Cooperation between Central Bank and Government

Michael Carlberg ()
Additional contact information
Michael Carlberg: Federal University of Hamburg

Chapter 14 in Strategic Policy Interactions in a Monetary Union, 2009, pp 1-5 from Springer

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

Keywords: Loss Function; Money Supply; Optimum Rate; European Central Bank; Minimum Loss (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-92751-8_14

Ordering information: This item can be ordered from
http://www.springer.com/9783540927518

DOI: 10.1007/978-3-540-92751-8_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().