Effects of financial development and capital accumulation on labor productivity in sub-Saharan Africa: new insight from cross sectional autoregressive lag approach

This study aims to shed light on the effects of financial development and accumulation of capital on the productivity of labor in the sub-Sahara African region within the period of 1990–2018. In this work, we used the (dynamic) common correlated effects estimator-mean group and additional techniques such as cross-section autoregressive distributed lag to calibrate the sample into the African subregion to ensure robustness. The findings reveal that financial progress in the region over time leads to an increase in productivity of labor and also the accumulation of capital. Furthermore, financial markets have a progressive impact on the productivity of labor within sub-Saharan African regions. We extend the very limited literature on the nexus between financial development and labor productivity by incorporating capital accumulation into our model which has not been previously studied.

and savings. Nevertheless, no specific theoretical framework has been established to forecast the nature of employment in relation to financial institution (FI) and FD.
Our research also contributes to the growing understanding of the diversity of the labor market and the importance of FD and FI toward a reduction in the rate of unemployment. In deliberation of the next segment, the development, employment, and unemployment levels are expected to function from diverse frequencies, and the net effect is likely to be uncertain. Although our study originally aims to conduct estimations beyond the 1990-2018 study period, it is impossible due to incomplete data for some of the variables in some countries.
Some researchers have drawn alternative conclusions from some well-established findings, implying that market credit failures may play an important role in the collective concepts of dynamic operations involving labor and divergent investment flows. Our research is unique in that it uses conventional theory to investigate the relationships between FD, CAPTA, and labor productivity (Fontaine et al. 2020;Iheonu et al. 2020;Ssozi and Asongu 2016).
Our study has two further interesting elements: first, a large sample of SSA countries is utilized, as estimations are performed for all 39 SSA countries and each subregion (South Africa, West Africa, East Africa, and Central Africa). Doing so ensures the robustness of our findings. Second, to obtain the empirical output, our study employs the (dynamic) common correlated effect estimator-mean group (CCEE-MG) through cross-section autoregressive distributed lag (CS-ARDL), second-generation unit root test, panel dynamic ordinary least square (PDOLS), and fully modified ordinary least square (FMOLS) estimation techniques. This method allows the heteroscedasticity and endogeneity problems to be solved, which are common issues associated with micro panel data. To the best of our knowledge, this method has not been utilized by previous studies in the context of SSA. Additionally, FI and other institutions are largely underdeveloped within the SSA region.
The remainder of the paper is structured as follows: Sect. 2 gives an overview of the reviewed literature. Section 3 contains the data description and methodology. Section 4 presents and discusses the observed results. Section 5 provides the conclusion and policy inferences.

Impacts of FD and FI on labor productivity
Insignificant attention has been paid in recent literature to FD impression, labor productivity, and its impact on employment. Nonetheless, existing empirical studies have thoroughly examined the impending breaks mediating the nexus between FD and labor productivity. Ibrahim and Alagidedeb (2018), Atiase et al. (2019), and Chao et al. (2021) examined the influence of finance on job creation, which explains the preliminary level of percapita income, human capital in nations, and FD for 29 African nations within the SSA region over the 1980-2014 period by applying the verge estimation and sample splitting technique. Their results indicated that FD is positively and significantly connected with economic development. However, the findings and policy implications drawn from the conclusion revealed that an increase in the FD level is essential in the long run besides the general levels of human capital and income, which is extremely important.
Other previous studies carried out on FI applied the variance decomposition VAR method and another causality test, which assumes that the existence of FI aids in promoting trade and commercial activities within the economy where linear correlation exists and activities are normally distributed. However, such an assumption is contrary to others because of the weakness in their financial system, whereby the reappearance of FI does not observe the normal distribution aspect. Therefore, a nonlinear connection tends to appear among FI (Hong et al. 2021;Li et al. 2018). Bernier and Plouffe (2019) studied the development spending in the financial sector and financial innovation research using a panel of 23 countries during the 1996-2014 period. The results validated a net positive correlation between gross capital formation (GCF) and financial innovation.
According to Sarwar et al. (2020), the relationship between FD and human capital development is significant and positive in developing economies. Barucca et al. (2021) and Shahbaz et al. (2011) examined the relationship between FI, output, and the unindustrialized sector in Pakistan using the Cobb-Douglas production function, which incorporates FD as the central production factor, for the period from 1971 to 2011. To examine the long-run relationships among the variables, the ARDL bounds test technique for cointegration was used. Based on their study outcomes, the researchers suggested that the government must encourage output development, particularly in the agricultural sector, to increase the effectiveness in the financial sector.

Influence of financial market (FM) and CAPTA on labor productivity
Other studies have examined associations between FM and various productivity factors, such as capital formation, productivity, and investment where the outcomes have shown that an improvement in finance and capital availability leads to an increase in investment (Joyce et al. 2020;Arcand et al. 2015). Iheonu et al. (2020) explored the influence of financial sector development on domestic investment in several ECOWAS countries. The Granger noncausality test was performed to examine for causality in the presence of cross-sectional dependence (CD), and the augmented mean group technique was used to account for country-specific heterogeneity and CD. The findings revealed that (1) the impact of financial sector development on domestic investment varies depending on the measure of the financial sector development used; (2) domestic credit to a private sector has a positive but insignificant impact on domestic investment in ECOWAS countries, whereas banking intermediation efficiency (i.e., banks' ability to convert deposits into credits) and broad money supply have negative and significant impacts on domestic investment. Our study suggests that the measure of FD used as a policy tool to encourage domestic investment should be carefully considered. We also stress the need to use country-specific domestic investment strategies rather than broad-brush initiatives. When anticipating future domestic investment, domestic lending to the private sector should take precedence.
Consequently, some recent studies on FM development with an emphasis on European countries propose that FM development can hinder inequality if further consideration is given to its development; hence, countries with FMs that are developed are considered to have better social equality than countries that have less developed financial systems (Baiardi et al. 2019). In their recent empirical studies, which propose that finance has a declining and ultimately negatively market improvement, Kou et al. (2022) and Bukhari et al. (2020) suggested that emphasis must also be placed on the positive effects of financial complexity and growth within the FMs of developing economies. Based on this evidence, questions have been raised regarding whether financial freedom may obstruct rather than guarantee a viable increase in the gross domestic product through finance, entrepreneurial process, FM, and innovation (Fonseca and Doornik 2022). Using a large sample of listed Chinese firms from 2007 to 2017, evidence shows that firms with high retail investor attention tend to have a low future stock price crash risk. Moreover, high-quality auditing can mitigate the impact of retail investor attention on the future crash risk of firms (Wen et al. 2019).
A theoretical debate has been continuing regarding the relationship between FD and human capital, technology, and labor productivity. Thus, Bosworth and Collins (2003) explained total factor productivity (TFP) and educational attainment and applied an extended structure, which includes human capital incorporation. That is, the role played by education in the Cobb-Douglas model is shown in the equation below: where Y t is the output, A t is the TFP, K [H t = h t , L t ] , α is the share of K, h t refers to educational attainment (human capital), and L t means labor. Therefore, the following model is considered: Finally, for improved economic development and performance, CAPTA and labor productivity are considered prerequisites. Other basics include growth in FI development, FM development, which transforms into an improved labor force, and technical progress along with the monetary impact (Hong et al. 2021;Asongu and Acha-Anyi 2020).
However, according to data sourced from the International Labour Organization (ILO) and the World Bank's World Development Indicators, the increase in labor productivity in Africa shows a similar pattern to the regions' FD, CAPTA proxies by GCF, FI, and FM development index. This graph is established to view the movements and trends among the variables under study. As observed, FD and CAPTA (proxied by GCF) exhibit similar movements to FI and FM, indicating that the variables have cluster relationships, which are displayed in Fig. 1.

Data description
Data from 39 SSA nations, which comprised countries from different regions as indicated in Table 1, were extracted and analyzed for the period from 1990 to 2018.
(1) Zoaka and Güngör Financial Innovation (2023)    However, because of inadequate data for some countries concerning the required variables, the initial plans of obtaining observations and exploring all SSA countries were disregarded.
Countries from various regions with the most available data for the required period under study were chosen. The panel method and model-based analysis were applied to resolve or adjust for heterogeneity changes and differences in various countries. Data were collected from different sources, which comprised data on labor productivity (LNPROD), which was proxied by output per worker sourced from ILO, CAPTA (LNCAPTA) proxied by GCF obtained from the recent 2019 form of the World Development Indicators, and a comprehensive financial index.

Descriptive statistics
To analyze the characteristics of the variables and the existing relationships among FI development, CAPTA, and labor productivity, a preliminary analysis was performed (Fig. 2). The results are presented as follows. Table 2 presents a summary of the dependent and explanatory variables used in this study. It enables a cursory examination of the statistical properties of the variables. Table 2 also shows descriptive statistics where the results revealed that for the sample of 39 countries across the period studied, the average overall FD of SSA countries is approximately 0.134% and the average value of PROD is 10,502. The overall FD ranges  The scatter graph presents a visualization of the relationships between labor productivity and other variables under study, which denotes a positive connection between CAPTA, FD, and FM and labor productivity. The variables are correlated, in accordance with the findings of Nakamura et al. (2019); thus, an improvement in capital, finance, and technology encourages productivity. Table 3 presents the correlation outcomes.
Correlation coefficients were applied to test for multicollinearity, and all variables were positively correlated. However, the results indicated a strong correlation between FD and its subcomponents, namely, FI and FM. Thus, FD, FI, and FM were included in the regression separately to control for the multicollinearity problem.

Model specification
Our model was construed based on the adjustment and extension of the model adopted by Hirono (2021), which is written below: where X it is the output per worker proxied by LNPROD in SSA country i at time t. Y it refers to the independent variables (LNCAPTA, FD, FI, and FM of country i at time t). Two of the variables are expressed in logarithmic form. (3)

Methodology and results
Before proceeding with our estimates, verifying the existence of long-run associations among all variables is necessary. In this regard, we first check for the existence of CD within the panel data, that is, to verify whether the cross-sectional units are independent of one another. One of the reasons for the presence of CD is the absence of unnoticed common shocks across countries.

Panel CD
We employ the test proposed by Pesaran (2015) to detect the existence of CD among variables. The correlation coefficient for each association between the variable's series of country i with country j is estimated through this test. The higher the correlation coefficient, the stronger the CD among the residuals. If the null hypothesis is rejected, then the panel is cross-sectionally dependent or correlated. A simple panel model is considered in this study.
where α i refers to the parameters to be estimated and β i represents time-invariant individual nuisance parameters. In testing for the existence of CD, the CD statistics tests proposed by Pesaran (2015) is as follows: where pti represents the sample evaluation of the correlation. Table 4 presents the outcomes of the Pesaran (2015) test. The null hypothesis of no CD is rejected by all tests in Table 4. Thus, CD exists within the sample".

Second-generation unit root tests
Considering the existence of CD in our variables, we cannot proceed with the firstgeneration unit root test, which is the conventional one, because it rejects the null hypothesis of nonstationarity in the presence of CD. To resolve this problem, we utilize second-generation unit root tests. The cross-sectionally augmented Dickey Fuller (CADF) test proposed by Pesaran (2015), which examines a unit root in the presence of one common factor, is applied in this study. This test is advantageous, as factor estimation is no longer needed. The common factor can be proxied by the (4) cross-section means of the lagged levels and the first difference of the variable. The test is based on the unit root hypothesis on the t-ratio of the ordinary least square estimate of α i in the following CADF regression: where x t represents the cross-section mean of the first differences of x it and the crosssection mean of the lagged values of x it is represented by" x t−1 ( Table 5). The second-generation panel unit root test outcomes are presented in Table 6, as suggested by Pesaran's (2015) findings. The existence of nonstationarity (unit root) is tested for the five variables (LNPROD, LNCAPTA, FI, FD, and FM). The test is conducted at both levels and the first difference for each of the abovementioned variables. At level, that is at 1(0), the variables are nonstationary for the versions with and without trend. Nevertheless, the variables become stationary at the differences in the versions with and without trend. Thus, the variables are 1(1) series. The results also include specific deterministic terms and are thus robust.

Testing for cointegration
We proceed by ascertaining the existence of a cointegrating association among the variables, after establishing that the variables are all 1(1) series. We consider the error correction-based panel cointegration test developed by Westerlund (2007) and the second-generation panel cointegration test for unnoticed factors. Each test allows for heterogeneity and CD. "c, b, and a denotes statistically significant at 0.01%, 0.05%, and 0.10%. Correspondingly. Z(t-bar) is the average of the individual t-ratios of the OLS estimate of" ∝ i

Westerlund (2007) error correlation model (ECM) panel cointegration test
The Westerlund (2007) ECM ascertains whether cointegration is present using four panel cointegration test statistics (Ga, Gt, Pa, and Pt). The four test statistics are normally distributed. The two tests (Gt and Pt) are computed with the standard errors of λ i logK estimated in a standard way, whereas the other statistics (Ga and Pa) are based on Newey and West (1994) standard errors, adjusted for heteroscedasticity and autocorrelations. We utilize this Westerlund (2007) cointegration test based on the following reasons: it has been developed to cope with cross-sectionally dependent data, and it allows for large heterogeneity in short-run dynamics and in long-run cointegration relationships.
The equation below represents the existence of cointegration in our study: where λ i k K ∈ (PROD) stands for the parameters of the error correction term, i represents the estimate of the speed of error correction, and Ɛ i,t is the white noise random disturbance term. Exploring the long-term equilibrium through the panel cointegration test is important (Table 7). The cointegration assessment from the Westerlund results depicts strong evidence to reject the null hypothesis of no cointegration because most group and panel statistics with their respective robust p-values are statistically significant. Based on the statistics with their respective p-values, although Model 3 is fully significant, which shows that some errors can be adjusted in the long run, the presence of long-run equilibrium relationships among variables is still confirmed for the panels that the model 3 is highly significant in the long run.. Therefore, the variables being analyzed are characterized by long-term links, which must be simulated, concurring with the studies of Coffie et al. (2020) and Matsuoka et al. (2019).

(Dynamic) CCEE-MG (CS-ARDL)
(Dynamic) CCEE-MG (CS-ARDL) is also conducted to observe the association among LNPROD, FD, LNCAPTA, FI, and FM for SSA countries for comparative purposes. CS-ARDL is deemed effective as an alternative model to the generalized methods of moments because it utilizes the cointegration form of the standard (ordinary) ARDL model  Pesaran, Shin, and Smith (1999). "The main features of the (Dynamic) CCEE-MG (CS-ARDL) are that it permits short-run coefficients (with error variances, speed of adjustment to long-run equilibrium values and intercepts) to be heterogeneous across countries, whereas long-run slope coefficients are restricted to be homogeneous across countries. According to Blackburne and Frank (2007), CCEE-MG is useful when reasons exist to believe that equilibrium relationships among variables appear within areas. ECM is the result of these properties, as illustrated in Eq. (7) in which divergence from the equilibrium influences the short-run dynamics of the variables in the system.
where where X it is labor productivity and Y it refers to the independent variables. Parameter ø i is the error correction speed of the adjustment term. If ø i = 0, then no evidence of a long-run relationship exists. This parameter is expected to be statistically significant. The long-run associations among the variables are shown by vector θi. The outcomes of the CS-ARDL are presented in Table 8. Due to the existence of CD, the CCEE-MG estimator through the CS-ARDL model is implemented, and the findings of which are displayed in Table 8. The coefficients of the CS-ARDL reveal that FD, FI, and FM have positive significant impacts on the labor productivity of SSA countries in the long run. A positive significant impact on CAPTA is also observed, implying that a 1% increase in FD, FI, CAPTA, and FM leads to 2%, 2%, 5%, and 3% decreases in labor productivity, respectively. Note that CAPTA has an enormous impact on the long-run reduction of labor productivity in SSA. Thus, CAPTA, FD, FI, and FM enhance the labor productivity of the SSA region in the long run.

PDOLS and FMOLS results
Equation (8) is estimated using the PDOLS technique proposed by Pedroni (2001) after detecting the existence of long-run associations among the sampled variables. This method is also used because the output per worker proxied by labor productivity can be endogenous. Furthermore, the exogeneity assumption is not required by PDOLS. Finally, it calculates the mean group estimator and considers heterogeneity across groups. The estimator of PDOLS is derived by taking the average of the conventional time series (DOLS) estimator. In our case, the regression is represented below: where X it refers to productivity, Y it represents the independent variables, and δ ij represents the lag/lead coefficients. The formula for calculating the estimator is as follows: FMOLS is also estimated using Eq. (9) below; this test is the upgraded form of the Phillip and Hansen (FMOLS) estimator proposed by Pedroni (2001). This estimation method is selected because it is appropriate for endogenous variable estimation, and the equation is recommended when series are stationary in the same order. FMOLS can also be powerful for any variable that does not appear to be stationary. Hence, the equation below shows the panel of FMOLS: where �εℓ denotes the serial correlation, y it + stands for the correction term, and Y it is the transformed variable, which is used to resolve endogeneity problems. Table 8 Results of (dynamic) common correlated effects estimator-mean group (CS-ARDL) Standard errors in parentheses ***p < 0.05; **p < 0.1

Financial markets development
Long  Table 9 shows the estimations of Pedroni's (2001) FMOLS and DOLS off stock and Watson arguments after testing and confirming that the variables are connected in the long run. In FMOLS and DOLS, the model estimations yield identical results. However, according to the outcomes of FMOLS and PDOLS, all variables used in our study are positive and statistically significant except for FI whose coefficients have negative values. Additionally, FI has a negative effect on labor productivity in the SSA region with a coefficient of 0.0002. Thus, a one-unit increase in FI development results in a decrease in labor productivity in SSA of 0.0002 units. It is a result of the developing nature of FI within the region and is in agreement with Dumitrache et al. (2021) and Bakas et al. (2020).
FD outcomes indicate that labor productivity has a positive contribution in the SSA region with coefficients of 0.015 and 0.009. Therefore, FD boosts labor productivity by less than a unit in the region. Another research has been carried out with an emphasis on FD whose outcomes are in line with the study conducted by Mohammed et al. (2019). Nevertheless, FM is also significant with a positive coefficient. Thus, a rise in FM by one unit results in an increase in labor productivity by 0.0012 and 0.0001 units. Therefore, given that FM development improves labor productivity in the long run, the hypothetical impact is presumed to be consistently long-and short-run events for SSA countries.
CAPTA is positive and statistically significant, meaning that labor productivity is fostered by a rise in CAPTA in SSA countries, considering the findings of Bustos et al. (2020) and Ibrahim and Alagidede (2018). Considering that most variables have significant values, no collinearity problem exists among them. Moreover, given that the main estimator, FMOLS, compensates for serial correlation, no serial correlation testing is performed for the models.

Structural stability check
To check the stability of model variables, Cumulative Sum of Recursive Residuals (CUSUM) and Cumulative Sum of Recursive Residuals Squares (CUSUMSQ) calculations are made. The CUSUM results indicate that the parameters remain constant throughout the research duration because the CUSUM numbers fall inside the threshold region of 5% (Fig. 3).

Discussion
In the early stage of the analysis, the Pesaran CD residual CD test rejects the null hypothesis of cross-sectional independence across all variables. This rejection implies the presence of cross-country connectedness between SSA nations among various study panels. Based on the economic, regional, and social experiences of the sampled SSA countries, the intersectoral dependency of these countries is unsurprisingly seen in their respective panels. This evidence is comparatively consistent with the studies of Coffie et al. (2020) for African states in terms of income levels and Mendez and Kataoka (2021) for South Asian countries together with Dumitrache et al. (2021) for industrialized countries but contrary to their findings. Therefore, the application of CADF stationarity tests reveals that all evaluated variables have homogeneous integration orders at first differences. Accordingly, the variables used are capable of producing prolific results as shown to be stationary. The findings of the stationarity tests confirm the results of Hong et al. (2021) regarding production, FD, and income in South Asian countries. However, the Westerlund ECM panel cointegration result reveals that the presence of long-run equilibrium relationships among variables is still confirmed for the panels from the economic perspective, which implies that the utilized CAPTA and financial indicators have elastic longterm effects on labor productivity. Therefore, this evidence supports the revelation of  (2019) had a contrary view from their findings, which state the nonexistence of long-run relationships amid FD.
Empirically considering the long-term simulation outcomes from the CCEE-MG-CS-ARDL approach and with the existence of CD and proliferation concerns, the CCEE-MG estimator through the CS-ARDL model is implemented, and the findings are indicated in Table 8. The effects on LNPROD and LNCAPTA concerning FD, FI, and FM are significant among most panels in the long run. The coefficients of CS-ARDL reveal that FD, FI, and FM have positive significant impacts on the labor productivity of SSA countries in the long run and still have positive significant impacts on CAPTA.
Furthermore, a positive significant impact of LNCAPTA on LNPROD, according to the outcomes of FMOLS and PDOLS within the SSA region, concurs with the findings of Fonseca and Doornik (2022) for Brazil. When LNCAPTA increases, it enhances productivity, thereby boosting the capacity of any ventures be they governmental or nongovernmental. Additionally, FI has a negative effect on labor productivity in the SSA region. This finding entails that an increase in FI development results in a decrease in labor productivity in SSA. It is a result of the developing nature of FI within the region and is in agreement with Khraief et al. (2020) and Bakas et al. (2020).
Last, FD outcomes indicate that FD makes a positive contribution to labor productivity in the SSA region. It further portrays how policymakers in SSA countries within this panel are saddled with the duty of promoting FD to improve labor productivity. This result is consistent with Baiardi et al. (2019) for African states. Meanwhile, the relationship between FD and labor productivity generally differs significantly from the report of Mohammed et al. (2019) for Turkey. Nevertheless, FM is also significant with a positive coefficient. Thus, a rise in FM by one unit results in an increase in labor productivity. Therefore, given that FM development improves labor productivity in the long run, the hypothetical impact is presumed to be consistently long-and short-run events for SSA countries. This result is in line with the findings of Ibrahim and Alagidede (2017) for SSA countries and Barucca et al. (2021) for the United Kingdom region.

Conclusions and policy implications
Our study uses effective and robust panel econometric approaches to model the impacts of CAPTA and FD on the validity of labor productivity within the SSA region in the presence of possible issues of heterogeneity and residual cross-sectional connectivity to avoid erroneous findings. Therefore, the key results drawn from the use of newly developed econometric techniques are in the following paragraphs.
The estimates on LNPROD and LNCAPTA concerning FD, FI, and FM suggest significant effects among the panels. The CS-ARDL coefficient reveals that FD, FI, and FM positively impact the labor productivity of SSA countries in the long run. PDOLS and FMOLS among other techniques are also applied, the results of which indicate that FD, CAPTA, and FM have significant positive impacts on productivity in the SSA region; this result is in line with the studies of Mohammed et al. (2019) and Mendez and Kataoka (2021). Furthermore, our findings reveal that the development of the financial sector of the continent improves labor productivity. FI development also propels further labor productivity on the one hand, and the FM development index has a positive correlation to productivity in the continent on the other hand. This case can be a result of the underdevelopment of FM in Africa. We conclude that FD, LNCAPTA, and FM are positively related to labor productivity in Africa and its subregions. Therefore, policymakers should consider FD and LNCAPTA as indispensable for the enhancement of labor productivity in Africa and its subregions. In conclusion, financial administrators and Apex Bank supervisors in different SSA nations should promote different programs and policies, which can heighten the development of the financial sector toward achieving great productivity in the region.