Figure 1 shows the evolution of the dimensions of financial inclusion in Sub-Saharan Africa between 2010 and 2018. In terms of financial service penetration, the number of commercial bank account holders per 1000 adults increased from an average of 164 adults in 2010 to 354 in 2018. Regarding the availability of financial services, the number of commercial bank branches per 100,000 adults increased on average from about 3.87 in 2010 to 4.89 in 2018. Finally, with respect to the use of financial services, the outstanding deposit with commercial banks increased on average from 21.80% of GDP in 2010 to 29.11% of GDP in 2018. The low level of financial inclusion in SSA compared to other regions can be explained by individual factors such as age, gender, level of education, wealth, GDP growth rate and presence of financial institutions or quality of institutions. However, the performance recorded in terms of financial inclusion seems to be the result of the introduction of ICTs and especially of financial technologies. In this vein, the share of the adult population in SSA that has used the internet to pay for something in the last year has increased from 6% in 2017 to 17% in 2021. The number of credit and debit card holders increased from 7% in 2017 to 12% in 2021. However, disparities persist among SSA countries. For example, some countries have very high (Kenya, 73%; Uganda, 50%), high (Botswana, 22%; Burkina Faso, 31%; Ethiopia, 36%; Ghana, 35%, Mali, 21%; Namibia, 39%; Rwanda, 30%; Senegal, 28%, Tanzania, 38%), low (Cameroon, 11%; Guinea, 10%; Madagascar, 10%), and very low (Sierra Leone, 8%; Niger, 7%; Republic of the Congo, 8%; Burundi, 1%) mobile account penetration rates.

Figure 2 displays the evolution of the informal sector in SSA and shows that this rate has declined slightly between 2010 and 2018. The average annual rate of the informal sector as a percentage of GDP fell from 40.6% in 2010 to 39% in 2018. However, disparities can be noted between countries. For example, Nigeria and Gabon have the highest informality rates at 56.84%, while Namibia has the lowest rate in SSA at 28.97% ( Elgin et al., 2021 ). The preponderance of the informal sector in SSA is generally due to the economic environment, regulatory, legal and policy frameworks and some micro-factors, such as low education, discrimination, poverty, lack of access to economic resources, property, financial and other business services, and markets.

Figure 3 shows that the informal sector is negatively correlated with different dimensions of financial inclusion in SSA. Indeed, the larger the informal sector of an economy, the less likely it is that governments will be able to mobilize the revenues to build the necessary infrastructure in terms of improving education, health, physical infrastructure (roads, ICT, etc.) that would boost financial inclusion. Moreover, the less informal an economy is, the easier it is for banks to collect funds from depositors and thus increase the accessibility, availability and use of financial services. An informal economy characterized by informal finance is sometimes too expensive for users with the practice of usury rates. Thus, migration to the formal sector is likely to increase the demand for financial services.

There are at least three main directions for analyzing the effects of the informal economy on financial inclusion. The first wave sheds light on direct effects by addressing either unidirectional or bidirectional causality. Ajide (2021) investigates the possible relationship between financial inclusion and the informal economy in selected African countries. The study uses panel data estimation technique and Toda and Yamamoto causal approach on data from selected African countries over the period 2005 to 2015. The results show that financial inclusion reduces the size of the informal sector. The causality results show that there is a unidirectional causality from financial inclusion to the informal sector. Thus, a country with a low level of corruption and a high level of growth may benefit more from reducing the size of the informal sector through financial inclusion.

Gobbi and Zizza (2012) studied the relationship between the informal economy and the development of the financial sector in the Italian debt market during the period 1997-2003 and found that the informal economy prevented the development of the financial sector, but that the development of the financial sector had no statistical impact on the informal economy.

Bose et al. (2012) studied the interaction between the informal economy and improvements in the banking sector in 137 countries over the period 1995-2007 using panel regression and found a negative relationship between the informal sector and banking sector development.

Berdiev and Saunoris (2016) examine the dynamic relationship between financial development and the informal economy using data for 161 countries over the period 1960-2009. Specifically, they use a panel vector autoregressive model to construct impulse response functions that illustrate the time path of one variable (e.g., the informal economy) following an orthogonal shock to another variable (e.g., financial development). They find that financial development reduces the size of the informal economy. Moreover, there is evidence of reverse causality between these variables; namely, a shock to the informal economy inhibits financial development.

The second wave focuses on the non-linear relationship. In this vein, Affandi and Malik (2020) studied the influence of the informal sector and the reach of financial institutions in six Balkan countries on financial inclusion from 2006 to 2017. The authors used the non-linear ARDL model, a non-linear cointegration approach, to identify asymmetric effects by investigating how the informal economy and the reach of financial institutions influence financial inclusion. The results suggest that the informal economy has a significant negative impact on financial inclusion, while the outreach of financial institutions has a significant effect on financial inclusion.

Hajilee et al. (2017) examine the impact of the informal economy on financial market inclusion by looking at both short-run and long-run effects simultaneously. They use the recent non-linear cointegration approach (i.e. NARDL), which introduces non-linearity in the model specification, to look for asymmetric effects of the informal economy on financial market inclusion. Using annual data from 1980 to 2013 for 18 selected emerging economies, they find that the informal economy has significant short-run asymmetric effects on financial market inclusion for a majority of the sampled emerging economies.

The third wave highlights the relationship between the informal sector and financial inclusion, assuming that this relationship is moderated by macroeconomic variables. Elgin and Uras (2013) examine the relationship between financial development and the size of the informal economy. They construct a model in which an exogenous change in the size of the informal sector creates two effects on financial development. Specifically, the informal sector harms financial development by increasing financial repression due to tax evasion. However, on the other hand, increasing the size of the informal sector facilitates financial development by alleviating the capacity constraint on the financial sector. Using an international panel dataset of 152 countries over the period 1999-2007, they find a relationship in the form of an inverted U between the size of the informal sector and financial development. The relationship was shown to occur through two operational channels. The first was financial repression from which a rise in the informal sector undermines financial development. The second was financial efficiency through which the size of the informal sector has a beneficial impact on financial development. In short, the growth of the informal economy increases the prevalence of tax evasion, which hinders financial sector development. Assuming that the informal sector exhibits a downward trend in SSA, we test the following hypothesis:

Hypothesis 1. The informal sector negatively affects financial inclusion in SSA.

In the literature, we identify ICT, and economic freedom as channels through which the informal sector can stimulate or hinder financial inclusion.

The first channel is ICT. ICTs represent an increase in public service delivery as well as a channel through which the size of informal economic activity could be reduced ( Haruna & Alhassan, 2022 ). Indeed, by facilitating the mobilization of resources from informal finance, ICTs stimulate access to and use of financial services. For Garcia-Murillo and Velez-Ospina (2017) , as ICTs are general-purpose technologies, they can provide people with information on education, employment opportunities and government services that can potentially enable them to migrate to the formal sector. The empowerment that comes from the use of ICTs means wider and deeper access to information and resources and helps to reduce the informal sector and potentially improve the lives of users. Lewin and Sweet (2005) argue that indirect social returns come from ICT use. The use of ICTs improves the functioning of the market and increases trade. Investments in ICT reduce costs because better communication systems reduce transaction costs ( Datta & Agarwal, 2004 ; Waverman et al., 2005 ). ICT enables markets to function better and supply and demand to be regulated. Consequently, it increases information about prices, job opportunities and markets ( Sridhar & Sridhar, 2004 ). In addition, good communication networks replace costly physical transport and thus expand networks (of buyers and suppliers) and markets. Ajide et al. (2022) find that the informal sector can have an effect on ICT development. Coupled with social protection and wage payments, ICT improves women financial inclusion ( Kankaria & Dutta, 2021 ).

The second channel is economic freedom: the indirect effect of the informal economy on financial inclusion is the result of an economically free environment. The choice of this channel is based on the fact that the establishment of a truly free market economy in terms of financial freedom, business freedom, government spending, protection of property rights, efficiency of justice, tax burden, public expenditure, fiscal health, monetary freedom, trade freedom and investment freedom reduce the negative effect of the informal sector on financial inclusion. For example, Loayza (1997) shows that an increase in the size of the informal sector negatively affects growth by, first, reducing the availability of public services for everyone in the economy, and, second, increasing the number of activities that use some of the existing public service less efficiently or not at all. Furthermore, the expansion of the informal economy reduces tax revenues ( Kodila-Tedika & Mutascu, 2013 ) and lower tax revenues reduce government revenues, which reduces the ability to provide high quality public goods ( Broms, 2011 ). Fugazza and Jacques (2004) conclude that labor market regulations and tax burden are the reasons for informal activities. Moreover, corruption not only increases the informal economy, but also reduces the impact of fiscal policy on the underground economy ( Huynh & Nguyen, 2020 ). Schneider (2005) estimates the level of the informal economy in 110 countries, including developing, transition, and developed OECD economies and finds that an increase in the size of the informal sector can lead to a reduction in state resources, which in turn reduces the quality and quantity of goods and services provided by the public sector. Assuming a sustained increase in ICT in SSA and given the role of economic freedom in the development of financial services markets, we test the following hypothesis:

Hypothesis 2. ICT and economic freedom reinforce the negative effects of informal sector on financial inclusion

The empirical model results from the work of Hajilee et al. (2017) who adopted specifications considering the informal sector from Hajilee and Al Nasser (2014) . Its choice is justified by the fact that the financial inclusion model predicts that a decline in the informal sector should increase the level of financial inclusion. The empirical specification is thus illustrated by Equation (1):

(1)

where is the dependent variable that describes the penetration, availability, usage of financial services and the financial inclusion index in SSA. Following Camara and Tuesta (2018) , we use a one stage Principal Component Analysis to construct financial inclusion index. represents the informal sector of the country at the period . This independent variable is the informal economy as a percentage of GDP, derived from Elgin et al. (2021) . The data cover 158 countries from 1993 to 2018. The informal sector index is estimated using the Multiple Indicators Multiple Causes (MIMIC) model, which is considered the best method to assess the size of the informal sector in relation to foreign exchange demand, electricity consumption and other methods.

is the vector of control variables consisting of: i) unemployment measured by total unemployment as a percentage of the population. Employment is a factor associated with financial inclusion ( Goodwin et al., 2000 ). The unemployed or those with irregular and insecure employment are less likely to participate in the financial system ( Sarma & Pais, 2011 ). ii) education measured by the adult literacy rate as a percentage of people aged 15 and above. Education is positively associated with formal account ownership ( Fungáčová & Weill, 2015 ). GDP per capita captures the standard of living of the population and is measured by GDP per capita in constant dollars. Demirgüc-Kunt et al. (2013) and Kabakova and Plaksenkov (2018) argue that GDP per capita plays a major role in explaining cross-country differences in the use of formal accounts. Population is measured by population density i.e. the number of people per kilometre of land area. Allen et al. (2014) points out that population density is important for financial inclusion. Gov-index is the index of institutional quality. It is calculated from the six World Governance Indicator (WGI) governance indicators namely political stability/absence of terrorism, control of corruption, regulatory quality, government effectiveness, voice and accountability and rule of law using Principal Component Analysis (PCA). We use this index in order to obtain overall information and thus avoid arbitrary selection or scattered information. In addition, the use of this index allows us to solve potential endogeneity problems caused by institutional variables and probably avoid multi-collinearity. Institutional quality has a positive impact on financial inclusion in terms of penetration, accessibility and use of financial services ( Nkoa & Song, 2020 ). Inflation is measured by the GDP deflator as an annual percentage. Kendall et al. (2010) argue that inflation has a negative and significant effect on deposit penetration. Andrianaivo and Kpodar (2011) , on the other hand, find that inflation has no effect on financial inclusion. Trade openness is proxied by the flows of exports and imports of goods and services as a percentage of GDP. Greater openness negatively affects financial inclusion ( Do & Levchenko, 2007 ). captures unobserved country-specific effects. ${\text{ν}}_t$ captures the time-specific effect common to all countries and ${\text{ε}}_{it}$ is the error term. Thus, $\text{α}$, $\text{β}$ and $\text{λ}$ are the parameters to be estimated.

The model to be estimated is specified by the following Equation (2):

$\begin{array}{c}I{F}_{it}=\text{α}+\text{β}S{I}_{it}+{\text{λ}}_{1}Unem{p}_{it}+{\text{λ}}_{2}Ed{u}_{it}+{\text{λ}}_{3}gd{p}_{it}+{\text{λ}}_{4}Den{s}_{it}+{\text{λ}}_{5}Gov\_inde{x}_{it}\\ +{\text{λ}}_{6}In{f}_{it}+{\text{λ}}_{7}Trad{e}_{it}+{\text{ν}}_t+{\text{μ}}_i+{\text{ε}}_{it}\end{array}$ (2)

The influence of interactive variables is considered in model (3) below:

$I{F}_{it}=\text{α}+\text{β}S{I}_{it}+\text{λ}{X}_{it}+\text{γ}{I}_{it}+{\text{ν}}_t+{\text{μ}}_i+{\text{ε}}_{it}$ (3)

where $I$ considers interactions illustrating the transmission channels through which the informal sector acts on financial inclusion. We consider Information and Communication Technology (ICT) and economic freedom as transmission channels ( Huynh & Nguyen, 2020 ).

$\begin{array}{c}I{F}_{it}=\text{α}+\text{β}S{I}_{it}+{\text{λ}}_{1}Unem{p}_{it}+{\text{λ}}_{2}Ed{u}_{it}+{\text{λ}}_{3}gd{p}_{it}+{\text{λ}}_{4}Den{s}_{it}+{\text{λ}}_{5}Gov\_inde{x}_{it}\\ +{\text{λ}}_{6}In{f}_{it}+{\text{λ}}_{7}Trad{e}_{it}+{\text{λ}}_{8}Interne{t}_{it}+{\text{λ}}_{9}Mobil{e}_{it}+{\text{λ}}_{10}Te{l}_{it}+{\text{λ}}_{11}Freedo{m}_{it}\\ +{\text{γ}}_1{\left(SI*Internet\right)}_{it}+{\text{γ}}_2{\left(SI\ast Mobile\right)}_{it}+{\text{γ}}_3{\left(SI\ast Tel\right)}_{it}\\ +{\text{γ}}_4{\left(SI\ast Freedom\right)}_{it}+{\text{ν}}_t+{\text{μ}}_i+{\text{ε}}_{it}\end{array}$ (4)

Drawing on the work of Kumar (2013) and Huynh (2020) , the relationship between the informal sector and financial inclusion is studied based on Equation (1). The coefficients in Equation (1) are estimated using two different estimation techniques: indicator variable least squares and system GMM.

The first estimation technique was used to estimate the static version of the model, while the GMM system is used to estimate the dynamic version of Equation (1). While fixed effects estimation addresses the issue of heterogeneity, this estimation approach does not address the issue of endogeneity, especially when Equation (1) includes the reflected dependent variable. Results based on the fixed-effects model should therefore be interpreted with caution because it is weakened by endogeneity.

Tests are performed to justify the choice of the fixed-effects model that provides the most appropriate coefficient estimates. The Lagrange test was performed to test the validity of the random model estimate against the OLS model and the Hausman test was performed to see the appropriateness of the fixed or random effect estimation approaches. When the Hausman test does not admit of a fit or when the probability of the test is less than 10%, the fixed effect model is preferred. When $p\text{-}value\succ 10\%$, the test does not permit to choose. The choice of the best model depends on the author’s conviction ( Kpodar, 2007 ). Hence, based on the comparison between the R2-Within and the R2-between $\left(R2\text{-}Within\succ R2\text{-}between\right)$, we choose the fixed effects. For all estimation approaches, we used robust estimators to deal with the existence of possible heteroscedasticity and autocorrelation problems using the so-called “clustering” technique.

There are several reasons for using the GMM approach in this study. The GMM method has the advantage of controlling and solving the problem of endogeneity. In this study, several sources of endogeneity can be noted. First, the problem of bi-directional causality. The informal sector can affect financial inclusion and vice versa ( Ajide, 2021 ); secondly, the calculation of financial inclusion and governance indexes, although objective, does not exclude the risk of errors measurement ( Nkoa & Song, 2022 ); finally, the use of dynamic panels ( $N\succ T$) can also be a source of endogeneity. Indeed, it is assumed that the first-order lag of the dependent variable is an independent variable, but this lagged variable is correlated with the error term. The absence of autocorrelation of the residuals guarantees that unbiased estimators are obtained. Moreover, two conditions have been satisfied and allow the use of the GMM technique in a system. First, the dependent variable of financial inclusion is persistent, given that the correlation between its current value and its lagged value is higher than the rule of thumb threshold of 0.800 ( Table 1 ) and the number of time series ( $T=9$) is lower than the number of cross-sections ( $N=25$). Therefore, $N\succ T$.

To deal with these sources of endogeneity, especially the latter, GMMs are appropriate. And for small samples as in this case, the literature recommends system GMMs. The system GMM addresses the shortcomings of the standard GMM estimator. In the end, Blundell and Bond (1998) developed the system GMM estimator to solve the problems of multicollinearity, endogeneity bias and omitted variables. Further details on the system GMM approach can be found in Arellano and Bover (1995) and Blundell and Bond (1998) .

Four post-estimation diagnostic tests are used to assess the validity of GMM models in systems ( Asongu & De Moor, 2017 ). Based on these criteria, two aspects deserve to be developed. On the one hand, Arellano and Bond’s second-order autocorrelation test (AR (2)) is preferred over the first-order test (AR (1)) because studies in the literature rely exclusively on the second-order test ( Narayan et al., 2011 ). On the other hand, Hansen’s test is preferred over Sargan’s test and such preference is justified by the rule of thumb that the number of instruments is less than the corresponding number of effective sections in each specification. While the Sargan test requires homoscedastic errors, which is too strong an assumption and sometimes unrealistic, the Hansen test is robust even in the presence of heteroscedasticity but is unreliable in the case of instrument proliferation. Therefore, this robust test can be adopted and the rule of thumb to avoid instrument proliferation followed ( Tchamyou et al., 2019 ).

The data for this study are from the World Development Indicators (2022), Elgin et al. (2021) the International Monetary Fund’s Financial Access Survey (2022) and the World Governance Indicators (2022). The sample includes 25 countries in Sub-Saharan Africa ( Table 2 ). The study covers the period 2010-2018. The descriptive statistics ( Table 2 ) show small variations. It is generally accepted that small fluctuations in data lead to unbiased results ( Nkoa & Song, 2022 ). The correlation matrix ( Table 3 ) shows a weak interdependence between financial inclusion and the informal sector. Moreover, the negative correlation assumes a negative effect of the informal sector on financial inclusion. Overall, the correlations are not high enough to cause serious problems of multicollinearity.

Source: Authors.

Source: Authors.

The results of the linear model show that the informal sector has negative and significant effects on financial inclusion in SSA ( Table 4 ). All else being equal, decreases in the level of the informal sector by 1% lead to an increase in the financial inclusion index of 0.000939 points. Specifically, the penetration, availability and use of financial services increase by 6.291, 0.124 and 0.216 points. There are at least two reasons for this result. First, a low level of informality is associated with high productivity, which favors capital gains and thus may increase the demand for financial services. Second, a less informal economy is correlated with fewer developmental challenges such as poverty, inequality, and disease, which may increase access to and use of financial services and thus financial inclusion.

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

This result corroborates those found by Hajilee et al. (2017) and Affandi and Malik (2020) who find that the informal sector negatively affects financial inclusion. This result is justified by the fact that services (especially financial) offered in the informal sector are generally very expensive. Borrowers usually pay back the loans they take out one hundred percent. This phenomenon is therefore likely to limit the demand for financial services. Migration to the formal sector offers cost benefits to financial service seekers, all of which increase the demand for formal financial services and thus the level of financial inclusion.

With regard to the control variables, two trends can be identified. On the one hand, unemployment and inflation have a negative and significant effect on financial inclusion. Indeed, the more an individual has a job that provides him with a regular income, the more he tends to be financially included. For example, the payment of salaries through formal financial institutions allows the worker to have a bank account and to use it more through credit applications, overdrafts, transfers for third parties or to receive money. This result is in line with those of Carbó et al. (2005) and Devlin (2005) who found that employment has a beneficial effect on financial inclusion. On the other hand, inflation, which reflects rising prices and microeconomic instability, is likely to limit financial inclusion. This result is similar to Allen et al. (2014) , Rojas-Suarez and Amado (2014) and Omar and Inaba (2020) , but contradicts Evans (2016) who find insignificant impact of inflation on the level of financial inclusion.

On the other hand, education, GDP per capita, population density, governance, and trade openness have a positive and significant effect on financial inclusion in SSA. This result is similar to Robinson (2014) who argues that there is a strong relationship between literacy and financial inclusion in that the ability to read and write is a prerequisite for opening and maintaining a bank account. Moreover, many other empirical studies so far show that having financial knowledge and skills is significantly related to people saving more and borrowing money, along with an increase in the chances of starting a new business ( Acemoglu et al., 2014 ). The coefficients of GDP per capita are positive and significant suggesting that countries with high GDP per capita also experience a high level of financial inclusion. This result is consistent with Kumar (2013) who finds that GDP has a positive and significant effect on financial inclusion. Economies with high population are expected to have better access to financial services due to convenient network effects. This result is positive and significant and thus corroborates with the findings of Chithra and Selvam (2013) , Allen et al. (2014) , and Park and Mercado (2015). With respect to governance, good governance and high institutional quality through strengthening the rule of law, good regulatory quality are more likely to foster voluntary financial inclusion. This result joins those of Avom and Bobbo (2018) , Nkoa and Song (2020) . Trade openness has a positive and significant effect on financial inclusion. This result is consistent with Kim et al. (2018) who show that in the long run trade openness has an effect on financial inclusion (Financial Development). This result is also similar to that of Rajan and Zingales (2003) who argue that trade openness, especially when combined with openness to capital flows, weakens the incentives of incumbent commercial firms or financial intermediaries to block financial development in order to reduce entry and competition.

The results reported in Table 5 and Table 6 show that the informal sector has significant negative effects on transmission channels. A decrease in the informal sector coupled with ICT including internet, mobile and fixed phone on the one hand and economic freedom on the other hand significantly increases several dimensions of financial inclusion. This result joins the work of Garcia-Murillo and Velez-Ospina (2017) and Chacaltana et al. (2018) who show that the combination of ICT and the informal sector promotes migration to the formal sector. This result also joins that of Jacolin et al. (2019) who find that mobile financial services reduce the size of the informal sector. Similarly, Nguimkeu & Okou (2021) who opine that instead of focusing on formalization as an imperative policy goal, more realistic short to medium term policies should leverage low-skill-biased digital technologies to upgrade the skills of workers and enhance the productivity of firms in the informal sector.

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Information and communication technologies (ICTs) can influence the effect of the informal economy on financial inclusion in several ways: namely: Access to digital financial services (ICTs can enable individuals and businesses in the informal economy to access digital financial services, such as mobile payments, online bank accounts and online loans); Reduced transaction costs (ICTs can reduce transaction costs for individuals and businesses in the informal economy, by enabling online transactions and reducing the need for cash); access to information and training (ICTs can provide individuals and businesses in the informal economy with access to information and training on financial services and management practices, which can help them improve their financial inclusion).

The informal sector indirectly affects financial inclusion through economic freedom. Indeed, the informal economy is generally stronger the weaker the capacity of the state. The preponderance of the informal sector is accompanied by significantly lower levels of revenue and expenditure, less efficient public institutions, significant regulatory and fiscal burdens and weaker governance. In this vein, in a recent study, Awasthi and Engelschalk (2018) show that cash transactions involving goods and services for which no receipts are issued significantly increase the risk of tax evasion. They show the existence of an apparent strong negative correlation between the use of formal electronic payments and the size of the underground economy. The non-participation of the informal economy in tax revenues reduces the ability of public authorities to intervene effectively. And the consequences are not only financial, but can also be social or economic, and in terms of governance.

This study adopts the System Generalized Method of Moments as an empirical strategy to check the robustness of the results. The specified model only considers the financial inclusion index as the dependent variable. The specification is Roodman’s (2009a, 2009b) extension of Arellano and Bover (1995) which has been documented to limit instrument proliferation and control for cross-sectional dependence ( Love & Zicchino, 2006 ; Baltagi, 2008 ).

The following equations in level (5) and difference (6) summarize the procedure for estimating the direct effects of the informal sector on financial inclusion, namely:

$I{F}_{i,t}={\text{σ}}_0+{\text{σ}}_{1}I{F}_{i,t-\tau }+\text{γ}S{I}_{i,t-\tau }+{\displaystyle \underset{h=1}{\overset{k}{\sum }}{\text{φ}}_h{W}_{h,i,t-\tau }+{\text{η}}_i+{\text{ξ}}_t}+{\text{ε}}_{i,t}$(5)

$I{F}_{i,t}-I{F}_{i,t-\tau }={\text{σ}}_0+{\text{σ}}_1\left(I{F}_{i,t-\text{τ}}-I{F}_{i,t-2\text{τ}}\right)+\text{γ}\left(S{I}_{i,t-\text{τ}}-S{I}_{i,t-2\text{τ}}\right)+{\displaystyle \underset{h=1}{\overset{k}{\sum }}{\text{φ}}_h\left(W_{h,i,t-\text{τ}}-W_{h,i,t-2\text{τ}}\right)+\left({\text{ξ}}_t-{\text{ξ}}_{t-\text{τ}}\right)+{\text{ε}}_{i,t-\text{τ}}}$ (6)

The level (7a) and (7b) and difference (8a) and (8b) equations summarize the ICT and economic freedom channels through which the informal sector affects financial inclusion.

$I{F}_{i,t}={\text{σ}}_0+{\text{σ}}_{1}I{F}_{i,t-\tau }+\text{γ}S{I}_{i,t-\tau }+{\displaystyle \underset{g=1}{\overset{3}{\sum }}{\varphi }_{g}IC{T}_{i,t-\text{τ}}}+{\displaystyle \underset{h=1}{\overset{k}{\sum }}{\text{φ}}_h{W}_{h,i,t-\text{τ}}+{\text{η}}_i+{\text{ξ}}_t}+{\text{ε}}_{i,t}$ (7a)

$I{F}_{i,t}={\text{σ}}_0+{\text{σ}}_{1}I{F}_{i,t-\tau }+\text{γ}S{I}_{i,t-\text{τ}}+\text{δ}Freedo{m}_{i,t-\text{τ}}+{\displaystyle \underset{h=1}{\overset{k}{\sum }}{\text{φ}}_h{W}_{h,i,t-\text{τ}}+{\text{η}}_i+{\text{ξ}}_t}+{\text{ε}}_{i,t}$ (7b)

$\begin{array}{l}I{F}_{i,t}-I{F}_{i,t-\tau }={\text{σ}}_0+{\text{σ}}_1\left(I{F}_{i,t-\text{τ}}-I{F}_{i,t-2\text{τ}}\right)+\text{γ}\left(S{I}_{i,t-\text{τ}}-S{I}_{i,t-2\text{τ}}\right)+{\displaystyle \underset{g=1}{\overset{3}{\sum }}{\varphi }_{g}IC{T}_{i,t-2\text{τ}}}+\\ {\displaystyle \underset{k=1}{\overset{3}{\sum }}{\text{β}}_k\left(S{I}_{k,i,t-\text{τ}}\ast IC{T}_{i,t-\text{τ}}-S{I}_{k,i,t-2\text{τ}}\ast IC{T}_{i,t-2\text{τ}}\right)}+{\displaystyle \underset{h=1}{\overset{k}{\sum }}{\text{φ}}_h\left(W_{h,i,t-\text{τ}}-W_{h,i,t-2\text{τ}}\right)+\left({\text{ξ}}_t-{\text{ξ}}_{t-\text{τ}}\right)+{\text{ε}}_{i,t-\text{τ}}}\end{array}$ (8a)

$\begin{array}{l}I{F}_{i,t}-I{F}_{i,t-\text{τ}}={\text{σ}}_0+{\text{σ}}_1\left(I{F}_{i,t-\text{τ}}-I{F}_{i,t-2\text{τ}}\right)+\text{γ}\left(S{I}_{i,t-\text{τ}}-S{I}_{i,t-2\text{τ}}\right)+\delta \left(Freedo{m}_{i,t-\text{τ}}-Freedo{m}_{i,t-2\text{τ}}\right)+\\ \text{ψ}\left(S{I}_{i,t-\text{τ}}\ast Freedo{m}_{i,t-\text{τ}}-S{I}_{i,t-2\text{τ}}\ast Freedo{m}_{i,t-2\text{τ}}\right)+{\displaystyle \underset{h=1}{\overset{k}{\sum }}{\text{φ}}_h\left(W_{h,i,t-\text{τ}}-W_{h,i,t-2\text{τ}}\right)+\left({\xi }_t-{\xi }_{t-\text{τ}}\right)+{\text{ε}}_{i,t-\text{τ}}}\end{array}$ (8b)

where $I{F}_{i,t}$ measures the country’s financial inclusion $i$ at year $t$; $S{I}_{i,t}$ measures the informal sector, $W_{i,t}$ is the vector of control variables (Unemployment, education, GDP/capita, population density, governance index, inflation, trade openness), $\text{σ}$, $\text{γ}$, $\text{ψ}$, $\text{δ}$ and $\text{φ}$ are parameters to be estimated, $\text{τ}$ represents tau. ${\text{η}}_i$ is the country specific effect, ${\text{ξ}}_t$ is the time specific constant and ${\text{ε}}_{i,t}$ the error term.

In this specification, two-stage estimation is preferred over one-stage estimation because it addresses the heteroskedasticity problem. In addition, the problems of identification ( Tchamyou & Asongu, 2017 ), simultaneity ( Asongu & de Moore, 2017 ) and exclusion restrictions ( Beck et al., 2003 ) are also addressed.

The results presented in Table 7 show that accessibility, availability and usage of financial services in the previous year positively and significantly affect financial inclusion. The diagnostic tests are also validated. Table 8 and Table 9 display the results of the transmission channels. First, the null hypothesis of no second-order autocorrelation of Arellano and Bond residuals (AR (2)) cannot be rejected for all specifications. Second, the Hansen OIR test, which is more robust than the Sargan OIR test, cannot be rejected because it is more robust and low in instruments.

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

Standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1.

A reduction in the informal sector significantly increases financial inclusion. There are at least two explanations for this result. First, a decline in the informal sector or a formalization of the economy increases the profitability of banks, which can offer more services through the opening of new bank branches and ATMs, thus increasing access to financial services. Secondly, the decline in the informal sector allows the establishment of formal financial services in banks, which increases the demand of economic agents in terms of demand for savings products, credit, support, etc. These results are consistent with those obtained by Ghate (1992) , Úbeda et al. (2022) .

Taking the control variables shows that they have for the most part the signs predicted by the literature. Indeed, the results show that the less unemployment there is, the more financial inclusion increases through its dimensions of availability and use of financial services. Improved employment encourages individuals to be more active, aware and interested in financial activity in a bank, which ultimately accelerates the speed of financial inclusion. This result is consistent with Kumar (2013) . GDP per capita positively and significantly affects financial services penetration and financial inclusion index. This result corroborates the result obtained by Sarma and Pais (2011) who believe that GDP per capita is a key ingredient of financial inclusion. Population density positively and significantly affects financial inclusion. Governance positively and significantly affects financial inclusion. Inflation negatively affects financial inclusion. Economic instability generally creates uncertainty and limits demand for financial services ( Lenka & Barik, 2018 ).