IRREVERSIBLE IMPORT SHARES FOR FROZEN CONCENTRATED ORANGE JUICE IN CANADA. Jonq-Ying Lee and Daniel S. Tilley

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1 SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS DECEMBER, 1983 IRREVERSIBLE IMPORT SHARES FOR FROZEN CONCENTRATED ORANGE JUICE IN CANADA Jonq-Ying Lee and Daniel S. Tilley Canada is he mos imporan U.S. expor marke for lagged dependen variables (Houhaker and Taylor), frozen concenraed orange juice, accouning for over segmened independen variables (Goodwin e al.; 8 million gallons of expors each of he pas 9 years. Tweeen and Quance; Houck), and a variey of oher Brazil and he U.S. are he dominan suppliers of or- echniques, including ime-varying parameers (Ward ange juice in Canada. Prior o 1975, he U.S. held more and Tilley). Each of hese approaches has been used han 60 percen of he Canadian marke. Brazil's share for a variey of reasons. The reasons for hypohesizing of he marke has grown dramaically in he pas en irreversibiliy can generally be classified as: (1) psyyears, capuring more han a 50 percen share in 1978 chological, (2) echnological, and (3) insiuional (see Table 1). Brazil's success in gaining a dominan (Nerlove, p. 1). marke share can be parially raced o freezes in Flor- In he Canadian orange juice marke, echnological ida in 1977, 1981, and 1982 ha severely curailed U.S. facors are a major source of irreversibiliy because of producion of oranges for processing. As a resul of he form in which he produc is impored from he U.S. hese shocks and concern abou he decrease in he U.S. and Brazil. marke share, compeiive adverising sraegies have Nearly 90 percen of U.S. expors o Canada are albeen adoped by he Florida Deparmen of Cirus. In ready packaged, wih he res delivered as high-denhis paper we examine U.S. and Brazilian marke-share siy bulk juice, eiher in drums or anker rucks. All relaionships in Canada o es he hypohesis ha he Brazilian juice arrives in 55-gallon drums and is packrelaionships are irreversible. aged in Canada. Frozen concenraed orange juice Graphically, he naure of he hypohesized rela- (FCOJ) in 6-, 12-, and 16-ounce cans is he dominan ionship is shown in Figure 1. Iniially, he price level form of orange juice consumpion in Canada (Surveys is Pi and he U.S. marke share is MS, (poin A). Prices Inernaional, Limied); hus, o use Brazilian FCOJ, increase o P 2 and he U.S. marke share is reduced o MS 2 (poin B). When prices reurn o heir original level, he U.S. marke share increases o MS3, which is less han MS 1. Irreversibiliies have long been recognized in applied economic models. Irreversible relaionships have been modeled by using disribued lags (Nerlove), Marke Share Table 1. Canadian OJ Impors, 1974 hrough 1982 M A Year Source U. S. Brazil Oher Toal Vol.a % Vo. Vol. %.a % Vol. % Vol.a MSV3C MS 2 MS B Price 1 P2 eamillion gallons 42 Brix equivalen. Figure 1. Irreversible Marke Share Relaionship. Source: Saisics Canada. Jonq-Ying Lee is an Associae Professor, Universiy of Florida, and Research Economis, Florida Deparmen of Cirus. Daniel S. Tilley is an Associae Professor, Oklahoma Sae Universiy. Florida Agriculural Experimen Saion Journal Paper Number

2 firms acquired he experise as well as equipmen o (POTH), can be included in equaion (1) using a simpackage FCOJ or reconsiue FCOJ for producion of ilar derivaion. Tha is chilled orange juice. In order o marke he producs, several brands of Canadian-packed FCOJ were esab- (2) USS, = C + apus + a 2 PUS* + lished. The exisence of he faciliies and brands for a 31 PBR+ + a 4,PBR* + Canadian-packed Brazilian FCOJ reduces he prospec for fuure dominaion of he Canadian marke by U.S. apoth + apoth* + blx, + el suppliers in he shor run. Brands are hough o pro- where moe loyaly and consumpion habis which cause irreversibiliy. The hypohesis is ha once price shocks (3) C* cause old habis o be broken and new brands are a0wi + a(1 -W 1 ) + au 1 + adoped, reurning o previous brands may be resised. a 0 o(l- Ul) + a Vi + ao(l - V,) EMPIRICAL MODEL PBR = Z US(PBR - PBRS 1 ) + UPBR s=2 The concepual model is designed o es for own- price effec irreversibiliies as well as subsiue-price PBR = (1-U) (PBR -PBRS 1 ) + effec irreversibiliies. The mehod of segmening s=2 variables as described by Nelson is used. 1 This mehod was chosen because he changes we are aemping o (1 - U)PBRi measure are governed by discree decisions made by large firms. Boh disribued-lag and lagged-dependen variable models assume smooh adjusmen pro- POTH+ = V (POTH s=2) POTH + + PTH cesses. The U.S. share of oal Canadian orange juice im- pors during ime period (USS) is considered a func- POTH* = E (1 -Vs) (POTH - ion of he impor price of orange juice from he U.S. s = 2 POTHSi) + (PUS) and oher exogenous variables (X). To accoun ( )POTH for he irreversibiliies, he price slope for posiive price V changes above PUS,,m, ha is, he maximum U.S. impor price aained from ime -n up o and including Us = 1 if PBRs > PBRsma, is hypohesized o be differen from he one for 0 oherwise negaive and posiive price changes below PUSmax. V = 1 Thus, he model (see Appendix for derivaion) is specified if POTHS POTHs max as: = oherwise. (1) USS, = C 1 + a 1 PUS+ + a 21 PUS* + PBRsmax and POTHsmax are he maximum Brazilian impor price and maximum impor price for orange blx + e juice from oher counries aained from ime -n up o and including, respecively. where A similar relaionship is hypohesized for he Brazilian marke share (BRS). Since all impors from Bra- C 1 = ao 0 W + aoo(1-w 1 ) zil were in bulk form raher han reail packages, he impor price of bulk U.S. FCOJ was used in lieu of PUS = E Ws(PUSs-PUSsl 1 ) + WIPUS 1 PUS. S=2 PUS* = S (1-W 5 )(PUSs-PUSs,) + BRS = -(4) C 2 + a, 2 PBUS + a 22 PBUS* + ~~~~~~~S=-~2 ~a 32PBR + + a 42 PBR* + (1 -WI) PUSI a 52 POTH + a 6 2 POTH* + W = 1 if PUS 3 PUS max b 2 X + e 2 = 0 oherwise. where The prices of subsiues for Unied Saes orange juice impors, ha is, he price of impored Brazilian juice (PBR) and he price of orange juice impored from PBUST+ = Z WS(PBUSS - PBUSs,_) + WPBUS counries oher han he Unied Saes and Brazil s=2 I See Wolffram for reasons for using he following model derivaion insead of he approach suggesed by Tweeen and Quance. The following approach is developed by Nelson and is similar o hose used by Traill e al., and Young. 100

3 Table 2. Regression resuls a PBUS = 5 (PBUS PBUSPBUS) - + s=2 Independen Marke Share (1 - W,)PBUS, Variable U. S. Brazil s= if PBUSS PBUSmax Inercep * = 0 oherwise + (.6526) (.8359) PUS * PBUSs is he impor price of bulk U.S. FCOJ during, (.3117) period s, while PBUSs,ma x is he maximum impor price PUS * of U.S. bulk FCOJ aained from s-n up o and in- + (.1838) cluding s. The definiions of oher variables are similar PBUS o hose defined in (3). Oher exogenous variables in- * (. 1257) cluded in he marke share equaions under X are Flor- PBUS.7566* ida Deparmen of Cirus (FDOC) adverising +(.3555) expendiures in Canada (ADV), a zero-one dummy PBR variable (D) o capure he impacs of he 1977 freeze, * ( 1863) (.4559) hree zero-one dummy variables (Q1, Q2, Q3) o show PBR.7865* ** seasonal variaions in he marke shares of FCOJ im- + (. 2059) (. 6077) pored during he year, and an income variable (INC) POTH.4750**.1884 o capure he composie effec of he ime rend and * (.3351) (.5107) he income effec. POTH Seemingly unrelaed regression was used o esi- (.1866) (.4782) mae equaions (2) and (4).2 A procedure proposed by INC Kmena and Gilber (pp ) was used o correc (. 0001) (.0003) for firs order auo-correlaion in equaion (2). Differ- ADV.0004* en values of n were ried in order o selec P,max. Based (.0002) ( ) on he expeced signs of he coefficiens and he ADV_-.0003** ** weighed mean square error for sysem, n = 2 was cho- (.0002) (.0004) sen, ha is, Pmax is defined as he maximum impor D *.3077* price of he FCOJ from a paricular origin aained from (.6453) (.1 399) ime -2 up o and including. 3 The resuls are pre- Q *. 1139* sened in Table 2. All price variables are deflaed by (.0412) (.0608) he Canadian wholesale price index and he income Q2.0808* variable is deflaed by he Canadian consumer price in- (.0360) (.0911) dex. The ime period used in his sudy is from he firs Q quarer of 1972 hrough he second quarer of (.0452) (.0741) RESULTS anumbers in parenheses are esimaed sandard errors. The weighed mean square error for sysem is wih 44 degrees of freedom. '*' indicaes he esimae is saisically differen from zero a a =.05 level and '**' indicaes he esimae is saisically differen from zero a a =. 10 level. Table 2 shows he esimaed parameers along wih bvariabe definiions: PUS, PUS: Average Canadian impor price of U.S. FCOJ during quarer in U.S. he esimaed sandard errors in parenheses. In gen- dollars per SSE gallon (U.S. Deparmen of Commerce). eral, he signs of he price slopes are consisen wih a PBUS, US: Average Canadian impor price of U.S. bulk FCOJ during quarer in priori expecaions. In hose cases where he signs were U.S. dollars per SSE gallon (U.S. Deparmen of Commerce). no as expeced, he esimaed coefficiens were no PBRT, PBR: Average Canadian impor price of Brazilian FCOJ during quarer in saisically differen from zero. The esimaed com- U.S. dollars per SSE gallon (Saisics Canada). posie effec of income and ime (measured by he POTH POTHT: Average Canadian impor price of FCOJ from counries oher han Brazil and he U.S. in U.S. dollars per SSE gallon (Saisics Canada). coefficien of he income variable) shows ha hese coefficien of he income variable) shows ha hese INC: Privae consumpion per capia in U.S. dollars (Inernaional Moneary facors had a negaive impac on he U. S. share of he Funds). Canadian FCOJ impor marke. The impac on Bra- ADV,: Florida generic adverising expendiures in Canada deflaed by he inzil's share was no eviden. dex per housand households reached (CPM) in U.S. dollars (Florida The adverising variables used in his sudy indicae Deparmen of irus). a decreasing rae of reurn from adverising. The esi- D: Zero-one dummy variable. D= l if is afer he fourh quarerof Oherwise D = 0. maed coefficiens of he adverising variables show ha Ql,Q2,Q3: Zero-one dummy variables. Ql= I if is he second quarer of a year, Florida orange juice adverising in Canada had a sig- oherwivse Ql = 0; Q2 = 1 if is he hird quarer of a year, oherwise si-- YT C1 - I Ig-Q2 = 0, and so on. nifican posiive effec on he U. S. marke share in 2 Under he linear form specificaion, he fac ha marke shares mus sum up o uniy implies ha he sum of all inerceps in he marke share equaions mus equal uniy and he sum of he esimaed coefficiens for each variable mus equal zero. Therefore, he marke share equaion for oher impors can be derived from esimaes for equaions (2) and (4). Since all shares sum o uniy, he disurbances across he hree-share equaions will add up o zero for each observaion; herefore, a seemingly unrelaed regression approach can be applied o only wo of he hree equaions. 3 n= 1, 2, 3, 4 were ried. 101

4 Canada for one quarer beyond he quarer during which FCOJ impored from he U. S. is in reail and insiuhe adverising acually occurred. The iniial impac of ional packages, which canno be readily replaced by adverising was greaer han he subsequen impac a Brazilian juices ha require reprocessing; ha is, i is quarer laer. The esimaed coefficiens of he adver- difficul for imporers o replace heir U. S. juice wih ising variables in Brazil's marke share equaion show impored juice from Brazil since reail-packed produc ha Florida orange juice adverising effors had a neg- is no available from Brazilian exporers. aive impac on he Brazilian marke share in Canada. The esimaed parameer for PBR + indicaes ha The resul shows ha he impac was no eviden dur- when he Brazilian FCOJ price is increased, he U. S. ing he quarer when adverising occurred, bu he marke share will increase. However, he parameer is lagged impac was boh negaive and saisically dif- very small relaive o is esimaed sandard error. The feren from zero. reason may be ha Brazilian FCOJ has been priced well The esimaed coefficiens of he zero-one dummy below U. S. FCOJ. Thus, even wih a moderae price variable, D, indicae ha he freeze in Florida during increase in Brazilian FCOJ, he price of U. S. FCOJ 1977 increased Brazil's marke share a he expense of would probably sill be higher han he price of Brahe U. S. marke share. The esimaed coefficiens for zilian FCOJ. On he oher hand, when he Brazilian he seasonal dummy variables show ha he U. S. FCOJ price declines, he U. S. marke share also demarke share was bigger in he hird quarer han in he dines. In his case, he decrease is saisically signiffirs quarer and smaller in he second quarer han in ican. In addiion, he difference beween he changes he firs quarer, while Brazil's marke share is bigger in he U. S. marke share resuling from Brazilian FCOJ in he second quarer han in he firs quarer. 4 price increases versus decreases is saisically signif- The esimaed impac of he price changes on mar- ican (he calculaed -saisic is ). Thus, a deke shares and he ess carried ou for he irreversibil- crease in he Brazilian FCOJ price had a bigger impac iy hypohesis are summarized in Table 3. The on he U. S. marke share han an increase in he Braesimaed impac of price on he U. S. share in Canada zilian FCOJ price. is presened in he upper half of Table 3, and he esi- The esimaed parameer for POTH + (ha is, he maed impac of price on Brazil's marke share is shown impac of price changes in FCOJ impors from counin he lower half of he same able. ries oher han he U. S. and Brazil on he U. S. mar- The esimaes of equaion (2) show ha if he aver- ke share) indicaes ha if POTH is increased by 10 age impor price of U. S. FCOJ is increased by 10 cens cens per SSE gallon, he U. S. marke share would be per single srengh equivalen (SSE) gallon, he U. S. increased by 4.75 percen, which is saisically sigmarke share would be decreased by 8.61 percen, given nifican; however, he impac resuling in a decrease in oher variables held consan. On he oher hand, if he he U. S. marke share was no significan, as indiaverage impor price of U. S. FCOJ is decreased by 10 caed by he esimaes for POTH*. cens per SSE gallon, he U. S. marke share would be The esimae of PBUS + shows ha increases in increased by percen. The difference beween he U. S. bulk FCOJ expor prices had no significan imchanges in U. S. marke shares in response o PUS + pac on Brazil's marke share, while he esimae of and PUS is no significan (calculaed -saisic is PBUS* indicaes ha for every 10-cen decrease in he ). The reason is probably ha 95 percen of he U. S. bulk FCOJ expor price, Brazil's marke share would be decreased by 7.57 percen. The difference Table 3. Esimaed Impac of a 10-Cen Change in beween he parameers of PBUS+ and PBUS* is sa- Prices on Marke Shares isically significan (he calculaed -saisic is ), which indicaes irreversible relaionship. Price 10 /SSE gal. Change in -saisic for The esimae of PBR+ shows ha when he impor Price Price Change Marke Share Irreversibiliy price of Brazilian FCOJ increases, Brazilian marke share decreases; however, he decrease was no sais- U. S. Marke Share ically significan. This may occur because Brazilian U. S. Reail (PUS) ncrease price increases generally follow U. S. price increases a and Brazilian juice becomes relaively less expensive Brazi Increase Brazil () Decrease because he magniude of heir change is generally her (POTH) Increase.75 b smaller. Oher (POTH) Decrease The coefficien esimae of PBR* indicaes ha for Brazil's Marke Share every 10-cen decrease in he impor price of Brazilian lk (PBUS) Increase a 8 6 Decrease FCOJ, Brazilian marke share would be increased by 9.87 percen, and he increase is saisically signifi- Brazil (PBR) Increase a can. The difference beween he parameers of PBR + Decrease 9.87 and PBR* is saisically significan (he calculaed - Oher (POTH) Decrease saisic is ), hus indicaing ha he relaionship is irreversible. asaisically differen from zero a a =.05 level. h i i s T* bsaisically differen from zero a a =.10 level. The esimaes of POTH + and POTH* show ha he impor prices of FCOJ from counries oher han he 4 These seasonaliy paerns can be aribued o producion differences in he wo counries and he desire of heir processing indusries o avoid holding large invenories of processed juice. 102

5 impac on he U. S. share. For he Brazilian share equaion, a Brazilian price increase had only one-enh of he impac of a Brazilian price decrease. The effec of U. S. bulk FCOJ prices on Brazilian marke share were asymmeric. The resuls suppor he general conclusion ha enry of new suppliers ino markes may cause asymmeric price effecs. This hypohesis has special meri in mar- kes subjec o dramaic shocks like he freezes ha oc- cur in he Florida cirus indusry. Thus, we feel he approach used in his paper can be applied o oher commodiies subjec o increased compeiion when prices increase dramaically. Segmening variables is a valid mehod of esimaing equaions when asym- meric responses are expeced. Unied Saes and Brazil do no have significan effecs on he Brazilian marke share. CONCLUSIONS Esimaes of irreversible funcions based on he segmened-variables approach provide explanaions for shifs in Canadian FCOJ marke share by alernaive suppliers. The U. S. marke share was found o have symmeric own-price effecs, bu he Brazilian price effecs were asymmeric. An increase in he Brazilian price resuled in an insignifican increase in he U. S. make share, while a decrease in he Brazilian price was esimaed o have a large and significanly negaive REFERENCES Florida Deparmen of Cirus. Adverising invoices. Lakeland, Florida: Goodwin, J. W., Reuven Andorn, and J. E. Marin. The Irreversible Demand Funcion for Beef. Tech. Bull. T- 127, Oklahoma Sae Universiy Agr. Exp. Sa., Houck, J. P. "An Approach o Specifying and Esimaing Nonreversible Funcions." Amer. J. Agr. Econ. 59(1977): Houhakker, H. S., and L. D. Taylor. Consumer Demand in he Unied Saes: Analyses and Projecions. Cambridge: Harvard Universiy Press, Kmena, Jan, and R. F. Gilber. "Esimaion of Seemingly Unrelaed Regressions wih Auoregressive Disurbances." J. Amer. Sa. Assoc. 65(1970): Nelson, Glenn. "Reversibiliy, Symmery and Fixiy of Economic Relaionships." Unpubl. ms., Purdue Universiy, Nerlove, Marc. Disribued Lags and Demand Analysis for Agriculural and Oher Commodiies. Agriculural Markeing Service (USDA) Agriculural Handbook No Washingon, D.C.: U. S. Governmen Prining Office, Saisics Canada. "Impors by Commodiies and Counries." Oawa: Informaion Canada, Surveys Inernaional Limied. "Canadian Consumer Marke Orange Juice and Orange Drinks." Rp. o Florida Deparmen of Cirus. Various quarerly repors Traill, Bruce, David Colman, and Trevor Young. "Esimaing Irreversible Supply Funcions," Amer. J. Agr. Econ. 60(1978): Tweeen, L. G., and C. L. Quance. "Posiivisic Measures of Aggregae Supply Elasiciies: Some New Approaches." Amer. J. Agr. Econ. 51(1969): U.S. Deparmen of Commerce, Bureau of he Census. "U.S. Expors-Schedule B Commodiy by Counry- Domesic Merchandise." Repor FT 410, Washingon, D.C., Ward, R. W., and D. S. Tilley. "Time Varying Parameers wih Random Componens: The Orange Juice Indusry." S. J. Agr. Econ. 12(1980):5-13. Wolffram, Rudolf. "Posiivisic Measures of Aggregae Supply Elasiciies: Some New Approaches-Some Criical Noes." Amer. J. Agr. Econ. 53(1971): Young, Trevor, "Modelling Asymmeric Consumer Responses, Wih an Example." J. Agr. Econ. 31(1980): APPENDIX (A.2) USS - USS_ = a,,(pus - PUS,) + Derivaion of Equaion (1) bl(x - Xl) + Following Nelson, he saisical model is e - e- (A.1) USS, = ao + a, 1 PUS, + b 1 X, + el ifpus ~ PUS max if PUS, : PUS, ax USS - USS,, = a 21 (PUS - PUS,) + - ao + a 21 PUS, + b,x, +- e,,( if PUS, < PUSx,) + where el is he error erm. Lagging equaion (A. 1) and subracing i from (A. 1) yields' if PUS, < PUS,ma 103

6 Equaion (A.2) can be rearranged ino (A.6) USS = aow + aoo(1-w 1 ) + (A.3) USS - USS_ = allw,(pus - PUS,,) + a,, [ E Ws(PUSs - PUSS_ 1 ) + a2(1 - W) (PUS - s=2 PUS,,) + bl(x, - WPUS,] + a 21 [ z (1-Ws) Xl) + el - el 1 s=2 wherew, = 1 ifpus PUS, (PUS SPUS,_) s_ + = 0 oherwise. (1-W,)PUSl] + Moving USS o he righ-hand side and making suc- bx, + e,, cessive subsiuions yields Noe ha X, is no longer ransformed, and he disur bance erm has he usual desirable properies, he (A.4) USS = USS 1 + all[ S W,(PUS, equaion can be esimaed by ordinary leas squares s 2 (OLS). The saisical es of wheher he relaionship is irreversible is merely he usual -es of he null hy- PUSsi)] + a 21 [ z (1-Ws) pohesis ha he wo parameers (a,, and a 21 ) are equal. s= 2 In order o simplify noaion le (PUSS - PUSsl)] + bl[ E (X, - C 1 = aow + aoo(1-wl) s-=2 Xs,_)] + (els- el,s l)(pu = PUS,) + WsPUS- WPU s=2 s Assume ha PUS* = E (1- W,) (PUSs - PUS-l) + s=2 (A.5) USS, = ao + alpusi + bx, + ell ifpusl > PUSo (1-W,)PUS, aoo + a 21 PUS, + blx + el, Then (A.6) can be wrien as ifpusi < PUSO Subsiuing (A.5) ino (A.4) and combining erms (A.7) USS, = Cl + allpus + + yields a 21 PUS* + bx, + el,. 104