The maximization problem facing a representative firm in the capital installation industry is solved by setting up the present-value Hamiltonian:
and deriving the following first-order conditions:
where q is the multiplier on the firms’s capital accumulation constraint. The firm is assumed to take P and r as given since it is small relative to the market. Equations (9) and (10) of the text are obtained by rearranging (A.2) and (A.3).
The maximization problem facing the representative household is solved by setting up the following present value Hamiltonian:
and taking first-order conditions:
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The author is Assistant Professor of Economics at Boston College, Chestnut Hill, Massachusetts. This paper was written while he was a Visiting Scholar in the Research Department of the International Monetary Fund. He wishes to thank participants in seminars at the International Monetary Fund and the University of Pennsylvania for helpful comments on an earlier draft of this paper.
See Williamson (1985) for a discussion of real exchange rate misalignment. Borensztein (1987) presents evidence that the appreciation of the U.S. dollar over the period 1980-84 is consistent with the hypothesis of a speculative bubble, although he is also unable to reject alternative explanations. Shiller (1984) describes stock prices as being determined in part by “fads.”
In Brock’s model, however, government subsidies to investment activity will drive a wedge between the market value of capital and the real exchange rate. This, though, is a one-time effect with subsequent changes in the market value of capital exactly equal to changes in the real exchange rate.
Bovenberg (1988) also uses an adjustment-cost framework to study capital accumulation in the open economy. His analysis, however, emphasizes the dynamics of the terms of trade rather than the adjustment of the real exchange rate.
See McKenzie (1982) for a similar adaptation of the dependent economy framework. McKenzie assumes that the traded good is the investment good and focuses on the roles of factor-intensity and intertemporal substitution in determining the dynamics of the real exchange rate. The present paper instead follows Brock (1987) in assuming that investment requires inputs of the non-traded good and in focusing on adjustment in response to changes in fiscal policies.
See Khan and Lizondo (1987) for a related discussion of how the mix of fiscal policies accompanying a nominal devaluation is of critical importance in determining the extent of real depreciation.
This assumption about factor intensities is sufficient to ensure that the steady-state equilibrium of the model is a unique saddlepoint. Previous work on capital accumulation in the open economy has employed non-optimizing models in which global stability of the model requires the traded sector to be relatively capital intensive (see, for example, Dornbusch (1980) and Obstfeld and Stockman (1985)). The optimizing model presented in this paper will always be saddlepath stable when the traded sector is capital intensive but will be globally unstable when the traded sector is labor intensive.
An increase in P thus represents a real appreciation. The model presented in this paper focuses exclusively on the real side of the economy in order to study the interaction of relative prices and capital accumulation. In order to determine nominal prices and the nominal exchange rate it would be necessary to add a monetary sector to the economy. This would then raise the important issue of how to model money demand in an optimizing framework; an issue that remains controversial and that is beyond the scope of the present analysis.
As discussed in Section 3, equation (3) implies that the long-run real exchange rate will be determined exclusively by the supply side of the economy. If instead capital were sector-specific rather than mobile between sectors, then rental rates in each sector would depend on the real exchange rate and the sectoral distribution of the capital stock. As noted in Murphy (1988), though, the long-run real exchange rate would continue to be determined exclusively by the supply side provided the two sectors have the same rates of depreciation and adjustment cost functions. The reason is that in the long run rental rates will be equalized across sectors even when capital is sector-specific.
The results of this paper will continue to hold if traded goods are used in the investment process provided some amount of non-traded inputs are also required.
The firm is assumed to borrow from residents at the world interest rate when its retained earnings fall short of its investment expenditures. Note that since bonds and equities are perfect substitutes in investor portfolios, the mix of external finance has no effect on the market value of the firm.
Note that if the firm were allowed to fully deduct its investment expenditures in calculating its taxable income, then changes in the tax rate would have no effect on investment incentives. Although equation (7) assumes zero deductibility, the results of this paper will continue to hold provided investment expenditures are less than fully deductible.
By assuming that only the traded good is consumed, the analysis leaves aside important issues concerning how the time profile of consumption is related to the domestic real interest rate. Incorporating non-traded consumption, though, would complicate the analysis and possibly obscure the specific mechanisms highlighted here. See Dornbusch (1983) for a model of optimal borrowing in which both traded and non-traded goods are consumed.
The household also receives income in the form of capital gains on equity. Since the number of outstanding equity claims is assumed to be constant (recall that firms finance investment expenditure out of retained earnings or by borrowing), the capital gain exactly equals the increase in the value of equity holdings. As a result, identical capital gain terms would show up on both sides of the accumulation equation for household wealth and would therefore cancel, yielding equation (16).
The results of this paper would continue to hold if government purchases were incorporated as a separable term in the utility function of the representative household.
From equation (29), it is clear that a real appreciation must accompany capital accumulation along the saddlepath. Whether this is associated with an expanding or contracting level of investment expenditure (I) (and thus an expansion or contraction in the non-traded sector) depends on whether or not the rate of increase in investment demand in equation (20) is greater than the rate of decline in the supply of the non-traded capital good. If investment demand rises more quickly than the supply falls, then the non-traded sector will expand and the traded sector will contract as the capital stock grows. To simplify the analysis of the current account in Section 3, we rule out this possibility by assuming that capital accumulation along the saddlepath is accompanied by a falling level of investment expenditure and thus an expanding traded sector.
The future level of lump-sum transfers to households is assumed to be the revenue variable that the government adjusts in order to ensure that the government’s budget is balanced intertemporally. Because households fully anticipate this future adjustment and because transfers are non-distortionary, the exact timing of the adjustment in transfers is irrelevant for the impact of the policy change on the economy. If instead the government adjusts a distortionary tax in order to ensure that its budget constraint is satisfied, then the timing of the adjustment would be of critical importance in determining the effect of the initial tax cut on the economy.
If the increase in the price of equity is either less than or greater than the amount needed to place the economy on the stable saddlepath, then the economy will never reach the steady-state equilibrium given by the intersection of the
As mentioned in Section 2, the analysis of the current account here and throughout the remainder of the paper assumes that the traded sector expands as capital accumulates along the saddlepath. If instead the traded sector were to contract as capital accumulates, then a current account surplus would accompany capital accumulation along the saddlepath.
Continued real appreciation is more likely the longer is the time during which the tax cut is in effect. What is needed is for the capital stock to be rising at a sufficient rate relative to the rate at which the price of equity is falling so that the change in the real exchange rate, as given by equation (29), is positive.
Again, the analysis assumes that the traded sector expands as capital accumulates along the saddlepath. Note that the non-monotonic adjustment of the current account, described as stages in the balance of payments by Fischer and Frenkel (1972), arises here because the dynamics of the economy off of the saddlepath are driven by both eigenvalues of the system.
A change in government spending on traded goods, however, would have an effect on the price of equity, the real exchange rate and investment if consumption included non-traded goods. The channel here would be through the change in non-traded consumption induced by the change in the future tax burden associated with the change in government spending.
As before, this section assumes that the traded sector expands (contracts) as capital accumulates (decumulates) along a saddlepath.
In Figure 5 it is possible that the adjustment trajectory actually crosses into the region where the capital stock begins to rise prior to the actual reduction in spending. This will occur if the price of equity increases sufficiently relative to the real exchange rate so as to actually raise the ratio q/P above its steady-state value. In this situation, the capital stock will begin to rise before the reduction in spending occurs.