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Empirical Measures of Regional Convergence

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Convergence Clubs and Spatial Externalities

Part of the book series: Advances in Spatial Science ((ADVSPATIAL))

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Abstract

The theoretical analysis of convergence presented thus far has examined the circumstances in which an economy converges towards an equilibrium level of output per-worker or a steady-state rate of growth. The possibility that groups of economies are likely to converge towards the same steady-state (absolute convergence) or towards different steady-states (conditional convergence) has also been examined. In discussing club convergence, the possibility of convergence towards a leading economy has also been addressed. In reality economies are not in equilibrium and are subject to all manner of shocks at different points in time. Therefore, an important question arises: ‘how is possible to test for convergence, when the steady-state is never achieved?’ The approach, in practice, is to direct empirical measures of convergence towards the process of convergence, rather than the equilibrium outcome.

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Notes

  1. 1.

    Standard deviation (\( {{\sigma }_{{i,t}}} \)) is measured as \( {{\sigma }_{{i,t}}} = \sqrt {{\frac{1}{n}\sum\limits_{{i = 1}}^n {{{{\left[ {\log \left( {\frac{{{{y}_i}}}{{{{y}^{ * }}}}} \right)} \right]}}^2}} }} \), where \( \log {{y}^{ * }} \equiv \frac{1}{n}\sum\limits_{{i = 1}}^n {\log {{y}_i}} \) (Dalgaard and Vastrup 2001). σ-convergence is signified when \( {{\sigma }_{{i,T}}}\ <\ {{\sigma }_{{i,0}}} \) or more generally, when \( {{\sigma }_{{i,t}}} \to 0 \), as \( t \to T \), where \( T \) is a terminal time. The coefficient of variation (\( {{c}_{{i,t}}} \)) is defined as the ratio of the standard deviation to the mean (\( \mu \)):\( {{c}_{{i,t}}} = \frac{{{{\sigma }_{{i,t}}}}}{{{{\mu }_{{i,t}}}}} \)

  2. 2.

    According to the ‘Williamson’s Law’, regional disparities are expected to stronger during the early phases of an integration process and they slowdown or even reverse as this process evolves (Camagni and Capello 2010).

  3. 3.

    Fisch (1984), also, supports, and extends Williamson’s argument, as by considering regional inequalities in terms of personal incomes across the US states in comparison to the national average.

  4. 4.

    Tondl (1999) attributes this pattern to the fact that throughout the 1980s several less prosperous members have jointed the EU.

  5. 5.

    Examining σ-convergence in terms of output per-capita across the EC regions over 1980–1989, Neven and Gouyette (1995) reach similar conclusions and argue that the ‘northern’ regions are more homogenous in term of per-capita output than the regions located in the ‘south’ of Europe. Fagerberg and Verspagen (1996) aptly note that over the period 1980–1990 the gap in per capita GDP between the richest and poorest EU region is roughly the same order as the difference between Germany and a developing country, such as Costa Rica or South Africa.

  6. 6.

    An interest in convergence can also be found to the writings of ‘classical’ economists, such as Ricardo, Marx and Malthus. In particular, for Ricardo the process of growth leads to convergence due to decreasing returns in agriculture and no institutional or technological change. Conversely, Marx and Malthus argue that growth exaggerates an already established unevenness leading to divergence. A more detailed discussion can be found in Boyer (1997).

  7. 7.

    Barro and Sala-i-Martin (1995) claim that this term essentially represents the steady-state growth rate.

  8. 8.

    The error term is assumed have zero mean and constant variance (uncorrelated with the initial level of output per-worker).

  9. 9.

    The time at which output per-worker (\( {{y}_{{i,t}}} \)) is halfway between the value during the initial year and the ‘steady-state’ (\( {{y}^{*}} \)) satisfies the condition \( {{e}^{{ - \beta t}}} = \tfrac{1}{2} \). As T gets larger, the effect of the initial level of output per worker tends to decline.

  10. 10.

    The convergence coefficient is bounded to the sign of β, implied by \( \log ({{y}_{{i,t}}}) = (1 - {{e}^{{ - \beta t}}})\log ({{y}^{*}}) + {{e}^{{ - \beta t}}}\log ({{y}_{{i,0}}}) \).

  11. 11.

    Reconciling \( {{b}_1} \) with the expression in Eq. 5.3 involves substitution of the absolute value of \( {{b}_1} \) into the expression for the rate of convergence (β).

  12. 12.

    A notable example of a ‘growth miracle’ consists of the Japanese economy during the post-war era and some South East Asian economies during the 1980s and early 1990s.

  13. 13.

    Arbia et al. (2008) note the absolute convergence model can be thought as an approximation of the original Solow-Swan model.

  14. 14.

    It is worthy of note that Persson (1997) identifies a weakness of most empirical studies concerning regional convergence in that data on regional per-capita income or output are often of poor quality and not adjusted for differences in the cost of living across regions; a technique which would permit comparisons of ‘real’ living standards across observational units. When such an adjustment is made, Persson (1997) finds stronger and more robust evidence on regional convergence across Swedish counties. The estimated convergence coefficient indicates a rate of 4% per year, which is almost double that obtained using unadjusted data (2.3%). This conclusion does tend to suggest that such ‘real’ comparisons are important.

  15. 15.

    Other studies use the level of regional income (e.g. Doyle and O’Leary 1999; Cheshire and Magrini 2000, regional wages (Mora et al. 2005), regional welfare inequalities (e.g. Álvarez-Garcia et al. 2004; Ezcurra et al. 2005) or specific aspects of regional economies, such as manufacturing (e.g. Pascual and Westermann 2002; Gugler and Pfaffermayr 2004), regional agriculture productivity (e.g. Alexiadis and Alexandrakis 2008) and the wages in the agricultural sector (Tavernier and Temel 1997). Bassino (2006) examines σ and β convergence in terms of the height and health stature of the population across the prefectures of Japan.

  16. 16.

    See also Quah (1993), Bliss (1999, 2000), Cannon and Duck (2000).

  17. 17.

    For a more detailed analysis of the relation between β and σ-convergence, see Furceri (2005).

  18. 18.

    Sala-i-Martin (1996a) claims that the conditional convergence and the absolute convergence hypotheses coincide, only if economies have the same steady-state. Furthermore, he claims that if the study of convergence is restricted to selected sets of economies, then the hypothesis of similar steady-states is apparent.

  19. 19.

    Martin and Sunley (1998) propose an alternative way to test for conditional convergence. According to their method, the analysis of convergence is restricted to sets of economies for which the assumption of similar structural characteristics or ‘fundamentals’ is not unrealistic. Thus, similar economies (countries or regions) should exhibit absolute β-convergence.

  20. 20.

    Button and Pentecost (1995), for example, use the share of agriculture in order to capture two factors. First, the differences in the composition and the structure of economic activities across the EU regions and second the impact of transfer payment through the CAP.

  21. 21.

    Development policies have become after the CAP the second largest policy area in the EU. In budgetary terms, development policies have grown from a mere 10% of the European Community’s budget and 0.09% of the EU-15 in 1980 to more than one-third of the budget and about 0.37% of the EU GDP, on average, in the period 1988–2001.

  22. 22.

    Early studies on spatial econometrics include Douglas-Carrol (1955), Fisher (1971), Hordijk (1974), Paelnick (1978), Steinnes (1980), Bennett and Hordijk (1986). For a more updated analysis of spatial econometrics see Kelejian and Prucha (2002), Dubin (2003), Saaverda (2003) and Arbia (2006).

  23. 23.

    The studies by Bernat (1996), Novell and Viladecans-Marsal (1999), Beardsell and Henderson (1999) are also relevant, although they refer to a context other than regional convergence. For a more detailed review on the empirics of spatial growth and convergence, see Fingleton (2000), Rey and Janikas (2005), Abreu et al. (2005).

  24. 24.

    \( u\sim N(0,{{\sigma }^2}I) \). For a more detailed analysis of the econometric treatment of spatial error terms see Anselin and Moreno (2003).

  25. 25.

    The spatial lag model can be written equivalently as \( {{{\mathbf{g}}}_{{\mathbf{i}}}} = {{({\mathbf{I}} - \rho {\mathbf{W}})}^{{ - 1}}}(b{{{\mathbf{X}}}_i} + {{\varepsilon }_i}) \), where \( {{{\mathbf{X}}}_i} \) is an \( (n\; \times \;2) \) vector containing the constant term and the observations of the initial per-capita income. Given that \( {{({\mathbf{I}} - \rho {\mathbf{W}})}^{{ - 1}}} = {\mathbf{I}} + \rho W + {{\rho }^2}{{W}^2} + {{\rho }^3}{{W}^3} + \ldots \), then the growth rate in a region is affected by a marginal change in the explanatory variable in this region and by marginal changes in the explanatory variables in the remaining regions.

  26. 26.

    There is also an alternative approach using Bayesian methods (e.g. Ertur et al. 2007; Arbia et al. 2008). This method tackles with problems due to heteroscedasticity and outliers from ‘enclave effects’, i.e. where a particular observation exhibits divergent behaviour from nearby observations.

  27. 27.

    One way to avoid this problem is by estimating a stochastic kernel, which can be regarded as a continuous version of the transition probability matrix. Nevertheless, Neven and Gouyette (1995) show that using the measures of σ-convergence (e.g. coefficient of variation), β-convergence and Markov-chain (movements-matrix) produce consistent results.

  28. 28.

    It is interesting to note that these conclusions are already familiar to development economists. Indeed, according to Nelson (1960) and Leibenstein (1957) some poor economies are ‘stuck’ in a ‘low level equilibrium’ (the poor ‘club’) or ‘poverty trap’ and a ‘big push’ is required in order to achieve high levels of per-capita income. Moreover, Nelson (1956) argues that even if production techniques are not improved and even in the absence of a massive investment, the ‘trap’ may still be escaped if the socio-political environment is favourable. A similar argument can be found in Folloni (2009).

  29. 29.

    The study by Leonida et al. (2003) employs the quadratic specification in the context of Italian regions, but does not addresses the issue of a convergence club directly.

  30. 30.

    Several studies (e.g. Soukiazis and Castro 2005; Badinger et al. 2004; Evans and Karras 1996a; Lee et al. 1998) implement panel data, which allow for time-varying and country-specific steady states.

  31. 31.

    There have also been studies using time-series data on regional employment or unemployment. See for example Baddeley et al. (1998), Fagerberg et al. (1996), Martin and Tyler (2000), Muscatelli and Tirelli (2001), Gray (2004). In this context, the Error-Correction-Model (ECM) is a useful econometric tool. See for example Martin (1997), Gray (2005), Alexiadis and Eleftheriou (2010), among others.

  32. 32.

    The approach to cointegration and the unit root hypothesis has been developed by Dickey and Fuller (1979, 1981), Engle and Granger (1987). For a more detailed review of the associated econometric test see Lee and Mosi (1996), Pesaran and Smith (1995), Lopez (1997).

  33. 33.

    Nahar and Inder (2002) use the following example. Suppose that the difference in income between two economies, \( {{y}_{{i,t}}} - {{y}_{{j,t}}} \), is a non-stationary process and is represented by \( {{y}_{{i,t}}} - {{y}_{{j,t}}} = \frac{\theta }{t} + {{u}_t} \) in which \( E({{u}_t}) = 0 \)and \( {{u}_i} \) is a stationary process. As \( t \to \infty \), then \( \frac{\theta }{t} \to 0 \) and \( {{y}_{{i,t}}} - {{y}_{{j,t}}} \) is also converging since \( \mathop{{\lim }}\limits_{{k \to \infty }} E({{y}_{{i,t + k}}} - {{y}_{{j,t + k}}}|{{I}_t}) = 0 \).

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    Dr. Stilianos Alexiadis

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Alexiadis, S. (2012). Empirical Measures of Regional Convergence. In: Convergence Clubs and Spatial Externalities. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31626-5_5

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