The existence of menu costs of price adjustment is one of the leading explanations for the delayed response of prices to changes in economic conditions. This paper investigates the relationship between menu costs of price adjustment at the micro level and aggregate inflation dynamics. For that purpose, it introduces a measure of frictionless inflation that estimates counterfactual inflation in the absence of menu costs. The measure is based on a novel smoother for a state-space representation that describes pricing dynamics at the micro level as implied by a random menu cost model. Combining the smoother with rich micro price data underlying the UK CPI, I produce a measure of frictionless inflation for the UK at a monthly frequency from 1997 to 2018. The analysis of that measure yields three main findings: (i) menu costs matter for aggregate inflation dynamics, but their importance decreased over time; (ii) the response of frictionless inflation to a monetary policy shock is at odds with the monetary transmission mechanism from the basic new Keynesian model and (iii) frictionless inflation contains useful information to forecast CPI inflation.
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