This paper investigates whether the persistence and the time‐varying nature of trend inflation can explain the persistence of inflation in Australia — that is, whether it can explain the apparent need for backward‐looking inflation term(s) in the new Keynesian Phillips curve (NKPC) estimated using Australian data. We derive and estimate an extended open‐economy NKPC equation, accounting explicitly for time‐varying trend inflation. Our preferred, best‐fitting estimates based on the closed‐form specification with two indexation lags indicate a significant degree of indexation to past inflation. Thus, in contrast to the result for the US economy, our estimates suggest that accounting for time variation in trend inflation in the NKPC cannot explain away the inertia in the Australian inflation data. The estimates suggest that lagged inflation and future expectations of inflation enter the NKPC with almost equal weights. Finally, notwithstanding the previous results, we find a marked decline in the role of the backward‐looking inflation terms since the adoption of an inflation‐targeting regime by the Reserve Bank in 1993.