Examining the impact of the free senior high school policy and women empowerment on secondary school enrolment in Ghana: The bounds test approach

Abstract This study aims to investigate the impact of women empowerment and free senior high school on secondary school enrolment in Ghana. The Autoregressive Distributed Lags (ARDL) estimation method, which examines both short- and long-term effects, was utilized to analyze data obtained from the World Bank database and the ILO database covering the period 1992–2021. Employing the autoregressive distributed lag (ARDL) modeling technique, it was observed that the proportion of women to men in parliament, the FSHS policy, and pre-secondary school enrollment all have positive effects on secondary school enrollment in both the short and long run. Again, though we observe a negative impact of FSHS on female secondary school enrollment in the short run, in the long run, it increases the enrollment by large, while we observe that women to men in parliament and presecondary school enrollment also increase female secondary school enrollment in the long run. These findings have important implications for policymakers and stakeholders in Ghana’s education sector.


ABOUT THE AUTHORS
Frank Gyimah Sackey, the corresponding author, is an Associate Professor and the Director of the Institute of Continuing and Distance Education of Ghana Communication Technology University.He holds a PhD in Economics from the Universitat Rovira i Virgili in Spain and he is a Marti Franques Fellow of Universitat Rovira i Virgili.Richard Kofi Asravor, a co-author, is a Senior Lecturer and the Head of Economics Department at Ghana Communication Technology University.He holds a PhD in Agricultural Economics from the University Ghana.Isaac Ankrah, a co-author, holds a PhD in Energy Economics from the Xiamen University in China and a Lecturer at the Economics Department of Ghana Communication Technology University.Lilian Arthur is a Lecturer in the Department of Economics of Ghana Technology University College.She holds an M.A. in International Economics from the Berlin School of Economics and Law, Berlin, Germany and currently a PhD candidate of University of Cape Coast, Ghana.

Introduction
The significance of good governance in the development of every nation cannot be understated.Achieving good governance is contingent upon several key characteristics, such as promoting women's empowerment and prioritizing gender equality in education, with particular attention given to the girl child.In sub-Saharan Africa, however, there are economic underdevelopment and little empowerment opportunities for women, owing to a confluence of cultural, social, economic, and traditional factors that hinder their education, health, nutrition, and political participation.A definition of good governance in any given society must necessarily incorporate fundamental components such as the protection of economic and social rights, as well as the fulfillment of basic needs for both men and women (Abdou, 2021).
In many sub-Saharan African nations, the accessibility of education as an inherent right for all citizens, irrespective of gender, is not universally acknowledged.Nonetheless, Ghana, as a member of international organizations like the African Union (AU) and the United Nations (UN), is bound by the human and people's rights charter of these entities, necessitating a commitment to fostering good governance through equitable access to education.Although there is no universally accepted standard for measuring good governance (Glass & Newig, 2019), certain criteria such as the fulfillment of basic needs, including access to education, a free press, protection of human rights (Fukuda-Parr & McNeill, 2019), poverty eradication, economic empowerment, a conducive environment for economic activities, the rule of law, and other social rights (Hemachandra et al., 2020), must be included.The challenge of achieving good governance and promoting women's empowerment in sub-Saharan Africa remains a significant issue for many governments in the region.While the education of children, especially the girl-child, is closely linked to the empowerment of women, the wide educational gap and inequality between girls and boys have left women unable to compete with their male counterparts (Bennell, 2023), who tend to have more opportunities and advantages.In 1996, UNICEF observed that the number of girls not attending school was twice that of boys, and similarly, the number of illiterate adults was twice as high among women as compared to men.
In recognition of the significance of education as a driver of economic growth, the free senior high school policy was implemented by Ghana in 2017 that ensures no parent is required to pay tuition fees or any other related costs associated with schooling of their wards.These efforts are seen to be crucial in advancing Ghana's progress towards achieving good governance and promoting sustainable economic development.Promoting secondary school and girl-child education are necessary prerequisite for improving the future prospects of the citizens especially women and promoting the growth of society as a whole.An educated woman is more likely to be a confident skilled worker and can make significant contribution to a country's economic growth (Wang et al., 2019).Furthermore, a woman with a strong educational background is inclined to marry at a later age and have fewer children, contributing to the mitigation of the high population growth rates that have adverse effects on economic growth and development in sub-Saharan Africa (Moyo & Dhliwayo, 2019).
The free senior high school policy is an effective means of increasing girl-child enrollment and secondary school enrollment in general, particularly in rural settings where cultural practices often favor the education of the boy-child due to the inability of parents to pay school fees for the education of both male and female children.Hjálmsdóttir and Bjarnadóttir (2021) and Ahmed et al. (2001) have posited that gender disparity is more widespread in developing countries compared to developed countries.Nevertheless, research findings reveal that an additional year of schooling of the female child has a more substantial positive impact on a woman's future earnings, with an increase of more than 15% compared to 11% for men (UNICEF, 1996;Yavorsky et al., 2019).This underscores the significance of women's empowerment and gender equality in achieving sustainable growth and development, as asserted by Abou-Shouk et al. (2021) and Alvarez (2013).These authors emphasize that gender equality is not only a human rights issue but also a precondition and indicator of sustainable development.
This study determines the extent to which women's empowerment and the free senior high school policy affect secondary school enrollment based on available data spanning from 1992 to 2021.The free senior high school policy is considered the most effective approach to bridging the gap in school enrollment between girl-child and boy-child.In the current study, we employ the proportion of female to male representation in parliament and the proportion of women employed as women empowerment variables as well as the free senior high school policy to examine how they impact on female secondary school enrollment and the overall secondary school enrollment.In addition, GDP growth and presecondary school enrollment are also included as covariates to also examine how they impact on secondary school and female secondary school enrollment.
Secondary school education is very crucial for any economy that seeks to achieving universal education where its citizens can read and write.According to Cohen et al. (2014), the inability of many girls and their families to attain secondary education tends to hold back their aspirations which in turn undermines prosperity and stability around the world.According to Ahmad and Cohen (2014) increases in secondary school enrollment offers advantages and opportunities to all levels of society.
To the best of our knowledge, there has not been any study that has examined the extent to which the free senior high school policy affects secondary school enrollment since the policy took effect in 2017.More than 30% of school children were unable to proceed to the secondary level after the basic level, which is already free, under the free compulsory universal basic education (FCUBE) in 1995 (World Bank, 2023).It has been 7 years since the introduction of the FSHS policy and by implication all basic school graduates with the requisite passes should have placement in the secondary schools in Ghana which is now free.Thus, it is expected that the policy should lead to an increase in secondary school enrollment, especially, the female child and with the support of women.According to Joshi and Echle (2022), Swiss et al. (2012) and Iwanaga (2008), women are more compassionate towards children and will enact policies aimed at promoting the wellbeing of children.However, the extent of this assertion has not been explored, at least, in most emerging economies including Ghana.As such, investigating the empirical and quantitative link between the free senior high school policy and women's empowerment and their impact on secondary school education is essential, given the potential of women's empowerment to promote girl child education and economic growth and development.It is therefore imperative that we examine the effect of the FSHS policy and women empowerment and how they impact female secondary school enrollment and the overall enrollment.

Limitations of the study
The study refrained from conducting a structural analysis of the FSHS policy's impact on secondary enrollment due to its relatively short duration, spanning only 7 years.Furthermore, there arises a necessity to explore its influence on higher education in Ghana, particularly concerning the country's cost-sharing policy.Such an examination would assess whether there is a need to revise Ghana's university education cost-sharing policy to accommodate a greater number of students who successfully complete their secondary education.These areas warrant investigation in future research endeavors.
The study is structured into five sections.Section one introduces the study, while section two delves into the theoretical and empirical framework.Section three outlines the theoretical and empirical model employed, elucidates the hypotheses, and provides definitions for the study's variables.Section four presents our findings and conducts an analysis thereof, and finally, section five encapsulates the study's conclusions and summarizes its key findings.

Women empowerment
Empowerment entails the capacity to make choices and requires the restructuring of societal systems that perpetuate power imbalances and unequal distribution of resources and opportunities.Empowerment comprises two closely intertwined components: resources and agency (Coy et al., 2021).Resources encompass both tangible and intangible assets, with tangible resources encompassing financial and material assets, and intangible resources encompassing knowledge, skills, abilities, and engagement in political and social activities (Frediani et al., 2019).Conversely, agency signifies the authority that individuals possess to set their goals and objectives and actively pursue them (Kapitsa, 2008).Empowerment is typically delineated into three interrelated elements: self-empowerment, mutual empowerment, and social empowerment.Self-empowerment involves individual efforts, mutual empowerment relates to interpersonal relationships, and social empowerment entails the removal of societal, political, legal, and economic barriers to enable individuals to exert influence (İ ̇şleyen & Kreitmeyr, 2021).However, concentrating solely on one or two elements of empowerment proves inadequate for effecting substantial change (Pigg, 2002).Development is not a process enacted solely on behalf of individuals; it necessitates their active engagement and participation.People should play an active role in decision-making and actions concerning their own well-being.Furthermore, investing in women's skills and granting them autonomy in decision-making not only holds immense significance but also contributes to economic growth and development (Anderson et al., 2021;United Nations, 2005).In many regions across the globe, particularly in sub-Saharan Africa and South Asia, females often face significant marginalization and barriers to accessing education.However, there have been promising advancements observed in Latin America and East Asia (Gacinya, 2020).Despite the considerable progress made by several countries in achieving the Millennium Development Goals (MDGs) since 2000, a fundamental challenge persists: insufficiently educated boys and girls are at greater risk of experiencing gender-based violence, exploitation, trafficking, and diseases like AIDS throughout their lives compared to their educated counterparts (Lorente et al., 2020).Therefore, the empowerment of women and the implementation of policies that bolster and expand school enrollment represent mutually advantageous strategies.Education not only fulfills individuals' rights but also bestows society with a multitude of educational benefits.This concept underlies the MDGs, which aim to ensure universal primary education and promote gender equality and women's empowerment.In the developing world, a significant proportion of girls did not attend primary school during the period between 1996 and 2005, as indicated by the net attendance rate, with the figure being as high as 25% (UNICEF, 2020).Furthermore, during the same period, only 43% of girls made the transition to secondary school, and less than three-quarters of adult women across developing countries were literate.Providing girls with a quality basic education is crucial as it can reduce early and forced marriage, maternal mortality, and promote healthy childbearing practices.Empowerment is a progressive process that spans generations, aiming for equitable power distribution and active participation by women in decision-making across all facets of society, encompassing households, the economy, and politics (Panigraphy & Bhuyan, 2006).Researches conducted by Desani (2010) and Choudhuri and Desai (2020) underscore the significance of women's empowerment, advocating for advancements in education, health care, economic opportunities, and political engagement.These studies emphasize the importance of granting women authority, influence, and priority in crucial decision-making processes.

Good governance and social development
In academic discourse, "good governance" is characterized as the process of developing institutions and procedures that are more responsive to the needs of ordinary citizens, including those who are economically disadvantaged.This concept involves the promotion of participation, accountability, and effectiveness across all levels of governance and is widely recognized as a pivotal element in advancing development.Scholars have posited that significant structural changes are necessary within political and administrative systems to facilitate such progress (Basheka, 2021;Turner & Hulme, 1997).In recent years, institutions such as the International Monetary Fund (IMF), the World Bank, the United Nations, and Western bilateral donors have universally embraced the objective of promoting good governance in the Third World, establishing it as a primary reform goal (Basheka, 2021;Pierre & Peters, 2000;Turner & Hulme, 1997).
The concept of governance has gained substantial traction in development discourse across various stakeholders, including political leaders, donors, developers, reformists, and experts.However, there remains divergence of opinion among development agencies regarding the precise operational definition of this concept.For some, good governance centers on the decision-making process, while others focus on decision implementation (Singh, 2003).In this context, good governance embodies the qualitative dimension of governance.Furthermore, according to Besancon (2003), governance encompasses the provision of political goods that commence with ensuring the security of a nation's citizens.She posits that good governance is achieved when countries deliver a high standard of specific political goods and effectively serve the interests of their populace.Besancon and the World Bank both contend that good governance encompasses not just the decision-making process and the formulation of public policy but also encompasses the regulations that establish a legitimate, effective, and efficient framework for guiding public policy.It revolves around the management of public affairs characterized by transparency, accountability, participation, and equity.This undertaking necessitates active involvement in public policymaking, adherence to the rule of law, the existence of an independent judiciary, institutional checks and balances achieved through horizontal and vertical separation of powers, and the presence of effective oversight agencies, as highlighted by Santiso (2001).
Considering the premise that governance typically enhances development, it is proposed that the international community focuses on targeted reforms that directly foster development, rather than pursuing a broad agenda with potentially limited indirect effects.A pragmatic approach to governance improvement should refrain from being doctrinaire or asserting universal applicability.Instead, it should involve the identification, analysis, and sequential resolution of primary constraints.Key objectives of the good governance agenda, such as empowerment, inclusion, participation, integrity, transparency, and accountability, can be integrated into practical solutions, not as external demands but as integral components necessary for effective solutions and relevant experiences.The implementation of the Free Senior High School policy serves as a notable exemplar of good governance in practice by all assessments.Any challenges that may impede its effectiveness and desired outcomes should be systematically addressed with utmost efficiency.

The free senior high school policy
In 2017, the Ghanaian government introduced its flagship initiative, the Free Senior High School (FSHS) policy, with the primary goal of ensuring access, equality, and equity in education in alignment with the United Nations' Sustainable Development Goals.As per Article 25, 1b of Ghana's 1992 constitution, secondary school education should be progressively made free and accessible.The FSHS policy encompasses various benefits, including tuition and admission fee waivers, complimentary textbooks, exemption from library fees, free access to ICT facilities, cost-free utility services, complimentary accommodation, and free meals.The overarching aim of the policy is to realize the vision of ensuring that all children attain high-quality and equitable primary and secondary education, resulting in effective learning outcomes by the year 2030.Preceding the FSHS policy, the Ghanaian government implemented the Free and Compulsory Universal Basic Education (FCUBE), which mandated free and compulsory primary school education.In 2017, the Ghanaian government allocated 400 million Ghana Cedis, equivalent to $36.4 million at an exchange rate of 11 Ghana Cedis to the dollar, toward the FSHS policy, averaging 2,312 Ghana Cedis per child.Subsequently, the government has consistently increased its annual expenditure on the policy since its inception.

Review of empirical studies
Gender equality embodies the principle of a just and balanced distribution of responsibilities between men and women.It is imperative to clarify that gender equality does not imply identical roles for men and women or an equal division of tasks.Rather, it revolves around establishing societal conditions and relationships that foster a shared vision of cooperation and mutual respect, enabling both men and women to realize their full potential.As emphasized by Hooks (2000) and Warren et al. (2019), gender equality transcends mere parity; it entails creating an environment where both men and women can flourish together.
The empowerment of women through gender equality plays a pivotal role in economic development.For instance, women in parliament have a positive influence on instigating social, cultural, and economic advancements pertaining to women's rights and freedoms.As Joshi and Echle (2022) asserts, women are more inclined to introduce and support legislation addressing women's rights, economic status, and health.Additionally, research conducted by Volden et al. (2013) reveals that women are more likely to champion legislation concerning children, particularly in areas such as education, family health, and childcare.Similarly, Swiss et al. (2012) observe that women in parliament are inclined to endorse bills aimed at increasing government spending on health care and other social policies.Furthermore, Swiss et al. (2012) note that countries tend to allocate more funds to social services, such as health care and education, when women hold governmental positions.
Gender equality and the empowerment of women are indispensable factors in the realm of economic development.Lots of studies underscore that the presence of women in parliamentary roles can yield positive societal, cultural, and economic transformations in relation to women's rights and liberties.As Iwanaga (2008) argues, women are more apt to champion legislation aimed at enhancing their economic standing, health, and rights.
Moreover, it is essential to underscore the paramount importance of women's empowerment in the pursuit of gender equality.A study conducted by Agu and Aguegboh (2021) underscored that gender equality in education significantly drives income growth.In middle and upper-income nations, an increase in girls' participation and higher levels of gender equality in secondary education correlate with elevated incomes.Additionally, Grantham et al. (2021) identified that countries investing in girls' education experience accelerated economic growth.Therefore, any form of discrimination against girls not only runs counter to principles of equity but also proves economically inefficient.
The global development agenda has increasingly prioritized gender equality and women's economic empowerment, recognizing the substantial impact of women's participation in economic activities on families, societies, and national economies.Consequently, it is imperative to equip women with the requisite skills, resources, and equal access to economic institutions, ensuring their active engagement in economic pursuits.Empowering women to make and implement economic decisions is pivotal for enhancing their economic status and ameliorating gender disparities (Golla et al., 2011).Facilitating women's greater access to economic resources and opportunities can significantly enhance their economic prospects (DAC Network on Gender Equality, 2011).
Research conducted by Roman et al. (2006) revealed that each additional year of formal education for girls results in up to a 20% increase in wages.Interestingly, the study also found that the overall returns on primary education were marginally higher for girls compared to boys.This suggests that education holds the potential to empower women within their families and communities, enabling them to make informed choices and assume more active roles.Abdi et al. (2006) underscores that education is highly esteemed not only for its direct utilitarian and economic benefits but also for its contributions to socio-cultural and community-based advancements.This sentiment is corroborated by Folson (2006), who posits that education fosters sociopolitical awareness, particularly among individuals residing in rural and low-income urban areas.Williams et al. (2019) identified a positive correlation between the presence of female representatives in state legislatures and the prioritization of bills addressing women, children, and family-related issues.Similarly, Hicks et al. (2016) discovered that increased female empowerment in national legislatures is linked to a shift in aid allocation towards education and health-related initiatives.Additionally, research by Hessami and Fonseca (2020) demonstrate that higher female political representation in developing nations has led to improved provision of public goods, particularly in the domains of education and health.Tusalem (2022) also observed a significant and positive relationship between female representation in legislatures and the provision of public goods.Guinid (2019) concluded that female legislators are more inclined to propose policies aimed at enhancing the well-being of women and children.Lastly, Dowe (2022) noted that successful black female political candidates are driven to address the needs of their communities.Bui et al. (2020) highlighted that an effective educational subsidy program often results in a significant rise in school enrollment among low-income households, contributing to overall enrollment growth.Prasetyia's (2019) research further demonstrated that local government education policies have a noteworthy impact on parents' decisions to enroll their children in school.
The concept that education serves as a catalyst for women's empowerment has garnered increasing attention and support from donors and international agencies over the past decade (Malhotra et al., 2002;Mosedale, 2005;Oxaal & Baden, 1997;Parpart et al., 2002;Salehi et al., 2020;Shah et al., 2020;Unterhalter, 2007).In the study area, many NGOs have implemented diverse programs and policies aimed at promoting education, especially for girls.These initiatives include attendance-based food rationing by the World Food Program (WFP), provision of bicycles to facilitate long-distance school commuters by the United Nations Children's Fund (UNICEF), and support schemes administered by the Campaign for Female Education (CAMFED).Nevertheless, there is still much to be comprehended about the multifaceted ways in which education genuinely empowers women (Dacosta, 2008;Murphy-Graham, 2008;Stromquist, 2002;Morgan & Winkler, 2020).

Data
Data on variables such as the GDP growth, female employed to the total female labor force, women to men in parliament, primary and secondary school enrolments were gleaned from the World Bank database.The data on these variables are annual data for the period 1992-2021.We used this time frame because this is the period Ghana has and continues to experience multi-party democracy.

The theoretical model
The classical linear regression model operates under the assumption that the impact of explanatory variables on the outcome variable is immediate and time-independent.Nevertheless, empirical applications of unit root tests have frequently revealed that this assumption is violated in the case of numerous macroeconomic time-series variables.In many instances, there exists a temporal delay, referred to as time lags, during which explanatory variables exert their influence on the outcome variable.This concept is exemplified in dynamic models (Jatiningrum, 2008;Supranto, 1995).A noteworthy example of estimating such models is the dynamic autoregressive approach, which combines elements of both the dynamic distributed lag model and the dynamic autoregressive model.

Given a dynamic distributed lag model: and a dynamic autoregressive model as
We combine equations ( 1) and (2) to form the autoregressive distributed lag (ARDL) model as where: X t ; X tÀ 1 ; X tÀ 2 X kt X tÀ k Y tÀ 1 Y tÀ z : the explanatory variables, Y t : the outcome variables α; β 0 ; β 1 ; β k ; δ 1 ; δ z : the coefficients ε t : the error term.
Thus, the autoregressive distributed lag model includes not only the variable in its present times but also past values since it may take time for a variable to have an impact on its outcome variable.

The empirical model
We utilize the Autoregressive Distributed Lag (ARDL) cointegration method to examine the shortterm and long-term relationships between secondary school enrollment and female secondary school enrollment as dependent variables.The independent variables considered in this analysis encompass the proportion of women to men in parliament, female labor force participation, and the presence of the free senior high school policy (represented by a dummy variable).Additionally, we incorporate GDP growth and pre-secondary enrollment as covariates.
Our empirical models for assessing the impact of the FSHS policy and women's empowerment on secondary school enrollment, as well as female secondary school enrollment, are as follows: where: SECSCHOOLENROL represents annual secondary school enrollment, FEMENROL represents female secondary school enrollment as the outcome or dependent variables in equations ( 4) and ( 5), respectively.The variable WOMENEMPLOYED represents women labour force participation being the proportion of women who are employed.The variable WOMTOMENPAR represents the proportion of women to men in parliament.The variables GDPGR and PRESECENROL denote the annual gross domestic growth and presecondary school enrollment, respectively, while the variable FSHS represented by a dummy signifies the government flagship free senior high school policy that takes the value of "0" from 1992 to 2016 and "1" from 2017 to 2021 while ε it is the error term.The coefficients of the independent or explanatory variable including the covariates are represented byβ 1 À β 5 while β 0 signifies the constant term.

Test of hypothesis
The following hypotheses shall be tested: (1) H0: the free senior high school policy does not have any significant impact on female secondary school enrollment and overall secondary school enrollment (2) H0: women empowerment does not have any significant impact on female secondary school enrollment and overall secondary school enrollment.

Step 1: stationarity test
It is important to ensure that all variables achieve stationarity to avoid any effects of spurious regression, hence the need to test to ensure that variables achieve stationarity and then use for our estimation.
We therefore test for the stationarity of the variables by doing the Augmented Dickey Fuller test (ADF).Where a particular variable is not stationary, we differentiate it until it becomes stationary.
Table 1 presents the augmented Dickey-Fuller test for stationarity results.The results show that the proportion of women labour force employed and secondary school enrolment variables are stationary at the second difference, while the rest of the variables are stationary at the first difference.The variables are therefore used according to their lags as indicated below.

Optimal lag selection criterion
According to Braun and Mittnik (1993), estimates of autoregression whose lag length differs from the true lag length as reported by the stationarity test lead to inconsistencies derived from autoregression estimates.Thus, the lag length criteria must be consistent with our stationarity tests to ensure consistency and validity of our estimates.
Table 2 presents the results for the optimal lag selection criterion using the AIC criterion.The table shows that proportion of women labour force that is employed has a lag of 2, and secondary school enrollment has a lag of 3, while Women-to-men in parliament, GDPgrowth, FSHS and Presecondary school enrollment have lags of 1 using the FPE, AIC, HQIC and SBIC criteria.These are consistent with our stationarity test, and therefore our estimation will be valid and consistent.

Has the free senior high policy and women empowerment impacted on secondary school enrolment in Ghana? The short-run effects
Table 3 displays the outcomes of the short-term autoregressive distributed lag analysis.First, we report on the robustness of the results.Our results show a high of 0.9964 and a high adjusted of 0.9922 with a significant p > F (0.0000), signifying that our model is good, reliable with high predictive power while the variables are jointly determined.
It is noticeable that an increase in the proportion of women to men in parliament leads to a rise in secondary school enrollment.These results support that of Hessami & Fonseca (2020), Hicks et al. (2016), Iwanaga (2008); Swiss et al. (2012), Tusalem (2022), andVolden et al. (2013) who have consistently shown that women are more inclined to sponsor legislation related to children, particularly in areas such as education, family health, and childcare.In the same manner, women in parliament tend to support bills aimed at increasing government spending on health care and various social policies.The findings in this study support that of Guinid (2019), Klasen (1999), and     Sue (1991) who observed that women empowerment promotes children's health and education.Regarding good governance and child education, the findings of the present study support that of Besancon (2003), Bishop (1977), Prasetyia (2019), andSingh (2003) who argued that good governance promotes child development.These findings are consistent with our findings that the free senior high school policy at a lag of 1 increases secondary school enrollment.Again, we observe that increases in pre-secondary enrollment also increase secondary school enrollment.

Pesaran/Shin/Smith (2001) ARDL bounds test
To effectively determine whether there exist long-run relationships among the variables used for our analysis, we conduct the Pearson-Shin-Smith Autoregressive Bounds Test.Table 4 presents the findings of the bounds test.The F-test result stands at 3.899, surpassing the upper boundary of our F-statistic, set at 3.79 (at the 5% significance level).Similarly, our t-test result registers −3.096, falling below the lower boundary t-statistic of −2.86.These outcomes strongly suggest the presence of long-term relationships among the variables.Consequently, we will proceed to investigate these long-term relationships and their influence on the outcome variable.

Has the free senior high school policy and women empowerment impacted on secondary school enrolment in Ghana? The long-run effects
Our test of robustness shows a high and a high adjusted that show that our model is good and has high predictive power and reliable.Our results report an adjustment of −1.53 indicating a longterm convergence among these variables, suggesting that any previous errors will likely be rectified in the current period.We observe that in the long run the proportion of women to men in parliament increases secondary school enrollment supporting similar findings of Dowe (2022), Hessami & Fonseca (2020), Hicks et al. (2016), Iwanaga (2008), Sue (1991), Guinid (2018), Swiss et al. (2012), Tusalem (2022), andVolden et al. (2013) that suggest that women are more compassionate towards children and tend to champion legislation related to children, particularly in the areas of education, family health, and childcare.We also observed that increases in presecondary enrollment as well as the FSHS policy increase secondary school enrollment supporting the argument raised by Besancon (2003), Bishop (1977), Prasetyia (2019), andSingh (2003) that good governance promotes child development.

Has the free senior high school and women empowerment impacted on female secondary school enrollment?
Since women empowerment is very vital to the development of every nation, we decided to disentangle the effects of free senior high school and women empowerment on female secondary school enrollment only.Our results are reported in Table 5.Just as in Tables 3 and 6, we observe a high and a high adjusted with a significant p > F, signifying that our model is good and has high predictive power and reliable.Our results show that in the short run, the free senior high school impacts negatively on female secondary school enrollment; however, in the long run, it increases female secondary school enrollment to a large extent.This finding supports that of Besancon (2003), Bishop (1977), Prasetyia (2019), Singh (2003).Similarly, we observe that in the long run women to men in parliament and presecondary school enrollment increase female secondary school enrollment.These findings are in line with the findings of Dowe (2022), Guinid (2019), Hessami & Fonseca (2020), Hicks et al. (2016), Iwanaga (2008), Sue (1991), Swiss et al. (2012), Tusalem (2022), Volden et al. (2013) that women are likely to sponsor and support legislations that enhances the welfare of children including their education.Furthermore, our findings reinforce the argument that good governance fosters child   development, as we identify a positive and significant relationship between pre-secondary school enrollment and female secondary school enrollment.Additionally, our results reveal an adjustment coefficient of (−1.53) along with a significant p-value, signifying the presence of long-term convergence among our variables and the likelihood of past errors being rectified in the current period.

Test for stability
The cumulative sum of squares (cusum graph) shows that there is stability.Though there was a very slight digression, it later came back to stability as the curve shows.Figure 1(1) is the cusum graph.

Summary
This study aimed to investigate the degree to which women's empowerment and the FSHS impact female secondary school enrollment and the overall secondary school enrollment.Proportion of female employed out of the total female labor force, proportion of women to men in parliament, secondary school enrolment and presecondary school enrollment were gleaned from the World Bank, while a dummy variable was created for the FSHS policy.Employing the autoregressive distributed lag modeling, we discovered that the ratio of women to men in parliament, the FSHS policy and presecondary school enrollment all have positive effects on secondary school enrollment both in the short and the long run.

Conclusions and policy implications
The results of this study carry substantial policy implications, as they illustrate that both good governance and the empowerment of women yield a positive influence on female secondary school and the overall secondary school enrollment.Education is crucial for a country's economic growth, and it is essential to provide education to all citizens as a fundamental right.However, many African countries struggle to provide education for all their citizens.Therefore, promoting and implementing policies that make secondary school education free will require good governance and increased women's empowerment to advance children's access to health, education, and various social services.To advance gender equality and uphold children's right to formal education, it is necessary for the government to practice good governance, particularly in the areas of participation and human rights.Sustainable economic opportunities must be provided by successive governments to promote human capital development, with women empowerment as a crucial component.Policies that empower women such as access to credit, skill training and job opportunities as well as those that increase their representation in policy-making bodies such as the parliament can significantly improve the welfare of children including education and health.The practice of early marriage, especially involving girls, should not be encouraged or tolerated, and laws prohibiting and penalizing parents and guardians who engage in such practices should be enacted and enforced.These policy implications highlight the importance of good governance, women empowerment, and the protection of human rights in the promotion of education and other social services.
The importance of investing in education cannot be overstated, particularly regarding educational infrastructure and teacher training.For Ghana to achieve gender equality, universal basic education, and sustainable growth and development, policies such as free primary and secondary education are crucial.Good governance is fundamental to democratic governance, and it plays a critical role in improving children's education in Africa, including Ghana.To this end, African countries must embrace democratic systems of governance that increase women's representation in parliament and empowerment of women thereby promoting gender equality and improving children's education and health outcomes.

Table 2
* inTable indicates the number of lags attained for the estimation of each variable

Table 5 . Impact of the FSHS and women empowerment on female secondary school enrollment
*** and ** denote significance levels at 1% and 5% respectively.