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We develop and test a New Keynesian model of inflation dynamics based on the presence of idiosyncratic shocks to firms’ marginal costs. We show that if firms ignore economy-wide influences on their marginal costs, inflation will exhibit a greater degree of inertia than the conventional New Keynesian model suggests. Credible disinflationary policies are likely to be accompanied by recessions rather than booms and the economy can, in principle, respond to monetary shocks in a way that is consistent with the stylised facts. The model imposes testable restrictions which cannot be rejected using quarterly data for the UK and the US. Finally we demonstrate, through a series of simulation experiments, the plausibility of the model’s central assumption that firms will rationally choose to ignore economy-wide influences on their costs.