Introduction

The poverty has been the dilemma for developed and developing nations in past and current decades. Poverty is reflection of miserable economic situations for countries, lifestyle of inhabitants, and difference among rich, poor, and middle-class families in different territories of the World. The scholars like Zheleznyakov and Tarasov. (2016) in their study explained that poverty is also name of the rapid decrease in middle-class families into poor class not only developing economies but also in developed states as well. They further explained that like United States of America (USA), Mainland of China, Japan, and Germany also come into this domain. The vulnerability of poverty in MENA countries is also an example which is investigated by Abu-Ismail (2021). Nowadays, many scholars and economic policymakers are trying to intensify the efforts and suggest policies for poverty reduction in different time spans and regions with different findings.

According to Michálek and Výbošťok (2019), there are many reasons behind increasing level of poverty in the countries which include unequal distribution of economic growth and its effects. It was also endorsed in the current study of Balasubramanian et al. (2023). They further reported in their research that increasing levels of inequalities are the main cause for poverty with bad impacts on countries’ economic growth and their population well-beings. In the world economies, the topic of economic growth and poverty has remained the part of vast discussions among the scholars (Wang, 2023).

There is no proper definition of poverty because it has a variety of dimensions in literature. But some scholars like Brady (2018) defined poverty is basically shortage of resources which are required for fulfilling the basic needs of routine life. Similarly, some scholars like Chatterjee (2012) explained in their research work that poverty is combination of complex phenomenon having variety of dimensions. They further stated on the basis of single definition it is not applicable to measure the basis of poverty in societies and regions. It is also mentioned in their work that there might be logical reasoning behind occurrence and reduction of poverty including equal division of money, economic growth, and social capital, and its productivity, social sector development, and infrastructure. This definition of poverty is also in line with the current study of Dayan (2022). Moreover, Zheleznyakov and Tarasov (2016) in context of Russia explained that high level of private property, unequal distribution of money and income, and consumption savings among population and economic as well as social potential of that particular area leads towards poverty. To that end, the level and reasons of poverty may differ according to countries states and their policies.

The nexus of economic growth and poverty has attained the attentions of scholars from the last few decades. However, the majority of research is done on this nexus in panel studies and scant literature is available in economic development studies on this nexus in form of single-country studies as well. In the MPI (Global Multidimensional Poverty Index), it is stated that the people with insufficient monitory resources, high level of unemployment, poor health and education, lack of housing facilities, empowerment, and insecure environment comes under the category of poverty (Alkire et al., 2018), and it was endorsed in the current literature of Ullah and Chishti (2023). Alkire et al. (2018) further stated that these determinants of poverty are associated with economic growth.

Mahembe et al. (2019), in their panel study for 82 developing economies with the data coverage of 1981–2013 by using the statistical technique of VECM (Vector Error Correction Model), explored a two-way relationship among the variables of poverty and economic growth. Similarly, Pérez-Moreno (2016), in 52 developing states with the data set ranging from 1970 to 1998 found one-way causal interaction running from economic growth to poverty reduction. Some scholars like Janvry and Sadoulet (2000), during the past decade in their panel study in twelve Latin American states by using data ranging from 1970 to 1994 stated that variable of economic growth has no significant effect in poverty reduction in specified states.

Limited literature is also available in development studies on time series data among the variables of growth and poverty. The study of Adelowokan et al. (2019), in the context of Nigeria, is between the time span of 1985 to 2015 by applying unit root tests and Granger causality. The findings of cointegrations reveal no long-term relationship between poverty and growth as well as unemployment in the Nigerian context. The study of Nindi and Odhiambo (2015) in the scenario of Swaziland by using data from 1980 to 2011 found that economic growth does not Granger cause poverty in both ends including the short and long run. These findings were opposite in unidirectional from poverty reduction to growth. Similarly, the causality results of Wycliffe and Sun (2018), in Rwanda for the time period of 1980 to 2016, observed no causal relationship between the linkage of growth and poverty reduction. The results in panel and time series studies are showing inconsistency due to different regions, time spans, and data sets. There is still a need to explore this linkage for different insights for value addition in the body of literature.

We also consider the complicated nexus of gender inequality and poverty that is considered more important for debate in literature by policy-makers. In the United Nations, development program Cagatay (2005) stated in a series of working papers by taking the example of countries including Mali, Sierra Leone, Burkina Faso, and Niger that these countries come under the umbrella of human poverty index due to gender inequality. Researchers like Qiang et al. (2008) explained in their research work the cause and effects of poverty and gender inequality upon each other. They pointed out that when there is unequal distribution of resources including material, natural, and financial capital, then there are more changes for women’s opportunities to be scarified. They also debated that these kind of unequal distributions at family level put restrictions on females to participate in political educational and skill-oriented activities. They concluded that when women are trapped in such type of restrictions, it produced poverty in those specific families.

It is stated in the recent work of Lawanson and Umar (2019) that gender inequality is the name of unequal distribution of multiple resources with no any regular and uniform measures in form of size, values, and ranks. They further extended that gender inequality is name of unequal distribution of control and command over resources; gender difference in labor markets and social norms between males and females is the main causative agent for poverty. In most recent work of Gaddis (2019), it was pointed out that, in the context of African countries, a majority of women are facing the challenges of inequalities in education, health, labor markets, small access to productive assets like land and credits, and lack of social and political rights. They further stated that women in African regions are under miserable condition with high burden for child cares and household work activities. The authors concluded that these types of gender inequalities are developing a poverty trap in economies of African countries. The current work of ALABUJA et al. (2023) is also evidence from Nigeria that due to inequality women in Nigeria are facing continuous poverty.

Similarly, understanding the nexus of financial development and poverty is of particular importance for this article. The nexus of financial development and poverty has been discussed in the literature with mixed findings. The positive relationship between financial development and reduction in poverty due to this development in case of Iran has been investigated by (Shahbaz et al., 2015). While some scholars like Dhrifi (2015) concluded in their research by using data from 1990 to 2010 in upper and lower middle-income countries that due to financial development in lower income countries, the poverty among the societies is increased. Moreover, some scholars like Odhiambo (2010) in case of Kenya observed unidirectional causal interaction from financial development to poverty reduction. Similarly, bidirectional causal interaction between financial development and poverty reduction and no any effect between these variables has been investigated by Uddin et al. (2012) and Uddin et al. (2014) respectively. The causal interaction between financial development and poverty reduction was observed in different countries with different time spanning with different insights. The motivation for conducting this study in Pakistan is to observe the importance of financial development for poverty reduction in Pakistan.

The main objective for conducting this research is to investigate the impact of financial development on gender imbalance and poverty in context of Pakistan. Moreover, we also extended our research after formation of research question “to what extent this nexus of variables including gender imbalance, financial development, economic growth and poverty has causal interaction with each other.” Finally, authors plaid this linkage with the help of ARDL and Granger causality tests. The motivation behind conducting this research is based on some realities which are reflected in past and current literature. Pakistan is 6th largest populated country of the world (Asghar et al., 2020) which is facing the issue of poverty (Arif et al., 2022) and gender inequality (Rubab et al., 2023) respectively. All authors stated these issues as most prominent issues which are being ignored by policymakers and scholars on continuous basis. To that end, we tend to investigate this complex nexus for different insights.

The contribution of this study is multifold. For societies everywhere, gender inequality and poverty are inextricably linked. By putting these problems in Pakistan in the spotlight, we can see how pressing it is to get to the bottom of what’s causing them. The study’s findings corroborate previous research linking gender inequality to lower incomes and slower economic growth. This study adds to the existing body of knowledge on these themes, which may help fill in some of the blanks in our understanding and shed light on some of the more nuanced processes at play in Pakistan. There are clear policy implications from investigating how economic growth might help alleviate poverty and lower gender inequality. Policymakers and other stakeholders in Pakistan can use the findings of this research to help them develop efficient interventions and policies to increase financial inclusion, reduce poverty rates, and close the gender gap. Making policies with this kind of data at hand could lead to significant social improvement. Including Pakistan as a focal point increases the study’s overall applicability. Furthermore, Pakistan’s large gender gap and widespread poverty make it a prime study site for examining the interplay between these factors and the advancement of the country’s economy. This research has the potential to aid in broader socioeconomic development initiatives by illuminating the connection between gender disparity, poverty, and monetary growth. Interventions that promote economic growth, social inclusion, and gender equity can be developed with more precision once we appreciate the catalytic role that financial development can play in lowering poverty and resolving gender disparities.

The rest of manuscript is divided as follows. The second section shows the literature review and theoretical background. The methods used and discussion of results are presented in third and fourth sections respectively. While fifth and sixth section describe the conclusion and policy recommendations.

Literature Review and Theoretical Background

The basic reason behind conducting this research work to empirically examine the effect of financial development on economic growth, gender imbalance, and poverty in case of Pakistan. The previous study of Kendo et al. (2008) in Cameroon is evident that financial level developments act as a stimulator to enhance the growth of the country. It also causes to increase the income level of males as well as females. They further stated that financial level developments in the countries play a significant role in poverty reduction. Moreover, nonlinear impact of financial developments was observed on gender imbalance in case of Cameroon. The relationships of underlying study are presented below.

Relationship Between Poverty and Financial Development

Many attempts have been made by scholars to empirical examine the causality interaction between the linkage of financial development and savings but a very little effort by researchers has been made to statistically explore the nexus of financial development and poverty. During the past decade, the study of Odhiambo (2010) in the context of Kenya investigated the causality between the nexus of financial development and poverty reduction. For empirical purpose, the authors used the data ranging from 1968 to 2006 and they applied tri-variate causality method for causal interaction. The findings of their study revealed the existence of distinct causal relationship from financial development to poverty reduction. The study of Uddin et al. (2014), in Bangladesh by using data from 1975 to 2011 for empirical findings with the help of ARDL methods for cointegration measurement, investigated that financial development acts as stimulator for productive investments. Furthermore, long-run bidirectional causal interaction between financial development, economic growth, and poverty was investigated. Moreover, the study of Hicham (2018) in Algeria by using data for the years 1970 to 2017 by applying the statistical method of Zivot and Andrew. Their findings revealed the financial level development cannot play a role in poverty reduction. Furthermore, it was confirmed in their results that the economic growth of the country is pro poor.

Similarly, in the panel study of Fowowe and Abidoye (2013) for African countries on the nexus of financial level development and poverty reduction by using the technique of generalized method of moment which is commonly termed as GMM, it was found that financial development in African countries does not affect the poverty reduction in that specific regions. They further explained that no effect of financial development on poverty reduction is due to poor management and distribution of financial measures. The research of Jalilian and Kirkpatrick (2005) found that after reaching a threshold level of economic development the financial level developments play a role for contribution in poverty reduction through growth increasing effect. They also plaid the relationship of financial development and its effect in poverty reduction for developing countries of the world.

There is also another school of thought on the relationship between financial development and poverty reduction. The studies of Beck et al. (2007) and Shahbaz and Islam (2011) pointed out that the directionality causality among financial development and poverty is not mean that poverty reduction is due to financial level developments. They further stated equal distribution of financial resources at population level can play a vital role for reducing poverty. Later on, it was endorsed by Inoue and Hamori (2012). The findings of the nexus of financial development and poverty are inconsistent and inconclusive and still need to be explored in the context of a single country. Due to mixed results, we explored this nexus in Pakistan for different insights.

Relationship Between Gender Inequality and Poverty

The reduction of gender imbalance and women empowerment is part of MDGs (Millennium Development Goals) set by UN (United Nations). The gender difference is problem for all developing and developed nations among the world. The scholars like Pervaiz et al. (2011) mentioned in their research work that gender imbalance is issue for all countries in the world which is not justifiable on the basis of ethical and philosophical point of views. The gender imbalance has negative outcomes for economic growth which is directly associated with poverty.

According to Niimi (2009), gender imbalance exists in societies due to inequalities in education, health, decision-making, earning opportunities, employment, occupational hierarchies, and bargaining authority as well as power in households. And according to Jayachandran (2015), the abovementioned reasons of inequalities usually occur in developing countries. The most standing social issues in current era which are capturing every nation in the world are poverty and gender imbalance or inequality (Dormekpor, 2015). In the study of Lawanson and Umar (2019), it was claimed in their study that poverty and gender effects badly on economic growth. Furthermore, by applying data of 1980–2022 with the help of ARDL approach in context of Nigeria, they sorted the data from World Development Indicator and National Bureau of Statistics. Their empirical findings justified that gender imbalance (in education and employment) in the short and long run has causal effects on growth with economic loses and enhancement in poverty.

Similarly, scholars like Egbulonu and Eleonu (2018) in the context of Nigeria conducted a research on economic growth, gender inequality, and their impact on human capital for the time span of 1990–2016. They collected data for empirical observations from different resources including ILO (International Labor Organization), UNESCO (United Nations Educational, Scientific and Cultural Organization), and World Bank data from National accounts. They further used the Esteve Voltar model for statistical observation. It was depicted in their findings that there is male dominancy in educational enrollment and employment which is attached with growth. They suggested the government should focus on the issue of gender imbalance in education, employment, and equal opportunities to retain sustainable development which is associated with poverty reduction.

The study of Bastos et al. (2009) in Portugal is evident for poverty of women. By using household data of 1995–2009, it was found in their research work that unequal opportunities for employment and educational activities are contributing a lot in vulnerable poverty in country particularly for women. The work of Wiepking ans Maas (2005) explored the effects of gender imbalance and the risk of promoting poverty in twenty-two industrialized states of the world. They observed that in majority of the countries the women are going to be poorer as compared to men. They explained the reason of low participation of women in labor market and lack of educational opportunities. The study of Gaddis (2019) is also supporting this evidence in panel of African countries. Furthermore, the impact of gender inequality has also observed in different past and current studies as well. The research work of Cabeza-García et al. (2018) found the negative impact of gender imbalance upon growth. Some scholars like Bandiera and Natraj (2013) investigated that inequality in gender is best for promoting economic growth. The results on the nexus of growth and gender inequality are with mixed findings. Furthermore, it is stated in the empirical study of Lawanson and Umar (2019) that poverty imbalance has direct and indirect effects on the economic growth in form of inequalities between health, education, and employment. They further stated that poor health, education, and inequalities in employment lead towards poverty with bad impact on growth. To that end, we explored this relationship of poverty and gender imbalance in context of Pakistan for different insights.

Relationship Between Poverty and Economic Growth

The relationship between economic growth and poverty is controversial in economic development studies with inconsistent and different causal interactions. The scholars like, Michálek and Výbošťok (2019), mentioned in their research that there are different sorts of factors which are influencing the poverty. They determined the major factors include the economic growth and its distributions effects. Moreover, in their study, the context of the European Union by using data of 2005–2015 by applying Bourguignon Model found a decrease in poverty with the increase in economic growth. They further stated that the increase in poverty is conditional when there is an increase in income inequality. Similarly, some researchers like Pérez-Moreno (2016), by using data from 1970 to 1998 in the context of fifty-two developing nations of the world with the help of causality analysis, found unidirectional linkage from economic growth towards poverty reduction. Some scholars like Korzeniewicz and Smith (2000), in scenario of Latin American countries, concluded in their findings that economic growth does not play a leading role in reduction of poverty in the mentioned region. In time series, study of Nindi and Odhiambo (2015), in the context of Swaziland for the time spanning of 1980–2011, found that there is no causal interaction from growth to poverty in the short run. They further investigated that poverty reduction has Granger causality effect on economic growth in the short run. Moreover, the scholars like Nuruddeen and Ibrahim (2014), in the context of Nigeria, found a unidirectional linkage from gross domestic product to poverty. They concluded that increasing trends of economic growth in Nigeria cause to increase in the poverty level. They used data ranging from years 2000 to 2012. The negative relationship between growth and poverty was also observed by some authors like Zaman et al. (2011). The above literature is showing mixed results in different time spans and regions in form of panel and single-country studies. Oloyede (2014) mentioned in their research work that poverty is now issue for entire world which is disturbing the nations with different levels. To that end, we tried to explore this relationship for Pakistan separately that how the government of Pakistan is committed to tackle with poverty by keeping in mind the economic growth.

The Case of Pakistan

Poverty in recent decades is considered central objective by governing bodies to achieve as a milestone after introduction of Millennium Development Goal. All developing countries including Pakistan are facing the problem of poverty and trying to tackle it by various ways. We selected Pakistan for this research due to multiple reasons. It is stated in the research work of Ullah Awan et al. (2019), poverty is the name of lack of resources including nutritional needs, health, education, proper housing, clothing sanitations, and clean water of drinking. They further stated that these issues are not new for Pakistan as it is cultural heritage of Pakistan. According to HDI (Human Development Index Report), Pakistan is ranked as 146th numbers out of list of 187 countries of the World. It is more shocking that this index is lower than Sri Lanka in the region. It was also explained in the research of Ullah Awan et al. (2019) that the trends of poverty in Pakistan are increasing with the passage of time. They stated that during the time span of 1963–1964 the poverty was 34% which decrease to 17% during the year 1987–1988. And now, the percentage of poverty during the years 2013–2014 is 30% which will create hurdles for achieving economic growth. The reasons behind continuous poverty in Pakistan may include gender inequality, floods, earthquakes and other disasters, political instability, terrorism unrest, and no proper rules and regulations. The continuous increasing trends of poverty will be dangerous for collapsing economy of the country in near future.

Similarly, according to Ahmed and Hyder (2006), it was pointed out in their research article that in every society among the different nations of the world the women are considered deprived part of the population particularly in developing countries. They further explained that women in developing countries are facing the problems of mal-nutrition, underpaid wages, minimum availability to health, and education facilities as compared to men. According to recent work of Bukhari et al.(2019), the widely participated and vigorous issue of Pakistan is gender imbalance which is creating alarming situation with bad impact on economy of the country as compared to other nations. And there is existence of gender gap among male and female in Pakistan gender as inequality is big issue of the societies in Pakistan (Pervaiz et al., 2011).

Moreover, in recent work of Bukhari et al. (2019), it was narrated that there is more dominancy of males in the society as compared to women. They further explained the school of thought of different societies of Pakistan as most of people link the working of women as a dishonor for their families. This school of thought only provides support to women if they are engaged in family chores only. And as gender inequality in many perspectives leads towards poverty with bad impacts on the economy to that end, we tend to fill this gap in case of Pakistan for different insights, as gender imbalance and poverty are the main issues for Pakistan in the current era. Ahmed and Hyder (2006) explained in their research work that women in Pakistan are facing the vulnerable issues of unemployment, health education and labor market. Furthermore, it was suggested in the empirical study of Bukhari et al. (2019) that gender equality can play a vital role in poverty reduction in Pakistan to that end, we tried to explore this combined nexus of gender inequality and poverty in the context of Pakistan in the presence of economic growth and financial development.

A plethora of literature is available on the nexus of economic growth and poverty and gender imbalance and poverty in previous studies. Similarly, scant literature is also available on the relationship of financial development and poverty reduction with different findings and scenarios. The results are different for different economies on this nexus. For example, Jalilian and Kirkpatrick (2005) stated in their findings that financial development plays a vital role in poverty reduction, while some scholars like Dhrifi (2015) pointed out that financial development is causing poverty in low-income countries. The findings are inconsistent and still there is need to observe the impact of financial development on poverty and gender imbalance in case of Pakistan for suggesting some fruitful policies for the issues which Pakistan is facing due to poverty and gender imbalance. As per authors best knowledge, this is novel study to explore this complex nexus as a combine study and their causal effects in case of Pakistan.

Data and Econometric Approach

The main motive for conducting this research work is the empirical and statistical investigations between dynamic link and nexus among financial developments, gender inequality, country growth, and poverty. Furthermore, what is causal interaction between the study variables which are named and explained in Table 1 of this manuscript will be explained. The data for study variables were gathered from World Bank database and Human development reports. The data is ranging from 1985 to 2018 for empirical investigations. All variables, their proxies, and data source are mentioned in Table 1 of the study.

Table 1 Variables and definitions of variables
Full size table

Moreover, as concerned with econometric approach, there is existence of different sort of statistical techniques in the literature for observing the cointegration and short- and long-run dynamics among the study variables. These approaches of integration have been introduced by scholars including Phillips and Hansen (1990); Engle and Granger (1987); and Johansen and Juselius (1990a, b). But as some shortcomings exist to that reasons, these methods are failed to satisfy the researches for appropriate findings. These cointegration tests are also not suitable for dealing with structural breaks. These breaks often happen in time series data in different time spans. Due to these reasons, we applied autoregressive distributed lag model for checking the integration and long- and short-term strength of association among nexus of constructs which are used in this study. The introduction for the method of ARDL was proposed by Pesaran et al. (2001). This method of measurement is considered also popular among researchers for finding integration among the variables and dealing with structural breaks accordingly. Some benefits of ARDL method which are making it noteworthy are given as in following lines.

The ARDL technique is important as it tells that variable is co integrated at level of 1st difference or 1(0) and 1(1) level. Moreover, the plus points of ARDL were also described by researchers like Harris and Sollis (2003). They stated the positivity of ARDL that this method is particularly helpful for robust results without considerations of sample size. This is also useful for adjustments of lags in the model by carrying solid estimations of t statistics for the models which are long run in nature. The ARDL method useful when working with small sample sizes because it permits trustworthy inference despite having only a few data points to work with. Since statistics on gender disparity, poverty, and economic growth in Pakistan are readily available, we were able to use the ARDL method effectively. The ARDL method’s strength lies in its ability to capture the interplay between the short- and long-term dynamics of a given set of variables. It enables us to examine the short- and long-term impacts of shifting gender roles and economic growth on poverty. This all-encompassing method reveals subtler connections between variables. This model also provides researcher the giddiness for pursuing the dynamics of UECM. The UECM is named as unrestricted error correction model which reflects a significant position for long-run equilibriums link with short term. During this linkage, the data for the long run is put together. This method of measurement is also helpful for time series data because it provides guidelines for proper correlation as well as finding endogeneity (Pesaran et al., 2001).

Research Methods and Model Specification

The relationship between incorporated variable has been tested through cointegration and causality methods. First, we have examined the stationary of time series data through unit root tests. The study employed both structural and conventional root test to detect the issue of stationary. After unit root test, the order of integration has been determined through using the Bayer and Hanck cointegration test to investigate the cointegration among constructs. The cointegration results have been tested through the ARDL bound test approach. Likewise, after testing co integration, the ARDL method has been used to determine the long-run dynamics and for confirmation of ARDL results; DOLS estimator is employed. Finally, the direction of causality among variable is determined through Toda and Yamamoto approach.

The steps of ARDL technique which are commonly followed by researchers are discussed below:

  1. (I)

    At first step, the unit root test determined by Zivot and Andrews was applied. This test is best for dealing with structural breaks which are present in the time series of the data.

  2. (II)

    Choosing of optimal lag length for model specification.

  3. (III)

    Applying bound testing for empirical findings.

  4. (IV)

    For observing cointegration among the set of variables, Johansen cointegration technique was also applied.

  5. (V)

    For determining long- and short-run relationships, the ARDL test was also applied.

  6. (VI)

    Applied CUSUM and CUSUM tests for estimations of square.

  7. (VII)

    Applied vector error correction model commonly known as VECM for determining the causal interaction among the variables.

Moreover, before using the autoregressive distributed lag model in our study for empirical investigation, it is necessary to check the data and its assumptions first to execute the process. The unit root tests are considered for checking the stationary level of the data. Similarly, the bound test is reflection of the not stationary (series) at 1(2) levels. According to Ouattara (2004) if these series are stationary at 2nd difference, then F values will be unreliable as determined by ARDL. They also mentioned that cointegrations should be occurred at the 1st difference level. Furthermore, as concerned with the unit root tests, it was recommended in the research of Shahbaz et al. (2013) that the unit root tests determined by Zivot and Andrews (2002) are most appropriate for dealing with structural breaks in series of data. On the basis of these recommendations, we applied this unit root test for accuracy and reliability of our data. While the other unit root tests of Kwiatkowski et al. (1992) and Phillips and Perron (1988) are not supportive to deal with structural breaks.

The study estimates the relationship between incorporated variable based on following two models:

$$\begin{aligned}LNGE{N}_{t}&={\lambda }_{o}+{\lambda }_{1}LNF{D}_{t}+{\lambda }_{2}LN{Y}_{t}+{\lambda }_{3}LNED{U}_{t}+\\&{\lambda }_{4}LNSUR{V}_{t}+{\lambda }_{5}LNPAR{T}_{t}+{\lambda }_{6}LNPO{V}_{t}+{\mu }_{t}\end{aligned}$$
(1)
$$\begin{aligned}LNPO{V}_{t}&={\lambda }_{o}+{\lambda }_{1}LNF{D}_{t}+{\lambda }_{2}LN{Y}_{t}+{\lambda }_{3}LNED{U}_{t}+\\&{\lambda }_{4}LNSUR{V}_{t}+{\lambda }_{5}LNPAR{T}_{t}+{\lambda }_{6}LNGE{N}_{t}+{\mu }_{t}\end{aligned}$$
(2)

Appliction of Unit Root Test

The process of cointegration has been performed after examining the orders of integrations. This cointegration order has been estimated by employing PP and ADF unit root tests. The PP and ADF test by default linger on the null hypothesis on the level of non-stationarity. Based on PP and ADF test, the null hypothesis remains rejected if the p-value remains lesser than 0.05 and t-value remains above than 1.96. However, both PP and ADF tests are presumed to provide biased results due to their potential limitation of structural break (Ahmed et al., 2020a, b, 2021). Therefore, to control this issue, we have also used conventional unit root tests as anticipated by Zivot and Andrews (1992), which is used to determine the structural breaks and orders of integrations.

Cointegration Analysis

The literate posits various approaches to estimates the cointegration to examine the long-run equilibrium relationship. Likewise, Engle and Granger (1987) offered a residual-based approach to estimate the cointegration. The seminal work of Engle and Granger (1987) set forth the foundation for various other co integration tests such as Johansen (1988) cointegration tests, Johansen and Juselius (1990a, b) cointegration tests, and Boswijk (1994) and Banerjee et al. (1998) ECM-related tests.

The cointegration test provides biased results when there is small sampling size, and additionally, various types of the cointegrations tests provide different results and no one remains exceptional for providing complete reliable estimates (Ahmed & Wang, 2019). The mixed results estimated through different cointegration tests often create chaos concerning the selection of a valid test of cointegration. Therefore, to avoid this confusion, in line with most recent literature, we have considered the cointegration methods and procedures proclaimed by scholars like Bayer and Hanck (2013) and ARDL bound test. The method offered by Bayer and Hanck (2013) combines the values for probability of four different cointegration methods namely Johansen (1991) and Banerjee et al. (1998). As per the combined co integration methods, there is rejection of null hypothesis while the fisher statistics exceed from the critical value of Bayer and Hanck (2013).

The study validates the outcomes of Bayer and Hanck tests with the support of ARDL bound tests. Moreover, ARDL approach has various advantages as compared to other prevailing co integration techniques. The ARDL approach is applicable to small sample size and provides reliable estimates (Pesaran et al., 2001). This technique is best suited to apply when the all variables are integrated in many sorts of orders, for example, 1(0) or 1(1) or when they are showing integrations at fractional level. However, the approach does not remain applicable when variable remain integrated as 1(2) (Ahmed et al., 2019). Furthermore, the ARDL approach remains robust to address the endogeneity and autocorrelation problem (Ahmed et al., 2020a, b). The adopted ARDL based on unrestricted error correlation models are stated as:

$$\begin{aligned}\Delta{(LNGEN)}_t&=\alpha_o+\sum_{k=1}^p\alpha_{1k}\Delta{(LNGEN)}_{t-k}+\sum_{k=0}^p\alpha_{2k}\Delta{(LNFD)}_{t-k}+\\&\sum_{k=0}^p\alpha_{3k}\Delta{(LNY)}_{t-k}+\sum_{k=0}^p\alpha_{4k}\Delta{(LNEDU)}_{t-k}+\\&\sum_{k=0}^p\alpha_{5k}\Delta{(LNSURV)}_{t-k}+\sum_{k=0}^p\alpha_{6k}\Delta{(LNPART)}_{t-k}+\\&\sum_{k=0}^p\alpha_{7k}\Delta(LNPOV)_{t-k}+\alpha_1(LNGEN)_{t-1}+\alpha_2(LNFD)_{t-1}+\\&\alpha_3(LNY)_{t-1}+\alpha_4(LNEDU)_{t-1}+\alpha_5(LNSURV)_{t-1}+\\&\alpha_6(LNPART)_{t-1}+\alpha_7(LNPOV)_{t-1}+\varepsilon_t\end{aligned}$$
(3)
$$\begin{aligned}\Delta{(LNPOV)}_t&=\alpha_o+\sum_{k=1}^p\alpha_{1k}\Delta{(LNPOV)}_{t-k}+\sum_{k=0}^p\alpha_{2k}\Delta{(LNFD)}_{t-k}\\&+\sum_{k=0}^p\alpha_{3k}\Delta{(LNY)}_{t-k}+\sum_{k=0}^p\alpha_{4k}\Delta{(LNEDU)}_{t-k}+\sum_{k=0}^p\alpha_{5k}\Delta{(LNSURV)}_{t-k}\\&+\sum_{k=0}^p\alpha_{6k}\Delta{(LNPART)}_{t-k}+\sum_{k=0}^p\alpha_{7k}\Delta{(LNGEN)}_{t-k}\\&+\alpha_1{(LNPOV)}_{t-1}+\alpha_2{(LNFD)}_{t-1}+\alpha_3{(LNY)}_{t-1}\\&+\alpha_4{(LNEDU)}_{t-1}+\alpha_5{(LNSURV)}_{t-1}\\&+\alpha_6{(LNPART)}_{t-1}+\alpha_7{(LNGEN)}_{t-1}+\varepsilon_t\end{aligned}$$
(4)

In the abovementioned models, lag length is denoted by p, while \({\varepsilon }_{t}\) represents residual terms, and ∆ is signifying for 1st difference operator. The very 1st segment of this equation with the symbol of summation (∑) represents short run, while in the 2nd segment it is determining long-run associations. The F-values as compared to critical values suggested by Narayan (2005) are determining the cointegrations among the defined variables. While in 3rd equation when there is case as the computed F-values go beyond or exceed the upper critical bound (UCB), than null hypothesis of no cointegrations (\({H}_{0}: {\mathrm{\alpha }}_{1}={\mathrm{\alpha }}_{2}={\mathrm{\alpha }}_{3}={\mathrm{\alpha }}_{4}={\mathrm{\alpha }}_{5}={\mathrm{\alpha }}_{6}={\mathrm{\alpha }}_{7}=0)\) is leading towards rejection and the 2nd alternative hypothesis of cointegrations (\({H}_{1}:{\mathrm{\alpha }}_{1}\ne {\mathrm{\alpha }}_{2}\ne {\mathrm{\alpha }}_{3}\ne {\mathrm{\alpha }}_{4}\ne {\mathrm{\alpha }}_{5}\ne {\mathrm{\alpha }}_{6}\ne {\mathrm{\alpha }}_{7}\ne 0)\) is considered to be accepted. In comparison, when values of F are less than lower critical bounds (LCB), it is a symbol of existence of no cointegrations among the variables.

In addition, the incidence of cointegration cannot be determined, if the values of F-statistics are ranging in between the upper and lower values. We have used the critical values as per suggestions by Narayan (2005) as well as Pesaran et al. (2001). The values usually known as critical values proposed by Narayan (2005) are based on thirty to eighty observations and these stay suitable when the size of the sample is small.

The study estimates Eq. (4) after testing the cointegration for examining the short- and long-run elasticity. However, the main concern of the study remains to establish the long-run relation; therefore, only long-run results are being reported. The study also conducted various robust tests to ensure that estimated model fulfil the underlying assumptions of serial-wise correlations, heteroskedasticities, and incorrect functional forms. This study is in line with Brown et al. (1975), who also performed CUSUM and CUSUMsq to confirm the parameters stability. We have validated the long-run findings of ARDL through employing DOLS estimators. The DOLS estimators remain robust to detect the endogeneity problem in the study models and fix the bias resulted due to small sample sizes. The DOLS estimators are applicable in the case of integrated variables such as (1(0) and 1(1)) (Masih & Masih, 2000).

Toda and Yamamoto Causality Approach

After cointegration and robust tests, the study estimates the Granger non-causality measurements and techniques suggested by Toda and Yamamoto (1995). Moreover, these tests for non-causality provide reliable estimates as compared to other prevailing causality tests. The test remains applicable if the variables are 1(0), 1(1), or 1(2), showing no cointegration or even if showing integration in form of arbitrary orders. It is also a characteristic of this approach, that, it is cohesive with ARDL approach because its input information contains lag lengths and maximum orders for integrations (Shahzad et al., 2017).

Additionally, Toda and Yamamoto technique asphyxiates the potential bias annexed with these tests (unit root) and cointegration. The estimation of this specific test (Toda and Yamamoto) does not involve pre-testing of equilibrium which is long run in nature for the rapport or relation between variables (Zhang, 2011).

Results and Discussions

The descriptive statistics are represented in Table 2 of the study variables. It is mentioned that gender inequality has a mean value of 4.8720 with smaller or minimum level value of 4.785 and a maximum value of 5.2327. Poverty has a mean value of 4.0791 while financial development (FD) has an average value of 9.2387 with a minimum value of 9.2466 and a maximum of 9.5931.

Table 2 Descriptive statistics
Full size table

Table 3 portrays the findings executed from the unit root methods. The results from the technique of PP and ADF methods indicate that the series used in the study possess a unit root at level; moreover, at their very 1st difference, all of the variables are stationary. Therefore, it is possible to move towards cointegration analysis using different methods.

Table 3 ADF and PP tests
Full size table

Moving towards the other step of our study analysis, we employed techniques of ZA tests because previous methods ignore structural breaks in the data during stationarity investigation. Whereas, the ZA unit root method not only captures stationary levels but also reports one structural break in data. Again, the findings in Table 4 illustrated that series is integrated at 1(1) with one break in every variable.

Table 4 Zivot and Andrews (ZA) test with occurance of structural breaks
Full size table

Next, we employed the Bayer and Hanck (BH) method for checking co integration. The BH method is applicable when variables have a uniform integration level, i.e., stationary level of 1(1) and our data meets this criterion. We inspected cointegration in two models and the findings given in Table 5 illustrate that in model 1 where gender inequality is dependent variable, both statistics generated by the BH test are significant. Hence, there is cointegration in this model. Similarly, in the second model, both statistics are significant and we can conclude cointegration in the model.

Table 5 Bayer-Hanck test for cointegration
Full size table

Next, we verified these results using the bound testing method in Table 6. This method can handle series integrated at different levels and small sample sizes; thus, this method is also very reliable to check the co integration. Results reveal that F-statistics for both models are significant; hence, we found evidence of cointegration in the analyzed models.

Table 6 Bound tests for cointegrations
Full size table

Next, we computed the long-run estimates in Table 7 and Table 8. In Table 7, the outcomes support that financial development (FD) play an important role for reducing gender inequality in the long run. This is a very positive sign because it implies that the financial sector is providing funding that is used by women as well to raise their income level and their status in the society of a developing country like Pakistan. Thus, support from the financial sector can raise the status of females in society and may help to reduce their financial dependence on male. This in turn can help to reduce gender inequality in society. Our research work has contradictions with the results of De Haan et al. (2021) in the panel of 84 countries. They concluded that financial development has no direct impact on poverty but it promotes inequality. But the findings of our manuscript are quite similar with the research work of Lassoued and others (2021) in the panel of 43 Sub-Saharan African countries by using data ranging from 1995 to 2015. They also specified in their results that financial development plays imperative function in reducing gender inequality.

Table 7 Long-run results (model 1)
Full size table
Table 8 Long-run results (model 2)
Full size table

Conversely, an increase in the GDP (Y) does not decrease gender inequality in Pakistan. This is a very negative sign for Pakistan as it shows that economic growth cannot reduce social problems like gender inequality in society and a rise in income level does not affect the norms, values, and thinking of the society. There are certain reasons of this negative relation. For example, the gender pay gap could not shrink along with the economy. In some circumstances, when the economy expands, there is a greater need for competent workers, which results in salary increases. Women may not benefit equally from wage rises if they are prevented from obtaining an education, training, or better-paying employment opportunities. Despite rising prosperity, this may help perpetuate the female pay gap (Zaidi et al., 2021). Women may also encounter substantial obstacles when trying to gain access to financial services, such as credit and capital, even as economic progress often leads to an extension of these options. The gender gap in economic opportunity is exacerbated by the fact that women still face barriers to starting businesses and putting money into investments (Aziz et al., 2022).

This is both in the ARDL and DOLS results. Our findings for this study are justifiable according to the study on the nexus of gender inequality and economic growth by Cuberes and Teignier-Baqué (2012). They explained that gender inequality is the name of gap among male and female employment opportunities, and discrimination among earning, managerial positions, education, and political representations. Shahbaz et al. (2015) in their research work explained that beyond the increase in economic growth the gender and income inequality in under developed countries cannot be disregarded.

Next, education in the long run reduces gender inequality and this finding matches our expectations because education raises awareness, and educated people can also know about the situation of developed nations where mostly both genders are treated equally. Also, education empowers women to start jobs and improve their earning, which can also be a reason for the reduction in gender inequality because less financial dependence on females can support gender inequality. This finding is consistent under DOLS as well. Survival is insignificant in both methods implying that it does not affect gender inequality in Pakistan. However, participation in both models boosts gender inequality in Pakistan. Surprisingly, even the increase in poverty will have a negative effect on gender inequality implying that showing that poverty does not increase gender inequality in Pakistan. Thus, these results indicate that government can decrease gender inequality through education and financial development only.

Besides, lagged ECT is 0.26 with the right sign implying that convergence takes more than 3 years. Also, the model is stable as indicated by the diagnostic tests’ results and the plots of CUSUM and CUSUMSQ (Figs. 1 and 2).

Fig. 1
figure 1

CUSUM for model 1

Full size image
Fig. 2
figure 2

CUSUMSQ for model 1

Full size image

In Table 8, the long-run results of our second model are presented. From these results, it is clear that financial development in Pakistan is increasing the poverty level. This finding matches the outcomes of Dhrifi (2015) who concluded in their research by using data of 1990–2010 in upper and lower middle-income countries that financial development in lower income countries increases poverty among the societies. However, economic growth (Y) is reducing the poverty level in Pakistan and this is a very good sign for Pakistan. It implies that increasing income levels can decrease the poverty levels in Pakistan because people will have access to more money and they will be able to increase their standard of life.

Education is not effective in reducing the poverty level in Pakistan. This may be due to the fact that poor people have less access to quality education in Pakistan. Thus, rich people enjoy quality education which helps them to become richer while the poor people do not get opportunities for education. Thus, education is not decreasing the poverty level in the society in Pakistan. Survival is insignificant in the second model as well while participation is increasing poverty rather than reducing it. However, an increase in gender inequality will boost the poverty level implying that Pakistan may reduce poverty by decreasing gender inequality.

Furthermore, the results are consistent in both ARDL and DOLS. Apart from this, all diagnostic tests indicate that the model is stable and the plots of CUSUM and CUSUMSQ are also stable (Figs. 3 and 4).

Fig. 3
figure 3

CUSUM for model 2

Full size image
Fig. 4
figure 4

CUSUMSQ for model 2

Full size image

The causal analysis is conducted using the Toda and Yamamoto (TY) test in Table 9. The main results for model with poverty indicate that financial development, education, and gender inequality Granger cause poverty. Likewise, other variables also Granger cause poverty. In the model with gender inequality, it is indicated that education, income, participation, and survival Granger cause gender inequality.

Table 9 Toda and Yamamoto causality test
Full size table

Conclusion and Future Recommendations

The main motive for conducting this piece of research is to determine the impact of financial development on gender inequality and poverty in case of Pakistan. The relationship among the study variables is investigated by using the autoregressive distributed lag model in the presence of unit root tests and vector error correction model to find cointegration, to deal with structural breaks and to observe causal interaction among the study variables. The data was collected from different sources which are highlighted in Table 1 of this study. The data is ranging from year 1985 to 2022 for empirical observations. It is depicted in the major results of this work that there exists cointegration among the variables. Additionally, our results are revealing that financial development can act as a stimulator to reduce poverty in the country.

Furthermore, the strength of association between poverty to economic growth is negatively associated which reflects an increase in the poverty level in Pakistan and affects economic growth negatively. Similarly, the positive and bidirectional relationship among the variables of gender imbalance and poverty has also been investigated in our results. It means that both poverty and gender inequality have causal interaction with each other. Furthermore, the two-way causal relationship between economic growth and financial development is also observed. Moreover, it is bitter reality that the lack of education and gender imbalance is stepping forward day by day in Pakistan which is causing to increase in the level of poverty in the country (Batul et al., 2019). Pakistan is harshly facing the troubles of gender inequality, poor health, and educational facilities, and increasing trends of poverty in the country are leading towards vulnerable situation. This vulnerability will create harmful circumstances on the growth of the nation state.

As concerned with the policy recommendation, Pakistan like all other Muslim states has discrimination among genders. Particularly, female community is victimized at a larger level. It is time for Pakistan to revise the policies to demolish gender imbalance for sustainable economic growth. The government of Pakistan should find the solution to overcome the severe issue of gender inequality. It is the responsibility of the government of Pakistan to provide equal employments opportunities to expose the hidden talents of women so that they can contribute well to the country’s economic growth. Similarly, policies are suggested by authors for equal treatment of women during working hours, representation and promotion of women in public and private sectors, and promotion of women empowerment so that they can raise their voice against any violence in their rights, ensure equal opportunities for health and education for both men and women, and formulate the regulation and protection against honor killing, domestic violence, and abuse, and the programs and sessions should be conducted at a community level for the development of women. Meanwhile, the policymakers of Pakistan are entreated and requested for making surety of better health, education, harmony, love, and respect among the genders. The subject of gender studies must be part of the educational system in Pakistan to avoid gender imbalance.

Similarly, our findings depict that financial development participates positively for increasing poverty in Pakistan, which is contributing a lot to increasing sense of deprivation among the inhabitants of Pakistan with miserable conditions. Moreover, poor community is mostly exploited by a society which is very pathetic. So, proper allocation of funds without any discrimination can reduce the poverty level. The government of Pakistan is working on multiple projects regarding financial development in the country with the collaboration of different foreign-funded projects. Particularly, China is investing a lot in boosting financial development of Pakistan under the umbrella of China-Pakistan Economic Corridor. So, it should be the responsibility of concerned authorities to reduce the gender gap by providing equal employment opportunities for poor and rich to overcome the severe issue of poverty.