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# THE PRICE LEVEL: THEORETICAL CONSIDERATIONS 4

The MD regime might seem like a rather special case, but it turns out that many different fiscal policy rules lead to MD regimes. Moreover, these rules can be quite lax. The MD regime is not as implausible as it may at first appear. To illustrate this point, suppose that the sequence {Sj} is expected to follow the rule where Cj is a time varying response parameter and ej is a random variable. €j could represent political factors or economic conditions, such as unemployment. We have the following proposition:
Proposition: Assume that {Cj}, {ctj} and {Gj} are deterministic sequences, that {€j} is bounded, and that the following conditions hold: (5) imply that the present value constraint (4) holds for any arbitrary value of wt. In other words, the fiscal rule (5) results in a MD regime if {€j} is bounded and conditions (Cl), (C2) and (C3) hold. We prove this proposition in an appendix, and we extend it to a stochastic environment.

The intuition behind the proof is more transparent in the case where Cj and ccj are constant (с: = с and ctj = a, for all j). If there is no stabilizing fiscal policy (because с = 0), then the flow budget constraint (3) is a dynamically unstable equation (since by assumption its root, 1/a, is greater than one); in this FD regime, wt has to jump to suppress this unstable root for (4) to hold in equilibrium.13 Substituting (5) into (3), the root of the equation becomes (l-c)/a. If the fiscal response coefficient, c, is sufficiently large to make (l-c)/a < 1 — which roughly corresponds to а fiscal response larger than the difference between the interest rate and the growth rate of GDP — then the flow budget constraint is dynamically stable, and (4) holds for any initial condition, wt.14 It turns out however that the fiscal response does not have to be strong enough to make the flow budget constraint stable; all that is required by (4) is that the discounted value of wt+T go to zero as T goes to infinity. Any positive value of с implies that this is the case. Moreover, allowing for a time varying fiscal response, condition (C3) says that the requisite fiscal response may be arbitrarily small and infrequent.