Export Taxation and Border Trading

Now consider producers in country A. They produce a certain amount, X^A, of the export commodity; they sell part of it, X^AA, to their own exporting firms and the rest, X^A – X^AA = X^BA, to firms in country B. For each unit of X, producers are made to pay a marketing cost (for storage and transport) that, without loss of generality, is assumed to be a constant percentage of sales irrespective of the volume of X; this marketing cost is mx_a in country A and mx_b in country B.

Pseudosmuggling is assumed to have a cost that further adds to the effective marketing cost of X^BA. Such a cost can result from the need for additional transport and for assistance along the way; such assistance can often be acquired only through substantial financial expenditures, particularly along the borders. It is further assumed that pseudosmuggling is subject to increasing marginal cost as X^BA increases relative to X^A. This pseudosmuggling (additional marketing) cost is expressed as a function of X^BA—that is, ε (X^BA)—for any given X^A.²

The producers in country A do not avoid export taxation even by selling in country B. Suppose that Pwx_i is the world price of X in local currency (of A or B). Suppose that πx_i is the producer price of country i (i = A, B) specified in local currency. Then if tx_i symbolizes the effective export tax rate in i, and mbx_i the international marketing cost per dollar of marketing-board gross sales, the effective tax rate is

In general, then, the revenue of producers in country A is the sum of the receipts when the export commodity is sold in A and the receipts when it is sold in B. Hence, if Rx_a is receipts of A producers and $P_{wx}^{*}$ is the world price in dollars,

The problem of producers in country A is to maximize Rx_a subject to the condition that

By use of the Lagrangian multiplier, it is a simple matter to show that the first-order condition for maximization of receipts is that

where ε’ is the first derivative of the ε(X^BA) function.

If there is no parallel market in A for B-currency, and vice versa, then e_pab = e_oab = e_oav/e_obv. In that case, equation (3) reduces to

Recalling that $P_{wx}^{*}$ /e_oav is the domestic currency equivalent of the world price of the export, evaluated at the official market exchange rate, one can obtain a real-value analog of equation (4):

where ε' has been divided by P*/e_oav to get ${\epsilon }_r^{\prime },$

Figure 1 gives a diagrammatic representation of the analysis. The β schedule is a constant; in real terms, and in the absence of parallel markets involving exchange of A-currency and B-currency, this curve is simply the left-hand side of equation (5); that is,

which is the marginal benefit of border trading or pseudosmuggling. The other schedule, ε', is of course the marginal cost of border trading.³ With reference to schedules β₀ and ${\epsilon }_0^{\prime }$ in Figure 1, the equilibrium condition (5) is satisfied at the point z₀. The share of X^BA in total output is shown on the horizontal axis in Figure 1; for schedules β₀ and ${\epsilon }_0^{\prime }$ this equilibrium share is X₀.

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Export Taxation and Border Trading

Citation: IMF Staff Papers 1987, 002; 10.5089/9781451972931.024.A006

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Starting with the schedules β₀ and ${\epsilon }_0^{\prime }$ suppose there is an increase in the costs associated with pseudosmuggling. This could happen, for instance, because of increased vigilance of customs and border patrol officials or because of increased transport costs in real terms. The effect would be an upward shift of the ε' schedule from ${\epsilon }_0^{\prime }$ to, say, ${\epsilon }_1^{\prime }$ Equilibrium shifts from z₀ to z₁, and the share of output sold to export marketing firms in country B declines from X₀ to X₁.

An increase in the effective export tax rate in country A or a decrease in the effective export tax rate in country B would lead to an increase in the marginal net benefit of border trading, as would a lowering of the marketing cost in country B (mx_b). Suppose that one or more of these events should occur. Then, starting with the β₀ and ${\epsilon }_0^{\prime }$ schedules in Figure 1, the β₀ shifts upward to, say, β₁. Equilibrium shifts from the point z₀ to z₂, and the share of country A’s exports that is sold to exporting firms in country B increases from X₀ to X₂.

Parallel Foreign Exchange Markets and Border Trading

Equilibrium condition (5) reflects the absence of parallel markets in countries A and B for each other’s currency. The exchange rates between A-currency and B-currency simply reflect the cross rates in relation to the dollar. But suppose that a parallel market exists for these currencies in which the relative valuation of the B-currency is greater than the relative valuation implied by the official exchange rates. That is, in terms of the previous notation, e_pab<e_oab so that e_pab<e_oav/e_obv. This relationship in turn implies that

Hence it is possible to write

where θ > 1. The value of θ will vary depending on the official cross rates and the premium for B-currency in the parallel market.

The implication of the parallel market and the fact that the cross rate in that market is different from the cross rate in the official market is that equation (5) now becomes

The consequence of a premium for the B-currency in relation to the A-currency in the A + B parallel market is, therefore, to cause the marginal net benefit schedule to shift upward. The equilibrium share of output sold by producers in country A to exporting firms in country B increases as a proportion of total exportable output in country A. That the currency of country A is being traded in parallel markets at a discount from the official rate, relative to the currency of country B, is tantamount to having a tax on the net receipts from all exports made through exporting firms in country A. Alternatively, the discount on A-currency can be viewed as the equivalent of a subsidy on net receipts from all exports through exporting firms in country B.

Whether there is a premium on B-currency in country A over the official exchange rate would depend on the degree to which the A-currency is considered overvalued, in terms of the dollar, in the official exchange market, compared with the degree to which the B-currency is considered overvalued, in terms of the dollar, in the official exchange market. Let Eov_i represent the perceived degree of exchange rate overvaluation of the i-currency in relation to the dollar (i = A, B). Then e_oab – e_pab would tend to increase with Eov_a – Eov_b.

Apart from the perceived degree of exchange rate overvaluation, a difference in the parallel and official exchange rates could ensue from differences in the degree of convertibility into dollars of the two currencies. Suppose R_i represents some index of the degree to which convertibility of the i-currency into dollars is restricted, as perceived by the traders in both countries. Then e_oab – e_pab would also tend to increase with R_a – R_b⁴. In brief,

The implication of the foregoing discussion is that θ would tend to be greater, the greater is ψ

Perceptions of exchange rate overvaluation (Eov_i) would, of course, depend on perceptions of what the true “equilibrium” exchange rate ought to be. This perceived equilibrium exchange rate of country i (i = A, B) in turn would be related to such factors as the inflation rate in country i in relation to that in the rest of the world (V), the stock of net foreign assets in country i relative to base (or high-powered) money, and the balance of payments situation of i and its stock of external debt relative to gross national product (GNP). Perceptions of restrictions would be related to the laws of the country and the degree to which they are known to be enforced, as well as to the economic priorities that are revealed in the government’s actions.

Import Taxation and Border Trading

So far the analysis has been concerned with the pseudosmuggling of exports. But border trading may occur not only to minimize effective export taxation but also to minimize effective import taxation. Consider producers and consumers in country A. They could import through importing firms in country A and pay import tax at a rate of tm_a. Alternatively, they could import through importing firms in country B—and pay import tax at a rate of tm_b. Let M^AA symbolize the quantity of imports they buy from importers in country A and M^BA the quantity of imports they buy from importing firms in country B. Just as in the case of border trading of exports, there is a pseudosmuggling cost associated with M^BA, and this cost is specified as a function γ of M^BA. Without significant loss, the markup of importing firms in countries A and B will be ignored.

The problems producers and consumers in country A have in purchasing imports is specified in a similar way to the problem of producers of exports in country A. If Cm_a is the total cost of imports in country A, then the problem is to minimize

subject to the condition that

Note again that M^AA and M^BA relate to imports originating in V.

Once again, using the Lagrangian multiplier yields the first-order condition for cost minimization:

where γ’ is the first derivative of the γ function.

Analogous with the export case, if there is no parallel market that results in an exchange rate between the A-currency and the B-currency different from the official rate, then equilibrium condition (12) can be written in real terms as

But if there is a parallel market in which there is a premium on the B-currency over the A-currency, then equilibrium condition (13) becomes

The situation is shown in Figure 2, where γ’ is the marginal cost of pseudosmuggling and σ is the marginal benefit. The σ curve clearly shifts up with tm_a and down with tm_b and θ. It is intuitively obvious that, whereas a premium on the B-currency over the A-currency has an incentive effect on the pseudosmuggling of exports from country A to country B. the premium has a disincentive effect on the pseudosmuggling of imports from B to A.

Sometimes countries will subsidize the importing of certain goods that are considered essential in production or consumption. The effect of such subsidization is to lower the effective tax rate on imports. Suppose that, from the initial schedules σ and γ’ in Figure 2, country B introduces or raises subsidies (per unit) of some of its import commodities. The effect is to shift the σ schedule up; that is, the share of imports of country A coming through country B increases.

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Import Taxation and Border Trading

Citation: IMF Staff Papers 1987, 002; 10.5089/9781451972931.024.A006

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Border Trading in Both Exports and Imports

So far the pseudosmuggling of exports and that of imports have been treated independently. The quantities and values involved may actually be related. For instance, the pseudosmuggling of exports by producers in country A may be induced by their desire to purchase import goods in country B. Although it is useful to think of the pseudosmuggling of exports and that of imports as two different activities, a slightly more complex framework will be introduced that facilitates consideration of the general case of border traders who engage in the pseudosmuggling of both exports and imports.

In the general case the problem of the representative producer in country A is to maximize imports M subject to the condition that the total cost of imports is equal to the total net receipts from exports. Nothing essential is lost by continuing to assume that there are no net capital inflows (or outflows). Hence the problem can be stated as

subject to

Use of the Lagrangian multiplier again yields the following first-order conditions:

Equation (17) gives the marginal rate of transformation of exports into imports when all importing and exporting are done through firms in country A. Equation (19) is the marginal rate of transformation when there is border trade only in exports, and equation (20) gives the marginal rate of transformation when there is border trade only in imports. Finally, equation (18) gives the marginal rate of transformation when border-trading export receipts are used to finance border-trading imports.

It is now easy to verify that, when pseudosmuggling (border trading) occurs only in exports, equilibrium condition (3) can be alternatively stated as

Similarly, when pseudosmuggling occurs only in imports, equilibrium condition (12) can be alternatively stated as

Now, when border-trading exports are used to finance border-trading imports and normal exports (X^AA) are used to finance normal imports (M^AA), the equilibrium for the producer is simply

At each of these equilibrium points, M^AA, M^BA, X^AA, and X^BA are chosen together so as to obtain the maximum amount of imports for any given quantity of export.

Economic Policy and Losses in the Absence of Policy Coordination

Consider now the dilemma of the government authorities of country A, whose citizens can engage in border trade with neighboring country B. The problem of the government in A is to fix its effective export tax rate (tx_a), its effective import tax rate (tm_a), and the official exchange rate between the dollar and the A-currency (e_oav).

The actual level of government revenue from exports (Grx) to GDP (Y) depends on the ratio of nominal exports to GDP (Xⁿ/Y) as well as on the effective export tax rate (tx_a). But from what has been said in Section I, it is clear that the Grx/Y ratio also depends on the difference between the export tax rate in country A and in country B, since the actual exports on which the export tax is collected depend, inter alia, on tx_a – tx_b. Thus, for country A it is hypothesized that

Similarly, for the case of imports it is hypothesized that

It is being assumed here that mx_a = mx_b. In addition, θ of equation (7) is set equal to unity.

Suppose now that, starting from some configuration of the arguments of F and H in equations (24) and (25), the authorities of country A wish to raise government revenue by increasing Grx_a and Grm_a. Then, given the initial ratios $X_a^n$/Y_a and $M_a^n$/Y_a, with $X_a^n$ and $M_a^n$ being the exports and imports on which the effective taxes are being collected.

and

If the authorities raise tx_a and tm_a in order to raise Grx_a/Y_a and Grm_a/Y_a respectively, the final effect cannot be predicted easily without a determination of how country B will react; that is, of how tx_a – tx_b and tm_a – tm_b will change. Depending on how country B reacts to the change in tax rates in country A as well as on the magnitudes of F₂ and H₂ (which in turn depend on the marginal cost schedules ε’ and λ’, respectively), the authorities in country A may not in fact be able to raise government revenue relative to GDP by raising tx_a, tm_a, or both.

In a situation of border trading, then, the targeting of Gr/Y is made difficult to the extent that a country depends heavily on taxes on international trade. In the case under discussion, when both A and B depend heavily on such taxes, noncoordination of tax policy may result in open competition for (taxable) exports and imports, in lower tax rates, and in lower aggregate tax revenue from these sources. The consequence could easily be values for Gr_a/Y_a and Gr_b/Y_b that are suboptimal from the viewpoint of economic growth and economic welfare.

It is perhaps noteworthy that the governments of the two countries find themselves in a situation similar to that of oligopolists. One major difference is that reaction functions are difficult to specify in this case because, unlike the profit maximization that is a legitimate assumption for the classical oligopoly, it cannot be said that the authorities here seek to maximize their revenue from trade taxes, although they might (as assumed in this paper) have clear targets for such tax revenue.

The pseudosmuggling (border-trading) costs also constitute a welfare loss. For instance, in the case of country A for the situations depicted in Figures 1 and 2 and for equilibrium at z₀ in each case, the total border-trading cost is equivalent to the area 0z_oX₀ in Figure 1 and the area 0z₀ω₀ in Figure 2. Paradoxically, the welfare loss involved in this diversion of resources from more productive activities is borne by the whole society.

Pseudosmuggling also involves a loss of government tax revenue that may have to be made up by alternative tax measures. The pseudo-smugglers are able to reduce their burden of taxation, and this amount of taxation may have to be obtained from other activities and persons. Apart from the welfare loss from suboptimal Gr/Y and the diversion of productive resources to pseudosmuggling, the income-distributional effects of the modification of the tax burden may also entail a welfare loss.

For any particular country, export and import taxation (and the associated Grx/Y and Grm/Y) may be too high in relation to taxation of other activities. That is, production and welfare may be augmented by reducing the taxation of exports and imports and increasing the taxation of other activities. If this is the case, it would appear that pseudo-smuggling, by helping to reduce the effective taxation of exports and imports, is a good thing. But clearly this is only a second-best solution. A straightforward restructuring of taxation is a much more efficient way to achieve optimality without the need to divert productive resources to pseudosmuggling.

The analysis in Section I also indicates that border trading is affected by the relationship between official and parallel exchange rates, as well as by the efficiency of marketing institutions in country A and in country B. Thus, if e_oab – e_pab or mx_a – mx_b (or both) tends to be increasing over time, then X^BA/X^A also tends to be increasing, with the consequence that Grx/Y tends to be decreasing for any given tx_a, tx_a – tx_b, and $X_a^n$/Y_a. The economic costs associated with the diversion of resources to pseudo-smuggling and with the income-distributional effects of altering the allocation of the tax burden are also operating here.

Possible Approaches to Trade Tax and Exchange Rate Coordination

For the two countries A and B in the region within which border-trading costs tend to be relatively low, it has been seen that the structure of export and import tax rates (tx_a – tx_b, and tm_a – tm_b) and the structure of exchange rates in relation to the dollar (e_oav – e_obv) have important economic effects on government revenue relative to GDP (Gr/Y), on the amount of productive resources spent on border trading or its policing, and on the redistribution of income resulting from tax evasion by producers of exports and purchasers of imports.

Given the relative marketing costs (mx_a – mx_b), the economic benefits of coordinating taxes and exchange rates within the region in such a way as to eliminate border trade are obvious. In terms of Figures 1 and 2, the aim is to reduce β and σ to zero. From the viewpoint of trade tax and exchange rate coordination, there are two possible approaches that seem useful. One may be termed the “reference-country” approach and the other the “full harmonization” approach.