THE PRICE LEVEL: TESTING FOR FISCAL DOMINANCE 3
Next we estimate a VAR with two lags of Surplus/GDP and Liabilities/GDP (and a constant).19 We tried other specifications: we added a deterministic trend; we used lags of one, three and four years; and we estimated the VAR in first differences. All of these VARs produced very similar results. Figure 3 shows the impulse response functions for an innovation in Surplus/GDP. Since the residuals in this VAR are highly (negatively) correlated, the ordering in the Cholesky decomposition may matter.
For this reason, we show the results for both orderings. In the top panel, Surplus/GDP comes first. This ordering allows for a contemporaneous affect on Liabilities/GDP as is consistent with a FD regime (where nominal GDP has to jump to make the value of the existing debt equal to the expected present value of surpluses). In the bottom panel, Liabilities/GDP comes first. This ordering may make more sense in a MD regime (where GDP can be determined elsewhere in the model) because it does not allow for a contemporaneous affect on Liabilities/GDP. The dashed lines represent the two standard deviation bands obtained by a Monte Carlo simulation with 500 repetitions.
We are most interested in the response of Liabilities/GDP one period after the innovation in Surplus/GDP. As explained in Section II, the Surplus/GDP innovation pays off some of the debt in a MD regime, and Liabilities/GDP should fall in the next period. In a FD regime, there are three cases to consider. Recall that the value of next period’s Liabilities/GDP can be found by moving equation (4) forward one period.
If the innovation in Surplus/GDP is not correlated with the surpluses and discount factors that follow, then next period’s Liabilities/GDP should not be affected by today’s innovation; if the innovation in Surplus/GDP is positively correlated with future surpluses and discount factors, then next period’s Liabilities/GDP should rise in response to today’s innovation; and if the innovation in Surplus/GDP is negatively correlated with future surpluses and discount factors, next period’s Liabilities/GDP should fall in response to today’s innovation in Surplus/GDP. The existence of this last case creates a potential identification problem. We will have to investigate the possibility of a negative autocorrelation in the surplus process and the possibility of a negative correlation between the current surplus and future discount factors.