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THE PRICE LEVEL: THEORETICAL CONSIDERATIONS 3

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The MD and FD regimes can now be defined in terms of the present value constraint (4). If primary surpluses (or more precisely the surplus to GDP ratios) are determined independent of the level of the debt, then nominal income and/or discount factors must “jump” in equilibrium to satisfy (4). We call this a FD regime. If on the other hand primary surpluses are determined in such a way that (4) is always satisfied no matter what nominal income and discount factors are fed into it, then nominal income and the discount factors can be determined elsewhere in the model. We call this a MD regime. In summary, nominal income is determined by the needs of fiscal solvency in a FD regime; it can be determined in more conventional ways in a MD regime. Once we specify the way in which changes in nominal income are split between price and output, we have a theory of price determination. This last step is obviously model specific, and controversial. Fortunately, the restrictions we need for Section III do not require us to take a stand on these issues.

One must also fill out the model to see how the choice of regime limits the way in which monetary policy can be modeled. Consider a very simple example: let output and government purchases be fixed each period, and let there be a cash in advance constraint (so that MJ+1 = P^y in equilibrium). The consumer’s Euler equation fixes the market discount factors, aj5 at the household’s discount factor, and an equilibrium sequence {MJ+1, Pj( s,} must satisfy the present value constraint, (4), and the cash in advance constraint. In a FD regime, the Sj do not respond to the level of the debt, and Pt has to “jump” to make wt satisfy (4).

If the central bank tries to set Мы, P, will be over determined; Pt can not (in general) satisfy both (4) and the cash in advance constraint. If on the other hand the central bank sets i„ then there is no problem; (4) determines P,, and the cash in advance constraint determines Mt+1. In a MD regime, things work out quite differently. The Sj are determined in such a way that (4) is satisfied for any value of P,y (or w,) that is fed into it; (4) can not be used to determine P,. Now, if the central bank sets Mt+1, P, is determined by the cash in advance constraint and there is no problem. If on the other hand, the central bank tries to set i„ we have a new problem. The cash in advance constraint can not simultaneously determine Mt+1 and Pt. So, the FD regime limits us to considering interest rate rules, while the MD regime limits us to considering money supply rules. As explained in the introduction, none of these results are new; they hold in a wide class of models.