Abstract
The publication of the ground breaking work of Baumol (1986) was the spark that ignited an enormous interest to the issue of convergence in per capita income (e.g. Aghion and Howitt 1998; Baldwin et al. 2003; Capello 2006; Le Gallo 2004; Overman and Puga 2002; Ioannides and Overman 2004; Li and Haynes 2010). As perhaps anticipated, there is a growing number of attempts to assess regional convergence using extensive datasets, such as the regions of the European Union (e.g. Button and Pentecost 1995; Cuadrado-Roura et al. 1999; Rodríguez-Pose 2001; Rodríguez-Pose and Fratesi 2004; Lopez-Bazo et al. 2004; Alexiadis and Tsagdis 2010), the US states (e.g. Christopoulos and Tsionas 2007; Checherita 2009) and the regions of individual countries (e.g. Rodríguez-López et al. 2009; Hierro and Maza 2010). Most of the literature concerning convergence has been developed in terms of per-capita income using cross-section data. Nevertheless, convergence is by no means a mechanical phenomenon, which happens everywhere and always (Cuadrado-Roura 1996, p. 47). Regional convergence is characterised by rapid transformations and adjustments, properties that are difficult to be examined in a cross-section context. This has led to the development of alternative methodologies based on cointegration analysis generating a considerable amount of empirical literature (e.g. Bernard and Jones 1996; Carlino and Mills 1993; Sun et al. 2010). Still, the crucial question of the adjustment towards steady-state equilibrium, which lies at the heart of the convergence debate, remains unanswered. An approach to this issue can be provided through an Error-Correction-Model (hereafter ECM). Recent years have witnessed a growing number of attempts to implement this model to examine the evolution of regional employment and unemployment (e.g. Baddeley et al. 1998, 2000; Martin and Tyler 2000; Gray 2004; Hunt 2006; Alexiadis and Eleftheriou 2010).
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Notes
- 1.
This kind of analysis has also been implemented in contexts other than regional convergence (e.g. Angulo et al. 2001).
- 2.
In this context, some remarks by Martin (1999, p. 73) are highly pertinent: ‘[T]he focus on long-run income convergence merely revives a theme that was first examined […] in the classic works by Borts and Stein (1964) and Williamson (1965)’. For useful reviews of the growth-convergence issue see Rogers (2003) and Islam (2003).
- 3.
Lichtenberg (1994, p. 576) offers an alternative description of the convergence hypothesis: \( \frac{{d[\operatorname{var}(\ln {Y_t})]}}{dt }<0 \), where \( {Y_t} \) is labour (or total-factor) productivity at time \( t \) and \( \operatorname{var}(\;\;) \) denote the variance across economies. When there are only two time periods, indexed by 0 and 1, the hypothesis may be expressed as \( [\operatorname{var}(\ln {Y_0})]/[\operatorname{var}(\ln {Y_1})]>1 \).
- 4.
Equation 10.1 can be enhanced by adding variables to account for technological and structural characteristics. In this case convergence is conditioned upon those characteristics. For example, Barro and Sala-i-Martin (1991) use an index of sectoral mix in several of their regressions, with the explicit aim to control for asymmetric shocks across economies. Paci and Pigliaru (1997) point out how the observed productivity convergence across the Italian regions is indeed generated by a strong process of structural change. Structural change can be regarded as a process that is altering traditional patterns of growth and provoking significant changes in regional disparities, as well as greater diversity in the patterns of development (Rodríguez-Pose 1999). This implies that convergence-dynamics can be examined more thoroughly using Markov chain models. For a more general treatment, together with an empirical application in the context of the EU regions, see Fingleton (1997).
- 5.
This means that on average, 2 % of the gap in income per capita between two regions is eliminated so that it takes more than 30 years to eliminate one half of the initial gap in per capita incomes.
- 6.
A simple example by Elster (1989) will illustrate what is meant by ‘Galton’s fallacy’ and the problems to which this mode of thinking can lead. ‘The Israeli air force at one time noted that, when pilots were criticized after a bad performance, they usually did better next time. When praised for a good performance, they tended not to do as well on the next occasion. The instructors concluded that criticism is effective in training pilots, […]. They were not aware of the simple statistical principal that a very good performance is on average followed by a poorer one, while a bad performance is on average followed by a better one’ (p. 39). Boyle and McCarthy (1999) propose a methodology to test for β-convergence that overcomes this bias. This methodology implements a Kendall’s measure of rank concordance (γ-convergence).
- 7.
- 8.
In terms of the existing literature, regional studies concentrate to a large extent on the US; the reader interest in these issues can, for instance, refer to the contributions of Carlino and Mills (1993), Tsionas (2000), to name but a few. Empirical studies of stochastic convergence have also been conducted for the regions of the UK (McGuinness and Sheehan 1998) and Greece (Alexiadis and Tomkins 2004).
- 9.
\( E({X_t})=\mu \) and \( Var({X_t})={\sigma^2}<\infty \).
- 10.
\( Cov({X_t},{X_s})={\sigma_{{\left| {t-s} \right|}}}(t\ne s) \).
- 11.
Phillips and Perron (1988) propose an alternative test.
- 12.
- 13.
Owing to the lack of data, Alaska and Hawaii had to be omitted, since the datasets for these states begin at 1950.
- 14.
σ-convergence is said to be present if the dispersion of income per capita (or worker) across countries, measured by some convenient measure of dispersion (such as the standard deviation or the coefficient-of-variation), display a tendency to decline through time (Dalgaard and Vastrup 2001, p. 283).
- 15.
The source for our data is the US Bureau of Economic Analysis.
- 16.
- 17.
Using data on output (GDP) per head for 141 NUTS-2 regions of Europe over the period 1980–1989 Neven and Gouyette (1995) provide two stylized facts. First, the process of convergence among the European regions is far from stable, even if differences in industrial structure is taken into account, and it tends to slow down in the late part of the 1980s. Second, it seems that northern European regions, after a period of stagnation in the early 1980s, converge strongly after 1985, at a time when southern European regions lagging, following a period of rapid convergence in the early 1980s. Neven and Gouyette (1995) estimate a low beta coefficient for the later part of 1980s (unconditional β = 0.251 and conditional with country dummies β = 2.01 for 1980–1985 while over the period 1985–1989 unconditional β = 0.77 and conditional with country dummies β = 0.42). According to their interpretation, this reflects a relative decline of agricultural activities and heavy industries which were concentrated in the poorer regions of the Community. Martin (1998) using a dataset for 104 European regions over the period between 1978 and 1992 estimates that about 1.28 % of the initial gap between regions is eliminated each year.
- 18.
Mankiw et al. (1992) provide empirical support for this view using and extension of the Solow model that incorporates human capital as a factor of production (de la Fuente 2002). Although this analysis is admittedly much less based on the ‘conventional’ neoclassical model, the ‘ghost’ of diminishing returns still lurks in the background.
- 19.
Nevertheless, one should bear in mind that a high level of per capita output in a region does not imply that a household or individual is rich. It is average output that is large, and household income depends, first, on whether the income associated with a region’s output of goods and services accrues to the region’s inhabitants, and second, on the personal distribution of income within the region (Dunford 1993).
- 20.
Spatial effects can be approximated in various ways. Quah (1996), for example, examining spatial clusters across Europe, normalises per-capita income in a region by the average of all the physically surrounding regions. This approach, however, it is difficult to be applied in an ECM.
- 21.
More technically, \( \max \{{{\bar{y}}_i}|i\in j\} \), where \( {{\bar{y}}_i}=\frac{{\sum\limits_{t=1}^m {{y_{it }}} }}{m} \) with \( j=1,\ldots,8 \) denoting each BEA Region and m is the number of years included in the empirical analysis.
- 22.
The term ‘intraregional’ is used to indicate the behaviour of States within a broad region, i.e. a BEA region, and not Metropolitan Areas.
- 23.
We also conduct the usual Ramsey RESET test (Ramsey 1969) for specification errors. The obtained p-values indicate that, in general, there is no such problem.
- 24.
There are only two cases which yield marginally significant test values.
- 25.
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Appendix
Appendix
The States used in the empirical analysis |
|---|
Alabama (ALB) |
Arizona (ARZ) |
Arkansas (ARK) |
California (CLF) |
Colorado (CLR) |
Connecticut (CNT) |
Delaware (DLW) |
District-of-Columbia (DCL) |
Florida (FLR) |
Georgia (GRG) |
Idaho (IDH) |
Illinois (ILL) |
Indiana (IND) |
Iowa (IOW) |
Kansas (KNS) |
Kentucky (KNT) |
Louisiana (LUS) |
Maine (MA) |
Maryland (MRL) |
Massachusetts (MSC) |
Michigan (MCH) |
Minnesota (MNN) |
Mississippi (MSS) |
Missouri (MSR) |
Montana (MNT) |
Nebraska (NBR) |
Nevada (NV) |
New Hampshire (NH) |
New Jersey (NJ) |
New Mexico (NM) |
New York (NY) |
North Carolina (NC) |
North Dakota (ND) |
Ohio (OH) |
Oklahoma (OKL) |
Oregon (ORG) |
Pennsylvania (PNN) |
Rhode Island (RI) |
South Carolina (SC) |
South Dakota (SD) |
Tennessee (TNN) |
Texas (TX) |
Utah (UT) |
Vermont (VRM) |
Virginia (VRG) |
Washington (WSH) |
West Virginia (WV) |
Wisconsin (WSC) |
Wyoming (WYM) |
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Alexiadis, S., Eleftheriou, K., Nijkamp, P. (2014). Intraregional Income Convergence: Cross Section and Time Series Evidence from the USA. In: Kourtit, K., Nijkamp, P., Stimson, R. (eds) Applied Regional Growth and Innovation Models. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37819-5_10
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