This paper investigates the relationship between government expenditure and economic growth in Ethiopia to test Wagner’s Law which postulates that as real income increases there is a tendency for the share of public expenditure to increase relative to national income. Using the bounds test approach to cointegration, the paper finds robust evidence of a long-run relationship between government expenditure and GDP. Using four long-run estimators, we obtained elasticities ranging from 1.73 to 1.79, implying that a 1% increase in income leads to a 1.73–1.79% increase in government expenditure. Applying a modified version of the Granger causality test, we also found a unidirectional causality running only from GDP to government expenditure thus supporting the Wagnerian hypothesis of an expanding public sector. Since there was no causality running from government expenditure to income, the evidence suggests that the Keynesian view that government expenditure can be an effective policy instrument for promoting economic growth in Ethiopia was not supported. Therefore, there is a need for making fiscal policy as a stabilizer to enhance economic growth.