We start from a specification of a linear panel model. Drawing on the work of Roser and Cuaresma (2016) who have worked on the causes of income inequality. The specification is presented by the following Eq. (1).

$${\text{l}\text{n}Income\_Ineq}_{it}={\alpha }_{0}+{\alpha }_{1}{{\text{l}\text{n}Income\_Ineq}_{it} }_{i,t-1}+ {\beta }_{1}{\text{l}\text{n}\text{T}\text{i}\text{S}}_{i,t}+{\beta }_{2}{\text{l}\text{n}\text{I}\text{C}\text{T}}_{i,t}+\sum _{j}{\delta }_{j}{X}_{ijt}+{\epsilon }_{i,t} \left(1\right)$$

The interaction model is represented by the Eq. 2.

$${\text{l}\text{n}Income\_Ineq}_{it}={\alpha }_{0}+{\alpha }_{1}{{\text{l}\text{n}Income\_Ineq}_{it} }_{i,t-1}+ {\beta }_{1}{\text{l}\text{n}\text{T}\text{i}\text{S}}_{i,t}+{\beta }_{1}{\text{l}\text{n}\text{I}\text{C}\text{T}}_{i,t}+ {\beta }_{3}{\text{l}\text{n}\text{T}\text{i}\text{S}\text{*}\text{I}\text{C}\text{T}}_{i,t}+\sum _{j}{\delta }_{j}{X}_{ijt}+{\epsilon }_{i,t} \left(2\right)$$

The term error is broken down into individual and idiosyncratic errors.

$$\epsilon it = \vartheta i +{\mu }_{it} \left(3\right)$$

In this equation, the dependent or explained variable is the logarithm of the income inequality noted lnIncome_Ineq measured by the Gini index. The variable lnTiS measures the logarithm of total trade in services as a percentage of GDP. ICT captures the infrastructures of telecommunications and is measured by the use of internet and telephone. X represents the vector of control variables that also affect income inequality. In this paper, we have drawn on the work of Dabla-Norris et al, 2015; Bumann and Lensink, 2016 using variables such as access to education, health, and electricity. To capture the cross-cutting role of telecommunications services, we interact with the trade in services variable with the internet access variable. i = 1, 2, …, N and t = 1, 2, … , T. ϑi is the individual error term and is IID (0, σ2) while μit is IID (0, σ2) are all independent of each other. The data come mainly from the World Bank database (World Development Indicators, 2020). They cover ten years from 2009 to 2018 and are based on a sample of 46 African countries3.

The model is estimated using dynamic panel data estimation techniques. The inclusion of the lagged dependent variable as one of the explanatory variables suggests a problem of endogeneity (Ametoglo et al, 2018; Wonyra and Okah Efogo, 2020). One of the solutions is the use of the Generalised Moment Method (GMM). (Arellano and Bond, 1991; Arellano and Bover, 1995; Blundell and Bond, 1998). The GMM estimator addresses issues of dependent variable shifts, unsupported fixed effects, independent regressor endogenous effects, as well as the presence of heteroskedasticity and autocorrelation between and within individuals or countries (Roodman 2009). However, the GMM method is only asymptotically effective for 'small T and large N'. Thus, it is not suitable for small samples. An alternative method is the least squares estimator with corrected dummy variables (Least Square Dummy Variable Corrected, LSDVC). The method calculates the corrected bias of the LSDV estimators for the standard autoregressive panel data model using the bias approximations in Bruno (2005 a), which extends the results by Bun and Kiviet (2003), Kiviet (1999) and Kiviet (1995). This method is an appropriate dynamic panel data technique for small samples where GMM cannot be applied effectively. We can rewrite the dynamic panel data model expressed in Eq. 1 as follows:

$${y}_{it}=\gamma {y}_{i,t-1}+{X{\prime }}_{it}\beta +{\eta }_{i}+{\epsilon }_{it} \left(4\right)$$

Where yit is the dependent variable, Xit is the set of independent variables, ηi is an unobserved individual effect, and εit an unobserved disturbance white noise.

The model can therefore be rewritten in the following way:

$$y = W\delta + D\eta + \epsilon \left(5\right)$$

*With* \(W = \left[y\right(-1\left) \right|X];\) *W* is the matrix of independent variables and the lagged dependent variable, D is the matrix of individual dummy variables (NTxN), η is the vector of individual effects (Nx1), δ is the vector of coefficients (kx1), and *ε* the usual error term.

The LSDV estimator is as follows:

$${\delta }_{LDSV}={\left({W}^{{\prime }} AW\right)}^{-1}{W}^{{\prime }}Ay \left(6\right)$$

where A represents a transformation that captures individual effects.

Chignon and Kiviet (2003) describe the bias associated with the LSDV estimator as:

$$E\left({\delta }_{LDSV}-\delta \right)= {c}_{1}\left({T}^{-1}\right)+{c}_{2}\left({{N}^{-1}T}^{-1}\right)+{c}_{3}\left({{N}^{-1}T}^{-2}\right)+O\left({{N}^{-2}T}^{-2}\right) \left(7\right)$$

In their Monte Carlo simulations, Bun and Kiviet (2003) and Bruno (2005a) examine the three possible nested approximations of LSDV bias, which in turn are extended to the first, second and third terms of Eq. (4)**6.**

The GVSL-corrected estimator (GVSLC) is equivalent to:

*LSDVC =* \({\delta }_{LDSV}-{B}_{i}\), *i = 1,2,3* (8)

In this article, we correct for them the most complete and precise (B3 in chignon and from Kiviet (2003) and Bruno (2005 a) ratings). We perform the bias correction with the Anderson-Hsiao estimator. (Ametoglo et al, 2018).

[3] Algeria, Angola, Benin, Botswana, Burkina, Burundi, Cape Verde, Cameroon, Chad, Congo, Côte d'Ivoire, Democratic Republic of Congo, Djibouti, Egypt, Eritrea, Ethiopia, Gabon, Gambia, Ghana, Guinea, Guinea Bissau, Equatorial Guinea, Kenya, Lesotho, Liberia, Libya, Madagascar, Malawi, Mali, Mauritania, Mozambique, Namibia, Niger, Nigeria, Rwanda, Senegal, Sierra Leone, Somalia, South Africa, Sudan, Tanzania, Togo, Tunisia, Uganda, Zambia, Zimbabwe.