Examining a Co-integration and Causality between Education and Economic Growth in India

: The study examines the empirical relationship between education expenditure, higher education and economic growth in the context of India using time series econometric analysis for the time period 1971-2015 based on Vector Autoregression (VAR) model and Johansen’s Cointegration procedure. The time series data were verified for the stationary properties by using Augmented Dickey Fuller and Phillips-Perron test techniques which showed the variables to be integrated of order one I(1). The Johansen co integration of trace and maximum Eigen value tests indicated the presence of one co-integrating relationship among the variables, that is, the existence of long run relationship among the variables under investigation. The Granger causality test results indicated a unidirectional causality that runs from government expenditure on education to economic growth and also the existence of unidirectional causality between higher education and economic growth that run from economic growth to higher education. The reverse causality did not hold in either cases. The error-correction mechanism gives evidence for the short-run dynamics. Impulse Response Function showed a sharp drop initially of GDP and then positive response of GDP to shock in education expenditure and higher education that appeal for productive investment in research and development and training with proper facilities and establishment of more educational institutions, particularly higher education institutions that will lead to higher economic growth of India.


Introduction
India is one of the fastest growing developing economies with third largest education system after US and China. It sets its goal of achieving $5 trillion economy by 2024 which largely depends upon, among other factors, the key factors of human capital and higher education. The present paper is undertaken to empirically examine whether human capital (measured in terms of government expenditures on education) and higher education (measured in terms the gross enrolment ratio in tertiary education) affect economic growth of India. This will help policymakers and national leaders to formulate strategies for achieving the targeted goal relating education to growth in the future. Education is deliberated as one of the most important aspects of overall human capital investments which includes health and other aspects of social capital. It hardly needs any justification that education carries utmost importance because it functions as an engine of economic growth, development and prosperity for any nation. In the current globalized knowledge-based economy, talented and skilled manpower in sufficient quantity capable of meeting future challenges thrown up by disruptive technology and big geo-political changes is anticipated strategically more crucial than ever before to win the global competition in future (IEPSI & IMC, 2019). Today, many developed nations are ahead from developing countries in every domain of the socio-economic and political indicators of sustainable development, because they prioritized education for substantial investment in human capital for improving both its quantity and quality aspects. Investment in education leads to the formation of human capital, comparable to physical and social capital, and that makes a significant contribution to economic growth (Babalola, 2011;Pradhan, 2009;Dicken et al., 2006;Loening, 2004; Barro, 2001).
Education converted into labour productivity by accumulating knowledge and skills of the labour force and by facilitating the technological progress and innovation, not only leads to formation of human capital of an economy but various aspects like health, nutrition and sanitation are also positively affected (Mariana, 2015;Chandra, 2010).
The relationship between human capital/education and economic growth was established since long. Over the period of time, many growth theories and models have been developed that predict that education has a positive effect on growth. The major theoretical contributions to the subject on the relationship between education and economic growth are the augmented neoclassical and endogenous growth theories developed by among other, Solow, 1957;Lucas, 1988;Romer, 1990;Mankiw, et al., 1992. Many studies and theoretical advancement on the education and growth nexus have been made from time to time all over the world by Becker, Denison, Dholakia, Harbison and Myers, Mukherjee and Rao, Psacharopoulos, Schultz, Solow, Tilak and Todaro (Goel & Walia, 2017). The theoretical approaches and modellings involving education and growth nexus in common have predicted that education has a positive effect on economic growth (Hanushek & Woessmann, 2012). They also stress its impact on long-run growth trajectories through its role in increasing the innovative capacity of the economy (Aghion and Howitt, 1998;Romer, 1990), and its role in facilitating the transmission and diffusion of knowledge needed to implement new technologies (Benhabib and Spiegel, 2005;Nelson and Phelps, 1966). It can be observed from the figure-1 that the literacy rate which was just around 18% in 1951 has increased to over 74 percent in 2011 as per Census report of India. There is more than 24 percent point increase in literacy rate since 1951 to 2011. There is also a significant rise in the number of students enrolled in higher education institutions which increased from 0.15 million in 1950-51 to 14.3 million in 2005-06 and then to about 36.6 million is 2017-18. Large numbers of graduates and post-graduates passing out each year from these institutions are supposed to be one of the contributing factors to steady and consistent economic growth during post 1990s. The government expenditure on education has been increased over the years, and the education expenditure (as a share of GDP%) which started off at just 0.64% in 1951 has gradually increased to around 4 to 4.5 percent in recent years. Thus, the tremendous efforts made by the people of India, national leaders, policy makers as well as government through various reforms measures from time to time for improving the education sector both quantitative and qualitatively in the post era of 1990s and 2000s has led to a speedy growth stage of the economy about 10 percent in most recent years establishing the direct relation between higher education growth and economic growth. In essence, there has been significant growth taken place in education, especially in higher education due to which national income and GDP Per capita income has increased manifold in India. Ahead this background, the present paper attempts to empirically investigate the linkages between the education and economic growth in the context of India.
The studies that exist in the Indian context ( Specifically, we use Granger Causality tests and impulse response function that detects the direction of causality and identify which variable is a determining factor for one another variable under investigation in the context of India. We will investigate the following specific objectives:  To examine the causal interrelationship among government expenditure on education, higher education and economic growth in India.
 To estimate the long run relationship and short run dynamics of government education expenditure, higher education and economic growth in India.
The main empirical findings from this study reveal that there is a long run relationship between government expenditure on education, higher education enrolment ratio and GDP per capita in India for the period 20171 to 2015. The Granger causality test results indicated a unidirectional causality that runs from government spending on education to economic growth and from economic growth to higher education while the reverses did not hold. The error-correction mechanism (ECM) gives evidence for the short-run dynamics. The rest of the paper is organized as follows: Section 2 provides a brief overview of theoretical studies and empirical evidence relevant to this study and Section 3 states the specific objectives of this study. Section 4 discusses the nature of data and data source and methodological framework used in this study while Section 5 provides the empirical results and the main findings of the study, and finally, Section 6 contains summary and conclusion.

Review of Literature
The centrality of education for economic growth has been acknowledged since the time of Adam Smith and Marshall and have overtime evolved many economic growth theories and models. The main theoretical models that link between education and economic performance are the neoclassical growth models of Solow (1957) and Romer (1990), Mankiw et al. (1992) and endogenous growth models of Lucas (1988), Aghion and Howitt (1998). The economic growth models emphasized different mechanism that links education to growth and all approaches predict that education has a positive effect on growth. More importantly, growth theories and models predict positive externalities (education investments' fostering technological innovation, thereby making capital and labor more productive, generating income growth) and spillover effects (other than improving labour productivity and benefiting the individuals who receive it) from development of a high valued-added knowledge economy to the development and maintenance of a competitive advantage across the globe ( Although the consensus in the theoretical approaches of modeling linkages between education and economic growth seems to establish a significant positive linkage between education and growth, such that education increases labour productivity, efficiency gains of labour force, thereby causingf higher growth and development; however, the empirical evidence is rather not unanimous and remains controversial. Up to the present moment, there have been different and sometimes conflicting empirical evidences in both cross-country and country specific education-growth nexus analyses (Benosa & Zotou, 2013). Among other factors, differences in data used, data measurement and definitions such as human capital, or education and growth, methodological approaches, model specification and time frame have been identified as a major factors responsible for these variances. More explicitly, Temple (2001) points out that the empirical relationship between education and growth is often weak and the fragile correlations in cross-country data due to large measurement errors and influential exceptions. Consequently, the empirical evidences on the presence of a relationship between education and economic growth, despite strong background of theoretical predictions, have long been inconclusive and unclear.
More specifically, in the context of India, despite rigorous empirical exercises on the relationship between education and economic growth, the evidences as regards to the impact and direction of causality relationship between education and economic growth remain ambiguous. For example, Self

Data and Research Methodology
The main aim of the present paper is to examine the interrelationship between education and economic growth in India, The econometric approach of this paper is based on the vector autoregressive (VAR) model that allows us to study the inter-relationships between the variables. The methodology involves carrying out stationary test, then cointegration test and depending on the co-integrated relationship among the variables, error-correction model (ECM) is applied before proceeding with Granger causality method ( The critical values for the two statistics are provided (Johansen & Juselius, 1990) and compared with the estimated values of the two test statistics for possible rejection or acceptance of H0 against H1.

Empirical Results and Discussions
This section discusses the main empirical findings based on the methodologies outlined in section 3. A graphical representation of the three variables in Figure 1 shows

Johansen Co-Integration Test and Error-Correction Model
All the three variables have shown to be stationary and integrated of same order of 1(1) and we now examine the existence of long run relationship, that is, co-integration among them by employing Johansen's maximum likelihood co-integration method. Table 2 summarises the results of Johansen Cointegration test which indicates both estimated values of the trace and max eigenvalue tests. A perusal of the table 2 provides the evidence that there is at least one cointegrating vector among GDP Per Capita, education expenditure and higher education for the study period. This has been confirmed by rejecting the null hypothesis of no cointegrating vector at the 5% level critical values of both the trace-statistic and maximum eigenvalue statistics. The values of trace and maxeigen tests are found greater than the 5% critical value when rank = 0 and when rank = 1, both tests estimated at lower than the 5% critical value (Table-3 Table 3 shows the Johansen normalization restriction (β') of the variables in the model.  increase in the number of students enrolled in higher education leads to a 0.45% increase in GDP per capita implication that higher education has a significant positive effect on economic growth. This is confirmed by the t-value (t=-5.35) of the coefficient of higher education which is statistically significant at 1% level. However, the impact of government education expenditure on the economic growth is negligible since it is insignificant. This points towards emphasizing more importance to the development of higher education as crucial factors in promoting development of Indian economy as compared to education expenditure.   Table 4 are as follows: The results in Table 4   Kurtosis and Jarque-Bera for normality of the model support that the residuals are normally distributed. The stability check also indicate that the model is well-specified. This is because the moduli of 3 eigenvalues are strictly less than one, placed inside of the unit circle, thereby confirming stability condition of our VEC model. The VECM specification imposes 2 unit moduli.

Granger causality Wald tests
There is growing interest in the causal relationship between economic growth and education especially in the context of development strategies, mainly in developing countries. The direction of causality among GDP per capita, enrolment in higher education and government educational expenditure from 1973-2015 are studies based on the VAR estimated results by using Granger causality wald tests. Table 6 presents the results of pairwise Granger causality among the GDP per capita, educational expenditure and higher education enrolment. The results show that the null hypothesis that educational expenditure by government does not Granger cause GDP per capita is rejected at 1 percent level of significance. This implies that educational expenditure does Granger cause economic growth through its contribution to human capital, and consequently government spending on education is helpful in predicting the economic growth. Similarly, the null hypothesis that economic growth does not Granger causes higher education is statistically rejected at 1 percent level of significance, thus implying a direct causality from economic growth rate to the number of students enrolled in higher education. However, null hypotheses that GDP Per Capita Granger causes government expenditure, higher education Granger causes GDP Per Capita and Granger causality between government expenditure on education and higher education could not be rejected, indicating no causality between them as estimated by Granger causality Wald tests. Thus we can conclude that there exists a unidirectional causality which runs from government expenditure on education to economic growth and from GDP per capita to higher education performance in enrolment rates, while reverse are not hold.
These results are consistent with similar studies by Pradhan (2009) and Mallick and Dash (2015) but contrast with study by Indira and Kumar (2018) who indicated a weak relationship between the student enrollment in higher education and GDP in India.

Impulse Response Function (IRF)
To trace out the time path of the various shocks on the variables contained in the VAR system, the IRF is demonstrated in figure-3 which shows the response of variables following a one standard deviation innovation or shock on the error term.  The first row in the IRF above shows the responses of GDP to a shock in education expenditure and higher education. Thus an impulse in the education expenditure causes a sharp decline in GDP per capita in the first years then follows an increase in the long-run, though it is still negative.
Likewise, an impulse in the number of students enrolled in higher education causes a sharp drop in GDP per capita in the first years then follows an increase in the long-run which is still negative.
Contrary to this, an impulse in the growth of GDP Per Capita witnessed a sharp rise in initial years and then an exponential rise in the number of students enrolled in higher education in the long run. The responses of educational expenditure (lngex_ed) to GDP Per Capita was zero in the initial period but afterwards it began to increase positively and reached its peak in the second period and then continue to maintain that level in the long run.

Summary and Conclusion
The objective of this paper was to show the linkage between education expenditure, higher education and real GDP Per Capita. In other words, we attempted to understand how these variables have contributed toward the growth of an economy in relation to the human capital development. Using various econometric and time-series tools, we conclude that there is a longrun relationship between education expenditure and real GDP Per Capita, while the latter is also affected in the long run by changes in higher education. Short run causality result showed a unidirectional causal relationship between education expenditure and GDP per capita, running from education expenditure to GDP per capita. On the other hand, GDP per capita is found to have a unidirectional causal relationship with higher education, running from GDP per capita to higher education. Impulse response function graphs showed the relationship between GDP per capita, higher education and expenditure on education last for long years provided that the government channels its education expenditure towards more productive expenditure such as research and development and training, establishment of more educational institutions particularly higher education and vocational training centres and procurement of adequate learning facilities that will lead to the economic growth of India.