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Journal of African Economies
, Volume Advance Article (3) – Nov 2, 2017

11 pages

/lp/ou_press/convergence-and-spillover-effects-in-africa-a-spatial-panel-data-lpiI9bOcLK

- Publisher
- Oxford University Press
- Copyright
- © The Author 2017. Published by Oxford University Press on behalf of the Centre for the Study of African Economies, all rights reserved. For Permissions, please email: journals.permissions@oup.com
- ISSN
- 0963-8024
- eISSN
- 1464-3723
- D.O.I.
- 10.1093/jae/ejx027
- Publisher site
- See Article on Publisher Site

Abstract This paper re-examines the question of beta convergence process among 45 African countries during the period 2000–2015, taking into account the existence of spatial dependence and spatial spillover effects. We use a spatial panel data approach to control both individual effects and interaction among geographical units. The exploratory spatial data analysis detects strong spatial dependence and clusters of high per capita income in northern, central and southern Africa. Our empirical results find the existence of beta convergence and suggest that dependence between economies has an adverse impact in the convergence speed for African countries. We also find the existence of spatial spillover effects. This result suggests that in Africa, having neighbours with higher levels of initial per capita income leads to higher growth rates. 1. Introduction The Organization of African Unity (African Unity since 2000) inscribed in its Charter the ultimate goal of an economic integration and monetary union. The political objective was formalised in the Treaty of Abuja (Nigeria) in June 1991. The economic community shall be established gradually in six stages: (i) establishing economic communities in regions where they do not exist, (ii) strengthening sectoral integration, coordinating and harmonising activities among the existing and future economic communities, (iii) establishing a free trade area of tariff barriers and non tariff barriers to intra community trade and the establishment of a customs union by means of adopting a common external tariff, (iv) coordinating and harmonizing tariff and non tariff systems among the various regional economic communities with a view to establishing a customs union at the continental level by means of adopting a common external tariff, (v) harmonizing monetary, financial and fiscal policies, (vi) implementing the final stage for the setting up of an African monetary union, the establishment of a single African central bank and the creation of a single African currency and for the setting up of the structure of the Pan-African Parliament. After the successful launch of the euro in 1999, the association of governors of African central banks has renewed their interest for the monetary integration. In this respect, a plan to coordinate and harmonise policies among existing and future economic communities was designed in order to increase economic self-reliance and promote an endogenous and self-sustained development. Thus, assessing convergence of per capita income across African countries to evaluate the effectiveness of the cohesion policies is relevant. The convergence hypothesis on the neoclassical growth model (Solow, 1956; Swan, 1956) occurs when poor countries grow faster than rich countries resulting to the catch up process. This phenomenon corresponds to the beta convergence (Barro and Sala-I-Martin, 1995). In the last few years, numerous studies have examined the question of convergence in the African context (McCoskey, 2002; Dufrénot and Sanon, 2005; Cuñado and Pérez de Gracia, 2006; Carmignani, 2007; Charles et al., 2009; Kumo, 2011). A great number of this empirical convergence literature have focused their studies only on a cross-section growth model or panel regression and tend to avoid the role played by space and geographic spillover effects. In a different light, this paper re-examines the question of convergence among African countries from a spatial panel fixed effects perspective. More specifically, the aim of this paper is: (i) to detect clusters of high or low income countries, (ii) to explain the role of spatial effects in the convergence speed and finally (iii) to identify spatial spillovers among African countries. Our findings reveal considerable spatial autocorrelation among African countries and three clusters of countries in the distribution of per capita income. Our results show the presence of convergence and also suggest that spatial dependence between economies has an adverse impact on convergence for African countries. Finally, spatial spillovers have an important influence on countries growth implying that a country surrounded by rich neighbours will grow faster than a country surrounded by poor neighbours. The remainder of the paper is structured as follows. Section 2 explores the spatial data analysis of Africa per capita income. Section 3 describes the methodology used to test beta convergence. Section 4 discusses the results and finally Section 5 draws a conclusion. 2. Exploratory Spatial Data Analysis of Africa Per Capita Income A popular indicator of spatial correlation is the Moran coefficient, defined as: I=n∑i=1n∑j=1nwij∑i=1n∑j=1nwij(yi−y̅)(yj−y̅)∑i=1n(yi−y̅)2, where yi is a the logarithm of per capita income in the country i, the bar indicates the average value of the corresponding variable, wij is the spatial weight of the link between i and j. It denotes the generic element of a n∗n matrix of weights, called the contiguity matrix (i.e., wij=1 if the country i and the country j share a common border and wij=0 otherwise). Centring on the mean is equivalent to asserting that the correct model has a constant mean, and that any remaining patterning after centring is caused by spatial relationships encoded in the spatial weight. Like the standard coefficient of correlation, Moran’s I statistics range from −1 to 1 and the insignificance of the statistics (i.e., I=0 suggests that there are no spatial autocorrelation). When per capita incomes are positively correlated, we would expect to have positive and significant values for this statistic. The results of Moran’s I are collated in Appendix Table 1. The first column contains the observed value of I, the second is the expectation, which is −1(n−1) for the mean-centred cases, the third is the standard deviation, and finally the last column represent the p-value of the test. We implement the test for each fifteen cross sections with 45 contiguous African countries. The results show that null hypothesis of no spatial autocorrelation is rejected for all years. The average value of statistics I for per capita income is approximately equal to 0.50 implying the importance of spatial autocorrelation among African countries per capita income. Global tests for spatial autocorrelation are calculated from the local relationships between the values observed at a spatial entity and its neighbours, for the neighbour definition chosen. Because of this, we can break global measures down into their components, and by extension, we construct localised tests intended to detect ‘clusters’—observations with very similar neighbours—and ‘hotspots’—observations with very different neighbours (Bivand et al., 2008). First, let us examine the Moran scatterplot which plot the standardised per capita income of a country against its spatial standardised lagged value (Anselin, 1995). By convention, this plot places the variable of interest on the X-axis, and the spatially weighted sum of values of neighbours—the spatially lagged values—on the Y-axis. The plot is further partitioned into four quadrants at the mean values of the variables and its lagged: low-low, low-high, high-low and high-high. The four different quadrants of the scatterplot identify four types of local spatial autocorrelation between a country and its neighbours: (HH) a high per capita income country with high income per capita income neighbours (quadrant I); (LH) a low per capita income country surrounded by high per capita income neighbours (quadrant II), (LL) a low per capita income country surrounded by low per capita income neighbours (quadrant III); and (HL) a high per capita income country with low per capita income neighbours (quadrant IV). Quadrants I and III represent positive forms of spatial dependence while the quadrants II and IV belong to negative spatial association. The local Moran's I statistic can be used to test whether the per capita income is clustered in space or not. The local Moran’s I statistic for country i takes the following form: Ii=(yi−y̅)1n∑i=1n(yi−y̅)2∑j=1nwij(yj−y̅), where yi is the underlying variable for the country i, y̅ the sample mean and wij the corresponding elements of a specified weight matrix W. The null hypothesis of the test statistic is the absence of spatial autocorrelation implying that location does not matter. The local Moran’s I decomposes the global pattern and indicates to which extend a geographical locality is surrounded by similar or dissimilar values forming a geographical pattern. This implies that some structure is present in the data, which can be regarded as additional information. Similar values are likely to cluster in space and negative autocorrelation implies that contiguous areas are more likely characterised by dissimilar values than in a random pattern, which is a result not to expect intuitively, since it is the opposite of clustering. Appendix Table 2 summarises the results of the local Moran’s I statistics for the logarithm of per capita income in each of the 15 years for every country. The first column is the number of years where local Moran’s I statistic is significant at the 5% level. It is also reported in the table the number of year local statistic is in the considered quadrant. The results reveal several points. First, we note the predominance of HH and LL clustering types of per capita income during the period of study. This result tends to confirm the positive spatial autocorrelation reported in Appendix Table 1. The second thing to note is that there are 14 countries for which the local Moran’s I value is significant. All significant indicators are either in quadrant HH or LL. These results suggest that the global trend is dominated by a positive spatial association of per capita income in Africa. Significant per capita cluster indicate that countries located in a dynamic surrounding of high per capita income areas are more likely to show high per capita income than those that are neighbours of low per capita income countries and vice versa. The third thing is the identification of clusters for per capita income during the period 2000–2015. Appendix Table 2 with the conjunction of Appendix Figure 1 reveals that Africa is divided into two growth zone regimes reflecting four spatial clusters. On the one hand, we have three clusters of high-high per capita income corresponding to countries in the northern, the central and southern Africa. The northern cluster includes countries from the Maghreb (Algeria, Tunisia, Libya and Egypt). The second cluster is in central Africa consisting of two countries (Gabon and Equatorial Guinea). The last cluster of high-high per capita income is in the southern is represented by South Africa, Botswana and Namibia. These three clusters regroup countries that appear in quadrant HH and present significant local Moran’s I statistic. On the other hand, we have the low-low cluster which is located in the central east. This cluster includes Central Africa Republic, Rwanda, Tanzania and Burundi. This spatial clustering phenomenon can be due to the existence of spatial spillovers across African countries boundaries. The rest of countries coloured in white are those that do not yield significant local Moran’s I statistics at 5% level during the considered period and therefore are not subject to a significant spatial clustering. Finally, the exploratory spatial data analysis illustrates that the spatial clustering of per capita GDP of African countries is persistent. 3. Convergence in Africa Countries: A Panel Spatial Econometric Analysis The conventional absolute beta convergence approach attempts to infer whether economies converge and how this happens. Reformulated in a panel data context, the model is given by: log(yi,t+kyi,t)=αi+βlog(yi,t)+μi+φt+ui,t, where i indicates the country (spatial units), with i=1,2,…,n and t is the time periods, t=1,2,…,T. The vector yi,t contains the observations on per capita income for country i at time t, αi is the constant term, μi and φt are, respectively, the spatial specific fixed effect and the time period specific effect and ui,t is an independent and identically distributed error term for i and t with zero mean and constant variance. According to this specification, absolute convergence is said if β is negative and significantly different from zero. Therefore, we can use the usual statistical hypothesis testing procedure to validate the economic theoretic hypothesis of convergence. Specifically, if the null hypothesis ( β=0) is rejected in favour of the alternative hypothesis ( β<0), we can conclude that all countries converge to the same level of per capita income (Arbia, 2006). In most cases, authors assume that the error term has zero mean and the same variance for all observations: E(uu′)=σ2I. This underlying assumption is particularly crucial and restrictive if observations are spatially organised. In fact, if spatial spillovers across countries boundaries exist, related by the presence of spatial autocorrelation, the assumption formulated on the sampling model would be violated. In this context of spatial dependence, we use alternative specification to reconsider the question of absolute β convergence of per capita income of African countries from a spatial panel econometric analysis. In recent years, we assist to an increasing of studies using spatial econometric approach to investigate growth, convergence and regional inequalities (Badinger et al., 2004; Abreu et al., 2005; Arbia et al., 2005; Rey and Janikas, 2005; Ertur et al., 2006; Ramajo et al., 2008; Yue et al., 2014; Lim and Kim, 2015). The spatial econometrics literature has exhibited a growing interest in the specification and estimation of econometric relationships based on spatial panels. This interest can be explained by the increased availability of more data sets in which a number of spatial units over time and by the fact that panel data offer more modelling advantages as compared to cross-sectional data (Elhorst, 2010). In addition to the greater number of degrees of freedom, one of the major advantages of panel data approach to convergence is the correction of the omitted variable problem of the cross-section model. In effect, modelling the country specific effect (individual effects) allow for technological differences across countries or other unobservable phenomenon (Islam, 2003). To know what model specification is more appropriate for the absolute convergence and for the data generating process, we first present the family of spatial panel regression models including SAR, SEM and SDM. The spatial autoregressive model (SAR) provides a starting point since it is the most basic spatial model. The SAR model estimated in this paper take this form: log(yi,t+kyi,t)=αi+βlog(yi,t)+ρ∑i=1nwijlog(yi,t+kyi,t)+μi+φt+ui,t, where ρ is the scalar spatial autoregressive parameter. The other parameters of this equation are defined previously. The SAR model can be considered as a spatially weighted average of all the neighbours of the country i’s per capita income. So, ρ captures the sensitivity of the endogenous variable to spatially lagged variable. On the other hand, the model statement when there is residual pattern in the error component that we label SEM can be written as follows: log(yi,t+kyi,t)=αi+βlog(yi,t)+μi+φt+ui,t, with ui,t=λ∑i=1nwijui,t+εi,t, and εi,t~i.i.d.(0,σε2), where λ being the spatial error parameter. Combining these two equations yields the data generating process of the SEM model: log(yi,t+kyi,t)=αi+βlog(yi,t)+μi+φt+(In−λ∑i=1nwij)−1εi,t. Finally, the SDM provides a more general view of the spatial regression model since the spatial lag of starting per capita income is added to the SAR specification: log(yi,t+kyi,t)=αi+βlog(yi,t)+ρ∑i=1nwijlog(yi,t+kyi,t)+γ∑i=1nwijlog(yi,t)+μi+φt+ui,t, where γ is the spatial cross regressive parameter. To test whether the spatial spillovers effects exist in the convergence process, we can reconsider the SDM model in a matrix form: Y=αιn+βX+ρWY+γWX+μ+φ+u, where Y is an nT∗1 vector of the logarithm of per capita income over each time period, ιn denotes a nT∗1 of ones associated with the constant term α, β represents the parameter of convergence ρ is the spatial autoregressive parameter, W is the weighted matrix adapted to the panel dimension n∗T. It is the Kronecker product of a T∗T identity matrix and the n∗n spatial weighted matrix defined previously. γ is the cross regressive parameter, μ and φ are respectively an nT∗1 vector of the spatial specific fixed effect and the time period specific effect, u is an nT∗1 vector of independent and identically distributed error term for i and t with zero mean and constant variance. Rewritten in a reduced form, the model becomes1: Y=S(W)X+V(W)αιn+V(W)μ+V(W)φ+V(W)u. S(W)=V(W)(Inβ+γW). V(W)=(In+ρW)−1=In+ρW+ρ2W2+… Then the matrix of partial derivatives of the endogenous variable (Y) with respect to the explanatory variable (X) in country 1 up to country n in a particular point in time can be expressed as: ∂Y∂X=S(W)=(In+ρW)−1(Inβ+γW). An implication of this is that a change in a single observation (country) associated to the explanatory variable will impact the country itself (direct effects) and potentially impact all other countries indirectly (indirect effects). The diagonal elements of the matrix S(W) contain the direct impacts and the off diagonal elements represent indirect impact (Lesage and Pace, 2009). The average total effect, the average direct effect and the average indirect effects are formally defined as: M¯direct=n−1tr(S(W)). M¯total=n−1ιnS(W)ιn′. M¯indirect=M¯total−M¯direct. Similarly, the measures of impact for the SAR model can be derived from the SDM specification: Y=S(W)X+V(W)αιn+V(W)μ+V(W)φ+V(W)u. S(W)=V(W)(Inβ). V(W)=(In+ρW)−1=In+ρW+ρ2W2+… Concerning the SEM model, the reduced form yields the data generating process. Using matrix form, the error term and the model would be defined as follows: u=(In+λW)−1ε. Y=αιn+βX+μ+φ+(In+λW)−1ε. These specifications show the transmission of a random shock through the system. It is evident that a shock introduced into a specific country will not only affects the per capita income in that country but, will also affect the per capita income of other countries. Given that the inverse operator represents the spatial matrix multiplier, it defines an error covariance structure that diffuses state-specific shocks not only that country’s neighbours but through the system (Rey and Montouri, 1999). 4. Empirical Results Appendix Table 3 reports the results of models estimated for the 45 contiguous African countries over the period 2000–2015. A long time span of 5 years is used (k = 5). A short time span will make the short term disturbances large and the error term should be less influenced by business cycle fluctuations and less likely to be serially correlated (Islam, 1995). Indeed, we assume that in spatial specifications, spillover effects might take a long time to exercise a significant influence. The first column of the table reports the ordinary least squares of the non spatial model without fixed effects and spatial dependence diagnostics for OLS residuals while the second column contents estimations with fixed effects. Based on the Hausman test, model with fixed effects is more appropriate. The estimate of the convergence rate increases strongly ever since fixed effects are introduced. We use the Lagrange Multiplier tests statistics for error and lag dependence (Anselin, 1988) and theirs robust versions (Anselin et al., 1996). The results show very strong evidence of spatial dependence. Then, if the spatial effects are not modelled in the convergence process, the OLS estimations suffer from a serious misspecification. We therefore focus our interpretation on the results of the spatial models. In order to identify the spatial specification with higher adequacy, we follow the strategy described by LeSage and Pace (2009) and Elhorst (2010). The SDM is used as a general specification (unrestricted model) to test for the alternatives. Thus, we estimate a SDM but we would like to know if it is the best model for our data. More precisely, we test the null hypothesis that spatial Durbin model can be simplified to a spatial lag model or a spatial lag model. We can therefore easily note that if γ=0, the model becomes a SAR, while if γ=−ρβ the model collapse to a SEM. To test the null hypothesis, Wald or likelihood ratio (LR) test can be performed. In our case, we use a Wald test which has one degree of freedom. These following results are obtained. For γ=0, we have a test statistic of 267.820 with a p-value smaller than 1% and for γ=−ρβ, the test statistic is 91.020 with a p-value also smaller than 1%. The test results imply that neither the first restriction nor the second are acceptable for our data implying that the most appropriate model is SDM. To the choice between fixed and random effects, we perform a robust version of Hausman’s specification test. The random effects are strongly rejected by the Hausman test (p-value smaller than 1%). We conclude that all tests specification point towards fixed effects SDM. This result is confirmed by the value of the Akaike Information Criterion (AIC) and those of log likelihood. In the traditional beta convergence model, the speed of convergence is calculated from the coefficient of initial per capita income. According to LeSage and Fischer (2008) and Fischer (2009), this interpretation is not valid in the case of SDM model. Indeed, in the SDM model, the correct way to calculate convergence rate is to use the total effect estimate. The total effect is highly significant (at 1% level) with a negative sign, confirming the presence of absolute convergence during the period 2000–2015. Its value of −0.157 implies an annual convergence speed of 1.068% and the time necessary for the countries to fill half of the difference from their steady states is about 64.901 years. The speed of convergence estimated using the fixed effects SDM is lower than those obtained with the other spatial specifications. Concerning countries within the African continent, studies reported either very lower speed or non-existence of convergence (McCoskey, 2002; Dufrénot and Sanon, 2005; Cuñado and Pérez de Gracia, 2006; Carmignani, 2007; Charles et al., 2009; Kumo, 2011). Note that the empirical studies of convergence in Africa largely uses cross-sectional regression, non spatial panel data fixed effects or non spatial pooled panel data estimators. To conclude, our results on convergence process highlights the importance of controlling fixed effects across countries and spatial dependence. The estimated coefficient of ρ is 0.342. This coefficient measures the degree of per capita GDP interdependence among African countries. It is positive and highly significant. This result suggests that per capita income proximity matters in the distribution of the starting level of income. The parameter of spatial cross regressive ( γ) is positive and significantly different from zero. Past studies have incorrectly interpreted the coefficient of the spatially lagged variables as indicating the impact of neighbouring units on the dependent variable (LeSage and Fischer, 2008; Fischer, 2009). In fact, each country is a neighbour to its neighbouring countries and a change in the initial income levels of country i will impact country i itself and therefore indirectly the income growth of neighbouring countries as country j. This is because any factor that influences per capita income of country i in a model containing spatial lag will also influence neighbouring country’s income growth (LeSage and Fischer, 2008). Thus, for a better interpretation, we consider the indirect effect and the direct effect. To control the spatial spillover effects into growth equation models, the economists usually refer to the indirect impacts. The results show that the indirect effect is positive and statistically significant at the level of 1% indicating the existence of spillover effects. This suggests that in Africa, having neighbours with higher levels of initial per capita income leads to higher growth rates. In other words, a country surrounded by wealthy neighbours would growth faster than a country which is surrounded by poor neighbours. The model is expressed by using a log transformation of both the dependent and independent variable, so the estimated parameters can be interpreted as elasticities. The coefficient of the indirect effect is equal to 0.386, and then a 10% increase in the initial level of income of the country’s neighbours would increase the income growth in the country by 3.86%. This result is of course contrary to convergence, since it points to growth rates that will increase the gap between high and low income countries leading to spatial clusters of high (and low) income countries, rather than an equal distribution of income levels across space. So, these positive spatial spillovers have an inhibitor role in the speed of convergence. Since the spatial dependence on neighbouring country’s per capita income growth ( ρ) is positive, a change in initial income influences positively other countries’ income growth which in turn impacts positively on the typical country’s income growth. Note that in the literature, the key theoretical mechanisms identified to lead to convergence across regions are factor mobility, trade relations, and technological diffusion. The direct effect estimated of the initial per capita income is negative and statistically significant. The negative direct effect is of course consistent with conventional reasoning regarding the negative relationship between initial income levels and income growth rates. The estimate of the direct impact is equal to −0.543, so we would conclude that a 10% decrease in country’s initial income level would increase the country income growth by 5.43%. This result confirms that in the context of Africa, a poor country tends to grow faster than a rich one (convergence). 5. Conclusions In this paper, we analysed convergence process in Africa. Our empirical strategy was based on spatial panel data approach. Controlling fixed effects in the panel allow us to disentangle the problem of omitted variables and modelling the regional interaction between countries correct the misspecification due to the omitted spatial dependence. More preciously, we have examined the spatial dependence, the beta convergence of per capita income and the effect of spatial spillovers in Africa during the period 2000–2015. Ours results can be summarised as follow. Firstly, the exploratory spatial data analysis shows that the economic geography of Africa presents a strong spatial dependence and a significant and persistent clustering of per capita income. Secondly, we find evidence for beta convergence during the period under consideration. Furthermore, it is remarkable that the spatial econometric analysis has shown that the spatial spillovers (indirect effects) studied here lead to decrease in the speed convergence in African countries. Thirdly, the empirical estimates indicate the existence of significant spatial spillovers. This result suggests that in Africa, having neighbours with higher levels of initial per capita income leads to higher growth rates. Overall, our findings highlight the importance of allowing for spatial dependence in empirical growth models and particularly for convergence process. Finally, the policy message emerging from our findings is that strengthening regional economic communities should play an important role in facilitating coordination and harmonisation of policies and in fine monetary integration, especially between countries that share a common border. We illustrate this implication with the fact that spatial spillovers exist and tend to be localised in northern, central and southern Africa. Supplementary material Supplementary material are available at Journal of African Economies online. Acknowledgement I would like to thank Peter Winker, Peter Tillmann and an anonymous referee for comments. However, the views expressed in this paper are those of the author. Footnotes 1 For further description of direct, indirect and total effects, see Lesage and Pace (2009). References Abreu M. , de Groot H. L. 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Journal of African Economies – Oxford University Press

**Published: ** Nov 2, 2017

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