adjustment, Bt is the debt-to-GDP ratio and BtT+1 is the trend debt ratio, that is, the debt
ratio that would prevail in period t + 1 in the absence of the fiscal correction.
Alternatively, X , can be viewed as a shock to the budget that occurs after the fiscal
adjustment has been carried out or as a debt increase due to the discovery of hidden
liabilities —“skeletons in the closet”.
Absent government intervention the debt ratio (at market values) increases because
of the interest payments on the outstanding debt minus the trend primary surplus and
the growth of nominal GDP. The debt also increases because of the revaluation of the
dollar-denominated debt due to the depreciation of the domestic currency. Hence, debt
accumulation ∆BtT+1 = BtT+1 - Bt is equal to:
∆BtT+1 = It+1Bt + ∆et+1qBt - StT+1 - (∆yt+1 + πt+1)Bt (2)
where It+1Bt are the nominal interest payments, et is the log of the nominal exchange rate,
q is the share dollar-denominated debt, StT+1 is the trend primary surplus, yt+1 is the log of
output and πt+1 is the rate of inflation.
The interest payments depend on the composition of public debt chosen at the end
of period t. The government can choose between bonds indexed to the Selic rate, dollar
denominated bonds, price-indexed bonds and fixed-rate bonds. We take the time period as
corresponding to one year and assume that all bonds have a one-year maturity, since the
relevant decision for the Brazilian Treasury is whether 1-year fixed-rate bonds should be
issued. Focusing on a one-year horizon is a reasonable approximation even if LFT, NTN and
dollar denominated bonds have much longer maturities, because the stochastic component
of their returns is dominated by movements in the Selic rate, the rate of inflation and the
exchange rate. Within a one-year horizon, the nominal rate of return on fixed-rate 1-year
bonds is equal to the long-term interest rate, Rt , at which such bonds are issued. The
nominal return on fixed-rate bonds is thus known at the time of issuance. The return in
Reais on dollar denominated bonds depends on the US interest rate, RtUS and the risk
premium RPt and exchange rate depreciation. The nominal return on price-linked bonds
is equal to the sum of real interest rate, RtI , known at the time of issuance, and the rate
of inflation, πt+1 . Finally, the return on Selic-indexed bonds is determined by the path of
the Selic rate over the life of the bond and thus between period t and t +1. The (average)
Selic rate over this period, it+1 ,isnotknownattimet when the composition of the debt is
chosen.
The interest payments are equal to
It+1Bt = it+1sBt +(RtUS + RPt)qBt + (RtI + πt+1)hBt + Rt(1 - s - q - h)Bt (3)
where s is the shares of Selic-indexed debt, q is the share of dollar-denominated debt and
h is the share of price-indexed debt at the beginning of period t and where the return on
dollar denominated bonds (RtUS + RPt)(1 + ∆et+1) has been approximated by RtUS + RPt.
Finally, the ratio of the trend primary surplus to GDP, StT+1 , is uncertain, since it
depends on cyclical conditions and on the rate of inflation as follows
StT+1 = Et StT+1 + ηy (yt+1 - Etyt+1) + ηπ(πt+1 - Etπt+1) (4)