The supply side effects of both the nominal interest rate (i.e., the cost channel) and import prices on inflation are very important for the design of monetary policy. However, the empirical identification of the cost channel (traditionally associated with the advance payment of wages) has ignored import prices. We start by deducting a New Keynesian Phillips Curve (NKPC) which shows that ignoring import prices in the estimation of the cost channel may lead to incorrect results. Taking this into account, we study the empirical relevance of the cost channel and import prices using the NKPC for the G7 countries. We test whether the estimation of the cost channel is affected when the price of imported inputs is considered; if it is relevant to extend the cost channel given that imports of final consumption goods are also paid in advance; if imports should be treated as inputs and/or consumption goods, and if there is an immediate or slow exchange rate pass-through. Empirical results indicate that the cost channel is present in imported consumption goods in particular, and import prices play an important role in explaining inflation dynamics.