We employ a recent time-varying cointegration test to revisit the usefulness of long-run money demand equations for the ECB, addressing the issue of their instability by means of a model evaluation exercise. Building on the results, we make a twofold contribution. First, we propose a novel stable money demand equation relying on two crucial factors: a speculative motive, represented by domestic and foreign price-earnings ratios, and a precautionary motive, measured by changes in unemployment. Second, we use the model to derive relevant policy implications for the ECB, since excess liquidity looks more useful for forecasting stock market busts than future inflation. Overall, this evidence points to (i) a possible evolution of the monetary pillar in the direction of pursuing financial stability and (ii) the exclusion of a sudden liquidity-driven inflationary burst after the exit from the prolonged period of unconventional monetary measures. JEL Classification numbers: E41, E52, C32. *The views here expressed are those of the authors and do not necessary reflect those of the Banca d'Italia or the Eurosystem.1 In contrast, Ireland (2004) has challenged this view and a number of more recent studies have included money in models aimed to monetary policy analysis (Zanetti, 2012;Benati et al., 2017).