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Figure 3 shows that the response of Liabilities/GDP in period 2 to an innovation in Surplus/ GDP in period 1 is negative and significant, regardless of the ordering used.20 The response of Liabilities/GDP in period 3 is also negative and significant. This can be readily explained in terms of a MD regime. But it is also consistent with a FD regime in which the primary surplus is exogenous (or at least unrelated to liabilities) but exhibits negative autocorrelation.

Does the primary surplus respond to liabilities thereby yielding a MD regime or is Surplus/GDP exogenous but negatively autocorrelated? We begin answering this question by examining the autocorrelation function of Surplus/GDP, which is found in Table 1. The autocorrelations and the corresponding Q-statistics clearly indicate that there is significant positive autocorrelation in Surplus/GDP, at least at lags of up to 9 years. Next, we return to the joint dynamics of Surplus/GDP and Liabilities/GDP and look at the impulse response functions from the VAR.

Figure 3 also shows that an innovation in Surplus/GDP in period 1 tends to produce a surplus in period 2, regardless of the ordering. (In a MD regime, this is consistent with the additional fall in period 3 Liabilities/GDP shown in Figure 3.) Beyond period 2, the impulse responses are negative and insignificant. These response functions are quite consistent with a MD regime—a deficit today means a higher debt next period, and in a MD regime that debt would have to be paid off at sometime in the future.

The difference between the positive autocorrelation we find when we look only at Surplus/GDP and the impulse responses that capture the feedback from Liabilities/GDP suggests that the surplus is not exogenous and is instead influenced by the level of existing liabilities. Bohn’s (1995) fiscal reaction function (which was discussed in the introduction) is also consistent with this interpretation.

What do we conclude from all this? Apart from the feedback from Liabilities/GDP that a MD regime would predict, there appears to be very little evidence that innovations in Surplus/GDP are negatively correlated with future surpluses.