This paper uses a numerical general equilibrium model to examine the quantitative importance of pre-existing factor tax distortions for the welfare effects of tariffs and import quotas. The presence of preexisting taxes can greatly raise the costs of these policies, possibly by over several hundred percent. For a tariff much of this extra cost can be offset if tariff revenues are used to reduce distortionary taxes. Hence there can be a large cost discrepancy between tariffs and quotas. The optimal tariff for a country with market power in trade can be reduced to zero, unless revenues finance cuts in distortionary taxes.
In recent years a literature has emerged that re-evaluates the costs of government policy instruments in a second-best setting that allows for pre-existing sources of distortion in the economy created by the tax system. Most of this work has focused on the costs of environmental regulations, however the implications apply broadly across a whole range of policy measures, including trade restricting policies. The key message from this literature is that any regulations that raise the prices of (final) goods in the economy tend to indirectly exacerbate the welfare costs of the tax system. In most models, this occurs through a reduction in labor supply in response to the effect of higher prices on reducing the real household wage. The reduction in labor supply results in a welfare loss, due to the wedge between the gross and net wage created by labor taxes. Taking into account this spillover effect in the labor market can raise the overall costs of regulatory policies by a substantial amount, and sometimes by enough to compromise their ability to improve overall welfare. In this paper we use a numerically solved general equilibrium model to assess the significance of pre-existing taxes in the context of restrictive trade policies.
Second-best considerations are obviously not new to trade economists. There is an extensive literature that examines the welfare impacts of restrictive trade policies in the presence of pre-existing sources of distortion in the economy. However most of this literature focuses on non-tax sources of distortion, such as imperfectly competitive product markets, institutional distortions in labor markets and alleged externalities associated with infant industries.
The link between trade policies and the tax system has been studied in the context of optimal tax systems. These studies find that, in the presence of optimal (i.e. Ramsey) commodity taxes, additional taxes on imports and exports are optimal only if the domestic country has market power in world markets.
In other words, for a given amount of revenue raised, these policies involve higher welfare costs than commodity taxes (in the absence of market power). This reflects their narrower base and hence the greater substitution possibilities for firms and households to avoid the tax.
More recently Williams (1999) has used an analytical model to examine the implications of preexisting factor taxes for the welfare impacts of (revenue-neutral) restrictive trade policies using a specific factors model of an economy with market power in trade. Assuming no retaliation by foreign governments, he shows that the optimal rate of tariff to take advantage of market power is unaffected by pre-existing taxes, unless the net impact of the tariff is to alter the relative burden of taxation born by labor and the specific factors. In contrast, allowing for pre-existing taxes reduces the tariff-equivalent of the optimal (non-auctioned) import quota, or voluntary export restraint (VER).
Two effects underlie these results. First, tariffs, and their non-tariff equivalents, raise the prices of goods in the economy. This reduces the real household wage, (slightly) reduces labor supply and exacerbates the welfare cost of taxes in the labor market. This type of effect has been termed the tax interaction effect in studies of environmental regulations (Goulder, 1995). Second, tariffs generate revenues for the government that can be used to reduce distortionary factor taxes. The potential welfare gain from this has been termed the revenue-recycling effect. The reduced optimal level of regulation under the import quota or VER in Williams (1999) reflects the inability of these policies to offset the costs of the tax-interaction effect with the welfare gain from the revenue-recycling effect.
This paper extends the work of Williams (1999) by using a numerically solved model to gauge the quantitative importance of pre-existing factor taxes for the welfare effects of restrictive trade policies.
We mainly focus on tariffs and import quotas, but we also discuss VER’s. We examine cases when the domestic country can and cannot affect world prices of traded goods, and we consider the possibility of retaliation by a foreign country. The model is calibrated using U.S. data for labor market parameters.
We find that pre-existing factor taxes can substantially raise the welfare costs of restrictive trade policies. This cost increase can exceed several hundred percent in the case of import quotas, or tariffs when revenues are returned as lump sum transfers. In contrast, the proportionate increase in costs under a revenue-neutral tariff (with revenues used to cut distortionary taxes) is smaller, though still significant (around 30 percent). The cost discrepancy between import quotas and revenue-neutral tariffs depends importantly on the extent of import reduction. It can be dramatic at modest levels of import reduction, but converges to zero as these policies become prohibitive.
In addition, we find that the traditional case for an optimal tariff (in the absence of retaliation) in economies that can influence world prices is dramatically reduced, if not eliminated altogether, unless tariff revenues are used to reduce other distorting taxes. That is, the tax-interaction effect can easily outweigh the welfare gain to the domestic economy from taking advantage of monopoly power in world markets. In cases where the foreign economy retaliates to domestic trade protection, pre-existing taxes can raise world welfare costs by an amount comparable to that caused by retaliation.
The second-best costs of VER’s (with distortionary taxes) are not much greater than the first-best costs (without distortionary taxes) when costs are measured by domestic welfare losses. This is because the first-best costs of VER’s include the income loss from the transfer of rents to foreign suppliers, and these costs are typically much larger than the first-best costs of import quotas. However, if the costs of VER’s are measured by world welfare losses, this income transfer is not included. In this case, the second-best costs of VER’s can exceed the first-best costs by several hundred percent.
Our results have some potentially significant implications for policy. They suggest that the welfare gains from free trade may be substantially larger than implied by earlier analyses that neglect preexisting factor tax distortions.6 They also imply that if, for whatever reasons, imports of a particular product are to be restricted, there is a potentially important efficiency case for using tariffs over quantity restrictions, or alternatively auctioning import quotas, so long as the revenues are used to cut other distorting taxes. In contrast, since the 1970’s tariffs in the U.S. have been reduced while (non-auctioned) non-tariff barriers have been expanded (Bhagwati (1988)).
The rest of the paper is organized as follows. We begin in Section 2 by providing a theoretical framework for interpreting the quantitative results. Section 3 presents our simulation results. Section 4 concludes and discusses some important caveats to the analysis.
2. Theoretical Framework
In this section we sketch out an analytical model that integrates factor taxation into a standard specific factors trade model. The model shows, qualitatively, how pre-existing factor taxes affect the welfare impacts of tariffs and import quotas. For simplicity, we focus on an economy facing exogenous world prices. Our discussion is fairly brief since the model is similar to that in Williams (1999).
We assume that the trade account balances; that is, expenditure on imports equals revenues from exports, where both are expressed in terms of foreign exchange. The world prices of these goods are determined exogenously in the foreign economy, and are normalized to unity. Therefore:
where M and X denote import and export quantities. The trade account balances via changes in the domestic currency price of imports relative to the price of exports, brought about by changes in the real exchange rate. We normalize the domestic currency price of good 2 to unity and denote the relative price of good 1 (gross of tariffs or tariff-equivalents) by p.
The government has an exogenous revenue requirement of G and levies a proportional tax of tL on labor income.10 For simplicity we assume that G is returned to households as a lump sum transfer. The government also regulates the quantity of imports using various policy instruments. For the moment, we assume no retaliation by the foreign country in response to trade protection by the home country. In addition we assume the government budget must balance, hence any revenues raised by the trade policies are used to reduce the labor tax (the implications of alternative assumptions are discussed later).[ 11]
We now discuss the welfare impacts of restrictive trade policies in this setting. Below, we present formulas for the welfare impacts; the derivations of these formulas are provided in Appendix A.
B. Comparing the Welfare Impacts of Trade Policies
(i) Import Tariff
The first term on the right hand side in this equation is the welfare gain in the labor market from using the additional tariff revenues to reduce the labor tax. This is the (marginal) revenue-recycling effect. It equals the product of the marginal tariff revenue and the marginal excess burden of taxation. The second term is the welfare loss from the (marginal) tax-interaction effect. Increasing the tariff rate drives up the price of good 1, and hence the price of consumer goods in general. This reduces the real household wage and induces a substitution out of labor and into leisure. The reduction in labor supply leads to an efficiency loss because of the wedge between the gross and net wage. In addition, the reduction in labor supply reduces labor tax revenues. The combined welfare loss from these two effects is the tax-interaction effect.
If consumption goods are equal substitutes in demand for leisure, and the labor to fixed factor input is the same in both domestic industries, then the marginal tax-interaction effect can simply be
The first term on the right in (2.7) is the welfare loss from the reduction in imports, and is equivalent to that under the tariff. The quota produces a welfare loss from the tax-interaction effect, since it also increases the price of consumption goods relative to leisure. 16 However, since it does not raise revenues for the government, it does not produce the benefit from the revenue-recycling effect. In this case, the effect of pre-existing taxes is to shift up the marginal cost curve for reducing imports such that the curve has a positive intercept. This is because the tax-interaction effect results in a first order (or nonincremental) welfare loss, given the tax wedge between the gross and net wage.
3. Numerical Analysis: World Prices Exogenous
We now explore the quantitative importance of pre-existing taxes for the welfare cost of trade policies. To do this we specify functional forms for the previous model and solve by numerical simulation.18 We also allow for a little more realism by including a non-traded goods sector. Subsections A and B describe the structure and calibration of the model. Appendix B provides more details on how the model is solved. Subsection C presents the main numerical results. Subsection D discusses the results from a model with endogenous world prices, and Subsection E presents further sensitivity analysis
percent, and 20 percent for each of the two traded goods (that is, imports account for 50 percent of importable consumption). The relative costs of policy instruments are not sensitive to alternative values for these shares (see later). The shares of labor income, and total specific factor income, in total income are initially 90 percent and 10 percent respectively. The ratio of labor to specific factor input is initially the same in each industry¾as discussed below, relaxing this assumption can strengthen or weaken the tax-interaction effect. We use estimates of U.S. labor market parameters¾estimates of labor supply elasticities for other countries are much more sparse. The consumption/leisure substitution elasticity sU, along with the labor time endowment, are chosen to imply uncompensated and compensated labor supply elasticities of 0.15 and 0.4 respectively. These are median estimates from the literature, and are meant to capture the effects of changes in the real household wage on average hours worked, the labor force participation rate and effort on the job. However there is uncertainty surrounding these elasticities, and the results are somewhat sensitive to alternative assumptions (see below). Following other studies, we assume a preexisting factor tax rate of 40 percent.[26 ]Higher tax rates, which are appropriate in, for example, the European Union, can greatly magnify our results. The marginal excess burden of labor taxation is 0.3, which is consistent with other studies (e.g. Browning (1987), Ballard et al. (1985)).
In our benchmark simulations we assume the elasticity of substitution between consumption goods is unity, implying the (uncompensated) own price elasticity of demand for consumption goods are all unity. We assume production elasticities of 0.5. Our results are not very sensitive to these elasticities.
Below, we refer to our benchmark case with the factor tax as the “second-best” case. We compare this with a “first-best” case in which the pre-existing factor tax is set to zero, and any revenue consequences from trade policies are neutralized by lump sum transfers from (to) households.
C. Main Results
(i) Marginal Costs. We begin in Figure 1 by comparing the marginal welfare cost curves of policies to illustrate some additional qualitative results.27 The horizontal axis shows import reductions over the entire range from 0 to 100 percent. The dashed curve with the triangle legend is the marginal cost under the tariff or import quota in the first-best scenario, which is the mirror image of the gap between the demand and supply of imports. This curve has a zero intercept and is upward sloping.
The solid curve with the triangle legend is the marginal cost under the tariff in the second-best case, with revenues devoted to cutting the factor tax. This curve also has a zero intercept but has a steeper slope than for the first-best tariff. As discussed in Section 2, this is because the tax-interaction effect dominates the revenue-recycling effect for a non-marginal reduction in imports. When tariff revenues finance lump sum transfers marginal costs are shown by the solid curve with the circle legend. This curve has a positive intercept, since there is no revenue-recycling effect to offset the tax-interaction effect.
However, marginal costs increase at a slower rate when tariff revenues finance lump sum transfers rather than cuts in distortionary taxes. This is because under the latter policy marginal tariff revenues, and hence the marginal revenue-recycling effect, declines as the quantity of imports¾the base of the tariff¾is reduced. Marginal tariff revenue becomes zero at around a 50 percent reduction in imports (the peak of the Laffer curve). Beyond this point the marginal revenue-recycling effect is negative and the marginal cost curve under the revenue-neutral tariff lies above that under the tariff with lump sum replacement.
Marginal costs under the import quota, indicated by the solid curve with the square legend, lie between those for the tariff, with and without the revenue-recycling effect. This is because the government captures a fraction¾40 percent¾of the quota rents through income taxation, and this produces a revenue-recycling benefit equal to 40 percent of that under the revenue-neutral tariff. If instead these revenues were returned to households as lump sum transfers, marginal costs would be equivalent to those under the tariff with lump sum replacement.
Finally, we also consider a VER (voluntary export restraint). This policy limits imports from foreign suppliers, but in this case the quota rents are transferred to foreign suppliers rather than accruing to domestic households. The dashed curve with the “X” legend indicates marginal costs under a VER in the first-best case. The curve has a substantial intercept. This reflects the first order income loss from the transfer of quota rents to the foreign economy (instead of the quota rents being recycled back into the domestic economy). However marginal costs are decreasing, rather than increasing as under the other policy instruments. This is because the incremental income loss from the transfer of rents is proportional to the import base, which is falling (see equation (2.8)). Finally, the solid curve with the “X” legend shows marginal costs under the VER in the second-best case. Marginal costs are higher in this case, due to the efficiency loss from the tax-interaction effect.
(ii) Total Costs. Table 1 shows the total (second-best) costs of the import-restricting policies at import reductions of 5, 20, 50 and 100 percent. These are expressed relative to the total cost of the same import reductions under the tariff in the first-best case. The first row indicates that pre-existing taxes raise the total cost of the revenue-neutral tariff by approximately 30 percent, at all levels of import reduction.
The proportionate increase in cost due to pre-existing taxes under the tariff with lump sum replacement is potentially very substantial. For example, the policy is 14 and 4 times as costly in a second-best case than in the first-best case, for import reductions of 5 and 20 percent respectively. Indeed it is infinitely more costly for an incremental reduction in imports, reflecting the positive intercept of the marginal cost curve in Figure 1. At higher levels of import restriction the discrepancy between the tariff with and without the revenue-recycling effect is less striking. The total costs of the two policies converge as the tariff becomes prohibitive, since tariff revenues converge to zero¾in Figure 1 the area between the corresponding marginal cost curves, integrated between 0 and 100 percent import reduction, is zero. The differences between the import quota and tariff are similar, though not quite as striking, since the quota creates a partial revenue-recycling effect. For the rest of the paper, we do not explicitly consider the import quota, since the difference in (marginal and total) cost between the import quota and the revenue neutral tariff is always equal to 60 percent of that between the tariff with and without revenue-recycling.
The VER is the most costly policy, due to the transfer of quota rents to the foreign economy.
Comparing the fourth and second rows in Table 1, this welfare loss is generally much larger than the welfare loss from the tax-interaction effect. The ratio of second-best costs to the first-best costs under the VER (the fifth row divided by the fourth row) is generally much smaller than for the other policy instruments. However, if the costs of the VER were measured by world welfare losses, the ratio of first-best to second-best costs would be much more dramatic, since quota rents would not be included in these costs. Note that the costs of all the second-best policies are identical at 100 percent reduction in imports.
At this point the entire consumer surplus from imports is eliminated, the increase in price of consumption, and hence tax-interaction effect, is the same across all policies, and there are no revenue-recycling benefits.
We summarize some of the key themes so far as follows. First, pre-existing taxes can substantially raise the costs of trade policies. Second, the increase in cost is much larger for policies that do not raise revenues that are used to cut distortionary taxes. Third, the relative cost discrepancy between policy instruments depends importantly on the level of import reduction.
D. Endogenous World Prices
We now consider the implications of market power in trade; that is, the domestic economy can influence world product prices. This introduces the possibility that trade policies can increase domestic welfare, though world welfare necessarily falls. Details of this extended model, and a much more comprehensive discussion of the results, are provided in the earlier working paper (Parry, 1998). Here we just summarize the main findings. In the model the world economy consists of two symmetrical countries (or trading blocs), with identical preferences, labor tax rates, shares of imports, exports and nontradable consumption in GDP.
(i) Results with No Retaliation. Table 2 decomposes the welfare effects of import-reducing policies imposed in the domestic economy, assuming no retaliation by the foreign economy. In row 1a we see that in a first-best setting, up to a point a tariff (or import quota) can increase welfare in the domestic economy (shown by the negative entries). The key difference compared with the small open economy case is that the domestic country now faces an upward sloping supply curve for imports. The tariff leads to a second-order domestic welfare loss by reducing import consumption. But part of the tariff burden is born by the foreign country, since the price they receive for exporting to the domestic country is reduced. Thus the policy enacts a transfer of surplus from the foreign to the domestic economy, and this gain dominates the welfare loss from reduced import consumption, for modest amounts of import reduction.
In the second-best case, the tax-interaction effect substantially reduces the potential welfare gain from a tariff with lump sum replacement, compared with the first-best tariff¾the welfare gain is reduced by 58 percent and 70 percent at import reductions of 5 and 20 percent respectively (comparing rows 1a and 1c). However, if tariff revenues are used to reduce distortionary taxes the overall welfare impact is similar to that of the first-best tariff (comparing rows 1a and 1b).34 In short the case for implementing the optimal tariff can critically hinge on whether the tariff revenues are used to cut distortionary taxes or not (more on this below).
The second set of rows in Table 1 shows world, as opposed to domestic, welfare costs (again expressed as a percent of domestic GDP). All cell entries are positive indicating that any gains to the domestic economy are always more than offset by losses to the foreign economy. From rows 2a and 2b, the tariff with revenue-recycling is around 30 percent more costly than the first-best tariff. From rows 2a and 2c, the tariff with lump sum replacement is around 14 and 4 times as costly as the first-best tariff, for import reductions of 5 and 20 percent respectively. Thus, pre-existing taxes raise the world welfare costs of tariffs in our model with endogenous world prices, by more-or-less the same proportionate amount as they raise the domestic welfare costs of tariffs in our exogenous world price model.
(ii) Results With Retaliation. We report results from Parry (1998) under the assumption that the foreign economy imposes the same tariff on domestic country exports, as the domestic country imposes on foreign country exports (revenues from trade policies are used in the same manner as in the domestic country). The resulting domestic and world welfare costs (as a percent of domestic GDP), compared with the situation when neither country restricts imports, are shown in Table 3. These are expressed for given reductions in domestic country imports from its own policy, prior to the retaliation by the foreign economy. Therefore, by subtracting row 1a in Table 3 from row 1a in Table 2 we obtain the domestic costs of a retaliatory tariff in a first-best setting. Then subtracting row 1a from rows 1b and 1c in Table 3, we obtain the additional costs due to pre-existing taxes, and so on.
The domestic welfare losses caused by retaliation are significantly larger than the additional costs due to pre-exiting taxes. For example, under the tariff with lump sum replacement, the additional welfare costs due to pre-existing taxes are 26 to 59 percent of the additional costs due to retaliation. This is because retaliation effects a first-order income transfer from the domestic to the foreign economy. When viewed from a global perspective however, pre-existing taxes can have a larger impact on increasing welfare costs than retaliation. For example, under the tariff with lump sum replacement the additional costs due to pre-existing taxes are 7.2 and 1.6 times as large as those due to retaliation, when the domestic tariff initially reduces imports by 5 and 20 percent respectively. Even when tariffs produce the revenue recycling benefit, the additional costs from pre-existing taxes are 50 percent of those from retaliation.
E. Sensitivity Analysis
(i) Degree of Market Power. In Table 4 we indicate how pre-existing taxes affect the optimal reduction in imports for the domestic economy (assuming no retaliation) under different assumptions about the share of the domestic economy’s GDP in world GDP.35 In the first-best case, when this share is relatively small the domestic economy has relatively little market power hence the optimal level of import restriction is relatively small. For example, when the share in world trade is 5 percent the optimal reduction in imports is 4.7 percent. In contrast when the share is 50 percent, the optimal import reduction is 31.5 percent.
In a second-best setting, the tax-interaction effect dramatically reduces the optimal amount of import restriction under a tariff with lump sum replacement, compared with the first-best case. For example, when the domestic economy’s share in world trade is 35 percent, pre-existing taxes reduce the optimal level of import reduction from 24.0 percent to just 2.2 percent. When the trade share is 5 percent or 20 percent, the optimal import reduction is zero. In contrast, when the tariff generates the revenue recycling effect, the optimal level of import reduction is very similar to that in the first-best case. Thus,
pre-existing taxes substantially reduce, if not eliminate, the case for an optimal tariff, unless the tariff revenues are used to cut other distortionary taxes. We now consider how alternative model specifications and parameter values affect the proportionate increase in costs of tariffs caused by pre-existing taxes, assuming fixed world prices. The cell entries in Table 5 show ranges for the ratio of second-best costs to first-best costs for the tariff with and without the revenue-recycling effect, for import reductions of 5 and 50 percent.
(ii) Relative Size of the Traded Goods Sector. In the first set of rows in Table 5 we vary the share of the traded goods sector in domestic GDP. First, we hold importable consumption at 20 percent of GDP, but vary the share of imports between 10 and 90 percent of importable consumption. Second, we vary the share of importable consumption in GDP between 5 and 40 percent (keeping the ratio of imports to importable consumption at 50 percent). In either case, this has virtually no impact on the ratio of second-best to first-best costs. In other words the tax-interaction and revenue-recycling effects are proportional to the first-best costs of the tariff.
(iii) Factor Input Ratios. When factor input ratios differ across industries, trade policies have an
additional impact on the labor market. Suppose import-competing production is labor intensive relative to that in the exporting industry. Import restrictions lead to additional production in the first industry and reduced production in the second. Thus they raise the demand for labor, and this serves to mitigate the tax-interaction effect. Conversely, if import-competing production is relatively intensive in the specific factor, the tax-interaction effect is larger.
In the second row of Table 5 we halve and double the ratio of specific factor to labor input in import-competing production (adjusting that in the export industry to keep total factor shares the same). This reduces and increases the tax-interaction effect by approximately 40 percent respectively. Indeed a modest, revenue-neutral tariff can produce an overall welfare gain if import-competing production is labor intensive (even though the country has no market power in trade). Effectively, the policy shifts the overall burden of taxation away from labor and onto the specific factors (see Williams, 1999).
(iv) Share of Fixed Factor Income in Total Income. Reducing the share of labor endowment in total factor endowment reduces the tax-interaction and revenue-recycling effects. However the quantitative importance of this is limited¾doubling the share of specific factor endowment in the total value of endowments has a relatively modest impact on reducing the net efficiency loss from interactions with the tax system (see row 3 of Table 5).
(v) Labor Market Parameters. The fourth set of rows in Table 5 varies the labor market parameters. We vary the initial factor tax rate between 20 and 60 percent. This has a disproportionate effect on the relative size of the revenue-recycling and tax-interaction effects. For example the proportionate increase in costs due to pre-existing taxes under the revenue-neutral tariff varies between 7 and 200 percent. The costs of the tariff with lump sum replacement in the presence of a 60 percent factor tax are 78 times as large as the first-best costs, for an import reduction of 5 percent!
Our results are also sensitive to alternative assumptions about labor supply elasticities. Based on the recent survey by Russek (1994), a plausible range for the economy-wide, uncompensated labor supply elasticity is 0 – 0.3. Using these values leads to a reduction and an increase in the tax-interaction effect of roughly 40 percent.
(vi) Consumption and Production Elasticities. In the final set of rows in Table 5 we halve and double the consumption goods and production elasticities. This has little effect on the ratio of second-best to first best costs. For a given reduction in imports, the more elastic the demand for imports (that is, the larger the consumption and production elasticities) the smaller the first-best welfare loss. However this also implies a proportionately smaller tax-interaction effect, since the increase in price of imported consumption is lower. It also implies a proportionately lower rate of tariff to induce the import reduction, and hence a smaller revenue-recycling effect.
This paper examines the quantitative importance of pre-existing factor tax distortions for the welfare effects of restrictive trade policies in small and large open economies. Using U.S. labor market parameters, we find that pre-existing taxes can substantially raise the costs of such policies, sometimes by over several hundred percent. This reflects the adverse impact on labor supply, stemming from the effect of trade restrictions that drive up domestic consumer prices and hence reduce the real household wage.
However, much of this added cost may be offset if the trade policy raises revenues for the government and these revenues are used to reduce other distortionary taxes. Thus, there is a potentially large discrepancy between the costs of revenue-neutral tariffs and (non-auctioned) import quotas. This is particularly the case for modest levels of import reduction. In addition, the case for an optimal tariff in an economy with market power in trade is dramatically reduced, if not eliminated, unless the revenues from the tariff finance cuts in other distortionary taxes.
There are a number of potentially important caveats to the above results. We have mainly focused on the central case of equal factor input ratios across industries. More generally, when factor input ratios differ the second-best costs of trade restrictions can be significantly larger or smaller than in the central case.
Our model incorporates only one imported good. More realistically countries import a variety of different goods and these may be subject to varying rates of tariffs or non-tariff barriers. Introducing a new tariff may affect the efficiency impacts of existing trade restrictions both directly through shifts in demand and supply and indirectly through changes in the real exchange rate, required to maintain trade balance equilibrium (Harberger, 1989). A more comprehensive second-best evaluation of particular trade restrictions would take into account these types of spillover effects, in addition to the spillover effects in distorted factor markets.
Another assumption in our analysis is perfect competition. Over the last two decades many trade models have been developed that incorporate imperfect competition and increasing returns at the industry level due to, for example, R&D spillovers and learning by doing. In these models trade protection can enhance domestic welfare (in the absence of retaliation) by, for example, inducing domestic firms to develop new products before foreign rivals, thereby capturing rents from a first-mover advantage.38 A useful extension to the above analysis would be to weigh the potential efficiency gains from trade policies in these types of situations against their costs, in terms of exacerbating factor market distortions.
We also assume the only source of distortion in the labor market is that created by the tax system. In many countries, non-tax factors such as trade unions, minimum wage laws and employment protection legislation may importantly affect the level of the distortion in the labor market.39 Taking into account these factors may significantly magnify the efficiency impacts of trade policies in factor markets. In addition, our analysis assumes labor is perfectly mobile between sectors and that workers respond to increases in the consumer price level in the same way that they respond to cuts in nominal wages.
Finally, our analysis is static and abstracts from interactions with the capital market. In a more general setting, to the extent that trade policies discourage investment rather than consumption they will tend to exacerbate the efficiency costs of taxes in the capital market rather than taxes in the labor market. Incorporating the capital market requires a more sophisticated dynamic analysis that allows for capital accumulation over time. Unfortunately, these types of dynamic models are difficult to implement empirically because of uncertainty over the consumption/savings elasticity.
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United States International Trade Commission (USITC), 1995. The Economic Effects of Significant U.S. Import Restraints: First Biannual Update. U.S. International Trade Commission, Washington, DC.
Williams, Roberton C., 1999. “Revisiting the Cost of Protectionism: The Role of Tax Distortions in the Labor Market.” Journal of International Economics 47: 459-477.
[1 ]For surveys of this literature see e.g. Bovenberg and Goulder (1998) and Parry and Oates (1999).
 In the context of environmental problems it has been shown that tradable emissions permit programs that fully internalize an environmental externality may actually lead to a reduction in overall social welfare. This is because the partial equilibrium welfare gain can be more than offset by the costs from exacerbating pre-existing tax distortions (see for example Parry et al. (1999)). In a somewhat different context, Browning (1997) finds that the costs of monopoly pricing in the U.S. are several times larger when the impact of restricted production on exacerbating tax distortions in the labor market are taken into acount.
 For reviews of this literature see for example Baldwin (1992) and Bhagwati (1971).
 See for example Dixit (1985), Broadway et al. (1973) and Dasgupta and Stiglitz (1972).
[5 ]Other theoretical studies have examined trade policies in the presence of differential tax treatment of factor inputs across industries (see for example Magee (1976)).
 See for example the estimates in USITC (1995) and Feenstra (1992). In the U.S. most trade now takes place with little restriction. However, a number of industries still receive significant protection, including textiles, steel and certain agricultural commodities (particularly sugar, cotton and dairy products). In addition, restrictions on trade with other countries are imposed from time to time to pressure these countries to change policies related to, for example, the environment, race, and nuclear weapons.
 The same policy implication emerges from studies that compare the costs of trade restrictions in the presence of rent-seeking activities. In this case, competition among firms for (non-auctioned) import quotas leads to additional rent-seeking efficiency losses that do not occur under tariffs (see Kreuger (1974) and Bhagwati (1982)).
 This assumption implies that the ratio of labor to specific factor input and the elasticity of substitution between factors in the production function is the same in both domestic industries (see for example Harberger (1962)). When these conditions do not hold there is an additional effect that could slightly strengthen or dampen the tax-interaction effect discussed below (see Williams (1999)). We explore the quantitative importance of this generalization in Section 3.
 That is, p is the additional units of good 2 that must be exported to pay for one more unit of imports of good 1.
 In this section we assume that non-labor income is not taxed. This is relaxed in later sections.
 Given our assumptions, in the absence of the trade policy there are no pre-existing distortions in the markets for goods 1 and 2, hence the trade policies necessarily reduce efficiency within these markets. Of course, more generally trade protection policies could conceivably increase welfare in the domestic economy, for example if the domestic economy has some influence over world product prices (see Section 3). On the other hand, we also abstract from a number of considerations that may compound the efficiency costs of trade policies, for example rent-seeking activities, the creation of monopoly power for domestic firms and distortions in the quality of imports caused by quotas. More generally, trade policies may stem from the government’s concern with distributional issues. For some discussion of the political economy of trade protection see e.g. Bagwell and Staiger (1999).
[13 ]The import tax has a narrower base and is therefore easier to avoid than a broad-based labor tax. Households can avoid the tariff by substituting into the other consumption good, leisure or purchasing more of good 1 produced by domestic firms. In contrast, a labor tax is equivalent to a uniform tax on both consumption goods, and can only be avoided by substituting into leisure.
 As well known, the optimal set of taxes to raise a given amount of revenue would involve taxing goods that are weak substitutes for leisure more heavily, and goods that are strong substitutes for leisure more lightly (for more discussion see for example Dixit (1985) and Sandmo (1975)).
 The effective price of imports exceeds the world price by tqp, even to quota holders. If a household uses a quota to increase its own consumption, it forgoes a rent of tq it could have obtained by selling the quota to another household.
 The dL/dtq coefficient in (2.7) is approximately equal to the compensated price coefficient (for small tq). This is because the income loss from the increase in tq is roughly offset by the income gain from additional quota rents. Thus the reduction in real wage reduces labor supply in this case because the compensated labor supply curve is upward sloping.
 An export tax would have equivalent efficiency impacts to that of the import tariff in our analysis. That is, despite pre-existing taxes, the Lerner symmetry property still applies: restricting imports by a tax is equivalent to restricting exports by a tax, since trade balance requires that the value of imports always equals the value of exports. Similarly, a domestic export quota has equivalent welfare impacts as the import quota. Export subsidies have symmetrical effects to import tariffs or export taxes. They expand the quantity of exports and reduce the price of consumption goods. This leads to an increase in labor supply and a welfare gain from the tax-interaction effect. However, in general this welfare gain is more than offset by the cost of financing the subsidy by raising the rate of factor tax. We ran some simulations for a revenue-neutral export subsidy in our numerical model of Section 3. Pre-existing taxes raise the overall cost of this subsidy policy by around 30 percent¾the same result as for a revenue-neutral tariff¾for any given increase in the quantity of exports.
 This enables us to obtain “exact” solutions for non-marginal policy changes. The analytical model could be solved for non-marginal policy changes by taking second order welfare approximations. However these may be unreliable for “large” policy changes.
 Unless otherwise indicated, variables are defined as in Section 2.
[20 ]This follows from the (weak) separability between individual consumption goods and leisure, and the homothetic preferences over consumption goods implied by (3.1b). For more discussion see Deaton (1981).
 We assume these prices are positive in equilibrium; that is, the constraints on the quantities of the specific factors are binding.
[22 ]The effective tax rates on labor and profit income are roughly the same in the U.S. (see for example Lucas (1990)). Labor is subject to personal income taxes and payroll taxes, and profits are subject to personal and corporate income taxes. We assume that rents raise firm profits above the normal rate of return and are therefore subject to the same rate of tax as profits.
 In practice there can be political links between tariffs and balanced budget rules. For example, when the United States lowered tariffs on imports from Mexico as part of NAFTA, budget law required that the revenue shortfall be made up by increasing revenues from other taxes.
 All these shares approximately represent the current situation in the U.S. (see the Economic Report of the President).
[25 ]See for example the survey by Russek (1994). We use a slightly higher value for the compensated elasticity since the studies in his survey do not capture effort effects.
 Other studies use similar values (for example Lucas (1990) and Browning (1987)). The sum of federal income, state income, payroll and consumption taxes amounts to around 36 percent of net national product. This average rate is relevant for the labor force participation decision. The marginal tax rate, which affects average hours worked and effort on the job, is higher because of various deductions.
 Marginal welfare costs are expressed as a percent of domestic GDP.
 Analogous results were derived by Goulder et al. (1997) in their comparison of pollution abatement policies that do and do not generate the revenue-recycling effect.
 The gap between the first-best and second-best marginal cost curves under the VER increases somewhat as the quantity of imports is reduced; that is, the marginal tax-interaction effect is smaller at more modest reductions in imports. The marginal tax-interaction effect is partially offset by an income effect: in response to the loss of income to the foreign economy households reduce their demand for leisure, a normal good. However the marginal income loss declines as the quantity of imports is reduced, hence the reduction in the marginal tax-interaction effect is smaller.
 Import restrictions are likely to have only minor impacts on the overall level of employment in the economy. However, the resulting welfare loss can still be “large” relative to the first-best costs because taxes drive a substantial wedge between the marginal social benefits and marginal social cost of labor. For a diagrammatic discussion of this, in the context of environmental regulations, see Parry (1997).
[31 ]The following example gives a very crude idea of how incorporating interactions with pre-existing taxes might affect the results from earlier studies. According to USITC (1995) there was a tariff of about 15 percent on apparel made from purchased materials in 1993 and a tariff equivalent quota of 20 percent. Normalizing the world price (p0) to unity, the domestic price (p1) is therefore (1.2)(1.15) = 1.38. The value of imports was $33 billion, implying the initial import quantity, M0, is 33/1.38 = 23.9 billion. If the tariff and quota were removed, USITC estimate that the increase in the value of imports, i.e. p0M1 – p1M0, would be $8 billion, hence M1 = 41 billion. Using the simple Harberger triangle approximation, the partial equilibrium welfare cost of the tariff and quota is therefore 0.5(.38)(41-23.9) = $3.25 billion. The trade restrictions reduce imports 40 percent below the free market level (M1). The tax-interaction effect raises welfare costs by about 160 percent for this amount of import restriction, implying the overall welfare cost is $8.45 billion. But if we take into account that the tariff raises revenues of 0.2(23.9), and that cutting distortionary taxes produces an efficiency gain of 30 cents per dollar, then the welfare gain from the revenue recycling effect is $1.44 billion. In this case, the overall welfare cost is $7 billion. These “back-of-theenvelope” calculations are limited, however, because they ignore the effect of US trade policies on world prices. They also assume that all non-tariff protection takes the form of import quotas, while in practice some protection is in the form of VERs.
[32 ]This is available at: www.rff.org/disc_papers/PDF_files/9837.pdf.
 Welfare effects are expressed as a percent of domestic GDP¾they may seem large, but recall that imports initially account for 10 percent of GDP.
[34 ]The difference in welfare impacts between the second-best tariff with revenue recycling and the first-best tariff is somewhat smaller in this case than the small open economy case. The reason is that some of the tariff revenue now comes at the expense of foreign producer surplus rather than domestic consumer surplus. This implies that not all of the tax-interaction effect occurs in the domestic labor market; a minor part of it occurs in the foreign labor market.
 Labor tax rates in some European countries (i.e. labor income plus consumption taxes) exceed 50 percent. In contrast, labor tax rates in Japan are roughly the same as in the US (see e.g. Mendoza et al. 1994).
 Note that second-best costs are a little larger than first-best costs when the uncompensated labor supply elasticity is zero. The labor supply elasticity is greater in the first-best model, because households face a wage of unity rather than one minus the labor tax rate. This means that the general equilibrium elasticity of demand for importable consumption is slightly greater in the first-best model. For a given reduction in imports then, the welfare loss corresponding to the area under the import demand curve is slightly larger in the second-best model than the firstbest model. Thus, in the second-best model, when there is no efficiency effect in the labor market the overall welfare costs are still a bit larger than in the first-best model
[38 ]For a survey of these models and their implications see for example Baldwin (1992) and Dixit (1983).
 For a recent discussion of labor market rigidities in European countries see Siebert (1997). Even in the U.S., which is thought to have a relatively flexible labor market, non-tax factors may significantly add to the distortions created by taxes (see Browning (1994)).
Ian W.H. Parry
Resources for the Future
Key Words: pre-existing tax distortions, tariffs, import quotas, welfare costs.
JEL Classification Numbers: F10, H21.
This paper can be downloaded from the
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I am grateful to Wally Oates, Mike Toman, Rob Williams, and two referees for very helpful comments.
The Costs of Restrictive Trade Policies in the Presence of Factor Tax Distortions