The Impact of Women Parliamentarians on Economic Growth: Modelling & Statistical Analysis of Empirical Global Data

The impact of empowering women on economic growth is investigated through testing the influence of proportion of women candidates in parliaments. To obtain a long-term view, cross-country analysis is performed in parallel using 10 years World Bank data of 72 countries divided into the UN income-groups: 1-high, 2-upper-middle, 3-lower-middle, and 4low-income. Statistical analysis reveals severe degree of multicollinearity. To unveil the desired connection, two approaches are implemented. Principle Component Regression is used to assess the independent impact of women parliamentarians. The results demonstrate a positive significant influence: 10% increase in female parliamentarians increase growth by 0.27%, 0.36%, 0.22%, and 0.49%, respectively. To unveil the joint influence of the considered indicators, interaction regression models are developed. The method demonstrates superior results. This work provides an empirical evidence on the positive impact of women political empowerment with respect to stimulating a sustainable economic growth.

exist in the literature, one of which is that of Jayasuriya and Burke (2013). The latter authors" method is based on using both the fixed-effects estimator and the system Generalized Method of Moments (GMM) estimator. Their results provide evidence that women participation in political life is important toward economic development.
Most of the available literature focus on only high-income economies. Khorsheed (2019), for example, studied the impact of proportions of seats held by women in parliaments on the growth of 02 high-income countries excluding USA. This research extends the work of Khorsheed (2019) by investigating the relationship between women parliamentarian and economic growth of all four UN income categories: high (including USA & Netherland), upper-middle, lower-middle, and low income. The analysis is administered using regression approaches and machine learning by the aid of the statistical software R.

Panel Data
Economic growth on the long term differs among countries. In the past, the diversity is due to a lack or wealth of natural resources such as fertile agricultural soils and deposits of oil & gas in countries" territories. Nowadays, all types of nation resources-natural capital, physical capital, and human capital are widely recognized as main indicator of economic development. A statistical universal metrics that is easy to calculate and provide a good estimate of the relative productivity of any nation is the gross domestic product (GDP) per capita. Depending on the gross national income (GNI) which includes GDP, the World Bank divided economies into four income groups: high, upper-middle, lower-middle, and low.
Education and health are the key dimensions of human capital that contribute to economic growth. Unlike most high-income countries, low-income nations suffer from unstable economic growth with greater proportions of uneducated and unhealthy populations. In the human capital growth model of Locas (1988), for example, the variety in the growth rate was found to be affected by the nation"s level of political stability and functioning of institutions. In this study, the main aim is to investigate the impact of women proportion of seats in national parliaments on economic growth. To account for other major determinants of growth and the potential effects of any possible interactions between these indicators, the following variables are also considered: population growth, initial Gross Domestic Product (GDP) per capita (constant 2006), & Foreign Direct Investment (FDI).
Taking into consideration the special features of each income category, panel data for these groups are aggregated from the World Bank database for the period 2006-2015. From the high-income economies, 22 countries are considered including USA and Netherland. From the upper-middle and lower-middle income groups 20 and 13 countries are involved including China and Liberia, respectively. Seventeen low-income countries are also considered. This group contains The Haiti and Nepal beside 15 African nations including Rwanda. The full list of countries included in this study categorized according to level of income are displayed in Table 1. Table 1. List of countries included in this study categorized according to level of income example, although Rwanda categorized in the low-income group, it has been on the top of the 2017 UN list of countries with the most women parliamentarians over the whole decade (61.3%). This is mainly because of the country"s legally set quotas, with the Constitution stipulating that at least 30% of the national parliament seats must be for women. On the other hand, the Middle-East countries in the high-income category reveal the lowest women parliamentarians ratio among the group. These differences are due to several factors related to the state"s customs and social traditions, religion, cultural, and political orientation.
The data consists of averages of ten years" development indicator time-series observations starting from year 2006. Table 2 displays the mean and standard deviation of every explanatory variable for each economy type. This table reveals that the highest averaged proportion of women parliamentarians is associated with the high-income group. The middle-income groups exhibit the largest mean economic growth that slightly exceeds 3.0. In addition, China, which is categorized within this group, has the largest GDP annual growth rate averaged 9.05% followed by Ethiopia. Although Ethiopia is a low-income country, it is among the fastest growing oil-free economies in the world after the government reforms that raised share of women political participation and opened the economy for foreign direct investments. On the other hand, the average GDP growth rate associated with the high-income economies is dominated by the recession experienced by some countries in this category. These countries are Kuwait, Oman, UAE, Greece, Italy and Spain. The recessions are expressed as negative growth rates in the dataset. Unexpectedly, the low-income group has the largest average FDI dominated by Liberia"s average FDI that exceeded 40% during the considered period. The low-income group has also the highest population growth percentages.

Methodology
At the first stage of exploring the relationship between economic growth and the adopted development factors, a linear regression model is fitted for each income-group displayed in Table 1. The main variable of women parliamentarians" proportion appears significant at level of 0.1 only in the low-income model with no other significant terms. The corresponding coefficient of determination is reasonable ( 4 . 0 2  R ). Other than this exception, the linear fits turned most explanatory variables insignificant in all developed models. This unveils the presence of the multicollinearity phenomenon detected from the 2D scatter plots of pairwise relations between the variables as demonstrated in Figure 1, and from the calculated significant correlations between different pairs of the considered variables. For example, the correlation between the proportion of female parliamentarians and population growth percentage within the high-income category is about -0.66.  Vol. 9, No. 3;2020 To investigate the effect of women proportion in national parliaments on growth in the presence of the other acknowledged development indicators, Principle Components Analysis (PCA) and multiple interaction regression analysis are performed for each income group independently. Both analysis types are technically proceeded using the powerful approaches of machine learning by the aid of the statistical software R. Two models for each income group are developed using the available panel data and will be discussed next.

Principal Component Regression Models
When multicollinearity exists between predictors, regression coefficients can be estimated but probably with inflated standard errors, see for example Wheeler (2007). Such errors can result in inaccurate conclusions of tests of significance, which means that truly influential predictors may be considered insignificant (Dormann et al., 2012).
One way to overcome the multicollinearity problem revealed in the initial analysis of the cross-country data is to use orthogonal transformation to convert the set of correlated variables into another set of values of linearly uncorrelated variables called principle components (PCs). 2.6 (1.4) 5.5 (9.4) The procedure for finding these components is known as the Principle Component Analysis (PCA). It is a powerful technique that has been widely used for dimensionality reduction. For more details on PCA, see Dillon et al. (1984).
Principal Component Regression (PCR), which is a type of regression analysis that uses the PCs to regress the dependent variable, can then be used to estimate the unknown regression coefficients in the standard linear regression model by only considering the significant PCs.  Tables (3-6). Furthermore, regression linear models are fitted for the new set of uncorrelated variables. The associated coefficient of determination 2 R are approximately 0.4, 0.4, 0.6, and 0.4, respectively. This process rendered some PCs insignificant in each case as summarized in Table 7. A communality gives a measure of the amount of variance in each variable that is accounted for. It has 1 as an initial estimate since this is the total variance across all 4 components. The final communalities after extraction are presented in Table 8 where c = 1, …, 20.

Principle Component Regression Results
The results of the PCR approach presented in models (1)-(4) reveal that all considered factors are significant at level 0.1 or lower. The key variable, seats held by women in parliament, which reflects the extent of female political empowerment, demonstrates a significant positive impact on economic growth regardless of nation"s income level. Moreover, the effect of women political participation appears slightly greater on the group of low-income countries, which witnessed a relatively high female parliamentarians" proportion that exceeded 20, and economic growth of 2.23, on average, in the last century. Based on this approach, a 10% increase in the proportion of seats held by women parliamentarians of income groups 1-4 results, on average, in an increase of approximately 0.27%, 0.36%, 0.22%, and 0.49% in economic growth, respectively.
Scientists have different views on the impact of population growth rates on GDP growth. Kelley and McGreevey (1994) found, in their historical study on developing countries, that high population growth rates have little effect on GDP growth. In economics, labor is considered an important factor of production and with an increase in the labor force by moderate population growth the nation"s GDP may increase. Simon (1981Simon ( , 1989 conducted two studies that harmonizes with this view. This author suggested that, in the long-run, population growth may have a positive impact on GDP through enhancing productivity by contributing new ideas and learning-by-doing. This may explain the positive impact of population growth on some nations such as China, which is now considered the second fastest economy in the world after USA. As models (2) and (4) reveal, the population growth of the upper-middle and the low-income nations may have a positive and almost equal effect on per capita GDP growth. Here, a 1% point increase in annual population growth may, on average, increase economic growth by approximately 0.1%. These results are supported by the general growth theories and studies discussed above.
On the contrary, Birdsall & Sinding (2001), Carlin (2006), and Headey & Hodge (2009) claim that rapid population growth may have a significant negative effect on economic growth. In this research, the impact of annual population growth on economic GDP growth is negatively significant on both high and lower-middle economies with a stronger effect on the latter, where a 1% point increase in population growth is expected to lead, on average, to a decrease of 1.1% points in GDP growth rate.
The negative effect of the initial level of GDP/capita for 2006 although small, appears significant in all four models. This result may support the theory of conditional convergence discussed in Barro (1996).
Foreign Direct Investment has been widely acknowledged as an economic growth-enhancing factor. This is because FDIs may deliver technological advances, increase the exporting capability of the host country, and lead to profit increase at a foreign exchange. Therefore, it is considered as one of the most famous sorts of investment in the world especially in developing countries. For some related studies, the reader is referred to (Younus et al., 2014;Dritsaki & Stiakakis, 2014;Falki, 2009;Saqib et al., 2013) and the references therein.
As expected, the foreign direct investment contributes positively and significantly to GDP growth in all income-based developed models. The strongest impact of this factor is associated with the lower-middle income cross-section, where a 1% increase in FDI is expected, on average, to increase growth rate by approximately 0.44%. The corresponding expected increment in the upper-middle, high and low-income nations" growth rates are 0.039%, 0.024%, and 0.007, http://ijsp.ccsenet.org International Journal of Statistics and Probability Vol. 9, No. 3;2020 29 respectively. These results match the existing empirical literature; see for example,  and Hermes & Lensink (2003).
The results of this approach and the associated diagnostic plots are displayed in Figure 2 and Figure 3. These results reveal a reasonable fit of the 72 nations" panel data and are discussed further in the last section.

Interaction Regression Models
Although the values of the coefficient of determination associated with the PCR linear models are reasonably good, they do not reflect highly accurate fits. This may be due to the existing multicollinearity between the original variables, or lack of other affecting factors or both. This problem justifies the need for higher-order interaction terms that may express the underlying physical behavior. Moreover, the inclusion of such terms can eliminate the simultaneity bias, which is important for better statistical results. By using machine-learning, the inter-associations among the independent variables are captured. This step contributed in the formulation of the following four interaction regression models: where c = 1, …, 20.

Discussion
The main objective of this paper is to assess the economic impact of women's political empowerment, through shares of females in national parliaments, on economic growth. The following four income nation categories of the World Bank are considered: high, upper-middle, lower-middle, and low-income. The sample include some of the top 10 countries by GDP: USA, China, Germany, UK, India, France, Brazil & Italy. Although this study focuses on the influential impact of women parliamentarians, it does not ignore the effect of other important development indicators such as population growth rates, foreign direct investment, and initial GDP per capita. Panel data for a period of ten years starting 2006 are considered to develop growth models for each economy type.
An initial analysis of the dataset exhibits signs of multicollinearity. To solve this problem and unveil the relationship between growth and women proportion of seats in national parliaments, two regression approaches are implemented. The first approach adopts Principle Components Analysis to fit models on an independent basis. All four developed PCR models explained reasonable percentage of the variations in the GDP per capita and produced "good" growth estimates, as revealed in Figure 2. The residual diagnostic Q-Q plots in Figure 3 confirm a good normality behavior of errors.
The PCR results provide useful insights into the adopted development factors. Empirical evidence suggests that growth will be enhanced by an increase in the proportion of seats held by women in parliament, where a 10% increment may rise economic growth of groups 1-4 by by 0.27%, 0.36%, 0.22%, and 0.49%, respectively. Findings from implementing this methodology are clearly consistent with the relevant economic theories and studies such as that conducted by Jayasuira and Burkes (2013).
Foreign direct investment is considered as an integral factor of an open international economic system. FDI can play a significant positive role in maintaining a long-run sustainable growth regardless of a nation"s level of income. This positive relationship is demonstrated by the corresponding regression coefficient estimates (0.024, 0.04, 0.44, and 0.007) of models 1-4, respectively. These figures indicate that the impact of FDI on growth of the lower-middle economies such as India, Egypt and Morocco can be at least 10 times greater than its impact on the other income groups. This is because such developing countries and emerging economies can benefit more from foreign presence in the domestic economy to increase their competitiveness business environment, enhance enterprise development, and provide employment and training opportunities beside advanced managerial and technological skills to citizens. Moreover, comparing these estimates with the corresponding women parliamentarian terms reveals that both factors may have the same growth stimulating impact on the high and upper-middle economies but FDI can have a stronger impact on the growth of the lower-middle nations. On the contrary, FDI seems to have a small impact on the low-income group, which may be due to the unattractive environment for foreign investments in most of these poor countries. The new results of this study cope with economic theory and previous applied studies, see Levine & Renelt. 2003).
As expected, the 2006 initial level of GDP per capita show a small but significant negative effect on the overall growth per capita of all types of economies. However, lower income countries growth rates are more sensitive to initial GDP. This result is consistent with other studies in the literature where, for example, Barro (1991) found growth negatively and robustly related to initial GDP. Levine & Renelt (2003) and Sala-i-Martine et al. (2004) derived a similar conclusion.
The PCR analysis yielded interesting results regarding the impact of population growth. A higher human growth rate may contribute to either higher or lower economic growth depending on a nation"s income. A rapid growth of human population and a high birth rate can have unfavorable effects on high and lower-middle income nations especially countries that are unable to absorb labor surplus. On the contrary, population growth may exert a significant positive impact on upper-middle and low-income countries on the long-run. This is because it is the main source of provision of labor, experts, and business personnel necessary for production activities in such countries (Prihanto, 2017). These results are, for example, in line with the Chinese government move toward ending birth restrictions by 2020, amid the growing concerns over an aging population, a dropping birth rate, and consequently an expected fall in labor force and productivity levels.
Multicollinearity suggests that some interactions between the original variables may have moderate to strong effects on the prediction process. Following the detection of symptoms of data multicollinearity at the initial stage, another regression approach that takes into consideration the joint effects of the adopted predictors on growth is implemented. Fortunately, the innovative method of machine learning technology utilized in this study has identified the significant interactions and links between the proportion of women parliamentarians, development indicators, and GDP/capita. This step produced four new interaction regression models associated with superior statistical results and accurate growth forecasts, as indicated by the fits and Q-Q plots displayed in Figures 2 and 3, respectively.
Despite only four development factors are considered, the new interaction models explain at least 90% of the variation in the growth rates. This can be interpreted as follows: the proportion of women in national parliaments, for example, may not only provide a measure of women political empowerment but also reflects the combined effect of other growth determinants not covered physically in this study. Some of these determinants may include female education, gender equality in different education stages, and female training/skills development, for which parliamentarian females probably benefited from, earlier in their lives, for them to be eligible for such leadership and decision-making positions. The FDI factor, as another example, may reflect the impact of other specific qualitative determinants such as economic openness, economic freedom, global competitiveness and technological progress. Moreover, interactions including proportions of female parliamentarians, FDI or both, for example, may give these factors an additional power that exceeds their impact as independent variables. This is because these joint relationships may represent other more factors such as trained national manpower, which can be achieved, for example, by training male and female citizens in investment projects.
It is impossible to include all factors that have influential effects on economic growth in a single study however; the results derived in this study reveal that the adopted indicators and underlying significant interactions can be adequate.
The remaining unexplained small percentages of change in economic growth rates (10% or less) are probably due to other determinants of GDP/capita, which are either not included nor represented by any terms in the derived models.
Both PCR and interaction regression growth results for all considered nations of the World Bank income groups provide an empirical evidence that reveals the significant role of women in parliaments in stimulating economic growth. Accordingly, the new study affirms that there may be attractive economic incentives for governments to invest women's participation in political life and national parliaments, in particular.
Nations with low proportions of female parliamentarians would have the most to gain from designing policies aimed at engaging more women in the national parliaments and decision-making positions, and from enacting laws and appropriate legislation that can help in achieving the sustainable development goals, of which gender equality represents the fifth UN goal.