The study was conducted through the application of cointegration regression test was conducted to ascertain the long run relationship and elasticity for the degree of responsiveness of GDP to changing government expenditure using a data series acquired from the world data bank for the period 1990-2014. Based on the results gained from the analyses, the results of the unit root propose that all the variables in the model are stationery and the causality test suggests that GDP causes government expenditure. The results obtained from the cointegration test revealed Government Expenditure (GE) is not equal to zero (insignificant) from the correlation analysis, indicative of a positive relationship between GE and GDP which is evidence that GDP and Government Expenditure (GE) move in the same direction. An increase in one affect the other positively. Conclusively, the results discovered a positively significant relationship between Government Expenditure and GDP.