Following Hamilton and Flavin other authors apply the cointe

Following Hamilton and Flavin, other authors apply the cointegration analysis to data of expenditure and revenue as the methodology to test the consistency of the temporal government budget constraint. Hakkio and Rush (1991) make assumptions about the stochastic process described by the revenue and expense variables and propose an alternative model for the testable implications. Similarly, Bohn (1991) estimated Eq. (3) below to test whether the debt sustainability is related to the existence of cointegration among the variables expenditures, revenue and debt.where B is the public debt, G is expenditures on goods and services, T is tax revenue and r is the interest rate. The error term is supposed to be a white noise. If B is not stationary with I(1), then is stationary, which is derived by subtracting from both sides of Eq. (3): Therefore, the stationarity of implies a cointegration restriction on the following vector: . By Eq. (4), the cointegration vector would be . Rocha (1997) applied this model to Brazilian data in the period 1980–1993 and concluded that revenues and expenditure cointegrate, so that the budget deficit is stationary. However, the sustainability of public debt occurs only when the revenue is adjusted by the inflation tax, that is, tax revenue and the monetary expansion contribute essentially to the government budget balance. Despite this application, the literature in Brazil is even enhanced due to the paper of Issler and Lima (2000), who built a similar analysis of Hamilton and Flavin (1986) using data in the period 1947–1992. They conclude that the sustainability of the Brazilian debt is not rejected as seigniorage is included in the government revenue. This conclusion reveals clearly the way fiscal funding is managed in an economy with high inflation. Contrary to any prior flavopiridol on the interest rate distribution, Bohn (1998) proposes a new test of sustainability. In order for the temporal government budget constraint to be satisfied, he argues that it is sufficient that the primary surplus increases when the debt/GDP ratio rises, which implies that the temporal government budget constraint is achieved and then the debt is sustainable. The budget constraint at the beginning of the period is defined as follows:where S is the primary surplus, is a factor of interest rate and B is the public debt. If an economy grows continuously over time, deflating the variables by the GDP (Y) would provide the following restriction:where and. The variable r is the real interest rate and y the real growth rate of the economy. By incorporating the tax smoothing model of Barro (1979) to this approach, the relationship between primary surplus and the debt/GDP ratio can be expressed by the equation:where the error term and Z is a vector composed of variables that explain the primary surplus and the debt, such as government expenditures and the output deviation relative to its potential level. The empirical exercise carried out by Barro through U.S. data demonstrated that the Dickey-Fuller and Phillips-Perron unit root tests do not reject the unit root hypothesis. The analysis conducted in this study meets further support on Goldfajn\'s (2004) work, which establishes that the main problem related to finance imbalance in Brazil is not the debt/GDP ratio itself, but its latest evolution. The government response to this is then the premise to generate primary surplus to stabilize the debt/GDP ratio. Garcia and Rigobon (2004) investigate the future dynamics of the Brazilian debt from a perspective of risk management. According to Goldfajn\'s (2004) arguments, risk management stems from the fact that the equation of debt accumulation, by any country encompasses variables that are stochastically related to one another. The formal procedure is then to specify a vector autoregressive (VAR) to estimate the pattern of correlations among macroeconomic variables and take the correlation matrix to conduct Monte-Carlo simulations. Thus, it is possible to calculate the probability that the simulation of the debt/GDP ratio exceeds a certain value, for instance 75%, and subsequently compare it with the perception of risk in the market, in which is provided by the index of the emerging countries bonds (EMBI). In spite of the debt tending to be sustainable within a riskless economic environment, there are several paths scenarios in which fiscal policy would not be sustainable.