# THE PRICE LEVEL: THEORETICAL CONSIDERATIONS 5

We don’t consider the above Proposition’s assumptions about fiscal policy to be overly restrictive. It seems natural to assume that the ratio of the primary surplus to GDP, and thus {e^}, is bounded and that an increase in debt does not cause a decrease in the primary surplus (so that Cj г 0 holds). The lower bound a. on aj and the upper bound c* on Cj are plausible (and analytically convenient) assumptions. The growth rate of the economy can exceed the interest rate for finitely many periods without violating (Cl). However, the condition lim sup otj < 1 is necessary for the government’s present value budget to be well defined; without it the government could roll over debt indefinitely regardless of the value of wt. The only substantive assumption is that Cj is bounded away from zero infinitely often. This will be the case unless the fiscal authority tries to rollover the interest due on debt indefinitely. In periods in which Cj > 0, Sj is indeed moving to stabilize Wj. However, it need not do so each and every period. A stabilizing policy could be in effect every other year, or every third year, or every decade. Indeed, the required fiscal retrenchment need not occur in the next 100 years! All that is necessary is that the private sector expects that there will sooner or later be a retrenchment. In the meantime, fiscal policy can respond to economic or political conditions (as represented here by the random variable €j).

With these insights, we are ready to develop the restrictions that will help us to differentiate between MD and FD regimes. This is not as straightforward as it may at first appear. Figure 1 illustrates the positive correlation between st and w, in the post war data. This might be viewed as evidence in favor of a MD regime; primary surpluses responded to liabilities in the manner prescribed by (5) and produced a MD regime. However, there is an identification problem here; a FD regime would also have produced the positive correlation between s, and w„ with causation going the other direction. To see why, consider the effect of a positive s, innovation in equation (4). In a FD regime, nominal income and/or expected future discounted surpluses must move to achieve fiscal balance. If an innovation in st causes the RHS of (4) to rise, then nominal income must fall to raise the LHS of (4). Simple correlations between st and wt are not very useful for our purposes.