Cooperation between European Central Bank,German Government, and French Government

Michael Carlberg ()
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Michael Carlberg: Federal University of Hamburg

Chapter 26 in Strategic Policy Interactions in a Monetary Union, 2009, pp 1-10 from Springer

Abstract: The model of unemployment, inflation, and the structural deficit can be characterized by a system of six equations: (1) $${\rm u}_{\rm 1} {\rm = A}_{\rm 1} - {\rm M} - {\rm G}_{\rm 1}$$ (2) $${\rm u}_{\rm 2} {\rm = A}_{\rm 2} - {\rm M} - {\rm G}_{\rm 2}$$ (3) $${\rm \pi }_{\rm 1} {\rm = B}_{\rm 1} + {\rm M} + {\rm G}_{\rm 1}$$ (4) $${\rm \pi }_{\rm 2} {\rm = B}_{\rm 2} + {\rm M} + {\rm G}_{\rm 2}$$ (5) $${\rm s}_{\rm 1} = {\rm G}_1 - {\rm T}_1$$ (6) $${\rm s}_{\rm 2} = {\rm G}_2 - {\rm T}_2$$ The policy makers are the European central bank, the German government, and the French government. The targets of policy cooperation are zero inflation, zero unemployment, and a zero structural deficit in each of the member countries. The instruments of policy cooperation are European money supply, German government purchases, and French government purchases. There are six targets but only three instruments, so what is needed is a loss function. We assume that the policy makers agree on a common loss function: (7) $${\rm L} = {\rm \pi }_{\rm 1}^{\rm 2} + {\rm \pi }_{\rm 2}^{\rm 2} + {\rm u}_{\rm 1}^{\rm 2} + {\rm u}_{\rm 2}^{\rm 2} + {\rm s}_{\rm 1}^{\rm 2} + {\rm s}_{\rm 2}^{\rm 2}$$ L is the loss caused by inflation, unemployment, and the structural deficit in each of the member countries. We assume equal weights in the loss function. The specific target of policy cooperation is to minimize the loss, given the inflation functions, the unemployment functions, and the structural deficit functions. Taking account of equations (1) to (6), the loss function under policy cooperation can be written as follows: (8) $${\rm L} = ({\rm B}_1 + {\rm M} + {\rm G}_1 )^2 + ({\rm B}_2 + {\rm M} + {\rm G}_2 )^2 + ({\rm A}_1 - {\rm M} - {\rm G}_1 )^2 + ({\rm A}_2 - {\rm M} - {\rm G}_2 )^2 + ({\rm G}_1 - {\rm T}_1 )^2 + ({\rm G}_2 - {\rm T}_2 )^2$$ Then the first-order conditions for a minimum loss are: (9) $$3{\rm G}_{\rm 1} = {\rm A}_1 + {\rm T}_1 - {\rm B}_1 - 2{\rm M}$$ (10) $$3{\rm G}_{\rm 1} = {\rm A}_1 + {\rm T}_1 - {\rm B}_1 - 2{\rm M}$$ (11) $$3{\rm G}_{\rm 2} = {\rm A}_2 + {\rm T}_2 - {\rm B}_2 - 2{\rm M}$$ Equation (9) shows the first-order condition with respect to European money supply. Equation (10) shows the first-order condition with respect to German government purchases. And equation (11) shows the first-order condition with respect to French government purchases.

Keywords: Loss Function; Member Country; European Central Bank; Policy Response; Demand Shock (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_26

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DOI: 10.1007/978-3-540-92751-8_26

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