Evidence in the literature points to a puzzling initial increase in inflation after an increase in nominal interest rates. This can be explained by the fact that firms have to borrow money to pay wages in advance, i.e., by the cost channel. In this paper, the study of the cost channel is extended to an open economy with sticky prices. It is shown that a broadened concept of the cost channel has significant implications for the economy's dynamics and monetary policy, and also contributes to explain some interesting empirical evidence.\ud Supply side effects of interest rates and import prices on inflation have important implications for monetary policy. Usually such effects are estimated using the New Keynesian Phillips Curve (NKPC). However, the estimation of the cost channel maybe distorted when import prices are omitted from that curve. To address this issue, we estimate empirically the NKPC for domestic and CPI inflations. In relation with this, we also study if imports of consumption goods are paid in advance, whether there is an immediate pass-through of exchange rates, and if imports should be treated as final consumption goods and/or as inputs in production.\ud Another concern of monetary policy in a monetary union is inflation differentials, since they can undermine the success of the union. Against this background, our goal is to explore the determinants of inflation differentials in twelve euro area countries, focusing on the role of the business cycle. On one hand, convergence of inflation rates and business cycles is analysed with both an unobserved component model estimated with the Kalman filter and a common factor approach. On the other hand, an econometric analysis of the determinants of inflation differentials is performed
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