Monetary Policy in Europe B

Michael Carlberg ()
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Michael Carlberg: Federal University of Hamburg

Chapter 16 in Strategic Policy Interactions in a Monetary Union, 2009, pp 1-8 from Springer

Abstract: The model of unemployment and inflation can be characterized by a system of four equations: (1) $${\rm u}_1 = {\rm A}_1 - {\rm M}$$ (2) $${\rm u}_2 = {\rm A}_2 - {\rm M}$$ (3) $${\rm \pi }_1 = {\rm B}_1 + {\rm M}$$ (4) $${\rm \pi }_2 = {\rm B}_2 + {\rm M}$$ The targets of the European central bank are zero inflation and zero unemployment in each of the member countries. The instrument of the European central bank is European money supply. There are four targets but only one instrument, so what is needed is a loss function. We assume that the European central bank has a quadratic loss function: (5) $$L = {\rm \pi }_1^2 + {\rm \pi }_2^2 + {\rm u}_1^2 + {\rm u}_2^2$$ L is the loss to the European central bank caused by inflation and unemployment in each of the member countries. We assume equal weights in the loss function. The specific target of the European central bank is to minimize the loss, given the inflation functions and the unemployment functions. Taking account of equations (1), (2), (3) and (4), the loss function of the European central bank can be written as follows: (6) $${\rm L} = ({\rm B}_{\rm 1} + {\rm M})^2 + ({\rm B}_{\rm 2} + {\rm M})^2 + ({\rm A}_{\rm 1} - {\rm M})^2 + ({\rm A}_{\rm 2} - {\rm M})^2$$ Then the first-order condition for a minimum loss is: (7) $$4{\rm M} = {\rm A}_1 + {\rm A}_2 - {\rm B}_1 - {\rm B}_2$$ Here M is the optimum level of European money supply. An increase in A1 requires an increase in European money supply. And an increase in B1 requires a cut in European money supply.

Keywords: Monetary Policy; Loss Function; Member Country; European Central Bank; Policy Response (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-92751-8_16

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DOI: 10.1007/978-3-540-92751-8_16

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