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Work on this paper started while Guillermo Calvo was a Senior Advisor at the Research Department of the International Monetary Fund. Comments and suggestions by Larry Christiano and Hugo Hopenhayn are gratefully acknowledged. This paper reflects the authors’ views and not those of the IMF.
As in Levhari and Srinivasan (1969), we impose certain properties on the stochastic process of rt so as to produce feasible plans. In particular, rt must satisfy the condition E[(rt)1-γ]<β-1.
For σr2 to increase while keeping μr unchanged, it must be the case that σ2 increases in such a way that μ is adjusted to keep μ+σ2/2 constant.
This expression is obtained by displacing the expected value E[rt1-γ] using the properties of log-normal i.i.d. distributions.
This also implies that an optimal tariff in this model is one that takes any value as long as it is constant over time.
For all dates t>0, solutions (5) and (6) hold. Given those solutions, we determine the value of A1 coming out of the period of the credibility test, which is implicit in the solution for C0. To find C0, we impose (5) updated one period in the right-hand side of (17), displace A1 using the resource constraint for t=0, and solve for C0.
There is also a feasibility constraint 0 < λ/η<1, or λ < η.
The difference is larger the lower the degree of risk aversion, but it is always positive.
A cross-country empirical analysis of the link between terms-of-trade and growth implied by this model is undertaken in Mendoza (1994).
Remember that r-1=R-lp-1/po and r0=R0po/p1 and p is the reciprocal of the terms of trade.
This experiment is interesting because trade reforms introduced in recent years were accompanied by a secular decline in the relative price of commodities in terms of manufactures (see Reinhart and Wickham (1994)).
Given the original μr at 1.07, this still allows for positive growth to continue on average, resulting in a new value of μr set at 1.0593.
Welfare costs are computed as percentage variations in stationary consumption paths that compensate households for the loss in lifetime utility resulting from existing distortions. For example, in the case of costs resulting from σ=0.025, we compute (21) under σ=0.025 and σ=0, assuming π=0, and then use (1) to compute two time-invariant levels of C that represent the same expected utility. The welfare cost is the difference between the two consumption levels in percent of the one corresponding to the economy with σ=0.025.
Given solutions for V* and Vτ, and the resource constraint at t=0, (26) is a straightforward maximization exercise.
This result is consistent with findings of Calvo and Drazen (1993) for the sustained boom of the reform of uncertain duration under incomplete markets and no rebates.
If the trade reform prevails, the term (1+τ) inside the square bracket of (35) disappears.
In the case with rebates both the free-trade economy and the economy with permanent tariffs produce the same welfare, and hence the difference between credibility and temporariness is immaterial.