How does public debt matter for inflation? If it is useful for the private sector to insure against idiosyncratic risk, as in recent Heterogenous Agents New Keynesian (HANK) models, then government debt expansions can be inflationary. This requires neither the absence of future fiscal consolidation, nor fiscal policy engaging in ex-ante redistribution or government consumption. After establishing these results using an analytically tractable model, I go on to demonstrate that in a full-blown quantitative 2-asset HANK model with active monetary policy, the time path of government debt can matter substantially for inflation persistence following inflationary supply shocks. Thus, according to HANK, even “passive” fiscal policy has important implications on how central banks can steer inflation.