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Costly Trade Liberalizations Durable Goods and Capital Mobility

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International Monetary Fund. Research Dept.
Published Date:
January 1988
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THIS PAPER DISCUSSES some simple examples intended to develop intuition about the costs of a temporary trade liberalization policy or, what amounts to very much the same thing, the costs of policies that are expected to be temporary. The motivation for this line of research is the observation that policies fall into the “temporary policy” category any time that their credibility is less than perfect. Because perfect credibility is likely to be more the exception than the rule, it follows that the case of temporary trade liberalization should be more relevant for actual policymaking than the free-trade-forever paradigm that has played such a central role in trade theory.

As elaborated in a previous study (Calvo (1987)), some of the costs of temporary policy are due to the intertemporal substitution in consumption that it generates. In contrast, the present paper will completely ignore those effects by assuming that there is no intertemporal substitution of that kind; instead, it will be assumed that consumption goods are durable and storable, thus opening the door for “supply-side” intertemporal substitution.

The examples assume the existence of a representative, infinitely lived individual; there are two goods—exportables and importables—and the economy is endowed with a fixed amount of each. Most of the paper assumes that consumption takes the form of importable goods, although extensions to fixed proportions are discussed. Moreover, the country is assumed to be “small” in both goods and capital markets; the latter are perfectly competitive. To highlight the role of durability, it is further assumed that individuals always choose a constant consumption path so that, given wealth, consumption is not affected by changes in rates of interest.

Section I discusses the basic and simplest example, in which goods are perfectly durable and storable at no cost and in which trade liberalization is announced at time zero (“initial time”) and is expected to be instantaneously reversed. This case is that of “one-instant liberalization”—a policy that is costly because it leads the private sector to accumulate inventories in anticipation of the future tariff. More interesting, however, is that these costs (measured as the proportional loss of consumption in relation to free trade) could be quite significant. The model is extended in Section II to consider finite-horizon liberalizations and imperfect durability and to allow for the consumption of exportable goods. It is shown that the quantitative results are not significantly changed.

A common feature of the above examples is that they imply unrealistically high inventory levels, in part because of the assumption that the economy can accumulate indefinitely large amounts of inventories at a point in time at no extra cost. Section III deals with this issue by discussing the implications of quantitative constraints and of storage costs. Examples are given to show that the presence of the latter succeeds in lowering the ratio of inventories to gross national product (GNP) to more realistic levels, but still the cost of the liberalization policy continues to be sizable. The reason is that, although storage costs help to reduce the social opportunity costs associated with speculative inventory accumulation, such costs contribute significantly to the total cost of temporary policy.

In Section IV the paper closes with some brief notes on temporariness, credibility, and capital mobility.

I. The Basic Model: One-Instant Liberalization

Assume that the economy is populated by identical individuals, each of whom receives an exogenous path of “mana-type” income in terms of exportable goods. Utility, however, depends only on the consumption of importables (extensions are discussed in Section II). For the sake of contrast with a previous study (Calvo (1987); see also Section IV), it is assumed that there is no intertemporal substitutability and that, therefore, in the absence of uncertainty (as assumed in this paper), consumers choose a level of consumption that is constant over time.

Individuals are perfect competitors in goods and bond markets. For simplicity, it is assumed that the terms of trade are constant—and equal, by normalization, to unity—and that the rate of interest r (that is, the own-rate of interest of tradable goods in international markets) is a positive constant through time. Furthermore, it is assumed that consumer goods can be stored with no direct cost to the consumer and are perfectly durable. These assumptions will be relaxed in Sections II and III.

The domestic relative price of importables, in terms of exportables, is denoted by p, which will differ from unity because of tariffs (p — 1 = the tariff rate). It is assumed that the proceeds of the tariff are given back to the public in a lump-sum (egalitarian) manner.

The “present” is time t = 0. The experiment examined in this section consists of setting the tariff equal to zero for t = 0, with the understanding (or the expectation) that it will be greater than zero (and constant) forever after. In other words, this is a case of a “one-instant” trade liberalization. Thus, more formally,

where p is a constant greater than unity.

Under the present circumstances, it is clear that if a utility-maximizing individual purchases inventories of importable goods at t = 0 (denoted by Z), he will plan to consume from his stock until it becomes depleted. Moreover, it is also clear that after f = 0 he would have no incentive to accumulate stocks any further because the interest rate is positive and p is expected to be constant.1

Thus, without loss of generality, the relevant budget constraint for the representative consumer may be expressed as follows:

where r is the own-rate of interest on exportables; K, Y, and G, also in terms of exportables, denote the present values of the initial holdings of the international bond, claims on future endowments of the exportable good, and (tariff-related) government lump-sum transfers, respectively; c stands for the constant level of consumption; and τ denotes the time at which the stock of importables, Z, is depleted. The integral in equation (2) runs from time τ because, as noted before, the individual is not going to import anything until his stock of importables reaches zero. Subsequently, he will import only what he requires for consumption.

Perfect durability implies that the inventory depletion time, τ, satisfies

Hence, by equations (2) and (3),

where x is the product of the rate of interest, r, and the inventory depletion time, τ; that is,

It is assumed, of course, that the representative individual attempts to maximize his consumption level, c, subject to his budget constraint, equation (4). This assumption obviously leads him to choose τ so that, by equation (5), the associated x maximizes

Thus, x is set such that

Hence, by equations (5) and (7), the individually optimal value of τ is determined solely by r and p, and it is positive if and only if p > 1 (that is, the future tariff is positive).

Now, given the assumption about the distribution of the tariff proceeds, one has

Table 1.Costs of Liberalization, Variable rT(In percent)
Price, prT = 0arT = 0.04rT = 0.12rT = 0.2
1.030.040.040.040.04
1.272.572.472.292.12
1.608.688.367.717.21
2.2019.5518.9217.7316.59
2.8928.9428.1226.5325.00
3.4034.1233.2331.4829.78
4.0038.8837.9436.0834.25

Corresponds to π (Section I).

Corresponds to π (Section I).

where a circumflex (^) on a variable denotes the equilibrium market value. Because each individual is identical, however, c=c^, and from equations (4), (5), (7), and (8) one has

Clearly, a planner who maximizes welfare of the representative individual will choose c to be constant and equal to r(K + Y), Thus, it is natural to define the cost of the present policy, π, as follows:

Hence, by equations (9) and (10), one has

An attractive feature of the present case is that the cost of the policy is merely a function of p; that is, it does not depend on the interest rate.2Table 1 (second column) displays the value of φ for some relevant values of p when rT = 0. Note that the 1 percent cost mark, a relatively large number in this literature (see Harberger (1959)), is quickly reached when the import tariff (p — 1) is less than 27 percent. As indicated in Table 2 (last column), however, the value of t is also very sensitive to p, implying perhaps implausibly long periods before the stock of importables is totally depleted and unrealistically high ratios of inventories to GNP. These limitations, and common sense as well, dictate that the model be extended to account for realistic features such as imperfect durability.

Table 2.Inventory Depletion Time, τ(In years)
Price, pρ = 0.1ρ = 0.5ρ = 1.5ρ = 2.5ρ = ∞a
1.030.070.240.440.530.73
(0.07)(0.23)(0.44)(0.56)(0.74)
1.270,501.993.584.275.97
(0.60)(2.14)(3.70)(4.33)(5,82)
1.601.073.927.058.3911.75
(1.32)(4.23)(7,27)(8.37)(10.73)
2.201.796.5711.8014.0819.55
(2.53)(7-75)(11.79)(13.15)(15.86)
2.892.418.8415.9218.9528.94
(3.79)(10.57)(15.00)(16.35)(18.53)
3.402.7810.2018.3621.8534.12
(4.65)(12.17)(16.59)(17.87)(20.16)
4.003.1511.5520.7924.7539.89
(5.57)(13.67)(17.96)(19.15)(21.18)
Note: It is assumed that r = 0.04 per year. Numbers in parentheses indicate the ratio of inventories, Z, to annual GNP at time zero, which equals r(K + Y).

Corresponds to perfect durability; that is, δ = 0.

Note: It is assumed that r = 0.04 per year. Numbers in parentheses indicate the ratio of inventories, Z, to annual GNP at time zero, which equals r(K + Y).

Corresponds to perfect durability; that is, δ = 0.

II. Imperfect Durability, Finite Liberalization, and Consumption of Exportable Goods

An easy extension of the above results is to assume that the liberalization lasts for T > 0 periods. It is quite intuitive that individuals will wait until time t = T before storing importable goods. At that point they will solve exactly the same problem as discussed in the previous section, except that now the inefficient accumulation of inventories happens at a later time, so one would expect the cost of liberalization to be lower than before. In fact, if the cost of this policy is defined as earlier, and denoted by πT one can show that

Clearly, ϕT is a function of the product rT. Table 1 shows some relevant numbers for this relationship.3 To confirm the intuition, the picture that emerges shows that costs are smaller than if T = 0.4 Most important, the quantitative significance of the costs is not shown to be substantially diminished.

A slightly less obvious extension would be to allow for imperfect durability. Consider, for example, the case in which durable goods depreciate at the constant rate δ≥0. Clearly, equation (3) becomes

hence, equation (4) becomes

Thus, consumption maximization is equivalent to minimizing the bracketed expression in equation (4a) with respect to τ, which yields

An implication of the above analysis is that

Consequently, if equation (14) is evaluated at δ = 0 (the case of perfect durability) and r — 0.04 per year is assumed, it follows that a 1 percent per year increase in the rate of depreciation results in a 25 percent shortening in the depletion time of inventories, τ. This relationship shows, in the simulations exhibited in Table 2, why there is such a sharp decrease in the depletion time as δ is increased above zero—the case of perfect durability.

Denoting by ϕδ the cost of a one-instant liberalization policy (that is, equation (1)) when the rate of depreciation is δ > 0, by equations (8), (4a), and (13) one obtains5

where ρ is the ratio of the rate of interest, r, to the rate of depreciation, δ; that is,

Thus, contrary to the results of Section I, costs are a function of the ratio of the rate of interest to the rate of depreciation.

Notice that, given r, there is no a priori reason to expect the cost to be a monotonic function of durability. When goods are instantly perishable (δ→∞), costs would be zero because there will be no inventory accumulation; but if stocks of durable goods reproduce themselves at the rate r (that is, δ = —r), then, once again, costs would be zero because the economy as a whole would be indifferent between holding a foreign bond and carrying inventories of importable goods. Because intermediate cases exhibit positive costs, it follows that it would not be possible to say in general whether more durability would increase or decrease the costs of a trade liberalization policy such as that specified in equation (1).

In Table 2 one sees a sharp fall in the depletion time, τ, and in the ratio of inventories to GNP with respect to the case of perfect durability, making the results somewhat more realistic. In Table 3 one notices that, even when a wide variety of depreciation rates is tried (if the annual r = 0.04, the simulations cover the cases of δ = 0.4, 0.08, 0.027, 0.016, and 0 per year), the 1 percent cost mark continues to be reached in most cases when the tariff (p — 1) is less than 30 percent. Furthermore, costs of more than 10 percent are still quite possible except for the rather extreme case in which durable goods depreciate at the rate of 40 percent per year (see the column corresponding to p = 0.01 in Table 2; for this computation it is still assumed that r = 0.04 per year).

Finally, the assumption that only importable goods are consumed domestically is relaxed. A simple way to do this is to assume that individuals consume both goods in fixed proportions.6 Thus, if the ratio of the consumption of exportables to the consumption of importables is a, the budget constraint (2) becomes

Hence, if in this case the costs under perfect durability are denoted by ϕ(α), one can show, on the basis of equations (3), (4), and (2a), that

Table 3.Costs of Liberalization, Variable Durability(In percent)
Price, pρ = 0.1ρ = 0.5ρ = 1.5ρ = 2.5ρ = ∞a
1.030.000.010.030.030.04
1.270.270.971.661.942.57
1.601.133,756.066.908.68
2.203.4010.2915.2016.7319.55
2.896.5817.8024.3726.1528.94
3.409.0022.8129.9231.6834.12
4.0011.8328.0533.5636.9738.89

Corresponds to perfect durability; that is, δ = 0.

Corresponds to perfect durability; that is, δ = 0.

which, as expected, reduces to ϕ in equation (11) when α = 0. Clearly, costs are a decreasing function of α As shown in Table 4, however, costs continue to be sizably large, even when individuals are assumed to consume equal values of importable and exportable goods.

III. Quantity Constraints and Direct Costs

The numerical examples presented thus far are not yet fully persuasive because they tend to imply levels of inventories that are several times annual GNP. Without this enormous accumulation of inventories, costs would probably not exceed the usual 1 percent or 2 percent levels.

The equilibrium level of inventories may change substantially if the accumulation of inventories is quantity constrained. Quantitative limits could be due to the existence of physical constraints, such as maximum port capacity, or to the existence of import quotas. The first type of constraint is likely to play some role under extreme circumstances, but it would probably be difficult to argue that, as a general rule, physical constraints will be the dominant force in limiting the size of inventories of international goods.7 The second possibility, quotas, is only one of the policies that could be employed to reduce the costs of the lack of a stable tariff policy and therefore does not affect the relevance of the previous results.8

Table 4.Costs of Liberalization, α= 1(In percent)
Price. pϕ(1)Z/r(K + Y)
1.030.020.74
1.271.305.89
1.604.5311.21
2.2010.8317.58
2,8916.9122.04
3.4020.5724.30
4.0024.1426.30
Note: The last column assumes that r = 0.04 per year.
Note: The last column assumes that r = 0.04 per year.

Another important factor that may have a sizable effect on the level of inventories and social welfare is the existence of direct costs of holding inventories—for example, warehousing costs. Consider a case in which the cost of accumulating a stock of inventories Z is βZ, where β ≥ 0. The budget constraint for the representative individual becomes

For the sake of brevity, one-instant liberalization policy such as in equation (1) will be examined when goods are perfectly durable. Recalling equations (3) and (8), and the procedure followed in Section I, one obtains the following expression for the cost of policy (1)—defined in the same manner as in the introduction to the paper:

The inventory depletion time, τ, however, satisfies

Table 5 shows results of some experiments in which β was chosen high enough so that the ratio of inventories to GNP is approximately equal to unity—a substantial reduction with respect to the corresponding numbers in Table 2, Note, first, that the required β is very large relative to the tariff-related gross revenue per unit of inventories (p — 1). Second, despite these enormous disincentives, the welfare cost hovers very near the 1 percent mark for a 27 percent tariff, and quickly rises above it. Finally, note that the depletion time of inventories, τ, is always less than five quarters.

Table 5.Costs of Instant Liberalization when Z/r(K + Y) ≃ 1
Cost
Price, pβ(percent)τ
1.270.220.951.00
1.600.532.411.12
2.201.114.511.04
2.891.777.061.06
3.402.259.301.12
4.002.8211.571.15
Note: τ is number of years; r = 0.04 per year.
Note: τ is number of years; r = 0.04 per year.

The main lesson from these experiments is that, although direct costs of holding inventories may induce a drastic reduction in their size and therefore result in a sharp decrease in the total opportunity cost of the funds devoted to acquire them (in previous sections, the only source of costs), the total costs, including direct costs, may still be quite sizable.

IV. Reinterpreting the Results: Credibility

The above framework is general enough to give some insight into the costs of credibility as regards liberalization policy. In common parlance, expressions such as “incomplete credibility” of policy are used to denote situations in which the public believes that there is a positive probability that policy announcements will not be carried out. Consequently, a policy that is not fully credible is one that elicits the expectation that it is going to be modified in the future. With this interpretation in mind, therefore, the examples in previous sections would correspond to situations in which the free-trade policy is not credible, and the public expects that it will be replaced by a constant-tariff policy after time T.

Obviously, the behavior of the economy during the transition (from zero to T) will be the same as in the previous examples. Furthermore, the actual cost of the noncredible liberalization policy would also be the same if inventories cannot be resold in international markets, and if a constant permanent tariff policy was expected after time T. Under these circumstances, let us consider the interesting case in which policymakers announce a free-trade-forever policy beginning at time zero, but, before time T, the public does not believe in its continuation after time T (the next elections, say), when they expect (with probability 1) that a constant and permanent tariff will be imposed. Furthermore, assume that if the public sees free trade continuing after time T, their disbelief will vanish altogether, and full credibility in the free-trade-forever policy will be ensured. Clearly, therefore, a free-trade-forever policy will be associated with exactly the same paths and the same welfare costs as in our examples. This illustrates the central point of the paper: a trade liberalization policy that is not fully credible may be costly, and its costs may not be negligible, particularly when they are compared with the usual estimates for the gains from trade.9

In closing. I would like to stress an obvious but important point. In the models developed here the distortions of credibility or temporariness were shown to be harmful because it was assumed that capital was perfectly mobile. In the context of the models, if there were no international capital mobility, the accumulation of inventories simply could not occur, and hence the social costs would be nonexistent. This observation provides some grounds for controlling international borrowing and lending during a trade liberalization program that is not fully credible. Such control could be accomplished by the sheer imposition of quantity controls (for example, quotas on durable goods or on foreign borrowing) or by a tax on international capital mobility. When credibility is at stake, however, there is a case for preferring direct quantity controls over taxes, since the latter require a good knowledge about the exact nature of the credibility problem. In the examples given here, for instance, the policymaker should be able to ascertain the expected future tariff, p - 1, and the expected timing of its implementation, T. This information is not required for quantity constraints.10

References

    CalvoGuillermoA.“Incredible Reforms” (unpublished; Philadelphia: University of PennsylvaniaNovember1986).

    CalvoGuillermoA.“On the Costs of Temporary Policy,”Journal of Development Economics (Amsterdam) Vol. 27(1987) pp. 245-62.

    EdwardsSebastian andSweder vanWijnbergen“The Welfare Effects of Trade and Capital Market Liberalization,”International Economic Review (Philadelphia) Vol. 27 (February1986) pp. 141-48.

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    HarbergerArnoldC.“Using the Resources at Hand More Effectively,”American Economic Review (May1959) pp. 134-46;reprinted as Chapter 5 ofArnoldC.HarbergerTaxation and Welfare (Boston: Little, Brown1974) pp. 108-19.

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    KruegerAnneO.“The Political Economy of the Rent-Seeking Society,”American Economic Review (Nashville, Tennessee) Vol. 64 (June1974) pp. 291-303.

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*Mr. Calvo is Professor of Economics and Co-Director of the International Economics Research Center at the University of Pennsylvania and holds a Ph.D. from Yale University. This paper was written while he was a visiting scholar in the Research Department.
1This, incidentally, shows that if p is expected to be always constant (that is, including t = 0), then there would be no incentive for storing importable goods.
2The calculations would also apply to an economy that produces the importable good, such that the output of exportables and importables is not affected by the tariff.
3Note that if r - 0.04 per year, Table 1 covers the cases of T - 0, 1, 3, and 5 years.
4This would not necessarily be so, however, if there were some intertemporal substitutability (Calvo (1987)).
5Costs are measured as in equation (10), with c standing now for the equilibrium consumption level when inventories depreciate at the rate δ.
6Given the purpose of this paper, this assumption is much less restrictive than it sounds: in allowing for substitutability between importables and exportables, one would imply the existence of gains from trade—from which the present paper is trying to abstract.
7A more plausible constraint would be international credit market rationing. This aspect will not be examined here, however, because the focus of the paper is on the harmful effects of capital mobility when it is combined with the existence of storable goods; rationing, of course, represents a constraint on capital mobility.
8In this respect note that, in any application of the “quotas solution,” the cost-reducing effect of a quota would have to be weighed against the rent-seeking costs that it may generate (Krueger (1974)).
9To avoid any confusion, I would like to point out that in the context of the model, a noncredible tariff—a tariff that is expected to be phased out in the future— -would have no welfare effects because there would be no incentive to accumulate inventories of importable goods. This asymmetry disappears immediately, however, when one allows for inventories of exportable goods. Consequently, the central problem is the lack of credibility of policy announcements, rather than the noncredibility of liberalization policies.
10This point is further elaborated in Calvo (1987). The role of capital mobility in the staging of economic liberalization policies has been recently discussed by Edwards and van Wijnbergen (1986).

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