TESTING SEPARABILITY FOR COMMON WHEAT QUALITIES IN FRENCH IMPORT DEMAND MARKET USING AIDS AND ROTTERDAM DEMAND MODELS

Transcription

1 UNIVERSITE CATHOLIQUE DE LOUVAIN RURAL ECONOMICS UNIT TESTING SEPARABILITY FOR COMMON WHEAT QUALITIES IN FRENCH IMPORT DEMAND MARKET USING AIDS AND ROTTERDAM DEMAND MODELS Rabelas Yankam Nonou (a), Bruno Henry De Frahan (b) and Yves Surry (c) A contrbuted paper to the Xth EAAE Congress Zaragoza, Span August, (a) Doctoral student, Rural Economcs Unt, Unversté Catholque de Louvan, Belgum (yankam@ecru.ucl.ac.be) (b) Professor, Rural Economcs Unt, Unversté Catholque de Louvan, Belgum (c) Senor researcher, INRA, Rennes, France Copyrght 2002 by Rabelas Yankam Nonou, Bruno Henry De Frahan and Yves Surry. All rghts reserved. Readers may make copes of ths document for non-commercal purposes by any means, provded that ths copyrght appears on all such copes. May,

2 Key words: Separablty, Import demand, Rotterdam and AIDS demand models, wheat qualtes Abstract: Ths study has used a corrected lkelhood rato, wth AIDS and Rotterdam demand models, to test separablty n three separable (A, B, C) wheat mport demand structures on the French common wheat market. It appears from the study that the three separable Rotterdam structures are accepted by the test, whle only two of them (B and C) are accepted n the case of AIDS at 5% level of sgnfcance. Meanwhle, model B seems to be more ndcated n demand analyss wth AIDS snce t s the only one accepted at 15% level of sgnfcance. The results obtaned demonstrate not only the necessty to test separablty n demand structures, but also the necessty to know how the allocaton models can be used for demand analyss purpose. The study has also shown a great dfference n econometrc results for AIDS and Rotterdam and pose once more the ssue of the choce of a functonal form n demand analyss. I. Introducton Allocaton models are usually used to analyse trade of agrcultural products, manly because they are well takng nto account the ntra-ndustry (product dfferentaton) exchange that characterzed the agrcultural trade. Dxt and Stgltz (1977), and Krugman(1980) have contrbuted to the theoretcal foundaton of those models whch are then conforms wth the new nternatonal trade theory based essentally on the monopolstc competton. Snce the crtcs of the Armngton model, (especally to what concerns homothetcty assumpton), whch s the precursor of allocaton models, these models are based essentally on the weak separablty (WS) assumpton of consumers preferences or producers technology. Weak separablty (WS) allows the splttng of a utlty functon (technology) nto many sub-utlty functons. As ponted out by Phlps (1983), t s a necessary and suffcent condton for mult-stage budgetng that allows condtonal demand systems where demand for a product belongng to a group depends only on the prce of products n the same group and on the expendture allocated to that group. The consequences of ths assumpton are of great mportance both to the method and to the polcy mplcaton of the results. Wth regard to the method, the condtonal demand systems allows to reduce the number of goods n the demand model, and consequently to facltate the econometrc estmaton. Ths allows the use of flexble functonal forms even f the number of goods n the demand system s large, avodng then the Hanoch (1975) apprehenson about the use of those functonal forms n demand or supply analyss. Ths assumpton also lmts the possblty of substtuton when goods are not closed to each other. Wth regard to polcy, the WS allows evaluatng prce polces on a specfc group of goods wthout carryng to the drect mpacts on the consumpton of goods not belong to that group. For ths mportance, and especally n what concerns econometrc analyss, WS s wdely used n mports demand analyss, but s not generally tested, leadng to bas elastctes estmates and to a consequently wrong polcy analyss when ths assumpton doesn t hold. The only way to effcently use WS s to test whether t s approprate n the gven context. Ths s the am of ths study whch ntends to know whether and how trade allocaton models can be used to analysed the EU common wheat mport demand. EU common wheat market s one of the more mportant n the world. Economc Research Servce (ERS) statstcs shows that between 1990/91 and 1994/95, the average annual EU wheat producton represents 15,8% of the world wheat producton n front of USA (11,7%) and behnd Chna (18%). EU s the frst world wheat exporter wth 32% of total world exports aganst 32% for the USA and 20% for Canada. EU also mports 16% of total world mports aganst 17% for the USA and 9% for Chna. The balance sheet of these fgures shows that EU s the second world wheat consumer wth 12% of the world wheat consumpton behnd Chna(20%). The mportance of EU market and 2

3 especally of the France Wheat market (whch represent more than 30% of the EU market) s manly due to the market protecton and prce support of the Common Agrcultural Polcy (CAP) mplemented snce Snce 1992, and followng the nternatonal trade negotatons, CAP have been reformed twce (Mac Sharry and Agenda 2000) n the sense of dmnshng market protecton and prce support). Ths new stuaton of wheat trade lberalsaton open the EU wheat market to the US, Canada and other European countres wheat. Because t s known that EU common wheat s not enough compettve ether n qualty or n prces as compared to the mported common wheat, and gven the current nternatonal trade negotatons, t appears necessary to know how the EU common wheat market reacts to ths trade lberalsaton polcy renforced by agenda 2000, especally n what concerns the common wheat mport demand. The use of trade allocaton models s sutable for ths analyss snce t has been demonstrated by Hort(1988) and Larue (1991) that wheat s not an homogeneous product. The wheat mport demand analyss should consequently take nto account, as stressed by Bale and Ryan(1977), the wheat end use and mport source dfferentaton. Ths dfferentaton, especally among the varous common wheat classes should be frstly tested by testng weak separablty among them. Because of the dfference n consumpton structure of dfferent EU members states, and because the EU common wheat s more concerns wth the competton of the mported wheat, ths paper s concentratng on the French common wheat market. Table 1 gves a summary characterstcs of French common wheat market manly n mport demand. Table 1: End use for dfferent qualty wheat (HQW, MQW and LQW) and the mean budget share ( ) for each mport source and for each qualty wheat. Mean budget share per mport source Common wheat qualty End use France EU USA Canada ROW Total Hgh Qualty Wheat Hgh qualty flour for hgh qualty 0,510 0,331 0,120 0,037 0, (HQW) bakeres products (0,047) (0,017) (0,009) (0,003) (0,000) (0.076) Medum Qualty Medum qualty flour for medum 0,986 0,003 0,009 0,002 0, Wheat (MQW) qualty bakeres products (0,718) (0,002) (0,006) (0,002) (0,000) (0.728) Low Qualty Wheat Low qualty flour for bscuts, cakes 0,996 0, (LQW) and pastres products (0,195) (0,001) (0) (0) (0) (0.196) Source: computed from the Offce Natonal Interprofessonnel des Céréales (ONIC) data. Fgures n brackets are budget share as compared to the total common wheat expendture. The other fgures are budget shares for an mport source as compared to the total expendture for the correspondng wheat qualty. Imports from France (as an mport source) are computed by removng stocks and exports from the producton. Canada and rest of the world prce for MQW and the world prce for HQW are not avalable. They are replaced by the USA prces. The French common wheat market s made up of three qualtes. () hgh qualty wheat (HQW) s used for hgh qualty bakeres product, () medum qualty wheat (MQW) s used n the medum qualty bakeres producton, and () low common qualty wheat (LQW) used n cakes, bscuts and pastres ndustry. There are some relatonshp between the three wheat qualtes. The HQW can be mxed wth the LQW to ncrease the ts qualty. Table 1 also shows that each wheat qualty s mported from dfferent sources. The French source domnates the French market for each wheat qualty. Canada and USA are the man extra UE mport sources. The weakness of the mean budget share of the extra EU mports sources can be explaned as a consequence of the protectve and nterventonst CAP. These budget shares are expected to ncrease wth trade lberalsaton, and ustfy more the need of analysng EU common wheat mport demand, and consequently the need to test weak separablty among the three common wheat qualtes. Numerous studes have tested the weak separablty n demand models usng dfferent tests. One can mentoned Wnters(1983), Eales and Unnevehr (1988), Brenton (1988), Lafrance (1993), Nayga and Oral Capps(1994), Moschn and al(1994), Sckoka and Moro(1995), Sellen and Goddard(1996), and more recently Eales and Henderson (2001). None of these studes has tested separablty of mport demand wth regard to wheat qualty n the E.U n general and on the French 3

4 market n partcular. De Gorter (1986) and Mohanty and Peterson (1999), have analysed, the wheat mport demand n the EU. But they only assume Weak separablty between the dfferent wheat classes, wthout testng t. The present study s made up of four sectons. It begns by an ntroducton, followed by theoretcal framework, emprcal results and dscussons, and concluson. II. Testng Weak separablty: Theoretcal framework Trade allocaton theory s based on ndvdual consumer theory or on frm theory dependng of the nature (fnal or ntermedate good) of the traded product. The present paper s dealng wth common wheat gran, and t s expected to use the frm theory. But ths s not the case because of the followng reasons: () a part of common wheat mported on French market s drectly consumed and another part s used n agro-ndustres. We don t have the accurate statstcs of each of these parts. () There s a lack of data concernng the prces of other nputs and prces of products produced by common wheat transformaton. There s also a possblty of substtutng and/or mxng two wheat classes and we don t have accurate nformaton about these relatonshps. In ths frame, we use the consumer theory to estmate mports demand models, beng conscous of the bas that can be ntroduced n the econometrc results as mentoned by Terry and Marsch (2000). But, we thnk that ths bas can be mnmsed f we consder that we are n a case of a mult-products mult-factors frm, were common wheat s consdered as a factor to produce manufactured products. In ths case, we consdered only that the frm, gven the technology used and the product market stuaton, decdes frstly for the total quantty of wheat to mport. In a second budgetng procedure, t allocates hs budget to the dfferent wheat classes, and so on. Thus, ths procedure ont the Davs and Jensen (1994) procedure of budgetng n whch the demand models n the ntermedary and the last stages of budgetng are almost equals, snce costs of common wheat as nput equals expendtures for common wheat as fnal product. Consumer theory stpulates that from a utlty functon u= u(q) maxmsaton, subect to a budget constrant y = p' q (where q s the vector of quanttes consumed and p the correspondng vector of prce) a Marshallan demand system q= ( p, y) s obtaned. When the number of good ( = 1,..., n) s large, then the demand system becomes dffcult to estmate. The WS assumpton allows separatng a set of goods nto bundles that become the arguments of the sub-utlty functons. Once the separablty condtons are respected, the utlty functon u can be wrtten as follows u = u( q) = u( u1( q1),... us( qs),..., ur( qr) (1) Where s = 1,...,r, and r s the total number of groups, us the sub-utlty functon assocated to the consumpton of qs, and qs the vector of goods belongng to the s group. Accordng to equaton (1), the consumer decdes frstly to allocate hs budget to the dfferent group of goods (frst stage) and secondly, he decdes for the quantty of good to be purchased n each group. Ths two stage budgetng allows dervng s condtonal demand systems; each one q s =qs( ps, ys) equals the non-condtonal demand system q= ( p, y). WS mposes restrctons on consumer behavour as ponted out by Alston and al (1990). Frst, the margnal rate of substtuton between two products from the same group s ndependent of the consumpton of goods n other groups. Second, the substtuton effects between goods n dfferent group s lmted, meanng that a prce change of a commodty n one group affects the demand for a commodty n another group only through the group ncome effect. Thrd, t mples a restrctve relatonshp between prce and ncome effect. Algebracally, the necessary and suffcent condton for weak separablty can be wrtten as follows: q q p h k Sk = = G H µ (2) k y y 4

5 Where G, k H, and G H denote two groups, µ GH s the proportonalty term that s the same for all goods n the two groups nvolved. Sk s the compensated cross prce effect, and h s the Hchksan demand functon. σ * = (where * Gven the equaton (2) and the Allen-Uzawa elastcty of substtuton s the w compensated cross prce elastcty, and w s the budget share), and the expendture elastcty, equaton (2), followng Goldman and Uzawa (1964), can be wrtten for symmetrc weak separablty: k k σ σ = (, ) G and ( m, k) H, for all G H, and (3) m m and for asymmetrc weak separablty, k σ σ = (4) k Because of the large number of restrctons that can be derved from (3) when the number of goods n (and the number of groups) s large, one needs only the non-redundant restrctons to test separablty restrctons n a demand or a supply model. The number of non-redundant restrctons R, followng Moschn and al (1994), s gven as follows: nr = n0 n (5) where n µ s ns( ns = 1 n0 ( n( n 1) 1) s the number of cross substtuton terms, and 2 1 nµ = s( s 1) 1 2 s the number of proportonalty terms. Theoretcally, separablty can be tested by usng Wald (W), Lkelhood Rato (LR) and the Lagrange multpler (LM) tests. All of these tests, as stressed by Italaner (1985) are asymptotcally equvalent. Because of the weakness of Wald test, due to ts non-nvarance accordng to the algebrac form of the non-lnear constrants, the Corrected Lkelhood rato test s used n testng weak separablty. The corrected LR test (CLR), s gven by the followng equaton: MT 1 ( NU + NR) 1 M( M + 1) CLR = LR 2 2 (5) MT Where LR = 2( lβnr lβr) s the classc Lkelhood Rato (LR) test wth lβnr and lβr whch are respectvely the log lkelhood of the unrestrcted model and of the restrcted (separable) model, NU and NR are respectvely the number of parameter n the unrestrcted model and n the restrcted model, M the number of equatons n the models, and T s the number of tme seres observatons. The CLR follows a ℵ² wth r degrees of freedom where r equals the number of constrants. III. Methodology: emprcal models, estmaton and data The CLR test consst of comparng a general unrestrcted (wthout an allocaton procedure) model to a seres of restrcted (many allocaton procedure) model usng two emprcal demand models. Emprcal demand models The Almost Ideal Demand System (AIDS) and Rotterdam models are used to estmate the French common wheat demand model. Ths choce s done only because these two models are the most popular flexble demand models. Meanwhle, the two models are dfferent. Rotterdam model s a frst dfference model whle AIDS model s at level. The two models used budget shares. As mentoned by Moschn and al (1994), Rotterdam demand model s separablty flexble, whch means that the separablty can be tested and mantaned at the whole pont, on the contrary to AIDS whch s a separablty nflexble demand model. On the other hand, AIDS s consdered as an exact representaton of consumer s preference at least at a pont whereas Rotterdam cannot be consdered as an exact representaton of preferences unless very strong condtons are mposed. Ths crtc on Rotterdam model, as notced by Barnett (1979), does not detract at all from hs usefulness. 5

6 Two varables have been ntroduced nto each of the two models to take nto consderaton some specfc aspect of food (wheat) mport demand n the French market. These varables are the trend (T ) for the evoluton of the consumers taste and a dummy for the 1992 Mac Shary (CAP) reform. The dummy (dum) s takng the value 1 before the CAP reform and 0 after. Consequently the two demand models used n ths study are specfed as follows: a) For the Rotterdam model: w d = + log q b w dlogq + cdlog p + e dlogt + d ddum vt (6) q Wth b = w = p (7) and c y w p p * = w s (8), where s s the y = st term of the Slutsky matrx of substtuton and the budget share of good n the system consdered. * s the compensated (Hcksan) prce elastcty and the non compensated (Marshalan) prce elastcty can be computed from the Slutsky 1 equaton usng elastctes. y= p s the total expendture of the n goods, b ' s, c ' s e ' s and d s are parameters to be estmated and vt s the error term. In, ' * the emprcal studes, budget shares are replaced by ther arthmetc mean w gven * by w = ( + 2. The theoretcal demand condtons are satsfed when b = 1 and c = 0, w t w t +1) /, c = and [ ] c = 0 c c 0. Gven the expresson of the Allen-Uzawa elastcty ( σ = c k w q k wk ), and b bk the expendture elastctes n Rotterdam models, (3) becomes c k =c m (9). The trend and b bm dummy enter the model as dfferental to be n conformty wth the specfcaton of the Rotterdam model. b) For AIDS model: w = α + γ log p + βlog( y/ P) + e logt + ddum+ vt, (10) Wth, = 1,..., n, charactersng the goods. P s a general prce deflator and s specfed as Log P = 0+ α log pk 2 α + 1 γ log p log p (11) k k Accordng to Deaton and Muellbauer (1980), the general prce deflator can be approxmated by the Stone ndex specfed as follows: log P = w log p. Despte the crtcs of Buse (1994) from whch ths approxmaton end up wth nconsstent parameter estmates whch yeld wrong elastctes, ths lnear approxmaton s very easy to use when testng separablty because the restrcted separable models become very non lnear as the number of separablty constrants ncrease. The addng up, symmetry homogenety and symmetry condtons respectvely requre that α = 1, β = 0, = γ, γ = 0, and γ = γ. The negatvty condton s verfed f the Slutsky matrces of 0 1 = * w 6

7 the terms of substtuton y s = c or c s negatve sem-defnte. Ths Slutsky substtuton terms p p y can be wrtten as y s = γ + w w δ w + β β log p p (12) P Where δ s the Kronecker delta takng the value 1 for = and 0 for. At the mean pont (where data can be scaled to obtan that pont of maxmum nformaton) p = y= 1, (12) can be wrtten as s = [ γ + w w δ w ] n whch wk s replaced by ak f the added varables could be scaled to one at the mean pont. Accordng to Green and Alston (1990), elastctes n AIDS can be expressed as: = 1+ β / w for ncome elastcty, * = δ + w + γ / w for compensated elastcty. The Allen Uzawa γ k β βk elastcty of substtuton s expressed as σ log y k = The separablty restrctons w wk w wk P n AIDS model at the mean pont s gven by the expresson ( a + β) ( ak + βk) γ k = ( γ m + a am ) a ak (13) ( a + β ) ( am + βm) Models to be tested Due to the reduced number of observaton, to the non-avalablty of certan data, and to the specfcty of common wheat as compared to durum wheat, ths paper s testng the separablty only between the dfferent common wheat classes (qualtes). The low budget share of certan mport sources has conducted to aggregate them wth other sources. It s the case of the EU low qualty wheat wth France source of the same qualty, the case of Canada and USA for the hgh qualty wheat, and the case of USA, Canada and EU sources for medum qualty Wheat. Accordng to ths aggregaton, the unrestrcted model, whch entals fnally sx goods, s expressed as follows: u NR= u ( q1, q2, q3, q4, q5, q6) NR (14) Where: q 1 s the quantty of low qualty wheat (LQW) mported from the world, ncludng France, q2 s the quantty of medum qualty wheat (MQW) mported from France q 3 s the quantty of medum qualty wheat (MQW) mported from the rest of World (ncludng EU, Canada and the USA), q4 s the quantty of hgh qualty wheat (HQW) mported from France, q 5 s the quantty of Hgh qualty wheat (HQW) mported from the EU, q 6 s the quantty of Hgh qualty wheat (HQW) mported from the rest of the world (ncludng USA, Canada). Table 2 below gves the dfferent separable structures or restrcted models to be tested. Table 2: The dfferent common wheat consumer s preference structures (A, B and C) to be tested and the correspondng non redundant restrctons SS (a) CRM (b) Utlty functon nr Non redundant restrctons (NRR) A1 u= ua1 ( q1,( q2, q3, q4, q5, q6) σ σ σ σ σ σ σ σ = 16 6 A2 A u= ua2( f( q1, h( q2, q3, g( q4, q5, q6))) 8 NRRA1, 24 4 σ σ σ σ σ σ σ σ =

8 B A3 ua3( f( q1, h( v( q2, q3), g( q4, q5, q6)) B1 u= 9 u= ub1 ( q1, q2, q3, ( q4, q5, q6)) B2 ub2( l( q1, q2, q3), k( q4, q5, q6)) u= 8 B3 ub3( l( q1, ( q2, q3)), k( q4, q5, q6)) u= 9 C C u= uc( q1, ( q2, q3), g( q4, q5, q6)) Source: The author (NRRX: The non redundant restrctons of model X) (a) Separable structure, (b) Correspondng restrcted model 6 8 NRRA2, σ 26 2 = σ σ σ σ σ σ σ σ σ σ σ σ σ = 36 NRRB1, σ σ σ 26 = 36 3 σ 36 NRRB2, σ 12 2 = σ13 3 σ 12 = 2, σ 2 3 σ σ 15 5 σ σ σ σ σ σ σ σ σ σ σ 26 = 36 6 σ Structure A entals 3 restrcted models. A1 assumes that the mporters, n a frst stage budgetng, frstly separate LQW from the other wheat. For a second stage, they separate HQW from the MQW sources, and n a thrd stage, they separate MQW from the HQW. Structure B s also a three stage budgetng that ends up wth a weak separablty between LQW and MWQ, and both are separated from the HQW. Structure C s the common structure based on the qualty dfference where the three wheat qualtes are separable each to other. The dfferent utlty trees entals by the structure A, B and C are reported n fgures 1a, 1b and 1c below. C.W C.W LQW HQW + MQW LQW MQW MQW 1 MQW MQW Fg1a: utlty tree entals by structure A (The numbers ndcate the mport sources) 6 Fg 1c: utlty tree entals by structure C (The numbers ndcate the mport sources) C.W HQW LQW + MQW MWQ LQW Fg 1b: utlty tree entals by structure B (The numbers ndcate the mport sources)

9 Data We use data coverng the perod For each wheat qualty, we know the annual quanttes mported from dfferent sources (ncludng the domestc source) and the correspondng annual prces at the French border have been collected. They have been collected manly from ONIC 2. The domestc quanttes mported have been computed (for each wheat qualty), from the dfference of French producton and exports. Prces of non-eu mport have been computed by addng mport taxes to the dfferent CIF Rotterdam prces. Data on mport taxes have been collected from IGC 3 for 1986 to 1999 and estmated for the perod. The EU quanttes and unt prces have been computed from the Eurostat data. USDA 4 and CWB 5 have also been consulted to complete the data. Quanttes are gven n 1000 tons whereas prces are gven n French Francs per ton. Estmaton The demand models estmated are of the followng econometrc form Yt = X tβ + vt (14) Where Y t s a ( MT x1) vector of dependant varables, X t a ( MT xk) matrx of ndependent varables, β a ( K x1) matrx of coeffcents to be estmated, and v a ( MT x1) matrx of error terms. M s the number of equatons or number of goods n the system, s the number of parameters and T the number of observaton. A contemporaneous auto-correlaton between equatons s assumed. Gven the addng up condtons and because of the sngularty of the covarance matrx, one equaton (and especally equaton 6: hgh qualty wheat from the rest of the world) s deleted for the estmaton purpose. The estmates obtaned by deletng ths equaton are consstent wth lkelhood estmators and nvarant to whch equaton has been deleted. After mposng addng up, homogenety and symmetry on each model, a lkelhood rato test s made to apprecate whether the two varables added (trend and dummy) are sgnfcant or not, n order to defntely choose the best model that the parameters should be used n the study. After ths lkelhood rato test, a Wald test 6 for seral auto-correlaton s done on the best model (retaned). When the Wald test shows that there s auto-correlaton n the errors terms, we used the Moschn and Moro (1994) test of the frst order auto-correlaton by posng v t = Rv( t 1) + xt where vt s assumed to be ndependent dentcally dstrbuted random vector wth E ( x) = 0 and E(xx')=Σ. General least square (LSQ) usng tme seres processor (TSP 5.1) s used for estmatons. For both AIDS and Rotterdam wheat demand models, the negatvty condton s verfed through the computed eghen values of the matrx of Slutsky terms of substtuton. When the Slutsky matrx s not sem-negatve defnte, the negatvty condton s mposed usng Cholesky decomposton (of ths Slutsky matrx) followng Dewaert and Wales (1987) method. In that case, we used a test of sem-flexblty to obtan the parsmonous estmates as ndcated by Moschn (1996). Due to the dffculty to mpose separablty and negatvty smultaneously n demand models, separablty test s done on demand model even f t doesn t satsfed spontaneously the negatvty condton. The results obtaned n that case are vald snce t s known that negatvty s not a necessary condton to mpose separablty as mentoned by Brenton (1989). Eales and Henderson (2001) also K= M = 1 K 2 Offce Natonal Interprofessonnel des céréales (A publc French cereal board) 3 Internatonal Gran Councl 4 Unted States Department of agrculture 5 Canada Wheat Board 6 The Wald statstc s gven by W = T 0.5 ρ, where T s the number of observaton, ρ the frst order autocorrelaton coeffcent of equaton. The W statstc s dstrbuted as a normal law and the null hypothess that there s no frst order f W<t0 9

10 demonstrated that the mposton of negatvty rarely alter separablty test when the model does not spontaneously satsfed negatvty condton. The separablty test usng the CLR s done by comparng the restrcted (constructed) separable demand models to the unrestrcted demand model. The null hypothess s that the restrcted model equals the unrestrcted ones, meanng that the unrestrcted can be, at a certan level of sgnfcance (generally 5%), wrtten as the restrcted models. Otherwse, the acceptaton of the null hypotheses means that consumers allocate ther resource as ndcated by the correspondng restrcted model. IV Emprcal results and dscussons Econometrc estmates and elastctes 7 The Lkelhood test results for the alternatves models to the general model show that the dummy and trend varables are sgnfcant n both AIDS and Rotterdam demand models at 10% level of sgnfcance, meanng that the concerned varables have a sgnfcant mpact on common wheat mport demand on French market. Meanwhle, at 5% level of sgnfcance, wth an upper tal area of 7.2% (more than 5%), dummy s not sgnfcant n the Rotterdam model. The econometrc results ncludng the added varables show that both AIDS and Rotterdam common wheat demand models behave dfferently: Dummy and trend are more sgnfcant n AIDS model than n Rotterdam model. At 5% level of sgnfcance, apart from the equaton 4 (HQW mported from France) the trend s sgnfcant n all AIDS common wheat demand equatons whereas only equatons 3 and 6 are sgnfcantly nfluenced by trend varable n the Rotterdam model. The dummy has a sgnfcant mpact on three AIDS equatons (3, 5 and 6) whereas t s sgnfcant only on equaton 5 n the Rotterdam model. The sngle R² are relatvely satsfactory n AIDS model wth almost all of them apart from the one of equaton 2 (41%) equals or hgher than 50% whereas the Rotterdam show very poor sngle R² for equaton 2 (30%) and equaton 4 (17%). Ths relatvely satsfactory values of AIDS sngle R² means that varatons n dependent varables n AIDS models are relatvely well explaned by the ndependent varables, meanng also that the parameters estmated are vald for mport demand and polcy analyss. The fact that the Rotterdam R² for equatons 2 and 4 are relatvely low s not a surprse snce Rotterdam s a frst dfferental equaton. The R² system for both models approxmate 100%, meanng that the demand systems are ft well wth the data. The AIDS demand model, on the contrary to the Rotterdam, ddn t satsfy spontaneously the negatvty condton. We then mposed t by Cholesky decomposton of the Slutsky terms of substtuton matrx usng Dewart and Wales (1987) method. The parsmonous estmates have been chosen from a sem-flexble AIDS that preserves, as notced by Moschn (1996), the dstngushng features of the orgnal AIDS. The sem-flexble AIDS estmates show that 32 estmates over 45 (more than 75%) are sgnfcant at 5% level of sgnfcance whereas only 6 over 39 (less that 20%) are sgnfcant n Rotterdam. A Wald test for auto-correlaton has shown that the AIDS resdues were not auto-correlated. Rotterdam model n the contrary shows that error term of equaton 4 s auto-correlated. We have tred to solve ths problem, whch makes the estmates obtaned be neffcent even f they are unbased (Judge and Al, 1985), by the Moschn and Moro (1994) general method. But we ddn t obtan the convergence of the estmates, probably due to the reduced numbers of observaton and 7 Due to space constrants, econometrc results and some computed elastctes are avalable from the authors upon request. 10

11 the loose of 2 degrees of freedom due to the double dfferentaton of the model n that case were we are tryng to solve the frst order auto-correlaton. We have then tred to solve the problem by usng a specfc Berndt and Savn (1975) method, but whle solvng the problem for equaton 4 (hgh qualty wheat from France), a new Wald test shows that the equaton 3 was auto-correlated n s error term. Ths result confrms very well the crtcs 8 of the specfc Berndt and Savn (1975) method for solvng auto-correlaton. Facng ths problem, we have decded to mantan the orgnal general Rotterdam model wth auto-correlaton n the error terms of equaton 4, as the best model we could obtan from the data avalable. The mpact of ths frst order auto-correlaton, gven the nterrelaton between the equatons, s not certanly lmted only on the equaton 4 parameters. The number of sgnfcant elastctes s about 50% for the sem-flexble AIDS (25 over 42) and less than 25% for the Rotterdam (9 over 42). The mposton of negatvty and the use of sem-flexble AIDS has ncreased the number of sgnfcant elastctes from 18 for the non negatve AIDS model to 25 for the negatve sem-flexble AIDS model. Some elastctes are very hgh (more than 1.5), partcularly n AIDS model where the Marshalan own prce elastcty of good 6 and cross prce elastcty for good 6 accordng to the prce of goods 3 and 4 are respectvely 8.83, and These hgh elastctes can be explaned by the followng reasons: (a) we are dealng wth complete systems of demand where the weak separablty assumpton have been made wthout takng care of the possble relatonshp between some common wheat mport sources wth other goods. Ths reason can be used to partally explan the level of sngle R² that are not often too near of 100%. (b) as explaned n secton II, we have consdered common wheat gran as food (fnal good) because of the lack of nformaton about the exact part of common wheat use n agro ndustry and as fnal good. (c) There s a great spatal and temporal varablty n the budget shares n the studyng perod as shown by fgure A2. AIDS general model show that good 5 s an nferor good wth an expendture elastcty that s 1.00, sgnfcant at 5% whereas Rotterdam show rather that good 4 s an nferor good wth an expendture elastcty of 3.33, sgnfcant at 10%. AIDS general model also shows a substtuton relatonshp between good 4 and good 6 whereas ths relatonshp doesn t exst n the Rotterdam model. There s even a contradcton n the relatonshp between goods from one model to another. Rotterdam shows for example a substtuton relatonshp between good 6 and good 3 whereas for the same goods, AIDS show rather a complementary relatonshp. The econometrc results obtaned confrm once more the mportance of model choce n the demand analyss procedure. For the present case, wth regard to the econometrc results obtaned, AIDS model seems to be sutable for French common wheat demand analyss. We are meanwhle conscous for the bas that can be ntroduced n our analyss by the unsolved frst order autocorrelaton problem on the Rotterdam model, not only on the elastctes, but also for separablty test. Separablty test results and polcy mplcaton Table 3a and 3b below exhbts the results of the corrected lkelhood test for weak separablty between the three separable structures tested. 8 The use of a dagonal matrx of error terms whch are all equals s very lmted to solve a frst order auto-correlaton. It consttute a specfc case of the general Moschn and Moro method. 11

12 Table 3a Test results for weak separablty at mean share wth the dfferent structures and correspondng models usng AIDS common wheat demand model Restrctons LL LR Test CLR Test Structure Model VLR UTA VCLR UTA Decson (5%) General General Restrcted A A Accepted A Accepted A Reected Restrcted B B Accepted B Accepted B Accepted Restrcted C C Accepted VLL= Value of the log of lkelhood. VLR= Value of the lkelhood rato. VCLR: Value of the Corrected Lkelhood Rato. UTA= Upper Tal Area. DF= degree of freedom or the number of separable restrctons. Decsons are made on null hypothess (H0) on the bass of the CLR results, at 5% sgnfcance level. Table 3b Test results for weak separablty wth the dfferent structures and correspondng models usng Rotterdam common wheat demand model Restrc- LR Test CLR Test Structure Model tons LL LR UTA VCLR UTA Decson (5%) General General Restrcted A A Accepted A Accepted A Accepted Restrcted B B Accepted B Accepted B Accepted Restrcted C C Accepted Tables 3a and 3b show that there s a dfference between AIDS and Rotterdam results as expected, gven the dfferences of the econometrc estmatons It appears that at 5% level of sgnfcance, the general Rotterdam model accepts the three separable structures tested, meanng that each of them can be used for the demand analyss purpose. Structure A s reected by AIDS model at 5%, meanng that ths structure doesn t reflect the allocaton procedure of the French common wheat mporters. By rasng the level of sgnfcance, the results become dfferent. At 15 % level of sgnfcance for example, structure C for AIDS s reected and the three structures are stll accepted by the Rotterdam model. Ths senstvty of results to level of sgnfcance rased the problem of approprate level of sgnfcance n ths knd of test. When consderng 5% level of error, as always used statstcally, we draw a statstcal concluson that s statstcally vald. But n the realty, for ths knd of test, may t not be possble to be very careful as mentoned by Morrn and Surry (1997) n the case of the level of sgnfcance to be consdered n the sem-flexblty test by consderaton a level of more than 25%? In the case of ths study, a hgh level of sgnfcance can be ustfed by the followng two non-exhaustve reasons. Frstly, the data have been constructed by ONIC n the absence of data avalablty collected by a specalsed structure. Secondly, some mport sources have been aggregated. These reasons are of nature to ntroduce bas n the data used that can be mnmsed by consderng the tradtonal 5% level of sgnfcance. Gven ths stuaton, t seems normal to deal wth a hgh level of sgnfcance. By workng at 25%, t appears that none of the AIDS structure s accepted. The presence of autocorrelaton n the Rotterdam model needs us to be very prudent n the use of the Rotterdam results. A reasonable level of sgnfcance of 15% allows 12

13 the AIDS model to accept only the structure B that seems to be the best one to analyse the French common wheat mport demand. By consderng structure B as the more ndcated one, we meant that the French mporters n a frst allocaton stage dstngush between the hgh qualty wheat and the other wheat. In a second stage, they dstngush between the medum qualty wheat and the low qualty wheat, whle allocates ther hgh qualty wheat resources to the dfferent mports sources (France, EU, and the rest of the world). In a thrd stage, they allocate the MWQ and the LWQ resources to the respectve sources. Ths allocaton procedure seems to be very normal n the sense that the mporters focus ther attenton to the hgh qualty wheat, especally the US hard red sprng (HRS) and the Canada western red sprng (CWRS) that ustfy partally the common wheat mport n the EU. The polcy mplcaton of ths structure B result s that, a polcy prce, specfc to hgh qualty wheat, can be mplemented on the common French market wthout takng care to the mpact ths polcy could have drectly to other qualty wheat n what concerns demand analyss. The hgh qualty wheat s weakly separable to the medum and low qualty wheat whch are also separable each from other on the French market. Ths result, f t could be the same at the European communty level, s an element to ustfy a specfc tarff polcy on the medum and low wheat qualty, dfferent from the hgh qualty tarff polcy. We have been nterested to analyse the mpact of mantanng separablty n both Rotterdam and AIDS models by comparng the elastctes n the unrestrcted and the ones n restrcted models A, B, and C that are the fnal models for the structures tested. It appears that there s a dfference even n the own prce elastctes from unrestrcted model to restrcted models, on the contrary of the Moschn and al (1994) results where at least own prce elastctes where mantaned between the compared models. These results necesstate a further nvestgaton to be explaned. V. Concluson Ths study attempted to use a corrected lkelhood rato to verfy weak separablty between the three common wheat classes or qualtes n mport demand on French market usng two popular demand models that are AIDS and Rotterdam. It appears wth the Rotterdam model that all the three separable structures are accepted even at a hgh level of sgnfcance. Wth AIDS, only the structure B s accepted at 15% level of sgnfcance, meanng that the hgh qualty wheat (HQW) s weakly separable from the Medum and low qualty wheat whch are weakly separable each from other on the French mport demand market. Ths results mplcates that a specfc prce or tarff polcy can be apply to the HWQ wthout havng a drect mpact on the demand of other wheat qualtes. Meanwhle, there exsts some dark ponts whch needs further nvestgaton, especally on why the elastctes, at least the own prce elastctes are not mantaned from the unrestrcted model to restrcted models. The study shows also that the estmaton results obtaned from the two models (AIDS and Rotterdam) are dfferent and ths can results to a dfferent polcy mplcaton. The mportance of functonal form choce becomes then very evdent. It s clear that the corrected lkelhood test rato used n ths study allows verfyng whether the unrestrcted model can be wrtten as the restrcted models wthout beng destroyed. Gven the power of Wald test as compared to the other asymptotc tests such as LR and Lagrange, t could be necessary to test ths weak separablty wth a corrected Wald test by usng the Phllps and Park method on the formulaton of Wald tests of non-lnear restrctons. Whle beng prudent n the Rotterdam separablty test results nterpretaton because of the unsolved auto-correlaton problem, we reman very careful n the nterpretaton of the AIDS results that are vald only at one pont (mean pont). Ths s the drawback of usng AIDS to test separablty n demand models. 13

14 References Alston, J. M.; A. C., Coln; R., Green; and D., Pck (1990) Whther Armngton Trade models? In Amercan Journal of Agrcultural Economcs, pp , AAEA. Armngton, P. S.; (1969) A theory of demand for product dstngushed by place of producton, n Internatonal Monetary Fund Staff Paper. Bale, M. D. and M. E. Ryan (1977) Wheat proten premums and prce dfferentals, n Amercan Journal of Agrcultural Economcs, 59 pp AAEA. Barnett, W. A., (1979) Theoretcal Foundatons for the Rotterdam model, n Revue of Economcs Studes, 46 (January), pp Berndt, E., R. and N. E. Savn (1975) Estmaton and hypothess testng n sngular equaton systems wth autoregressve dsturbances, n Econometrca, 42, pp Brenton, P. A.; (1989) The allocaton approach to trade modellng: some tests of separablty between mports and domestc producton and between dfferent mported commodty groups, n weltwrtschaftlches archv, pp Buse, A. (1994) Evaluatng the lnearzed Almost Ideal Demand System, n Amercan Journal of Agrcultural Economcs, 76 pp: Davs, G. C. and K. L. Jensen (1994) Two-stage maxmsaton and mport demand systems revsted: lmtatons and an alternatve, n Journal of Agrcultural and resource Economcs, 19 (2), pp Deaton, A. and J. Muellbauer (1980) An Almost Ideal Demand System, n The Amercan economc Revue, vol 70, n 3, pp Dewart, W. E. and T. J. Wales (1987) Flexble functonal forms and global curvature condtons, n Econometrca, 55, 1 pp Dxt, A. K. and J. E. Stgltz (1977) Monopolstc competton and optmum product dversty, n The Amercan Economc Revew, June Eales J. and J. R. Henderson (2001) The mpact of negatvty on separablty testng, n Amercan Journal of Agrcultural Economcs, 83 (2), pp Edgerton, D. L.; (1997) Weak separablty and the estmaton of elastctes n multstage demand systems, n Amercan Journal of Agrcultural Economcs, vol 79, pp 62-79, AAEA. Goldman, S. and H. Uzawa (1964) A note on separablty n Demand Analyss, n Econometrca 32, pp Green, R. and J. M. Alston (1990) Elastctes n AIDS Models, n Amercan Journal of Agrcultural Economcs, pp: Haley, S., L. (1995) Product dfferentaton n wheat trade modellng, an economc research servce report. Unted States Department of Agrculture; Techncal bulletn number, New York Avenue. Hanoch, G. (1975); Producton and demand models wth drect or ndrect mplct addtvty, n Econometrca, vol 43, n 3 (may, 1975), pp

15 Hort, (1988) Class and source substtutablty n the demand for mported wheat, Volume I. Non Publshed PhD thess, Perdue Unversty. Italaner, A. (1985) A small-sample Correcton for the lkelhood Rato test, n economc Letters 19 pp Judge, G. G.; W. E. Grffths, R. Carter hll; H. Lütkepohl; and T. C. Lee (1985) The theory and practce of econometrcs, second edton. Wley seres n probablty and mathematcal statstcs. Krugman, P. (1980) Scale economes, product dfferentaton, and the pattern of trade, n the Amercan economc revew, vol 70, n 5. Lafrance, J. T. (1993) Weak separablty n appled welfare analyss, n Amercan Journal of Agrcultural Economcs, , AAEA. Larue, B. (1991) Is wheat a homogeneous product? In Canadan ournal of Agrcultural Economcs 39, pp Lord, M., J. (1989) Product dfferentaton n nternatonal commodty trade. Oxford bulletn of economcs and statstcs, Internatonal Amercan Development Bank, Washngton. Mohanty, S. and Peterson, E. W. F. (1999) Estmaton of demand for wheat by classes for the Unted states and the European Unon, n Agrcultural and Resource Economcs Revew; pp Morn, L. and Surry, Y. (1997) Modélsaton et estmaton de la demande almentare d hules et de grasses dans l unon européenne. Un système complet de demande sem-flexble, n cahers d économe et socologe rurales, n 45, pp Moschn, G.; (1996) A sem-flexble Almost deal Demand System, n European Economcs Research 42, (1998) pp Moschn G. and D. Moro (1994) Autocorrelaton specfcaton n sngular equatons systems, n Economc letters 46, pp: Moschn, G.; D., Moro and R. D., Green (1994) Mantanng and testng separablty n demand systems, n Amercan Journal of Agrcultural Economcs, vol 76, pp 61-73, AAEA. ONIC: varous annual reports; Phllps, P. C. B. and J. Y. Park (1988) On the formulaton of Wald tests of non-lnear restrctons, n Econometrca, vol 56, No 5, Sellen, D. and E. Goddard (1996); Weak separablty n coffee demand systems, n European Revew of agrcultural Economcs, 24 pp: Terry, J. J. and T. L. Marsh (2000) Derved demand for wheat by class. Unpublshed paper presented at the Western Agrcultural Economcs Assocaton Annual Meetngs. Vancouver, Brtsh Columba, June 29, July 1, 2000 Wnters, L. A.; (1983) Separablty and the specfcaton of foregn trade functons, n ournal of nternatonal economcs, vol 17, pp , North Holland. 15

16 Annexes Table A1a: Non compensated prce elastctes and expendtures elastctes for the General unrestrcted sem-flexble AIDS model (wth negatvty mposed) at the mean share Prces Quanttes P1 P2 P3 P4 P5 P6 Expendture Q1-1,008*** -2,539*** 0,023-0,170** 0,174** 0,036 3,484*** (0,370) (0,431) (0,021) (0,068) (0,072) (0,033) (0,781) Q2-0,105-0,396*** 0,015*** -0,027 0,000 0,027*** 0,486** (0,096) (0,129) (0,006) (0,026) (0,020) (0,009) (0,230) Q3 1,066*** 1,212*** -2,163*** 3,800*** -0,336-3,960*** 0,381* (0,405) (0,375) (0,546) (0,762) (0,304) (0,676) (0,205) Q4 0,060 0,243 0,797*** -2,533*** -0,333 2,201*** -0,435 (0,277) (0,516) (0,159) (0,818) (0,244) (0,647) (0,915) Q5 2,934*** 1,079-0,184-0,921-2,269*** 0,362-1,001** (0,853) (0,885) (0,179) (0,691) (0,729) (0,225) (0,496) Q6 1,220** 1,795*** -3,116*** 8,326*** 0,465-8,829*** 0,140 (0,519) (0,491) (0,533) (2,453) (0,300) (2,371) (0,211) Fgures n brackets are asymptotc standard errors. The stars ndcate the sgnfcance of the parameter at dfferent levels (*=10%. **=5% and ***=1%). Table A1b: Non compensated prce elastctes and expendtures elastctes for general unrestrcted Rotterdam model at the mean share Prces Quanttes P1 P2 P3 P4 P5 P6 Expendtures Q1-4,177* -0,258-0,008 0,393 0,112-0,011 3,949*** (2,214) (1,897) (0,021) (0,640) (0,104) (0,034) (1,258) Q2 0,592-1,144** -0,001-0,049 0,030 0,005 0,567* (0,567) (0,547) (0,007) (0,217) (0,035) (0,012) (0,327) Q3 0,629* 0,406-0,649* 1,391* 0,010-1,732*** -0,055 (0,347) (0,448) (0,351) (0,796) (0,212) (0,643) (0,202) Q4 3,059 2,058 0,321* -2,535 0,008 0,422-3,333* (2,882) (3,750) (0,168) (3,872) (0,517) (1,956) (1,779) Q5 2,311* 2,474 0,016-0,082-3,899*** 0,275-1,096 (1,246) (1,620) (0,124) (1,439) (0,836) (0,225) (0,777) Q6 0,678 0,972-1,361*** 1,461 0,356-1,720-0,386 (0,509) (0,643) (0,506) (7,416) (0,303) (7,415) (0,271) Fgures n brackets are asymptotc standard errors. The stars ndcate the sgnfcance of the parameter at dfferent levels (*=10%. **=5% and ***=1%). Fgure A2: budget shares evoluton of the dfferent common qualty mport sources from 1980 to Budget shares 1,000 0,900 0,800 0,700 0,600 0,500 0,400 0,300 0,200 0,100 0, Years W1 W2 W3 W4 W5 W6 1=Low qualty Wheat, 2= medum Qualty Wheat from France, 3= medum qualty wheat from the EU, 4=hgh qualty wheat from France, 5= hgh qualty wheat from the EU, 6= hgh qualty wheat from the rest of World (USA and Canada) 16