Growth and Convergence in Africa: A Dynamic Panel Approach

Abstract

This study focuses on standard of living convergence within African countries. It evaluates the convergence process of per capita income using the concepts of σ-convergence and β-convergence. The analysis covers 46 countries from a variety of different regional economic communities (RECs); the period studied spans 1985–2005, using data from the World Bank’s World Development Indicators (2007) database.

The methodology adopted to test the convergence hypothesis was inspired from that used by Evans and Karras (J Monet Econ 37:249–265, 1996). The originality of the latter is that it combines both panel data and determination of stochastic series dynamics for per capita income in each country. Two estimation techniques were applied: the generalised method of moments (GMM) and the least squares dummy variable corrector (LSDVC) model, which is more effective on smaller samples.

The results indicate an absence of income convergence for all African countries. This non-convergence is primarily due to the great heterogeneity that exists among the countries. However, analysis of the RECs shows some β-convergence. Indeed, out of the five groupings studied, four constituted convergence clubs: ECOWAS, CEMAC, WAEMU and SADC.

In these RECs, a fixed-effects analysis was carried out, showing that the investment-to-GDP ratio is significantly linked to unobservable structural disparities. For example, demographic growth influences convergence in income level in the ECOWAS, while trade supported income convergence in the WAEMU area and proved to be insignificant in other RECs. This situation could be inherent to the low levels of intra-regional trade in the various RECs (under 13%).

The study recommends policy measures aimed at promoting intra-regional trade, the harmonisation of investment policies in the various RECs, along with policies that aim at making the African Union more effective in order to facilitate African integration and, in this way, standard of living convergence.

Appendices

Appendices

Appendix 1: Regional Economic Community (REC) Member Countries

• ECOWAS (Economic Community of West African States): Benin, Burkina Faso, Cape Verde, Côte d’Ivoire, Gambia, Ghana, Guinea-Bissau, Guinea, Liberia, Mali, Niger, Nigeria, Senegal, Sierra Leone and Togo

• CEMAC (Economic and Monetary Community of Central Africa): Cameroon, Central African Republic, Chad, Congo, Equatorial Guinea and Gabon

• COMESA (Common Market for Eastern and Southern Africa): Angola, Burundi, Comoros, Democratic Republic of Congo, Djibouti, Egypt, Eritrea, Ethiopia, Kenya, Madagascar, Malawi, Mauritania, Namibia, Rwanda, Seychelles, Soudan, Swaziland, Uganda, Zambia and Zimbabwe

• SADC (South African Development Community): Angola, Botswana, Democratic Republic of Congo, Lesotho, Madagascar, Malawi, Mauritania, Mozambique, Namibia, South Africa, Swaziland, Tanzania, Zambia and Zimbabwe

• WAEMU (West African Economic and Monetary Union): Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Senegal and Togo

LSDVC Estimators: The Principle

Consider the following standard dynamic model with panel data:

$$ {y_{it}} = \gamma {y_{i,t - 1}} + {x^{\prime}_{it}}\beta + {\eta_i} + {\varepsilon_{it}}\;\; \left| \gamma \right| < 1\;i = 1, \ldots, N\;\; et\;\; t = 1, \ldots, T $$

(3.11)

where ${y_{it}}$ is the dependant variable, ${x_{it}}$ is a vector ((k−1) × 1) explicative exogenous variables, ${\eta_i}$ unobservable individual effects and ${\varepsilon_{it}}$ an unobservable white noise. In compiling the observations over time and for individuals, one obtains the matrix form of model 3.11:

$$ y = D\eta + W\delta + \varepsilon $$

where y and $W = \left[ {{y_{ - 1}}:X} \right]$ are matrices of observation of order (NT × 1) and (NT × k), respectively, $D = {I_N} \otimes {i_T}$ is the individual dummy matrix (${i_T}$ is a vector (T × 1) composed of ones), $\eta$ is the vector (of order (N × 1)) of individual effects, white noise vector (of order (NT × 1)) and $\delta = \left[ {\gamma :\beta ^{\prime}} \right]$ is the vector of order (k × 1) of the coefficients.

LSDV estimators of model 3.11 are non-converging and in general biased.¹⁴ Bruno (2005) draws on the approach developed by Bun and Keviet¹⁵ (2003), whose principle is described below.

The LSDV estimator of $\delta$ is given by:

$$ {\delta_{LSDV}} = {\left( {W^{\prime}MW} \right)^{ - 1}}W^{\prime}My $$

where $M = I - D{\left( {D^{\prime}D} \right)^{ - 1}}D^{\prime}$is a symmetric matrix enabling one to annul individual effects.

Approximation of bias is given by:

$${ c_1 = \ (T^{-1}) = \delta_{\varepsilon}^2 tr(\wedge)q_1 \\c_2 (N^{-1} T^{-1}) = \ -\sigma_{\varepsilon}^2 [Q\bar {W}^\prime \wedge M\bar {W} + tr (Q\bar {W}^\prime \wedge M\bar {W}) I_{k+1}] + 2 \sigma_{\varepsilon}^2 q_{11} tr(\wedge^\prime \ \wedge \ \wedge)I_{k+1q_1} \\c_3 (N^{-1} T^{-2})= \ \delta_{\varepsilon}^4 \left\{ 2q_{11} Q\bar {W}^\prime \Lambda\Lambda {}^\prime \bar {W} q_1 + \left[ (q^\prime_1 \bar {W}^\prime \Lambda\Lambda {}^\prime \bar {W} q_1) + q_{11} tr(Q\bar {W}^\prime \Lambda\Lambda {}^\prime \bar {W})\\ + 2tr(\Lambda^\prime \Lambda\Lambda^\prime \Lambda)q_{11}^2 \right] q_1\right\}.}$$

where $Q = {\left[ {E(W^{\prime}\;MW} \right]^{ - 1}} = {\left[ {\bar{W}^{\prime}MW + \delta_\varepsilon^2tr(\Lambda \Lambda ^{\prime}){e_1}{{e^{\prime}}_1}} \right]^{ - 1}} \bar{W} = E(W)$, ${e_1} = \left( {1,0, \ldots.0} \right)^{\prime}$ vector $\left( {k \times 1} \right) {q_1} = {Q_{{e_{_1}}}}$ and ${q_{11}} = {e^{\prime}_1}{q_1} {L_T}$ the matrix of order $\left( {T \times T} \right)$ made up of 1 under the diagonal and zeros everywhere else; $L = {L_N} \otimes {L_T}$, ${\Gamma_T} = {\left( {{I_T} - \gamma {L_T}} \right)^{ - 1}}$, $\Gamma = {I_N} \otimes {\Gamma_T}$ and the matrix $\Lambda$ is then defined by $\Lambda = ML\Gamma$. With an increase in the level of precision, the three approximations of bias are:

$$ {B_1} = {c_1}\left( {{T^{ - 1}}} \right),{B_2} = {B_1} + {c_2}\left( {{N^{ - 1}}{T^{ - 1}}} \right){\text{and}}{B_3} = {B_2} + {c_3}\left( {{N^{ - 1}}{T^{ - 2}}} \right) $$

(3.12)

LSDV corrector estimators of bias are obtained by subtracting any term of Eq. (3.12) from the LSDV estimator. In practice, consistent corrected estimators are obtained by looking for consistent estimators of $\delta_\varepsilon^2$ and $\gamma$. This enables:

$$ {\text{LSDV}}{{\text{C}}_i} = {\text{LSDV}} - {\hat{B}_i},\quad i = 1, 2, 3 $$

(3.13)

The possible consistent estimators are the Anderson and Hsiao (1982) (AH) estimator, the Arellano and Bond (1991) estimator, and the Blundell and Bond¹⁶ (1998) (BB) estimator. Depending on the choice of $\gamma$ (from among the three earlier proposals), a consistent estimator of $\delta_\varepsilon^2$ is given by:

$$ \delta_h^2 = \frac{{{{e^{\prime}}_h}M{e_h}}}{{(N - k - T)}} $$

(3.14)

where ${e_h} = y - W{\delta_h} h = AH,ABetBB.$