AbstractThe role of money in the design and conduct of monetary policy has reemerged as an important issue in both advanced and developing economies, especially since the 2007 global financial crisis. A growing body of recent literature suggests that the causal relationship between money supply growth and inflation remains intact across countries and over time and that this relation is not conditional on the stability of the money‐demand function or whether money is endogenous or exogenous. Moreover, critical for a rule‐based monetary policy is the presence of a long‐run stable money‐demand function, rather than a short‐run money‐demand model that may exhibit instability for many reasons, including problems with estimating a money‐demand model with high‐frequency data. Provided that a stable money‐demand function exists, it could be useful to establish long‐run equilibrium relations among money, output, prices, and exchange rates, as the classical monetary theory suggests. Within this analytical framework, this paper addresses the question of whether money has any role in the conduct of monetary policy in Australia. The conventional wisdom is that the money‐demand function in Australia has been unstable since the mid‐1980s due to financial deregulation and reforms; this led to a change in the strategy of monetary policy for price stability in the form of inflation targeting that ignores money insofar as inflation and its control are concerned. This paper reports empirical findings for Australia, obtained from a longer quarterly data series over the period 1960Q1–2015Q1, which suggest that instability in the narrow‐money‐demand function in Australia was primarily due to the exclusion of variables which have become important in the deregulated environment since the 1980s. These findings are confirmed by an expanded form of the narrow‐money‐demand function that was found stable over the past two decades, although it experienced multiple structural breaks over the study period. The paper draws the conclusion that abandoning the monetary aggregate as an instrument of monetary policy in Australia, under a rule‐based monetary policy such as inflation targeting, cannot be justified by instability in the money‐demand function or even by lack of a causal link between money supply growth and inflation.