Policy, Research, and Extemal Affairs WORKING PAPERS Trade Policy Country Economics Department The World Bank April 1990 WPS 352 Voluntary Export Restraints and Resource Allocation in Exporting Countries Jaime de Melo and L. Alan Winters By reducing the marginal revenue of the factors of production, a voluntary export restraint (VER) causes an exporting country's industry to contract. Efficiency losses depend on whether sales can be diverted from restricted to unrestricted markets. A VER is likely to produce a welfare loss if demand is relatively elastic and supply is not. The Policy, Research, and External Affairs Complex distribuLes PRE Working Papers to dissaninate the findings of woik in progress and to encourage the exchange of ideas among Bank staff and all others intersted in deveopment issues. These papas carry the names of the authors. reflect only their views, and should be used *nd cited accordingly. The findings, interpations, and conclusions are the authors' own. They should not be attributed to the World Bank, its Board of Diectors, its managenent, or any of its member courdes. Policy, Research, anld Extemnl Affairs = ~~~Trade Policy This paper- a product of the Trade Policy Division, Country Economics Department- is part of a larger effort in PRE to study the effects of cuantitative restraints imposed by developed countries on developing country expons (research funded by RPO 672-40). Copies are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Maria Ameal, room N10-035, extension 37947 (40 pages with figures and tables). Most literature on voluntary export restraints markets and a sharp fall in the marginal revenue (VERs) analyzes the welfare costs of VERs to product of factors employed in the Korean consumers in the importing country. De Melo leather footwear industry during the period the and Winters propose a method tor measuring the OMA was in effect. effects of a VER on the productivity of factors employed in the exporting industry. They found that the marginal revenue product of factors employed in leather footwear Their model measures how a VER affects declined as much as 9 percent because of the both revenues and efficiency (which may be OMA. This estimate was corroborated by time affected by contraction of output) in an export- series on output, employment, and wages in the ing industry. They used the model to estimate Korean footwear sector. the effects of the U.S. Orderly Marketing Agree- ment (OMA) on Korean producers of leather Based on illustrative counterfactual simula- footwear in 1 977-8 1. tions, de Melo and Winters show that a VER is likely to produce a welfare loss if demand is Their econometric estimates indicate a relatively elastic and supply is not. Iimited ability to redirect sales to unrestricted The PRE Working Paper Series disseminates the findings of work under way in the Bank's Policy, Research, and External Affairs Complex. An objective of the series is to get these fmdings out quickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official policy of the Bank. Produced at the PRE Dissemination Center Voluntary Export Restraints and Resource Allocation in Exporting Countries* by Jaime de Melo The World Bank and Centre for Economic Policy Research and L. Alan Winters University of Wales, Bangor and Centre for Economic Policy Research Table of Contents 1. Introduction 1 2. Resource Allocation Implications of a VER 2 3. Estimating the Reduction in Factor Demand: Korean 11 Leather Footwear 4. Illustrative Welfare Calculations 19 5. Conclusions 22 Footnotes 24 References 26 Appendices 28 * This research was financed by World Bank Research Project 672-40. We thank three referees, Wendy Takacs, Paul Brenton, Taeho Bark, participants at the STEP/CEPR Conference in Venice, May 1988 and at the European Research Workshop in International Trade in Bergen in July 1989 for helpful comments on an earlier draft. We thank Maria Ameal and Alexander Pfaff for logistic support. 1 1. Introduction The.bulk of empirical work on voluntary export restraints (VERs) has focused on establishing the welfare costs of these arrangements to the consumer in importing countries. Examples include: the quality-adjusted welfare cost estimates to consumers of VERs on autos (Feenstra (1984), and Dinopoulos and Kreinin (1988); the argument that for products where differentiation and start-up costs are low (e.g. footwear, textiles), VERs are ineLfective and hence that protection is porous (Baldwin (1982), Bhagwati (1986)); and the use of calibrated simulations to show that terms of trade effects are likely to reduce substantially the costs (gains) to importing (exporting) countries (Tarr (1987), Trela and Whalley (1988)). None of these studies, however -- even those which look into the implications of VERs for exporters -- estimates directly the resource allocation implications of VERs for o:xporters. The purpose of this paper is to fill that gap. More precisely, the contribution of this paper is to propose a method to measure the effects of a VER on the productivity of factors employed in the exporting industry. In section 2, an intuitive discussion establishes that, under fairly general conditions, a VER will lead the industry to contract. In section 3, we estimate econometrically the effects of the U.S. Orderly Marketing Agreement (OMA) for non-rubber footwear imports on the marginal revenue product of factors employed in the Korean leather footwear industry during 1977-81. We estimate that the fall in the marginal revenue product of factors in footwear was as much as 92 because of the OMA. We then use in section 4 our econometric estimate of the ease with which sales were diverted from restricted to unrestricted markets to give illustrative calibrated estimates of the likely welfare 2 effects of the OMA on Korean leather footwear exporters. Conclusions follow in section 5. 2. Resource Allocation Implications of a VER In this section, we discuss the revenue and the resource allocation implications for an exporting country entering a VER. To simplify the exposition, we assume that all output (produced by identical firms in perfect competition in all product and factor markets) is sold in one of two foreign markets, and that a VER restricts exports to one of these markets while those to the second market remain unrestricted. (In the empirical application, output is sold to three markets.) In addition, we assume that individual exporting firms are price-takers in each export market, though the industry as a whole faces downward sloping demand curves in each market. The purpose of the analysis is to establish under fairly representative conditions that a VER will reduce the marginal revenue product of factor inputs in the affected industry, and hence reduce the size of the industry. For expositional purposes, we discuss the effects of the VER in two steps. First, we discuss the effects of the VER on the assumption that industry size is fixed and that there are costs to diverting sales from the restricted towards the unrestricted market. With the assumption that the size of the industry remains unchanged it is easy to analyze intuitively the revenue and distortionary implications of the VER. In a second step, we show that a VER will likely lead the industry to contract. Besides being expositionally convenient, this two-step analysis corresponds to the two-stage assumption about firm decisions that has to be adopted in the econometric work of section 3. However, as we show in appendix B, the weak 3 separability between input decisions and sales decisions that it implies is not necessary for the results that are established here. The assumption that there are increasing marginal costs to diverting sales from the restricted towards the unrestricted market may be interpreted as indicating the short-run effects of a VER. In the short- run, with the quantities of factors employed in the industry being fixed, different factor intensities will result in increasing marginal costs to altering the product mix. Alternatively one can view the two products as differentiated. 1/ The above assumptions allow us to represent our model diagrama- tically. In figure 1, foreign export demands in the restricted (A) and unrestricted (B) markets are represented in quadrants I and II, respective- ly, while quadrant III depicts the substitution possibilities facing the Industry as it reallocates production between sales foru-rket A and those for market B. It is obtained by the aggregationz ot the substitution possibilities facing each representative exporter. The bowed-out shape of the *export transformation" curve, G(XA, XB) = X, reflects the assamption of increasing costs to product mix shifts. Assuming that one can write an aggregate footwear production, X, successive increments in sales to market B impose increasing resource costs in terms of larger and larger decreases in export sales to market A. Quadrant IV is the 45° line which translates export sales to A from quadrant III to quadrant I. The unrestricted allocation, A*, is represented by the price- quantity pairs (P*A, X*A) and (P*B, X*B), where superscript asterisks are used to denote the unrestricted equilibrium. 2/ The slope of the export transformation curve is given by 4 II I AB l p I A B fP ll(P Ps A~~~~~~~X ~A A X 1f(P) , a \ P \450 I; I450X X I"~G( A a I I~~~~~~~~~~~~I A P AS 5 dXA GB T.B dXB GA where Gi - 8G/8Xi > 0, i - A,B, iadizates pos tive marginal costs, and the bowed out transformation curve reflects the fact that marginal costs increase with output. 3/ The equilibrium for the competitive industry requires that * * G, P GA pA B B and Pi - O*Gi where G* is the marginal cost of producing a unit of X. In figure 1. the equilibrium condition (1) is represented by the tangency of the export transformation curve and the price line P*, at the unrestricted equilibrium, A*. Now impose a VER which restricts exports to A to the level XA. The restricted allocation is represented by the new price-quantity pairs (PA, XA) and (PB, XB) where superscript bars indicate the restricted equi- librium. Because we have assumed that the industry as a whole does not behave like a discriminating monopolist (due to the assumption of an atomistic industry), it is possible that the VER will raise revenues. Denoting by LA, 6, '< 0 the elasticities of demand in the restricted and unrestricted markets respectively, a departure from the free trade equilibrium will raise revenues if marginal sales revenue is higher in B than in A, i.e. if PB(1- l1/B) > PA(l - VLWA). Thus if the elasticity of demand is much greater in the unrestricted than in the restricted market, a 6 VER may push sales allocation towards that which would be selected by a discriminating monopolist. 4/ Consider next the distortionary implications of the VER. Because we have assumed at this stage that firms maximize profits for a given level of X, the new allocation must lie on the same export transformation curve, and, given the exogenous falue of XA, the chosen point will be R. Thus, given the overall level of input, the VER determines sales to the unres- tricted market as well as to the restricted market. At the new equilibrium the equality of relative prices to the marginal rate of transformation no longer holds. The relative price of A has been forced up by the constraint on sales, but the marginal rate of transformation (MRTA,B) has fallen as the relative output of A has fallen. Hence > P PB ) whereas 'EA GA This violation entafl.s a well-understood distortion cost, regardless of whether total sales revenues have increased after the imposition of the VER. For producers to choose point R voluntarily, they would have to be confronted by the relative price line (PA/PB) which equals the marginal rate of transformation at R. We now turn to the second step of the discussion and show that the VER will create an incentive for the industry to contract. With production and allocation decisions separable, input mixes (which depend on factor prices) are independent of output mixes (which depend on output prices); hence given exogenous factor prices we can construct a composite factor, 2, 7 with wage W. This allows us to characterize production in terms of the aggregate output index as X - X(Z), and assuming constant retuArns to scale, we can select units such that X E Z. In an unrestricted equilibrium, bvIes are allocated between markets in such a way that the marginal revenue product of a factor devoted to producing goods for market A equals that of the factor if it were used to produce for market B. Thus we may write dRA dB dR (2) dZ dZ dZ W where RA is the revenue derived in market A, etc. and where, in our earlier notation. dR Pi * T- *0 9 Gi To assess the effects of the VER on the size of the industry (and hence on the size of the representative firm) as measured by the aggregate input Z, we need to consider whether thie marginal revenue product uf Z is increased or decreased by the VER. This can be done entirely in terms of market B. Under free trade the marginal revenue products are equal across markets, while under the binding VER, only market B can accommodate marginal sales. (When the VER is binding, the marginal revenue product -vailable in market A is zero.) Constrained revenue maximization by the representative firm implies that in the new equilibrium: 8 (3) dZ . - dZGB Since the VER redirects sales from market A to market B, it drlves up the costs of producing for market B, since GB > 0. Thus, even if demand in market B is perfectly elastic -- i.e., PB . PB -- the marginal revenue product of Z is reduced by the VER. If demand is less than perfectly elas- tic, i.e. gB < PB this effect is exacerbated by the drop in price. Thus, even if the VER increasrs the representative firm's total ravenue, it always reduces the marginal revenuse product of its factor inputs. If the firm is a price-taker in factor markets, falling MRP will cause it to reduce its output and input levels. Return now to the market for the composite factor Z. Figure 2 illustrates the two cases of interest. The VER causes the marginal revenue product curve to fall, say from MRP1 to MRp2. In the very short-run in which factor inputs cannot be altered at all, the input level remains at Z*, but the rents lost amount to area AEFC. This, of course, is the impli- cation derived by considering the allocation model in isolation. In the opposite case, when the footwear industry (in cddition to each of its indi- vidual firms) faces an infinitely elastic supply of Z, then the new input level is given by Z; this implies large outv losses, but no distortionary resource costs because factors may shift to industries in which they are just as productive as in footwear. Under these circumstances, 0 - O. and the shift in the marginal revenue product curve must be accommodated by output contraction alone. If, on the other hand, the industry faces an 9 figur'-9 w A w = Ai I I~~~~~~~~ * s ___ _ - - _--- I MR? I z c [-- - [-- - - :\ -R z _ * 10 upward-sloping supply curve for factors, the final input level is Z; this entails a smaller contraction, but additionally imposes losses of rent -- and hence of welfare -- on factor owners. The losses are given by area AEDB. Now, GcG, and there is an efficiency loss, but it is smaller than that impLied in the very short run in which industry factor inputs are fixed. A more conmplete exposition of the implications of a VER would relax the representation of the problem in terms of two markets and the two-stage decision by firms. The empirical analysis in section 3 treats the more general case where sales are allocated to one restricted and two unrestricted markets, and we discuss below how to modify the analysis to admit several unrestricted markets. As to the two-stage decision assumption, de Melo and Winters (1989b) show for the general case of a two- output one-input general technology that spillover to unrestricted markets and output contraction will occur unless there is a very strong positive relationship between output destined for one market and the costs of producing for others. Since marginal production costs for each market are likely to show only small interdependencies, it is unlikely that the qualitative predictions of the above analysis would differ in a more general set-up. Because we have only two markets, we have been able to establish the contractionary effect of a VER by considering the marginal revenue product in each market directly. With more markets, as in the empiricdl application below, it is convenient to use an alternative approach, derived from Neary and Roberts (1980). These authors show that a constrained equilibrium can be expressed as an unconstrained equilibrium at a different set of prices. These latter prices, which are known as virtual prices, are 11 simply the set of prices at which, given the overall level of activity, producers would supply voluntarily the actual quantities supplied in the constrained equilibrium. For unconstrained markets, virtual prices are equal to actual prices. Referring back to figure 1, the quantities given by R would be willingly supplied at the set of prices (P,A PB). For any unconstrained equilibrium the marginal revenue accruing from an extra unit of aggregate output X, optimally allocated, can be written as P - P (P1, ..., Pn); OP/8Pi > 0, for all i. For a constrained equilibrium, the Neary-Roberts results allow us to calculate the marginal revenue by evaluating the same function at virtual prices (p). The effect of a binding VER in market j is to reduce Pi below the actual price, but since the virtual and actual prices of the unconstrained markets are equal, this is sufficient to deduce that P < P . This is the procedure we adopt in section 3 to measure the equivalent of distance EF in figure 2. 3. Estimating the Reduction in Factor Demand: Korean Leather Footwear In this section, we estimate the effect of the USA's Orderly Marketing Agreement (OMA) on non-rubber footwear on the demand for Korean leather footwear producing factors. To keep the results transparent, we coatinue with our very simple model of footwear exporting. The Korean industry is presumed to produce an aggregate quantity of footwear using a single composite factor of production, and subsequently to allocate this aggregate to one of three markets according to a constant elasticity of transformation (CET) allocation function. This simple function allows us to analyze, albeit indirectly, the efficiency implications of the OMA without access to specific data on the allocation of factor inputs to sales in each market. The crucial parameter in determining the effects of the 12 OMA is the elasticity of transformation -- i.e. the extent to which production mAy be shifted betweon outputs destined for different markets. Using quarterly data over the period 1975 I to 1986 IV, we estimate the elasticity of transformation between supplies of leather footwear destined for three markets -- the USA, wunconstrained-EC' and the rest of the world. The USA imposed the OMA on Korean exports of non-rubber footwear between the third quarter of 1977 and the second quarter of 1981, inclusive. As explained below, the observations corresponding to the OMA period are not included in the estimation period. The second group -- unconstrained-EC -- comprises France, West Germany, Italy and the Netherlands -- which, according to Hamilton (1989), imposed no quantitative restrictions on Korean footwear exports over our sample period. The rest of the world comprises all other countries, some of which did have import restrictions on footwear, but which may be reasonably treated as unconstrained overall. Although the OMA operated formally betbreen 1977 and 1981, the evidence suggests that the restrictions on Korea ceased to bind by mid-1980 (Aw and Roberts, 1986). As in the analysis in section 2, the export allocation model presumes that individual Korean exporters are price-takers and that they seek to maximize profits subject to a CET transformation function relating the quantities of each type of footwear export to an overall index of output (input). That is max E Pi Xi subject to [ EaiX7 | -X Xi 13 where Xi is exports to market i, at price pi, X is the index of aggregate output, and 7 > 1. Writing p = 1/(7-1) for the elasticity of transformation, standard manipulation allows us to express the share of market i in total exports as (see Hickman and Lau, 1973): (4) st a ai (Pi/P)P i - 1, 9, 3 where si is the share of i in the volume of exports, si - Xi/EX1, P E a; p p ]llp/ is a fixed weight price index, i J ai ai, Both the danger of simultaneity and of errors in variables suggest the need for more robust methods of estimation than are possible for non- linear systems of equations with complex error structures. 5/ We decided, therefore, to linearize the model about a base period (see Hickman and Lau (1973)). Setting prices to unity in the base period (quarter II, 1984), introducing a time-trend with value zero in the base, and adding seasonal factors and dynamics, we estimated (5) Yit P pi t P Fit + 5iit-l 4yit-4D uit 14 Yit! 5 it- ai is the deviation of i's share from its base value, ait t 0 ai' Pt - Ej a jt, is a based-weighted price index, t is a time-trend incremented by one per quarter. E D are seasonal effects for quarter 1, 1 - 1.3,4 where the dummy for quarter two has been suppressed because the base period is a second quarter. )l, X4 represent dynamic effects on the share of market i, felt through lags of itself, and uit are stochastic errors. The Yit sum to zero over i in each time period, and so one of equations (5) must be dropped in estimation -- we dropped that for unconstrained Europe. We then estimated the remaining equations by a three-stage procedure allowing the errors, uit, to be autocorrelated and correlated across markets, imposing the cross-equation parameter constraints (p. X, and X4 appear in both equations), and using instrumental variables to allow for the simultaneity and errors af observation. 6/ Because the OMA disturbed export allocation, the observations 1977 III to 1980 II (when it bound) must be dropped from the estimation period. It also proved unnecessary to include the fourth order lag on yit. Thus the final equation is as given in table 1. The estimated elasticity of transformation is perhaps a little low, given the anecdotal evidence that exists on the degree of competition and product substitution/homogeneity in world footwear markets; but it is a fairly robust result. Moreover, two other pieces of evidence suggest that Korean exports to different markets 15 Table ls THE ALLOCATION FUNCTION FOR KOREAN LEATHER FOOTWEAR EXPORTS Leather Footwear p 1.311 (0.756) 7R -0.0013 (0.0009) 7U 0.0024 (0.0010) 6R1 0.074 (0.022) 5u1 -0.076 (0.021) 6R3 0.060 (0.019) 6U3 -0.063 (0.018) 6R4 0.058 (0.019) 6U4 -0.060 (0.020) 0.401 (0.102) r 0.137 R2 Row 0.80 USA 0.88 EC-unconstrained 0.75 Long-run elasticity of transformation 2.19 Subscripts R refer to the "rest of the world" and U to the USA. r is first-stage estimate of the autocorrelation parameter. Standard errors in parentheses. 16 are imperfect substitutes. First, as we noted above, the unit values of Korean exports to different markets differ by up to 50S, suggesting that there may indeed be genuine product heterogeneity. Second, the estimates in table 1 display dramatically different seasonal patterns -- with the allocation between the US and the rest of the world switching by over ten percentage points with the season. Table 2 explores the effects of the OMA on Korean exports to the USA more closely. Column 1 reports the difference between the actual share and that predicted by our equation for the constrained period. It is consistently negative suggesting a binding restriction, but it shows signs of weakening over 1980. The second column approximates the proportionate difference between the virtual and actual prices of exports to the USA. Because the actual US share falls short of that predicted by the export allocation model, the virtual price for the USA is below the actual price, by as much as 122 in 1977 III. Thus, the OMA may be seen to have had an effect equivalent to a 52-122 drop in the price of exports to the USA with no compensating price rises in other markets. This makes it clear that the OMA put pressure on the Korean footwear industry to contract. The extent of the contractionary pressure can be calculated as the difference in the aggregate price index evaluated at actual and at virtual prices. This calculation is reported in column (3) of table 2, and is a linear approximation to the change in the marglnal return on aggregate activity in the leather footwear sector. It shows that the marginal revenue product of the factors of production in the leather footwear industry declined by as much as 92 because of the OMA, and that the OMA imposed significant pressure for contraction. 17 Table 2: THE EFFECTS OF THE OMA ON KOREAN LEATHER FOOTWEAR EXPORTS TO THE USA Residual Price change Change in in share equivalent aggregate - Quarter equation of OMA price index (P/P -1) 77.3 -0.176 -0.121 -0.095 77.4 -0.024 -0.017 -0.013 78.1 -0.076 -0.050 -0.039 78.2 -0.159 -0.103 -0.081 78.3 -0.098 -0.056 -0.044 78.4 -0.093 -0.051 -0.040 79.1 -0.208 -0.096 -0.076 79.2 -0.188 -0.081 -0.063 79.3 -0.284 -0.110 -0.087 79.4 -0.159 -0.065 -0.051 80.1 -0.052 -0.023 -0.018 80.2 -0.092 -0.040 -0.031 EMPLOYMENT AND OUTPUT IN FOOTWEAR FOOTWEAR RELATIVE TO ALL MANUFACTURING 1.8 - 1.7 - 1.6- 1.5- 1.4- 1.3- 1.2 - x w~~~~~ z L- ~0.9 Ii.. ~ ~ ~ ~ ~ ~ ~ ~ ~ YA 0 0 0.8 0.7 0.6 0.5 LL~0. 1974 1975 1976 1977 197Li 1979 1980 1981 1982 1983 YEAR 0 EMPLOYMENT 4- OUTPUT 19 The econometric estimates strongly suggest that the Korean footwear industry would have contracted during the period of the OMA. This prediction is borne out by inspection of time series on output, employment, and wages of the Korean footwear sector (see table Al in the appendix). The data displayed in figure 3 report footwear output and employment relative to the corresponding series for the entire manufacturing sector. This normalization is necessary to control for the Korean recession of 1980. Even when it is made, the time patterns show clearly that the footwear sector experiences a notable slump during the period when the OHA with the U.S. was in effect. 7/ 4. Illustrative Welfare Cilculations The results above confirm that a VER leads to output contraction and has adverse efficiency effects if the factors employed in the industry are not available to it in perfectly elastic supply. However, as discussed in section 2, a VER also results in a sales revenue effect which may either reinforce or counteract the efficiency effects. This section provides rough orders of magnitude of the potential welfare effects of a VER, using the US OMA on Korean exports of leather footwear as a reference. For the illustrative calculations, we retain our estimate of the elasticity of transformation of section 3 as an estimate of the ease with which exporters may divert sales from restricted to unrestricted markets and complement it with guesstimates of factor supply elasticities and price elasticities of export demand. 8/ The calibrated counterfactual simulations are for the model presented in section 2 with: constant foreign price elasticities of demand; a CET function describing sales allocation; and a constant 20 elasticity of factor supply. The welfare measure is given by the sum of profits and factor incomes, and the change in welfare is expressed as a share of initial variable factor (Z) income before the VER. The change in factor demand from the restricted industry affects the wages throughout the markets in which they are traded. Because the share of the industry in the market for Z will vary depending on the industry under a VER, we give calculations for cases where the market for the variable factor Z is either 1,5, or 10 times the initial allocation of 2 to the industry under the VER. (The details of the model are given in Appendix B.) The results of our illustrative calculations for a range of elasticities are given in Table 3. For all calculations, the simulations consist of a 1lO reduction in the volume of sales to the restricted market, where the initial share of exports to the restricted market is 42t of total exports (a figure corresponding to the leather footwear case of section 3). Before examining the results in the different columns of the table, where several elasticities are varied simultaneously, we briefly describe the effects of varying elasticities one by one and compare the results with those in column 1 where all elasticities are unity. In the case of unitary export demand elasticities, there are no sales revenue effects, so it is easy to isolate the effects of varying supply elasticities. The more difficult it is to reallocate the existing volume of production, the higher the efficiency cost of a given VER because the adjustment comes from output contraction rather than from sale reallocation. Likewise, as explained in section 2, the higher the elasticity of factor supply, the lower the efficiency costs of a VER. However, a similar variation (around unity) of the elasticity of factor supply has more of an effect on efficiency than an equal variation of the 21 Table 3: ILLUSTRATIVE WELFARE CALCULATIONS Elasticities \ Column (1) (2) (3) (4) (5) Price Elasticity of Restricted Demand (CA) 1.0 0.3 0.5 1.0 2.0 Price Elasticity of Unrestricted Demand (CB) 1.0 0.6 1.0 2.0 4.0 Elasticity of Transformation (p) 1.0 0.5 1.5 1.5 3.0 Elasticity of Factor Supply (ES) 1.0 0.5 2.0 2.0 3.0 cl Simulation Results Z output a/ -5.0 -3.9 -4.3 -4.5 -4.1 Sales Revenue a/ 0.0 11.6 4.6 0.0 -2.1 Factor Wage a/ -4.0 -7.7 -2.2 -2.3 -1.4 Welfare b/ 1 6.2 19.7 10.2 5.5 2.7 5 -0.5 6.9 6.5 1.7 0.4 10 -8.9 -9.1 1.9 -3.0 -2.5 Notes: Notation is given in appendix B.2. Unrestricted equilibrium: XA - 100; XB - 140; Pi - 1.00; Z = 100. a/ Percent change. b/ Change in level value. c/ Size of market for Z in relation to initial allocation of 2 in industry subject to VER. 22 elasticity of transformation. As expected from figure 2, efficiency costs are more sensitive to the elasticity of factor supply than to the elasticity of transformation. Columns (2) to (5) give estimates of the welfare effects of a VER for low, medium, and high sets of elasticities. The results in column (4) may be viewed as best guess calculations. In this case, there is a net loss if the market for Z is large. On the other hand, if the market for Z is small (relative to the initial allocation of Z to the industry), there is a net gain in spite of the negative efficiency effects because of their smaller weight in the welfare calculation. The same is true for column (2) in the low elasticity case because the larger efficiency costs are offset by larger sales revenue gains with low elasticities. 9/ The simulated decreases in the marginal revenue product of Z (factor wage row in the simulation results section of table 3) are similar in magnitude to the range reported from the econometric estimates in column 3 of table 2. Finally in column (5), with higher demand elasticities, the revenue effect becomes negative implying larger welfare losses. Thus, if demand elasticities are not too low (and supply elasticities are not too high), then a VER is likely to lead to a welfare loss. 5. Conclusions This paper has presented a simple model to analyze the revenue and efficiency effects of a VER at the industry level. Inspired from the evidence that developing countries often have limited success in switching sales towards unrestricted markets, we have separated out revenue effects arising from sales reallocation towards unrestricted markets from efficiency effects arising from output contraction. 23 The analytical discussion of the effects of a VER was then corroborated with an application to the U.S. OHA agreement with Korean expurters of leather footwear. The econometric estimates indicate both a limited ability to switch sales towards unrestricted markets and a sharp fall in the marginal revenue product of factors employed in the Korean leather footwear industry during the period where the OHA was in effect. Combined with extraneous price elasticity estimates of export demand and factor supply elasticity estimates, illustrative welfare calculations suggest that the OMA may well have resulted in a welfare loss, especially if demand elasticities are relatively elastic and the supply response is not very elastic. 24 Footnotes 1/ There is plenty of evidence to suggest that, even at the most disaggregated level for which data exist, export sales to different markets are imperfect substitutes. To take the concrete example of footwear, Korea exports leather outdoor sports shoes to many different markets every year and at prices differing by factors of at least 50 percent (see de Melo and Winters (1989a)). Besides differences in the composition of the export bundle, product differentiation may reflect any of several factors: production to order; the need for marketing structures in importing countries; differences in taste; or a desire for market diversification to reduce uncertainty. 2/ This unrestricted aLlocation represents the solution of the problem: Max PAXA + PBXB s.t. G(XA, XE) = X taking prices as parametric, but where at the final equilibrium, prices and quantities must also satisfy S.T. XA = fA(PA) XE = fB(PB) where fA( ) and fB( ) are demand schedules in markets A and B, and G( ) is the index aggregator for footwear exports, which is assumed to be linear homogeneous and quasi-concave. 3/ Increasing marginal costs requires G , GEE> 0 and G G -G > 0. 4/ While we do not wish to stress the empirical relevance of this possibility, it has been pointed out in previous theoretical discussions of the effects of VERs in non-competitive markets. See e.g. Harris (1985) and Krishna (1988). It is interesting to speculate that the two-tier quota allocation system used in Korea (and elsewhere) implies that greater sales towards non-restricted markets may have the objective of revenue maximization. For further analysis see Bark and de Melo (1988). 51 With unrestricted trade, equations (4) could in principle be estimated by system estimation methods. They can also be manipulated to allow estimation under the rationing caused by the OMA, but only at the expense of having to model a very complex error structure during the rationed period (see Winters and Brenton (1988)). Unfortunatelv, our attempts to apply such manipulations in this case were frustrated by severe numerical difficulties, probably for one of two reasons. First, simultaneity: if Korean footwear are imperfect substitutes for those of other producers, the Korean footwear sector as a whole will face a downward-sloping demand curve, and price will no longer be 25 exogenous. Second, all trade data, but especially those of developing countries, are subject to recording error. 6/ The IV technique was programmed in GAUSS and was based on Aigner, Hsiao, Kapteyn and Wansbeek (1984). It presumes that the instrumental variables (aggregate industrial production, prices and exchange rates in the markets and in Korea) are correlated with the true values of the variables in equation (5) but not their errors of observation. If that is true, our estimates are consistent and asymptotically efficient. Further details on the estimation technique are provided in the appendix. 7/ The peak of the footwear industry occurred in 1978, one year after the signing of the OMA agreement. Although this peak is later than predicted by our model, it is not out of line with the detailed account of the CMA given by Yoffie (1983). He remarks that Korean producers went to considerable lengths to negotiate the OKA in a fashion that allowed extended periods of adjustment. Thus it is quite conceivable that output and employment remained high into 1978. 8/ Our estimates of the price elasticity of export demand are consistent with the range of 0.5 to 1.0 reported in Goldstein and Khan (1985). 9/ The size of the industry in the market for Z and eC aLe not independent. For example, for an industry like footwear e5 is likely to be in the range of 2 to 4 and the size of the market, L, for Z in relation to the initial allocation of Z in footwear is likely to be 5 or more whereas in textiles, the corresponding pair would be es in the range of 0.5 to 2.0 and L in the range of 1 to 5. 26 References Aigner, D.J., C. Hsia, A. Kapteyn, and T. Wanebeek. 1984. 'Latent Variable Models in Econometrics.' Chapter 23 of Z. Griliches and M.D. Intrivigator (eds.), Handbook of Econometrics, Vol. II, North Holland, Amsterdam, pp. 1333-1393. Amemiya, T. 1985. Advanced Econometrics. Basil Blackwell, Oxford. Armington, P.S. 1969. "A Theory of Demand for Products Distinguished by Place of Production." International Monetary Fund Staff Papers, vol. 16, pp. 159-176. Aw, B.Y. and H.S. Roberts. 1986. 'Measuring Quality Change in Quota- Constrained Import Markets." Jourral of International Economics, vol. 21, pp. 45-60. Baldwin, R. 1982. "The Inefficacy of Trade Policy," Frank D. Graham Memorial Lecture, Essays in International Finance, No. 150, Princeton University, Princeton. Bark, T. and J. de Melo. 1988. 'Export Quota Allocations, Export Earnings and Market Diversification," World Bank Economic Review, pp. 341-8. Bhagwati, J. 1986. "VERs, Quid Pro Quo DFIs and VIEs: Political Economy Theoretic Analyses," International Economic Journal, pp. 1-14. Dinopoulos, E. and M. Kreinin. 1988. 'Effects of the U.S.-Japan Auto VER on European Prices and U.S. Welfare," Review of Economics and Statistics, pp. 484-91. Feenstra, R. 1985. 'Automobile Prices and Protection: The U.S.-Japan Trade Restraint," Journal of Policy Modeliing, pp. 49-68. Goldstein, M. and M. Khan. 1985. Ir.come and Price Effects in Foreign Trade," in Handbook of International Economies, vol. 2, R. Jones and P. Kenen, eds., North-Holland, pp. 1041-1050. Hamilton, C. 1989. 'The Rise and Fall of Footwear Protectionism,' Weltwirtschaftliches Archiv (forthcoming). Hickman, B.G. and L.J. Lau. 1973. 'Elasticities of Substitution and Export Demands in a World Trade Model." European Economic Review, vol. 4, pp. 347-380. Hufbauer, G.C., D.T. Berliner, and K.A. Elliot. 1986. Trade Protection in the United States: 31 Case Studies. Institute for International Economics, Washington, D.C. 27 Melo, J. de and L.A. Winters. 1989a. 'Price and Quality Effects of VERs Revisiteds Case Study of Korean Footwear Exports." PPR Discussion Paper No. 216, World Bank. Melo, J. de and L.A. Winters. 1989b. "Do Exporters Gain from VERs?" (mimeo), World Bank. Neary, P. and K. Roberts. 1980. "The Theory of Household Behavior Under Rationing," European Economic Review, vol. 13, pp. 25-42. Nogues, J., A. Olechowski, and A. Winters. 1986. Extent of Non-tariff Barriers to Industrial Countries' Imports," The World Bank Economic Review, 1, 1, pp. 181-99. Parks, R.W. 1967. Efficient Estimation of a System of Regression Equations when Disturbances are Both Serially and Contemporaneously Correlated, Journal of the American Statistical Association, vol. 62, pp. 500-9. Tarr, D.G. 1987. "Effects of Restraining Steel Exports from the Republic of Korea and Other Countries to the United States and the European Economic Community," The World Bank Economic Review, 1, pp. 397-418 Trella, I. and J. Whalley. 1988. "Do Developing Countries Lose from the HFA?" NBER Working Paper No. 2618. Winters, L.A. and P.A. Brenton. 1988. "Non-Tariff Barriers to International Trade: UK Restrictions on Imports of Leather Footwear from Eastern Europe," mimeo, University of College of North Wales. Yoffie, D. 1983. Power and Protectionism. New York: Columbia University Press. 28 Appendix A: This appendix gives a more detailed account of the econometric model of export allocation and its estimation than the text. We assume that exporters are price-takers and that they seek to maximize their revenues subject to a CET transformation function relating the quantities of each type of footwear export to an overall index of output (input). Their objective is (A.1) max £ pi Xi subject to f EaiX7 1 X Xi i i where Xi is exports to market i, at price pi, X is the index of aggregate output, and 7 > 1. Standard manipulations (cf Armington, 1969) produce supply functions for the individual markets (A.2) Xi = aiP (Pi/p ) where p* is the dual CET price index of X given by: (A.3) p = [ E aipi l | P and 29 is the (negative of the) elasticity of transformation between exports for any pair of markets; p > 0. Further manipulation (cf Hickman and Lau, 1973) transforms (A.2) into the more convenient form: Xi - aippi | ai PpP | l or (A.4) asi a (Pp)P + U where X _ £ Xj, is a simple aggregation of exports, si is the share of i in the volume of exports. - i E a[ pp 11 is a fixed weight price index, ai aiS and ui is a stochastic component added at this stage for estima- tion purposes. To facilitate the treatment of simultaneity and errors in variables (A.4) is linearized about a base period. We used 1984 quarter II as base because it lay well outside the period of possible rationing, and yet was relatively central to our sample of unrationed observations. Subsequent tests suggested that the choice of base period affects the results slightly, but not sufficiently to disturb the qualitative conclusions in the text. Setting prices to unity in the base period, introducing a time-trend with value zero in the base, and adding seasonal factors and dynamics, the linearization gives 30 (A.5) Yit P ai(pit-pt) + 7it + E 6ilDl + \l yit-l 4yit-4 it Yit Sit- a: is the deviation of i's share from its base value, 0 aif Pt -E Pit is a based-weighted price index, t is a time-trend incremented by one per quarter. E6 ilD1 are seasonal effects for quarter 1, 1 - 1,3,4 where the 1 dummy for quarter two has been suppressed because the base period is a second quarter. and )., )4 represent dynamic effects oni the share of market i, felt through lags of itself. Adding up requires the E aj = 1 and that E 6jl - E 7j - E ujt -0 all 1 and t. The first condition is satisfied automatically and the latter is handled by dropping the equation for unconstrained-EC. Normally, the final estimates are invariant with respect to the equation dropped, but with the methods required by the errors in variables this is no longer so. However, in practice the choice made very little difference. Adding-up also requires that, unless the errors are characterized by full vector autoregression, the dynamic structure must be common to all commodities. The use of lagged dependent variables may be justified on several grounds -- e.g. partial adjustment of price expectations, as in Hickman and Lau, or habit formation. For systems of sum-constrained equations it represents by far the most :,onvenient approach to dynamic generalization. The choice of lags 1 and 4 to capture the dynamics was made a priori on the basis of previous experience with quarterly data sets. 31 Equation (A.5) may be stacked over i and written in matrix form: Yi la(Pl-p) t 0 D1 0 D3 0 D4 0 Ly1 L4y1 p ut (A.6) . 72 + P2P t 0 D 0 D 0 D4 Ly2 L4y2 62 u2 613 523 614 624 where L is the lag opeastor and all the Roman letters denote (nxl) vectors, where n is the number of observations. Ignoring the errors in variables (A.6) may be simply estimated allowing for the autocorrelation and cross equation correlations. Following Parks (1967), we first estimate (A.5) for each commodity separately, and calculate a single first-order autocorrelation coefficient. (The serial correlation adjustment factor must be common to all equations if the system is to add-up). Transforming the data appropriately, we then re-estimate by commodity to calculate E(uit ujt), where the ui are the errors from the transformed equations. Finally, using these variances and covariances, we transform the data again to estimate (A.6) by GLS. To allow for the simultaneity and the errors in variables we use instrumental variable estimation. Instruments were drawn from both the importing countries (industrial production, the wholesale price index for 32 manufactures, and the exchange rate via-&-via the dollar) in order to reflect demand factors, and from Korea (the unit value of manufactured exports, the index of industrial production and the dollar exchange rate) to reflect broad supply-side phenomena. Whenever Ly and L4y are included in the equation the instrumental variables are also included in the correspondingly lagged form. Finally, the genuinely exogenous variables in (A.6) -- i.e. Di and t -- are also included in the set of instruments. The estimation method is based on Aigner, Hsiao, Kapteyn and Wansbeek (1984). We assume that there exists a true relationship equivalent to equation (A.6), but without errors in variables, and which may be written in obvious notation as: (A.7) y = H p + u ; that the relationship between the true (2) and the observed (X) independent data is (A.8) X- + V; and that there exists a set of relationships between the k true independent variables and the 1 indicator (instrumental) variables (Z). (A.9) Z = _ r + A . The error terms V and A are assumed to be independently normally distri- buted with zero means and also to be independent of -. The covariances of the rows of V and A (vt and 6t) are given by D and O respectively and the 33 variance of u by o2. The true independent variables are assumed to have an expected scaled cross-product matrix, K, K - Em21 ='H, where m - 2n is the number of rows in the matrices y,X,Z, H. V and A. Following Aigner et al. we can write the various covariance matrices Elj - Em-lI'J. I,J X, Y. z as (A.lOa) E - or2 + P (A.lOb) £ F (A.lOc) E y r Kp (A.lOd) E * K + R zz (A.lOe) E = rK (A.lOf) Z - rKr' + B Equations (A.lOc) and (A.lOe) yield E Zy Ezxp from which, multiplying both sides by Eix ZZ, and substituting sample va- lues SIJ for population values Elj we obtain (A.ll) p - ( S - s 1 zz s Zy W (X'Z (Z'Z) Z'X)-1 X'Z (Z'Z)-1 Z'y P is multivariately normally distributed with asymptotic variance 34 (A.12) var (p) - (a2+ (six S- s 1 zz 5zx which is the minimum variance bound that can be derived from (A.12) by li- near methods. We approximate (A.12) below by substituting p for p and using (A.10) to express the first bracket in terms of observables. System (A.10) presumes that the errors are i.i.d., but in our case we need to allow for the prer-nce of autocorrelation and the fact that E (ult u2t) # 0 where ul and u2 are svb-vectors of u zeferring to the first and second equations. Zn fact, however, these modifications make virtually no difference to the estimator. Taking the latter first, partitioning all variables in (A.7) to (A.9) conformably with ul and u2, versions of (A.10) may be derived for all combinations of yi, Xi and Zi, i - 1.2. If the only change in assumption is that E(ui uj) = ij. i $ j, only (A.lOa) is changed; it becomes (A.lOa') Eyiyj + 'K In all other equations the partitioned covariances are the same as the un- partitioned ones in (A.10). This means that the same instrumental estima- tion method may be applied to a set of first stage estimators to derive the aij, which are then used to transform all the observable data into the form assumed in the main stage just described. Provided that the estimates of 0ij are consistent, the asymptotic properties of the final estimates are unchanged. A similar approach is taken to the autocorrelation. The variance estimate (A.12) may be used to conduct statistical inference on the coefficients. The validity of a set of linear constraints Qp = r may be explored by means of the test statistic 35 A A ¶~~~~~~ A (Qp -r)' t Q Var (P) Q' ], ( X - r) which is distributed X2under the null hypothesis, see Amemiya (1985). q The data were collected and prepared by Taeho Bark aM Paul Brenton, to whom we are most grateful. They are fully described in the Appendix of de Helo and Winters (1989a). In terms of the final classifications used in table 2 of that source, leather footwear comprises headings 6402.1000-6402.4900. 36 Table Al: THE KOREAN FOOTWEAR SECTOR. 1974-83 Footwear Footwear As percent of total manufacturing Employment a/ Output b/ Wages c/ Employment a/ Output d/ Wages 1974 6600 33 303 0.518 85.3 85.3 1975 11000 53 364 0.788 114.5 77.9 1976 14200 74 493 0.84 121.3 82.6 1977 19800 108 657 1.046 147.1 85.1 1978 26000 159 846 1.249 174.9 79.3 1979 22000 107 1136 1.055 105 81.1 1980 22700 100 1366 1.127 100 79.2 1981 26000 111 1538 1.293 97.9 74.8 1982 36500 113 1809 1.77 94.6 78.4 1983 40500 122 2025 1.86 87.8 80.2 al In thousands. h/ Index 1980 - 100. c, (thousands of won)/year d/ Ratio of index numbers (1980 100). 37 Appendix B 1/ General Model and Welfare Calculations Bl General Model Consider the general case of firms in perfect competition in which the allocation and input decisions are made jointly. In this case weak separability is not imposed so that allocation and production decisions must be considered together. Technology is represented by a one-input, two-output production function. Let variable factor requirements, Z, destined to the restricted (XA) and unrestricted (XB) markets be given by: (Bl) Z - G(XA, XB) where Z is the quantity used of the composite factor Gi is 82/Xi > 0 G is homothetic and homogenous of degree r < 1 Under the assumption of profit maximization, de Melo and Winters (1989b) show that the imposition of a VER on sales to A (XA c XA), leads to the following expressions for output (B2) and for national welfare (B3). GB ~~G (B2) 1 dZ [XBeB BB GA BA H (B2) GA di, G -HB A dXA tXBeB BBB Z z 11 This appendix draws on de Melo and Winters (1989b). 38 (B3) W |[1 -1 1 - e ] H GA d'A cA B eB cN where CA, eB, eN < 0 are respectively the elasticities of demand for A and B and the elasticity of demand for the variable factor Z with respect to the wage in other sectors using Z, and eZ > 0 is the elasticity of supply of 2. From (B2), it is clear that a VER in A will most likely lead the industry to contract if one assumes increasing marginal costs, i.e. Gii > 0, and if one recognizes the constraints imposed by the second-order conditions for profit maximi;.Ition. On.y very strong (and implausible) interactions between A and B leading to a large positive value for GAB would lead the industry to expand. Hence, a VER is likely to lead the industry to contract. From (B3), the change in national welfare (where national welfare is the sum of industry profits and payments to the factors of production) is determined by an allocation component which measures whether switching sales from A to B raises revenue, and a size component which measures whether switching factors across sectors is beneficial. B2. Welfare Calculations The welfare calculations in section 4 comes from a numerical application of the model presented in section 2 with: constant elasticity of demand curves (equations B4 and B5); a CET function to allocate sales between the restricted and unrestricted markets A and B (equation B6); a constant elasticity of s.Dply function for the factor, Z (equation Bll). An unrestricted equilibrium is described by the following set of equations: 39 (B4) X -A P A A > ° A A AA (B5) XB AB B eB > 0 (36) X' AC ("AA XZ + GBXB) 7 P 1/7-1; 7 > 0 (B7) PA - AC 0IPaA(XA/ P)1 /P (B8) B = AC P 4) (XB/R) (B9) X x (B10) xS (Bll) Z -A PZ e > _ * (B12) P_ -A z S where Ai, i e A, B, C, Z, S are normalizing constants determined by calibration, i.e. constants calculated so that the set of equations describing the model is satisfied for initially. set of prices and quantities. In the free trade equilibrium, industry profits, w, are zero as sales revenue equal payments to Z, PZZ. With the VER, XA is fixed at XA < XA and the first order condition for the allocation to the restricted market (B8) is dropped. As explained in section 2, as a result of the VER, j < 9 (unless CZ = 6). The welfare measure is: (B13) aw - 'W - W - (Ar + APZL) / PZZ 40 where L is a scalar indicating the size of the industry in the market for Z. The calculations in section 4 are obtained from solving the model represented by equations (B4)-(B12) for an unrestricted equilibrium and for a restricted equilibrium with XA - 0.9 XA. Where elasticities are varied, the Ai paramaters are recalibrated so as to start from the same initial unrestricted values for prices and quantities. PRE Working Papar Sarles Contact iwa Aulhor DM for paper WPS333 An Option-Pricing Approach to StiJn Claessens January 1990 S. King-Watson Secondary Market Debt (Applied Sweder van Wijnbergen 31047 to Mexico) WPS334 An Econometric Method for Jaber Ehdaie February 1990 A Bhalla Estimating the Tax Elasticity and the 37699 Impact on Revenues of Discretionary Tax Measures (Applied to Malawi and Mauritius) WPS335 Macroeconomic Adjustment and Ramon E. Lopez December 1989 L. Riveros the Labor Market in Four Latin Luis A. Riveros 37465 American Countries WPS336 Intermediate Inputs, Tariffs, and Arvind Panagarlya Duty Drawbacks on Expons WPS337 Projecting Mortality for All Rodolfo A. Bulatao December 1989 S. Ainsworth Countries Eduard Bos 31091 Patience W. Stephens My T. Vu WPS338 Bank Lending for Divestiture: A Sunita Kikerl Review of Experience WPS339 Private Investment and Macro- Luis Serven December 1989 E. Khine economic Adjustment: An Andres Solimano 37469 Overview WPS340 Prudential Regulation and Banking Vincent P. Polizano January 1990 WDR Office Supervision: Building an Institutional 31393 Framework for Banks WPS341 Cost-of-Living Differences between Martin Ravallion December 1989 C. Spooner Urban and Rural Areas of Indonesia Dominique van de Walle 30464 WPS342 Human Capital and Endogenous Patricio Arrau December 1989 S. King-Watson Growth in a Large Scale Life-Cycle 31047 Model WPS343 Policy Determinants of Growth: William R. Easterly December 1989 R. Luz Survey of Theory and Evidence Deborah L Wetzel 39059 WPS344 Policy Distortions, Size of Wiliam Easterly December 1989 R. Luz Government, and Growth 39059 WPS345 Private Transfers and Public Policy Donald Cox December 1989 A. Bhalla in Developing Countries: Emmanuel Jimenez 37699 A Case Study for Peru PRE Workino Paper Series Contact Ia Author ftfor palar WPS346 India's Growing Conflict Hans Jurgen Peters January 1990 T. Lim between Trade and Transport: 31078 Issues and Options WPS347 Housing Finance in Developing Robert M. Buckley December 1989 WDR Office Countries: A Trr nsaction Cost Approach 31393 WPS348 Recent Trends and Prospects Takamasa Akiyama December 1989 D. Gustafson for Agricultural Commodity Exports Donald F. Larson 33714 in Sub-Saharan Afrkca WPS349 How Indonesia's Monetary Policy Sadiq Ahmed February 1990 J. Rompas Affects Key Variables Basant K. Kapur 73723 WPS350 Legal Process and Economic Cheryl W. Gray December 1989 B. Dhomun Development: A Case Study of 33765 Indonesia WPS351 The Savings and Loan Problem in Stanley C. Silverberg March 1990 WDR Office the United States 31393 WPS352 Voluntary Export Restraints and Jaime de Melo April 1990 M. Ameal Resource Allocation in Exporting L Alan Winters 37947 Countries WPS353 How Should Tariffs be Structured? Arvind Panagariya February 1990 K. Cabana 37946 WPS351 How Commodity Prices Respond Dhaneshwar Ghura February 1990 S. Lipscomb to Macroeconomic News 33718 WPS355 The Evolution of Credit Terms: An Sole Ozler February 1990 S. King-Watson Empirical Study of Commercial Bank 31047 Lending to Developing Countries WPS356 A Framework for Analyzing Financial Ian G. Heggie February 1990 W. Wrght Performance of the Transport Michael Quick 33744 Sector WPS357 Application of Flexible Functional Ying Qian February 1990 S. Lipscomb Forms to Substitutability among 33718 Metals in U.S. Industries WPS358 The Long-Term Behavior of Pier Giorgio Ardeni March 1990 A. Kitson-Walters Commodity Prices Brian Wright 33712 WPS359 A Survey of Recent Estimates of Tae H. Oum January 1990 W. Wright Price Elasticities of Demand for W. G. Waters, II 33744 Transport Jong Say Yong