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• The oil price-inflation pass-through is analyzed using a wavelet coherency analysis. • The oil price-inflation pass-through has decreased during the analyzed period. • The oil price-inflation relationship varies across frequencies. This paper analyzes the oil price-inflation pass-through by studying the relationship between oil prices and U.S. Consumer Price Index (CPI) over the period January 1871–June 2018, at different frequencies, using a wavelet coherency analysis. In this long period of time characterized by significant structural changes, which have changed the role of fossil fuel prices (specially, crude oil) relative to renewable and alternative fuels, our main results suggest that the relationship between oil prices and CPI has changed over the analyzed time period, implying a decrease in the oil price- inflation pass-through over time. Furthermore, this relationship also varies across frequencies, suggesting that the evidence of oil price-inflation pass-through with oil prices leading CPI is weaker in the short-run. [ABSTRACT FROM AUTHOR]