Redundant tariffs as rational endogenous protection.

Feldman, David H.

I. INTRODUCTION

In a competitive market, tariff protection is redundant whenever the tariff exceeds the difference between the domestic autarky price and the world price. With redundant protection, domestic price rises by less than the full nominal tariff since a smaller tariff would be sufficient to generate prohibitive protection. Such excess protection is easily dismissed as economic ignorance on the part of lobby groups and/or policy makers. Yet redundant tariff protection (also called "water-in-the-tariff") is a common feature of 19th and early 20th century U.S. tariff history. More recently, the developing nations' penchant for redundant nominal tariffs has complicated World Bank attempts to calculate effective rates of protection.

This paper develops political-economy models in which the endogenous tariff may be redundant when the world price is uncertain, even if agents themselves are risk-neutral. The possibility of world price declines (or domestic cost increases) creates positive expected benefits to producers from tariffs that are initially redundant. These positive expected benefits provide the rationale (or demand) for redundant protection. Embedding this demand within simple political-economy models generates endogenous tariffs that appear redundant to casual observation. These political-economy models also permit us to assess the comparative static effects of changes in the mean-preserving spread of the world price.

An extensive literature explores the links between protection and world price uncertainty. Most authors address one or more of the following: (i) the optimal choice of protective instrument, (ii) risk-aversion by private agents, or (iii) protection as social insurance. Young and Anderson |1980~ show that the optimal policy to maximize expected consumer surplus given a constraint on expected imports (on expected import expenditure) is a specific (an ad valorem) tariff. Using the same constraint on expected imports, they demonstrate |1982~ that quantitative restraints dominate tariffs if consumers exhibit risk aversion toward real income fluctuations. In the same vein (but in a dynamic setting), Falvey and Lloyd |1986~ show that producers prefer non-tariff barriers since they concentrate protection on down-side risk. Cassing, Hillman and Long |1986~ examine trade policy as social insurance in a Ricardo-Viner model. Given sufficient risk aversion both mobile and immobile factors exhibit an ex ante preference for reduced domestic price variability under terms of trade uncertainty. These papers, however, do not address the empirically relevant case of above-prohibitive protection.

An existing rationale for tariffs that exceed the prohibitive level is that they facilitate cartel formation. Fishelson and Hillman |1979~ show that a domestic monopoly benefits from tariff protection that exceeds the prohibitive level since the tariff that yields full monopoly profit (and beyond which additional protection is redundant) may exceed the tariff that drives imports to zero. An interesting example of this is the formation in 1898 of the American Tin Plate Company. This trust was formed to exploit tariff protection that exceeded the prohibitive level. The company sold stock whose par value was set at four to five times the cash price of the assets of other tin plate manufacturers that it acquired.(1) The existence of (potential) domestic market power forces a distinction between prohibitive and redundant protection, and in this example the above-prohibitive tariff is clearly not redundant since domestic price rises by the full amount of the tariff.(2)

In the U.S., the 19th century protectionist weapon of choice was the specific tariff, usually in the form of a minimum valuation proviso so that all products worth less than a certain amount were taxed as if they were worth the specified minimum. Specific tariffs generated high, and often redundant, levels of protection for domestic producers of the coarser grades of manufactures while allowing continued imports of the finer grades that were not produced domestically.(3) They were also cheap to administer and did not encourage the under-invoicing that accompanies ad valorem tariffs. As an additional political inducement, specific tariffs are less transparent to consumers since the effective rate of protection is more difficult to discern.(4) In its current incarnation in developing economies, redundant tariff protection works in much the same way. Tariffs are often assessed as a percentage of a set reference price which itself need not bear any relationship to the world price.(5)

The following section models the benefits of protection and introduces the role of world price uncertainty. Section III develops the idea of optimal redundant protection in a variety of political economy settings. I show how redundant tariff protection emerges from both pluralist (passive state) and more autocratic (active state) political economy models. The final section contains concluding remarks and policy implications for trade reform in developing economies.

II. THE EXPECTED BENEFIT FUNCTION

Consider a domestic market with a simple supply side in which production is costless up to a binding capacity constraint. Suppose also that entry is not possible, so domestic supply is perfectly inelastic and all revenue is economic rent. The number of domestic firms may be large or small. Market concentration presumably affects the costs of lobbying for protection; a concentrated industry likely faces lower monitoring costs and thus more easily deals with potential free-rider problems. In what follows I assume that the number of firms is sufficiently high and/or the legal sanctions sufficiently punitive to deter price fixing in the output market as an alternative to lobbying. The domestic industry also is presumed small on world markets and transport costs are ignored. These assumptions allow us to focus narrowly on what Bhagwati |1982~ calls distortion-seeking DUP (directly-unproductive profit-seeking).

Suppose that domestic supply is sufficient to meet domestic demand at the initial world price. The world price (P) and the domestic autarky price (P*) are thus the same. In the usual static framework, any tariff protection would be wholly redundant since prices and quantities would be unaffected. If instead the world price is a random variable, we must differentiate between tariff protection that is redundant ex ante or redundant ex post. A specific tariff is redundant ex ante whenever the expected world price plus the tariff exceeds the domestic autarky price. Ex post redundancy occurs when the actual (realized) world price plus tariff exceeds the prohibitive level and imports equal zero. The redundancy is total when the tariff has no impact on domestic price (when P |is greater than~ P* in the current example), and partial if domestic price rises by less than the tariff. Consider now a world price distribution whose mean is P*. Any tariff (t) would be redundant ex ante. For all world prices between P* and P* - t the tariff is partially redundant ex post. If the realized world price is low enough the tariff is fully utilized and domestic price would exceed the world price by the full amount of the tariff.

Since domestic supply is perfectly inelastic the free trade relationship between rents and the world price is R = PQ, where Q is the fixed domestic supply and P is the world price. With a specific tariff of size t |is less than~ P*, the rents available under the tariff regime equal tQ + |R.sub.FT~ for P |is less than or equal to~ P*-t, and equal P*Q for P* |is greater than or equal to~ P |is greater than~ P*-t. As the world price moves from P* to P*-t the fraction of the tariff that is utilized approaches one and the fraction that is redundant ex post approaches zero. Within this world price range the tariff is prohibitive, so rent equals its autarky value. Rents decline for world prices below P*-t (along the segment XY), though they exceed the corresponding free trade value since the domestic price is higher by the full amount of the tariff. The gain from tariff protection is the probability weighted trapezoid OXYZ in Figure 1. Increases in the tariff generate parallel upward shifts of the segment XY. This yields gains that diminish at the margin since the remaining possible gain (XNY) is associated with lower probability world price deviations and itself diminishes at the margin.

More formally, the expected benefit (B) from tariff protection is the difference between expected rents with and without a given tariff, or

|Mathematical Expression Omitted~

where f(P) is the probability density function for the world price distribution. The marginal benefit from a higher tariff is

|B.sub.t~ = |Delta~B / |Delta~t, while |B.sub.tt~ = ||Delta~.sup.2~B / ||Delta~t.sup.2~ |is less than~ 0 would assure diminishing marginal returns. Using equation (1),

(2) |B.sub.t~ = Q|integral of f(p)dP between limits of 0 to p*-t~,

and

|B.sub.tt~ = -Qf(P* - t).

The marginal benefit is positive, but diminishing, and it approaches zero as the specific tariff approaches the mean world price.(6)

The expected benefit from tariff protection is also a function of the mean preserving spread (|Sigma~) of the world price distribution. An increase in the mean-preserving spread of the world price distribution would raise the probability of large downward deviations of the world price from its mean value. This would raise the expected gain from any level of tariff protection since a given t is more likely to be fully utilized in the realized state of the world. Thus B is an increasing function of |Sigma~, or |Delta~B / |Delta~|Sigma~ |is greater than~ 0. The marginal benefit of tariff protection (|B.sub.t~) is also an increasing function of world price variance. From equation (2), |B.sub.t~ = QF(P* - t), where F is the cumulative density function associated with f(P). Increases in the likelihood of low world price realizations (fatter tails) enlarge the cumulative density function for any given tariff, thus |B.sub.t|Sigma~~ = Q(|Delta~F / |Delta~|Sigma~) |is greater than~ 0.

III. TARIFF ENDOGENEITY

Since redundant tariff protection can occur in pluralistic political environments (19th century U.S.) and in more autocratic ones (many modern LDCs), the model must be closed in ways that reflect these varying initial circumstances. I set up the political optimization problem from two differing perspectives: (i) a producer interest who faces a "supply" of protection and (ii) an autonomous policy maker (a government or an elite) whose welfare depends on its ability to generate income for itself and/or political support from rent-seeking private interests. The former is a "passive state" model in which the state as such is weak. This is the perspective of much of the New Political Economy literature in which organized private interests achieve desirable legislation directly or through the intermediation of expected-vote-maximizing political parties. Brock, Magee, and Young |1989~ provide a thorough survey of this literature. In the latter, the state is the leader and private interests (civil society) are weaker followers. This "active state" approach seems appropriate for understanding government behavior in many developing economies, especially those that are autocratic in the sense that decision making is centralized and in which the policy makers themselves (or a ruling elite) are the beneficiaries of power.(7) Findlay |1990~ adopts this view and develops a series of political economy models to explain important features of the developing economies' experience. The discussion that follows develops the motives for tariff redundancy in both the passive state and active state models, and suggests ways of comparing the two approaches.

Supply of Protection

Tariff bills are an infrequent occurrence in U.S. commercial policy history.(8) This is compatible with the existence of large sunk lobbying costs associated with initiating a tariff bill. These costs likely include acquiring the "ear" of a sufficient core of sitting representatives and/or candidates. Such access costs may be independent of the size tariff the lobby seeks. In other words, the lobby may face a two-part pricing scheme for desired political outcomes.(9)

If the producer interest's lobbying activities were costless at the margin, the marginal benefit would be driven to zero, i.e., the tariff would be set high enough to shut out imports for all possible realizations of the world price. Higher proposed tariffs for one's own industry are an increasingly visible distortion (and income transfer) that may stimulate progressively more powerful opposition.(10) Thus the lobbying costs of acquiring higher levels of tariff protection may increase at the margin.

To explore the impact of exogenous world price variability on tariff formation I assume the lobby's optimization problem is non-stochastic in that it faces only the sunk costs and increasing marginal costs mentioned above. In Figure 2, C(t) represents the cost function of acquiring protection and is thus the "supply" of protection. If the world price is P* (the domestic autarky price) with certainty, expected benefits from tariff protection are zero. |B.sub.1~ is the relationship between expected benefit and the tariff if the world price is uncertain but varies around a mean of P*. Tariff protection that is redundant ex ante (t |is greater than~ 0) now yields positive benefit that diminishes at the margin. Benefit ceases to rise when the tariff is redundant ex post for any realization of the world price. Since the world price is bounded by zero, this occurs when the specific tariff exceeds the domestic autarky price (t |is greater than~ P*). The tariff the producer interest will "purchase" is t*, which is redundant ex ante. In this simple vote-buying framework the producer interest can be interpreted as the Stackelberg leader and C(t) as a government reaction function.(11) Tariff redundancy does not depend on risk aversion by the producer interest. Risk aversion adds an insurance motive that reinforces the basic result.

Let us turn now to the effects of an increase in the mean-preserving spread of the world price distribution. This raises the probability of large downward deviations of the world price from its mean value. Thus B and the marginal benefit (|B.sub.t~) both rise and the benefit function in Figure 2 shifts upward to |B.sub.2~. The producer interest's optimal tariff unambiguously rises.(12) Thus the penchant for ex ante tariff redundancy should be reinforced, ceteris paribus, in industries in which the variance of the world price is relatively high.

The relationship between world price variance and redundant protection ex post is more ambiguous. Consider two (symmetric) world price probability density functions that share a common mean (P*) and that represent a high variance case and a low variance case. For a given tariff, t, the probability of observing ex post tariff redundancy is the cumulative density function for world price realizations above P* - t. This probability is a decreasing function of world price variance. If, however, the endogenous tariff is positively related to world price variance, the floor world price realization that yields some redundant protection ex post is lower in the high variance case. Whether increased world price variability raises the probability of observing redundant protection ex post is ambiguous, since the lower floor price of the high variance case must be compared with the higher central tendency of the low variance case.(13)

The model generates two additional empirical implications. First, tariffs that are redundant ex ante are less likely in industries whose marginal lobbying costs of higher protection are high (steeper C(t)), such as industries in which counter-interests are easier (or more likely) to organize. This suggests an evolutionary explanation for why redundant protection is not a prominent feature of the current trade regimes in developed industrial nations. The growth of intra-industry trade within the post-war climate of multi-lateralism has aided trade liberalization among the industrial democracies. The "spiders-web" phenomenon described by Bhagwati |1988, 71-80~, in which production is globalized through criss-crossing patterns of foreign direct investment, has also increased the political costs of raising protectionist barriers. Thus the marginal lobbying costs of higher protection have likely risen as counter-interests (exporters, consumers of imported inputs, or multinational firms) mobilize more easily to oppose specific acts of sectoral protection and protectionism in general. These forces account, at least in part, for why the recent re-emergence of protectionist sentiment is still a weak image of its 1930s counterpart.

Redundant tariffs ex ante are also more likely if the mean world price and domestic autarky price are close together, as would be the case for industries on the margin between exporting and import competing (this paper's case). Clearly, if two otherwise identical import-competing industries face differing mean world prices, the endogenous tariff is more likely to cross the threshold into ex ante redundancy in the industry whose mean world price is closer to the domestic autarky price. Likewise, if an export industry's mean world price is significantly higher than the price at which imports would enter, then the expected benefit from any protection (which would, of course, be redundant ex ante) would be quite small. The model does imply that competitive export industries can benefit from import tariffs. For an export industry, any world price realization above the domestic autarky price (P*) renders tariff protection totally redundant ex post. If P* |is greater than~ P |is greater than or equal to~ P*-t, the tariff raises domestic price to P* and yet is still above-prohibitive, so no imports would be observed. Taussig |1931, 249~ argues that 19th century U.S. duties on most agricultural goods were designed primarily "to maintain the fiction that the agricultural population secured through them a share of the benefits of protection." Although agricultural interests may indeed have been subject to some form of 'tariff illusion', the model suggests that tariffs may raise expected incomes in export sectors and that the gains may be masked if protection is prohibitive in all time periods.

Policy Maker Welfare Function

In this section I presume the policy maker is an autonomous welfare maximizer whose welfare depends on expected industry benefits from tariff protection and on the tariff itself. The specific tariff, t, is chosen by the authorities to maximize a political support function for that industry,

(3) M = M|B(t,|Sigma~),t~.

Increases in industry rents raise policy maker welfare, so |M.sub.B~ |is greater than~ 0. A higher tariff improves policy maker welfare through its effect on expected benefits from protection (|M.sub.B~|B.sub.t~ |is greater than~ 0), but diminishes welfare directly by generating consumer animosity (|M.sub.t~ |is less than~ 0).(14) This welfare function is presumed strictly quasi-concave with diminishing marginal utility of industry support as expected benefit increases (|M.sub.BB~ |is less than~ 0) and increasing marginal consumer hostility to higher tariffs (|M.sub.tt~ |is less than~ 0). An envy effect can be expressed through |M.sub.Bt~: if consumer anger increases the more the industry is perceived already to have gained from protection, then |Delta~|absolute value of~|M.sub.t~ / |Delta~B |is greater than~ 0, or |M.sub.Bt~ |is less than~ 0.

Equation (3) is consistent with several interpretations of the political process. The policy maker may benefit directly from private rent-seeking behavior that increases government (ruling elite) income. The expected benefit function (B) becomes a rent-seekers' reaction function and the policy maker chooses the tariff that generates the optimal tradeoff between consumer animosity from the tariff itself and revenue from rent-seeking. This interpretation is consistent with Findlay's |1990~ typology of the traditional dictatorship which he describes by "the derogatory rubric of 'kleptocracy'." Alternatively the policy maker may benefit non-monetarily in the form of "political support."(15) Under this interpretation the optimal tariff maximizes the policy maker's probability of remaining in power.

Maximizing policy maker welfare subject to the expected benefit constraint (eq. 2) yields the usual first-order condition,

(4) |M.sub.B~|B.sub.t~ + |M.sub.t~ = 0.

Figure 2 illustrates this form of endogenous tariff. As before, the endogenous tariff is zero if the world price equals the domestic autarky price with no uncertainty. |B.sub.1~ is expected policy-induced benefit if the world price is a random variable whose mean is the domestic autarky price. Equation (3) gives rise to a family of utility level contours for the policy maker, of which |M.sub.0~ represents maximum policy maker welfare and t* is the endogenous tariff. Again, the endogenous tariff is redundant ex ante, and the result does not depend on risk-aversion by the policy maker or by the producer interest.

The influence of world price uncertainty enters through the expected benefit function, and its effect on the endogenous tariff depends in part on which interpretation of equation (3) one adopts.(16) If the government benefits from private rent-seeking expenditures, then an increase in the mean preserving spread of the world price distribution has an ambiguous effect on the tariff the policy maker will select. Totally differentiating equation (4) yields the effect of higher world price variance on the endogenous tariff,

(5) dt / d|Sigma~ = -||B.sub.|Sigma~~(|B.sub.t~|M.sub.BB~ + |M.sub.Bt~) + |M.sub.B~|B.sub.t|Sigma~~ / ||B.sub.t~).sup.2~|M.sub.BB~ + |M.sub.Bt~ (1 + |B.sub.t~) + |M.sub.B~|B.sub.tt~ + |M.sub.tt~~.

The denominator of (5) is clearly negative so the sign of dt / d|Sigma~ depends on ||B.sub.|Sigma~~(|B.sub.t~|M.sub.BB~ + |M.sub.Bt~) + |M.sub.B~|B.sub.t|Sigma~~~. The sign is ambiguous since the policy maker experiences an income effect and a substitution effect of higher world price variance. Using Figure 2, the higher variance raises expected benefit to |B.sub.2~, so policy maker welfare rises at the initial tariff. This income effect (|B.sub.|Sigma~~ |is greater than~ 0) works to lower the endogenous tariff since (|B.sub.t~|M.sub.BB~ + |M.sub.Bt~) |is less than~ 0. The marginal benefit of tariff protection also rises (|B.sub.t|Sigma~~ |is greater than~ 0), which leads to the usual substitution effect in favor of a higher tariff. The government can play the populist, however, by lowering the tariff while also extracting increased revenues from the producer interest. Note, however, that the policy maker unambiguously benefits from increased uncertainty faced by the producer interest.

Suppose instead that equation (3) is a political support function. Following Hillman |1982~ we need to differentiate policy-induced changes in expected benefit from exogenous changes due to increased variability of the world price. Producers are presumably beholden to the government for policy changes that raise expected benefits. As the world price variance rises, producers' willingness to pay for the existing tariff also rises, but this form of expected benefit need not translate into increased political support for the government.(17) Instead, we must decompose the change in expected benefit into its policy-induced component, which raises political support for the government, and its exogenous component, which does not. This point is easily seen using equation (5). The income effect, |B.sub.|Sigma~~, measures the exogenous increase in the industry's willingness to pay for the existing tariff. Setting |B.sub.|Sigma~~ = 0 reveals that the endogenous tariff must rise with increases in world price variance.

Alternatively, using Figure 2, suppose the initial political equilibrium (point A) is disturbed by an increase in world price variance that raises total expected benefits from protection to |B.sub.2~. Extracting the exogenous component involves shifting the expected benefit function down by AY, the producer interest's increased willingness to pay for the existing tariff. Since the marginal benefit of tariff protection has increased, the policy maker will opt to raise the tariff. Under political support maximization of this sort, the likelihood of observing redundant protection ex ante over time and/or across industries will be positively correlated with the variance of world price.

In both versions of the active state model the policy maker benefits from exogenous world price variability. The effect is most pronounced in a predatory kleptocracy since increased variance directly raises policy maker income. Thus the form of state may be endogenous since active state predators may be more likely to exist where the range of domestically produced output is subject to high world price variance.(18) This endogeneity may offer one argument for why evolutionary liberalization seems difficult to achieve in many developing nations. Tariff rates, however, may be lower in a predatory kleptocracy than in less authoritarian regimes because the positive income effect of higher variance likely diminishes the endogenous tariff.

IV. CONCLUDING REMARKS AND POLICY IMPLICATIONS

The established explanation for tariffs that exceed the prohibitive level is based on market power in the output market. These above-prohibitive tariffs are not redundant, however, since the domestic price can exceed the world price by the full amount of the tariff. World price uncertainty creates expected gains from redundant tariff protection for risk-neutral producer interests and policy makers. I have argued that these potential gains form the basis of redundant protection in pluralistic political environments in which interest group interaction determines policy outcomes and in more autocratic political structures in which a ruling group uses the power of the state to maximize its own welfare. If redundant protection serves producer interests and/or policy makers in the developing world then calls to "rationalize" the tariff structures in these countries by eliminating "meaningless" water-in-the-tariff are likely to be resisted.

Recently the World Bank has encouraged countries to convert existing quantitative trade restrictions into price constraints as a prelude to gradual, scheduled reductions in barriers to trade.(19) Where the expected benefit from tariff protection is positively related to world price variance, gradual liberalization in industries that receive redundant protection could be facilitated by switching to a variable levy that reduces domestic price fluctuation. In the small country case, where domestic commercial policies have no effect on the world price, a variable levy that fixes the domestic price is identical to a fixed quota if the only disturbance is a fluctuating world price.(20) By reducing domestic price fluctuations the levy permits the policy maker to reduce the industry's effective rate of protection without diminishing that industry's expected income.(21) Domestic price stabilization may be a means to "buy" commitment to lower levels of domestic protection.

1. This example comes from Taussig |1971, 180~. An additional case from Taussig |1971, ch. 11~ is the U.S. copper act of 1869 which aided the formation of a domestic cartel. By the time the cartel coalesced in the late 1870s imports had all but ceased and the U.S. had become a significant exporter. Yet the duty on copper permitted cartel profits, while excess domestic output was dumped on the world market at the lower world price.

2. Similarly, Kaempfer, McClure and Willett |1989~ use Becker-style |1983~ interest group competition to analyze the politically efficient form of incremental import protection (tariff/quota) for a domestic monopoly. Above-prohibitive protection may occur since their results hold even if the firm seeking import protection is an exporter.

3. Cotton and woolen textiles are a prominent example.

4. A zero quota or a variable levy can also be used to provide prohibitive levels of protection, but each has certain liabilities. To be effective, zero quotas must be targeted narrowly on the specific product types to be excluded. Where many quality grades exist this encourages mislabelling to avoid the quota. Thus even a zero quota may involve higher administrative costs than a prohibitive specific tariff. A variable levy would involve complicated rules and would diminish the government's ability to use discretionary policy.

5. Often the redundant tariff is combined with a zero quota to create an additional layer of redundancy in case "liberalization" pressure requires the elimination of one variety of protection. This layering of protective instruments suggests that strategic bargaining considerations may play a role, and also that standard insurance motives exist for redundant protection.

6. In "The Political Economy of Protection," Baldwin's |1982, 275~ benefit curve for non-stochastic protection-seeking is convex over tariff rates between zero and prohibitive. This convexity results from implied increasing marginal costs of production so that tariff increases generate producer surplus gains that rise at the margin. I have assumed no supply response and no gains from protection in the non-stochastic case in order to focus on the role of world price uncertainty alone as a motive for tariff redundancy.

7. This characterization of the Third World State reflects Christopher Clapham's |1985~ concept of "neo-patrimonialism" in which the modern state's universalistic rational-legal forms are used for private purposes by a leader or ruling group. A traditional patrimonial leader uses his personal resources to develop and strengthen ties between him and his followers. The autocratic Third World ruler or ruling elite can use the power of the state to apportion jobs, import licenses, or scarce foreign exchange.

8. This pattern is not restricted to the U.S. After the U.K. formally abandoned free trade with the 1915 McKenna duties, other tariff revisions occurred every four to five years until the war, and each revision affected only a subset of imported items.

9. Young |1991~ has recently shown how demand complementarities can give rise to social welfare improving collusion among sellers in the presence of two-part pricing in output markets. If creating political "access" involves real resource costs, cooperation between like-minded lobbies may shrink the sum of these costs and thus diminish to some extent the social costs of their activities.

10. As in Brock, Magee, and Young |1989, ch. 2~.

11. Brock, Magee, and Young |1989~ model the tariff-making process as a general equilibrium interaction between two political parties who act as Stackelberg leaders with respect to their lobbies, but who engage in Cournot rivalry between themselves. Since my purpose is to show the logic behind redundant tariff protection I opt for the simplest plausible structure consistent with that goal.

12. This assumes a stationary world price distribution. If the mean of the world price distribution follows a random walk, then deviations from the mean would not be transitory. This suggests that tariff changes might occur more frequently, ceteris paribus, in those industries where the mean world price was less stable.

13. Good evidence on the relationship between tariff redundancy and world price variance (ex ante or ex post) is naturally hard to find. Some evidence, however, can be gathered from 19th and early 20th century U.S. data found in Taussig |1931~, pp. 124 and 152, and Taussig |1971~, pp. 140, 160, 164, 180, and 444. These price series use U.K. prices, except for Wool and Rayon, which are domestic prices. Using the coefficient of variation as a measure of price variability, industries in which protection was periodically redundant (ex post), such as steel rails (.436, 1871-1911), foundry pig iron (.302, 1873-1912), and Bessemer pig iron (.169, 1886-1912), exhibit more price variability as a group than do import competing industries such as wool (.125, 1852-60), pig iron (.206, 1847-60), and rayon (.429, 1911-29), or industries that quickly became export oriented such as copper (.235, 1869-1913) or in which protection interacted significantly with domestic market power such as tin plate (.118, 1891-1913).

14. There exists plentiful anecdotal evidence that autocratic governments in the developing world must consider popular reaction when undertaking policies that increase domestic prices of consumer goods, especially commodities consumed by city dwellers who live within easy march of the president's palace. Note also that this formulation ignores tariff revenue as a determinant of policy maker welfare. This is a safe assumption for industries in which tariff protection is redundant ex ante.

15. This is the approach taken by Hillman |1982~ and Cassing and Hillman |1985~.

16. I presume that consumer animosity is focussed on the expected domestic price and not on its variability. This is a reasonable simplification in light of the likely information asymmetry between the producer interest and opposing consumer interests about the behavior of the world price.

17. In Hillman's |1982~ model the political-support maximizing government would spread the benefits of a terms of trade improvement, providing some benefit for consumers and partially compensating import-competing producers. Hillman's interest is senescent industry protection where the world price undergoes a one time permanent decline. In the context of my paper this would involve a decline in the mean value of the world price. Alternatively, Hillman's framework may be more suitable where the time period between price changes is relatively long, and thus the transactions cost of adjusting the tariff is low, while mine better reflects industries that experience more frequent fluctuations of the world price.

18. I thank an anonymous referee for noting this point. A fuller analysis requires accounting for tariff revenues in the policy maker welfare function (see Cassing and Hillman |1985~ for example). In this paper, tariff revenues can safely be ignored since all protection is redundant ex ante. Note also that a kleptocratic regime can threaten to create domestic price uncertainty even if the world price is stable. The threat of a randomized tariff, if credible, could be used to extract 'certainty' payments from domestic interests. In this sense the state acts as a protection racket.

19. See Michaely |1986~. Since "liberalization" pressure may lead in some instances to the replacement of zero quotas by redundant tariffs, this "tariffication" process may initially increase the frequency with which we observe redundant protection.

20. If the domestic economy is "large," and there exist random fluctuations in domestic import demand and/or foreign export supply, a variable levy magnifies the volatility of the world price. In such a world the variable levy can be used to capture as tariff revenue any export subsidies paid by "small" nations. See Vousden |1990, 100-103~.

21. For a given expected quantity of imports a specific tariff yields higher consumer surplus than does the levy's implicit quota. This is a question addressed by Young and Anderson |1980~.

APPENDIX

1. Deriving equation (1)

For P |is less than or equal to~ P* - t:

|R.sub.t~ - |R.sub.FT~ = (tQ + |R.sub.FT~) - |R.sub.FT~ = tQ.

For P* |is greater than or equal to~ P |is greater than~ P* - t:

|R.sub.t~ - |R.sub.FT~ = P*Q - PQ - Q(P* - P).

Thus, the expected benefit of the tariff is the expected value of the benefit expressions above, or

|Mathematical Expression Omitted~.

2. Deriving the marginal benefit and its slope

|Mathematical Expression Omitted~,

so

|B.sub.tt~ = Qf(P*-t)(-1) = -Qf(P*-t).

3. Deriving equation (5)

Totally differentiating equation (4) yields

|B.sub.t~ { |M.sub.BB~||B.sub.t~(dt / d|Sigma~) + |B.sub.|Sigma~~~ + |M.sub.Bt~(dt / do) } + |M.sub.B~||B.sub.tt~ (dt / d|Sigma~) + |B.sub.t|Sigma~~~ + |M.sub.tB~||B.sub.t~ (dt / d|Sigma~) + |B.sub.|Sigma~~~ + |M.sub.tt~(dt / d|Sigma~) = 0.

Solving this equation for dt / d|Sigma~ yields equation (5) of the text.

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