Abstract
The study of regional growth has been dominated by two broad and contrasting theoretical approaches regarding regional convergence. According to the first, market forces will lead to a general convergence of per-capita incomes across an integrated space economy over time. This approach is labelled as ‘neoclassical regional growth theory’ and its premises are based upon the standard growth model, as outlined by the pioneering work of Solow (1956) and Swan (1956). Using a general equilibrium framework these models predict that disparities in per-capita incomes across regions are unlikely to occur or, at least, to be persistent, thus creating a pattern of convergence towards a unique level of per-capita income. By contrast, there is a large body of theoretical and empirical work, known as the ‘post-Keynesian approach’, which supports the argument that regional disparities in per-capita incomes are permanent and self-perpetuating and therefore divergence in per-capita incomes is the most likely outcome. Representative models can be found in the work of Myrdal (1957), Perroux (1950, 1955) and Kaldor (1967, 1970 and 1972). This chapter outlines the major approaches to regional growth, as put forward by the neoclassical and post-Keynesian schools of thought. Throughout this and subsequent chapters more emphasis is placed upon the neoclassical model, for two reasons. First, the neoclassical model offers both a theoretical explanation and testable predictions concerning the possibility of convergence in per-capita incomes across regions. Indeed, most of the conceptual definitions of regional convergence used in empirical studies derive directly from the neoclassical model. Second, the vast majority of empirical literature has in fact tested the neoclassical model rather than alternative models.
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Notes
- 1.
- 2.
Income and output are used interchangeably. Nevertheless, throughout this and subsequent chapters output instead of income is used. Moreover, the hypothesis of regional convergence in a neoclassical context is related to output per-worker rather than income per-capita.
- 3.
Nevertheless, this is valid only in the short-run, since reproduction can and does change in the long-run in response to changes in income levels. However, the neoclassical model does not include a theory of population change. See also McCombie (1988a).
- 4.
A dot over a variable indicates its rate of change with respect to time.
- 5.
For a more detailed analysis of savings behaviour in the neoclassical model, see Cesaratto (1999).
- 6.
In a closed economy, saving equal investment, namely the only use of investment is to accumulate physical capital. This assumption might be considered as unrealistic in a regional context, where regions are by definitions open economies. Feldstein and Horioka (1980), however, have shown that the coincidence of investments and savings is empirically valid across regions.
- 7.
Solow (1957) suggested that gross output per man hour in the US manufacturing doubled between 1909 and 1949. However, only 12.5 % of this trend is attributable to increases in capital per worker while the remaining 87.5 % was the outcome of improvements in technology. Solow’s model implies that in the absence of any improvements in technology, output per worker in the long-run will be constant while total output increases at the same rate as the growth of population.
- 8.
The properties of the neoclassical model can be shown using the theory of optimal control (Novales et al., 2010). Consider the production function:\( {{y}_{{i,t}}} = f({{k}_{{i,t}}}) \), where \( {{y}_{{i,t}}} = {{Y}_{{i,t}}}/{{A}_{{i,t}}}{{L}_{{i,t}}} \)and \( {{k}_{{i,t}}} = {{K}_{{i,t}}}/{{A}_{{i,t}}}{{L}_{{i,t}}} \). Let \( {{L}_{{i,t}}} = {{L}_{{i,0}}}{{e}^{{nt}}} \), \( {{A}_{{i,t}}} = {{A}_{{i,0}}}{{e}^{{gt}}} \), \( {{\dot{L}}_{{i,t}}}/{{L}_{{i,t}}} = n \) and \( {{\dot{A}}_{{i,t}}}/{{A}_{{i,t}}} = g \), then \( A{{\dot{L}}_{{i,t}}}/A{{L}_{{i,t}}} = n + g \). Given that\( {{Y}_{{i,t}}} = {{C}_{{i,t}}} + {{S}_{{i,t}}} \Rightarrow {{S}_{{i,t}}} = {{Y}_{{i,t}}} - {{C}_{{i,t}}} \), \( {{\dot{K}}_{{i,t}}} = {{I}_{{i,t}}} - \delta {{K}_{{i,t}}} \), where \( {{I}_{{i,t}}} \) is net investment, and \( {{S}_{{i,t}}} = s{{Y}_{{i,t}}} {{S}_{{i,t}}} \equiv {{I}_{{i,t}}} \), then \( {{\dot{K}}_{{i,t}}} = {{S}_{{i,t}}} - \delta {{K}_{{i,t}}} \Rightarrow {{\dot{K}}_{{i,t}}} = {{Y}_{{i,t}}} - {{C}_{{i,t}}} - \delta {{K}_{{i,t}}} \). Dividing by \( {{A}_{{i,t}}}{{L}_{{i,t}}} \) yields: \( {{\dot{K}}_{{i,t}}}/{{A}_{{i,t}}}{{L}_{{i,t}}} = {{y}_{{i,t}}} - {{c}_{{i,t}}} - \delta {{k}_{{i,t}}} \Rightarrow {{\dot{K}}_{{i,t}}}/{{A}_{{i,t}}}{{L}_{{i,t}}} = f({{k}_{{i,t}}}) - {{c}_{{i,t}}} - \delta k \), where \( {{c}_{{i,t}}} = {{C}_{{i,t}}}/{{A}_{{i,t}}}{{L}_{{i,t}}} \) and \( {{\dot{k}}_{{i,t}}}/{{k}_{{i,t}}} = {{\dot{K}}_{{i,t}}}/{{K}_{{i,t}}} - A{{\dot{L}}_{{i,t}}}/A{{L}_{{i,t}}} \). Therefore, \( {{\dot{k}}_{{i,t}}} = {{\dot{K}}_{{i,t}}}/A{{L}_{{i,t}}} - (n + g){{\dot{k}}_{{i,t}}} \)or \( {{\dot{k}}_{{i,t}}} = f({{k}_{{i,t}}}) - {{c}_{{i,t}}} - (n + g + \delta ){{\dot{k}}_{{i,t}}} \). The representative household is assumed to maximize total utility, which in each period is weighted by the size of population and the rate of time preferences, ρ, thus, \( Max\int_0^T {{{e}^{{ - \rho t}}}u(c)dt} \), subject to \( {{\dot{k}}_i} = f({{k}_i}) - {{c}_i} - (n + g + \delta ){{\dot{k}}_i} \), with \( {{k}_i}(0) = {{k}_{{i,0}}} \), \( {{k}_i}(T) = {{k}_{{i,T}}} \). The Hamiltonian associated with the problem is: \( H = {{e}^{{ - \rho }}}u(c) + \mu [\;f({{k}_i}) - {{c}_i} - (n + g + \delta ){{k}_i}] \), with the necessary conditions \( \partial H/\partial {{c}_i} = 0 \Rightarrow {{e}^{{ - \rho t}}}{{u\prime}_{{{{c}_i}}}} - \mu = 0 \) and \( \partial H/\partial {{k}_i} = - \dot{\mu } \Rightarrow - \mu [\;f({{k}_i}) - (n + g + \delta )] \). Given that \( \mu = {{e}^{{ - \rho t}}}{{u\prime}_{{{{c}_i}}}} \), the shadow price of capital equals the present value of the marginal utility of consumption. This condition must hold at all time t: \( \dot{\mu } = - \rho {{e}^{{ - \rho t}}}{{u\prime}_{{{{c}_i}}}} + {{e}^{{ - \rho t}}}{{u\prime\prime}_{{{{c}_i}{{c}_i}}}}\dot{c} \). The equation of motion for \( {{\dot{c}}_i} \) is \( {{\dot{c}}_i} = (\rho + n + g + \delta - {{f\prime}_{{{{k}_i}}}})({{u\prime}_{{{{c}_i}}}}/{{u\prime\prime}_{{{{c}_i}{{c}_i}}}}) \). Given that \( {{u}_{{{{c}_i}}}} > 0 \), then \( {{\dot{c}}_i} = 0 \)only when \( {{f}_{{{{k}_i}}}} = \rho + n + g + \delta \). Under the neoclassical conditions for the marginal productivity of \( {{k}_i} \) (\( {{f}_{{{{k}_i}}}} \;>\; 0 \), \( \;{{f}_{{{{k}_i}{{k}_i}}}} \;<\; 0 \) and \( f(0) \to \infty \)) there is a unique value of capital per-worker (\( {{\hat{k}}_i} \)), such that \( {{f}_{{{{k}_i}}}}({{\hat{k}}_i}) = \rho + n + g + \delta \).
- 9.
Sometimes referred to as the ‘output-technology’ ratio since technological progress is assumed to be of the labour-augmented form, i.e. labour becomes more productive when the level of technology is higher, and AL is the ‘effective’ amount of labour used in production. For a more detailed discussion see Hahn and Matthews (1964).
- 10.
For a more detailed analysis see Appendix I.
- 11.
Equation (2.15) can be derived by taking a first order Taylor expansion of the right hand side of equation (2.13) around the steady-state value of the effective capital-labour ratio.
- 12.
If a = 1, then the property of convergence is not apparent. This is an outcome implied by the various models of Endogenous Growth Theory, which will be examined in more detailed in Chapter 3.
- 13.
Richardson (1973c) notes that it is often permissible, if incomplete, to treat a national economy as closed. This assumption, however, can never be made for regional economies.
- 14.
Tselios (2009) examines empirically the relation between income convergence and regional inequalities across the European regions.
- 15.
- 16.
- 17.
North (1955) initially articulated the idea of regional growth propelled by exports. See also Tiebout (1956a).
- 18.
- 19.
- 20.
Given that \( \ln \frac{{{{Y}_{{i,t}}}}}{{{{A}_{{i,t}}}{{L}_{{i,t}}}}} = \ln \frac{{{{Y}_{{i,t}}}}}{{{{L}_{{i,t}}}}} - \ln {{A}_{{i,t}}} \)and \( {{A}_{{i,t}}} = {{A}_0}{{e}^{{gt}}} \Rightarrow \ln {{A}_{{i,t}}} = \ln {{A}_0} + gt \), then substituting equation (2.23) into (2.19) yields:
$$ \ln \left[ {\frac{{{{Y}_{{i,t}}}}}{{{{L}_{{i,t}}}}}} \right] = \ln {{A}_0} + gt - \frac{{\alpha + \beta }}{{1 - \alpha - \beta }}\ln (n + g + \delta ) + \frac{\alpha }{{1 - \alpha - \beta }}\ln ({{s}_k}) + \frac{\beta }{{1 - \alpha - \beta }}\ln ({{s}_h}). $$ - 21.
It is not uncommon, however, in most empirical studies for the rates of depreciation and technological progress to be considered as being constant for all the economies included. Indeed several authors (e.g. Yao, 1999; Zhang and Yao, 2001; Fingleton and Fischer. 2010) assume that\( (g + \delta ) = 0.05 \).
- 22.
A cumulative process in can be generated by the demand–supply interaction on the markets for goods and labour in advanced-core regions. Investment in core regions causes further expansion, increasing in-migration and local demand, which in turn brings new investment and further development.
- 23.
The concept of cumulative causation was first introduced in Myrdal’s book: An American Dilemma (1944). See Streeten (1998) for further details.
- 24.
- 25.
Friedmann (1969, 1972) provides a broader version of the cumulative causation model by introducing ‘core-periphery’ relations in the context of a ‘colonial’ system.
- 26.
Perroux’s theory of growth poles has been used extensively in regional economics and economic geography (Hayter, 1997). However, the transmission of the ‘growth pole’ concept into geographical rather than abstract economic space is attributed to Boudeville (1966) who has defined a regional ‘growth pole’ as ‘a set of expanding industries located in an urban area and inducing further development of economic activity throughout its zone of influence’ (p. 11). For a more detailed review on the concept of ‘growth poles’ see Lasuen (1969), Parr (1999a,b).
- 27.
- 28.
- 29.
- 30.
Spatial externalities is one of the earliest concepts and is extensively used in economics and economic geography, e.g. Weber (1929), Lösch (1938, 1954), Harris (1954), Lampard (1955), Leser (1948), Isard (1954, 1956), Nicholson (1956), Moses (1958), Tiebout (1961), Winnick (1961), Marcus (1965), Moses and Williamson (1967), Alonso (1968), Webber (1972), Henderson (1974, 1982), Richardson (1969), Mulligan (1984), Weiss (1972), Carlton (1983), Dicken and Lloyd (1990), Phelps (1992). More recently theoretical aspect of agglomeration are suggested by Glaeser (1999), Netzer (1992), Crampton and Evans (1992), McCann (1995), Dekle and Eaton (1999), Quigley (1998).
- 31.
Empirical studies on spatial externalities are extensive and usually pay attention to industry-specific models without considering regional growth and convergence explicitly. The majority of empirical literature is concentrated on the US experience, e.g. Duffy (1987), Henderson (1994, 2003), Henderson et al. (1995), Ellison and Glaeser (1997, 1999), Pascal and McCall (1980), Carlino and Voith (1992), Desmet and Fafchamps (2005) while similar studies were conducted for Sweden (Åberg, 1973; Braunerhjelm and Borgman, 2004), Germany (Gross, 1997), Japan (Kawashima, 1975; Nakamura, 1985), Malaysia (Bhattacharya, 2002), Nepal (Fafchamps and Shilpi, 2005), Canada (Soroka, 1994; Baldwin et al., 2008), Korea (Henderson et al., 2001a); Poland (Bivand, 1999), India (Mitra, 1999), Italy (Mion, 2004), the UK (Graham, 2001), Spain (Viladecans-Marsal, 2004; Alonso-Villar et al., 2004), Mexico (Hanson, 1996), Holland (de Vor and de Groot, 2010) and Finland (Mukkala, 2004).
- 32.
The Heckscher-Ohlin (factor endowment) theory predicts that an economy with abundance in skilled labour relative to unskilled labour will expand production and exports of goods that are relatively skill-intensive in their production, when trade between economies is allowed. Increased specialisation in the comparative advantages sectors would eventually become an increased agglomeration through space. Indeed, ‘[…] international trade theory cannot be understood except in relation to and as a part of the general location theory’ (Ohlin, 1993, p. 97).
- 33.
This leads to formation of ‘clusters’; a notion that emphasises synergy, a creative milieu, innovation and quality of life and urban environment for attracting highly skilled labour.
- 34.
- 35.
Nevertheless, Setterfield (1997) argues that it is possible to extend Kaldor’s model to allow for the limits to increasing returns, the dynamic of structural change, growth reversal and relative decline. This argument has caused a considerable debate (e.g. Toner, 2001; Argyrous, 2001; Setterfield, 1998, 2001) while Alexiadis and Tsagdis (2010) attempt to examine it empirically.
- 36.
- 37.
- 38.
Richardson (1978a,b) attempts a formulation of cumulative causation in more narrow terms; it does not include an explicit demand function for exports nor any kind of balance of payment conditions.
- 39.
Thirlwall (1980a) expressed this relationship in almost identical terms, namely that regional growth rates in balance of payments equilibrium approximates to the growth of regional exports divided by the regional income elasticity of demand for imports (‘Thirlwall’s Law). See Gibson and Thirlwall (1993).
- 40.
In algebraic terms Verdoorn’s Law is specified as follows: \( {{\dot{e}}_i} = {{a}_i} + \lambda {{\dot{q}}_i} \), where \( {{\dot{e}}_i} \) is the rate of employment growth in a region, \( {{a}_i} \) is the rate of autonomous productivity growth, \( {{\dot{q}}_i} \)is the rate of output growth and λ is the Verdoorn coefficient.
- 41.
Verdoorn’s Law has been tested across a number of countries, e.g. for the UK (Stoneman, 1979), Australia (Whiteman, 1987), Holland (Fase and van den Heuvel, 1988; Fase and Winder, 1999), Turkey (Bairam, 1991), Greece, (Drakopoulos and Theodossiou, 1991) the US (McCombie, 1983; 1985, Atesoglu, 1993); Japan (Wulwick, 1991); China (Hansen and Zhang, 1996), Eastern Europe (Gomulka, 1983), Columbia (Rivas, 2008) and in various regional contexts, e.g. for the USA states (Casetti, 1984; Casetti and Jones, 1987; McCombie and deRidder, 1983; 1984, the EU regions (Fingelton and McCombie, 1998; Dall’erba et al., 2008; Alexiadis and Tsagdis, 2010), the UK regions (Hildreth, 1989), the regions of Japan (Casetti and Tanaka, 1992), the Greek regions (Alexiadis and Tsagdis, 2006b). In general, the majority of the empirical literature seems to confirm the validity of this relation both across countries and regions.
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Alexiadis, S. (2012). Neoclassical and Post-Keynesian Theories of Regional Growth and Convergence/Divergence. In: Convergence Clubs and Spatial Externalities. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31626-5_2
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