At the margin, the impact on the probability of debt stabilization of assuming more
risk must be equal to the impact of reducing the expected cost of debt servicing. Hence,
the marginal increase in probability can be used to price risk against the expected cost of
debt service and thus find the optimal combination along the trade off between cost and
risk minimization. For example, equation (15) shows that issuing bonds indexed to the
Selic rate is optimal until the uncertainty of the Selic rate raises the probability of failure
as much as paying the term premium on fixed-rate bonds.
Therefore, the objective of debt stabilization offers a solution to the identification of the
optimal debt structure which is independent of the government’s preferences towards risk.
This is because both the risk and the expected cost of debt service affect the probability of
debt stabilization.
To derive an explicit solution for the the optimal shares of the various types of debt
we must specify the probability density function, φ(X). Since this function cannot be
estimated, we take a linear approximation of φ(X) over the range of bad realizations,
X>0, of the fiscal adjustment.7 This implies a triangular probability density function
equal to
Xe - X
Φ(X ) = -x-2- (18)
where X>0and X is the worst possible realization of the fiscal adjustment.
In fact, the triangular density is the linear approximation of any density function de-
creasing with - (for ->0); it implies that bad realizations of the fiscal adjustment are
less likely to occur the greater is their size.
Substituting equations (18) and (2)-(4) in the first order conditions (15)-(17) yields the
optimal shares of Selic rate indexed debt, s*, dollar denominated debt, q*, and price-indexed
debt, h*:
s*
(ηy + Bt) Cov(yt+1it+1)
Bt Var(it+ι)
(η∏ + Bt) Cov(∏t+1it+1) *Cov(et+1it+1)
--——∖— — q---/—∖—
Bt V ar(it+1) V ar(it+1)
(19)
h* Cov(∏t+1it+1)
Var(it+1)
+ TPt-
2P Et(At+ι — ∆Bt+ι)
— ∖2∕'r BtVar(it+ι)
* = (Пу + Bt) Cov(yt+1et+1)
Bt Var(et+1)
(ηπ + Bt) Cov(πt+1et+1) * Cov(et+1it+1)
--— s -----------
Bt V ar(et+1) V ar(et+1)
(20)
h* Cov(∏t+1et+1)
Var(et+ι)
√2Pr Et(At+ι — ∆BtT+ι)
+ Fp t-------/ ----~------7-----7----
1 — ∖2∕'r BtVar(et+ι)
h* = (Пу + Bt) Cov(yt+Iπt+1)
Bt Vαr(∏t+ι)
(η∏ + Bt) *
— q
Cov(et+ι∏t+ι)
Var(∏t+ι)
(21)
s∙ Cov(πt+1i<+1) + IPt-
Var(∏t+ι) 1
2Pr_ Et(At+ι — ∆Btτ+ι)
√2Pr BtVar(∏t+ι)
7We assume that the fiscal adjustment is expected to stabilize the debt, so that At+1 > BtT+1 - Bt .
More intriguing information
1. Wounds and reinscriptions: schools, sexualities and performative subjects2. The name is absent
3. Prizes and Patents: Using Market Signals to Provide Incentives for Innovations
4. NATURAL RESOURCE SUPPLY CONSTRAINTS AND REGIONAL ECONOMIC ANALYSIS: A COMPUTABLE GENERAL EQUILIBRIUM APPROACH
5. The name is absent
6. Multimedia as a Cognitive Tool
7. Word Sense Disambiguation by Web Mining for Word Co-occurrence Probabilities
8. Auctions in an outcome-based payment scheme to reward ecological services in agriculture – Conception, implementation and results
9. The name is absent
10. Exchange Rate Uncertainty and Trade Growth - A Comparison of Linear and Nonlinear (Forecasting) Models