# Methods of Analysis

There are two main concepts of convergence. The first, called a sigma convergence, refers to the downward trend in the relative differences in per capita income. The second, called a beta convergence, means a negative influence on the initial level of per capita income in a regression of growth. When this regression takes into account exogenous growth factors other than the initial level of the GDP per capita, the beta convergence is called conditional.

#### 6.1 Sigma Convergence

An analysis of sigma convergence will be used to determine if the real income per head in WAEMU countries converges or diverges over the period of analysis. This analysis will be based on the calculation of the dispersion σ of GDP per capita according to the following formula:

Where yit and y:t denote the logarithm of per capita GDP of country i at time t and its average level and n is the number of countries. We conclude convergence when the dispersion decreases over time and divergence otherwise.

#### 6.2 Beta Convergence

The beta convergence model is used to test the phenomena of convergence or divergence between countries in accordance with the work of Barro and Sala-IMartin (1991, 1992). The general formulation is as follows:

(1)

where Xit is the level of per capita wealth achieved by the country i in period t and Zit a set of structural explanatory variables. The convergence process will cover a period of n years (from the initial year t n to the final year t).

Depending on whether or not the model includes structural variables Zit, we have conditional or absolute convergence (unconditional). This study adopts the hypothesis of conditional convergence in WAEMU due to the existence of different countries in the Union. This assumption goes beyond absolute convergence, which suggests similarities among the economic and social structures of membercountries who only differ in their level of initial per capita GDP.

Thus, for better test quality, explanatory variables, characteristics of different countries (conditional convergence), are introduced into the basic model.

#### 6.3 The Empirical Model of Conditional Convergence

As previously announced, the regional convergence has been addressed by introducing intrinsic characteristics of each member country.

The model takes into account the impact on growth and convergence of a set of control variables representing traditional growth factors. These variables with the expected sign of the corresponding coefficient (in parentheses) are:

– The average growth rate of GDP per capita of the previous year (+);

– Population growth (-);

– Health measured by life expectancy at birth (+);

– The level of education measured by the primary and secondary enrollment ratio (+);

– Investments in transport infrastructure measured by the density of the road network (+);

– Investments in electric power measured by the rate of electrification (+);

– Investments in telecommunications infrastructure measured by the rate of connection to mobile or fixed telephony (+).

The convergence rate will be calculated from the equation according to the model of neoclassical convergence. The coefficient β= ̶ ( ̶ exp (- λn))n, where λ is defined as the rate of convergence to steady state.

Empirically, the conditional convergence model to estimate is written as follows:

(2)

is the growth of per capita GDP of country i at time t;

Xit is per capita GDP of country i at time t;

Xi0 is per capita GDP of country i at the initial year (traditional convergence

factor);

Zkit is a vector of growth factors that takes into account the basic infrastructure (transport, electricity, telecommunications);

ui incorporates unobserved national characteristics that may influence the average growth rate of per capita GDP; λt is time specific effects and εit is a random error term.

#### 6.4 Data and Estimation Method

• Data

The empirical study will be conducted using panel data from the eight member-countries of WAEMU (Coˆ te d'Ivoire, Benin, Burkina Faso, Guinea Bissau, Mali, Niger, Senegal, and Togo) from 1980 to 2012. This statistical data is from the World Bank (WDI 2013) and the African Development Bank, “the Africa Infrastructure Development Index, AIDI, 2013” (see Table 2).

• The GMM dynamic panel

The econometric methodology for estimating equation (2) is the GMM (General Method of Moment) method in dynamic panel. Standard econometric techniques, such as OLS, do not provide efficient estimates of such a model, because of the presence of the lagged dependent variable among the explanatory variables. In fact, the unobserved individual effects are structurally correlated with the lagged dependent variable, causing non robust estimators.

The Arellano and Bond GMM estimator (Arellano and Bond 1991) provides solutions to the problems of simultaneity bias and omitted variables. The method consists of taking the first difference of the equation to eliminate country- specific effects and then using the lagged value of the explanatory variables as an instrumental variable in the first difference equation.

Table 2 Description of variables and source of data

Variables |
Description |
Source |

GDP per capita |
Gross domestic product per capita |
Africa Development Indicators, 2013, The World Bank |

Pop growth |
Population growth |
Africa Development Indicators, 2013, The World Bank |

Roads |
Density of the road network (in km/10,000 inhabitants) |
The Africa Infrastructure Development Index, AIDI, 2013 |

ICT |
Access rate to mobile and fixed phone services (subscribers/100 inhabitants) |
The Africa Infrastructure Development Index, AIDI, 2013 |

Electrical energy |
Electrification rate (in kwh/inhabitant) |
The Africa Infrastructure Development Index, AIDI, 2013 |

Primary education |
Primary enrollment rate (%) |
Africa Development Indicators, 2013, The World Bank |

Secondary education |
Secondary enrollment rate (%) |
Africa Development Indicators, 2013, The World Bank |

Life expectancy |
Life expectancy at birth |
Africa Development Indicators, 2013, The World Bank |

Investment |
Gross capital formation |
Africa Development Indicators, 2013, The World Bank |

Source: Author