metadata: authors: 0: author: Anderson, James E.
1: author: Neary, J. Peter
docna: 0: docna: A new approach to evaluating trade policy
docty: Policy Research Working Paper
subtopic: Trade Policy,International Trade and Trade Rules,Rules of Origin,Trade and Services,Macroeconomic Management,Trade and Multilateral Issues
teratopic: Transport
abstracts: cdata!: The authors introduce a new measure, the
            Trade Restrictiveness Index, to measure the restrictiveness
            of a system of trade protection. They propose an alternative
            to the commonly used ad hoc indexes of trade
            restrictiveness, such as the trade-weighted average tariff.
            That measure has no welfare-theoretic basis and can be
            highly misleading, in practice. For example, the complete
            exclusion of trade in a commodity would usually lower the
            index, because its trade weight would fall to zero. The
            authors show that their proposed index is soundly based in
            standard welfare economics. When trade is restricted by
            tariffs only, the Trade Restrictiveness Index equals the
            uniform tariff, which would be equivalent to the existing
            system of tariffs in the sense of yielding the same level of
            aggregate welfare. But tariffs have declined in importance
            in recent years as a means of restricting trade, so the
            measure must also be able to take account of quantitative
            restrictions on trade. Where quotas are the only form of
            restriction, this is easy: the Index equals the
            equiproportionate reduction in permitted import volumes that
            is welfare-equivalent to the initial structure of quotas.
            When both quotas and tariffs are present, the Index can be
            defined as the uniform tariff factor (one plus the uniform
            tariff) and uniform import reduction factor which would
            yield the same level of welfare as the initial system of
            trade restrictions. The authors show how this can be
            formulated, noting that if a single good is subject to both
            a binding quota and a tariff, it should be viewed as
            quota-constrained - the tariff serves merely to ensure that
            some of the rents accrue to the importing country. These
            theoretical derivations permit a major synthesis of the
            theory of protection and suggest how the results of
            computable general equilibrium models might be presented to
            make them internationally and intertemporally comparable.
            But in most cases such a model is not available and, even if
            it were, it would not be sufficiently disaggregated to deal
            with a complicated system of trade protection. So the
            authors present some empirical short-cuts that can be
            adopted for estimating changes in the Index. Chief among
            these is the assumption that the goods under consideration
            are separable from others in an appropriate
            general-equilibrium sense. This can provide a rigorous
            foundation for a form of partial-equilibrium analysis (the
            consideration of a subset of markets in an economy). They
            also show how the Trade Restrictiveness Index can be adapted
            to allow for different forms of rent sharing and for a
            country's ability to influence its terms of trade.
            Applying these empirical methods to exports of textiles and
            apparel from Hong Kong to the United States, the authors
            find that the protective system becomes more restrictive for
            both countries over the seven years considered (1982-88).
            Increased trade restrictiveness does not necessarily mean
            that quotas have been tightened. When there is economic
            growth, constant or even rising import quotas might still
            amount to a tightening of protection. Results based on the
            trade-weighted average of "tariff equivalents"
            (the gaps between Hong Kong and U.S. prices) diverge
            significantly from those of the Trade Restrictiveness Index.
            The two measures have opposite implications for the change
            in trade restrictiveness for two-thirds of the observations.
repnme: repnme: A new approach to evaluating trade policy
display_title: A new approach to evaluating trade policy
listing_relative_url: /research/1992/11/699515/new-approach-evaluating-trade-policy
topicv3: Trade m1326924 698,Trade in Services m1326928 780,Trade Policy and Integration m1327407 775,Trade Policy m1327640 776,Trade Balance m1327679 1136
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Transport
origu: UNKNOWN
no_of_pages: 37
model_extractions: b.

**A**

<!-- Start of picture text --> Pollcy Research<br>International Trade<br>WPS 1022<br><!-- End of picture text --> This paper-a product of the International Trade Division, Intemational Economics Department-is part of a larger project to study the cost of protection. The study was funded by the Bank's Research Support Budget under research project "The Cost of Protection Index" (RPO 67649). Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington, DC 20433. Please contact Maria Teresa Sanchez, room S7-025, extension 33731 (November 1992, 30 pages).

Anderson and Neary introduce a new measure, the Trade Rt,strictiveness Index, to measure the restrictiveness of a system of trade protection. They propose an altemative to the commonly used ad hoc indexes of trade restrictiveness, such as the trade-weighted average tariff. That measure has no welfare-theoretic basis and can be highly misleading, in practice. For example, the complete exclusion of trade in a commodity would usually lower the index, because its trade weight would fall to zero.

Anderson and Neary show that their proposed index is soundly based in standard welfare economics. When trade is restricted by tariffs only, the Trade Restrictiveness Index equals the _uniformn_ tariff, which would be equivalent to the existing system of tariffs in the sense of yielding the same level of aggregate welfare.

But tariffs have declined in importance in recent years as a means of restricting trade, so the measure must also be able to take account of quantitative restrictions on trade. Where quotas are the only form of restriction, this is easy: the Index equals the equiproportionate reduction in permitted import volumes that is welfareequivalent to the initial structure of quotas.

When both quotas and tariffs arc present, the Index can be defined as the uniform tariff factor (one plus the uniform tariff) and uniform import reduction factor which would yield the same level of welfare as the initial system of trade restrictions.

The authors show how this can be formulated, noting that if a single good is subject to both a binding quota and a tariff, it should be viewed as quota-constrained - the tariff serves mereiy to ensure that some of the rents accrue to the importing country.

These theoretical derivations permit a major synthesis of the theory of protection and sugge-t how the results of computable general equilibrium models might be presented to make them internationally and intertemporally comparable. But in most cases such a model is not available and, even if it were, it would not be sufficiently disaggregated to deal with a complicated system of trade protection.

So the authors present some empirical shortcuts that can be adopted for estimating changes in the Index. Chief among these is the assumption that the goods under consideration are separable from others in an appropriate general-equilibrium sense. This can provide a rigorous foundation for a forn of partial-equilibrium analysis (the consideration of a subset of markets in an economy). They also show how the 'rade Restrictiveness Index can be adapted to allow for different forms of rent sharing and for a country's ability to influence its terns of trade.

Applying these empirical methods to exports of textiles and apparel from Hong Kong to the United States, the authors find that the protective sysiem becomes more restrictive for both countries over the seven years considered (198288). Increased trade restrictiveness does not necessarily mean that quotas have been tightened. When there is economic growth, constant or even rising import quotas might still amount to a tightening of protection.

Results based on the trade-weighted average of "tariff equivalents" (the gaps between Hong Kong and U.S. prices) diverge significantly from those of the Trade Restrictiveness Index. The two measures have opposite implications for the change in trade restrictiveness for two-thirds of the observations.

**The Policy Research Working Paper Series disseminates the findings of work under way in the Bank. An objective of the series is to get these findings out** quickly, **even if presentations are less than** fully **polished. The** findings, **interpretations, and conclusions in these** papers do **not necessarily represent official Bank policy.**

**Produced by the Policy Research Dissemination Center**
# A NEW APPROACH TO EVALUATING TRADE POLICY*

James E. Anderson Boston College and J. Peter Neary University College Dublin and CEPR
# A NEU APPROACH TO EVALUATING TRADE POLICY

# TABLE OF CONTENTS

# I Introduction

- 1I The Trade Restrictiveness Index with Tariffs Only

- III The Trade Restrictiveness index with Quotas Only

- IV The Trade Restrictiveness Index with Tariffs and Quotas

- V Changes in the Restrictiveness of Quota Policy in the Presence of Growth

- VI Operationalising the Trade Restrictiveness Index

- A. Separability Assumptions

- B. Tariffs as a Rent-Sharing Hechaniss

- C. Market Power

VII An Application: U.S. Textile Imports from Hong Kong VIII Conclusions and Suggestions for Further Research

# Appendix: Neutral Growth and the Balance of Trade Function
- E This paper was written in part with the support of a World Bank project on the Cost of Protection. Much of the paper was written while the first author was a Visiting Scholar at the Institute for International Economic Studies, Stockholm. The support and stimulation of the Institute are gratefully acknowledged. Earlier versions of the paper were presented to a World Bank seminar, to ES 90 in Washington, to ERWIT 91 in Stockholm and to ESEM 91 in Cambridge. We are grateful to participants at these meetings and to Refic Erzan and Kala Krishna for helpful comments, to Chris Holmes for able research assistance and to Carl Hamilton for assistance with data.

Address for correspondence: Professor J. Peter Neary Department of Economics University College Dublin Belfield, Oublin 4. Ireland Tel: (+353) 1-2698808 FAX: (+353) 1-2830068
A NEW APPROACH TO EVALUATING TRAOE POLICY

# I Introduction

How should we measure trade restrictiveness? This important question arises repeatedly in international trade negotiations, in discussions of World Bank loan conditionality and in the new literature relating openness to growth. A distinct but related question is: how costly is trade restrictiveness? Both questions have simple answers in the case where a single good is subject to an import tariff: the height of the tariff is an unambiguous measure of trade restrictiveness and its relative welfare cost equals the "Harberger triangle," the area under the compensated import demand curve, mormalised by gross domestic product. (The questions are distinct, since the same tariff could produce a different relative welfare cost in two different economies if their elasticity of import demand or share of trade in GOP varied; conversely, the same relative welfare cost could be produced by two different tariffs.) With more than one tariff, the welfare cost measure is a well-known matrix expression.I In contrast, the literature contains no theoretically based measure of trade restrictiveness in the realistic case where trade in many commodities is restricted, analogous to the height of the tariff in the simple case. For want of a better alternative, analysts have usually calculated trade-weighted average tariffs or (in the case of quotas) average tariff equivalents. However, these have no welfare foundation and suffer from the problem that highly restricted imports which 'should' get a high weight in the index have low levels of imports and so get a low weight. Hence there is currently no good answer to the question of how to measure trade restrictiveness. This paper aims to provide one.

See equation (2.3) below.

I
In measuring the welfare cost of Protection there is one well-known case where the simplicity of the one-dimensional analysis is Preserved no matter how many tariffs are in place: this is where tariff cuts are _uniform_ or e;%:jiproportionate across all goods. In this paper. we propose a solution to the aggregation or index number problem of measuring trade restrictivenss in the presence of many tariffs which builds on this insight. Essentially, it asks 'What _uniform_ tariff structure is equivalent (in a welfare sense) to a given tariff structure?"2 The answer is a scalar measure of the overall protective impact of an arbitrary tariff structure. Moreover, the proportionate rate of change of our index turns out to be equal to the standard measure of the cost of tariff protection, normalised by what we call the "shadow value of distorted trade." By contrast. most existing studies norealise the cost of protection by some other deflator, frequently the level of GOP. Our measure has the advantage of normalising in a manner which is intuitively appealing and which can be given a rigorous welfare interpretation. Its most important advantage is practical: since our -;sasure is a uniform tariff equivalent index, it permits comparisons of the restrictiveness of trade policy across countries and across time periods. A further advantage of our approach is that it can be extended to la,corporate quantitative trade restrictions as well as tariffs. Such restrictions are increasingly important in world trade but the theory of protection has been extended to take account of them only relatively recently.3 From a theoretical point of view, our Paper therefore serves to link this recent literature with the work on scalar distance function' 2 Corden (1966) is an early paper which considers the possibility of calculating the 'uniform tariff equivalent of a non-uniform tariff structure. Note that our analysis does not imply that uniform tariffs are necessarily welfare superior to a non-uniform tariff structure with the same average tariff level. For contrasting views on the optimality of uniform tariff structures, see Fukushima and Hatta (1987) and Stern (1990); and also Lopez and Panagariya (1991). 3 See Corden and ralvey (1985), Dixit (1986), Falvey (1988), Neary (1988, 1989) and Anderson and Neary (1992).

2
measures of efficiency in production or consumption by Oebreu (1951), Deaton (1979), Diewert (1985) and Anderson and Neary (1990). From a practical point of view, we a'lso argue that our measure can be made operational and in Sections VI and VII we illustrate its use with an application to measuring the restrictiveness of U.S. Volt;ntary Export Restraints on textile imports from Hong Kong. The results are dramatic. In our application, in four out of six years, the trade restrictiveness index has opposite implications to those of the commonly-used (and theoretically inferior) average tariff equivalent.

# II The Trade Restrictiveness Index with Tariffs Only

In this section we begin by reviewing the standard theory of the cost of protection in an economy where tariffs are the only form of trade restriction. We then show how this can be related to our measure, the 'Trade Restrictiveness Index' or TRI.4 We consider a competitive small open economy, producing tradeable goods only,5 in which specific tariffs t drive a wedge between the domestic prices (n) and the world prices (0e) of goods which are indexed by i. In vector notation, n = ntS + t 6 The behaviour of the economy is most conveniently sumearised in terms of the _trade expenditure function._ which equals the difference between the value of consumption (given by a standard expenditure function) and production (given by a GNP function):7

- 4 In Anderson and Neary (1990), we used the term "coefficient of trade utilisation" to reflect the relationship between our index and the 'coefficient of resource utilisation* of Debreu (1951).

- 5Non-traded goods can be subsumed into the background so long as their prices are determined competitively.

- 6We adopt the convention that a is the vector of all goods prices (or, **from** Section III onwards, of the prices of all goods not subject to quotas). The numeraire good can then be thought of as a good with a zero tariff; and if good i is exported then t is an export subsidy.

- 7The properties of these functions are set out in Dixit and Norman (1980).

3
(2.1) E(i,u) a e(n,u) - _g(X)._ Here u is the utility of the aggregate household sector (so that issues of distribution are ignored) and the economy's t-hnokLgy and factor endowments are subsumed in the g(.) function. The function E has the standard properties of an expenditure function: it is concave in n and, by Shephard's Lemma, its derivatives with respect to X are the economy's net (i.e., import) demand functions. We assume that all tariff revenue is redistributed costlessly to the household sector, so that in equilibrium the trade expenditure function must equal the sum of tariff revenue and the trade surplus **p,** if any (assumed throughou **t** o be exogenous): (2.2) E(n,u) = t'm + Here a prime (') denotes a transpose and o is the vector of import demand functions for imports subject to tariffs, equal to E (x,u). Differentiating (2.2) leads to the standard result for the welfare effect of a small change in tariffs: (2.3) (1-t'xI)E du = t'mcdt.

The left-hand side is the change in utility, converted to numeraire units by the tern E (the inverse of the marginal utility of income) and multiplied by **U** (1-t'x ), which is the inverse of the 'tariff multiplier" or "shadow price of foreign exchange."8 Following standard convention, we shall assume that this term is positive. This leaves the right-hand side as the standard cost-of-tariff-protection measure. As is well-known, this depends on all the terms in the matrix of price derivatives of the import demand functions **aX** (which equals E.) and it cannot be signed unambiguously in general. The one exception is the case of a uniform change in tariffs: dt = tda. where du is a positive or negative scalar. In this case we can call a the average See Neary (1988. 1989) for further discussion.

4
level of tariffs and the weifare effect of a change in a equals t'lmt, which is a scalar quadratic form in a negative definite matrix and so is negative. We now want to show how any tariff siructure can be made equivalent (in welfare terms) to a proportionate tariff structure. To do so, it is convenien **t** o switch from the vector of specific tariffs, t, to the vector of _tariff factors._ 0. which equal the rroportional mark-ups over world prices: n = nX ; or in matrix notation: X = nf0. (ON is a diagonal matrix with world prices on the principal diagonal.) for later use, the relationship between the levels of and changes in t and * are as follows: (2.4) t = nH(O-J) and dt = nIdO where ".J denotes a vector of ones. Now, rewrite the equilibrium condition _(2.2)_ in terms of *, and define a new function, the _Ba,ance of rrade Function._ as a measure of the extent to which the economy diverges trom balanced trade equilibrium: (2.5) B(O,u;) _a_ E(I1s,u) - _(0-l)'nsh_ -e Here the parameter I represents all the exogenous variables other than trade policy (such as the levels of factor endowments, world prices, the trade surplus P. tastes, etc.). We do not need to assume that these remain constant, although changes in them raise some specific issues in the presence of quotas, which we postpone until Section V.

We now wish to compare the restrictiveness of trade policy in two periods, denoted "0" and '1" respectively. The economy must be in equilibrium in both periods, so: (2.6) B(o° u<sup>0</sup> ;t<sup>m</sup> ) 2 **B(tOtu; )** S 0.

9 The trade expenditure function is concave in prices and so the matrix of price derivatives must be negative semi-definite. Provided we assume that there is some substitutability between the numeraire good and the goods subject to tariffs, we can go further and assert that this matrix must be negative definite.

5
We define the Trade Restrictiveness,Index as the factor of proportionality 4 by which period-I tariff factors must be scaled up or down in order to reach period-O utility: 1 0 (2.7) a(<sup>1</sup> .u<sup>0</sup> ;7<sup>0</sup> ) C Ca B(Ao& u<sup>0</sup> ;y<sup>0</sup> ) 0].

If trade policy does not change between the two periods (00=01), A equals one. If free trade prevails i. period l. so that *<sup>1</sup> is a vector of ones, A equals (one plus) the uniform tariff rate which would have yielded the same level of welfare as the initial non-uniform vector of tariff factors 00 In other cases, A eouals (one plus) the uniform tariff _surcharge_ rate which copepsrates for the non-uniform change in the tariff structure from 00 to t. As the period-i tariff factor vector 0l varies from 00 towards free trade, A rises above one. Thus a _rise_ in a means that trade policy has become _less_ restrictive. 11 Figure 1, drawn in tariff factor space, illustrates the interpretation of A. Assuming that only two goods are subject to tariffs. point F, with coordinates (1,1). corresponds to free trade and point A, with coordinates (OX, o0), is an arbitrary initial protected equilibrium. To compare these two points, we draw through A an iso-welfare locus, which represents those combinations of tariff factors on the two goods which yield the same level of welfare as A and also preserve balance of payments equilibrium. 2 The ray 10 Since this asks how the new" tariff factors must be scaled to attain the old' level of welfare, it is a compensating variation type of welfare measure. Me assume that a is single-valued. This requires that the denominator of equation (2.9) (or, more generally, that of equation (4.10) in Section IV) does not change sign. We assume that this is the case throughou **t** he theoretical discussion, and consider Possible exceptions in the empirical application in Section VII. This slight potential source of confu".;pn Iouid be avoided by the use of an equivalent variation measure A B(A0 ,u ;I ) = 0]. However, this is not necessarily defined for all parameter values and, even when it is, it is not as easily implementable as (2.7). unless the analyst has access to a computable general equilibriu **m** odel. 12 The properties of this locus **may** be established by expanding the right-hand side of (2.3) and they are considered in detail in Neary (1989). It is shown there that, provided all goods are substitutes, the points of 6
from the origin through F meets this locus at point C, and so the Trade Restrictiveness Index equals the ratio of OC to OF. Keeping A as the reference equilibrium, successive moves of the new equilibrium towards free trade lead to rises in A.

Both the interpretation and the potential applicability of the Trade Restrictiveness 7rJex are enhanced by considerinsig wmall changes in the period-I tariff factor vector 0. Totally differentiating the equation which implicitly defines A in (2.7), holding uo and y° constant, yields: (2.8) 8'4dA + ABed0 0.

This may be solved for the proportional change in 4. denoted by &: Each of these three alternativ **e** xpress5ons throws light on the interpretation of changes in A. From (2.5), B, gives the vector of transfers needed to compensate for increases in tariffs, or minus the marginal cost of tariffs. It equals: (2.10) **B -(frj)'f'mnfl** = -tV'mfln.

The term B'# in the denominator of (2.9) may therefore be interpreted as (minus) the total welfare cost of the initial tariff structure, which we call the "shadow value of distorted trade." As for the numerator.it is the cost of an arbitrary change in tariffs, as derived in (2.3). Thus the proportional change in A , for a small change from the initial equilibrium, equals the conventional measure of the cost of tariff protection, normalised by the shadow value of distorted trade. The final expression in (2.9) suggests how this might be operationalised: it equals a weighted average of inflection of the locus, 6 and H, must lie to the north-east of F and must lie on either side o the 45-degree line OF. A sufficient condition for the locus to enclose a convex set is that the trade expenditure function be quadratic in prices.

7
the changes in tariff factors, where the weights, a., (which are not necessarily Positive) are the contribution of each protected good to the total shadow value of distorted trade: We will return to the issue of operationalising the Trade Restrictiveness Index in Section VI. First, we turn to consider quantitative trade restrictions.

# III The Trade Restrictiveness Index with Quotas Only

When we turn to quantitative restrictions on trade, it is necessary to disaggregate the net import vector. Henceforward. we let q represent the permitted trade volumes in the quota-restricted product group, with foreign prices p* and domestic prices p. For the unrestricted group, we use the same notation as in Section II: a is the trade volume and n is the domestic price vector. equal (until Section IV) to world prices n*. Of course, the domestic prices p of the quota-constrained goods are not exogenous but must adjust to ensure that the quota levels (which we assume are always binding) equal domestic excess demands.

To derive the cost of protection in this case, it is convenient to consider an alternativ **e** xpression for the trade expenditure function defined in (2.1):13 (3.1) E(p,n,u) a Min (p'q+x'm : U(q.m)-u).

## q,m

Here U is a "eade trade utility function definedE over the trade vector (q.m). This function is appropriate when prices (P,x) are given so that the trade vector is endogenous. When quotas are in force so that q is fixed, it 13 The results which follow draw on Anderson and Neary (1992) and are related to results in the theory of consumer rationing; see Neary and Roberts 8
is more convenien **t** o characterise the aggregate consumer as choosing expenditure on the tariff-restricted product group only. This leads to the _distorted trade expenditure function:_ (3.2) t(q,n,u) a min (z'm ' U(q.m)=u). m The relationship between the two functions is straightforward: (3.3) t(q,n,u) = Max {E(p.n,u)-p'q}. p Since E is concave in P, the first-order conditions from (3.3) give the prices which equate demand E (p,n,u) with supply q. The first derivative p properties of t are therefore: (3.4) n(q,n,u) = E tp(q.n,u),n,u] = (3.5) t (q,n,u) = -p(q,n,u). q The first property follows from Shephard's Lemma: the price derivatives of the distorted trade expenditure function equal the import demand functions for the unconstrained goods (with the tilde over the "i' indicating that these demands are conditional on given levels of the quotas rather than on given levels of p). The second property, (3.5), equates the quantity derivatives of the distorted trade expenditure function to the economy's marginal willingness to pay for, or the 'virtual prices" of, the quota-constrained goods. (See Neary and Roberts (1980).) ' is concave in _n_ and convex in q, by its minimum in i and maximum in P properties. We assume, with only mild loss of generality, that the matrix of quantity derivatives of the virtual price unctions p (equal to -E or E 1) is q qq pp negative definite.

Equilibrium is now easily described using the distorted trade expenditure function: (3.6) E(q.x,u) + p'q = (p-p:)'q + The left-hand side equals net domestic expenditure on all goods (from the 9
definition of t in (3.2)); and in equilibrium this must equal the sum of total quota rents and the trade surplus, given by the right-hand side. (In the next section we will allow for the possibility that not all quota rents accrue to domestic residents.) Differentiating (3.6) yields a simple 14 expression for the welfare cost of changes in quota levels: (3.7) fdu = o-px)'dq. u As before, it is desirable to obtain a scalar measure of the severity of an arbitrary system of quotas. To do this, we proceed as in the last section. We first define a balance of trade function, equal to the deviation of equation (3.6) from equilibrium: (3.8) 8(q,u;l) ***** t(q.x,u) + p'q - (p-ps)'q The Trade Restrictiveness Index for quotas can now be defined as the proportionate change in period I quotas required to reach period 0 utility: (3.9) A(q',u°;y°) C,& : B(q<sup>1</sup> /A,u<sup>0</sup> ;yo) = 0].

This is illustrated in Figure 2, where point A represents an arbitrary initial equilibrium and point F a new equilibrium (which may, but need not be, identified with free trade). The value of A is the distance OF/OC, where point C lies on the same iso-utility locus as A.

Proportionate changes in a can once again be identified with the welfare effect of arbitrary quota changes normalised by the total welfare cost of the initial quota vector: <!-- Start of picture text --> B'dq (p-px)'dq<br>(3.10) A = = £ a q ,<br>Bq (p-p*)'q J J<br>q<br><!-- End of picture text --> where: 14 This result is derived and discussed in Cordon and Falvey (198S) and -eary (1988).

10
q (3.11) 8 - p-ps and ° = J J **q** B'q **q** The interpretation is identical to that of equation (2.9), with the additional convenience that the denominator of (3.10), (p-ps)'q, equals the actual value of total quota rents at the initial equilibrium. Once again, an increase in A. starting from the reference equilibrium u°, implies that trade policy has become _less_ restrictive.

# IV The Trade Restrictiveness Index with Tariffs and Quotas

We now wish to consider the realistic case where trade is restricted by both tariffs and quotas. As before, q and m represent the trade voluses in the quota- and tariff-restricted groups, respectively. I In addi on, we assume that a fraction w of quota rents accrues to foreigners. 6 This is consistent with awarding the fraction X of ali quota licenses to foreigners, or with voluntary esport restraints (VER's) where foreigners return a fraction (1-w) of the rents to domestic residents, or with a tariff on quotacontrolled imports at the specific rate (1-0)(P-P*) 17 We also assume that the rent share is uniform across commodities and that it is fixed by a process which is independent of q and t i<sup>8</sup> With these assumptions, the equilibrium condition therefore becomes: is Some of the items in the q group may be subject to _both_ tariffs and quotas. Such goods should be counted as falling in the quota-restricted group, since the quota constraints bind at the margin. The effect of the tariff is then to increase the share of rents on these goods which accrues to the domestic economy. For an illustration of this, see Section VII below. 16 me continue to assume that all tariff revenue **t'm** is retained at home and accrues to the private sector, an assu ption which can easily be relaxed.

17 Alternatively, this is the result of an _ad valoree_ tariff on the quota-constrained good at a rate equal to (1-w) times (p-p*)/p. In either of these cases, the tariff must change when p changes if w is to remain constant. _We_ assume in this section that this change occurs, so that quota reform does not alter the rent share. The alternative case, whbre the tariff is fixed and w adJusts, is considered in Section VII. la Relaxation of these assumptions is discussed in Anderson and Neary (192).

11
(4.1) t(q,g,u) + p'q = **t'M +** (l-c)(P-p*)'q + The right-hand side of this differs from that of (3.7) in two respects: consuoLrs now receive tariff revenue as well as quota rents; and they receive only a fraction of the latter, with w(p-p*)'q accruing to foreigners.

To derive the welfare effects of different policy changes, we now need to differentiate equation (4.1). To do so, it is convenient once again to introduce the balance of trade function, defined as the deviation of (4.1) from equilibrium, and with tariff factors X replacing tariff levels t: (4.2) O(q.4.u;y) * E(q,jlO,u) + p'q - _(4-J)'fm_ - (1-w)(p-pX)'q - . Differentiating this yields:

> (4.3) 8 du = -B'd - B'dq.

where: (4.4) a **u** = (1-t' **+wq** P I _)t_ **U** (4.5) -8' = (t' P-)*C.q'Pn)fl (4.6) -B' t'` -wq'p +(i-.)(p-px)'. **q q q** The term B equals the inverse **u** of the marginal utility of income, , **U** multiplied by the shadow price of foreign exchange, which differs from unity to the extent that there are income effects on the demands for tariff- or quota-constrained goods. As always, we will assume that the distortions are not so severe as to render this term negative19 and shall not consider it further. As for the coefficients -B. and -eq. they measure the _margiAal cost of tariffs_ and the _shadow prices of quotas_ respectively. Clearly, the simultaneous presence of tariffs and quotas complicates the expressions considerably relative to the special cases considered in Sections II and

> 19 If they were, then there would be a welfare gain from disposing of some of the economy's factor endowment, and so the policy reform issue would be trivial.

12
III.20 However. in principle they are still<sup>computable, an issue to which we</sup> will return in Section VI.

We are now ready to define the Trade Restrictiveness Index for this general case. We wish to have a single<sup>scalar measure of the severity of a</sup> given protective structure. To do<sup>this, it is necessary as in Section II to</sup> switch from specific tariffs to tariff<sup>factors. Moreover, it is convenient</sup> to go further and to work with the<sup>inverse of the tariff factors. This</sup> allows us to define "liberalisation factors" l, which equal quota levels for quota-constrained goods and the inverse of tariff factors<sup>for tariff-</sup> constrained goods: q for quota-constrained goods (4.7) x = I 1/0. for tariff-constrained goods We may now define the full Trade Restrictiveness Index in terms of these liberalisation factors: The value of A has the interpretation of the equal proportionate _tightening_ of all quota levels and _raising_ of all<sup>tariff factors which would be</sup> equivalent in welfare terms to a given<sup>initial protective structure with any</sup> arbitrary pattern of quotas and tariffs.<sup>As before, a rise inAcorresponds</sup> to a move towards a new equilibrium with<sup>trade policyX1 which is</sup><sup>_less_</sup> restrictive relative to the initial equilibrium<sup>with trade policyX</sup> Differentiating the index gives the effects on the measure<sup>of a small change</sup> in trade policy relative to the initial<sup>equilibrium:</sup> or, writing out the weights in full for<sup>quotas and tariffs (the difference in</sup> sign between the two reflecting the fact<sup>that trade restrictiveness</sup> rises with 20 See Anderson and Neary (1992) for<sup>further discussion.</sup> 13
louer quota levels but with _higher_ tariff factors):21 Since all the terms in this expression can be calculated from (4.5) and (4.6), we have thus derived a scalar operational seasure of the overall change in restrictiveness as a result of any change in trade policy. Once again, the denominator of the expression for Z is the shadow value of distorted trade, this time equal to the **sum** of each quota times its shadow price and each tariff factor times its marginal cost.

Y Changes in the Restrictiveness of Quota Policy in the Presence of Growth As already noted, our measure of trade restrictiveness does not require that exogenous variables other than trade policy (as sumearised in the y vector) remain constant. 22 However, if trade is restricted in part by quotas, we need to be careful in interpreting the phrase 'change in trade policy^ when other exogenous variables are also changing. For example, if real growth takes place in the economy, maintaining constant quota levels amounts to an _increased_ restrictiveness of trade policy.3 It is still possible to calculate A from equation (4.8), of course, but it must be interpreted as an _uncoapensated_ index, measuring the restrictiveness of trade policy relative to a benchmark equilibrium with fixed quotas. By contrast, for many purposes it may be more appropriate to calculate a _compensated_ index, which corrects for changes in exogenous variables by taking an alternative benchmark equilibrium in which the domestic prices of the 21 Henceforward, wherever the context permits it without ambiguity, we use subscripts -i" and 'j' to refer to individual tariff factors and quotas respectively. Thus Bi gives the derivative of B with respect to i , etc. 22 It is straightforward to adapt our methods to develop a measure of the welfare effects of changes in y. but this is not our concern. 23 Growth may also alter the welfare cost of tariff protection, but we would not wish to say that it makes given tariffs _more_ restrictive.

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quota-constrained goods are kept constant. (These considerations are familiar to policy-eakers, who frequently build in automatic adjustments to quotas in line with economic growth).

To formalise these ideas, we write q° for the vector of quotas which would compensate for a change in an exogenous variable in the sense of maintaining domestic prices p constant. This quota vector is implicitly defined by the following: (5.1) p(q°,n u°) = p(q<sup>0</sup> ,r<sup>0</sup> ,u<sup>0</sup> ,°y), where ° is the initial value and y1 the new value of the exogenous variable, assumed henceforward to be a scalar. In equation (5.1), ao is the level of utility which would be attained in equilibrium if trade policy were to remain constant in this sense: (5.2) 13(q',°,iu , I) 0.

We may now define the compensated TRI, Q, as tne equiproportionate change in trade policy which would return the economy, not to the initial utility level u ° but to the hypothetical 'equirestrictive quota policy level u`: (5.3) A a [A : B(q<sup>1</sup> /&AO',u0<sup>0</sup> .1) = O] This is identical to the definition of the uncompensated TRI, (4.8), except that it is evaluated at the compensated utility level u° rather than uo and at the new exogenous variables y1 rather than °. Changes in A must then take account of changes in u° and 11 as well as of changes in trade policy: where Q is simply E _ai_ i, as in (4.9) (although evaluated at a different point).

A particularly simple form of (5.4) results if tastes are homothetic and growth is 'balanced' in the sense that all sectors grow at the same rate 15
at constant prices. We will refer to this combination of assumptions as "neutral growth"; note that I can then be interpreted as the rate of growth. It can now be shown (details are given in the Appendix) that the balance of trade function is homogeneous of degree one in (q,u,y):24 This implies that the solution to (5.1) and (5.2) takes the particularly simple form: Hence it follows that: In words, "coapensating" for neutral growth requires that all quota levels, and the growth-compensated reference utility level itself, rise at exactly the rate of growth. Substituting from (5.5) and (5.7) into (5.4) yields finally: Thus, compensating for the increased restrictiveness of quotas as a result of growth at _given_ quota levels requires that the standard TRI be reduced by the rate of growth times the contribution of quota restrictions to the shadow value of distorted trade. The reason why we must _subtract_ a term in the growth rate of real income is that, if trade policy parameters are given, then growth renders the quota **regime** _sore_ restrictive.

# VI Operationalising the Trade Restrictiveness Index

> 24 It is convenien **t** o assume henceforward that the trade balance l is initially zero. Alternatively, equation (A.4) in the Appendix implies that (5.8) also holds if l rises at the rate of economic growth.

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When we turn to consider how the TRI nay be operationalised, we have a clear choice. On the one hand, the analyst may already have access to a fully-fledged computable general equilibrium (CGE) model of the economy, in which case the _level_ of the TRI provides a convenient method of summarising the model's results, permitting consistent cross-country and intertemporal comparisons. On the other hand, if a CGE is unavailable, the _change_ in the TRI may still be calculated provided a number of analytic short cuts are taken. In principle, the use of a CGE model is the ideal Procedure. However, in practice, CGE models are typically based on a relatively small number of goods with inappropriate aggregation of the fine structure of trade restrictions. By contrast, the payoff to the local approximation approach is that we can devote more attention to the detailed commodity-by-commodity structure of protection. In this section, we outline the simplifications which were made in our own application of the TRI to U.S.-Hong Kong trade in textiles, described in Section VII.

A. Separability Assumptions The general theoretical framework has assumed that the analysis is to be carried out at the level of the economy as a whole. However, in many applications the analyst may be interested in only a few markets. In such circumstances it is natural to define a _partial_ Trade Restrictiveness Index, defined over the trade policy instruments applicable to the markets of interest only. For example, if only quota-constrained markets are being considered, the partial index is, instead of (4.8): (6.1) &(<sup>0</sup> ,q ,u°;y<sup>0</sup> ) a **[A 8(q**<sup>**1**</sup> **/A,**<sup>0</sup> ° u;y 0 ) * 0].

In addition, it is very convenient in this case to assume that the goods to be considered are _separable_ from others. In our Hong Kong applications, all the goods examined were subJect to binding U.S. import quotas, so

**25** In spirit, our approach resembles the 'local' general equilibrium analysis of Desrdorff and Stern (1986).

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separability can be viewed as a restriction on the cross relationships between quota-constrained and other goods. This amounts to imposing a specific structure on the trade expenditure function: (6.2) E(p,n,u) = C M(p,u),Vn.u),u].

The implications of this specification for the derivatives of the balance of trade function have been examined in Anderson and Neary (1992). In particular, the expression for the shadow price of quotas, equation (4.6), simplifies in this case to: (6.3) _-8' = -_Tp' -_ E P' + (l-0)(p-ps)'. **q** Comparing this with (4.6), we see that separability has allowed us to simplify two complicated matrix expressions. The term t'eq (measuring the change in tariff revenue arising from a quota relaxation) is replaced by the much simpler term **-w',** where T is the import-weighted average _ad valor&e_ tariff on the m goods; and the term -wq'p (measuring the change in rents **q** accruing to foreigners arising from the effect of a quota relaxation on **home** prices) is replaced by the term -(kfc)p', where _E_ is the aggregate elasticity of demand for quota-constrained goods.

3. Tariffs as a Rent-Sharing Nechanism A key aspect of operationalising the TRI is obtaining estimates of the rent share parameter w. Hong Kong exports of textiles and apparel to the U.S. are subJect to binding VER's under the Multifibre Arrangement (WA). However, not all of the rents accrue to Hong Kong exporters since the U.S. levies an _ad valores_ tariff of around 20. 26 This implies that the rent share o is not fixed but varies with q and also that it varies across comodities. Naturally, this alters the expression for the shadow price of quotas. To see how, we assume that international arbitrage equates U.S.

26 Since the quotas always bind, the goods are quota-constrained throughout and the tariff serves solely as a rent-sharing **mechanism.** 18
import prices p to Hong Kong export prices p*, plus the price of a Hong Kong export license p. grossed up by the U.S. import tariff **r** (which is the **same** for all goods):27 (6.4) p (1+trq)(ps + p).

The rents accruing to the U.S. equal the total rents (p-p*)'q less Hong Kong lic;ense revenue p'q. Using (6.4) to simplify, this becomes: Substituting into the balance of trade function (4.2) and simplifyin **g** ives: (6.6) B(q.,Ou;y) a ti(q. MO.u) + 1r p Iq - t I - q Differentiating and simplifying yields. instead of (4.6), the following expression for the shadow price of quotas fros the U.S. point of vie*: Finally, imposing the separability restrictions discussed in Section VI.A gives the following simple expression: Since the U.S. tariff on Hong Kong exports of textiles and apparel (r ) of **q** about 20* exceeds the U.S. average tariff (r) of about 4%. the shadow price of quotas is positive for the U.S.

C. Harket Power In this application we assume plausibly that the U.S. is a small open economy: it faces constant marginal costs of Hong Kong textiles and apparel so **pa** is fixed in the relevant range of exports. However, the same cannot 27 ge follow other researchers in assuming that the license price is included in the FOB price and so is subject to the tariff. Estimates based on the alternative assumption. p (= r q)p* + **p.** are available on request.

1,
be assumed of Hong Kong, since it faces downward-sloping demand curves in the U.S. Strictly speaking, this should be taken into account in our theoretical derivation. 28 However, a simpler approach is to view the terms of trade loss to the U.S. of a quota change, measured in (6.8) by -(li/(l., )]P', as equalling the gain to Hong Kong. The other two terms in **q** the expression for the shadow price of quotas are easily modified. Since Hong Kong does not impose tariffs on other goods, the term X is zero and the first term vanishes; and since Hong Kong exporters receive the full license price, the third term is simply p. The shadow price of quotas from Hong Kong's perspective is therefore: A final complication in the case where a country has monopoly power in trade is that the adjustmen **t** o quota policy to compensate for econosic growth should be modified. AS we saw in Section U, when tastes are homothetic and growth is balanced, a growth-compensated quota policy in a small open economy is one whereby all quotas rise at the rate of growth. Uhen prices are variable. we would expect the required changes in quota levls to be smaller in absolute value, since some of the welfare gain from growth is offset by a worsening of the terms of trade, necessitating a snaller growth in quotas to maintain the same level of trade restrictiveness. However, attempts to take account of this in the empirical application have so far proved unsuccessful, so we have simply imposed the value of minus one in the results reported below 29 VII An Application: U.S. Textile Imports from Hong Kong We turn finally to our empirical application, which calculates a partial 28 See Neary (1989) and Anderson and Neary (1992), Section II.4, for further details.

29 This amounts to applying equation **(5.8)** ignoring the term B¢# 20
index for the restrictiveness of U.S. quota policy on imports from Hong Kong under the MFA. Our sample consists of exports of twenty seven categories of textiles and apparel from Hong Kong to the U.S. over the six years 1983 to 1988. The choice of coverage was determined by the availability of data on Hong Kong export quota licence prices, p; for these we used data collected by Carl Hamilton supplemented by World Bank estimates. Data on export prices and quantities and U.S. tariffs in each category were extracted from the World Bank's MFF data base; and changes in real income for the two countries were measured by the growth rates in real disposable income.

Estimates of the price elasticity of U.S. demand for Hong Kong imports were not available. If we assume that imports from Hong Kong are perfect substitutes for other textile imports,30 the elasticity we require, c, equals the elasticity of U.S. demand for all textile imports. E. divided by the Hong Kong import share. The latter fluctuated around .15 during the period considered; the exact values are given in Table 1. We present results for three values of c, -0.5, -1 and -2. with the unitary case being the 31 literature's consensus.

The results are presented in Table 2. For each year and each value of **w** e give the changes in the uncompensated and compensated TRI's from the U.S. and Hong Kong points of view (using the formulae in equations (6.8) and (6.9)).32 These are compared with the changes in the average tariff equivalent, calculated in the conventional manner as a trade-weighted average of the implicit tariffs, pi. (Table I gives the levels of this measure.) 30 Strictly speaking, this is inconsistent with our assumption of general equilibrium separability. Since the results turn out to be relatively insensitive to the elasticity value assumed, this is not perhaps a critical point. 31 See Trela and Whalley (1990).

32 The formulae for S are for local changes whereas the data refer to discrete intervals. To allow for this, the changes given are Divisia indices, calculated using the arithmetic averages of the parameters in two successive periods.

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Consider first the results from the U.S. point of view. Our measure suggests that over the period there was a marked increase in the protectiveness of the trade regime. Although the uncompensated index rose slightly in all years except 1984, it did so by less than the growth rate of real income, so that the value of a fell in five of the six Years, with a cumulative fall (representing an effective tightening of the quotas) of 14.9%. By contrast, the traditional measure, the average tariff equivalent, fluctuated widely over the same period, with an average annual rate of increase of about 6.3X. While this has the same qualitative implication (an increased restrictiveness of the quota regime) as our estimates of changes in the true measure, its variability from year to year is highly implausible. Moreover, in four out of six years. the average tariff equivalent has the opposite isplication for the change in trade restrictiveness as our index. This dramatic finding, similar to that in Anderson (1991), reveals the serious practical inadequacy of the standard measure of trade restrictiveness. Note that our estimates are not at all sensitive to different assumptions about the elasticity of demand, s. Although, from (6.9), all shadow prices rise as the elasticity falls, this tends to affeci all categories uniformly in both the numerator and denominator of Z and so does not significantly alter the estimated change in A.

Turning to the results from the Hong Kong point of view, they reveal further interesting properties of the TRI approach. 'he estimates are much more sensitive to the value of the elasticity than were those for the U.S. Noreover, in four years when E is at its low value, most or all of the estimated quota shadow prices are negative, with the result that the shadow value of distorted trade, -B'q, is itself negative. This implies that a **q** _fall_ in A is welfare-improving; i.e., that in those cases tiong Kong's monopoly power in trade is so great that the actual quota levels are above 22
their optimal value. 32 If we confine attention to the central case (E -1), & fell in five of the six years, implying that Hong Kong as well as the U.S. has been losing from the direction of policy. Once again, the implications of our measure are very different from those of the crude change in the average tariff equivalent.

# VIII Conclusions and Suggestions for Further Research

In this paper, we have presented a new approach to measuring the restrictiveness of a protective structure. The measure we ProPose, the Trade Restrictiveness Index, has a firm welfare-theoretic basis yet can be implemented fairly readily. In the case of tariffs, the TRI equals the uniform tariff which is equivalen **t** o (in the sense of yielding the same level of aggregate welfare as) a given tariff structure. We have shown how this approach can be extended to allow for quotas as well as tariffs and to encompass partial rent-sharing, which arises, for example, from voluntary export restraints. Implementing the TRI requires more data than calculation of standard measures of protection such as the trade-weighted average tariff equivalent. However, the latter is quite unsatisfactory as a summary measure of trade restrictiveness. Mereover, our empirical application in Section VII has shown that, with appropriate additional assumptions, the TRI can be readily implesented and that it yields very different conclusions from the standard approach.

In further work we hope to carry out more espirical applications of the TRI to demonstrate its usefulness in both International and intertemporal comparisons. Further theoretical refinement would also be desirable to improve the treatment of neutral quota policy in the presence of real income growth and to incorporate terms of trade changes. Finally, the TRI can in 32 Trela and Uhalley (1990) also find that a reversion to free trade hurts Hong Kong. because of its large terms of trade loss, although their results are not fully comparable with ours.

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principle be extended to represent the uniform level of trade restrictiveness which would be welfare-equivalent to a given set of _domestic_ as well as trade distortions. This would allow a quantitative assessment within a consistent welfare-theoretic framework of many of the issaes concerning the trade effects of domestic policies which have been raised in negotiations on US-EC and US-Mexico trade.

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# APPENDIX: NEUTRAL GROWTH AND THE BALANCE OF TRAOE FUNCTION

If tastes are homothetic, the household expenditure function e(p,R,u) may be written, without. loss of generality, as ue(p,n). Similarly, if growth can be represented by a scalar parameter y and if it is "balanced' (in the sense that all sectors grow at the same rate when prices are given), then the GNP function g(p,n,y) can be written, without loss of generality, as l(P,) Combining these assumptions, the trade expenditure function in the absence of quota distortions becomes: (A.1) E(p,a,u,) a ue(p,n) - _i(P,)_ This is clearly homogeneous of degree one in (u,).

The next step ia to consider the distorted trade expenditure function: (A.2) t(q,,u.y) - Hax (E(p,a,u,'y)-p'q). This will be homogeneous of degree one in (q,u,y) provided that the domestic price function p(q,n,u,) is homogeneous of degree _zero_ in (q.u,y). out this must be the case, since the first-order condition from (A.2) is: (A.3) q = ue (p.n) - yi (p,n).

Since the left-hand side is homogeneous of degree one in q and the right-hand side is homogeneous of degree one in (u.y), it follows that p(q,x,u.j). which is defined implicitly by (A.3), must be homogeneous of degree zero in (q.u,y). Hence the distorted trade expenditure function t(q9x,u9,V) must be homogeneous of degree one in (q.u,y), as required.

Finally, we must ask what this impies for the balance of trade function: (A.4) B(q,x,u,y) * t(qpx9u,y) * p(q,x.,u,l)q - (x-n)1(q.x,u,) - (l-.)[p(q.w.u.j)-ps]'q - P.

From Shephard's Leoma, **s(q,ff,u,j)** equals t¢ q,x,u,) and so is homogeneous of degree one in (q,u,). It follows that each individual term on the right-hand side of (A.4), and hence the expression as a whole, is homogeneous of degree one in (q,u,g,p).

25