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Calvo and Obstfeld (1988) have shown, however, that their stronger claim that today-planner’s optimum can be decentralized by choosing an appropriate maturity structure does not hold true in general.
As will become clear below, the presence of a “genuine” revenue effect of inflation is important. The assumption that the demand for money is interest-inelastic introduces this effect in the simplest way. Assuming that the demand for money is interest elastic would make the analytical presentation more complex without providing additional insights.
It is assumed that the price level at period zero is a predetermined variable. This makes the output value of the initial stock of debt an exogenous variable.
In addition, V(0) = 0 and H’(1) = 0.
The assumption of perfect certainty helps showing in a dramatic way the revenue-ineffectiveness of expected inflation when applied to the stock of nominal bonds. Under uncertainty, however, the government would be able to collect inflation tax on nominal bonds as long as inflation is unanticipated. On average, of course, unexpected inflation would anyway collect nothing from nominal bonds. For a discussion, see Calvo and Guidotti (1989).
Recall that Π=1 is the first best level of inflation when k=0.
The fact that x2 is lower than its first-best level follows from the fact that, since we have shown that > x2, the opposite would imply excess government revenues.
See Obstfeld (1988) where debt aversion is shown to arise even though bonds are fully indexed to the price level.
All that is needed is the ability to make precommitments about inflation in period 2.
We assume that the conditions of the Implicit Function Theorem obtain. Moreover, the following results assume existence of a regular minimum (i.e., a minimum where the second-order sufficient conditions are satisfied).
The intuition behind the effects of a change in b02 can be obtained through contradiction. Using the fact that H”>0 and S”<0, we can observe that equation (17’) implies that Π1 and x move always in the same direction. Consider now the effects of an increase in b02, ceteris paribus. If an increase in b02 increases x, it must also increase Π1. However, from equation (18’), it can be seen that the increase in both x and Π1 implies an increase in Π2, which is inconsistent with budget constraint (5). Therefore, an increase in b02 must reduce x and Π1. It is clear that, if x and Π1 fall, only an increase in Π2 is consistent with both equations (18’) and (5).
Notice that if b02=b, then Π1=Π2 and H’ (Π1)/H’ (Π2) = S’ (Π1),S’ (Π2).
Again, we assume that the conditions of the Implicit Function Theorem obtain, and we assume existence of a regular minimum.
In the numerical simulations presented in the next section an increase in b02 has always a positive impact on Π2.
Note that if in this model debt were indexed, as in Obstfeld (1988), there would be no time-inconsistency problem because we are assuming that the demand for money is interest-inelastic.