The non-linear effects of fixed broadband on economic growth in Africa

The study focuses on the non-linear nexus between information and communication technology (ICT) development and economic growth in Africa for three main reasons, which build from the extant literature. These include (1) the relevance of economic growth in driving development outcomes, (2) the importance of ICT in boosting the catch-up process and facilitating human development and (3) the imperative to fill existing gaps in the body of knowledge on the role of ICT in driving development outcomes. These three elements of motivation are put in more perspective in what follows.

First, though there are cases where economic growth could be immiserizing, there is a general consensus that economic growth is needed for many avenues of economic development to be realized (Vu, 2011; Peprah et al., 2019; Asongu and Odhiambo, 2020). This is essentially owing to the premise that economic growth engenders a plethora of favorable economic development outcomes, inter alia, consumption and investment opportunities, social mobility, employment avenues, amelioration of living standards and enhancement of overall societal well-being (Hassan, 2005; Ngouhouo and Nchofoung, 2021). Accordingly, with the advent of globalization, there has been a growing body of literature on the importance of information technology in boosting outcomes of economic development (Veeramacheneni et al., 2008; Tchamyou et al., 2019a, b).

Second, from intuition and empirical evidence, economic growth within a country can be improved through factors such as ICT, which enhances the capacity of economic sectors in facilitating the catch-up process in terms of economic development (Hong, 2016; Tchamyou et al., 2019a, b). As posited by the attendant literature, ICT is relevant in driving activities of production as well as global value chains because it inter alia, mitigates poverty, boosts competitiveness, increases transparency and consolidates the management of public affairs (Sassi and Goaied, 2013; Tchamyou, 2017).

Moreover, relative to other continents of the world, the policy relevance of ICT is more worthwhile in Africa because while the continent is characterized by the lowest ICT penetration rate, it equally has the highest growth rate in ICT (Asongu and Odhiambo, 2019a, 2019b) which is a determinant of the catch-up process (Vu and Asongu, 2021). This tendency is indicative of the potential that policy makers have to leverage ICT for targeted development outcomes such as economic growth. The present study is premised on how such ICT can be leveraged to improve economic growth potentials in the African continent.

Third, the positioning of this research, as articulated in the previous paragraph, is also motivated by a gap in the existing literature. Accordingly, the extant literature on economic growth in Africa has focused on the following strands, for the most part: assessing determinants of external flows (Okafor et al., 2017); investigating nexuses between financial access and economic prosperity (Adam et al., 2017; Assefa and Mollick, 2017); understanding country-centric cases related to economic output and inflation (Bonga-Bonga and Simo-Kengne, 2018); linkages between foreign aid, volatility and growth that are sector-specific (Kumi et al., 2017); nexuses between variations in economic prosperity and access to finance (Ibrahim and Alagidede, 2017) and connections between innovation and economic growth variation (Yaya and Cabral, 2017).

The remainder of the study is structured as follows: Section 2 provides insights into the theoretical underpinnings while the data and methodology are discussed in Section 3, and the empirical results are disclosed in Section 4 before the study concludes in Section 5 with implications and future research directions.

This section is focused on theoretical underpinnings pertaining to the linkage between ICT and economic growth. According to the attendant literature (Hassan, 2005; Asongu and Odhiambo, 2020), the theoretical nexus between ICT and economic growth can be articulated along a plethora of channels which include (1) the competitive mechanism, owing to the fact that ICT provides opportunities by which companies, as well as nations, can become more competitive in order to improve corporate and cross-country catch-up, respectively.

According to the argument, ICT improves competitive prospects because it, inter alia, contributes to efficiency, more productivity and improvements in capital (i.e. human and physical). (2) The training channel is relevant in that ICT provides opportunities for labor activities, especially in the management of human resources. (3) With regards to the linkage channel, ICT by definition represents a factor through which technology can be transferred from one corporation or country to another. (4) Looking at the demonstration channel, firms and countries can use ICT to imitate other firms and countries in order to catch up in corporate performance and economic development, respectively. The underlying catch-up avenues that are facilitated by ICT ultimately boost output and economic prosperity in firms and countries, respectively.

The discussed theoretical linkage is consistent with non-contemporary literature on linkages between ICT and economic growth documented in Ofori and Asongu (2021a, b). According to the authors, technology is fundamental in both firm and cross-country catch-up processes (Ohlin, 1933; Samuelson, 1939; Stolper and Samuelson, 1941). Emara (2022), in analyzing the asymmetric dynamic relationship between FinTech adoption and poverty reduction in Sub-Saharan Africa (SSA), shows that an improvement in FinTech can initially decrease the extreme poverty rate, leading to a decrease in total poverty as a percentage of the population. Moreover, Emara and Katz (2022) examine the economic impact of telecommunications on economic growth in Egypt and show that for every 1% increase in mobile unique subscriber penetration and mobile broadband device adoption, the average annual contribution to gross domestic product (GDP) growth is estimated to be 0.172% and 0.016%, respectively.

A corresponding theory is the modernization theory which is consistent with the position that information technology is quite relevant in driving economic prosperity by means of inter alia, consumption, employment and transfer of technology (Sen, 1999; Bengoa and Sanchez-Robles, 2003; Durham, 2004; Li and Liu, 2005; Solomon, 2011; Messer and Townsley, 2003; Kwan and Chiu, 2015; Vu, 2019). The theoretical premise shows that ICT enables economic agents to provide a level-playing field that is relevant for opportunities that drive economic growth (Duncombe, 2006). On the basis of the discussed theoretical insights, this study tests one main hypothesis as follows:

This section focuses on the choice and model of specification: threshold panel modeling. Most studies on threshold panel models most often refer: either to the panel threshold regression (PTR) modeling proposed by Hansen (1999) or to the panel smooth threshold regression (PSTR) modeling initiated by Gonzalez et al. (2005). These are models that can highlight several regimes of a relationship between two or more variables. In Hansen's (1999) model, the transition from one regime to another is abrupt.

As for the PSTR modeling, the passage from one regime to another is done gradually (i.e. smoothly) through a continuous transition function and not as in the PTR. It allows the elasticity of the outcome variable in relation to the explanatory variable not only to be time dynamic in terms of variation, but also to be space dynamic in terms of variation contingent on the threshold variable. It follows that PSTR modeling incorporates the heterogeneity of the nexus between the outcome variable, the explanatory variable and the transition variable.

As part of the analysis, this study tests the existence of a non-linear relationship between ICT and economic growth through PSTR modeling. The PSTR model is presented as follows in Equation (1):

where $i=1,……,N$ is the number of individuals and $t=1,……,T$ determines the period of analysis, $yit$ is the dependent variable, $αi$ and $λt$ the vectors of the individual country and time fixed effects, respectively, and $Xit$ is the matrix of explanatory variables.

$G(qit;γ,c)$ is the continuous and normalized transition function and associated with the threshold variable $qit$ (which in our case is the proportion of the population with access to electricity), with the threshold parameter c and a smoothing parameter $γ$⁠, $β0$ and $β1$⁠, respectively, denoting the vector of the parameters of the linear model and of the non-linear model and $εit$ a vector of the error terms iid (0, $σε2$⁠).

The normalized transition function $G(qit;γ,c)$ takes values that are comprised in the interval (0 1) and enables the system to gradually make a transition from one regime to another. For the functional form of this transition, function to be defined, Gonzalez et al. (2005) is consistent with less-contemporary studies by Granger and Teräsvirta (1993) and Teräsvirta (1994) in suggesting that the following logistic form of order m in Equation (2) should be retained:

where, $γ>0$ et $c1<c2<…<cm$⁠, où $cj$ = $(c1…cm)$ is a vector grouping the threshold parameters. For $m$ = 1, the model has two extreme regimes that distinguish the low values of $qit$ to its high values, and $γ$ is a positive parameter that describes the transmission from one regime to another. When $γ→∞$⁠, the indicator function approaches an indicator function $I(qit>cj)$ which takes the value 1 si$qit>cj$⁠. Moreover, when $γ→0$⁠, the transition function becomes a homogeneous fixed effects panel that is linear. Indeed, a very high value of γ leads us toward a model with respect to Hansen (1999) with a sudden transition.

Taking into account the transition function described above, the theoretical modeling of PSTR looks like the Equation (3) as follows:

In the light of the threshold incidence introduced by the transition function $G$⁠, the sensitivity of the outcome variable in relation to the explanatory variable of country $i$ at the date $t$ as in Equation (4) as follows:

Equation (4) above illustrates how the dependent variable being sensitive with respect to the explanatory variable can be taken into account as a combination of the coefficients $β0$ and $β1$ obtained in the two extreme regimes. In order to define the transition function, the following requirement is worthwhile:

1. 0 $<G(qit;γ,c)<1$⁠, for $β1<0$⁠, we have $β0+β1<sit<β0$⁠, and

2. If $β1>0$⁠, we have: $β0<sit<β0+β1$⁠.

If $γ$ is substantially high, the PSTR becomes a two-speed threshold model (PTR model). Hence, the direct impact of the variable of interest on the endogenous variable is$β0$ for individuals characterized by a variable of interest that is below the threshold and $(β0+β1)$ for individuals characterized by a variable of interest that is higher than the threshold.

The first step in estimating a PSTR is first to check for non-linearity. In order to make an assessment, Gonzalez et al. (2005) propose a test that consists in comparing a linear model to a PSTR model. Accordingly, when $γ=0$⁠, then the function $G (,)$ has the value ½ whatever the value of the threshold variable is assigned. The threshold incidence hence disappears, and the model is simply a linear panel. It is the same when $β1=0$⁠. Given the fact that under the null hypothesis nuisance parameters are contained in the model (Davis, 1987), Gonzalez et al. (2005), just as Luukkonen et al. (1988), propose to replace the transition function $G(qit;γ,c)$ by its Taylor expansion of order 1 in the neighborhood of $γ=0$⁠.

For $m$ régimes, the regression to be estimated is Equation (5) as follows:

where the vectors of parameters $β0′,…,βm′are multiples ofγ$ and $εit∗=εit+Rmβ∗Xit$ with $Rm$ being the residual of the Taylor expansion. The null hypothesis of the linearity test becomes as follows: $H0:β1′=β2′=…=βm′=0$⁠. The linearity assumption is tested using standard tests. We use the Wald statistic (⁠$LMF$⁠) in Equation (6) as follows:

where $SSR0$ and $SSR1$ denote, respectively, the sum of the squares of the panel residuals under the null hypothesis (linear panel model with individual effects) and the sum of the squares of the panel residuals under the alternative hypothesis (model PSTR with m regimes). When the sample size is small, Gonzalez et al. (2005) suggest using Fisher (⁠$LMF1$⁠) which is defined in Equation (7) as follows:

where k is the number of explanatory variables, LMF follows a Fisher law to $mK$ and $TN−N−m(K+1)$ degrees of freedom F $(mK,TN−N−m(K+1))$⁠. Under the null hypothesis, all linearity tests follow a chi-square with $k$ degrees of freedom $χK2$⁠. Testing the linearity hypothesis for $m$ regimes (⁠$γ=0$⁠) again amounts in Equation (8) to testing as follows:

An extension of these tests is performed on the premise of the pseudo-likelihood ratio (⁠$pseudoLRT$⁠). In Equation (9), the statistic for the underlying test is presented as follows:

where, $SSR0$ is the sum of the squares of the residuals of a linear model with individual, $SSR1$ represents the sum of the square of the residuals of the model that is unconstrained (PSTR). With respect to the null hypothesis, the lagrange multiplier (LM) statistic is distributed according to a chi-square law with$mK$ degrees of freedom where $K$ is the number of independent variables and m the number of regimes.

However, with a small sample size, Gonzalez et al. (2005) propose the employment of an alternative statistic $LMF$ which is distributed under the null hypothesis according to a Fisher F′s law $(mK,TN−N−m(K+1))$⁠.

The underlying test makes it possible to reject or not the linearity hypothesis in favor of a PSTR model, but also to determine an “optimal” value of the transition variable. With respect to Gonzalez et al. (2005), this value corresponds to the one that minimizes the p-value of the linearity test.

In this study, the endogenous variable is the growth rate of the economy as measured by the growth rate of real GDP (⁠$y$⁠) and the exogenous variable of interest is the rate of subscriptions to fixed-line broadband access services (⁠$dig$⁠). The transition variable here is the proportion of the population with access to electricity (⁠$elec$⁠). The choice of the endogenous, exogenous and transition variables is informed by contemporary information technology and economic growth literature (Asongu and Odhiambo, 2022; Odhiambo, 2009, 2022; Emara and Katz, 2022).

The control variables selected are as follows:

1. Output per capita defined by the lagged variable of real GDP growth rate (⁠$y(−1)$⁠).

2. Private investment $(Inv)$⁠, measured by the share of private sector gross fixed capital formation in GDP, captures the influence of the private sector on economic activity. The theory predicts that investment generally stimulates economic growth and the expected sign is positive.

3. Trade openness (⁠$Ouv$⁠) obtained by dividing the difference between exports and imports as a % of GDP by 2 $(X−M2GDP)$⁠. The reason for taking this variable into account in this study is that liberal theories of international trade and endogenous growth admit that a country's openness to the outside world promotes growth, provided that it has relative price competitiveness.

4. Public expenditure (⁠$Dep$⁠). The inclusion of this variable is justified by the numerous existing studies on the links between public spending and economic growth. Several empirical works indeed establish that public spending can influence economic growth either negatively or positively depending on the nature and quality of public spending (Devarajan et al., 1996; Gupta et al., 2005).

5. The inflation rate (π) captured by the growth rate of the consumer price index (CPI). The CPI is one of the better proxies for prices than the GDP deflator in developing countries because a large proportion of spending is consumer spending (Mondjeli andTsopmo, 2017).

6. The population growth rate (⁠$pop$⁠). The potential effects of population growth on economic growth remain an object of debate among economists. The two theses that drive the debate are the orthodox and heterodox theories. Proponents of the orthodox theory argue that population growth positively affects economic growth (Chan et al., 2005; Dao, 2012; Thuku et al., 2013), while proponents of the heterodox theory argue that population growth negatively affects the growth of the economy (Song, 2013).

This paper aims to show that the effects of information technology (captured here by the number of fixed-line broadband subscriptions per 100 inhabitants) on economic growth in Africa are a function of the electricity coverage of territories (proportion of the population with access to electricity). The procedure for determining this optimal electricity coverage consists of three steps. First, we justify the non-linearity between fixed broadband and economic growth by conducting a linearity or homogeneity test.

For this purpose, we conduct the appropriate Fisher standard test in small sample sizes. Then, we determine the number of regimes or the number of transition functions of the PSTR model using the Fisher test. Finally, we estimate the PSTR model using the non-linear least-squares method, after which the value of the optimal inflation rate is determined endogenously. Thus, if electricity coverage is higher than the optimal value determined, any improvement in the number of fixed-line broadband access subscriptions would have positive effects on economic growth. Otherwise, the effects would be negative.

The data used are annual, taken from the World Bank's World Development Indicators (2021) and cover the period from 2010 to 2020. The sample considered includes 33 African countries. The choice of this country is mainly based on the availability of data. Accordingly, a balanced panel dataset is needed for the implementation of the PSTR regressions. The definitions of variables, corresponding sources and expected signs are disclosed in Table A1 while Table A2 presents the corresponding descriptive statistics.

The verification of the stationarity of the data of our model (i.e. non-existence of unit root) is conducted in order to avoid a possible spurious regression. In so far as our methodological framework takes into account the possible existence of unobservable heterogeneities in our sample, we performed five-unit root tests among which (1) the Im, Pesaran and Shin - IPS (2003) test, which takes into account heterogeneities under the alternative hypothesis of absence of unit root and (2) the Levin et al. (2002) test, which is instead based on panel homogeneity under the alternative hypothesis. The results of these unit root tests are reported in Table 1 below.

The homogeneity test aims to verify the existence of a possible non-linearity between fixed broadband and economic growth conditional on the level of access of the population to electricity. The non-linearity test allows us to demonstrate that there is a threshold from which the number of individuals with a subscription to fixed broadband access services would affect growth differently (positively/negatively).

The hypotheses of the linearity test are as follows: the null hypothesis is $H0: β0=0$ against the alternative $H1: β1≠0$⁠. However, this test is not standard since, under the null hypothesis, the PSTR model contains unidentified nuisance parameters (Hansen and Teräsvirta, 1996). Thus, consistent with Seleteng et al. (2013), we adopt the solution developed by Luukkonen et al. (1988), who propose to replace the transition function $G(qit;γ,c)$ by the limited expansion first-order Taylor and at point $γ= 0$ the null hypothesis of the test becomes $H0$ : $γ= 0$⁠.

The results of the non-linearity tests are presented in the table below. We present, respectively, the $LMW$ and $LMF$ statistics described previously. These tests allow the null hypothesis of the linear model to be rejected at a 5% significance level (⁠$pvalue<0.05$⁠).

This is to test the number of regimes or, equivalently the number of transition functions. The test consists in verifying the null hypothesis that the PSTR model has only one transition function (⁠$m=1$⁠) versus the alternative hypothesis that the PSTR model engenders a minimum of functions of transition (⁠$m=2$⁠). Test decisions are based on the $LMw$ and $LMF$⁠.

If the corresponding coefficients are statistically significant at the critical threshold of 5%, the null hypothesis is rejected and the position that there are at least two transition functions is upheld. Otherwise, we do not reject the null hypothesis and establish that the model has two regimes and therefore has a threshold.

Regarding the number of regimes, it emerges from the table below that the null hypothesis (H0) is not rejected for a critical threshold of 5%. In other words, at a significance level of 5%, it is impossible to reject the null hypothesis of a PSTR model with one threshold (two regimes). There is thus a single threshold allowing the transition from a regime of small proportion of the population with access to electricity (regime 1) to a regime of a large proportion of the population with access to electricity (regime 2). This threshold is expressed in the form of a score.

Given the choices of rmax = 2 and m = 1, the optimal number (⁠$LMF$ criteria) of threshold functions is r = 1. This result reflects the existence of a non-linearity in the relation between fixed broadband and economic growth conditional on the level of access of the population to electricity.

The estimated parameters of the PSTR model are reported in Table 2. According to the objectives of the research, two main conclusions can be drawn from this table (column 1). First, the proportion of the population with access to electricity is around 60%. We obtain a unique rate because in the estimation procedure of the PSTR model, the first step is to eliminate specific effects (Gonzalez et al., 2005).

Second, the rate of fixed broadband access subscriptions (dig) significantly explains economic growth and has the expected sign in both regimes. Thus, below the 60% threshold (indicating that the population's access to electricity is low), any increase in the fixed broadband subscription rate by 1% induces a decrease in economic growth of 2.56%. However, above this threshold (indicating that a high proportion of the population has access to electricity), an increase in the rate of fixed broadband subscriptions of 1% leads to an increase in economic growth of 2.43%.

In order to test the robustness of the PSTR model results, we estimate a growth equation that is expressed as follows:

where the variables are defined as indicated for equation (1). To estimate equation (10), we use the dynamic panel generalized method of moments (GMM), which has the advantage of controlling for endogeneity between variables (Tchamyou, 2019, 2020). The instrumentation method chosen is as follows: (a) for the control variables, lagged values of one period are used while the endogenous variable is lagged by two periods. The disadvantage of the GMM method is that it no longer allows for the representation of a smooth transition.

In Table 3, the estimated results of the GMM confirm those obtained from the PSTR model, particularly with regard to the sign of the variable of interest, which is the number of subscriptions to broadband Internet services.

The GMM estimation shows that the sign of the variable is negative while it is positive when the variable is squared; this reflects the existence of a U-shaped relationship between the number of subscriptions to high-speed Internet services and economic growth in Africa. The insignificance of the variable of interest and its squared series on the one hand and, of some control variables on the other hand, lies in the fact that GMM modeling leads to a loss of information related to the linearity constraint that the quadratic model imposes on the marginal effect (Eggoh and Villieu, 2013). Moreover, given that the GMM technique is employed exclusively as a robustness check, the computation of the total effect of fixed broadband as in corresponding literature (Emara, 2022) is not indispensable because the GMM results inform the study of the presence of a non-linear nexus between fixed broadband and economic growth.

The J-Statistics values of the Hansen test in the three specifications informs that study that the instrumental variables used in the GMM system are exogenously related to the error term using the probability value. The probability associated with the first statistics is 0.77, which reflects the validity of the instruments used (orthogonally conditions verified). According to Sargan (1958), a minimum probability of 0.25 is required to accept that the instrument is valid and exogenously related to the error term. Thus, the three statistics from the three specifications meet the orthogonally conditions. It is worthwhile to note that a probability value of less than 0.25 implies that the instrument is not valid and is endogenously related to the error term, and, therefore, does not meet the orthogonal condition.

Since the onset of the COVID-19 pandemic, access to technology has become more essential than ever to ensure the continuity of economic life and to make a real and lasting contribution to economic development. In the empirical literature, many authors support this thesis and attribute economic growth to the development of technology.

However, the impact of technology on growth has not yet been unanimously accepted by economists. Indeed, several works establish that better access to technology would positively affect growth (Latrach and Bouhajeb, 2015; Khan et al., 2016; Ildı rar et al., 2016; Garza-Rodriguez et al., 2020; Makonda, 2018), while others argue that the effects would be rather negative (Napo, 2018) or even neutral (Houngbedji, 2018).

In general, these authors establish that the relationship between fixed broadband and economic growth is linear. The originality of our study lies in the fact that it shows that the effects of fixed broadband on economic growth are rather non-linear in Africa when we consider the number of people with access to electricity. To do so, we apply a panel smooth transition regression model initially developed by Gonzalez et al. (2005), which is estimated from World Bank data over the period 2010–2020 on a panel of 33 African countries.

After showing the stationarity of the variables used with the unit root tests of Im et al. (2003) and Levin et al. (2002), we arrive at the results as follows: (1) the proportion of the population with access to electricity above and below which the relationship between fixed broadband and economic growth in Africa would change sign is about 60%; (2) below this threshold, each 1% increase in fixed broadband subscriptions induces a decline in economic growth of about 2. 58%; but above the threshold, economic growth would increase by 2.43% when fixed broadband subscriptions increase by 1%. Sensitivity analyses and GMM estimation of the dynamic panel (Tchamyou, 2020) show that these results are robust.

In the light of the established findings, due to the COVID-19 pandemic, which requires countries to take adequate measures to curb the spread of the pandemic (facilitation of distance work, distance education, access to health care, payment of bills, inter alia), any national policy aiming at improving the access of populations to high-level fixed broadband services should be preceded by the implementation of an electrification program for at least 60% of the total population. Otherwise, the provision of a good quality connection for the benefit of the population would not produce the expected effects on economic growth and would, therefore, be counterproductive.

The findings in the study leave room for improvement, especially within the perspective of considering other mechanisms and policy variables by which economic growth can be enhanced. Moreover, given the fact that in the post-2015 era of sustainable development goals, inclusive and sustainable development are important in policy and scholarly discourses, focusing on other sustainable development goals (SDGs)-specific outcomes would provide more room for policy implications.

The authors are indebted to the editor and reviewers for constructive comments.