Why Money Talks and Wealth Whispers: Monetary Uncertainty and Mystique
Journal article by Sylvester Eijffinger, Marco Hoeberichts, Eric Schaling; Journal of Money, Credit & Banking, Vol. 35, 2003
Journal Article Excerpt
Why money talks and wealth whispers: monetary uncertainty and mystique by Sylvester Eijffinger , Marco Hoeberichts , Eric Schaling In a comment on our recent paper in this journal (Eijffinger, Hoeberichts, and Schaling 2000) (hereafter EHS), Beetsma and Jensen (hereafter B J) claim that Propositions 3 and 4 of our paper are incorrect due to minor computational errors. In this reply we correct the computational mistakes and derive the correct Propositions 3 and 4. We also show that the results derived in EHS, including the main result that a country that faces large supply shocks in relation to its output target may be better off with a central bank that has uncertain preferences, still stand. 1. RECAPITULATION OF THE ARGUMENT EHS show that increasing monetary policy uncertainty increases the mean and the variability of inflation and may decrease the variability of output. Thus monetary policy uncertainty may be good for social welfare if the beneficial effects of output variability are larger than the harmful effects on inflation and its variability. This result remains intact in spite of BJ who, however, are right on minor computational points, notably with respect to the Taylor-expansions used to approximate the variances of inflation and output. More specific, the expected loss depends on three components [[pi].sup.e], Var [pi], and Var y. The expression for [[pi].sup.e] is given in EHS Equations (7) and (8). Throughout this reply we use the same equation numbers as in EHS. The correct versions of the expressions for the variances of inflation and output can be found below: (15) [MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]. (16) [MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]. Note that these equations are more general than BJ's equations (A. 11) and (A. 13), (1) as they focus only on the case where society's credibility problem is absent (z = 0). If we set z = 0, our equations collapse to BJ's expressions. As said before, the crucial effect on social welfare is through a lower output variance. If and only if the following condition is satisfied, then higher monetary policy uncertainty decreases the variability of output. (D.2) [z.sup.2]/[[sigma].sup.2.[epsilon]]<[a.sup.2](2a - [b.sup.2])/[b.sup.2][(a + [b.sup.2]).sup.2], where we have used the correct Taylor-expansions given in Equations (15) and (16). This implies that our third proposition now reads: PROPOSITION 3: If and only if [z.sup.2]/[[sigma].sup.2.[epsilon]]<[a.sup.2](2a - [b.sup.2])/[b.sup.2][(a + [b.sup.2]).sup.2], the variance of output is minimized at a positive level of preference uncertainty. A lower variance of output is a necessary condition for higher monetary policy uncertainty to increase social welfare. However, in order to increase social welfare the lower output variability has to overcompensate for the higher mean and variability of inflation. For that to be the case, a necessary and sufficient condition is (D.3) [z.sup.2]/[[sigma.sup.2.sub.[epsilon]]<[a.sup.3](2a - [b.sup.2] - 3[alpha]/[(a + [b.sup.2].sup.2](a[b.sup.2] + 3a[alpha] + 2[b.sup.2][alpha]). This implies that our fourth proposition now reads: PROPOSITION 4: It is optimal for society to have a central bank with uncertain preferences ([[sigma].sup.*2.sub.x] > 0) if and only if [z.sup.2]/[[sigma].sup.2.sub.[epsilon]]<[a.sup.3(2a - [b.sup.2] - 3[alpha]/[(a + [b.sup.2]).sup.2](a[b.sup.2] + 3a[alpha] + 2[b.sup.2][alpha]). The intuition behind Proposition 4 is the following. The benefits of higher monetary policy uncertainty arise through its benefits for stabilization policy. In order for this to overcompensate the harmful effects on credibility issues (mean and variance of inflation), society needs to have a more pressing need for stabilization (high [[sigma].sup.2.sub.[epsilon]]) than a need for credibility (measured by z). Note that the intuition of this result is exactly as in EHS. Thus, the incorrect Taylor expansions used in the original version of our paper to derive Equations (15) and (16) have no bearing on the validity of the general results. 2. CONCLUSION We are grateful to BJ for pointing out some computational errors in our paper, notably with respect to the second-order Taylor expansions used in deriving Equations (15) and (16). However, as we have shown in this reply, with slightly modified conditions on the parameters, the results of EHS still stand. Central bank preference uncertainty may be desirable if the beneficial effects on output variability dominate the detrimental effects on the level and variability of inflation. NOTES (1.) Unfortunately, BJ provide the key equations only in their technical appendix (not published). However, when the central bank targets the natural rate of output (z = 0), our Equations (15) and (16) collapse to BJ's Equations (A. 11) and (A. 13), respectively. LITERATURE CITEDBeetsma, Roel, and Henrik Jensen. (2003). "Comment on `Why Money Talks and Wealth Whispers: Monetary Uncertainty and Mystique.'" Journal of ... |
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