Economic Models - Convex Optimization
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Economic Models - Convex Optimization

Economic Models - Convex Optimization Economic Models - Convex Optimization

convexoptimization.com
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10.03.2015 Views

The Advantages of Fiscal Leadership in an Economy 99 Table 4. Data for the deficit rule calculations. α β γ s θ φ λ g 2 France 0.294 0.500 0.570 1 0 1.147 0.25 Germany 0.176 0.533 0.430 1 0 1.094 0.25 Italy 0.625 0.433 0.600 1 0 1.271 0.25 Netherlands 0.625 0.489 0.533 1 0 1.306 0.25 Sweden 0.333 0.489 0.533 1 0 1.163 1 New Zealand 0.244 0.400 0.850 1 0 1.098 1 UK 0.385 0.133 0.580 1 0 1.038 1 United States 0.278 0.467 1.150 1 0 1.130 0.5 Canada 0.200 0.400 0.850 1 0 1.080 0.5 Switzerland 0.323 0.489 0.533 1 0 1.158 0.5 security sectors in the Netherlands and Sweden. Similarly, θ is set to give a debt target somewhat below each country’s 1998 debt ratio and the SGP’s 60% limit. Likewise, λ g 2 was set to imply a low, high, or medium commitment to debt/deficit limits, as reflected in actual behavior in 2004. Finally, I have set λ g 1 = 1 in each country to suggest that governments, if left to themselves, are equally concerned about inflation and output stabilization. For Table 4, I suppose that the deficit that remains after growth effects and new discretionary taxes are accounted for will be spent (s = 1), and that the medium-term deficit target is zero (θ = 0). Appendix B: Derivation of the Change in Fiscal Stance Between Regimes The expected value of s(by t − τ t ) under fiscal leadership and simultaneous moves can be obtained by inserting values first from Eq. (29), and then from Eqs. (31) and (32), respectively. Taking the expected values, this yields zero and φλ cb∗ /(α 2 γ) > 0 in each case. Applying this result to Eq. (4), it shows that the expected change in output between regimes, which we know to be zero, is (β − γ)m − βλ cb∗ /(αλ g 1 ) + γ[s(by − τ)] = 0. Hence, m ={γ[s(by − τ)] + βλ cb∗ /(αλ g 1 )}/(β − γ) which, given the change in s(by t − τ t ), is positive, if β>γ. In this case, the simultaneous move regime is unambiguously more expansionary, and will run larger deficits, than a regime with fiscal leadership. But, since

100 Andrew Hughes Hallet γ/(β − γ) > 1, this result may not follow if β

100 Andrew Hughes Hallet<br />

γ/(β − γ) > 1, this result may not follow if β

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