The main purpose of this section is to show that the SS follows from the existence of tax distortions and not from the knife-edge feature of the model in the text. With that in mind, I will modify the previous model and assume that investment is subject to adjustment costs. More concretely, I will assume that the output cost per unit of capital associated with capital growth z is portrayed by φ(z), where function φ is strictly convex and twice continuously differentiable (implying φ” > 0). Notice, incidentally, that in the text I assume φ(z) = z. Thus, to stay close to that model in a neighborhood of 0, I will further assume φ(0) = 0, and φ’(0) = 1; moreover. I will assume that there exists
Therefore, the value of the firm at time 0, V, satisfies (see equation (4)):
and, if ∂V/∂z = 0, then:
Thus, first-order conditions are sufficient for a maximum of V with respect to z because V does not contain a local minimum.
Plugging budget constraint (6) to substitute for ι in expression (19), we get:
Previous assumptions ensure that J(z,D) converges to ∞ as z goes to z from the right, and to -∞ as z goes to
I will now show an example where equilibrium is not unique (in absence of the equilibrium-selection principle). By expression (21), and recalling that φ(0) = 0 and φ’(0) = 1, we have:
Let Dc be such that J(0,Dc) = 0. This implies that if D = Dc, then z = 0 maximizes the value of the firm V with respect to z. Clearly, by expression (22),
Moreover, by expressions (21) and (22), at D =Dc
Hence, given r, for α sufficiently large or φ”(0) sufficiently small, we can ensure that Jz(0,Dc > 0. Thus, drawing the J function, given D, under these conditions readily shows that, if D = Dc, the economy will exhibit at least three equilibrium solutions (illustrated by the solid line in Figure A1). Moreover, by expression (21), the J function shifts down as D increases. Hence, there exists some
In closing, notice that the share of distorting debt in output at time zero, θDc/α, satisfies, by expression (23),
Thus, distorting debt in the multiple equilibria example can be made as small a share of output as desired by selecting a sufficiently close to r, and α > r. This shows that the example does not require unrealistically high debt ratios.
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Chief Economist and Manager of the Research Department of the Inter-American Development Bank. Distinguished University Professor and Director of the Center for International Economics at the University of Maryland. I am grateful to Fernando Broner, Kevin Cowan. Alejandro Izquierdo, Michael Kumhof, Eduardo Levy-Yeyati, Luis Fernando Mejía, Enrique Mendoza, Ned Phelps, Ernesto Talvi, and seminars participants at IADB, Di Telia University, and the University of Maryland for valuable comments. I would like to dedicate this paper to the memory of Rudi Dornbusch, whose insight, wit, and whip inspired generations of scholars and policymakers in international finance and development economics.
The expression sudden stop was first suggested, and the phenomenon highlighted, in Dornbusch, Goldfajn, and Valdes (1995).
For an earlier attempt to rationalize SS on the basis of multiplicity of equilibria and in an essentially static nonmonetary framework, see Calvo (1998b).
Real depreciation also takes place if the crisis is fully anticipated and, for example, it entails a higher consumption tax.
The borderline cases in which expressions (8) or (9) hold with equality are of no interest and will not be discussed here.
In my view the IFI’s coordination role was successfully carried out in Mexico (1995), Korea (1997), and Brazil (1999), and helps to explain the rapid (V-shaped) recovery of those economies.
For a discussion of this model in the more general case in which the rate of discount is different from the international interest rate, see Calvo (1998c). The latter also addresses welfare issues and the impact of controls on capital outflows that will be skipped in the present paper.
This does not hold true in the Appendix model because in the latter investment is a continuous function of time. Even though investment does not display a discontinuous fall, however, it will show a declining trend.
Again, this does not follow in the Appendix model, in which a lower growth is attained in a continuous manner.
Contrary to this scenario, however, most recent BOP crises seem to have been driven more by an expansion of domestic credit from the central bank than by a fall in the demand for monetary aggregates (see Flood, Garber, and Kramer, 1996; Kumhof, 2000; and Calvo, 2001). This issue will be taken up in the next section.
This is one of the key new topics in the EM literature. See, for example, Calvo (2001) and Jeanne (2001).
This line of research has been pioneered by Kiyotaki and Moore (1997) for the closed economy, and extended to the open economy by Caballero and Krishnamurthy (2001a, b, and c), Izquierdo (2000), and others.
Thus, this section departs from the basic model in Section I, and is more speculative than earlier sections.
This requires changing the anti–Krugman example in Section II to allow for the central bank to issue domestic credit in response to a SS. Central bank hyperactivity during BOP crises, incidentally, is a widely observed fact, as noted by Flood, Garber, and Kramer (1996) and Kumhof (2000).
Once again, this policy would be especially relevant if the private sector suffers a credit crunch. Brazil offers a recent example of this kind of central bank policy; see the Financial Times (2002).
In actuality, however, as shown in the earlier discussion of the monetary economy, a SS gives rise to both real and nominal shocks. Thus, if anything, the standard literature would call for a dirty float.