Educational Expansion and Economic Growth Nexus in Pakistan: Instrumental Variable Approach

This study examines the relationship between economic growth and the expansion of education in Pakistan. The study utilizes 2SLS and GMM estimators to estimate the growth equations with a potential issue of endogeneity using data for the period 1973-2018. Empirical results show that educational expansion at the primary and secondary level effect economic growth positively. The evidence is quite compelling that the effect of educational expansion on economic growth is low due to the poor quality of education. Also, the lower effect of physical capital is due to lower human capital embodied in the labor force.


Introduction
Education has become an indispensable tool for sustainable development. Its role is more profound and broad which is recognized for sustainable development goals (Sterling, 2016).
Education is necessary for a country to have a knowledge-based economy. Endogenous growth models acknowledge education as a major element of human capital. Education is recognized as one of the most significant investments in human capital among all the factors influencing human capital. This investment improves the mental ability of people and increases their productivity. The importance of education as a critical input for human development has been underlined by several economists in the literature on human capital (e.g. Schultz, 1961;Barro, 1991: Mankiw, et al., 1992: Barro & Lee 2013Benos & Zotou, 2014).
Neoclassical growth models did not pay much attention to education as input for economic growth. The new growth theory offer explanations on how educational expansion is imperative to economic growth (Aghion & Howitt, 1992;Lucas, 1988;Romer, 1990;Romer, 1986). In the existing empirical literature, a positive relationship between education and economic growth is reported by the studies (e.g. Lin 2003;Islam, et al., 2007;Pink-Harper, 2015;Teixeira & Queirós, 2016;Yu, et al., 2017;Siddique, et al., 2018). However, despite the strong theoretical basis for the effect of education on economic growth, some studies do not find a significant positive relationship between education and economic growth. The results of these studies show inconsistency in the findings (e.g. Benhabib & Spiegel 1994;De-Meulemeester & Rochat, 1995). This contradiction in results may be due to two reasons. Firstly, it has been identified that studies employ inadequate econometric estimation techniques which leads to spurious results (see Bils & Klenow, 2000;Jones, 1995;Loaning, 2005). Most importantly, the issue of endogeneity of independent variables in growth regression. Secondly, these studies are confined to use cross-country data of heterogeneous nature (Pritchett, 2001;Temple, 2001;Sial, et al., 2018).
In light of the above-mentioned limitations, the present study concentrates on these deficiencies in the existing empirical literature and chooses a research design that can handle such issues. Motivated by this interest, this study investigates the role of educational expansion in Pakistan's economic growth by considering the endogeneity issue and using time series data for estimation of empirical growth equations. This adds to the literature

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Volume 5(1): 2021 on education and economic growth being one of the few countryspecific studies conducted in this area. This study is important as it is one of the few studies which identify the shortcomings of using conventional techniques as it implements 2SLS and GMM to examine the link between economic growth and educational expansion in the context of Pakistan. Moreover, it is imperative to investigate this relationship as this would inform us about impact of educational policy. The rest of the study proceeds as follows: the literature review is discussed in section 2. Section 3 outlines empirical models and the econometric methodology. The results of empirical growth equations are presented in section 4. The conclusion of the study is given in section 5.

Literature Review
A considerable number of studies have examined relationship between education and economic growth using time series data. Lin (2003) revealed that education has a positive and significant effect on economic growth in Taiwan. In a time series analysis for Guatemala, Loaning (2005) studied the relationship between education and economic growth for the period 1951-2002. The results showed that the educated labor force was positively related to economic growth. In another study, Lin (2006) proposed an alternative measure of education for the estimation of an empirical growth model. The results revealed a positive impact of education on economic growth at all levels of education during 1964-2000. Islam, et al. (2007 studied the relationship between education and growth for Bangladesh. The results showed long-run relationship between the variables for the period 1976-2003. Pradhan (2009) looked into the causal relationship between education and economic growth in India for the period 1951-2001. The finding of the study indicated the existence of a relationship between economic growth and education in long run. In a recent study, Dauda (2010) carried out an empirical investigation to find the association between education and economic growth in Nigeria for the period 1977-2007. Empirical results confirmed the long-run relationship between education and economic growth.
Ganegodage and Rambaldi (2011)  and found a positive significant relationship. Mercan and Sezer (2014) found that a direct association of public educational expenditures and economic growth for Turkey from 1970 to 2012.
Hassan and Cooray (2015) showed that the education of males and females have positive externality effects for economic growth for Asian economies. They suggested that Asian countries may grow faster by investing in the education of girls. Teixeira and Queirós (2016) reported that education's interaction with the structural change of the economy is critical for economic growth. However, the intensity of the relationship depends on the country and time considered for analysis. This effect is positive for OECD countries for the period 1960-2011 while the relationship is negative for transition and Mediterranean countries during 1990-2011. Moreover, education itself has a positive and significant impact on economic growth in these countries. More recently, Woo, Kim, and Lim (2017)  The results indicate causality between education and sustainable economic growth and education has a positive and significant impact on sustainable economic growth. In Pakistan, attempts have been made to identify the role of education for economic growth. For example, Abbas and Foreman-Peck (2008) investigated the relationship between economic growth and education for the period 1960-2000. The results of the study showed that human capital has a critical role in boosting the economy's capacity to absorb technological progress. Chaudhary, et al. (2009) examined the relationship of economic growth and higher education in Pakistan, for the period 1972-2005. The empirical results implied that higher education and economic growth have long run relationship but it was not significant. Qazi, et al. (2014) investigated the link between higher education and economic growth and found a positive of higher education on economic growth. Moreover, using data for the period 1972period -2010period , Afzal et al. (2012 found a positive relationship between education and economic growth. These are the few studies from the literature on economic growth that used time series data. Contrary to the verification of the above studies, the direction of causality remained an issue in the literature. That is, 'does a higher education level lead to higher GDP' or 'higher GDP leads to higher education'. Bils and Klenow (2000) argued that higher incomes allow nations to achieve higher levels of education. Islam et al. (2007) reported a bidirectional causality between education and GDP. Stengos and Aurangzeb (2008) indicated that primary education had no causal impact on growth while secondary as well as tertiary education had a strong causal impact on economic growth. The only primary enrollment rate for females had a significant effect on economic growth. Chaudhary et al. (2009) showed causality from economic growth to higher education but higher education did not cause economic growth. Pradhan (2009) reported uni-directional causality from economic growth to education but not from education to economic growth. Liao et al., (2019) reported two-way causality between education and sustainable economic growth in short run while there is unidiresctional causality that runs from education to sustainable economic growth in long run in China.
Despite a strong theoretical basis for the effect of education on economic growth, some authors have noted a failure to detect a significant positive effect of human capital on economic growth (e.g. Barro & Sala-i-Martin, 1995;Bils & Klenow, 2000;Benhabib & Spiegel, 1994;Pritchett, 2001). However, Krueger and Lindahl (2001) argued that this failure may be attributed to improperly formulate econometric specifications.
Another strand of literature has focused upon the use of proxies for education and the role of outliers in growth regressions. For example, Cohen and Soto (2007) explain that the difference in results is due to usage of different proxy variables for education in growth regressions. The reason for this is that there is no clear-cut definition of human capital. They also highlighted that quality data is an additional problem faced by these studies. Moreover, Krueger and Lindahl (2001) emphasized on measurement errors of proxy variables for education, hence their estimated effect on economic growth. Temple (1999) discussed the role of outliers as a potential

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Volume 5(1): 2021 cause for the significance of schooling. He provided evidence that the effect of schooling increases and becomes significant if some outliers are dropped from the data utilized by Benhabib and Spiegel (1994). Similarly, Temple (1998) has shown that the education variable in Mankiw et al. (1992) regressions may be significant because of some outliers in the data. Contrary to (Temple, 1998(Temple, ,1999Cohen & Soto, 2007) have shown that the significant impact of education is not due to the presence of outliers.

Methodology Empirical Models
Two growth equations are specified to investigate the relationship between economic growth and educational expansion, which is based on the growth model of Mankiw et al. (1992). Various functional forms of growth model are used to estimate the relationship between economic growth and education in the empirical literature. That is, these functional forms consider different proxy variables for education e.g. education index, gross enrollment ratio at primary or secondary level, which depends on availability of data. Therefore, to capture the effect of educational expansion at primary and secondary on economic growth, the following equations have been estimated = + + + + ( ) = + + + + ( ) where, Y is real GDP in million (constant 2010 US$) and it is a proxy variable for economic growth. K represents real gross fixed capital formation in million (constant 2010 US$) and it is a proxy variable for physical capital. L represents the total number of employed persons in million and it is a proxy variable for labor force. PRI and SEC are the number of enrolled students in thousands at the primary and secondary levels, respectively. PRI and SEC are proxy variables for educational expansion.

Econometric Methods
We know theoretically that factors of production (e.g. L, K, or human capital) affect economic growth by production of goods and services. Economic growth in turn affects demand for these factors of production. That is, dependent and independent variables are determined jointly. Moreover, other variables also affect independent variables that are not included in the growth equations. Therefore, growth equations have a potential issue of endogeneity. The study utilized Two Stage Least Squares (2SLS hereafter) and Generalized Method of Moments (GMM) estimators to estimate the growth equations. In doing so, lags of variables are used to circumvent the problem of endogeneity in time series analysis e.g. first lag of dependent variable and lags of physical capital. Two important diagnostic tests are implied to evaluate the stability of the model. Durbin-Wu-Hausman (DWH) Test is utilized to test the endogeneity of independent variables. The test statistic has a Chisquare distribution with number of independent variables tested for endogeneity as degree of freedom. The null hypothesis is that independent variables are exogenous. The validity of instruments is tested using J-Statistic, it tests the null hypothesis that instruments are valid. J-Statistic has a Chi-square distribution with number of over-identifying restrictions as degree of freedom. Table 1 presents the summary statistics of variables namely means, median, maximum, minimum, standard deviation, skewness, kurtosis, Jarque-Bera test, and their probability values. For most of the variables, the mean and median are approximately equal while the standard deviation ranges from 0.16 to 0.30 which is very small. Measure for skewness shows that distributions of variables are not skewed. Moreover, values of Jarque-Bera statistics and its probability values indicate that all the variables are normally distributed.

Results and Discussion
The 2SLS and GMM estimates of the first growth equation is presented in Table 2. This equation is based on primary education. All estimates are with expected signs and are highly significant. The physical capital, labor force, and primary education have a

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Volume 5(1): 2021 significant positive impact on real GDP in Pakistan. The coefficients may be interpreted as elasticities of output with respect to inputs because dependent and independent variables are in log form. The findings are consistent with economic theory. GMM estimate shows that one percent increase in primary enrollment brings 0.25 % increase in real GDP whereas 2SLS estimate reports 0.30 % rise in real GDP. This result supports the idea of (Becker, et al., 1990;Barro, 1991). Similarly, this finding is in line with the findings of previous studies (for example Lin, 2006;Loening, 2005;Self & Grabowski, 2004;Pegkas, 2014;Mariana, 2015;Kotásková 2018). The 2SLS estimates indicate that a 1 % increase in real gross fixed capital formation results in 0.52 percent increase in real GDP while GMM estimate is somewhat higher i.e. 0.56. Both 2SLS and GMM estimates indicate that a 1 % increase in the employed labor force increases real GDP by 0.63 percent. The lower panel of Table  2 reported two important diagnostic tests to evaluate the stability of the model. The DWH statistics for 2SLS and GMM show that null hypothesis that independent variables are exogenous is rejected. J-Statistic values show instruments are valid as we accept the null hypothesis. To find out the effect of educational expansion at the secondary level on economic growth, the study estimates the same model by replacing primary education with secondary education as in equation 2. The 2SLS and GMM estimates of growth equation 2 are presented in Table 3. The estimated relationship reveals that educational expansion does not alter its long-run elasticity if secondary education is used as an explanatory variable instead of primary education in the case of 2SLS estimate i.e 0.30. Whereas, GMM estimate is somewhat higher that is one percent increase in secondary enrollment results in 0.31 percent increase in real GDP. This finding follows (Mankiw et al., 1992;Petrakis & Stamatakis, 2002;Gylfason & Zoega, 2003;Leoning, 2005;Lin, 2006;Mariana, 2015;Ali, 2017;Kotásková, 2018;Marquez-Ramos & Mourelle, 2019).
Both 2SLS and GMM coefficients on physical capital are positive and highly significant if secondary education is used as an

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Volume 5(1): 2021 explanatory variable. Moreover, the effect of labor force on real GDP is lower, both 2SLS and GMM estimates show that the employed labor force has a similar effect on real GDP i.e. 0.42 percent. The results support the findings of previous studies by (Self & Grabowski, 2004;Chaudhary et al., 2009). The lower panel of Table 3 reported DWH statistics and J-Statistic for 2SLS and GMM models. They show that null hypothesis that independent variables are exogenous is rejected and instruments are valid.

Conclusion
The study estimated the relationship between economic growth and educational expansion at the primary and secondary levels. The analysis shows that educational expansion has a positive effect on economic growth. This tends to support the notion that human capital accumulation leads to a higher rate of economic growth. However, its effect on economic growth is low. The possible reason for this is that the quality of education is so low that year of schooling creates low human capital and it does not raise cognitive skills or productivity. In addition, Pakistan's fragmented educational system is the main reason for low educational status, which has formed some intractable problems in the optimal utilization of human resources. Moreover, the possible reason for the low impact of physical capital on economic growth is the complementarity of physical capital with education which is of low quality.
Educational expansion can promote the economic growth of Pakistan. Expenditure on education will improve the quality of education and will boost efficiency and productivity. Moreover, the education system requires a thorough review and particularly, the amendment of the current curriculum to improve the quality of education at all levels. The curriculum should be reviewed to make it more relevant to the needs of the job market.
It is well understood that all type of education raises cognitive skills. So, the implication of low or poor past returns from education in a perverse policy environment is not "do not educate your people" but rather reform your system of education so that investment in education will pay off better in the future. Moreover, future empirical studies should estimate a measure of quality of education and investigate its impact on economic growth. This direction should be of interest in future research on education and economic growth nexus.

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Funding
This research received no external funding