Regional income club convergence in US BEA economic areas: a spatial switching regression approach

The conditional convergence hypothesis suggests that each particular economy approaches its own but unique equilibrium. In contrast, the concept of club convergence is based on models that yield multiple equilibria. In the case of club convergence, regional economies that are identical in their structural characteristics converge to one another in the long run provided that their initial per capita income levels are similar as well (Galor 1996; Islam 2003; Magrini 2004). As Galor (1996) has demonstrated that the assessment of the conditional and the club convergence hypotheses is nearly isomorphic from a neoclassical perspective, the inclusion of empirically significant structural variables (such as human capital, income distribution, fertility, government policies, etc.) strengthens the viability of multiple equilibria and presents club convergence as a competing hypothesis with conditional convergence. In light of this consideration, our empirical analysis focuses on the club convergence hypothesis which suggests that per capita incomes of regional economies with similar structural characteristics converge to one another provided that their initial per capita income levels are similar as well.

Higgins et al. (2006) use the data drawn from 3058 county-level observations. By splitting the large number of observations into two sets of subsamples, they attempt to explore the possible heterogeneity across the US regions. The first set separates the data into 867 metro and 2191 non-metro counties, and the second set separates the data into five regions: the Northeast, Great Lakes, West, Plains and South. However, the role of spatial effects in regional income convergence is virtually ignored in their study on regional income growth and convergence across counties.

Cheshire and Magrini (2000) examine regional growth performance of 122 functionally defined urban regions of the EU of 12 member countries over the period 1978–1994. They are defined on the basis of urban cores identified by concentrations of employment and hinterlands from which commuters flow to the employment core. Niebuhr (2001) investigates regional convergence in West Germany over the period 1976–1996 using the West German planning regions (Raumordnungsregionen) as spatial units of observation. The German planning regions are functionally defined and are composed of several NUTS level-3 regions linked by intensive commuting. Using data on per capita personal incomes in the 172 BEA economic areas over the period 1969–1997, Miller and Genc (2005) provide new insights on the geographical specifications of US regions in the analysis of regional income convergence. However, they do not explicitly consider the role of spatial effects in the process of regional income convergence nor do they examine whether economic areas displaying high or low values of per capita income are randomly distributed across space, or conversely, are clearly concentrated in particular territories.

Johnson and Kort (2004) provide a detailed account of the BEA’s procedures that are used to disaggregate the country into economic areas. The definition of the BEA economic area is based on commuting data from the 2000 decennial census. In less populated parts of the country, newspaper circulation data from the Audit Bureau of Circulations for 2001 are also used to measure the relevant regional markets. The BEA economic areas are defined in three major phases: (i) the identification of economic nodes, (ii) the assignment of counties to BEA component economic areas (CEAs) and (iii) the aggregation of the CEAs to the economic areas. For more specific procedures, see Johnson and Kort (2004).

Following the recommendations of Anselin and Bera (1998) and Getis (2010), we adopt a distance-based contiguity approach based on pure geographical distance due to its unambiguous exogeneity. We use the median as the cut-off parameter above which spatial interactions are assumed to be negligible (Ertur et al. 2006; Ramajo et al. 2008; Chapman et al. 2012). Because the results were robust to the specification of the spatial weights matrix, only the results from the median cut-off value are presented.

This could also imply that part of the positive spatial autocorrelation derives from nuisance spatial dependence, which can result from a mismatch between the spatial boundaries of the growth and convergence processes and the spatial breakdown adopted by BEA. As previously mentioned in Sect. 2, although the BEA economic areas are economically coherent, self-contained spatial units in the contiguous US, these functional regions are dynamic rather than static such that their spatial boundaries may not be fixed in time as economic processes themselves are likely to be evolving over time (Cheshire and Carbonaro 1995; Cheshire and Magrini 2000; Magrini 2004; Rey and Janikas 2005; Fischer and Stirböck 2006).

The Moran scatterplot map may be useful for visualizing atypical localizations, i.e., regions in the HL or LH quadrants of the scatterplot (Anselin 1996). Ord and Getis (1995) suggest the use of the Getis–Ord \(G_i^*\) statistic to detect local “pockets” of dependence that may not show up when using global statistics. Once standardized, a positive value of the Getis–Ord \(G_i^*\) statistic indicates a spatial cluster of high values, whereas a negative value indicates clustering of low values around region i. We use the Getis–Ord \(G_i^*\) statistic to identify spatial regimes in the regional income convergence process in accordance with Fischer and Stirböck (2006) and Gallo and Dall’erba (2006).

Given the context of \(\beta \)-convergence analysis, we choose to define local spatial association on the logarithm of the initial level of per capita income. As noted by Durlauf and Johnson (1995), the use of split variables which are known at the beginning of the period under study is necessary to avoid the sample selection bias problem that has been pointed out by De Long (1988).

As shown in Fig. 3, the economic areas in Florida also tend to cluster in spatial regime 1, whereas those in North Dakota tend to cluster in spatial regime 2. For the per capita income levels in 2008, spatial regime 1 consists of 76 economic areas, whereas spatial regime 2 is made up of 101 economic areas.

According to the decision rule based on the LM test suggested by Anselin and Florax (1995), if the LM-Lag is more significant than the LM-Error and the robust LM-Lag is significant but the robust LM-Error is not, the appropriate model is the spatial lag model. Conversely, if the LM-Error is more significant than the LM-Lag and the robust LM-Error is significant but the robust LM-Lag is not, the appropriate specification is the spatial error model.

Using data on per capita incomes in the 48 contiguous US states over the period 1929–1994, Rey and Montouri (1999) find an implied convergence rate of 1.8 % per year based on the estimates from the spatial error model.

Using the functionally defined regions as spatial units of observation, Niebuhr (2001) finds strong evidence of substantive spatial dependence in regional income convergence in West Germany. This finding is consistent with our results on substantive spatial dependence.

The empirical studies on regional club convergence draw on formal growth theories in order to construct convergence equations, which in turn are estimated using observations from regional economies. In addition, the choice of convergence clubs is based on a priori theoretical, geographical, economic considerations. As pointed out by Martin and Sunley (1998) and Chapman and Meliciani (2012), however, abstractly theoretical models of convergence may fail to capture the importance of the socio-institutional context and embeddedness of economic geography. Growth and convergence theories need to be spatialized in the sense of recognizing that economic geography can make a contribution to the development of evolutionary economic thinking.