The ultimate determinants of central bank independence

25

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", E_t—1 L_t^A (equation (3.1) of the text). Unemployment under regime A is
given by

^uA = ^u - ɪɪe (Pt^A-Et_iPt^A + M_t⁾                                                  (A∙¹)

Squaring and taking expectations yields

E_bι(u^)2 = ^u2÷E,-ι[_τμt_β ÷ _τ1_β (pA-EtιPtA)]2                                     (A∙2)

The price level under regime A can be expanded as

PA = ^ptA + (PtA -Et-ιPtA)                                                                        (A∙³)

where p_tA is the mean (expected) price level in period t. Squaring and taking expectations,
in turn, yields

E,.i (PtA)² = (PA)² + E_m(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∙

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