The origins of vulnerability transcend the geographical, economic and political. Primary concerns associated with negative events are their impacts on productivity growth, development potential and the extent to which they alter vulnerability (Guillaumont 2004).¹ However, before vulnerability can be accurately measured, attention needs to be focused on where potential shocks may arise. Three basic channels of origin can be identified: (1) environmental or natural shocks, such as natural disasters; (2) other external shocks (trade and exchange related), such as slumps in external demand, and (3) other (non-environmental) internal shocks, such as political instability (Guillaumont 2004).

Once the origins of vulnerability have been identified, the next stage in any vulnerability empirical analysis is to decide on the appropriate spatial scale. Literature pertaining to the study of vulnerability has focused on three levels of analysis: household, regional and national. A large majority of this literature is devoted to measuring the relative vulnerability of a country.² Turvey (2007) advocates the need for place-specific vulnerability indices and constructed a Composite Vulnerability Index for 100 developing countries out of four sub-indices: a coastal index, a peripherality index, an urbanisation index and a vulnerability to natural disasters index. She argued that if the measurement of vulnerability excludes a geographical component, then the construction of vulnerability profiles might be useless for framing development policy and evaluating developing countries.³

Although the majority of analysis has focused on the country-level spatial scale, there are a growing number of articles that examine vulnerability at the household level. For instance, Bird and Prowse (2008) investigated the vulnerability of households in Zimbabwe and found that if official donors did not intervene then the poor and very poor were likely to be driven into long-term chronic poverty and such chronic poverty would be extremely difficult if not impossible to reverse. Gaiha and Imai (2008) also argued that idiosyncratic shocks (e.g. unemployment or illness) were the primary cause of Indian rural households’ vulnerability, although poverty and aggregate risks (weather and crops) were also important contributory factors; the last of these is clearly a geographical issue.⁴

Not a lot of attention has been given to the vulnerability of regions within a country. Hulme, Moore and Shepherd (2001) linked poverty to the vulnerability of specific regions, and Kanbur and Venables (2005) showed that not only is spatial inequality between regions on the increase but it will ultimately cause an overall increase in the inequality of specific countries. Similarly, Ivaschenko and Mete (2008) presented evidence of poverty traps and argued that higher levels of poverty in a region appear to reduce radically the chance of a household emerging out of poverty and that living in a region with a slow economic growth weakens the odds of a household exiting poverty and increases its risk of slipping into poverty.⁵

As regards to South Africa, vulnerability as currently understood in this and the Naudé et al. (2009b) paper has not been high on the priority list. There are studies which comes close in nature to this article but focuses either on quality of life (see Greyling & Rossouw 2016; Naudé, Krugell & Rossouw 2009a; Rossouw & Naudé 2008) or ex post poverty outcomes (see Alderman et al. 2000; Klasen 2000; Mattes, Bratton & Davids 2003; Noble et al. 2006). This reiterates the importance of increasing the literature base available as regards to incorporating spatial contiguity as regards to vulnerability measures.

Much development literature still relies on income per capita measures as an indication of development and vulnerability. Naude et al. (2009b) underscore the shortcomings of focusing only on incomes when assessing vulnerability by stating that ‘equal incomes do not translate into equal outcomes for all … (and) different people are faced with different environments for translating income gains into non-income wellbeing gains’ (p. 4). An important, though not new, contribution of their study was to emphasise that vulnerability is a multidimensional phenomenon that requires and deserves a multidimensional analysis. It is uplifting to see this underlying multidimensional theoretical perspective being adopted empirically in their subsequent analysis. They constructed a composite index of local vulnerability using principal component analysis (PCA).⁶ The execution of PCA⁷ is thought to reveal the internal structure of the data with each component being ranked in accordance with its importance to the multidimensional phenomena and with the first component known to capture most of the data’s variability.

In line with theoretically driven multidimensional considerations, Naudé et al. (2009b) proposed the construction of an LVI based on 10 different and distinct domains,⁸ which are constructed from sub-domains stated in brackets:

Size of local economy [gross domestic product (GDP), population size, population density, urbanisation rate]: It is argued by Liou and Ding (2004) that larger economies are prone to being less vulnerable.

It should be emphasised that Naudé et al. (2009b) include both geographical and environmental indicators, which they strongly and correctly suggest are important for economic vulnerability measurement. They applied the following structured method to a data set detailed in the ‘Data’ section. Initially, PCAs were run on each of the individual domains that had more than one sub-domain (i.e. domains 1–6). Although it would be possible to appoint different weights to each subsequent component, this would require an appropriate selection of weights. Instead, the principal components of each of the individual domains PCA’s results were selected and pooled into a data set that already contained the non-multidimensional individual domains (i.e. domains 7–10). Then, a second PCA was estimated on these data and the principal component again chosen for subsequent interpretation; the result is a single principal component used to represent their multidimensional LVI from which district ranks and area comparisons can be made. Note that each of Naudé et al. (2009b)’s domains are aspatial by construction: each area’s estimate does not explicitly consider what is happening in an area’s neighbouring areas.

Naudé et al. (2009b) also propose the construction of a VII that is designed to reflect the vulnerability associated with per capita income, such that: LVIi=α+βYi+μi[Eqn 1] where i=1,…,354[Eqn 2] where α is an intercept, β is a slope coefficient, Y is the per capita income of magisterial district i and µ is the well-behaved error term. If β is equal to one, then any change in the LVI is a proportional response to the corresponding change in income per capita. Assuming that there are no scale returns disparity issues across areas, estimation of equation: (1) leads to a vector of residuals, one for each area, where each individual residual represents the deviation between the actual and the predicted LVI based on per capita income. Naudé et al. (2009b) examined the absolute values of these residuals to identify areas which deviate strongly from the average and found that although the LVI was highly correlated with per capita income (with greater income per capita being associated with lower vulnerability) it was far from being equal to unity; this led them to believe that there were reasons other than achieved incomes that drive vulnerability levels.⁹ As far as policy formation is concerned, this belief is in line with the suggestion that any policies aimed at reducing area level vulnerability should not rely solely on increasing incomes.

In contrast to Naudé et al. (2009b), we apply the following structured method:

Begin with exactly the same original data and standardised variables as Naudé et al. (2009b). This is so as to ensure comparability of the various results obtained by the different studies.

The result is two principal components: one that will represent the multidimensional LVI from Naudé et al. (2009b)’s aspatial perspective and one that will represent the multidimensional LVI from a spatial perspective, which we denote by spatial Local Vulnerability Index (sLVI):

Reconstruct Naudé et al. (2009b)’s VII to reflect vulnerability associated with per capita income. Estimating LVI_i = α + βY_i + μ_i(i = 1,…,354) to replicate Naudé et al. (2009b)’s results and estimate sLVI_i = α + βY_i + μ_i to capture the spatial equivalent set.

Interpret the absolute values of these sets of residuals and identify which areas deviate strongly from predicted.

It is emphasising that this retention and subsequent analysis of the residuals is a clear extension of the methodology employed by Naudé et al. (2009b), as they take the absolute residual values as an indication of the level of vulnerability of an area. Collating absolute values will muddle areas into a VII irrespective of whether they were performing much better (a good form of vulnerability) or much worse (a bad form of vulnerability) than expected under the fitted model. Good (and bad) forms of vulnerability may be the result of appropriate (and inappropriate) policy; for instance, some areas may have been influenced by beneficial policy or naturally occurring economic phenomena (such as urbanisation and localisation economies) that make areas perform better than would be expected otherwise, while the absence of appropriate policy (or the application of inappropriate policy) may result in the deterioration of other areas.

Figures 3 and 4 present local indication of spatial association (LISA) maps based on the results of LVI and sLVI estimations. LISA maps are special choropleth maps that highlight those locations with a significant local Moran statistic classified by type of spatial correlation (Anselin 1995). They highlight areas with high (low) vulnerability that are surrounded by areas with relatively high (low) vulnerability; LISA maps can also highlight areas with high (low) vulnerability that are surrounded by areas with relatively low (high) vulnerability. Through visual inspection, it becomes clear that an appreciation of the influence of contiguity effects will affect LVI estimates.

Several observations obtainable from comparing Figures 3 and 4 are worth highlighting. Firstly, magisterial districts within and surrounding Cape Town, Durban and Johannesburg are least locally vulnerable. This emphasises a large urban–rural disparity vulnerability effect. The same pattern is not identifiable for other urban areas, with the only exception being Umtata. Taken together, the results suggest that Umtata is an area that is doing relatively well in comparison to its hinterland (see Figure 3), but it is at risk because its hinterland is performing relatively poorly and spatial spillovers might deteriorate the extent of vulnerability within this conurbation (see Figure 4). Umtata’s extent of vulnerability could be the result of policies that have been directed at this large conurbation without concern for its surrounding hinterland.

Secondly, Figure 4 suggests that the greater hinterland of the three main urban areas of Cape Town, Durban and Johannesburg are much less vulnerable than those indicated in Figure 3. This is illustrated by the significant spillovers between contiguous districts which, in these cases, appear to diminish vulnerability. Such a contagion issue will be related to either spatial feedback, grouping or response forces. Of particular interest are the magisterial districts of Heidelberg and Bronkhorstspruit which are low–highs according to Figure 3 and high–highs according to Figure 4; these differences are because of the spatial spillovers between contiguous districts, and without these spatial spillovers, it is likely that these two districts would be much more vulnerable. An alternative perspective is that individuals are being marginalised in and around Johannesburg and are being forced out of relatively affluent areas and clustered into these two relatively poorly performing districts. Thus, policy geared towards diminishing the vulnerability of people in Heidelberg and Bronkhorstspruit should be both district specific (as highlighted in Figure 3) and take account of spatial spillovers (as highlighted in Figure 4).¹⁶

Thirdly, there are also important differences between Figures 3 and 4, which reflect differences in estimates obtained that result from the inclusion of spatially weighted sub-domains. The results presented in Figure 3 suggest that there are magisterial districts that suffer high levels of vulnerability, but the results presented in Figure 4 illustrate that this is not an attribute that stops at areas’ borders. Instead, the most vulnerable areas are clustered and contiguous in several areas. Of most concern is: (1) magisterial districts occupying the area to the south of Swaziland and which continues, mainly inland, down to Ladysmith, (2) much of the eastern part of the Eastern Cape to the south of Lesotho, and (3) a large, central part of the Northern Cape. The extent of vulnerability is not fully emphasised in Figure 3; the reason why this spatial perspective is so important is because any attempts by policy-makers to alleviate vulnerability in these areas need to take a larger spatial perspective and explicitly consider large swathes of districts in their policy formations rather than simply considering the circumstances within specific districts in isolation.

When account of spatial spillovers in vulnerability sub-domains is explicitly considered in the estimation process, the rankings of districts can differ substantially from estimates where account of spatial spillovers is excluded. Table 2 presents the sLVI estimates of the top and bottom 20 magisterial districts and each of these districts’ ranks that have been replicated using the (non-spatial) LVI. Although there are some districts where the rank is unaffected, such as Nelspruit (rank = 1) and Soweto (rank = 354), the estimates of the ranks of many other districts do alter substantially; for instance, Rustenburg’s rank improves from 228th to 18th after taking into account spatial spillovers, while Simonstown’s rank falls from 62nd to 350th.¹⁷

Residual estimates are presented for the top and bottom 20 districts in Table 3, and Figures 5 and 6 provide visual support. Table 3 highlights the importance of accounting for spatial spillovers in VII estimates; although the top three districts (Johannesburg, Soweto and Durban) only switch places when the VII and sVII estimates are compared, many of the ranks of the other districts detailed do change rank substantially.

Several observations can be made when interpreting Table 3 together with Figures 5 and 6. Firstly, the association of urbanisation and vulnerability alleviation, perhaps associated with agglomeration economies, around Johannesburg, Cape Town, Durban, Richard’s Bay and Hluhluwe is much clearer from the visual examination of Figure 6, where the residuals are the result of an equation that explicitly considered spatial spillovers. Many economic geographers would expect this result.

Secondly, although Figures 5 and 6 highlight large areas of central South Africa in white, therefore suggesting that the areas are not performing substantially different than expected given their GDP per capita level, and the Northern and Western Capes have much worse vulnerability rates than we would expect given their GDP per capital levels, the area of greatest disparity between the VII and sVII estimates are in the province of Limpopo. The sVII perspective suggests that Limpopo is an area that deserves much more policy focus as spatial spillovers are resulting in much deeper vulnerability than one would otherwise expect. Policy directed towards individual magisterial districts in isolation within Limpopo will probably be relatively inefficient as the province requires a more holistic policy approach which explicitly accounts for spatial spillovers

Thirdly, the values of the VII shown in Table 3 do not have a large spread: the value for the 15th highest spatially ranked district (Bloemfontein) is equal to 1.88, whereas the value for the bottom spatially ranked district (Pelgrimsrus) is equal to −1.34. This is in contrast to the top 14 spatially ranked districts, which vary between 6.47 (Johannesburg, 1st) and 2.05 (Cape Town, 14th). Further examination of this data is carried out using the multivariate Moran scatterplot, as show in Figure 7, which presents the sVII estimates on the horizontal axis and the sLVI on the vertical axis. Initial execution of this technique reveals a strong, statistically significant Moran’s I value of 0.616, but the exclusion of these top 14 ranked areas reveals a much shallower Moran’s I value of 0.104. Although this latter value is still statistically significant, it becomes clear that a substantial part of the spatial correlation between sVII and sLVI is because of a large conurbation effect.

The large conurbation effect reflects the fact that those areas that are wealthier also have better vulnerability values. Such attributes could be because of the benefits of agglomeration, typically associated with urbanisation and location economies, but may also be because of national policies that are geared towards improving the lives of urban dwellers rather than their rural counterparts. This is in line with Friedmann (1963), Alonso (1968) and Yang (1999) who found that regional policies are biased in that they are likely to reflect the development of the urban areas as they are seem to have the most potential for development but ultimately cause greater spatial inequality. Little (2009) found that government policy needs to change in order to rectify the geographical imbalances in both recorded and hidden unemployment in urban and rural areas. Etherington and Jones (2009) argued that the policies implemented for city-regions emphasise and have the potential to increase, rather than resolve, uneven development and socio-spatial inequalities.

There is an alternative method of generating estimates of sVII using spatial econometrics. The first stage is to estimate a standard ordinary least squares (OLS) estimate of LVI_i = α + βY_i + μ_i (i = 1,…,354) and to incorporate a spatial weights matrix to permit the diagnosis of spatial dependence. This can be carried out using the GeoDa freeware, as employed above to generate spatial weights. Application of the OLS procedure yields results presented in Table 4.

Several values presented in Table 4 are worth emphasising. Firstly, the GDP value is greater than unity, suggesting that a one unity increase in GDP will result in a larger than one-unit increase in the LVI. This would lead to the conclusion that, on average, GDP has a stronger than proportional effect on the LVI thereby emphasising that GDP is vital to the alleviation of vulnerability. That GDP is important for the LVI is not surprising, but this very strongly emphasises the importance of policies designed to stimulate the economy of South Africa so that they can ‘grow out of vulnerability’. Although this result is based on the multidimensional PCA estimation of the LVI, the result does not support a multidimensional policy alleviation perspective.

Secondly, the Moran’s I statistic indicates that there is strong spatial autocorrelation in the errors. This implies that an area’s LVI value is very strongly and positively associated with its contiguous areas’ LVI values and that policies to reduce vulnerability should not target areas in isolation; policy-makers should examine the cause and consequences of spatial spillovers that contribute to an area’s vulnerability.

Thirdly, the Lagrange multiplier and robust Lagrange multiplier statistics indicate that the preferred spatial econometric model is the spatial error model, although this is by no means definite. If there were strong theoretical reasoning to believe that the errors of an OLS regression would be spatially autocorrelated, then the appropriate technique is to estimate a spatial error model, which in our case is specified as follows: LVIi=α+βYi+μi[Eqn 3] where μi=ρWui+εi[Eqn 4] in which ρ represents the spatial error parameter to be estimated, W represents our spatial queen-weights matrix such that Wu captures the spatial lags of the model’s disturbance term, u, and ε represents the independently distributed error term. Under this specification, spatial autocorrelation of the LVI is the result of exogenous influences captured in the error term and not directly from the GDP explanatory variable. Selection of the spatial error model tends to be because of the list of explanatory variables excluding a variable that may have otherwise captured the spatial autocorrelation of the LVI.

The results of the spatial error model are also presented Table 4. The spatial error results are noticeably different from the OLS results in the following ways. Firstly, Lambda is positive and strongly statistically significant. This indicates that the spatial component in the error term is capturing some positive spatial autocorrelation, again suggesting spatial spillovers between contiguous areas are important in influencing an area’s economic vulnerability.

Secondly, inclusion of Lambda strongly affects the coefficient of GDP. Interpretations of this effect can be numerous. One option is that the OLS coefficient for GDP included both the effects of GDP on LVI and the spatial spillover component and that entering the spatial spillover effect separately reveals the effect of GDP on LVI once we hold the spatial spillover effect constant. Contrary to the OLS results, the magnitude of the GDP coefficient is now less than unity, suggesting that a one-unit increase in GDP will result in a smaller than one-unit increase in the LVI. Now this leads to the conclusion that, on average, GDP has a smaller than proportional effect on the LVI, thereby emphasising that although GDP is important in the alleviation of vulnerability, the economy needs to grow substantially more to achieve a measured reduction in vulnerability than was suggested in the OLS results.

Thirdly, although the proportion of the variation of the LVI that is now explained by the model has increased substantially from 0.36 to over 0.7, there is still evidence of spatial dependence as indicated by the likelihood ratio test.

As the Lagrange multiplier tests were not conclusive about whether the model should be estimated with either a spatial error or a spatial lag, it is worth complementing the spatial error results with the spatial lag results. The spatial lag model captures spatial autocorrelation as an explanatory variable, which in our case will take the following form: LVIi=α+λWLVIi+βYi+μi[Eqn 5]

In our formulation, WLVI is the queen-contiguous spatially weighted average of the dependent variable for area i and λ is the spatial lag parameter to be estimated.

Although the results of the spatial error and spatial lag models originate from different theoretical concerns for the origins of spatial spillovers, our results for the spatial lag and spatial error models effectively corroborate each other: the magnitude of the impact of GDP on the LVI is positive and around 0.8, and therefore, GDP does not have a more than proportional effect on LVI. Therefore, there may be important roles in vulnerability alleviation associated with factors other than stimulating GDP.

The residuals of the three models whose results are presented in Table 4 were retained, as before, to identify the top and bottom ranked areas and are presented in Tables 5 and 6. A number of important issues that corroborate our previous results can be made.

Firstly, the most consistent set of results are identifiable for the top seven regions. All three model estimates suggest that Cape Town is the least vulnerable. All three models suggest that the next six areas are consistently in the top 15 area for low amounts of vulnerability. These results hold when the spatial and aspatial perspectives are accounted for, but this time using the spatial error and spatial lag models. Also of note is how the magnitudes of the residual values are relatively stable, large and positive for these seven areas.

Secondly, there is substantial rank switching at the bottom end between the aspatial and spatial models. For instance, out of the bottom 20 in the OLS, only six remain in the bottom 20 using either of the spatial models. Also noticeable is that there is substantial rank switching at the top end between the aspatial and spatial models. For instance, ignoring the top seven, out of the next 13 in the OLS results, only two remain in the top 20 using either of the spatial models. Taken together, these results indicate that the method of analysis is important when identifying the relative vulnerability position of areas.

Thirdly, when the magnitude of the difference in the residual values are observed, it appears that the gaps in vulnerability are much smaller between areas that do not make up the top seven, which are areas that are very urban. This highlights the importance of the urban–rural divide in vulnerability terms and that the beneficial effects of urbanisation on vulnerability does not reach far into rural areas to alleviate vulnerability.