The perfect foresight solution requires that at T, the transition to the system with 0 < σ < 1 occur without a jump in either the marginal utility of wealth or the stock of wealth. Consider first the solution that obtains for t≥T, and suppose for the moment that no exchange rate adjustment takes place at period t - 0. The solution of the model consisting of equations (18b), (18c) and (31) is given by, with
where Ω is as defined in the text, and
The solution of the model that prevails during the transition period is the general solution to system (21). Let v (= v) be the negative root and the positive root of system (21). We then have
where κ1 = κ2 < 0, κ >0, A1 and A2 are constant terms, and
To determine the values of A, A1 and A2 requires three conditions: the initial condition on private wealth
Solving this system yields
where ψ = (κ+κ2)exp[(v+v2)T] > 0. It is easy to verify that, given equations (A3) and
Assume now that a reduction in the devaluation rate takes also place at t = 0. The solutions for A1 and A2 are now given by
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Calvo, Guillermo A., and Carlos A. Végh, “Exchange-Rate Based Stabilization with Imperfect Credibility,” in Open Economy Macroeconomics, ed. by Helmut Frisch and Andreas Worgotter, St. Martin’s Press (New York: 1993).
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I am grateful to Joshua Aizenman, José De Gregorio, Donald Mathieson, Jorge Roldós, Murat Ucer and Carlos Végh for many helpful discussions and comments on preliminary versions of this paper.
See Agénor and Montiel (1994) and Calvo and Végh (1994) for a disusssion of the Rodriguez model, particularly the role played by backward-looking expectations and sticky prices.
See, for instance, Patinkin (1993). The restrictive credit stance was brought by an increase in the discount rate and the level of reserve requirements on bank deposits.
The link between anticipations about future policies and current policy outcomes is, of course, central to rational expectations macroeconomics. Recent developments, in particular, have emphasized the relation between government deficits, fiscal policies, and inflation. See for instance Drazen and Helpman (1990).
Imperfect capital mobility arises here not as a result of domestic restrictions on flows or on holdings of foreign assets, but from imperfect substitutability between domestic and foreign bonds. The role of imperfect asset substitutability in analyzing the response of real interest rates to disinflation measures was emphasized by Kamin and Spigelman (1988) in a portfolio-balance framework.
Except otherwise indicated, partial derivatives are denoted by corresponding subscripts, while the total derivative of a function of a single argument is denoted by a prime.
This specification has been used, in a different context by Turnovsky (1985), who also provided a different rationale. The stock treatment adopted here differs substantially from the flow formulation adopted in nonoptimizing models, such as Kiguel (1987).
Appropriate restrictions must be imposed on a to ensure that steady-state consumption is stationary under perfect capital mobility and that the real interest rate is independent of the foreign interest rate under zero capital mobility; see Turnovsky (1985).
For simplicity, we assume that the central bank does not receive any interest on its loans to the government. Since we consider only the consolidated budget of the public sector in what follows, this assumption is inconsequential.
The net effect of a change in the real money stock on gross consumption is in general ambiguous. On the one hand, an increase in real money balances raises net consumption (by reducing the nominal interest rate), while on the other (for a given level of expenditure) it reduces transactions costs. We assume, however, that the net effect is positive.
The determinant of the coefficient matrix is given by
The second term in the expression in brackets is always positive. Also, since
Since the central bank does not hold domestic government bonds, the existing stock of these assets cannot be altered through sterilization operations. Recall also that the level of the exchange rate does not change.
See for instance Frenkel and Rodriguez (1975) for a model that also features both types of adjustments. As indicated earlier, under perfect capital mobility the model has no transitional dynamics, and only the instantaneous portfolio adjustment takes place.
Steady-state effects can be derived along the lines discussed above. For instance, since
Real money balances therefore always rise on impact.
Regardless of whether the nominal interest rate rises or falls initially, private holdings of foreign bonds always fall (as indicated earlier) since, using equations (18) to (20):
Since lump-sum taxes are endogenously adjusted to equilibrate the budget, there is no intrinsic rationale in the present model for justifying the use of distortionary taxation from the point of view of public finance. However, the decision to raise the income tax rate may rest on distributional considerations being pursued simultaneously with the stabilization objective, or because a tax hike is viewed as having a “signaling” effect regarding the policymakers’ commitment to reform and adjustment.
See Daniel (1989) for elaborations on this point.
The quasi steady-state nominal interest rate, in particular, would rise from