The Role of Productive Structures in the Attractiveness of African Economies: A “Lucas Paradox” Approach

The purpose of this article is to analyze the paradox of atrophy of capital flows to African countries, while economic theories predict that such flows of investment should be large enough because of higher returns on capital in countries where its presence is relatively low in production factors. The GMM estimate of a system of two equations for a sample of 25 African countries over the period 2004-2014 gives the following results: the low investment flows are due to the production structures of African economies, which lack efficiency and attractiveness. Also, by improving the structural elements of the economy that render production ineffective, African countries can thus increase their potential to raise larger flows of foreign direct investment.


Introduction
In line with the principle of declining marginal productivity, so dear to neoclassical theory, capital must migrate from the industrialized countries where it is abundant, to the developing countries where it is scarce and where its remuneration is consequently higher. In this context, low-income countries should not have particular difficulties in financing their development projects. But it is clear that developing countries in general and those in Africa in particular have difficulties in attracting foreign direct investment (FDI): this phenomenon is not new, it is the famous paradox of Lucas [1]. Moreover, well before Lucas and criticizing the theory of HOS, Wassily Leontief [2] had already "thrown a pavement relative to FDI flows. Indeed, local conditions can affect attractiveness by making productivity. It is then necessary to show, firstly, that attractiveness depends on the overall productivity of the factors and then to determine the factors that affect this productivity.
To achieve this dual objective, this article uses an econometric methodology based on a two-stage model. The first, based on Alfaro et al. [8], measures the impact of Total Factor Productivity (TFP) on the inflow of foreign direct investment; the second floor starts from Jajri [9] to examine the influence of the structural features of economies on TFP. In this perspective, the chosen model is a system of simultaneous equations. However, their estimation poses some problems, two of which are major. Firstly, the temporal dimension, which is rather weak because of a decline of only ten years. Secondly, there is work that argues that FDI can boost TFP growth, thanks to the externalities of technology diffusion. This is obviously a problem of double causality. To correct this inverse causality, we apply the estimation by the so-called generalized moment's method (GMM), which has the merit of correcting the endogeneity of the explanatory variables of interest and other explanatory variables, especially for small panels whose temporal dimension is small compared to the number of individuals.
For the rest of the article, Section 2 makes a statistical analysis of FDI flows. Section 3 presents a review of the literature on the determinants of FDI. Section 4 describes [10] the methodology and presents the data used. The results and their analysis are discussed in Section 5 and Section 6 concludes.

Analysis of the Distribution of FDI around the World
The analysis of the distribution of FDI flows shows that developed economies are the preferred destination for FDI over time, even if their attractiveness has been somewhat eroded. More specifically, Figure 1 shows that between 1995 and 2016, developing countries received between 15% and 34% of FDI inflows, while developed countries had most of these flows ranging from 43% to at 83%. But the distribution of FDI flows between developing economies itself is far from uniform. Since the 1990s, developing countries in Asia have consistently received most FDI to developing economies, while Africa has been the least attractive region.
Africa's share of world flows has been stable, although the reading of this progression can be analyzed in two phases. A first where flows go from close to 10% to less than 1% in 1980. Then the second phase where the influx of capital rises to stabilize at an average around 3% until 2013. The process of globalization that was developing at that time left Africa behind. The share of African economies in the flows of developing countries is also falling, it has remained below 10%.
While Asia grew from 22 billion inflows in 1990, to a peak of more than 430 billion US dollars in 2011, an increase of 408 billion, the African rose from 2 billion US dollars to 57 billions of dollars over the same period, an increase of 55 billion, which corresponds to only 13.48% of the increase of flows towards Asia. It must be said that this volume appears relatively small, compared to the performance of Asia and given the context of globalization.
This limited influx of investment in developing countries in general ( Figure  2), while these countries are characterized by the scarcity of capital, has sparked a great deal of research in order to explain the reasons for the paradox.

Literature Review
Two main explanatory approaches emerge to explain the "Lucas paradox". The first approach concerns differences in the fundamentals of economies. More specifically, these are factors affecting total factor productivity, such as the heterogeneity of factors of production and the institutional structure [Lucas (1990) [1] and Alfaro (2003) [4]].
The second approach, advocated mainly by Reinhart and Rogoff (2004) [5] and Portes and Rey (2005) [10], is based on the imperfections of international capital markets, such as asymmetric information and funding frictions.
With regard to human capital, Lucas (1990) [1] shows, in a theoretical study between India and the United States, that India has a productivity 58 times higher than that of the United States. But taking into account the heterogeneity  of the factors and the externalities it generates eliminates this productivity gap. Indeed, human capital can make a significant contribution to the ability to adapt and implement new, more productive technologies. Similarly, in the context of the use of existing technologies, capital productivity may also depend on human capital in the broad sense, that is, not only literacy and other aspects of education, but also the industrial experience. However, for Darreau and Pigalle (2008) [11], the human capital productivity gaps obtained by Lucas (1990) [1] are quite unrealistic in order to be able to retain the unique hypothesis of differences in terms of human capital endowment. Other factors such as institutions will emerge to explain this state of affairs. North (1991) [12] defines the institutions of a society as the set of rules of the game. These rules shape the relationships between companies and provide an essential framework for an agent to enter into transactions. A suitable institutional environment would reduce transaction costs [Williamson (1975) [13] and Williamson (1985) [14]]. Nielsen et al. (2017) [15] note that the literature focuses primarily on the additional risks and costs of performing certain economic activities in territories characterized by poor institutions. Thus, the poor quality of institutions affects the attractiveness of low-income countries, where property rights are not always respected, corruption is endemic, revolutions, coups and expropriations are more frequent.
Also, the results of authors such as Alfaro et al. (2003) [4] corroborate these intuitions and show that institutional weaknesses create a gap between expected returns and actual returns. While technology is easily accessible to all countries, barriers to adoption or differences in the effective use of technology can significantly change the return on capital. In such a case, the equalization of returns does not necessarily imply capital flows from rich to poor countries. Later work by Alfaro (2008) [4] reveals that the quality of institutions is the main causal variable explaining the Lucas paradox. Modern Economy But for Azemar et al. (2013) [16], these empirical works are controversial.
First, the quality of institutions is inherently difficult to measure. According to the author, many cross-sectional studies ignore important fixed country effects, panel data would not allow to measure the impact of institutions, in light of the small variation over time. Second, the sense of causality is uncertain: although good quality institutions can encourage capital flows, they can also foster institutional development. Third, the mechanism by which institutions affect capital flows is often unknown. Therefore, the imperfections of the capital markets can be another way to explain the paradox of Lucas.
The main explanations for the imperfection approach in international capital markets are information asymmetry and sovereign risk [Reinhart (2004) [5]; Rogoff and Gertler (1990) [17]]. According to Montiel (2006) [18], the paradigm of the simple neoclassical growth model assumes an absence of informational frictions that can hinder investment. However, the asymmetry of information is deemed to significantly hinder the execution of financial transactions by driving up their cost. Clearly, it is not enough that there are opportunities for productive investment on the continent, it is also necessary that potential external creditors be informed.
The work of Ahearne et al. (2004) [19] show that the poor quality and low credibility of financial information in foreign countries has strong explanatory power over the lack of capital flows to poor countries. Vasileva (2008) [20] goes on to say that investors prefer to invest in countries near their country of origin, or countries of the same economic union or with a similar legal system. They feel more optimistic and confident in investing in the most familiar countries because of informational benefits, despite potentially more attractive returns from developing countries.
African countries do not have a well-developed financial system that can play an effective intermediary role between domestic and foreign private creditors on the one hand, and domestic private enterprises on the other, resulting in significant external financing premium. Mendoza et al. (2009) [21] explicitly associate financial development with the ability to enforce financial commitments. A more sophisticated financial sector can simply facilitate international transactions. It can also lead to better capital allocation, thereby increasing marginal marginal productivity.
Odedokun (2003) [22], however, estimates a positive development impact of the financial sector on all capital flows, including FDI. The same is true of the more recent study by Djahini (2015) [23], which shows that the development of the financial system plays a positive role in the attractiveness of FDI of African economies. Rancière et al. (2008) [24] argue that some of the contradictory results can be attributed to the fact that financial development promotes growth but also makes a country more vulnerable to crises.
The risk associated with the host country is also an important factor. Indeed, the risk is deemed to increase the cost of investments and uncertainty: even if the private return is expected to be high, a large amount of uncertainty surrounding  [17] or for Reinhart and Rogoff (2004) [5], episodes of default in the past are the key explanation for the low volume of capital inflows to poor countries. Capital would thus remain in rich countries, even if the theoretical investment opportunities are far from exhausted in poor countries.
Odedokun (2003) [22] notes that external public debt discourages foreign investors, suggesting that fear of future taxes acts as a deterrent. In the framework of West African Economic and Monetary Union (WAEMU), Koudou (2014) [25] shows that in the short term, the external debt of one year has a statistically significant impact on the variation of the net inflow of FDI of the following year.
This implies that better risk sharing facilitates the financing of investment ogies sometimes involve large-scale production. In such cases, the small size of the economies, the persistence of trade barriers, as well as the infrastructural deficiencies mentioned above may limit the scope of the market and thus hinder efficient production.
In total, the structural factors of an economy can affect the efficiency of the productive system and reduce the profitability of investments. This will ultimately lead to a reorientation of the destination of investments. It is then necessary to build an evaluative approach of the role of the structures of the economies on their attractiveness vis-à-vis FDI.

Methodology
The methodological approach adopted is presented in three stages: first, the presentation of the empirical model; then the justification of the choice of the estimation method and finally the presentation of the data.

Empirical Model
The work on the explanation of the Lucas paradox is generally based on a Cobb-Douglas production function, assumed to have constant returns. In addition, the assumption of free movement of factors of production is retained. In this context, considering two countries producing the same good, the decrease in the marginal productivity of capital and the direction of corresponding investment flows can be approached from Equations (1) and (2).
where Y is production and A is the productivity parameter, K and L are respectively capital and labor and α, the share of capital in income.
This model predicts that capital should migrate freely from rich to poor countries until marginal returns are equal between these two groups of countries.
Therefore, for countries i and j, Lucas (1990) [1], in considering the existence of capital flows to poor countries, shows that they are well below their level predicted by neoclassical theory.
This could explain why the return on investment in Africa is not high compared to that obtained in these rich countries.
This gap between theoretical profitability and actual profitability of capital could be explained by the fact that the structural features of economies hinder the adoption and/or efficient use of technology, which results in lower capital productivity and, in turn, fine, to a limited attractiveness. Prescott (1998) [28] argues that effective use of existing technologies or reluctance to adopt new ones depends on the "combination" that a society holds for them-the ability to better combine same amounts of capital and labor to produce more. In these conditions, marginal capital returns are evenly spread across countries, without converging capital levels per capita. This difference is explained by the fact that production is more efficient in rich than in poor countries because of local production conditions and the level of productivity associated with it.
So for two countries i and j, the equalization of the yield is given by: In order to achieve this dual objective, this article uses an econometric methodology based on a two-stage model.

Source of Data and Preliminary Analyzes
The data used come from four main sources: the World Development Indicators (WDI), the Penn World  [34], which takes into account interindividual dependence. This is why QTI and ICT variables are introduced into the differentiated form. We also studied the links with the differentiated values of non-stationary variables by the Levin and Lin (2002) [32] test, in order to be reassured of the optimality of the choice of modeling.
The analysis of the correlation matrix in the Appendix shows that the variables TFP and LCAP are correlated and strongly correlated with the variable LFDI (r = 0.52 and r = 0.80). Similarly, the FD variable is correlated to FDI (r = 0.46). In addition, the variables HC, QTI, LCAP and SIZ are strongly correlated with the variable TFP. The variables QTI, SIZ and FD are strongly correlated with the variable HC. We also noted a strong correlation between SIZ and FD on the one hand, LCAP and FD on the other hand. It then appears a problem of multicolinearity between the explanatory variables that should be corrected from an appropriate estimation method.

Estimation by the Method of Generalized Moments
Given the literature review and the descriptive analyzes above, the estimation method chosen is that of generalized moments (GMM) on a dynamic panel. Indeed, the literature suggests the possibility for past values of an endogenous variable to influence the dynamics of future values of the explained variable. Baltagi (2012) [36] proposes the use of delayed values of the explained variable, or even other endogenous variables, as an explanatory variable in such a case. In addition, there are descriptive analyzes, a correlation between certain variables that can explain the evolution of FDI flows in Africa. This can be a source of autocorrelation of errors and also of heteroskedasticity. The general form of the model is therefore the following: where δ is a constant, β the vector 1 K × of the coefficients corresponding to K explanatory variables; it X the matrix whose columns represent the expla- -The estimation of the first difference model with instrumental variables of Arellano and Bond (1991) [37], which makes it possible to cancel the effects specific to individuals.
-The estimation of a system of two equations of Blundell and Bond (1998) [38], one in first difference and the other in level. The authors show by Monte Carlo simulation that the GMM estimator in the system is more efficient than that obtained in the first difference, because the latter gives biased results in finished samples when there are few valid instruments.

Results and Analyzes
As the methodological approach suggests, the presentation of the results will also be done in two stages: first, the results of the first stage of the model, which links the volume of FDI received to overall factor productivity; secondly, those of the  Total factor productivity is the most favorable factor for increasing net FDI flows in Africa and the West and Central Africa sub region, which confirms the intuition of Prescott (1998) [28], as well as he extends the results of Piteli (2010) [39], which presented total factor productivity as a major determinant of FDI in developing countries. An increase of one unit of total factor productivity (TFP)

The Effects of Total Factor Productivity on the Attractiveness of FDI
contributes on average to a 5.5% increase in net FDI inflows in Africa. However, increasing the human capital of a unit reduces net inflows of FDI by an average of 4.3%. This result, although in contradiction with most of the work (Cleeve, 2008) [40] on the effects of human capital on the influx of FDI, is confirmed both in Africa in general and in West and Central Africa. The result obtained can be justified by several arguments. Given that, on the one hand, most FDI in Africa is directed towards sectors requiring little qualified local labor, and on the other hand, human capital is here evaluated by the number of years of study. it can be expected that the more years an individual is studying, the less likely he is to be underemployed; and even if it were, its high wage claim would discourage foreign investors from hiring it, especially since they are interested in cheaper labor. Moreover, it can be assumed that educated people can be potential entrepreneurs and compete with foreign investors; As a result, they can block the flow of inward FDI or channel their investment abroad, reducing the net flow of FDI.
Differences in results between the global sample and that of Central and West Africa appear mainly on the role of ICT and inflation. On the sample in general, the increase in the number of ICT users in a country causes FDI inflows to grow by almost 0.60%. In other words, the increase in the number of ICT users is accompanied by an increase in inward FDI flows compared to the previous year. This confirms Lee's (2016) [41] result on the positive effect of FDI diffusion on capital inflow, as ICT facilitates coordination of activities and reduces uncertainty. However, in West and Central Africa, this variable does not have a significant effect, although this effect goes in the same direction as in the global model.
In contrast, the role of macroeconomic stability, approximated by the rate of inflation, is a determinant of the attractiveness of FDI in West and Central Africa, but not in Africa in general. This can be explained by the fact that this variable plays a marginal role in the other regions. The results of Mhlanga et al. (2010) [42] show that the inflation rate has no effect on FDI flows in the Southern African Development Community (SADC) zone.

The Explanatory Factors of the Evolution of Total Productivity in Africa
To determine the factors that may explain changes in total factor productivity, we start with an estimate of the time averages. In addition to the correlation analysis, the inter-country estimate shows that, on average and over the study period, the change in total factor productivity is mainly due to the capital structure, the quality of transport infrastructure and the size of the economy. An increase in total factor productivity in Africa in general, all things being equal, stems from the growth of at least one of these variables. Thus, total factor productivity influences FDI inflows to Africa in a global way, through these factors (Table 3). For West and Central Africa, the estimation results show that: if we omit the likely effects of past values of total factor productivity and country-specific characteristics, the capital structure and the size of the market factors that may explain a possible change in total factor productivity. Indeed, these two causes of autocorrelation make it necessary to estimate the model for the countries of Central and West Africa from the least generalized squares. The result is that an increase in total factor productivity results from a growth in the capital structure or the size of the economy.
These two steps show that structural factors that are specific to an economy may be obstacles to FDI flows to Africa through TFP. Indeed, the small size of the African economies and the shortcomings of the transport network, by reducing the efficiency of the productive combination, are likely to reduce the effective profitability of the investments, compared to the yields observed on the continents with more efficient structures. Reducing the return on investment in Africa means that a rational investor will have to reorient the destination of his investments, which helps to explain Lucas' paradox.

Conclusions
The purpose of this article was to determine the role of the structures of African economies on the attractiveness of foreign direct investment, i.e. specifically, on the one hand, to measure the impact of the total productivity of foreign direct investment factors on the attractiveness of African economies through FDI, and on the other hand, to assess the influence of each component of the structural characteristics on total factor productivity. The application of the generalized method of moments on a database of WDI, AIDI, PWT, WGI, made up of 25 African countries, gives some significant results.
It appears that both for Africa in general and for Central and West Africa, the Lucas paradox is explained by the fundamentals of economies that affect the ability of the economy to effectively combine its factors of production. In other words, the overall factor productivity is determined by the size of the economies, the capital structure and the quality of transport infrastructure for African economies in general. The first two factors are also significant for the economies of Central and West Africa. Therefore, to improve the attractiveness of African countries for FDI, the recommendations go in the direction of building better transport and communication infrastructure, which would reduce transaction costs, because a reconciliation of companies with their customers and their suppliers. Moreover, the promotion of sub-regional integration and the development of cross-border transport infrastructures can prove to be a saving one, since it would lead to an increase in the size of the markets, and thus to an improvement of the attractiveness, investors being in constant search of outlets.
African economies need to invest more to improve their production structures to enhance the production efficiency and attract more FDI. The priority sectors identified are transport infrastructure and ICT use. In addition, it is good to encourage the development of free trade zones to increase the size of the markets accessible by multinational firms.