Granger Causality between Growth in the Education Sector and Socio-Economic Services in Nigeria

The relationship between two variables has been mush studied using the concepts of Granger causality. In this study, Nigeria economic data from 1981 to 2015 is used to investigate the causal relationship between education sector growth and socio-economic services (education, health, road & construction and transport & communication), employing unit root test, Johansen co-integration and Granger causality approaches. The result of the study showed that there is long run Granger causality between the education growth and the recurrent expenditure on socio-economic services.


Introduction
The relationship between two variables has been mush studied using the concepts of Granger causality.
Granger causality is a term for a specific notion of causality in time-series analysis. The idea of Granger causality is a pretty simple one: A variable X Grangercauses Y if Y can be better predicted using the histories of both X and Y than it can using the history of Y alone.
Granger introduced the concept of Granger causality in 1969 and it has been widely used in econometric studies to test availability and the direction of the causality (Granger 1969).
Furthermore, Johansen's cointegration analysis is employed to determine any long-term relationship between the variables before the causality test. The first step in time series analysis is to investigate the Electronic copy available at: https://ssrn.com/abstract=2939300 Alabi and Olarinde (2017) 45 stationarity of variables, also called 'the unit root test'. Accordingly, the existence of a unit root at frequency zero would imply that the stochastic trend is non-stationary (Torraleja et al, 2009;Aniefiok and Udensi, 2016;Essien, M-epbari, Nwikiabeh and Piabari, 2016). Gujarati and Porter (2009) point out that it is so often to meet non-stationary time series and the estimates of non-stationary variables will lead to spurious regression. Thus, their economic interpretation will not be meaningful. Furthermore, unrelated time series may appear to be related using conventional testing applications such as ordinary least squares regression. To this end, we utilise the Augmented Dickey-Fuller test (ADF), and the Phillips-Perron test (PP) to examine whether the data are non-stationary (Dickey and Fuller 1981; Phillips and Perron 1988). The augmented Dickey-Fuller (ADF) unit root test is one of the most accepted and widely used tests to investigate the stationarity of series (Park et al. 2016).
Regression analysis based on time series data implicitly assumes that the underlying data is stationary (Gujarati and Porter 2009) and it is usually the case that time series variables of macro economy are nonstationary. Alternatively, cointegration analysis allows for spurious results to be avoided by using non-stationary data, but all those series have to be integrated into the same order. Despite the range of different cointegration tests in the literature, the Engle-Granger (Engle and Granger  1987) and Johansen (1988,1991) tests are widely used. In this study, the Johansen cointegration test is employed to test the existence of a long-run equilibrium relationship among the variables and employed Granger causality analysis to determine the direction of causality between education sector growth and socio-economic services.
The adequacy of socio-economic service determines a country's success in education and another; failure to improve quality and efficiency of the entire education system, coping with population growth reducing poverty, or improving environmental conditions. A good socio-economic service in a country reduces outbound education, provide access at all levels of education and improve the quality and efficiency of the entire education system. Alabi and Olarinde (2017) 46 investment on growth is not significant however, it has the correct sign. On the other hand, private investment is shown to have a long run growth impact in South Africa and Namibia. However, they find evidence indicating a reverse causality from GDP growth to public investment. The causality is negative in the case of Botswana suggesting that as the economy grows investment in public goods declines, which contradicts both the Keynesian theory and Wagner's law.
Loizides and Vamvoukas (2005) employed the trivariate causality test to examine the relationship between government expenditure and economic growth, using data set on Greece, United Kingdom and Ireland. The authors found that government size granger causes economic growth in all the countries they studied. The finding was true for Ireland and the United Kingdom both in the long run and short run. The results also indicated that economic growth granger causes public expenditure for Greece and United Kingdom, when inflation is included. McCories and Chambers (2006) formulating models in continuous time offers a basis for correcting for the effects of temporal aggregation in observed discrete data through a discrete time analogue, in a way that does not rely on our positing a definite time unit in which the data are generated. In an empirical application, they showed that imposing these restrictions, and precisely, matters in testing for Granger causality. Their results complement those in the fixed-interval time aggregation literature, especially those recently obtained by Marcellino (1999) and Breitung and Swanson (2002).

Hooi
and Russell (2010) employed annual data for Malaysia from 1970 to 2008 to examine the causal relationship between economic growth, electricity generation, exports and prices in a multivariate model. Their first major finding of the study is that there is unidirectional Granger causality running from economic growth to electricity generation. The second major result is that neither the export-led nor handmaiden theories of trade are supported. The third main finding is that there is no causal relationship between prices and economic growth.
Nurudeen and Usman (2010) applied cointegration and error correction methods to determine the relationship between government expenditure and economic growth in Nigeria. Their results show that government total capital expenditure, total recurrent expenditures, and government expenditure on education have negative influence on economic growth. On the contrary, increasing government expenditure on transport and communication results to an increase in economic growth. Pradhan (2010) explores the nexus between transport infrastructure (road and rail), energy consumption and economic growth in India over the period 1970-2007.
He finds evidence of unidirectional causality from transport infrastructure to economic growth.
Siyan et al (2015) carry out cointegration test to determine the long run relationship between economic growth and road transportation in Nigeria. Their result show that road transportation has an impact in the economic development in Nigeria. From the result, economic growth in Nigeria depended on the level of good Electronic copy available at: https://ssrn.com/abstract=2939300 Alabi and Olarinde (2017) 47 and accessible road transportation and the level of road transport infrastructures that will complete the business activities and facilitate trade of Small and Medium scale Enterprises in Nigeria. A recent work, Harun (2016) examine the effect of health and social service sector growth on the flow of inbound health tourism between 2004:Q1 and 2015:Q4 by employing Granger causality and Johansen cointegration approaches. Their findings suggested that there is a long-run Granger causality from domestic health and social work expenditures to health tourism income whereas this is non-existence in the opposite direction. However, this study will investigate the granger causality between education sector growth (amount of gross domestic product in education sector) and socio-economic services and the direction of the relationship of the variables.

Materials and Method
The study is based on time series data obtained from National Bureau of Statistics bulletin Republic of Nigeria that covers the period from 1981 to 2015. The GDPt in the education sector (EGDP) is used as a proxy variable for economic growth of the education sector, which is reported in current basic prices. And the recurrent expenditure on socio-economic services i.e health (HEXPt), education (EEXPt), road & construction (RCEXPt) and transport & communication (TCEXPt).
The following model was used to investigate the relationship between education sector growth and socioeconomic services.
The model formulation of rooted in the theoretical framework as postulated by Bloch and Tang (2003), the model was specified as follows:  Now that we know the problems associated with non-stationary time series, the practical question is what to do. To avoid the spurious regression problem that may arise from regressing a nonstationary time series on one or more non-stationary time series, we have to transform non-stationary time series to make them stationary. Alternatively, to avoid spurious results co-integration analysis could be adopted, using nonstationary data, but all series have to be integrated to the same order. For the purpose of the study Johansen cointegration test would be used.

Ganger Causality
Granger causality test can be assess by regressing each variable on lagged values of itself and the other and it can be implemented as follows: where n, p, q, r, s denote the number of lagged variables, it  are error terms that are assumed to be normally distributed and white noise.

Discussion of Results
Time series plots for all variables employed in the study are provided in From the analysis, the unit root test was conducted to ascertain the stationarity of the data using both the Augmented Dickey Fuller (ADF) and the Philips-Perron (PP). The results of the test in table 1 show that all the variables in the model are stationary at 0.05 significant level. Knowing the unit-root properties of the variables, co-integration test was conducted to ascertain the long-run relationship between education sector growth and socio-economic services (education, health, road & construction and transport and communication). The Johansen co-integration test result in Table 2a and 2b reveal the empirical reality of four (4) co-integrating equations at 0.05 significant level. The hypothesis which states there is no long-run relationship between growth in education and socio-economic services is rejected at 0.05 significance level. Therefore, there is a long-run relationship between growth in growth in education sector and socio-economic services in Nigeria.
The empirical analysis from table 3 shows the estimation results of the equation used in the study, the Rsquared of 0.96 is the coefficient of determination indicates that 96 percent variation in education growth can be explain by the socio-economic services. The Adjusted R-squared is a standardized measure which controls the effect of any differences that may due to chance. The adjusted R-square of 95 percent suggests that the model in used is fit in explanation the variation in amount GDP in education sector put in consideration the losses of degree of freedom cause by the number of independent variables (education, health, that is the independent variables are statistically significant in determining the total variation in education sector growth in Nigeria. The t-statistic suggests that each parameter in the model employed in the study is statistically significant at 0.1 level of significance. According to the findings, the 2  statistics test rejects the null hypothesis of no Granger causality from HEXP and RCEGDP to EGDP, from EEXP and HEXP to RCEXP and from EEXP to EGDP, which indicate that there is bidirectional Granger causality from recurrent expenditure on health and road & construction to education sector growth, also that there is unidirectional Granger causality from recurrent expenditure on education and health to recurrent expenditure on transport & communication, and from recurrent expenditure on education to education sector growth, at 0.05 level of significance.

Conclusion
Granger (1988) pointed out that if co-integration exists in a pair of I (1) series, there must be causation in at least one direction. The study investigates the relationship between education sector growth and socioeconomic services, and to identify any possible direction of causality between them. The main result of the study shows that socio-economic service has much to contribute to education sector growth. Furthermore, it sends an important message to policymakers about the developments of socioeconomic sectors in providing potential as a service sector. Another finding of the study is that there are both bidirectional and unidirectional causality from education sector growth to recurrent expenditure on some socio-economic services in Nigeria. This can be explained by the economic contribution of education sector growth to the whole sector, which is still limited. However, the revenue collected through fees constitutes an insignificant proportion of the revenue of the institutions, using the fund allocated for socio-economic service appropriately may improve quality of education, education sector growth such that outbound education may also be reduce to minimum in Nigeria.