Eléazar Zerbo
email: eleazar.zerbo@univ-nantes.fr

Lemna

What determines the long-run growth in Sub-Saharan Africa? Exploring the role of energy, trade openness and financial development in six countries

Keywords: Economic Growth, Energy, Trade openness, Financial development, Cointegration, Sub-Saharan Africa JEL classification: C32, E44, F43, O47, Q43

This paper investigates the effect of energy efficiency, international trade and financial development on long-run income per capita growth of six Sub-Sahara African (SSA) countries, namely Botswana, Cameroon, Kenya, Senegal, South Africa and Togo. The Autoregressive Distributed Lag (ARDL) bound approach to cointegration is applied with (possible) structural breaks to examine both the short-term and long-term effects. Furthermore, generalized forecast error variance decomposition is applied to decompose the forecast variance of GDP per capita attributable to the selected independent variables. The long-term results show that trade openness and financial development affect positively and significantly income per capita in South Africa and Kenya, respectively. A compelling evidence of energy efficiency involvement in growth is found in Togo. The short-term estimations highlight the significant role of investment and energy in output process in virtually all the countries and the role of trade openness in South Africa and Togo. The findings also provide major policy implications for sustainable economic growth in SSA countries.

Introduction

A major current focus in policy management of developing countries is how to achieve a high sustainable economic growth. The importance of growth has been demonstrated and is considered as not sufficient but necessary in reducing poverty and improving the well-being of the population in developing countries [START_REF] Fagnart | Environnement and développement économique: Introduction[END_REF][START_REF] Hugon | Peut-on parler d'une crise ou d'un renouveau de l'économie du développement durant la dernière décennie?[END_REF]. For African countries, especially Sub-Sahara African (SSA) countries, sustainable growth is as well the main goal of policymakers. During the last decade, most African countries have experienced a revival in economic performance due to a growth rate close to 6% and an increase in per capita income by 30% [START_REF] Jacquemot | Perspectives économiques pour l'Afrique Subsaharienne. Questions et scénarios[END_REF]. This improvement follows a period of poor economic performances recorded in the continent. During the 80s, the real per capita income growth had been negative and then reached from -2.2% to 1.2% in the 1990s [START_REF] Basu | Promoting growth in Sub-Saharan Africa: Learning what works[END_REF]. [START_REF] Ghura | Growth in Sub-Saharan Africa[END_REF] stated that the unsatisfactory growth rates of SSA countries in the 80s in comparison to other developing countries were due to lower commodity prices, deteriorating terms of trade, adverse weather conditions, rapid population growth, political and economic instability. The implementation of structural adjustment program in most countries, although socially consequences remain debatable, helped lay down the base of successful business environment. Thus, between 2000 and 2012, African continent recorded average economic growth rate around of 5.1% [START_REF] Hugon | La croissance de l'Afrique peut-elle durer?[END_REF], owing to 5.6% for SSA and 4.5% for the North of the continent (AfDB, 2013). With an annual population growth above 2%, the poverty reduction assumes that this performance should be sustained in the long-term (AfDB, 2013). For this purpose, a basic issue is to understand the determinants of long-run economic growth in these countries.

In economic literature, the failures of countries to converge in per capita income and the determinants of economic growth have been extensively studied. One of the best known growth theoretical models is the neoclassical growth model developed by [START_REF] Solow | A Contribution to the Theory of Economic Growth[END_REF]. This model predicts that in the steady state the level of per capita output is determined by exogenous factors i.e. the rate of population growth and the saving rate. Then, the different values of these factors across countries explain different steady state levels experienced by each country. Furthermore, [START_REF] Solow | Technical Change and the Aggregate Production Function[END_REF] explains the long-term output growth by technical progress. He found that 87.5% of US income growth per worker during the period 1909 to 1949 is due to technical progress. [START_REF] Mankiw | A Contribution to the Empirics of Economic Growth[END_REF] found the effect of saving and population growth over evaluated and extended the [START_REF] Solow | A Contribution to the Theory of Economic Growth[END_REF] model by incorporating human capital accumulation to physical capital. Their findings certainly reduced the proportion of Solow residual, but a large part of growth determinants remains unknown. For [START_REF] Rao | Time-series econometrics of growth-models: A guide for applied economists[END_REF], the Solow residual is more a measure of our ignorance than a true value of technical progress.

Alternative growth theories have attempted to identify endogenous factors that influence the Solow tech-2 nological progress. [START_REF] Romer | Increasing Returns and Long-Run Growth[END_REF] and [START_REF] Lucas | Making a Miracle[END_REF] showed that technological change is endogenously determined by accumulation of knowledge and human capital, which are assumed as crucial determinants of economic growth. Based on endogenous growth theory, numerous factors have been identified as determinant to technological progress. [START_REF] Jones | Time Series Tests of Endogenous Growth Models[END_REF] in his review, refers to Grossman and Helpman (1991a,b) who cited no less than 10 potential determinants of long-run growth. For example, he mentions the rate of investment in physical and human capital, the export share, the orientation of local policies, the strength of property rights, the government spending, population growth and regulatory pressure. Although endogenous growth theories are useful, they suffer from few limitations. [START_REF] Kumar | What determines the long run growth rate in Kenya?[END_REF] pointed out that endogenous growth equations are intrinsically difficult to estimate and when estimating it is necessary to use cross-section dimension. Moreover, these theoretical models do not use more than one or two variables. Time series data are suitable in examining the long-term of growth determinants of each country. One of the principal assumptions of endogenous growth theory is that a change in the structure of some variables due to public policies has a permanent effect on economic growth. However, empirical evidence of [START_REF] Jones | Time Series Tests of Endogenous Growth Models[END_REF] on times series did not support this hypothesis. [START_REF] Parente | The failure of endogenous growth[END_REF] and [START_REF] Rao | Time-series econometrics of growth-models: A guide for applied economists[END_REF] suggested that a modified version of Solow exogenous growth model is more appropriate to account for change in production level over time.

Hence, this study uses an extended Solow Cobb-Douglas production function to investigate what determine SSA1 long-term growth with a particular attention to energy efficiency, international trade and financial development. Because there is an urgent need of sustainable development, this study focuses on factors that are relevant for this region. Actually, there is a need to expand access to energy for consumption and production process due to a lack access in SSA. According to United Nations Development programme (UNDP), 69 percent of the region's population have lack access to energy live in 2011, and 78 percent of people who do, use traditional biomass. However, the development of energy sector differs from countries.

For example, the World Bank reported that 85.4% of South Africa population had access to electricity in 2012, while it had been 23% in Kenya and 56.5% in Senegal. Then, this paper agrees with Brew-Hammond (2010) that energy is an essential input for socio-economic development and examines the effect of a gain in energy efficiency on long-run growth. Furthermore, SSA has a low integration rate to international trade and a low degree of financial development. Its share in world trade is less than 3% and is dominated by export of a narrow range of primary products2 . The financial sector is underdeveloped and bank-centered.

A small range of the population has a bank account (34% of adults in 2014 according to World Bank) and an access to formal financial services. The inclusion in investment and production process is as well limited.

The domestic credit provided by financial sector in 2014 was estimated to 35.2% of GDP by the World Bank. Following this background, this study examines the contributions of energy efficiency, trade openness and financial development on economic growth in SSA countries, especially in Botswana, Cameroon, Kenya, Senegal, South Africa and Togo.

Few studies have been concerned with this issue in SSA countries and previous work has focused mainly on individual effect of these factors using different specifications and/or estimation methods leading to inconclusive results. [START_REF] Hossain | The Determinants of Economic Growth in Africa: A Dynamic Causality and Panel Cointegration Analysis[END_REF] applied a panel causality and cointegration methods on 33 African country for the period 1974-2009 and found as for domestic investment and government spending, a long-run positive effect of trade openness on economic growth. In the same line, [START_REF] Kumar | What determines the long run growth rate in Kenya?[END_REF] found for Kenya that trade openness is the key determinant in improving total factor productivity and consequently promoting long-run growth rate while [START_REF] Musila | The impact of trade openness on growth: The case of Kenya[END_REF] established the opposite and asserted that a policy that induces trade openness in Kenya has an adverse effect on growth. [START_REF] Adu | Financial development and economic growth in Ghana: Does the measure of financial development matter[END_REF] investigated the long-run effect of financial development in Ghana and found a mixed effect depending on the indicator used to proxy financial development. The credit to the private sector and total domestic credit led to growth while broad money stock to GDP ratio did not. [START_REF] Rousseau | Monetization, Financial Development, and Growth: Time Series Evidence from 22 Countries in Sub-Saharan Africa[END_REF] used time series method and data for 22 SSA countries over the period 1960 to 2009 to explore if financial development supports economic growth. They found evidence for a positive and unidirectional statistical link from finance, even proxied by narrow or broad money to output in 16 of the 22 SSA countries studied. [START_REF] Kumar | Exploring the role of energy, trade and financial development in explaining economic growth in South Africa: A revisit[END_REF] used an extended Cobb-Douglas framework and the ARDL bound cointegration method to investigate the role of energy, trade and financial development in explaining the long-run growth in South Africa. They found in the long-run positive elasticity coefficients associated with energy and trade openness and a negative effect of financial development on economic growth.

This study contributes to the literature on growth determinants in three main ways: First, the use of appropriate growth specification as suggested by [START_REF] Rao | Time-series econometrics of growth-models: A guide for applied economists[END_REF] on time series analysis might enable consistent results and deal with country heterogeneity; Second, the focus on economically important factors for SSA countries which have not been sufficiently studied; Finally the study extends that of [START_REF] Kumar | Exploring the role of energy, trade and financial development in explaining economic growth in South Africa: A revisit[END_REF] (1) by considering the efficiency aspect of energy use and a composite financial indicator which captures a broad information of financial development and fixes the inconsistencies observed in [START_REF] Adu | Financial development and economic growth in Ghana: Does the measure of financial development matter[END_REF], and (2) by expanding the study to five more SSA countries besides South Africa.

The remainder of this paper is structured as follows: Section 2 introduces our econometric specification and methods, Section 3 presents the empirical results while Section 4 discusses these results, and Section 5 concludes the study.

Model specification and Methods

Model specification

The paper assumes an extended Cobb-Douglas production function as follow:

Y t = A 0 e [g1t+g2Zt] K α t L 1-α t ( 1
)
where Y is the real production, K the stock of physical capital, L the labour force, A 0 an index of initial stock of knowledge which is assumed to growth at rate g 1 function of unknown trended variables proxied with time t and at rate g 2 function of a vector of promoting shift variables Z, α < 1.

Suppose that labour rise at exogenous rate of population growth n according to the following function:

L = L 0 e nt (2)
with L 0 the initial stock of labour force.

Let s and δ be respectively the fraction of income invested in physical capital and the rate of depreciation of physical capital. Then, capital accumulated function can be expressed as follow:

dK t t = sY t -δK t (3)
Next, let y t and k t be the output and physical capital per unit of labour. Rewriting the production equation (1) and capital accumulation equation (3), we have:

y t = A 0 e [g1t+g2Zt] k α t (4) and dk t dt = sy t -(δ + n)k t (5)
According to exogenous growth theory, in the steady state (in long-term), the level of physical capital per worker is constant. Thus, setting equation (5) to zero, the result gives:

k t = sy t δ + n (6)
Substituting equation ( 6) in ( 4) and considering natural logarithms gives:

lny t = lnA 0 + g 1 t + g 2 Z t + αln(sy t ) -αln(δ + n) (7)
Taking variables in their first differences gives:

∆lny t = g 1 + g 2 ∆Z t + α∆ln(sy t ) (8)
Some features of these specifications are noticeable. The equation ( 8) is the short-term dynamic equation of the rate of change of output and the equation ( 7) is the long-run relationship of the production function in the levels of the variables. These equations are useful to estimate the effect of some growth promoting variables expressed in vector Z. This study investigates the effect of energy efficiency, trade openness and financial development on production.

Energy efficiency

Growth theories have paid only small or no attention to the role of energy in promoting economic growth [START_REF] Stern | Energy and economic growth[END_REF]. Thus, the authors mentioned the virtual absence of theoretical and empirical studies that examine the role of energy in growth process, highlighting the involvement of thermodynamics in production. It is [START_REF] Georgescu-Roegen | The Entropy Law and the Economic Process[END_REF] who introduced the laws of thermodynamics in economics.

According to the first law (law of matter conservation), matter is neither lost nor created in the production process or any transformation process. And according to the second law (entropy law), processing material involves an irreversible process of energy available to an unavailable energy [START_REF] Smulders | Entropy, environment, and endogenous economic growth[END_REF]. For [START_REF] Stern | Energy and economic growth[END_REF], the second law implies that a minimum amount of energy is required to perform any transformation process. Then, energy is an essential factor to take into account in the production process.

van [START_REF] Van Zon | An endogenous growth model with embodied energy-saving technical change[END_REF] extended the model of [START_REF] Romer | Endogenous Technological Change[END_REF] by including energy consumption, which is considered as an intermediate factor of production and energy efficiency as a technological advance in the production function. Their results show that the efficiency can be improved through research and that any increase in energy prices, which would correspond to a high cost of intermediate factor, could have an adverse effect on production. This study contributes to fill the gap in empirical literature by examining the effect of energy efficiency, considered as an advance in technological process on economic growth.

Trade openness

International trade could affect positively economic growth by generating competitiveness in production process. According to Grossman and Helpman (1991c) technological progress results from profit maximization of entrepreneurs and the productivity of their employees depends on the state of scientific and industry knowhow in the country, state of know-how which is related to the number of contacts that local agents have with counterparts in international community. For the authors, this number of contacts increases with commercial exchange. Thus, foreign trade of goods promotes exchange of ideas and then technological progress. [START_REF] Romer | Endogenous Technological Change[END_REF] considers technological progress as the product of rational agents who are encouraged by the market to maximize their profit. Invest in technology is equivalent to support a fixed cost, which would require a huge market. Foreign trade can promote technological progress by providing a huge market, generate positive externalities for others countries and lead ultimately to faster growth. Empirically, prior studies have linked openness and the rate of growth. [START_REF] Sachs | Economic reform and the process of global integration[END_REF] found that open economies experienced faster growth in real GDP per capita over the period 1970[START_REF] Perron | The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis[END_REF][START_REF] Frankel | Does trade cause growth?[END_REF] handled trade potential endogeneity by constructing an instrument for international trade based on geographic characteristics. Their estimations across a panel of 150 countries showed that increasing the ratio of trade to GDP by one percentage point raises income per person by between one-half and two percent. More recently, [START_REF] Yanikkaya | Trade openness and economic growth: A cross-country empirical investigation[END_REF] studied a panel of hundred countries and found that countries with higher trade shares are likely to grow faster than other countries. [START_REF] Dowrick | Trade openness and growth: Who benefits?[END_REF] tested the benefits of trade for growth across countries and over time and showed that trade openness benefits is accrued mostly to the richer economies and little to the less developed economies. They supported the finding of [START_REF] Sachs | Sources of slow growth in African economies[END_REF] that specialization in primary exports is bad for growth. In their studies on the determinants of growth in Pakistan, [START_REF] Shahbaz | Economic Growth and Its Determinants in Pakistan[END_REF] found a negative effect of international trade on growth while Shahbaz (2012) found a positive impact. [START_REF] Shahbaz | Economic Growth and Its Determinants in Pakistan[END_REF] explained their finding by the low rate of Pakistan integration in world trade at this time. [START_REF] Chang | Economic growth and openness in Africa: What is the empirical relationship?[END_REF] examined the effects of trade policies on economic growth in 36 African countries and found that trade openness is positively related to economic growth significantly.

Financial development 3

The existence of costs for access to information and transaction has motivated the establishment of a financial market with a primary role of mobilizing and allocating financial resources among different agents in capacity

3 [START_REF] Ncube | Financial Services and Economic Development in Africa[END_REF] reported that there remains an inconclusive debate in the literature about the appropriate financial system. [START_REF] Stiglitz | Credit markets and the control of capital[END_REF], [START_REF] Levine | Bank-based or market-based financial systems: Which is better?[END_REF] and [START_REF] Chakraborty | Bank-based versus market-based financial systems: A growth-theoretic analysis[END_REF] suggested a bank-based financial system while [START_REF] Rajan | Insiders and outsiders: The choice between informed and arm's-length debt[END_REF] and [START_REF] Weinstein | On the costs of a bank-centered financial system: Evidence from the changing main bank relations in Japan[END_REF] supported the market-based financial system. Since SSA financial sector is dominated by the banking sector and in order to overcome the no readily availability of financial indicators , this study focuses on the bank-based sector and uses standard financial deepening indicators to evaluate the effect of financial development on income per capita.

and/or needing a funding. For [START_REF] Schumpeter | The Theory of Economic Development An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle[END_REF] the efficient functioning of banks encourages technological innovation by identifying and funding investors who are most likely to produce in innovative way. In economic literature, the debate on the effect of financial structural on growth was actually initiated by the comparative work of [START_REF] Goldsmith | Financial Structure and Economic Development[END_REF] between the financial and macroeconomic statistics of some countries. For [START_REF] Levine | Financial Development and Economic Growth: Views and Agenda[END_REF], a financial market that fulfils his duties, which are (i) facilitate the trading, diversifying and pooling risk, (ii) allocate resources, (iii) exert corporate control, (iv) mobilize savings and (v) facilitate the exchange of goods and services, promotes capital accumulation and technological innovation, will have in term a positive effect on growth. Thus, financial development would be a determinant in promoting economic growth in the sense that it would increase savings and then capital accumulation. Numerous empirical investigations have supported this assumption. For instance, [START_REF] Zhang | Financial development and economic growth: Recent evidence from China[END_REF] found that financial development is positively associated with growth in China. Likewise, [START_REF] Thangavelu | Financial development and economic growth in Australia: An empirical analysis[END_REF] and [START_REF] Ang | What are the mechanisms linking financial development and economic growth in Malaysia?[END_REF] showed that the development of financial market leads to higher output growth of the Australian and Malaysian economies, respectively. [START_REF] Shan | Does financial development'lead'economic growth?[END_REF] also validated these findings by investigated quarterly data from OECD4 countries and China. [START_REF] Shahbaz | Economic Growth and Its Determinants in Pakistan[END_REF] defining domestic credit to private sector as financial development, found that it is positively associated to growth in Pakistan. [START_REF] Bittencourt | Financial development and economic growth in Latin America: Is Schumpeter right?[END_REF] examined the case of Latin American countries and found a positive effect of financial development on production. In contrast, [START_REF] Hsueh | Economic growth and financial development in Asian countries: A bootstrap panel Granger causality analysis[END_REF] and [START_REF] Kar | Financial development and economic growth nexus in the MENA countries: Bootstrap panel Granger causality analysis[END_REF] performed a bootstrap panel Granger causality analysis between financial development and economic growth among ten Asian countries and MENA5 countries, respectively. They found no clear consensus and that the results are sensitive to the financial measurements as well specific to the countries.

As for SSA countries, [START_REF] Adeniyi | Financial development and economic growth in Nigeria: Evidence from threshold modelling[END_REF] found evidence of threshold effects in Nigeria i.e. financial development initially matters little for growth but conditional on a level of the former being exceeded some positive growth influence hits the surface. [START_REF] Ghirmay | Financial Development and Economic Growth in Sub-Saharan African Countries: Evidence from Time Series Analysis[END_REF] empirical investigation in 13 SSA countries showed that financial development plays a causal role on economic growth in the long-run in eight (Benin, Ethiopia, Ghana, Kenya, Malawi, Tanzania, Rwanda, and South Africa) of thirteen countries studied. Wolde-Rufael (2009) explored four measures of financial development in Kenya and found evidence of a two-way Granger causality between three out of the four indicators and economic growth, suggesting that financial development and economic growth are jointly determined. [START_REF] Rousseau | Monetization, Financial Development, and Growth: Time Series Evidence from 22 Countries in Sub-Saharan Africa[END_REF] found evidence from 22 SSA countries that financial development enable economic growth for about thirds of them. Ahmed and Mmolainyane (2014) examined the role of financial integration in Botswana and did not find a direct robust and statistically significant association with growth. [START_REF] Adu | Financial development and economic growth in Ghana: Does the measure of financial development matter[END_REF] found a conflicting result of financial development effect on growth by using different financial indicators in Ghana. With regard to these contradictions, this study constructs a financial development index in order to cover a large amount of financial sector.

ARDL cointegration approach

The current investigation involved determining some growth promoting factors in six SSA countries. Thus, the Autoregressive Distributed Lag (ARDL) bounds testing approach to cointegration developed by [START_REF] Pesaran | Bounds testing approaches to the analysis of level relationships[END_REF] is performed to study the dynamic relationship between the production and the independent variables. This approach is suitable in this case as the long and short-run parameters are estimated simultaneously.

Furthermore it avoids endogeneity problems and can be used whether the time series data have a unit root or not in their process. According to [START_REF] Narayan | The saving and investment nexus for China: Evidence from cointegration tests[END_REF], it is more appropriate for small samples than traditional cointegration methods, such as the test of [START_REF] Engle | Co-integration and error correction: Representation, estimation, and testing[END_REF] and the test of [START_REF] Johansen | Maximum likelihood estimation and inference on cointegration with applications to the demand for money[END_REF].

The empirical representation of ARDL bounds testing approach to cointegration is formulated following the aforementioned specifications ( 7) and ( 8). Moreover, as SSA countries might have faced external shocks such as socio-political crises, currency devaluation, financial or economic crises, etc., dummy variables DU i (i = 1, ..., k; k is the number of breaks) are included to account for their effect on the production function.

According to [START_REF] Pesaran | Bounds testing approaches to the analysis of level relationships[END_REF] the asymptotic theory of the ARDL approach is not affected by the inclusion of such dummy variables. The dummy variables are defined by DU i = 1 over the period t > τ i (τ i is the date that the shock occurred) and 0 elsewhere. The Bai-Perron sequential procedure is applied to the logarithm of the production per capita in order to check the number of breaks and the corresponding dates. [START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF] and [START_REF] Bai | Computation and analysis of multiple structural change models[END_REF] proposed a consistent procedure that test the null hypothesis of l changes in a series versus the alternative hypothesis of l + 1 changes. Since each country has its own experience, the break dates may vary with countries. Then, the ARDL representation can be written as follow:

∆lny t = α 0 + k i=1 α Di DU i + α t t + α y lny t-1 + α I lnI t-1 + α E lnE t-1 + α T lnT t-1 + α F lnF t-1 + p1 i=1 m i ∆lny t-i + p2 i=0 v i ∆lnI t-i + p3 i=0 g i ∆lnE t-i + p4 i=0 h i ∆lnT t-i + p5 i=0 j i ∆lnF t-i + t (9)
where y is the income per capita (2005 $ US) 6 , I is the fraction of income invested divided by the population, E is energy efficiency, T is the ratio of openness to international trade, F is financial development, t is time trend variable, and is the regression error term.

The ARDL approach computes an F-statistic to compare with the critical bounds generated by [START_REF] Pesaran | Bounds testing approaches to the analysis of level relationships[END_REF] to test for presence of cointegration between variables. The F-statistic is calculated following the null hypothesis H 0 : α y = α I = α E = α T = α F = 0 against alternative hypothesis of cointegration.

The F-test does not have a standard distribution. Consequently, the upper and the lower critical bounds computed in [START_REF] Narayan | The saving and investment nexus for China: Evidence from cointegration tests[END_REF] were used as they are more appropriate for small sample size. for the ARDL model. This selection is done according to the Bayesian information criterion (BIC) and the Akaike's information criterion (AIC). Once a cointegration has been established, a long run relationship and an error correction model between the selected variables are estimated as formulated in equations below:

lny t = θ 0 + θ 1 t + θ 2 lnI t + θ 3 lnE t + θ 4 lnT t + θ 5 lnF t + µ t ( 10
)
∆lny t = β 0 + k i=1 β 1i DU i + β 2 t + p1 i=1 β 3i ∆lny t-i + p2 i=0 β 4i ∆lnI t-i + p3 i=0 β 5i ∆lnE t-i + p4 i=0 β 6i ∆lnT t-i + p5 i=0 β 7i ∆lnF t-i + γECT t-1 + ν t ( 11
)
where the long run elasticities are defined as follow:

θ 0 ≡ α 0 /α y , θ 1 ≡ α t /α y , θ 2 ≡ -α I /α y , θ 3 ≡ -α E /α y , θ 4 ≡ -α T /α y and θ 5 ≡ -α F /α y ,
ECT t-1 is the lagged residual term obtained from the long run relationship equation

ECT t = lny t -(θ 0 + θ 1 t + θ 2 lnI t + θ 3 lnE t + θ 4 lnT t + θ 5 lnF t )
γ is the speed of the adjustment process, and µ and ν are regression error terms.

Data

Based on the above econometric specifications, the study employes annual time series data from 1980 to 2011 to examine the impact of energy efficiency, international trade and financial development on the economic growth of six SSA countries namely, Botswana, Cameroon, Kenya, Senegal, South Africa and Togo. Energy efficiency is defined as the energy use per GDP, international trade as the sum of import and export in percentage of GDP, and a composite indicator of financial deepening is constructed to account for financial development. This construction is carried out through principal component analysis following [START_REF] Gries | Linkages Between Financial Deepening, Trade Openness, and Economic Development: Causality Evidence from Sub-Saharan Africa[END_REF] and [START_REF] Menyah | Financial trade openness and economic growth in African countries: New insights from a panel causality approach[END_REF] in order to capture a broad aspect of financial system development. Moreover this approach is suitable as it avoids multicollinearity and over-parameterization problems and the imbalanced representation of some dimensions of financial system due to the use of only one financial indicator. Since SSA financial sector is bank-centered, the financial development index is constructed using three standard employed. The null hypothesis of these tests is that the series has a unit root process versus an alternative hypothesis of stationarity. These tests are suitable as they allow for an arbitrary number of changes in both the level and slope of the trend function under the null and alternative hypotheses. [START_REF] Perron | The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis[END_REF] showed that standard Dickey-Fuller type unit root test is not consistent when the alternative hypothesis is a stationary process with a break in the slope of the deterministic trend. Then, he proposed a method that allows for a break under both the null and alternative hypotheses. However, the [START_REF] Perron | The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis[END_REF] test supposes a break at known date. [START_REF] Zivot | Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis[END_REF] dealt with this issue and developed a unit root test, commonly used in literature, that allow for a break at unknown date. Carrion-i Silvestre et al. ( 2009) noted the limit of this approach as it does not allow a break under the null hypothesis, but only under the alternative hypothesis.

Results

Unit root tests

They proposed a method which does and adopted the quasi-generalized least squares detrending method supported by [START_REF] Elliot | Efficient tests of the unit root hypothesis[END_REF] and the M-class tests analyzed in [START_REF] Ng | Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power[END_REF]. [START_REF] Harvey | Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey-Fuller statistics[END_REF] recognized that Carrion-i Silvestre et al. ( 2009) approach is efficient both when breaks occur or not, but revealed that the power can be low for the magnitudes of trend breaks typically observed in practice.

They suggested a method that takes this issue into account.

The results of CKP and HLT unit root tests are presented in Table 2. The tests are applied at the nominal asymptotic 5% significance level with the appropriate lag selected by the MAIC criterion. We find that the

ARDL result

The ARDL bound test developed by [START_REF] Pesaran | Bounds testing approaches to the analysis of level relationships[END_REF] is used to investigate the presence of long-term relationship between the selected variables. The test consists in determining first the optimal lag length (p 1 , p 2 , p 3 , p 4 , p 5 ) to include in the auto-regressive model. The maximum lag is set to two, and the AIC and BIC criteria are used to identify the appropriate lag length. Moreover, dummy variables are considered in the ARDL model to take into account breaks occurred in SSA economies due to external shock. The time break τ i is treated as unknown. Hence, the sequential procedure of Bai-Perron is applied to the GDP per capita series 8 . The results of the Bai-Perron test are presented in Table 3 and show the existence of one break in the growth process in Cameroon (1989), South Africa (2005) and Togo (1990), two breaks in Senegal (1989 and[START_REF] Narayan | The saving and investment nexus for China: Evidence from cointegration tests[END_REF], and no break in the case of Botswana and Kenya. All these breaks are considered in the ARDL F-test. The F-test results of the long-run relationship between income per capita, investment per capita, energy efficiency, trade openness and financial development for each country are presented in Table 3. The calculated F-statistics are compared to the critical bounds of [START_REF] Narayan | The saving and investment nexus for China: Evidence from cointegration tests[END_REF] for the test conclusion.

The results fail to reject the null hypothesis of no long run relationship for Botswana and Kenya, show the opposite for Cameroon and South Africa, and are inconclusive for Senegal and Togo as the F-stat fall between the lower and the upper bounds. The inclusion of dummy variables in the ARDL models is relevant in enhancing the results of the F-test. The F-stats are improved when the effect of the dummy variables is statistically significant. The best models are used in estimating the long-run elasticities between income per capita and the independent variables.

Table 4 summarizes the estimated long-run elasticities results. Excepting Cameroon and Kenya, the long run results are in accordance with the F-test. Indeed, no significant long-term elasticities are found for Botswana, Senegal and Cameroon whereas the F-test suggested the opposite for the latter. Moreover, a significant relationship between income per capita and independent variables is observed in Kenya, South

Africa and Togo. Thus, the findings show that investment per capita has a positive and significant effect on income growth 8 Appendix A displays the graphical representation of real GDP per capita in Kenya and South Africa. A one percent increase of per capita raises income per capita by 0.04% in Kenya and by 0.15% in South Africa. One of the main determinants of economic growth in Togo is energy efficiency.

The absolute value of the coefficient associated to this variable is more than unity. The SSA countries have an output process which is highly dependent on fossil fuel. Moreover, the technologies used are not necessarily efficient in energy consumption, so that they face a high production cost, reducing their competitiveness. A gain of one unit in energy efficiency, which would represent a decline in the proportion of energy needed for a unit of production, leads to an increase of 1.87% of income per capita in Togo. Concerning the effect of international trade and financial development, the estimation gives respectively a positive effect on production in South Africa and conflicting results for Kenya and Togo.

We find that international trade promotes long-term growth in South Africa. A one percent increase of foreign trade ratio leads to 0.34% increase of income per capita. This result supports the views of Grossman and Helpman (1991c) and [START_REF] Romer | Endogenous Technological Change[END_REF] that foreign trade affects positively economic activities by providing a wide market and leading to technical progress. Then the participation of South Africa to international trade generates positive externalities so that agents have incentive to invest in technology and physical accumulation due to the reduction of fixed costs. Financial development contributes to increase per capita income in Kenya (0.22) while the opposite effect occurs in Togo (-0.26). Following [START_REF] Levine | Financial Development and Economic Growth: Views and Agenda[END_REF], the findings suggest that financial sector fulfils his function in Kenya by promoting capital accumulation and technological progress.

Khalifa [START_REF] Al-Yousif | Financial development and economic growth: Another look at the evidence from developing countries[END_REF] notices two main channels through what financial development promotes economic growth. It affects growth by raising the efficiency of capital accumulation and by raising the saving rate and consequently investment. However, this positive effect of financial development is not observed in the case of Togo. [START_REF] Saxegaard | Excess Liquidity and Effectiveness of Monetary Policy: Evidence from Sub-Saharan Africa[END_REF] and Nketcha Nana and Samson (2014) argue that in many African countries and particularly in some SSA countries, credit rationing encourage many banks to hold a large amounts of liquid assets. According to [START_REF] Tybout | Credit Rationing and Investment Behavior in a Developing Country[END_REF] and [START_REF] Mckinnon | Money and Capital in Economic Development[END_REF], poor financial intermediation reduces the quality of capital accumulation and thus can be damaging to the development prospects of a country.

In order to check for the stability of the long-term elasticities, diagnostics test on the ARDL models are The estimation of an error correction model also validated the existence of a long run relationship in these countries as the error correction term (ECT ) has the right sign, i.e. negative and is significant. The error correction term represents the speed of adjustment required to re-establish equilibrium in the short-term. A deviation from long-run growth due to an external shock is corrected by 41.5% over one year in Kenya and 27.1% in South Africa while 45.1% of the deviation is corrected within one year in Togo. We also examine the short-term effect of investment per capita, energy efficiency, trade openness and financial development on production, so to regard the countries where a long-run relationship is not found.

Table 5 shows the results of the estimated short-term model. We find that investment per capita and a gain in energy efficiency affect significantly and positively the variation of GDP per capita in the short-term. The results reveal also that energy is a crucial issue in SSA countries as an energy efficiency due to a decrease in energy cost, and less energy use per unit of GDP leads to more variation of production in the short-term than let the others factors like investment or trade. Trade openness is involved positively in production variation only in South Africa and Togo. Furthermore, the short-term result highlights the underdeveloped financial sector in SSA countries. We find no significant effect of financial development on the rate of change of income in the short-term.

Variance decomposition analysis

To complement our ARDL cointegration testing, a variance decomposition analysis is implemented to examine the effect of an innovation in the selected independent variables on economic growth. We apply the generalized impulse response approach developed by [START_REF] Pesaran | Generalized impulse response analysis in linear multivariate models[END_REF]. This approach is suitable than the orthogonalized approach because it is invariant to the variables ordering in the VAR model. Moreover, according to [START_REF] Payne | Inflationary dynamics of a transition economy: The Croatian experience[END_REF] and [START_REF] Sari | The growth of income and energy consumption in six developing countries[END_REF] the difference between both approaches is that in the orthogonalized decomposition the total of the variance decomposition for a variable will sum up to one while the generalized forecast error variance decomposition (GFEVD) approach accounts for the optimal proportion of each variable. The GFEVD is performed after the estimation of a vector autoregression (VAR) model and consists to decompose the forecast error variance of GDP into proportions attributed to shocks in all variables in the system including itself [START_REF] Menyah | Energy consumption, pollutant emissions and economic growth in South Africa[END_REF]. For [START_REF] Litterman | Techniques of forecasting using vector autoregressions[END_REF] the main weakness of the general VAR specification is that the number of free parameters increases quadratically with the number of variables in a system, and for even moderately-sized systems the model becomes highly over-parameterized relative to the number of available observations. Thus, considering the small sample size involved in this study, the number of variables and their additional lags, the estimated VAR model would have a small degree of freedom and a large mean square of out-of-sample forecast. To give thought to this problem, we use the Bayesian prior method to estimating a VAR model. According to [START_REF] Koop | Bayesian multivariate time series methods for empirical macroeconomics[END_REF] Bayesian VAR (BVAR) is a popular VAR to overcome over-parameterization problems. We use the normal-Wishart prior which generalizes the Litterman prior by treating the error variance-covariance matrix as unknown matrix positive definite symmetric matrix rather than a fixed diagonal matrix [START_REF] Karlsson | Forecasting with Bayesian VAR models[END_REF]. The Bayesian approach incorporates restrictions in the form of a prior distribution on the parameters [START_REF] Karlsson | Forecasting with Bayesian VAR models[END_REF].

This study focuses on the proportion of GDP per capita error variance due to the selected independence variables. We therefore present the result of forecast error variance decomposition with income per capita as the response variable and the impulse variables are investment per capita, energy efficiency, trade openness and financial development. The results are presented in Table 6. The results show that the forecast error variances of income per capita are essentially explained by innovations in investment per capita and energy efficiency. A shock on investment per capita explains income per capita error variation respectively by 17.94%

in Botswana,33.43% in Kenya,47.84% in Senegal,51.53% in South Africa and 48.32% in Togo. The variance decomposition for Cameroon reveals that investment per capita has a limited effect (0.02%) in explaining the error variation of the production. These findings support the ARDL and the short-term estimation results as we find no significant effect of investment per capita on income in Cameroon while it does in the rest of the sample. Moreover, the forecast error variance of energy efficiency explains about 11.11% of the forecast error variance of GDP per capita in Botswana, 51.59% in Cameroon, 41.31% in Kenya and 51.40% in Togo. In the contrast, the proportions are low for Senegal and South Africa both in the short-run (1 to 5 years) than the long-run (15 to 20 years). The finding of South Africa is noteworthy as we find no significant effect of energy efficiency in explaining the output. This could mean that energy issues are particularly critical for the other SSA countries than for South Africa. The forecast error variance of trade openness accounts substantially for the forecast error variance of income in Cameroon, South Africa and a little less in Togo. Furthermore, 9.87% of income per capita error variance in the short-term and up to 10.42% in the long-term is due to a shock on financial development in Senegal while it accounts for 36.59% in the long term in Togo.

Discussion

The determinants of economic growth have been the primary focus of theoretical and applied research over the last two decades [START_REF] Shahbaz | Economic Growth and Its Determinants in Pakistan[END_REF]. Various factors have been identified in explaining long-run economic growth. A range of researchers has examined the impact of such factors on SSA growth. [START_REF] Kumar | What determines the long run growth rate in Kenya?[END_REF] and [START_REF] Musila | The impact of trade openness on growth: The case of Kenya[END_REF] for example explored the effect of trade openness on growth in Kenya and found mixed results as the first study found a positive effect of trade openness while the latter found the adverse effect. [START_REF] Adu | Financial development and economic growth in Ghana: Does the measure of financial development matter[END_REF] were concerned with the contribution of financial development to economic growth and also found an inconclusive result depending on financial indicator used. However, Note: The GFEVD computes the optimal proportion of the amount of forecast error variance decomposition for each variable. Unlike the orthogonalized decomposition, the row values do not sum up to 100.

prior works have focused essentially on individual effect using different methods and leading to inconclusive results. Furthermore, the role of certain factors has not been sufficiently studied. Hence, there remains a need of a multivariable approach that uses an efficient estimation method in examining the dynamics of long-run growth in SSA countries. This study investigates the impact of trade openness, energy efficiency and financial development on the long-run income per capita in six SSA countries namely Botswana, Cameroon, Kenya, Senegal, South Africa and Togo. To our knowledge, only [START_REF] Kumar | Exploring the role of energy, trade and financial development in explaining economic growth in South Africa: A revisit[END_REF] have this kind of purpose with some differences. We improve the study of [START_REF] Kumar | Exploring the role of energy, trade and financial development in explaining economic growth in South Africa: A revisit[END_REF] in four ways: Firstly, we use energy efficiency than total energy consumption as describes as well a technology innovation and is suitable to our specification; Secondly, we use a composite indicator of financial development rather than an unique financial development indicator; Thirdly, we consider dummy variables in the ARDL models to improve the quality of the F-test and take into account external shocks that occurred in SSA countries. The ARDL approach is suitable to test the effect of the selected factors on short-term and long-term growth; Finally, we carry out a GFEVD to examine the part of forecast error variance of income per capita explained by each variable.

The results show that in virtually all the countries studied, investment per capita and energy efficiency are essential in short-term output. This finding corroborates the neoclassical growth model view that investment in capital accumulation is the main determinant of growth in the short term. In the specific case of SSA countries, investment should also concerned the energy sector as regard to the lack access of energy and the high cost of production owing to energy. As for the long-term relationship, we find that investment per capita is positively associated to income per capita in Kenya and South Africa. These results are compatible with those of [START_REF] Kumar | What determines the long run growth rate in Kenya?[END_REF] and [START_REF] Kumar | Exploring the role of energy, trade and financial development in explaining economic growth in South Africa: A revisit[END_REF] who found that investment in physical capital accumulation were the main determinant of growth respectively in Kenya and South Africa. In addition, the positive elasticity of trade openness is in line with that of [START_REF] Kumar | Exploring the role of energy, trade and financial development in explaining economic growth in South Africa: A revisit[END_REF] for South Africa although the coefficient is quite superior. However, the results contrast for energy and financial development owing to the indicators used to proxy these factors. We use energy use per GDP to account for energy efficiency and constructed a composite financial indicator in order to have a broad view of financial sector. Then, we find no significant effect of both factors on long-run growth in South Africa. However, the study proves that financial development is favorable to growth in Kenya while the opposite is observed in Togo. In the short-term, results

suggest no significant effect of financial sector on the rate of change of income per capita. As mentioned earlier, only a small range of SSA population participates actively in the financial sector development. Additionally, the banking sector practices credit rationing and has a limited participation in funding private sector. This weak and/or missing links between financial sector and economic actors may explain the non-significant effect of financial development on production in the short-term and its negative effect in the long-term as observed in Togo. Most notably, this study indicates that energy is undeniably a vital factor in promoting long run growth in SSA countries, especially in Togo. [START_REF] Brew-Hammond | Energy access in Africa: Challenges ahead[END_REF] reported that SSA region compares poorly with others in the developing world in terms of the population relying on traditional biomass and in terms of access to electricity, whether electricity in the home or within given geographical area, averaged around 25% for the region. This lack access to energy induces high production costs so that a gain in energy needed to produce one unit increases more than proportionally the production per capita. Moreover, the inability of energy sector supply to meet the raising energy demand causes electrical generation shortfall and then production losses. With regard to energy as an important factor, the mobilization of domestic and external funding and the implementation of innovative policy are required to improve energy access and therefore economic growth in SSA countries [START_REF] Brew-Hammond | Energy access in Africa: Challenges ahead[END_REF]. For instance, World Bank (2006) indicated that the amount of investment needed to achieve 47% or 100% electrification (access of people to energy) by 2030 is estimated to US$ 4 billion or US$ 11 billion, respectively per year in SSA.

Conclusion

This study examined the effect of energy efficiency, international trade and financial development on long-run income per capita growth of six SSA countries. Since we used time series data, non-stationary properties were discussed using unit root tests with structural breaks. We performed an ARDL bound testing approach to check for both the short-term and the long-term effects. To complement our analysis, a GFEVD was applied to decompose the forecast variance of GDP per capita attributable to the selected independent variables.

The results showed the existence of a long-run relationship between the variables in Kenya, South Africa and Togo. The short-term estimation pointed out the significant role of investment and energy in output process in virtually all the countries and the role of trade openness in South Africa and Togo. Based on the aforesaid outcomes, investment in capital accumulation and energy sector should be encouraged. Financial sector could contribute by enhancing access to financial services and financing more private sectors. The mobilization of external funding is also required. In view of SSA low rate of integration to foreign trade and its potential positive effect on growth, SSA countries should implement policy that promotes international trade and generates positive externalities due to external market and technology exchange. This study has focused on three factors and six SSA countries and the results are encouraging. However, a large amount of macroeconomic factors has not been extensively studied and the unavailability of sufficient data restrains the possible direction. Future work should deal with this issue and take a view of other determinants of SSA long-term growth.

  financial indicators: the broad money to GDP (M2 to GDP), total domestic credit to the private sector to GDP, and total domestic credit provided by the banking sector to GDP. Data on gross domestic product, total population, imports, exports, energy use per GDP and financial indicators are collected from World development indicators (2013) of World Bank, and total investment is from World economic outlook (2013) of International Monetary Fund (IMF).

  HLT tests which permit both a single break in trend (MDF1) and two breaks in trend (MDF2) reject the unit root null for investment per capita in Botswana and Cameroon, GDP per capita and trade openness in Senegal while only the MDF2 statistic rejects the null hypothesis for trade in Cameroon and financial development in Kenya and Togo. Nearly, the results of HLT tests are in accordance with the ADF statistic of the CKP test. In contrast, the M-class (MPT, MZA and MPT) and the feasible point optimal (PT) statistics of the CKP unit root tests support no rejection of the unit root null across all the series. Overall, the CKP and HLT unit root tests indicate that the series are I(0) or I(1) validating the use of ARDL cointegration testing approach. Furthermore, the[START_REF] Elliot | Efficient tests of the unit root hypothesis[END_REF] and[START_REF] Ng | Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power[END_REF] unit root tests are carried out on the first differences of the variables and the findings demonstrated that none of the variables is I(2) 7 .

  performed. These tests include the Lagrange multiplier test of residual serial correlation (χ 2 sc ), the normality test based on the test of skewness and kurtosis of residuals (χ 2 n ) and the ARCH test for heteroscedasticity (χ 2 hc ). The diagnostics tests fail to reject the null hypotheses of no serial correlation, of normality and no heteroscedasticity for all the countries. Moreover, the CUSUM and CUSUMSQ figures are used to examine the stability condition of the parameters where a significant long term is established, namely for Kenya, South Africa and Togo. The statistic figures are presented in Appendix B. The stability condition is fulfilled if the CUSUM and the CUSUMSQ statistics fall inside the critical bounds of 5%. The tests show that the parameters in the model are stable over the period studied.

Figure 1 :Figure

 1 Figure 1: Time series plot of real GDP per capita (constant US$, logarithm value) in the selected countries

  If the F-statistic exceeds the upper bound, H 0 is rejected suggesting there is cointegration between variables, but if it falls below the lower bound, the null hypothesis cannot be rejected and if it is between both bounds, the test is uncertain. Before computing the F-test, it is necessary to choose the appropriate lag level (p 1 , p 2 , p 3 , p 4 , p 5 )

Table 1

 1 summarizes the result of the principal component analysis. It reveals that the index contains at least 60% of the initial variance for each country, suggesting that sufficient financial sector information is considered.

Table 1 :

 1 Results of principal component analysis

	Country	Principal component		Component matrix
		(%)	Broad money credit to private	credit provided
				sector	by banking sector
	Botswana	92.95	0.7071	0.7071	-
	Cameroon	80.04	0.5609	0.6265	0.5412
	Kenya	60.62	-0.0747	0.6993	0.7109
	Senegal	64.29	-0.1288	0.6899	0.7123
	South Africa	87.73	0.5337	0.5941	0.6018
	Togo	77.68	0.5557	0.5980	0.5776

Note:

The column Principal component represents the value of the initial eigenvalues as a percentage of the total variance the first principal component contains.

  Time series analysis requires examining first the non-stationarity properties of the selected variables. Before applying unit root tests, the sequential procedure of Bai Perron is used to check if the series are independently and identically distributed with constant mean and finite variance against the alternative hypothesis of m

time changes at unknown date. The findings validate the use of unit root tests that consider breaks in level and/or slope of the trend function. Consequently, the unit root tests with structural breaks proposed by Carrion-i Silvestre et al. (2009) and Harvey et al. (2013) (henceforth CKP and HLT, respectively) are

Table 2 :

 2 Results of unit root tests

	Country	Variable		CKP test			HLT test
			PT	MPT ADF	MZA MZT	MDF1 MDF2
	Botswana	lny	16.12 17.12 -2.65	-9.35	-2.10	-2.54	-2.80
		lnI	12.27 11.68 -4.12* -13.48 -2.55	-4.50* -6.19*
		lnE	17.62 18.26 -2.41	-9.18	-1.82	-2.91	-3.46
		lnT	11.96 12.30 -2.77	-9.74	-2.16	-2.87	-3.13
		lnF	21.84 23.20 -2.21	-7.16	-1.88	-2.75	-3.37
	Cameroon	lny	30.13 23.22 -2.64	-7.15	-1.88	-2.81	-3.83
		lnI	12.14 11.88 -4.81* -13.85 -2.63	-4.83* -5.48*
		lnE	30.62 24.14 -2.75	-6.86	-1.84	-2.68	-3.69
		lnT	12.31 11.76 -3.74* -13.04 -2.55	-3.45	-4.65*
		lnF	24.99 25.42 -1.71	-6.04	-1.51	-2.14	-3.24
	Kenya	lny	18.06 19.13 -2.10	-6.72	-1.83	-2.07	-2.69
		lnI	14.22 13.28 -3.49* -12.55 -2.50	-2.44	-4.19
		lnE	10.45 11.03 -2.95 -10.60 -2.30	-2.85	-3.12
		lnT	16.25 17.17 -2.65	-9.66	-2.14	-2.92	-3.30
		lnF	18.40 18.89 -2.25	-8.44	-1.80	-2.70	-5.68*
	Senegal	lny	13.36 12.01 -3.17 -13.12 -2.52	-4.10* -5.09*
		lnI	13.59 13.98 -3.31 -11.71 -2.41	3.68	-4.30
		lnE	10.72 10.96 -3.60* -12.48 -2.49	-3.08	-4.34
		lnT	16.30 14.66 -3.81* -11.15 -2.36	-4.03* -5.22*
		lnF	16.07 14.87 -3.16 -11.62 -2.22	-3.05	-5.05*
	South Africa lny	18.74 18.82 -2.50	-8.40	-2.05	-2.82	-3.40
		lnI	17.99 17.24 -2.50	-7.69	-1.96	-2.51	-3.72
		lnE	12.91 13.66 -3.33 -12.40 -2.39	-3.27	-4.44
		lnT	12.88 12.89 -3.68* -12.93 -2.50	-3.28	-3.92
		lnF	9.88 10.26 -3.02 -11.81 -2.42	-3.41	-3.86
	Togo	lny	16.91 17.07 -2.95	-9.68	-2.20	-2.84	-3.28
		lnI	20.50 17.88 -3.23	-9.24	-2.15	-3.78	-4.19
		lnE	13.30 13.54 -3.28 -11.64 -2.35	-3.72	-3.75
		lnT	12.62 13.17 -3.51* -12.62 -2.49	-3.04	-3.82
		lnF	19.15 16.51 -1.50	-8.03	-1.94	-3.56	-6.35*
	Note: * denotes rejection at 5% level of significance.

Table 3 :

 3 The ARDL F-test cointegration results

	Country	break date	BIC lag	F-stat	ECT t-1	Dummy coefficient
	Botswana	-	(1, 0, 0, 0, 0)	2.43	-0.257**
	Cameroon	-	(1, 0, 1, 1, 1)	4.25
		1989	(1, 0, 1, 1, 0) 7.43** -0.196***	-0.078***
	Kenya	-	(2, 0, 1, 0, 1)	3.27	-0.415***
	Senegal	-	(2, 0, 1, 0, 0)	1.90
		1989; 2002 (1, 0, 0, 2, 2)	3.64	-0.236***	-0.042*; 0.042*
	South Africa	-	(1, 1, 0, 1, 0) 5.95** -0.271***
		2005	(1, 0, 0, 0, 0)	1.40		0.026
	Togo	-	(1, 2, 2, 1, 2)	3.52	-0.451***
		1990	(1, 2, 2, 1, 2)	3.18		-0.010
	Note: The critical values are from Narayan (2005), case IV: unrestricted intercept and unrestricted trend,
	n=30 and k= 4; *, ** and *** represent 10%, 5% and 1% level of significance, respectively.

Table 4 :

 4 Long-run estimates based on ARDL approach

	Dependent variable = lny
	Variable	Botswana Cameroon	Kenya	Senegal South Africa	Togo
	lnI	-0.062	0.026	0.044**	0.024	0.148***	-0.087
		(-0.953)	(0.301)	(2.47)	(0.281)	(5.973)	(-1.200)
	lnE	-0.621	0.300	-0.121	0.477	0.103	-1.865***
		(-1.49)	(0.418)	(-0.215)	(0.739)	(0.573)	(-3.684)
	lnT	-0.176	0.529	0.034	-0.149	0.341***	-0.051
		(-0.636)	(1.6)	(0.544)	(-0.635)	(3.306)	(-0.423)
	lnF	-0.153	-0.045	0.221**	-0.219	-0.300	-0.259*
		(-1.302)	(-0.33)	(2.842)	(-0.673)	(-1.3)	(-2.079)
	trend	-0.021	0.003	-0.008***	-0.004	-0.021***	-0.024***
		(-1.358)	(0.351)	(-3.081)	(-0.641)	(-3.127)	(-3.046)
	constant	-12.984***	-3.385	-5.474	-5.267*	-5.883***	-18.705***
		(-4.582)	(-0.627)	(-1.457)	(-2.003)	(-3.593)	(-5.168)
	Diagnostic tests
	Serial correlation χ 2 sc (1)	1.353	4.472	0.239	2.752	1.067	0.979
		[0.245]	0.035]	[0.625]	[0.097]	[0.302]	[0.322]
	Normality χ 2 n (2)	2.915	0.878	0.244	1.073	1.052	0.456
		[0.233]	[0.645]	[0.885]	[0.585]	[0.591]	[0.796]
	Heteroscedasticity χ 2 hc (1)	0.007	0.185	0.322	0.023	0.684	0.515
		[0.932]	[0.667]	[0.571]	[0.880]	[0.408]	[0.473]

Note: *, ** and *** indicate significance level at 10%, 5% and 1%; Student t-statistics are in parentheses and p-value are in brackets.

Table 5 :

 5 Short-run results

	Dependent variable = ∆(lny)
	Regressors	Botswana Cameroon	Kenya	Senegal South Africa	Togo
	∆(lnI)	0.037***	-0.001	0.036**	0.040**	0.063***	0.038*
		(3.354)	(-0.055)	(2.758)	(2.165)	(4.497)	(2.002)
	∆(lnE)	-0.287*	-0.865*** -0.596*** -0.297**	-0.025	-0.560***
		(-1.812)	(-9.238)	(-4.468)	(-2.687)	(-0.305)	(-4.601)
	∆(lnT )	0.192	-0.006	0.011	-0.053	0.116***	0.141**
		(1.521)	(-0.148)	(0.403)	(-1.508)	(3.670)	(2.069)
	∆(lnF )	0.060	0.062	-0.005	-0.038	0.010	-0.064
		(0.907)	(1.574)	(-0.152)	(-0.696)	(0.171)	(-1.129)
	trend	-0.002**	-0.001*	0.000	0.001	0.001	0.000
		(-2.072)	(-1.715)	(0.894)	(1.441)	(1.357)	(0.287)
	constant	0.067***	0.010	0.001	-0.010	-0.001	0.000
		(3.833)	(0.998)	(0.194)	(-1.058)	(-0.145)	(0.006)
	F-statistic	4.317***	20.993*** 8.777*** 3.875***	11.486***	14.254***
	R2-Adjusted	0.372	0.775	0.564	0.324	0.636	0.688
	RSS	0.026	0.013	0.005	0.013	0.006	0.026
	DW	2.001	1.324	1.698	2.06	1.453	1.911
	Note: *, **, and *** denote 10%, 5% and 1% level of significance, respectively.
	Student t-statistics are in parentheses.

Table 6 :

 6 Results of the generalized forecast error variance decomposition of ∆(lny)

	Country	Horizon ∆(lny) ∆(lnI) ∆(lnE) ∆(lnT )	∆(lnF )
	Botswana	1	100.0	17.94	11.11	3.17	0.00
		5	89.28	18.82	11.32	3.23	1.53
		10	89.28	18.82	11.32	3.23	1.53
		15	89.28	18.82	11.32	3.23	1.53
		20	89.28	18.82	11.32	3.23	1.53
	Cameroon	1	100.0	0.02	51.59	11.68	1.44
		5	72.42	3.23	46.88	43.03	1.70
		10	72.40	3.23	46.87	43.04	1.70
		15	72.40	3.23	46.87	43.04	1.70
		20	72.40	3.23	46.87	43.04	1.70
	Kenya	1	100.0	33.43	41.31	0.48	0.01
		5	84.44	44.02	33.99	3.07	4.61
		10	83.08	43.66	33.48	3.66	5.03
		15	82.71	43.88	33.30	3.78	5.20
		20	82.69	43.89	33.29	3.79	5.20
	Senegal	1	100.0	47.84	1.80	2.24	9.87
		5	87.23	47.91	4.73	7.78	10.52
		10	86.22	48.30	4.77	7.78	10.43
		15	86.17	48.30	4.77	7.78	10.42
		20	86.17	48.30	4.77	7.78	10.42
	South Africa 1	100.0	51.53	0.31	34.72	2.28
		5	83.72	67.09	4.32	25.94	2.60
		10	83.11	66.79	4.40	26.01	2.64
		15	83.10	66.79	4.40	26.02	2.64
		20	83.10	66.79	4.40	26.02	2.64
	Togo	1	100.0	48.32	51.40	21.43	24.17
		5	76.69	57.39	42.90	14.85	36.84
		10	72.33	58.08	40.69	14.54	36.48
		15	72.07	58.20	40.60	14.45	36.59
		20	72.05	58.20	40.59	14.45	36.59

The study focuses on six SSA countries namely Botswana, Cameroon, Kenya, Senegal, South Africa and Togo.

Early versions of this study considered the effect of international commodity price fluctuations besides energy, trade and financial development on the growth of SSA countries. The results were inconclusive and the study seemed to address two important issues simultaneously. Then future studies will focus on the problematic of international commodity prices and economic growth in SSA countries.

Organisation for Economic Co-operation and Development.

Middle East and North African.

Following the assumption that labour rise at rate of population growth, income per capita and investment per capita were used as alternative to income per labour regressed on investment per labour to deal with the no readily availability of labour data.

The[START_REF] Elliot | Efficient tests of the unit root hypothesis[END_REF] and the[START_REF] Ng | Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power[END_REF] tests are also applied to the variables in level. The results are not in line with those of CKP and HLT, supporting the use of appropriate tests that allow breaks under both null and alternative hypotheses.


H Arbess

M Bafleur

D Trémouilles

M Zerarka

Optimization of a MOS-IGBT-SCR ESD protection component in smart power SOI technology

A MOS-IGBT-SCR component that was proposed in a previous paper to increase the device robustness and the cost of ESD protection circuit is optimized in this paper. In order to improve its latch up immunity, several variations of geometrical parameters that have been simulated using TCAD Sentaurus Device in another previous paper have been implemented and compared in this paper. The drift area, the form factor, and the proportion of P + sections inserted into the drain are the main parameters, which have a significant impact on the latch up immunity. TLP characterization, and curve tracer measurements have been carried out to evaluate the proposed solution. Holding current increases up to 70 mA and holding voltage up to 10 V.

Introduction

The electrostatic discharge (ESD) has always been one of the highest reliability concerns in the integrated (IC) manufacturing industry. With the continuous miniaturization process, the integrated circuits become more and more vulnerable to ESD. The miniaturization of the ESD protection blocks is one of the greatest challenges of smart power technologies. Silicon On Insulator (SOI) technologies allow extending the operational temperature range while providing the necessary isolation between components with a reduced silicon area.

SOI technology is becoming more and more attractive to manage very high voltage blocks, to reduce parasitic NPN effect and to increase Integrated Circuit (IC) speed as well as for applications operating at high temperature [START_REF] Celler | What is SOI? Do we really need it?[END_REF], [START_REF] Udrea | SOI power devices[END_REF].

Electro Static Discharge (ESD) protections occupy a significant silicon IC area. Using a LDMOS as main ESD protection component is not optimal due to its high onresistance, but it could be the only solution for some technologies.

In a previous work, we proposed a new ESD component (MOS-IGBT-SCR) and improved it in order to increase ESD performance and improve the latch up immunity [START_REF] Arbess | Hightemperature operation MOS-IGBT power clamp for improved ESD protection in smart power SOI technology[END_REF] [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF]. ESD performance was excellent but margin to prevent latch up was not satisfying. In this paper, an optimized version of this structure is discussed and experimentally validated.

As the technological parameters of the used technology (TFSMART1: SOI smart power technology) cannot be changed, we explored various layout-design solutions such as the device topology or the architecture.

2

Structure description and preview solution

The chosen technology is a smart power SOI one (TFSMART 1) provided by Telefunken Semiconductors [START_REF]Release: SIS1_0.32_071005[END_REF]. This technology parameters are detailed in [START_REF] Arbess | Hightemperature operation MOS-IGBT power clamp for improved ESD protection in smart power SOI technology[END_REF].

The device under study is a MOS-IGBT-SCR component. It is built by implementing, within the structure of the N-LDMOS, a lateral IGBT formed by inserting in the drain region both N + and P + diffusions (Fig. 1). The initial NLDMOS is composed of two 150 µm-width fingers with central drain diffusion, the body being connected to the source. Three silicon runs have been realized in order to optimize the MOS-IGBT-SCR structure. The principal problem of this device is the control of the SCR triggering [START_REF] Vashchenko | Mixed device-circuit solution for ESD protection of highvoltage fast pins[END_REF]- [START_REF] Li | Junction engineering for SOI SCR triggering and performance improvement[END_REF]. Results of the first two runs are discussed in [START_REF] Arbess | Hightemperature operation MOS-IGBT power clamp for improved ESD protection in smart power SOI technology[END_REF], [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF]. the minimum holding current of the SCR to avoid any latch-up is equal to 100 mA (Fig. 2) [START_REF] Vashchenko | High holding voltage cascoded LVTSCR structures for 5.5-V tolerant ESD protection clamps[END_REF]. The highest obtained holding current was equal to 50 mA. The holding voltage was also very low (b 3 V).

Proposed new solutions and results

To assess the ESD behavior and robustness of the proposed structures, TLP measurements were carried out at wafer level on a Celestron TLP (50 Ω) test bench. A calibration is performed before starting the measurement to eliminate the series resistances due to setup wire connections. TLP pulses have 100 ns duration and a rise time of 1 ns. To evaluate the holding current and holding voltage level, curve tracer has been used on tens of components. Three or four components have been tested for each configuration. The three chosen configurations in this study are the 1P2N (33% IGBT), 1P4N (20% IGBT) and 3P1N (75% After carrying out TCAD simulation using Sentaurus Device based on previous results obtained in [START_REF] Udrea | SOI power devices[END_REF][START_REF] Arbess | Hightemperature operation MOS-IGBT power clamp for improved ESD protection in smart power SOI technology[END_REF][START_REF] Li | Junction engineering for SOI SCR triggering and performance improvement[END_REF], three major topolo modifications have been applied in order to make this compo latch-up compliant:

A Channel width reduction B Form factor C N drift length.

The variation of holding current, holding voltage and robustne the different configurations are studied and discussed in the follo sections.

Channel width reduction

Due to the significant improvement obtained with a channel w In a previous work [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF], we proposed and studied several layout variations (different P + diffusion proportions in the drain, different configurations of the IGBT section in the drain and the reduction of the channel width). They resulted in a clear but insufficient experimental improvement of the holding current and voltage after triggering. Indeed, the minimum holding current of the SCR to avoid any latch up is equal to 100 mA [START_REF] Mergens | High holding current SCRs (HHI-SCR) for ESD protection and latch-up immune IC operation[END_REF] (Fig. 2). The highest obtained holding current was equal to 50 mA. The holding voltage was also very low (< 3 V).

Proposed new solutions and results

To assess the ESD behavior and robustness of the proposed structures, TLP measurements were carried out at wafer level on a Celestron TLP (50 Ω) test bench. A calibration is performed before starting the measurement to eliminate the series resistances due to setup wire connections. TLP pulses have 100 ns duration and a rise time of 1 ns. To evaluate the holding current and holding voltage level, curve tracer has been used on tens of components. Three or four components have been tested for each configuration. The three chosen configurations in this study are the 1P2N (33 % IGBT), 1P4N (20 % IGBT) and 3P1N (75 % IGBT). This choice can be explained by the fact that the obtained results in the previous silicon run exhibited the maximum and the minimum holding current for the 1P4N and 3P1N respectively, and the best ESD performance for the 1P2N. The results confirmed that the effect of P + diffusion percentage in the drain, corresponding to the IGBT one, has the same effect as shown and explained in [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF].

The new architectures were achieved using two distinct approaches. The first one is to increase the holding current so as it is greater than 100 mA. The second one is to increase the holding voltage so as it is greater than the power supply of the block to be protected, here 5 V.

After carrying out TCAD simulations using Sentaurus Device and based on previous results obtained in [START_REF] Arbess | Hightemperature operation MOS-IGBT power clamp for improved ESD protection in smart power SOI technology[END_REF], [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF], [START_REF] Arbess | Structures MOS-IGBT sur technologie SOI en vue de l'amélioration des performances à haute température de composants de puissance et de protections ESD[END_REF], three major topological modifications have been applied in order to make this component latch-up compliant:

A-Channel reduction B-Form factor C-N drift length The variation of holding current, holding voltage and robustness for the different configurations are studied and discussed in the following sections.

Channel reduction

Due to the significant improvement obtained with a channel reduction of 20% [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF] (implemented by replacing 20 % of the N + source diffusion by a P + one), we decided to explore the increase of this percentage up to 40% (Fig. 4).

The compared configurations are: without channel reduction, 20% channel reduction, 30% channel reduction and finally 40% channel reduction.

Using an analog curve tracer, the holding current and holding voltage values were measured. Indeed, the curve tracer apply a sinusoidal voltage on the device through a serial resistance: during the increasing part of the sinusoid, the device is triggered-on and on the decreasing one the holding current and voltage are revealed by the voltage increase while the current is decreasing (Fig. 3). Fig. 3: Schematic presentation of electrical characterization using curve tracer showing the evolution of the characteristics Fig. 5 shows the channel reduction impact on the characteristics of the MOS-IGBT-SCR structure 1P2N (33% IGBT) at room temperature and with V GS = 5 V. In this figure the holding current increases from 32 mA up to 66 mA when the channel reduction varies from 0 up to 40%. Indeed the channel reduction topology helps decrease the Pwell resistance and as a result, increases the holding current that is by definition, the current level under which the SCR turns off. The effect of this parameter variation on the holding voltage was also studied. Increasing the channel reduction from 0 % to 40 % induces an increase in the holding voltage from 1.5 V up to 9.5 V (Fig. 5). Indeed, the increase of the holding current makes the voltage drop greater for the same N drift resistance.

However, concurrently to its positive effect on the holding current and holding voltage, the channel reduction shows a negative effect on the device robustness (see Fig. 6). Indeed, the channel reduction lowers the SCR action since it tends to locally cancel the NPN bipolar transistor. This phenomenon increases the current focalization and results in a premature failure. However, for the structure 3P1N (75 % IGBT), this detrimental effect is much less important and the robustness decreases from 10.2 A down to 6.3 A (see Fig. 6) that corresponds to 9.7 kV HBM level.

Form factor

The second parameter that allows increasing the holding current, is the form factor. Indeed, in the case of long fingers, despite the gate biasing and the resulting homogenous current across the channel there is a high risk to have a current focalization upon the triggering of the SCR [START_REF] Pogany | Nonlinear dynamics approach in modeling of the on-state-spreading -related voltage and current transients in 90nm CMOS silicon controlled rectifiers[END_REF]. Therefore, the idea is to split the structure in two or three parallel ones in order to have the same total width as the initial one. Reducing the width of the fingers decreases the probability of current focalization. However, to guarantee homogeneous triggering of the structure, the access resistances to these parallel structures need to be carefully balanced. To assess the impact of this parameter, three configurations have been implemented. The initial one (init) is the initial structure width (150µm * 2 fingers), the second one is made up of two structures of 75µm in parallel (D2) (Fig. 7) and finally by putting three structures of 50 µm in parallel. Fig. 8 shows the results of the three configurations for the structure 1P2N (33% IGBT) with channel reduction equal 30%, at room temperature and for V GS = 5V. The holding current increases from 57 mA to 67 mA when the structure is divided in three parallel devices.

Fig. 9 shows the variation of the TLP characteristics versus the form factor. The robustness increases from 4 to 7.2 A when the initial single-finger structure is compared to the three-fingers one having the same total width. This result confirms undoubtedly that, there was a current focalization in the initial structure probably due to imbalanced parasitic resistances. As a result, the form factor can be used to partially compensate the robustness decrease induced by the channel reduction topology. Fig. 8: Form factor effect on the holding current for the structure 1P2N with channel reduction equal to 30% at room temperature and for V GS = 5V. (INIT, D2 and D3 present successively the structure with a single finger, two fingers in parallel and three fingers in parallel, all having the same total width. Fig. 9: Form factor effect on the ESD robustness for the structure 1P2N with channel reduction equal to 30% at room temperature and for V GS = 0V.

N drift length

The final parameter that allows optimizing this device is the N drift length. Therefore, increasing the N drift length would result in a higher voltage drop, for a given holding current. Three configurations have been designed in addition to the initial structure INIT (Ndrift width = 2 µm): P2, P4 and P6 (initial Ndrift length plus 2, plus 4 and plus 6 µm, respectively).

Table 1 shows the holding voltage and holding current using the curve tracer. It can be noticed that, these configurations have a non-linear variation effect on the holding voltage and holding current values. As shown on the TLP I-V characteristics of the 1P2N structure with a channel reduction of 30 %, presented in Fig. 11, the impact on the ESD robustness is very important. It increases from a value of the failure current It2 of 4.5A for the initial structure up to almost 8 A for the structure P6. This confirms that, the increase of the N-drift improves the current homogeneity without degrading the on-resistance of the structure. According to these results, the best configuration to get the maximum holding current is to combine a large Ndrift length, a high channel reduction percentage and a form factor. Nevertheless, for cost efficiency, a trade-off has to be found between the induced silicon area increase and the targeted ESD robustness.

Discussion

This component has been proposed as an ESD protection device in order to minimize the silicon footprint of this part in the integrated circuit. The highest holding current obtained in this work is equal to 70 mA. This value can be raised by increasing the component width. Indeed, for some configurations (1P4N with channel reduction higher than 30 %...), the component exhibits an early failure due to high power consumption (High I H and high V H ). Therefore 150 µm width corresponds to a very small ESD protection component.

The highest holding current has been obtained with a biased gate. Therefore, a trigger circuit is needed to control this component. However, this circuit will be considered as a future work in order to have a complete power clamp.

Conclusion

We proposed further improvement for an innovative ESD protection structure presented in a previous work [START_REF] Arbess | Combined MOS-IGBT-SCR Structure for a Compact High-Robustness ESD Power Clamp in Smart Power SOI Technology[END_REF]. It is based on combining and properly controlling in a single structure a MOS, an IGBT and a SCR. This paper describes the optimization of these MOS-IGBT-SCR protection structures and their characterization.

Three new parameters (channel reduction percentage, form factor and drift zone length) were tested to study their influence on the holding current, holding voltage and the ESD robustness of the mixed component (Table 2).

With this layout optimization, the greatest measured holding current is smaller than 75 mA but this structure can be safely used to protect components working at 5V according to the obtained holding voltage that is greater than 5 V even if its holding current is lower than 100 mA.

Fig. 1 :

 1 Fig. 1: Mixed structure MOS-IGBT-SCR

Fig. 1 .

 1 Fig. 1. Mixed structure MOS-IGBT-SCR.

Fig. 2 :

 2 Fig. 2: I-V characteristics of SCR as ESD protection component. This schematic shows the safe operating area of the SCR and the danger zone.

Fig. 4 :Fig. 5 :

 45 Fig. 4: Source side optimization of 1P1N (50 % IGBT) mixed structure (a), mixed structure with 20 % (b) and 30 % (c) channel reduction.

Fig. 6 :

 6 Fig. 6: Effect of channel reduction from 0 to 40 % to the TLP characteristics of the 3P1N (75% IGBT) structure.

Fig. 7 :

 7 Fig. 7: Two components with the same total width (init) and different form factors (D2).

Fig. 10 :

 10 Fig. 10: Cross sectional view of MOS-SCR structure with presentation of the N drift length

Fig. 11 :

 11 Fig. 11: TLP characteristics of the structure 1P2N with channel reduction equal to 30% at room temperature, for V GS = 0V and different N drift lengths.

Table 1 :

 1 Curve tracer measurement of the holding voltage and current of the structure 1P2N with channel reduction equal to 30% at room temperature, for V GS = 5V and different N drift lengths.

	Configuration	INIT	P2	P4	P6
	Holding voltage (V)	3.5	5.6	4.7	5.2
	Holding current (mA)	56	60	70	70

Table 2 :

 2 Summary of geometrical parameters effects on the holding current, holding voltage and robustness of the mixed

		structures
		Increase of channel reduction	Form factor decreasing	Increase of N drift length
	Holding current	Higher	Higher	Higher
	Holding voltage	Higher	---	---
	Robustness	Lower	Higher	Higher