Economic Models - Convex Optimization
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Economic Models - Convex Optimization

Economic Models - Convex Optimization Economic Models - Convex Optimization

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4.1. Monetary Responses The Advantages of Fiscal Leadership in an Economy 77 For monetary policy, it is widely argued that the authorities’ decisions can best be modeled by a Taylor rule 9 : r t = ρr t−1 + αE t π t+k + βgap t+h α, β, ρ ≥ 0 (1) where k, h represent the authorities’forecast horizon 10 and may be positive or negative. Normally, α>1 will be required to avoid indeterminancy: that is, arbitrary variations in output or inflation, as a result of unanchored expectations in the private sector. The relative size of α and β then reveals the strength of the authorities’ attempts to control inflation vs. income stabilization; and ρ their preference for gradualism. I set h = 0 in Eq. (1), since monetary policy appears not to depend on the expected output gaps (Dieppe et al., 2004). In order to obtain an idea of the influence of fiscal policies on monetary policy, I include some Taylor rule estimates — with and without fiscal variables — in Table 1. They show such rules for the United Kingdom and the Eurozone since 1997 and 1999, respectively, the dates when new policy regimes were introduced. The Eurozone has been included to emphasize the potential contrast between fiscal leadership in the United Kingdom, and the lack of it in Europe. 4.2. Different Types of Leadership Conventional wisdom would suggest that Europe has either monetary leadership or independent policies, and hence policies which are either jointly dependent in the usual way, or which are complementary and mutually supporting. The latter implies that the monetary policy tends to expand/contract whenever fiscal policy needs to expand or contract — but not necessarily vice versa, when money is expanding or contracting and is sufficient to 9 Taylor (1993b). One can argue that the policy should be based on fully optimal rules (Svensson, 2003), of which Eq. (1) will be a special case. But, it is hard to argue that policy makers actually do optimize when the additional gains from doing so may be small and when the uncertainties in their information, policy transmissions, or the economy’s responses may be quite large. In practice, therefore, the Taylor rule approach is often found to fit central bank behavior better. 10 In principle, k and h may be positive or negative: positive if the policy rule is based on future-expected inflation, to head off an anticipated problem, as in the Bank of England. But negative if interest rates are to follow a feedback rule to correct past mistakes or failures.

78 Andrew Hughes Hallet control inflation on its own. This is a weak form of monetary leadership in which fiscal policies are an additional instrument for use in cases of particular difficulty, rather than the policies in a Nash game with conflicting aims that need to be reconciled. More generally, leadership implies complimentarity among policy instruments in the leader’s reaction function, but conflicts among them in the follower’s responses. A weak form of leadership also allows for independence among instruments in the leader’s policy rules. Thus, monetary leadership would imply some complimentarity (or independence) in the Taylor rule, but conflicts in the fiscal responses.And fiscal leadership would mean complimentarity or independence in the fiscal rule, but conflicts in the monetary responses. Evidently, from Section 3, we might expect Stackelberg leadership (with fiscal policy leading) in the UK, but the opposite in the Eurozone. 4.3. Observed Behavior The upper equations in each panel of Table 1 yield the standard results for the monetary behavior in both the United Kingdom and the Eurozone. Both monetary authorities have targeted expected inflation more than the output gap since the late 1990s — and with horizons of 18–21 months ahead. The European Central Bank (ECB) has been more aggressive in this respect. But, contrary to conventional wisdom, it was also more sensitive to the output gap and had a longer horizon and less policy inertia. However, if we allow monetary policies to react to the changes in fiscal stance, we get different results (the lower equations). Here, we see that the UK monetary decisions may take fiscal policy into account, but the effect is not significant or well defined. However, this model of monetary behavior does imply more activist policies, a longer forecast horizon (up to two years as the Bank of England claims) and greater attention to the output gap — the symmetry in the UK’s policy rule. And to the extent that fiscal policy does have an influence, it would be as a substitute (or competitor) for monetary policy — fiscal deficits lead to higher interest rates. This is potentially consistent with fiscal leadership, since this form of leadership can allow independence or complimentarity between instruments in the leader’s rule. We need to check the fiscal reaction functions directly. The lack of significance for the debt ratio is easily understood, however. Since this is a declared long-run objective of the fiscal policy, it would not be necessary for the monetary policy to take it into account. So far, the evidence could

78 Andrew Hughes Hallet<br />

control inflation on its own. This is a weak form of monetary leadership in<br />

which fiscal policies are an additional instrument for use in cases of particular<br />

difficulty, rather than the policies in a Nash game with conflicting<br />

aims that need to be reconciled.<br />

More generally, leadership implies complimentarity among policy<br />

instruments in the leader’s reaction function, but conflicts among them in<br />

the follower’s responses. A weak form of leadership also allows for independence<br />

among instruments in the leader’s policy rules. Thus, monetary<br />

leadership would imply some complimentarity (or independence) in the<br />

Taylor rule, but conflicts in the fiscal responses.And fiscal leadership would<br />

mean complimentarity or independence in the fiscal rule, but conflicts in<br />

the monetary responses. Evidently, from Section 3, we might expect Stackelberg<br />

leadership (with fiscal policy leading) in the UK, but the opposite in<br />

the Eurozone.<br />

4.3. Observed Behavior<br />

The upper equations in each panel of Table 1 yield the standard results for<br />

the monetary behavior in both the United Kingdom and the Eurozone. Both<br />

monetary authorities have targeted expected inflation more than the output<br />

gap since the late 1990s — and with horizons of 18–21 months ahead. The<br />

European Central Bank (ECB) has been more aggressive in this respect.<br />

But, contrary to conventional wisdom, it was also more sensitive to the<br />

output gap and had a longer horizon and less policy inertia.<br />

However, if we allow monetary policies to react to the changes in fiscal<br />

stance, we get different results (the lower equations). Here, we see that the<br />

UK monetary decisions may take fiscal policy into account, but the effect is<br />

not significant or well defined. However, this model of monetary behavior<br />

does imply more activist policies, a longer forecast horizon (up to two years<br />

as the Bank of England claims) and greater attention to the output gap —<br />

the symmetry in the UK’s policy rule. And to the extent that fiscal policy<br />

does have an influence, it would be as a substitute (or competitor) for monetary<br />

policy — fiscal deficits lead to higher interest rates. This is potentially<br />

consistent with fiscal leadership, since this form of leadership can allow<br />

independence or complimentarity between instruments in the leader’s rule.<br />

We need to check the fiscal reaction functions directly. The lack of significance<br />

for the debt ratio is easily understood, however. Since this is a<br />

declared long-run objective of the fiscal policy, it would not be necessary<br />

for the monetary policy to take it into account. So far, the evidence could

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