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have a suboptimally low degree. For Denmark, Ireland, the Netherlands and the United
States, it is fair to conclude that these countries have more or less an optimal degree of
independence.
Finally, it should be mentioned that both our theoretical and empirical model can be
extended with other economic and political determinants of central bank independence.
One could, for example, extend the model with the degree of openness of a country to
comply with differences between small and large countries. These extensions constitute
our research agenda for the future.
APPENDIX A. THE DERIVATION OF THE EXPECTED VALUE OF SOCIETY’S
LOSS FUNCTION UNDER AN ARBITRARY MONETARY POLICY REGIME
In this Appendix, following Rogoff (1985), pp. 1175—1176, we develop a notation for
evaluating the expected value of society’s loss function under any arbitrary monetary
policy regime "A", Et—1 LtA (equation (3.1) of the text). Unemployment under regime A is
given by
uA = u - ɪɪe (PtA-Et_iPtA + Mt) (A∙1)
Squaring and taking expectations yields
Ebι(u^)2 = u2÷E,-ι[τμtβ ÷ τ1β (pA-EtιPtA)]2 (A∙2)
The price level under regime A can be expanded as
PA = ptA + (PtA -Et-ιPtA) (A∙3)
where ptA is the mean (expected) price level in period t. Squaring and taking expectations,
in turn, yields
E,.i (PtA)2 = (PA)2 + Em(p,α-E,-ipa)2 (A∙4)
The expected value of society’s loss function under regime A is
Et-1LA = ɪ E,√pA)2 ÷ -2 E. ) (A∙5)
Substituting (A∙2) and (A∙4) into (A∙5), one obtains equation (3∙1) of the text∙