pected output fluctuations. In fact, fixed-rate bonds appear the only available instruments
to insure against the impact of unanticipated output slowdowns on debt sustainability. As
highlighted in the discussion above, the fact that such shocks have played a minor role
compared to variations in the exchange rate and inflation over the period considered does
not mean that they will continue to do so in the future. A debt structure that comprises
fixed-rate conventional bonds along with price-indexed bonds would better balance the risks
that the Brazilian economy may face in the years ahead.
In order to examine whether and how the optimal debt composition depends on the
types of shocks hitting the economy, in the next Section we present results for different
shocks identified with a structural model of the Brazilian economy.
5.2 Estimating the debt composition with a structural model
The structural model used to estimate the optimal debt composition is made of five
equations for: (i) the inflation rate; (ii) the output gap; (iii) the Selic rate; (iv) the exchange
rate and; (v) the EMBI spread.
The model is estimated on monthly data for the period 1999:3-2003:7 and is presented in
the Appendix. We consider three types of shocks: a supply shock (in the inflation equation),
a demand shock (in the output-gap equation) and a shock to the EMBI spread. Then, we
compute the 12-months cumulated impulse responses of the Selic rate, the exchange rate,
inflation and output for 1000 extractions from the distribution of each type of shock.10 The
cumulated responses are then used to estimate the ratios of conditional covariances relative
to conditional variances which are shown in Tables 4, 6 and 8 for the demand shock, the
supply shock and the EMBI shock, respectively. The optimal debt composition is reported
in Tables 5 7 and 9 for each type of shock.
5.2.1 Demand shocks
Table 5 shows the debt composition that stabilizes the debt ratio against demand shocks
-i.e. against shocks to the output gap equation. The first Column of Table 5 reports the
shares of each type of debt which are optimal for minimizing the risk of variations in the
primary surplus and the debt ratio, that is, when we abstract from hedging against variations
in the interest payments (or returns) of the other instruments. The shares of Selic and price
indexed bonds are positive and exceed several times the total debt. This evidence suggests
that such instruments offer a valuable insurance against variations in the primary surplus
and in the debt ratio. As demand shocks induce a positive covariance of output and inflation
and a strong reaction of the policy rate, the returns on both Selic and price indexed bonds
are strongly correlated with output and inflation. As the monetary reaction leads to an
appreciation of the exchange rate, the return on dollar denominated bonds is negatively
correlated with both output and inflation. This explains the large negative share of dollar
denominated debt; the government should rather hold foreign assets to hedge against output
shocks.
Column 2 shows the debt composition that minimizes risk when we consider, along
with budget and debt-ratio uncertainty, the role of each instrument in hedging against the
returns of the other instruments. Since Selic and price indexed bonds are close substitutes
10For the exchange rate the response at the 12th month was used instead of the cumulated responses.
13