the The law of motion for the capital stock in per capita terms becomes: (FUNDAMENTAL DIFFERENTIAL EQUATION FOR CAPITAL STOCK ACCUMULATION IN THE SIMPLE NEOCLASSICAL SOLOW-SWAN MODEL) 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 6.

17 L’incremento netto nello stock di capitale in un certo punto eguaglia gli investimenti meno il deprezzamento del capitale (indicheremo con un punto sopra una lettera la differenziazione rispetto al tempo) (2) dove La (2) determina la dinamica del capitale data una certa tecnologia e una certa forza lavoro. Si assume che la crescita della popolazione sia esogena e costante Normalizzando a 1 il numero di persone al tempo 0 e l’intensità di lavoro, la popolazione e la forza lavoro al tempo t sono uguali a Il modello di crescita neoclassico (Solow-Swan)

18 Sulla base della funzione di produzione neoclassica (1) e delle premesse appena enunciate deriviamo l’equazione fondamentale del modello di Solow- Swan e l’equazione per lo steady state. Analizziamo passaggio per passaggio. Il modello di crescita neoclassico (Solow-Swan) La condizione (b) dei rendimenti costanti di scala implica che l’output si può riscrivere come dove è il rapporto capitale/lavoro mentre è il prodotto pro-capite; da cui la funzione di produzione si può esprimere nella forma intensiva come Utilizziamo la condizione e differenziamo rispetto a K, fissato L, e rispetto a L, fissato K, verificando così che la produttività marginale dei fattori è data da

19 Il modello di crescita neoclassico (Solow-Swan) Consideriamo ora il comportamento dinamico di un’economia descritta da una funzione di produzione neoclassica. Dividendo ambo i membri dell’equazione (2) per L si avrà Possiamo scrivere come funzione di k usando dove come abbiamo visto Sostituendo questa quantità otteniamo (3) L’equazione differenziale fondamentale del modello di Solow-Swan

20 Steady-State Equilibrium At the steady state the rate growth is constant 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 6.

21 Il modello di crescita neoclassico (Solow-Swan) Modelli di sviluppo e misura della convergenza. Un’analisi delle regioni europee con particolare attenzione a quelle in ritardo di sviluppo. Lo Steady-State k è costante nello steady state (si può dimostrare facilmente) y e c sono anch’esse costanti con valori pari a rispettivamente Ne consegue che nel modello neoclassico, le quantità pro capite k, y e c non crescono nello stato stazionario e che i livelli delle variabili K, Y e C crescono allo stesso tasso di crescita della popolazione n.

22 4. Convergenza assoluta e condizionale Modelli di sviluppo e misura della convergenza. Un’analisi delle regioni europee con particolare attenzione a quelle in ritardo di sviluppo. Convergenza Assoluta C’è una tendenza alla convergenza tra le economie? Considerando un insieme di economie chiuse, che sono strutturalmente simili cioè che hanno gli stessi valori dei parametri ed hanno la stessa funzione di produzione f() avranno anche gli stessi valori k* e y* per lo steady-state: (Da questo momento indicheremo un tasso di crescita di una variabile come gamma e il pedice che indica la variabile) Se l’unica differenza tra le economie è il livello iniziale di k(0) senza dubbio il tasso di crescita di k,, è sicuramente più alto per le economie con livello iniziale di k(0) più basso.

23 Absolute Convergence Catching Up Absolute convergence, which can be defined as a process in which economies with lower capital per worker grow faster than economies with higher capital per worker. Growth Rate> 0 K(0) poors K(0)richs k* Growth Rate< 0 s*f(k)/k 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili Neo-classical approach 7.

24 Steady-State with technology parameter Robinson (1938) and Uzawa (1961) also include A(t) a technological index labor augmenting: output growths as the labour stock k and A(t) growth at the same rate x, LA(t) is the effective quantity of labour ( labour per its efficiency) dove x è il tasso di crescita del progresso tecnologico Equation at steady state 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili

25 Conditional Convergence However, when we take into account empirical observations, the hypothesis of absolute convergence is in breach of reality for the high capital per worker economies also achieve faster GDP growth per worker. K(0) poors K(0)richs k*poors s poors *f(k)/k s richs *f(k)/k k*richs 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili

26 Beta convergence 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili

27 Beta convergence 3. Convergence measures Economic Convergence. Parametric Methods - Cristina Brasili

28 5. Sigma convergenza The concept of σ-convergence Dalgaard and Vastrup (2001), Lucke (2008), Miller and Upadhyay (2002) also comes from neoclassical growth theory. The σ-convergence is defined as lowering of variance of real GDP per capita logarithm among economies in time.

29 Sigma Versus Beta-convergence in EU28: do they lead to different results? KATEŘINA DVOROKOVÁ, Mathematical Methods in Finance and Business Administration Button K., Pentecost E., Regional Economic Performance within the European Union Edward Elgar, 1999 da pag 84 a pag 100 Convergence issues in the EU ed. by W. Meeusen J. Villaverde da pag 62 a pag 82 Convergence measures: Beta and Sigma convergence

Sigma Versus Beta-convergence in EU28: do they lead to different results? KATEŘINA DVOROKOVÁ, Mathematical Methods in Finance and Business Administration Button K., Pentecost E., Regional Economic Performance within the European Union Edward Elgar, 1999 da pag 84 a pag 100 Convergence issues in the EU ed. by W. Meeusen J. Villaverde da pag 62 a pag 82 To deepen THE NEOCLASSICAL SOLOW-SWAN GROWTH MODEL Sarantis Kalyvitis Italian L’approccio parametrico alla convergenza economica, Maria Sassi da pag. 31 a pag. 45 in Cambiamenti strutturali e convergenza economica nelle regioni dell’Unione europea a cura di Cristina Brasili, Clueb Bologna, 2005 References Economic convergence - Cristina Brasili