The link between inflation and its variability has been a topic of considerable interest and dispute, with theoretical disagreements and inconclusive empirical results. Empirical problems often arise from endogeneity and reverse causality. This paper reassesses the link through a system of simultaneous equations that addresses the reverse causality issue. Employing the identification through heteroskedasticity approach as an identification strategy and using a panel of 105 countries over the period 1960–2007, we find a two-way interaction between inflation and its variability. In particular, higher inflation increases inflation volatility, which is in line with the Friedman-Ball Hypothesis. Consistent with the Cukierman-Meltzer arguments, moreover, greater inflation volatility fuels inflation. The evidence is robust to alternative model specifications, time periods, and country characteristics.