that the overall effect of a larger debt reduction is to reduce the impact of the expected cost
differential.) Finally, a greater variance of the return on a given debt instrument reduces
the importance and the impact of interest cost differentials on its optimal share as much
as it reduces the relevance of its hedging characteristics. For example, equation (20) points
out that the share of bonds denominated or indexed to foreign currencies should increase
with the excess return, FPt. However, as the variance of the exchange rate increases, cost
considerations become less important for the choice of dollar denominated bonds.
4. Estimating the optimal debt structure
The optimal debt composition depends on the sensitivity of the primary surplus to
unexpected variations in output and inflation, ηy and ηπ , on the reduction in the debt ratio,
and on the probability of debt stabilization as perceived by the government. At the end of
October 2003, mainly because of lower nominal GDP growth, the net public debt was 57.2%
of GDP, one percentage point higher than in 2002. Although the debt ratio is currently
above the “optimistic” scenario presented in “Politica Economica e Reformas Estruturais”
(Ministerio da Fazenda, April 2003), the debt should stabilize next year at around 56% of
GDP. Therefore the expected debt reduction is assumed to be 1%. The probability that
the stabilization plan may fail is tentatively set at 2% which corresponds to a maximum
negative shock to the budget, X, equal to 1.5% of GDP. This scenario reflects the lower
interest rates associated with restored market confidence as well as the high primary surplus
targeted by the government.
For the increase of the primary surplus (as a percentage of GDP) due to a 1% growth
in real GDP we rely on the estimate by Blanco and Herrera (2002) who suggest a 0.2
semi-elasticity of the primary surplus with respect to GDP (see also Bevilaqua and Wer-
neck (1997)). Evaluating the effect of unexpected inflation on the primary surplus (as a
percentage of GDP) is a more difficult task. Although the effect should be substantial,
as witnessed by the remarkable budget improvement in the first quarter of 2003, coming
down to a single number is difficult.8 As indirect taxation is the main source of revenues,
these should remain roughly constant in terms of GDP. Public spending should instead fall
relative to GDP because many categories of spending remains constant in nominal terms
as set in the budget.9
Primary public spending is equal to 32% of GDP, but social security benefits and other
components are linked to the inflation rate. This suggests a tentative estimate of the price
elasticity of the primary surplus equal to 0.2, that is, lower than the ratio of primary public
spending to GDP.
4.1 Expected return differentials
The expected return differential between fixed-rate bonds and Selic indexed bonds over
one-year horizon, TPt, is the difference between the yield at auction of fixed-rate LTN bonds
and the expected return on Selic indexed LFT bonds. The latter can be estimated as the
sum of expected Selic rate from the daily survey of expectations and the discount at which
1-year LFT bonds are issued. At the end of October the average auction yield on 1-year
8The positive effect of inflation is known as “Patinkin effect” (acc. to Eliana Cardoso); it is the opposite
of the Olivera-Tanzi effect.
9 This information was provided by Paulo Levy at IPEA.