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.
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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
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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
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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.
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