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The Political Economy of Sovereign Default

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Sebastian Hohmann

Annexe

I. Algebra

Texte intégral

1Subheadings are as in the thesis. Each derivation is identified with the number of the equation in the main text.

2.2 The Winning Coalition’s reaction to a default

(1) Utility of a member of W loyal to a defaulting government

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(2) Utility of a member of W deposing a defaulting government and once again member of W

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(3) Utility of a member of W deposing a defaulting government and shut out of the new W

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(4) Expected utility of a member of W deposing a defaulting government

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(6) The deposition condition

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2Since 0 < δ < 1, I can multiply both sides by 1 − δ without changing the direction of the in- equality. Hence

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(7) An increase in Selectorate size

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(8) An increase in the size of the Winning Coalition

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2.3 The Government

(9) Expected utility of a government honouring its debt

3A government honouring its debt receives a utility of Ψ today and incurs a cost of repayment of θ. In the next period, it can then again choose to default or not. The utility from this choice-situation is gC. Since the outcome of θ next period cannot be foreseen, the government will receive a utility of gH if it again honours its debt and gD if it defaults. The probabilities of these choices are determined by the realization of θ. For θ ≤ θT, the government will choose to repay. For θ > θT default is the better option. Thus:

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(10) Utility of a defaulting government

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(13) Threshold cost of repayment

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Section 4 Lenders and interest rates

(16) The competitive interest rate

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(17) An increase in the risk of default

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(18) Probability of default in terms of threshold cost of repayment

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(19) Interest rate in terms of threshold cost of repayment

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(20) The effect of higher threshold costs of repayment on interest rates1

  • 1 Assuming that f() is continuous at (...)

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Notes

1 Assuming that f(Image 100000000000001F0000002BA7FEF3EE.png) is continuous at Image 100000000000001F0000002BA7FEF3EE.pngT, we can use the fondamental theorem of calculus. See Ron C. Mittelhammer, 1999. Mathematical Statistics for Economies and Business, Springer, New York, p. 52.

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