STRUCTURAL CONVERGENCE BETWEEN AFRICAN COUNTRIES: EMPIRICAL EVIDENCE

This paper aims to investigate structural convergence in selected African countries over the period 1994-2019. Using panel data for 48 African countries and several estimation methods [Panel-Corrected Standard Errors (PCSE), Feasible Generalized Least Squares (FGLS), tobit model, instrumental variable, and Granger non-causality], the results show the existence of the phenomenon of sectoral structural convergence in Africa, i.e. a greater similarity in sectoral structures while income gaps are narrowing. The paper also highlights the service sector's low relative productivity level and industrial sector's low labor force attractiveness despite a significant shift in labor from the agricultural sector and a higher level of relative productivity respectively. To address this issue, the development and acquisition of human and physical capital would be necessary to develop the industrial sector and increase the service sector's productivity. find results very similar to Wacziarg (2001) . C. Longhi and Musolesi (2007) study the structural convergence between forty European cities. Using the method by Wacziarg (2001) , they use sectoral employment and sectoral value -added data to test the relationship between structural similarity and real convergence. The ir results are similar to those of Wacziarg (2001) and confirm the existence of a phenomenon of structural convergence between these European cities. Palan and Schmiedeberg (2010) investigated the structural convergence of 14 EU countries from 1970 to 2005. Their analysis is based on employment data. They investigated inter -sectoral and inter- industry convergence, focusing on changes between the agricultural, manufacturing, and service sectors. They find a significant and rapid inter- sectoral convergence, accompanied by a mixed picture concerning inter- industry convergence. The results also show a general shift towards technologically advanced industries, while employment shares in traditional low-tech industries decrease. Based on sectoral employment shares, Albu (2012) studies the structural convergence between European countries (EU -27), Eastern European countries (EU -10), and Western European countries (EU -15) during the period 2000-2011. To assess changes in the economic structure, the author expresses the employment shares in the three sectors of the economy as a function of the Gross Domestic Product ( GDP) per capita. His results show a process of structural convergence in the EU over the period analyzed, as GDP per capita increases. Marelli and Signorelli (2 010) use a β convergence test to test structural convergence in EU -27 countries from 1990 to 2007. The results show that convergence of sectoral structures is well e stablished for the EU, the old members (EU -15),


INTRODUCTION
The convergence theory, which states that lagging countries grow faster than leading countries, has been in the economic literature since Veblen (1915), Ramsey (1928), Viner (1950), Solow (1956), Gerschenkron (1962), Abramovitz (1979Abramovitz ( , 1986. More recently, authors such as Krugman (1991) and Wacziarg (2001) focused on structural convergence, another equally interesting aspect of convergence. According to Wacziarg (2001) "two countries are said to structurally converge if convergence in their per capita incomes is accompanied by convergence in their sectoral structure". This definition refers to sectoral structural convergence, limited to sectoral structure similarity. Absolute structural convergence refers to a process that extends beyond sectoral similarity and includes business cycle synchronization and foreign trade integration (Alexoaei and Robu 2018).
There are many reasons to be interested in the phenomenon of structural convergence.
First, the structural transformation of a country's economy is one of the main factors in economic development (Lewis, 1954;McMillan and Rodrik, 2011). Structural convergence is only the result of multiple converging structural transformations in several countries.
Second, structural convergence suggests that countries follow similar development paths characterized by increases and decreases by types of similar sectors as per capita incomes increase and those countries can converge towards a structural "steady-state", in which the sectoral composition of production becomes more uniform across countries.
Third, if shocks to the macroeconomy are sector-specific, structural convergence has implications on the international transmission of business cycles: it should give rise to increased international business cycle correlations (Imbs, 2000).
Fourth, understanding the factors that induce structural convergence can advance theory on a long- find results very similar to Wacziarg (2001). C. Longhi and Musolesi (2007) study the structural convergence between forty European cities. Using the method by Wacziarg (2001), they use sectoral employment and sectoral value-added data to test the relationship between structural similarity and real convergence. Their results are similar to those of Wacziarg (2001) and confirm the existence of a phenomenon of structural convergence between these European cities. Palan and Schmiedeberg (2010) investigated the structural convergence of 14 EU countries from 1970 to 2005. Their analysis is based on employment data. They investigated inter-sectoral and inter-industry convergence, focusing on changes between the agricultural, manufacturing, and service sectors. They find a significant and rapid inter-sectoral convergence, accompanied by a mixed picture concerning inter-industry convergence. The results also show a general shift towards technologically advanced industries, while employment shares in traditional low-tech industries decrease. Based on sectoral employment shares, Albu (2012) Crespo and Fontoura (2007) studied the determinants of structural similarity in Portugal. They use employment data from these counts to estimate their structural similarity. The results show that there is an evolution towards more sectoral similarity over time between these regions. Also, the results show that the structural similarity between the Portuguese counties increases with geographical proximity, a common border, the similarity of factor endowments in terms of physical and human capital, and the similarity in terms of centrality and market size.
In addition to empirical evidence of structural convergence by sectoral employment shares, several authors have also used sectoral value-added shares (sectoral productivity), business cycle synchronization, and trade integration to highlight structural convergence between groups of countries and/or regions (Landesmann, 2000;Fagerberg, 2000;Gács, 2003;Gugler and Pfaffermayr, 2004;Abegaz, 2002Abegaz, , 2008 database. The database includes value added by sector 1 , employment by sector, population, GDP, Gross National Income (GNI), and gross savings.

Empirical models for structural transformation in Africa
To investigate empirically the structural transformation processes underway in African countries in terms of sectoral value-added and sectoral employment as a function of GDP per capita and inspired by Duarte and Restuccia (2010), Albu (2012), and Herrendorf, Rogerson, and Valentinyi (2014) we express the sectoral shares (employment and value-added in agriculture, industry, and service in Africa) in terms of GDP per capita.

Sectoral
[( , To calculate the relative productivity level of each sector in the whole of Africa, we followed De Vries, Timmer, and De Vries (2015). We first calculate the sectoral productivity level, i.e. the value-added of each sector divided by the population engaged in that sector. Secondly, we calculate the productivity of the economy (Africa), i.e.
the value-added of the entire economy divided by the total population engaged in the economy. The relative productivity level is calculated as the ratio of the productivity level of the sector to the productivity level of the whole economy. This index allows us to see what the productivity level of each sector represents in the entire economy.

Empirical models for structural convergence between African countries
To empirically investigate the existence of structural convergence in Africa, we estimate the following empirical models in the spirit of Wacziarg (2001) and Barrios, Barry, and Strobl (2002). We build a model that relates the sectoral structure to the income gap to investigate whether the reduction in the income gap is associated with greater sectoral similarity.
This model is presented as follows: Where ksiVA AG ij (t) refers to the Krugman Specialization Index (Krugman, 1991) computed with value-added (VA) data from the agricultural (AG) sector between countries i and j at year t. We first evaluate the share of the value-added in the agricultural sector in the total value-added produced in the country i at year t which we denote as ℎ (t). We then evaluate the share of the agricultural sector value-added in the African region (country j), i.e. all the other African countries in our database except country i at year t as in S.
Longhi, Nijkamp, and Traistaru (2004) or Palan and Schmiedeberg (2010) for computing KSI. We note this value as ℎ (t). The ksiVA AG ij (t) will be equal to the absolute value of the difference between ℎ (t) and ℎ (t).
ksiVA IND ij (t) and ksiVA SERV ij (t) are computed in the same way as ksiVA AG ij (t) with respect to value-added data from the industrial sector and service sector. The KSI in equations (3)(4)(5), (3)(4)(5)(6), and (3-7) are also computed in the same way as the previous ones but with sectoral employment data. The KSI takes a value of zero if the country i has a perfectly identical sectoral structure to the rest of Africa, and a maximum value of 1 if it has no sectoral similarity with the rest of Africa.
INCOMDIFF ij ( ) is the absolute value of the difference in GDP per capita between countries i and j at year t.
is the absolute value of the difference in market size measured by population (POP) between countries i and j at year t.
( ) is a year-specific effect materialized by a set of time dummies, and ε ij (t) is the usual error term.
Since our dependent variable KSI is bound between 0 and 1, we estimate our equations in logarithmic form.
Equations  to (3-7) allow relating income convergence to sectoral similarity. If reduction in income gaps is associated with a reduction in gaps between sectoral structures then we are in a situation of structural convergence so the coefficient 1 will then have a positive and significant sign. If the coefficient 1 is negative, then we are in a situation of structural divergence where the reduction in income gaps is associated with greater sectoral heterogeneity. The second independent variable POPDIFF is a kind of control variable that allows seeing the effects of the reduction in domestic market size gaps, thus a positive sign of the coefficient α 2 of this variable implies that the reduction in domestic market size gaps is associated with more sectoral similarity and a negative sign implies that the reduction in domestic market size gaps is associated with more sectoral heterogeneity.
As mentioned above, two countries are said to structurally converge if convergence in their per capita incomes is accompanied by convergence in their sectoral structure. Convergence of per capita income occurs if the difference or ratio of per capita income between the richest to the poorest country in each pair decreases. In our case, each pair consists of one of the 48 African countries (represented by index i), and another country that represents all other African countries (represented by index j) except country i. Figure 1 presents the ratio of GDP per capita between two pairs of countries, the Africa-Rwanda pair and the South Africa-Africa pair (the richest country divided by the poorest country). Rwanda at the beginning of our study period had the lowest level of GDP per capita while South Africa had one of the highest GDP per capita, Figure 1, elaborated by authors, shows that the Africa/Rwanda and South Africa/Africa ratios are continuously declining. This decline implies that Rwanda, which was poorer than Africa, is converging toward Africa and Africa, which was poorer than South Africa, is converging toward South Africa.

STRUCTURAL CONVERGENCE BETWEEN AFRICAN COUNTRIES: EMPIRICAL EVIDENCE
Page 10 of 32    close to 10. This shows that the service sector in Africa has a low level of relative productivity 5 because while the share of labor is increasing considerably, the share of value-added is not following the same trend and seems to be decreasing. Based on the employment data, the industrial sector increases slightly, whereas considering the value-added data, it increases more significantly and even exceeds the service sector for values of lnGDP Per-capita close to 9. In contrast, for this same value for the employment data, the service sector is far above the industrial sector. This shows that the industrial sector in Africa has a better level of relative productivity than the service sector. This finding is characteristic of a structural transformation process, and that result is similar shift of labor seems to show a general structural convergence process. While the GDP per capita is increasing, the sectoral employment and value-added shares in the three sectors follow a similar trend. Table 1, elaborated by authors, shows that in 1994 the productivity level in agriculture was 0.32 times that of the total economy, while in the industry it was 2.6 times that of the total economy, and in the services sector, it was 1.6 times that of the total economy, the end of the period shows values similar to that of 1994.
Thus, the productivity level in the industrial sector in Africa, over the entire period is higher than that of the service sector and itself far higher than that of the agricultural sector.  Table 1 shows that in 1994 the productivity level in the agriculture, industry and services sectors were 0.32, 2.6, and 1.6 times that of the total economy respectively. The trend remained almost the same in 2017, although the values for the industry show a peak around 2017 before declining towards its value at the beginning of the period, while the value for services has declined slightly. Thus, the productivity level in the industrial 5 Considering only the workforce factor. Page 13 of 32 ERUDITUS® -PUBLISHER OF SCHOLARLY, PEER-REVIEWED OPEN ACCESS JOURNALS https://www.eruditus-publishing.com/jowett sector in Africa, over the entire period is higher than that of the service sector and itself much higher than that of the agricultural sector. This is because agricultural production is still done traditionally in many African countries and is also subject to climatic uncertainties. The productivity level of the service sector is higher than that of agriculture over the entire period, which is shown in the Figure 4, elaborated by authors. The diversity of activities in this sector and their permanent nature make its relative productivity much better than the agricultural one. The industrial sector has the best relative productivity of all three sectors (Figure 4), as the labor force is better qualified and has access to better physical capital. Most of the labor entering the service sector come from the agricultural sector, which is generally unskilled and usually engages in traditional service sector activities (security services, cleaning, parcel deliveries, dry cleaning, etc.). This would be an explanation for the fact that the productivity level of the service sector over the whole period is slightly decreasing despite the fact that this sector continues to receive labor ( Figure 4). The productivity level of the industrial sector, after a slight increase, is also slightly continuously decreasing since the years 2005 (Figure 4). Page (2012) states that "deindustrialization after 1990 in Africa was characterized not only by a decline in the share of manufacturing output and employment but also by a decline in the diversity and sophistication of the region's manufacturing sectors". This partly explains this decline in the relative productivity level of the industrial sector. Also, the globalization of international trade, which became more pronounced in the 2000s, followed by the rapid industrialization of some countries, particularly in Asia, has put a strain on the weak African industrial sector, which could also explain the continuing decline in its productivity levels.
According to McMillan and Zeufack (2021), the fact that the African industrial sector has a higher relative productivity level despite having the lowest labor share shows it is becoming more capital-intensive.

Descriptive statistics
In this section, we address equations  to (3)(4)(5)(6)(7) in order to investigate the structural convergence of African countries. The basic statistics for the annual frequency data for all the variables used in this section are summarized in Table 2 calculated by authors. It is worth noting that the database sample has a large number of available observations (1,248). It should also be noted that the minimum and maximum values of all KSI ranging between 0 and 0.5 indicate a low degree of sectoral heterogeneity at first glance, as a KSI close to 0 is synonymous with sectoral homogeneity.  Table 3, calculated by authors, shows pairwise correlations between variables. We observe a positive and significant correlation between incomdiff and all the KSI. This seems to suggest that greater sectoral similarities accompany narrower income gaps. However, correlation does not necessarily mean causality. The (1) ksiEmpAG 1.000 (2) ksiEmpIND 0.737*** 1.000

Panel-corrected standard errors (PCSE) method results.
To investigate the existence of structural convergence between African economies, we run fixed-effect 7 regressions of the KSI indexes on the values of real convergence and domestic market size (incomdiff and popdiff), after which we perform tests of autocorrelation, heteroscedasticity and crossectional dependence. Tests reveal that the models suffer from autocorrelation and heteroscedasticity. We circumvent these problems by which show that a shrinking income gap ceteris paribus, is significantly linked to greater similarity in economic structure. Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 Indeed, the positive and significant coefficients of incomdiff indicate the structural convergence of African economies using both sectoral employment data and sectoral value-added data 9 . Market size differences, on the other hand, once controlling for incomdiff, appear to act against the similarity of sectoral structures.
Indeed, the negative and significant signs of the popdiff 10 coefficients indicate this 11 .

4.2.4.
African sub-regional features of structural convergence In this section, we investigate whether the evidence of structural convergence found in the previous section is only driven by specific subsets of the sample, or whether it is a reality across all the African continent?
For this purpose, we consider 5 Regional Economic Communities (RECs) on the African continent for which  Table   7) show a partial structural divergence. Indeed, a negative and significant coefficient of incomdiff for the agricultural and services sector shows that a reduction in income gap, ceteris paribus, is significantly related to greater heterogeneity of these sectoral structures. For the industrial sector, the coefficient remains positive and significant, indicating the structural convergence in this sector. A positive and significant coefficient of popdiff for all three sectors shows that the difference in market size favors the similarity of sectoral structures. 9 These results are very similar to those of Wacziarg (2001), Barrios, Barry, and Strobl (2002) and C. Longhi and Musolesi (2007). 10 Except for ksiEmpIND and ksivaAG where the difference in market size acts positively for the similarity of sectoral structures. 11 These results are very similar to those of Barrios, Barry, and Strobl (2002). 12 List of countries by RECs in appendix.   (3)(4)(5), (3)(4)(5)(6) and ( Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

STRUCTURAL CONVERGENCE BETWEEN AFRICAN COUNTRIES: EMPIRICAL EVIDENCE
The partial structural divergence observed in the AMU can be explained by the small size of the database, but also by the important differences in factor endowment and in developmental options of the countries of that union. Algeria is endowed with oil and gas resources and has opted since its independence for industrial development, Egypt still has an agricultural sector that employs more than 20% of the workforce while Morocco and Tunisia are more tourism-oriented. The global structural convergence highlighted by Wacziarg (2001) no longer exists when considering only OECD 13 countries, this seems to be the case for our results with AMU as this community is relatively richer on the continent when compared to others. This result is in line with findings from Imbs and Wacziarg (2000), who showed that rich countries appear to be in a stage of sectoral specialization, while others are in a stage of sectoral diversification. 13 Organization for Economic Co-operation and Development. For the ECCAS community (Tables 9 and 10, estimated by authors), despite a positive sign in almost all the incomdiff coefficients, their non-significance means no conclusion can be drawn, except for the data on value-added of the industrial sector, which shows a positive and significant coefficient indicating structural convergence. Table 9: FGLS estimates employment data for ECCAS [equations (3)(4)(5), (3)(4)(5)(6) and (3-7)] For the remaining communities, namely ECOWAS, IGAD+EAC, SADC, structural convergence is a widely shared reality for all data (employment and value-added, Tables 11 to 16, estimated by authors). The difference between market sizes is sometimes in favor and sometimes against sectoral similarity. The coefficient implying a structural divergence in Table 15 for SADC with value added data is certainly due to significant industrial gaps in this community, as countries such as South Africa, Botswana, and Mauritius show significant differences in industrial value-added with other countries in the community.

Tobit model
The dependent variable KSI is bounded below by 0 as shown in Table 2, this may firstly create problems for out-of-sample predictions, secondly, it may also lead to inconsistent parameter estimates if a linear model is fitted to a bounded dependent variable (Wacziarg, 2001). To correct this possible problem, we apply a Tobit model with a left-censoring limit with random effects. The results presented in Tables 17 and 18 show that this method also confirms the structural convergence of African economies for both sectoral employment and sectoral value-added data 14 . Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Instrumental variable (IV) approach
The meaning of the causality between the reduction in income gaps and the homogeneity of sectoral structures may not be clearly accepted despite the positive link we have highlighted through our estimates. It is easy to accept that the industrial specialization of a country can be both an outcome and a determinant of per capita income. Specialization in high value-added sectors is likely to generate higher incomes than specialization in traditional sectors. Beyond this, there may well be other factors changing over time, such as changes in economic, social, and industrial policies, which affect both industrial structure and incomes that we have not taken into account, but which could bias our estimated coefficients. In order to investigate how these factors may affect our results, and inspired by Barrios, Barry, and Strobl (2002) we use an IV approach. We instrument our independent variable that materializes income convergence incomdiff, with an instrument that materializes the difference in savings per capita between countries (savingcapdiff) 15 . It is easy to see that savings may affect the wealth of a country, but it is unlikely to affect, at least in the short term, the structure of that country's sectors.
To verify the above statements and the validity of the instrument, we perform post-estimation endogeneity tests on the independent variable incomdiff, over and under-identification tests on the instrument savingcapdiff, and heteroscedasticity tests to see the disturbance in the models.  show that the instrument is valid and the models do not suffer from heteroscedasticity for all data and sectors.  Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1

Granger non-causality test
To investigate whether the reduction in income difference (incomdiff) Granger-cause homogeneity in sectoral structures (KSI), a Granger non-causality test is used. The variables incomdiff and KSI are all stationary, so this method can be applied. The results in Tables 22, 23, and 24 estimated by authors show that the null hypothesis that incomdiff does not Granger-cause KSI is rejected with a highly significant probability for all three sectors with employment data 16 . Thus, the alternative hypothesis is accepted which implies that the reduction in income difference Granger-cause homogeneity of sectoral structures for several panels, which is synonymous with structural convergence. H1: incomdiff does Granger-cause ksiEmpAG for at least one panelvar (countrinum). 16 For sectoral value-added data, the non-strongly balanced nature of the panel makes estimates impossible.  H1: incomdiff does Granger-cause ksiEmpIND for at least one panelvar (countrinum). H1: incomdiff does Granger-cause ksiEmpSERV for at least one panelvar (countrinum).

CONCLUSION AND POLICY IMPLICATIONS
Structural convergence among African countries is a topic that has not gained much attention in the literature. The paper contributes to fill this gap by producing a comprehensive survey of the sectoral structural convergence of African countries over the period 1994 to 2019. Based on sectoral employment data, sectoral value-added data, income differences, and market size differences, the paper documented the existence of sectoral structural convergence in Africa, i.e. a greater similarity in sectoral structures while income gaps are narrowing. The occurrence of structural convergence among African countries implies that globally these countries follow similar stages of development characterized by the rise and fall of similar sectors, and those countries can converge towards a structural 'steady state'. Thus, African countries have the opportunity to develop common policies to achieve their latent comparative advantage. Indeed, the growth potential available in Africa should encourage countries to pool their efforts in order to achieve their latent comparative advantage