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Identifying price linkages: a review of theliterature and an application to the world marketof cottonJohn Baffes & Mohamed Ihsan AjwadPublished online: 04 Oct 2010.

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Identifying price linkages: a review of the

literature and an application to the world

market of cotton

JOHN BAFFES and MOHAMED IHSAN AJWAD

The World Bank, 1818 H Street, NW Washington DC, 20433, USA.E-mail: [email protected]

This paper reviews the literature of price linkages and examines the degree to whichcotton prices are linked; it also tests whether such linkages have improved over thelast decade. It concludes that the degree of linkage has improved over the last decadewhile the main source of this improvement appears to be a result of short-run pricetransmission and to a lesser extent long-run co-movement.

I . INTRODUCTION

In the absence of impediments, the comparative advantageargument of trade theory dictates that resources will be

allocated in an e� cient manner. In turn, factor and prod-

uct prices in diVerent locations will be equalized ± subjectto transfer costs. Under certain conditions, the existence of

strong price linkages, therefore, may be viewed as a necess-

ary requirement for e� cient allocation of resources andhence maximum welfare (Samuelson, 1952; Takayama

and Judge, 1964). This paper focuses on the degree of

price linkages of the world market of cotton.The issue of price linkages in product markets both at

local and international levels has been studied in the litera-

ture extensively either under the notion of the law of oneprice (e.g. Protopapadakis and Stoll, 1983, 1986; Ardeni,

1989; BaVes, 1991) or under the notion of market integra-

tion (e.g. Ravallion, 1986; Sexton et al., 1991; Gardner andBrooks, 1994; Baulch, 1997a). Moreover, re¯ecting on the

market liberalization and structural adjustment eVorts

undertaken by a number of developing countries in recentyears, the degree to which markets are integrated has been

used quite often as a yardstick in assessing the success of

policy reforms (e.g. Alexander and Wyeth, 1994; Golettiand Babu, 1994; Gordon, 1994; Dercon, 1995).

As many authors have cautioned, however, price conver-

gence does not necessarily imply e� cient allocation ofresources unless the setting in which trade takes place is

competitive (e.g. Faminow and Benson, 1990; Baulch,

1997b). For example, consider the extreme case of two

duopolists who agree to charge the same price in two seg-mented markets. While convergence in prices (whenever

changes occur) would take place instantaneously , the

oligopolistic setting of the market may not necessarilyallocate resources in the most e� cient manner. The same

argument may be advanced for a number of developing

countries where parastatal s assign panterritorial and pan-seasonal prices on certain commodities. In such cases the

law of one price holds by de®nition without necessarilyimplying that resources are allocated e� ciently.

The present paper examines the strength of price link-

ages in the world market of cotton. In pursuing this objec-tive, the paper contributes to the literature of price linkages

in two respects. On the theoretical side, it introduces a

measure of price linkage and also identi®es its source (i.e.short-run price transmission versus long-run comovement.)

On the empirical side, it applies this measure to the world

market of cotton for two diVerent time periods, therebyexamining whether improvements in price linkages have

taken place.

The remainder of the paper proceeds as follows. In thenext section the model along with the explicit measure of

the degree of market linkage is outlined. Moreover, in dis-

cussing the model, an extensive literature review on thesubject of price linkages is undertaken and show, that

most models are in fact restricted versions of the ErrorCorrection Model (ECM) speci®cation introduced by

Hendry et al. (1983). Sections III and IV discuss estimation

Applied Economics ISSN 0003±6846 print/ISSN 1466±4283 online # 2001 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/0003684001002378 8

Applied Economics, 2001, 33, 1927±1941

1927

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issues and the results respectively. The last section con-cludes by discussing some avenues for further researchand also addressing some policy implications.

II . DETECTING PRICE LINKAGES

Earlier studies examining the relationship between priceseither have looked at correlation coe� cients (e.g. Lele,1967; Southworth et al., 1979; Timmer et al., 1983;Stigler and Sherwin, 1985) or have used the followingtype of regression (e.g. Isard, 1977; Mundlak and Larson,1992; Gardner and Brooks, 1994):1

p1t ˆ · ‡ 1p2

t ‡ "t …1†

where p1t and p2

t denote prices from two origins of thecommodity under consideration, · and 1 are parametersto be estimated while "t denotes an i.i.d.(0, ¼2) term. Thehypothesis that the slope equals unity and the interceptequals zero can be tested; formally, H0: · + 1 = 1 =1. Under H0 the deterministic part of Equation 1 becomesp1

t ˆ p2t , in turn implying that the price diVerential, p1

t ¡ p2t ,

is an i.i.d.(0, ¼2) term. Often, prices are expressed in loga-rithms in which case the intercept would represent a pro-portionality coe� cient.

Estimating Equation 1 and testing H0 presents twoshortcomings. First, the presence of nonstationarity , mayinvalidate standard econometric tests and thus give mis-leading results regarding the degree to which price signalsare being transmitted between markets. Second, in primarycommodity markets with characteristics such as diVerencesin quality, high transfer costs etc., it is unlikely that the twoprices will only diVer by an i.i.d.(0, ¼2) term as H0 ofEquation 1 dictates. Therefore, H0 would be rejected with-out necessarily ruling out a high degree of price linkage.Consequently, it is necessary to employ a more generalmodel that imposes no a priori requirements on the statio-narity properties of the variables in question and alsoallows for some speci®cation ¯exibility.

With respect to the nonstationarity problem, one canexamine the order of integration of the error term inEquation 1 and make inferences regarding the validity ofthe model. Under nonstationary prices, the existence of astationary error term implies comovement between the twoprices. However, if 1 6ˆ 1, the uniqueness of the cointegra-

tion parameter in the bivariate case implies that the corre-sponding price diVerential would be growing and suchgrowth would not be accounted for, although prices maymove in a seemingly synchronous manner. Hence, statio-narity of the error term of Equation 1 while establishingco-movement, should not be considered as a testable formequivalent to that of the H0 of Equation 1. Moreover, anumber of authors have warned against interpreting non-unity slope coe� cient as a sign of market integration (e.g.Barrett, 1996).

To account for the non-unity slope coe� cient one canrestrict the parameters of Equation 1 according to H0, inwhich case the problem is equivalent to testing for a unitroot in the following univariate process (Engle and Yoo,1987):

…p1t ¡ p2

t † ¹ I…0† …2†

If the price diVerential as de®ned in Equation 2 is station-ary, then one can conclude that price signals are trans-mitted from one market to another, in the long run. Theassumption (or ®nding) that the cointegration parameter isunity is very crucial, as it ensures that there is no othernonstationary component entering the system. As Meese(1986) and West (1987) observe, the absence of cointegra-tion (with unity slope coe� cient in our setting) can beattributed to omitted nonstationary variables, in turnimplying that an additional component would have to beincluded in Equation 2 in order to account for the varia-bility of the price diVerential.2

From the preceding discussion, it is evident that cointe-gration tests are not very informative as they only makeinferences about the existence of the moments of the distri-bution of (p1

t ¡p2t ) and not about certain restrictions that

may be required by economic theory. Therefore, Equation2 cannot serve as a substitute for the H0 of Equation 1; itcan only serve as an intermediate step in establishing itsvalidity.

With respect to the restrictive nature of Equation 1,one can circumvent it by introducing a more generalautoregressive structure. Following Hendry et al. (1984)by appending one lag to Equation 1, gives:

p1t ˆ · ‡ 1p2

t ‡ 2p2t¡1 ‡ 3p1

t¡1 ‡ ut …3†

where ut is i.i.d.(0, ¼2) and j 3j < 1. Hendry et al. (1984)discuss a number of testable hypotheses resulting from

1928 J. BaVes and M. I. Ajwad

1 See Harris (1979) for a comprehensive (and critical) review of the literature on market integration studies undertaken in the 1960s and1970s.2 If the cointegration parameter is unity, it is immaterial for all relevant aspects of the analysis whether Equation 1 or 2 is employed aslong as the sample is su� ciently large. This is the case because as the sample size increases, regression 1 should yield 1 equal to unity.However, in small samples this may not be necessarily the case. For example, Ardeni (1989), using Equation 1 in logarithms for a numberof internationally traded primary commodities, found that the corresponding error term was not stationary, thus rejecting the law of oneprice. BaVes (1991), on the other hand, by using the same data set found that in the majority of cases the price diVerential was stationary,hence providing supportive evidence for the law of one price as a long run relationship. Zanias (1993) examined spatial marketintegration in European Community agricultural product markets. Two important articles dealing with expectations and time issuein the law of one price are Goodwin et al. (1990a, 1990b).

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corresponding restrictions on the parameter space ofEquation 3. The most important one is the long-run

proportionality or homogeneity hypothesis, the validityof which ensures that price movements in one market willeventually be transmitted to the prices in the other market.

Such a hypothesis can be tested by the restriction §i i ˆ 1.Under long-run proportionality, Equation 3 can be re-

parameterized as follows:

…p1t ¡ p1

t¡1† ˆ · ‡ …1 ¡ 3†…p2t¡1 ¡ p1

t¡1† ‡ 1…p2t ¡ p2

t¡1† ‡ ut

…4†

Relationship to Equation 4 belongs to the family of error-correction models (ECM). Because of the equivalence of

the existence of cointegration and ECM, stationarity of theprice diVerential Equation 2 implies Equation 4 and vice-

versa (see Appendix A for a proof). On the other hand, therestriction j 3j < 1 implies that 0 < 1 ¡ 3 < 2. The sign of

3, or alternatively whether (1 ¡ 3) falls between zero andone or between one and two indicates the type of conver-gence (monotonic versus oscillatory).

The main feature of Equation 4 is the economic in-terpretation of its parameters: 1 indicates how much of

a given price change of the commodity in location 2 will betransmitted to location 1 within the ®rst period (referred toas initial adjustment, short-run eVect, or contemporaneous

eVect); (1 ¡ 3) indicates how much of the price diVerencebetween the two prices is eliminated in each subsequent

period (referred to as error-correction, speed of adjust-ment, or feedback eVect). The coe� cient of the short-runeVect can, in theory, take any value. The adjustment coe� -

cient, however, is restricted between zero and two. Thecloser to unity is (1 ¡ 3), the higher the speed at which

convergence will take place. Symmetric with respect tounity values of (1 ¡ 3) (e.g. 0.75 and 1.25) indicate that

the adjustment speed will be the same but the adjustmentpath will diVer (monotonic in the former and oscillatory inthe latter case).

It is worth reemphasizing here that (1 ¡ 3) diVerentfrom zero is a necessary and su� cient condition for long-

run convergence. However, signi®cantly diVerent from zero

1 is neither a necessary nor a su� cient condition for long-run price convergence; even if 1 = 1 (i.e. perfect short-run

adjustment) the series may still drift apart in the long run.3

An alternative testable hypothesis emerges when 1 = 0.

Then Equation 4 becomes:

…p1t ¡ p1

t¡1† ˆ · ‡ …1 ¡ 3†…p2t¡1 ¡ p1

t¡1† ‡ ut …5†

The interpretation of Equation 5 is that while the contem-poraneous eVect is zero, prices converge in the long-runwith speed (1 ¡ 3).

On the other hand, letting 1 = 1, Equation 4 is re-parameterized as follows:

…p2t ¡ p1

t † ˆ ¡· ‡ 3…p2t¡1 ¡ p1

t¡1† ‡ ut …6†

Equation 6 implies that while price changes in one marketare fully transmitted in the other market within the sameperiod, long-run price convergence depends on the size of

3 (Equations 5 and 6 correspond to cases (i) and (g) ofTable 2.2 in Hendry et al.) A number of studies examiningthe linkages between futures and cash prices for commod-ity and asset markets have employed Equations 5 and 6(e.g. Garbade and Silber, 1983; Schroeder and Goodwin,1991; Wang and Yau, 1994; Fortenbery and Zapata, 1997).

Alternatively, setting 3 = 1 in Equation 4, gives:

…p1t ¡ p1

t¡1† ˆ · ‡ 1…p2t ¡ p2

t¡1† ‡ ut …7†

Equation 7 (case (c) of Table 2.1 in Hendry et al.) oftentermed the ®rst diVerence approach, has also been used inthe literature extensively (e.g. Richardson, 1978; Tomek,1980; Leavitt et al., 1983; Hudson et al., 1996). First diVer-ences along with detrending have been traditionally themost widely used ®lters in time series analysis. It shouldbe noted here that if (p2

t ¡ p1t ) and (p2

t ¡ p2t¡1) are orthogo-

nal, estimating short-run and dynamic adjustment eVects(i.e. Equation 5 and 7) separately will yield the same par-ameter estimates as estimating them jointly throughEquation 4.4

Finally, by restricting 2 = 3 = 0, Equation 3 reducesto Equation 1, which is one of the most commonly usedmodels in the literature. To these models one should alsoadd Granger-causality tests since a signi®cantly diVerentfrom zero error-correction term implies Granger-causalitywith feedback from p2

t to p1t . Petzel and Monke (1979,

1980) used Granger-causality for the international ricemarket.

It is clear that a wide variety of `law of one price’, marketintegration, or market e� ciency models are special cases ofEquation 3, possibly with a diVerent lag structure. Baulch(1997b), however, in examining the same class of models,distinguishes among the following four speci®cations: Thelevel/cointegration version of the law of one price;Speci®cation (1), the ®rst diVerence version of the law of

Identifying price linkages 1929

3 Although the fact that the short-run eVect is 1 while there may be no long-run convergence seems counter-intuitive it should notbe surprising. Consider the following thought experiment: two series are generated as p2

t ˆ …¡1†trend…0:75† ‡ "t and p1t ˆ p1

t¡1‡…¡1†trend…1:5† ‡ 0:5 ‡ "t, where trend denotes time (1; 2; 3; . . .) and "t is a white noise. p2

t oscillates between §0:75 (1.5 unit swing) andp1

t rises by 2 in one period and falls by 1 in the next period. On average, p1t also demonstrates a swing of 1.5. Estimation of Equation 3

gives a short-run eVect of one. However, it is clear that the two series are diverging over time. On the other hand, if p1t ˆ 1 ‡ "t, the short-

run adjustment is eVectively zero, i.e. changes in p2t are completely innocuous to changes in p1

t while the error-correction coe� cient is one.4 On this issue, Kennedy (1992) notes that (p2

t ¡ p1t ) and (p2

t ¡ p2t¡1) are `. . . closer of being orthogonal than the variables in the original

relationship (i.e. Equation 3)’ (p. 264).

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one price; Speci®cation (7), the autoregressive distributedlag/error-correction; Speci®cations (3) and (4), possiblywith a higher lag structure; and Granger-causality patterns(inferred from speci®cations 3 and 4).

Estimating Equations 5, 6, 7, or even Equation 4 withoutensuring that the appropriate cointegration or orthogonal-ity restrictions hold may bias coe� cients and hence givemisleading results regarding the underlying economic be-haviour. For example, 1 = 1 in Equation 7 may erro-neously lead one to conclude that there exists strong linksbetween the two prices where in fact, the prices may noteven converge in the long run. On the other hand,Equation 5 imposes the restriction that no adjustment inthe short-run takes place, which may not necessarily be thecase.

The model outlined above suggests that, given long-runproportionality, the choice of Equation 3 or 4 to recovershort- and long-run dynamic price behaviour is a matter ofstationarity properties. If prices are stationary, Equation 3would be the preferred structure and long-run proportion-ality could be tested by restricting the slope parameters tosum to unity. Under non-stationarity , Equation 4 is thepreferred structure and long-run proportionality can betested by examining the stationarity properties of theprice diVerential (Engle and Yoo, 1987) or testing whether(1¡ 3) is diVerent from zero (Phillips and Loretan, 1991).Then, with appropriate tests one can determine whetherany of the underlying restrictions implied by Equations 5,6, or 7 can be in fact validated by the data.

The next task is to transform the information containedin the parameter space so that a succinct interpretation ofboth short-run and feedback eVects (and hence price link-age) can be given. In other words: How long does it take forthe price of cotton in origin 1 to adjust to a given pricechange in origin 2?

Let n be the period by which k per cent of the cumulativeadjustment has taken place. In the current period, n ˆ 0; ktakes the value of 1 [= 1¡(1¡ 1)], which is the short-runimpact of (p2

t ¡ p2t¡1) on (p1

t ¡ p2t¡1). When, n ˆ 1; k takes

the value of 1+(1¡ 1) 3, which is the impact of the pre-vious period, 1, plus the feedback eVect, (1¡ 1) 3 [=1¡(1¡ 1)(1¡ 3)]. For n ˆ 2; k takes the value of the pre-vious period’s adjustment, 1+(1¡ 1) 3 plus 3(1¡ 1

¡(1¡ 1) 3) [=1¡(1¡ 1)(1¡2 3+ 32)] or 1¡(1¡ 1) 3

2.Hence, the cumulative adjustment at period n is given by:

k ˆ 1 ¡ …1 ¡ 1† n3 …8†

Alternatively, solving for n in Equation 8 gives the numberof periods required to achieve a certain level of cumulativeadjustment, i.e. n ˆ [log(1¡k) ¡log(1¡ 1)]/log 3.

Although most models in the literature of price linkageshave based the discussion on estimated model parameters

and F-tests, there have been a number of exceptions, which

have quanti®ed the linkage either on a discrete or contin-uous basis. Ravallion (1986), for example, using an auto-

regressive distributed lag model and appropriate parameter

restrictions made a distinction among market segmenta-

tion, long-run market integration, and short-run marketintegration and applied it to the rice market in

Bangladesh. A number of researchers have applied

Ravallion’s formulation since then (e.g. Palaskas and

Harriss (1993) applied it to the food markets in WestBengal while Gordon (1994) applied it to grain markets

in Tanzania).

Timmer (1987) introduced a measure of price linkage

based on the unrestricted version of Equation 3 and

applied it to the corn market of Indonesia. Timmer’sIndex of Market Connection, converted to the parameters

of Equation 4 is equal to 3/(1¡ 3). For values of 3 close

to unity, the index takes large values (at the limit approach-

ing in®nity), in turn indicating weak price linkage. If 3 =0 the index takes the value of zero, which corresponds to

error-correction coe� cient being equal to unity, conse-

quently indicating strong price linkage ± for negative values

of 3 the measure falls within the interval (¡0.5, 0).Heytens (1986) and Alderman (1992) used Timmer’s meas-

ure of market connection to examine the performance of

food markets in Nigeria and Ghana, respectively.

Delgado (1986) developed a variance components meth-

odology by making a distinction among diVerent levels ofmarket integration between harvest and post-harvest peri-

ods and applied it to food markets in Northern Nigeria.

Goodwin and Schroeder (1991) in examining spatial price

linkages in US regional cattle markets used the magni-tudes of cointegration statistics of bivariate regressions as

measures of price linkages. Lutz et al. (1995) introduced a

measure of market integration by calculating short- and

intermediate-run impact multipliers and then a measureof adjustment; they applied the model to wholesale and

retail food markets in Benin. More recently, Badiane and

Shively (1998) investigated the roles of spatial integration

and transport costs in explaining price changes in Ghana

by using Timmer’s index of market connection.

III . STATIONARITY TESTS

Two samples, one covering the period August 1985±

December 1987 (122 weekly observations) and a second

covering the period August 1995±January 1997 (73 weekly

observations) were constructed for the USA, Greece,Central Asia, and W. Africa.5


5 The four countries/regions considered in the sample account for 65% of world exports and 85% of the northern hemisphere’s exports.Furthermore, because all four prices represent cotton from the northern hemisphere, no seasonal adjustment due to diVerent harvestingcycles is needed.

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To determine the order of integration the augmented

Dickey-Fuller (ADF) and the Phillips-Perron (PP) pro-

cedures were utilized. Because the decision on whether touse Equation 3 or 4 ultimately depended upon the statio-

narity properties of the prices, the authors supplemented

the unit root tests with a variance-ratio test (Cochrane,

1988). The ADF was based on the following regression:

…pt ¡ pt¡1† ˆ · ‡ pt¡1 ‡ lags…pt ¡ pt¡1† ‡ "t, where pt

denotes the series under consideration (Dickey and

Fuller, 1981). A negative and signi®cantly diVerent fromzero value of indicates that pt is I(0). The PP test is

similar to the ADF; their diVerence lies on the treatment

of any nuisance serial correlation aside from that generated

by the hypothesized unit root (Phillips and Perron, 1988;

Phillips, 1989). To identify the presence of one unit rootH0: pt is not I(0) was tested against H1: pt is I(0). Trend

stationarity can be detected by appending a time trend inthe relevant regression. Finally, the signi®cance level of the

error-correction coe� cient itself, (1 ¡ 3), can serve as

cointegration test (Phillips and Loretan, 1991).

The variance ratio test is de®ned as (1/k)Var(pt ¡ pt¡k )/

Var(pt ¡ pt¡1), where k denotes the lag length. It exploitsthe fact that the variances of conditional forecasts explode

for nonstationary series and converge for stationary (or

trend stationary) series as the forecast horizon grows.

The idea behind Cochrane’s test goes as follows. If pt is arandom walk (i.e., pt = · + »pt¡1 + "t, where » = 1), the

variance of its k-diVerences grows linearly with k, i.e.

Var(pt¡pt¡k ) = k¼2" . If, on the other hand pt is stationary

or trend stationary, the variance of its k-diVerences will

eventually approach zero. As a consequence, in the former

case (1/k)Var(pt¡pt¡k) will remain constant at ¼"2 as k

grows ± possibly after an initial jump if » is greater thanone ± while in the latter case it will approach zero ± slowly

for values of » close to but less than one. Dividing by

Var(pt¡pt¡1) (which is independent of k) normalizes the

®rst period to unity.

Stationarity results for the ADF and PP tests for bothperiods are reported in the upper panel of Table 1. The

tests indicate that stationarity in levels is rejected in allcases. The middle panel of Table 1 reports results for

trend stationarity tests. Here the picture changes slightly

since the A Index, the USA and Greece show evidence of

trend stationarity.

Figures 1a±1e provide information regarding the unitroot structure in the form of the variance-ratio statistics.


Table 1. Stationarity tests

Period 1 Period 2

ADF PP ADF PP

Levels w/o trendA Index 71.24 70.70 71.18 70.84USA 71.40 71.10 71.38 71.53Greece 71.26 70.78 71.18 70.96W. Africa 71.33 70.72 71.11 70.67C. Asia 71.30 70.75 71.24 70.86

Levels w/trendA Index 72.42 72.03 73.51** 73.44*USA 71.83 71.55 74.80*** 74.84***Greece 72.55 72.27 72.87 73.08W. Africa 72.56 72.07 73.71** 73.58**C. Asia 72.80 72.35 72.38 72.59

Price DiVerentialsA Index ± USA 71.71 71.40 73.11** 73.26**A Index ± Greece 72.94** 72.82* 73.58*** 73.16**A Index ± W. Africa 73.70*** 73.77*** 72.48 72.41A Index ± C. Asia 73.39** 73.53*** 72.97** 72.65*US ± Greece 71.87 71.71 72.81* 73.03**US ± W. Africa 71.74 71.46 73.42** 73.55***US ± C. Asia 71.68 71.28 73.31** 73.36**Greece ± W. Africa 73.02** 72.96** 72.49 72.35Greece ± C. Asia 72.85* 72.80* 72.26 72.40W. Africa ± C. Asia 73.87*** 73.82*** 73.00** 72.87*

Notes: One (*), two (**) and three (***) asterisks indicate signi®cance at the 10%, 5%, and 1%levels. Critical values are ¡2.58 (10%), ¡2.89 (5%), and ¡3.51 (1%) without trend and ¡3.15 (10%),¡3.45 (5%), and ¡4.04 (1%) with trend (Fuller, 1976). The Akaike Information Criterion was usedto determine the number of lags in both ADF and PP tests.Source: Estimated by the authors.

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1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 1 4 15

Pe riod 1 Perio d

(a) Index

1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5

Period 1 Pe rio d 2

(b) USA

1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5

Pe rio d 1 Period 2

(c) Greece

1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5

Pe rio d 1 Pe rio d 2

(d) W. Africa

1 .0 0

1 .5 0

2 .0 0

2 .5 0

3 .0 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5

Pe riod 1 Pe riod 2

(e) C. Asia

Fig. 1. Variance ratio tests for price levels.

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Undoubtedly, the pattern of all variance-ratios is explosivein both periods, therefore pointing to the fact that we aredealing with non-stationary price series.6 In what follows,we proceed under the assumption that prices are non-stationary.

The lower panel of Table 1 reports stationarity statisticsof the price diVerential, a measure of the degree of comove-ment between pairs of prices. Note that because the coin-tegration parameter is assumed rather than estimated, thesame critical values are used for both levels and price dif-ferentials ± if the parameter was to be estimated throughOLS, more `demanding’ critical values would have been used.

Consider ®rst the A index. When compared to the USAin period 1 no comovement appears to be in place, while ahigh degree of comovement is present in the second period,a result re¯ected in both tests. A very small improvement isdetected for A Index±Greece. The A Index±W. Africaprice diVerential, while stationary in period 1, it is non-stationary in period 2. The link between the A Index andthe remaining two prices, however, appears to be weakeningin period 2. In terms of variance-ratio statistics (depicted inFigures 2a and 2j), while for the A Index±USA case thepattern is explosive in both periods, it converges at a ratherslow rate for the remaining three cases, with no distinguish-able pattern between the two periods.

The degree of co-movement of prices increased substan-tially in Greece, W. Africa, and C. Asia when coupled withthe USA. In most cases, stationarity statistics more thandoubled and in all but one case they exceeded the 5%signi®cance level. However, the variance ratio statistics forUSA±W. Africa and USA±C. Asia, indicate non-stationaryprice diVerential in both periods (more so in the latterthan former case). Comparing Greece with W. Africa andC. Asia, the co-movement sharply deteriorates accordingto stationarity statistics but the diVerential is stationary inboth cases as the variance-ratio statistic indicates. Finally,for W. Africa±C. Asia, while the statistics become lower inabsolute value, they are still signi®cant in both periods.

To conclude, results from the lower panel of Table 1indicate that, excluding the A Index, price linkages in thecotton market improved relative to the USA but a deterio-ration was detected among some non-US markets.Although these results are robust with respect to both sta-

tionarity tests (PP and ADF), they are in contrast to whatwas expected. The variance-ratio statistics, however, indi-cate that while small changes may have taken placebetween the ®rst and second period, in no case did thestationarity properties change for both levels and diVeren-tials, as indicated by the ADF and PP statistics in a numberof cases. Therefore, the error-correction term is expected toyield more insights on the long-run convergence issue andespecially regarding the validity of the variance-ratio versusADF and PP stationarity tests.

IV. RESULTS

A Chow test was employed to determine whether the par-ameters of period 1 were signi®cantly diVerent from thoseof period 2. The À2 testing procedure proposed by Hansen(1982) and White (1980) was utilized to estimate thecovariance matrix consistently. Initially Equation 4 wasestimated with four lags, subsequently only the signi®cantones were kept. With the exception of four cases, the sig-ni®cance of the higher order lags was very low.7

To assess the overall performance of the model, thegoodness of ®t is ®rst examined (Table 2). Given thatEquation 4 can be re-parameterized in terms of currentand lagged price diVerentials as well as one of the two(also current and lagged) price diVerences (Campbell andShiller, 1987), one can view the R2 as a measure of basisrisk (i.e. the unpredictable movements in the basis) wherebasis is de®ned as the diVerence between the two pricesrather than its traditional de®nition as the diVerencebetween cash and futures price of the same commodity.Then, the lower the R2 the higher the basis risk and vice-versa. The R2 has been used in the literature extensively asa measure of basis risk (e.g. Lindahl, 1989; Faruqee et al.,1997).

With one exception, the R2 has improved considerably inall cases. On average, about 50% of the price variabilityfrom one origin was explained by the variability of anotherorigin’s price in period 1. In period 2 the explanatorypower of the model increased to 75%. Excluding the AIndex, the relative increase in the explanatory power ofthe model becomes even greater (from 40% to 71%).8


6 Hamilton (1994) emphasizes the di� culty in distinguishing truly non-stationary processes from processes that are stationary butpersistent. He also suggests comparing estimates obtained under alternative speci®cations and choose the one that performs betteraccording to several criteria, which is the avenue we pursue in the present case. In view of the trend stationarity evidence of the secondperiod, we also estimated the model in levels and log-levels (i.e. Equation 3 with a trend variable) by testing and subsequently imposinglong-run proportionality. In all cases, the model exhibited R2s close to unity and extremely high t-ratios. In no case did we ®ndstatistically signi®cant diVerences in the estimates of periods 1 and 2. Cochrane (1988) also points to the di� culties of parametrictests in distinguishing between true random walk models and trend stationary models with a small random walk component, whichappears to be the case in the period 2.7 The lag structure of the six cases (all in the ®rst period) was: Greece±USf2; 3g, W. Africa±USf0; 3g, C. Asia±USf0; 3g, A Index±USf0; 3g, W. Africa±Greecef1; 0g, and W. Africa±A Indexf0; 3g. For consistency, we retained the same lag structure in the secondperiod.8 Because the A Index may contain one of the prices under consideration it explains why when the A Index models are excluded, theaverage R2 declines in both periods.

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Thus, with the evidence at hand, price linkages within cot-

ton markets appear to have improved substantially overthe last decade. In what follows we identify and quantifythe sources of such improvement.

The upper and middle panels of Table 3 report theadjustment taking place within the ®rst period. A coe� -

cient of one is consistent with perfect transmission of price

shocks, while a coe� cient of zero represents a short-runinvariance to changes in prices elsewhere. Since the short-run eVect is in principle unrestricted, 1 greater than unity

would suggest an over-reaction to changes in prices in thecurrent period. The lower panel contains the p-values of the


0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5


(a) A Index±USA

0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5


(b) A Index±Greece

0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 15

P e rio d 1 Pe r io d 2

(c) A Index±W. Africa

0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 1 5

Period 1 Pe rio d 2

(d) A Index±C. Asia

0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 15

Pe riod 1 Period 2

(e) USA±Greece

0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5


(f) USA±W. Africa

Fig. 2. Variance ratio tests for price diVerentials.

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hypothesis of equality in the 1s in the two sub-sample

periods, against the two-sided alternative.

At the 5% signi®cance level, six of the nine overallimprovements in the short-run eVect were signi®cant,

while only three of the eight remaining cases represented

signi®cant reductions in the amount of adjustment withinthe ®rst period.9 Further analysis of the nine signi®cant

changes in the short-run eVect reveals that the average

deviation of the adjustment coe� cient from unity fellfrom 0.32 to 0.25, indicating an overall improvement in

the initial adjustment. More speci®cally, Greece showed

the most improvement in the short-run adjustment whencoupled with the A Index, USA and C. Asia. W. Africa and

C. Asia revealed signs of improvement when paired with

Greece, while the opposite was the case when paired withthe USA.

The measure of long-run co-movement is presented in

Table 4, with the upper and middle panels representing

periods 1 and 2, respectively. In essence, the measure of

long-run adjustment captures the correction to a given

price change from another origin, subsequent to the cur-

rent period. In fact, the absolute deviation from the long-

run steady-state declines from period to period (i.e., sug-gesting long-run convergence in prices) when this par-

ameter is statistically diVerent from zero. The lower panelof Table 4 reports the p-values for the test of the hypothesis

that the dynamic adjustment eVect remained the same

against the two-sided alternative. Note that for the cases

where the error-correction parameter is not signi®cant, spe-

ci®cation Equation 7 (i.e. the ®rst diVerence model) is thevalid characterization of the data.

Twelve improvements were observed, while declines in

the degree of co-movement were present in three cases.

The remaining ®ve cases revealed no appreciable change

between periods 1 and 2. Signi®cant improvements in the

long-run eVect were observed when Greece was coupled


0 .0 0

0 .5 0

1.0 0

1.5 0

1 2 3 4 5 6 7 8 9 10 11 1 2 13 1 4 15

Pe riod 1 Pe riod 2

(g) USA±C. Asia

0 .0 0

0 .5 0

1.0 0

1.5 0

1 2 3 4 5 6 7 8 9 10 11 12 13 1 4 1 5


(h) Greece±W. Africa

0 .0 0

0 .5 0

1.0 0

1.5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 1 4 15

Pe rio d 1 Pe riod 2

(i) Greece±C. Asia

0 .0 0

0 .5 0

1 .0 0

1 .5 0

1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 14 1 5

Pe rio d 1 Pe riod 2

(j) W. Africa±C. Asia

Fig. 2. (continued)

9 The symmetry of the short-run coe� cient with respect to unity is interpreted as an equal departure from perfect short-run transmis-sion.

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with A Index and W. Africa at the 2% and 6% levels of

signi®cance. All other changes in the measure of long-run

comovement between the two sub-samples are not signi®-

cant at conventional levels (on average the adjustment

coe� cient increased from 0.08±0.11). This results in total

agreement with the variance-ratio ®ndings (depicted in

Figures 2a±2j), which apparently do not detect any changein the stationarity properties of the price diVerentials

between the two periods.

Table 5 presents the number of weeks, n, required to

achieve 95% of the adjustment to a given price change.

Note that n, which is calculated using Equation 8 is only

meaningful when long-run co-movement, in the Engle-

Granger sense, is detected. Faster adjustment is observed

in 14 cases while a slower adjustment is observed in only

two. Except Greece±USA in period 2, with the USA as a

reference, it is clear that none of the other origins exhibited

convergence towards the price levels in the USA, a fact

which becomes apparent when the insigni®cant error-cor-

rection coe� cient is considered.However, Table 5 reveals that nine of 14 changes in the

number of periods required to achieve 95% of the adjust-

ment, were signi®cant at the 7% level. Hence, price shocks

were transmitted at higher speed in period 2 compared with

period 1. Additionally, in period 1, nine cases of non-

convergence were evident while only three cases appeared


Table 2. Goodness of ®t

A Index USA Greece W. Africa C. Asia

R2 in Period 1A Index ± 0.49 0.40 0.80 0.88USA 0.50 ± 0.18 0.32 0.43Greece 0.46 0.16 ± 0.44 0.44W. Africa 0.80 0.31 0.36 ± 0.72C. Asia 0.88 0.42 0.35 0.71 ±

R2 in Period 2A Index ± 0.73 0.84 0.81 0.87USA 0.74 ± 0.62 0.73 0.76Greece 0.85 0.59 ± 0.62 0.80W. Africa 0.81 0.72 0.62 ± 0.75C. Asia 0.87 0.75 0.79 0.74 ±

Notes: Goodness of ®t is the adjusted-R2 of Equation 4.Source: Estimated by the authors.

Table 3. Short-run eVect


Estimate of 1 in period 1A Index ± 0.51 0.54 0.94 0.83USA 0.98 ± 0.49 0.81 0.80Greece 0.70 0.37 ± 0.67 0.56W. Africa 0.85 0.39 0.49 ± 0.72C. Asia 1.05 0.53 0.58 1.00 ±

Estimate of 1 in period 2A Index ± 0.49 0.85 1.05 0.93USA 1.48 ± 1.22 1.68 1.50Greece 1.00 0.49 ± 0.99 0.97W. Africa 0.78 0.41 0.63 ± 0.72C. Asia 0.94 0.49 0.82 1.02 ±

Test of equality of 1 between the two periods: p-valuesA Index ± 0.90 0.00 0.16 0.17USA 0.00 ± 0.00 0.00 0.00Greece 0.00 0.39 ± 0.02 0.00W. Africa 0.29 0.90 0.19 ± 0.92C. Asia 0.13 0.80 0.02 0.80 ±

Notes: All reported coe� cients are signi®cant at the 1% level. p-value is the signi®cance level of the F-statisticof the hypothesis that 1 in Equation 4 is the same in the two periods.Source: Estimated by the authors.

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Table 4. Dynamic adjustment


Estimate of (1 ¡ 3) in period 1A Index ± 0.01 0.01 0.20*** 0.13***USA 0.02 ± 0.04** 0.03* 0.02Greece 0.14*** 0.02 ± 0.16*** 0.17***W. Africa 0.21*** 0.00 0.00 ± 0.17***C. Asia 0.14*** 0.00 0.02 0.17*** ±

Estimate of (1 ¡ 3) in period 2A Index ± 0.02 0.22*** 0.16*** 0.13***USA 0.10** ± 0.12*** 0.09** 0.08**Greece 0.25*** 0.04* ± 0.16*** 0.11**W. Africa 0.14*** 0.00 0.11** ± 0.17***C. Asia 0.11** 0.02 0.08* 0.17*** ±

Test of equality of (1 ¡ 3) between the two periods: p-valuesA Index ± 0.60 0.02 0.71 0.96USA 0.12 ± 0.15 0.21 0.14Greece 0.22 0.52 ± 0.99 0.51W. Africa 0.34 0.81 0.06 ± 0.91C. Asia 0.61 0.51 0.44 0.92 ±

Notes: One (*), two (**) and three (***) asterisks indicate signi®cance at the 10%, 5%, and 1% levels. p-valueis the signi®cance level of the F-statistic of the hypothesis that (1 ¡ 3) in (4) is the same in the two periods.Note that for the cases where the adjustment term is signi®cantly diVerent from zero, there exists causalitywith feedback in Granger’s sense (Granger, 1969).

Table 5. Number of periods required to achieve 95% of the cumulative adjustment


Estimate of n in period 1A Index ± n.c. n.c. 0.8 8.7USA n.c. ± 54.8 46.4 n.c.Greece 12.3 n.c. ± 11.2 11.4W. Africa 4.6 n.c. n.c. ± 9.6C. Asia 0.4 n.c. n.c. 0.0 ±

Estimate of n in period 2A Index ± n.c. 4.5 0.0 2.9USA 22.3 ± 11.5 26.3 27.0Greece 0.0 54.3 ± 0.0 0.0W. Africa 9.6 n.c. 17.2 ± 9.0C. Asia 1.5 n.c. 16.2 0.0 ±

Test of equality of n between the two periods: p-valuesA Index ± n.a. 0.00 0.32 0.37USA 0.00 ± 0.00 0.00 0.00Greece 0.01 0.55 ± 0.06 0.00W. Africa 0.39 n.a. 0.13 ± 0.99C. Asia 0.30 n.a. 0.07 0.95 ±

Note: p-value is the signi®cance level of the F-statistic of the hypothesis that (1 ¡ 3) and 1 in Equation 4 (andhence k and n) is the same in the two periods. n is calculated as [log(0.05) ¡ log(1 ¡ 1)]/log 3 ± a result ofsetting k = 0.95 and solving Equation 8 for n. `n.c.’ indicates that long-run convergence never takes place asthe error-correction parameter is not signi®cantly diVerent from zero; `n.a.’ indicates that the test is notreported because the respective prices did not converge (for both cases 10% level of signi®cance was thecut-oV point).

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in period 2 at the 10% level of signi®cance, indicating thatprices from more origins achieved long-run convergence inthe second period.

V. CONCLUDING REMARKS

This paper examined the degree to which price linkages incotton markets have improved over the last decade.According to the goodness of ®t criterion in almost allcases a substantial improvement in price linkages hastaken place. For example, while on average about 50%of the variability of price from one origin was explainedby the variability of another origin’s price in period 1, thevariability explained in period 2 increased to 75%.Moreover, if one excludes the A Index, the relative increasein the explanatory power of the model is even higher (from40% to 71%).

A number of interesting conclusions emerge from thispaper. First, the main source of this improvement inprice linkages appears to be a result of short-run pricetransmission and to a very limited extent a result oflong-run co-movement. To the degree that short-runprice transmission re¯ects demand conditions while long-run convergence re¯ects supply conditions, the ®ndings ofthis paper suggest that over the last decade, information ondemand changes have been re¯ected in price changes muchfaster now than a decade earlier.

A second conclusion relates to the relatively high long-run convergence between C. Asia and W. Africa observedin both periods (with an estimated adjustment coe� cient at0.17) and the non-existence of convergence between theUSA and the three other origins (especially in the ®rstperiod). Cotton produced in W. Africa and C. Asia isexported almost in its entirety, hence making both marketssubject to the same world demand conditions (pricesrespond only to world demand since domestic demand isvery small). On the contrary, only 40% of US cotton isexported while the corresponding ®gure for Greece is60% (1996/1997 averages), in turn making their respectiveprices subject to both domestic and world demand con-ditions. This ®nding not only reinforces warnings cited inthe literature that volume of trade may aVect the conclu-sions regarding the degree of price linkage, but also indi-cates that exports relative to the size of the domesticmarket may be an important factor determining the degreeof price linkage.

The results of this paper have also important implica-tions with respect to risk management and price discovery.Low co-movement between US and non-US cotton pricesimplies that there is a need for a futures contract other thanthe one currently traded at the New York CottonExchange (NYCE) which is the only contract currentlytraded (apart from the SaÄ „o Paulo contract at theBrazilian commodity exchange introduced in 1996, albeit

with an extremely low liquidity). The NYCE contractserves primarily domestic US needs and is not being usedextensively by non-US hedgers and speculators (Lake,1992). This is not surprising if one considers that on 31December 1990, the May 1991 contract closed at 76.19 ¢,8.21 ¢ below the A Index while it expired on 8 May 1991 at92.22 ¢, 8.92 ¢ above the A Index.

The need for an exchange for non-US hedging needs, hasbeen apparent as noted by Cotton Outlook (12 December1997, p. 3): `The lack of an international trading instrumentother than the No. 2 (i.e. NYCE) contract ± one whichconsistently re¯ects broad world cotton market develop-ments but is capable of being used as ``hedge’’ ± continuesto be a shortcoming of the current pricing system.’ Anattempt, however, to create a `world’ futures contract byNYCE in 1992 failed. On the other hand, slow price con-vergence suggests that a non-US cotton contract is unlikelyto attract business from cotton merchants other than theones that are interested in that particular style of cottonand therefore may be expected to succeed only on anational or regional basis.

The last ®nding relates to the methodology. It has beenextensively argued that conventional stationarity tests exhi-bit low power and may give misleading results regardingthe true degree of co-movement. This study con®rmed this,i.e. stationarity tests by themselves may be incapable ofuncovering the co-movement. Additional measures, suchas Cochrane’s variance-ratio tests or Hamilton’s advice oflooking at the overall sensibility of the model and theresults should be used to appropriately assess the presence(or absence) of price linkage.

Finally, two notes on further research are in order. First,one important issue not considered here is endogeneity.For policy related reasons, however, one would have to®rst detect any endogeneity patterns and correct for themthrough an instrumental variables model. Second, all mar-kets should be treated in the same model beyond thecentral-periphera l model adopted here.

ACKNOWLEDGEMENTS

The ®ndings and conclusions of this paper are those of theauthors and should not be attributed to the World Bank.The authors would like to thank a reviewer for valuablecomments and suggestions.

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APPENDIX A

Proposition

Examining long-run proportionality in Equation 3 bytesting if §i i = 1 when p1

t and p2t are I(0), is equivalent

to testing for stationarity of the price diVerential (i.e.(p1

t ¡ p2t ) ¹ I(0)) when p1

t and p2t are I(1).

Proof

Consider Equation 3 in text again:

p1t ˆ · ‡ 1p2

t ‡ 2p2t¡1 ‡ 3p1

t¡1 ‡ ut …A1†

where ut is i.i.d.(0, ¼2) and Î j 3jÎ <0. To solve for the long-run equilibrium set p1

t = p2t¡1 and p2

t = p2t¡1 in (A1). Then,

the deterministic part of (A1) (excluding the constant term)becomes (1 ¡ 3)p

1t = ( 1 + 2)p

2t or p1

t = [( 1 + 2)/(1¡ 3)]p2

t . If p1t and p2

t are I(0), the hypothesis of long-runproportionality can be examined by running regression(A1) and then testing H0: ( 1 + 2)/(1 ¡ 3) = 1 (oralternatively 1 + 2 + 3 = 1).

Setting 2 = 1 ¡ 1 ¡ 3 in (A1) gives:

p1t ˆ · ‡ 1p

2t ‡ p2

t¡1 ¡ 1p2t¡1 ¡ 3p2

t¡1 ‡ 3p1t¡1 ‡ ut

…A2†


Table B1. Composition of the Cotlook A index

Price of cotton (US ¢/lb.)

Origin of Quotation 17 October 1996 2 January 1997 31 July 1997

USA (Memphis Territory)* 83.00 84.00 85.25@

USA (California/Arizona) 83.00 84.00 87.50 NMexico 79.75 NQ NQParaguay NQ NQ NQTurkey NQ NQ NQSyria NQ 79.50@ 79.50@

Greece* 74.00@ 79.00@ NQCentral Asia* 71.00@ 75.50@ 79.50@

Pakistan 76.00@ NQ NQIndia NQ NQ NQChina NQ NQ NQTanzania 78.00@ NQ NQAfrica `Franc Zone’* 75.00@ 79.00@ 80.00@

Australia 80.50 84.00@ 87.00@

COTLOOK A INDEX 74.80 79.40 82.25

Notes: `NQ’ indicates that cotton from the respective origin was not traded in North Europe. `*’ denotes the cottonquotations analysed in this study. `@ ’ denotes the A Index quotations over which the average is taken. `N’ meansthat the particular style of cotton is not oVered in volume and hence it is not used in the composition of the Index.Source: Cotton Outlook.

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Subtracting p2t¡1 from both sides of (A2) and collecting

terms results in:

…p1t ¡ p1

t¡1† ˆ · ‡ …1 ¡ 3†…p2t¡1 ¡ p1

t¡1†

‡ 1…p2t ¡ p2

t¡1† ‡ ut …A3†

If p1t and p2

t are I(1), then (A3) is a valid error-correctionmodel if and only if 3 is signi®cantly diVerent from unity(or alternatively (1¡ 3) is signi®cantly diVerent from zero)(Engle and Granger, 1987), which because of the equiva-lence between error-correction representation and the exist-ence of cointegration implies that (p2

t ¡ p1t ) ¹ I(0).

APPENDIX B

Data Description

The price quotations used in the analysis are weekly andcover the periods August 1985±December 1987 and August1995±January 1997 and refer to CIF prices in North

European ports for the following four styles of cotton:USA (Memphis), Greek, West African and Central

Asian. These quotations are oVer prices, i.e. the pricethat the agent would ask for the particular type of cotton.

We are also including the A Index in the analysis. This

index, which is the average of the ®ve less expensive out of14 styles of cotton (Middling 1-3/32’’) traded in NorthEuropean ports include styles from the following origins

(in addition to the ones referenced above): California/Arizona (USA); Mexico; Paraguay; Turkey; Syria;

Pakistan; India; China; Tanzania; and Australia (seeTable B1 for an example).

To account for the fact that agent’s quotation is likely

to be above the actual transaction price, the index usesthe ®ve lowest priced styles. The index is constructed

daily by Cotlook Limited and is published in CottonOutlook. Since not all styles of cotton from the eligibleorigins are traded in North Europe all year around,

not all 14 quotations are available for the A Index at alltimes.


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identifying price linkages: a review of the literature and an application to the world market of...

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