Abstract This paper estimates the New Keynesian Phillips Curve (NKPC) with imperfect exchange rate pass-through (alternatively, deviations from the law of one price). Our results describe the nature of inflation dynamics and business cycles under imperfect pass-through, with importance of both domestic price rigidity and import price rigidity for the US and other four open economies. The estimates of structural parameters of the import price and domestic price rigidities are not same and affect inflation-output gap elasticity and inflation-law of one price gap elasticity. The results yield implications for the stabilisation of real activity (also domestic inflation) compared to the deviations from the law of one price.