Observed random walk behaviour of a tax rate does not necessarily support the tax smoothing hypothesis though the latter implies the former. This article presents a direct test of tax smoothing by showing that if the tax smoothing hypothesis holds then the future tax rate should cointegrate with the current permanent government expenditure rate even though the tax rate is a random walk. This test is a direct and robust test of a number of ‘random walk models’ available in the literature. This procedure also enables us to differentiate among ‘strong tax smoothing’, ‘weak tax smoothing’ and ‘no-tax smoothing’, all of which are consistent with the random walk behaviour of a tax rate. Application of this test to Australia, Canada, Italy, Japan, the Netherlands, New Zealand, the UK and the US show evidence in support of weak forms of tax smoothing. [ABSTRACT FROM PUBLISHER]