Canadian Orange Juice Imports and Production Level Import Demand

Transcription

1 Journal of Agrbusness 251(Sprng 2007):17S Agrcultural Economcs Assocaton of Georga Canadan Orange Juce Imports and Producton Level Import Demand Yan Lu Rchard L. Klmer and Jonq-Yng Lee Import demand equatons are estmated n order to dentfy the own- cross-prce and volume elastctes that can be used to determne the best marketng strategy to ncrease U.S. orange uce gallons n the Canadan mport market. Ths study uses the frm s verson of producton dfferental AIDS CBS and NBR models. An expanson of total Canadan orange uce mport gallons usng advertsng favors the U.S. much more than t does the other three orgns nvestgated Brazl Mexco and ROW. A 1% ncrease n mported gallons of orange uce due to advertsng wll ncrease U.S. mports by 1.20% and Brazl s gallons by 0.60%. Key Words: AIDS model CBS model mport demand nternatonal trade NBR model Although U.S. ctrus processors have not been advertsng n Canada for the last several years the value of U.S. orange uce sold n Canada has been ncreasng relatve to other compettors. Snce 1990 the U.S. dollar share of orange uce (OJ) mports nto Canada has ncreased 24.8 percentage ponts whle Brazl s dollar share decreased 22.9 percentage ponts; yet the U.S. gallon share ncreased only 9.1 percentage ponts and Brazl s decreased 7.1 percentage ponts (table 1). U.S. prce on the other hand ncreased 23.4% ($0.51) and Brazl s prce decreased 35.9% ($0.55). U.S. producers would lke to ncrease ther OJ exports to Canada; however they want to know f lowerng prce and/or adoptng advertsng are the approprate tools for use n ncreasng ther gallon market share. To employ the best marketng strategy for ncreasng U.S. gallons mport demand equatons are estmated n order to dentfy the own- cross-prce and volume elastctes that can be used to answer the marketng strategy queston. Toward that end ths paper proceeds as follows. Frst the dfferental nput demand model and the frm s versons of the AIDS model CBS model NBR model and Barten s (1993) synthetc model are descrbed n the Theoretcal Models secton below. Ths s Yan Lu s former graduate student and Rchard L. Klmer s professor both n the Food and Resource Economcs Department Insttute of Food and Agrcultural Scences Unversty of Florda. Jonq-Yng Lee s research economst Economc Research Department of the Florda Department of Ctrus and courtesy professor Food and Resource Economcs Department Insttute of Food and Agrcultural Scences Unversty of Florda. The authors are grateful to Statstcs Canada for provdng the data used n ths study.

2 18 Sprng 2007 Journal of Agrbusness Table 1. Orange Juce Import Cost Shares Gallon Shares and Average Prces by Country of Orgn Year U.S. Brazl Mexco ROW Annual Cost Share % 53.5% 0.6% 1.6% Average 60.1% (9.0%) 38.8% (8.9%) 0.7% (1.17%) 0.4% (0.5%) % 30.6% 0.1% 0.2% Annual Cost (Can$) Average $ ($ ) $ ($ ) $ ($ ) $ ($ ) Annual Gallon Share % 61.7% 0.6% 1.9% Average 42.0% (11.1%) 56.4% (11.7%) 1.0% (1.7%) 0.6% (0.7%) % 54.6% 0.3% 0.2% Annual Gallons Average ( ) ( ) ( ) (805995) Annual Average Prce (Can$/gallon) 1990 $2.18 $1.53 $1.73 $1.52 Average $2.94 ($2.01) $1.23 ($0.18) $1.37 ($0.74) $1.37 ($0.22) 2005 $2.69 $0.98 $0.96 $1.60 Source: Statstcs Canada Internatonal Trade Dvson. Note: Values n parentheses are standard devatons. followed by a dscusson of the emprcal models that are used to estmate these fve nput demand allocaton models. The data used n the analyss are then presented. Next we report the emprcal results of the four models and the results of a synthetc test to establsh whch functonal form provdes the best explanaton of the data. The fnal secton hghlghts summary remarks conclusons and mplcatons of the study. Theoretcal Models Ths study uses Latnen (1980) and Thel s (1980ab) dfferental nput demand model and three addtonal nput demand models whch are the frm s versons of the AIDS CBS and NBR on the consumer sde. To the best of our knowledge ths s the frst producton nterpretaton of the AIDS CBS and NBR models. Ultmately

3 Lu Klmer and Lee Canadan OJ Imports and Producton Level Import Demand 19 the choce among dfferent specfcatons for the nput demand allocaton models s made on emprcal grounds. Ths nvestgaton examnes the emprcal performance of four smlar nput demand allocaton models n an econometrc study of the mport market for orange uce nto Canada. Barten s (1993) synthetc model s used to compare the emprcal results of these four models. Consumer demand allocaton models have been used extensvely n mport demand studes (e.g. Lee Seale and Jerwryapant 1990; Seale Sparks and Buxton 1992; Lee Brown and Seale 1992; Satyanarayana Wlson and Johnson 1999). Four alternatve approaches to the functonal specfcaton of the consumer demand allocaton model have been derved wth well-known demand systems as an llustraton. These four systems are the Rotterdam model (Barten 1964; Thel 1965) the Almost Ideal Demand System (AIDS) model (Deaton and Muellbauer 1980) the Dutch Central Bureau of Statstcs (CBS) model (Keller and van Drel 1985) and the Netherlands Natonal Bureau of Research (NBR) model (Neves 1994). In these studes mports are consdered to be fnal goods that enter drectly nto the consumer s utlty functon. Here we use producton nput demand models to estmate mport demands. The assumpton that mportng decsons are made by a proft-maxmzng or costmnmzng frm s more consstent wth how trade data are typcally reported (Washngton and Klmer 2002ab). Gven the nature onternatonal trade where mported goods are used n domestc producton processes or go through a number of domestc channels before reachng the consumer a domestc value s added to mported goods before the fnal product reaches the consumer. Furthermore the mported nputs are typcally reported n bulk quanttes and values at docksde. Consumers almost never purchase commodtes n such quanttes or at the port. It s approprate to vew mported goods as nputs even f no transformaton takes place (Kohl 1978; Dewert and Morrson 1989). Therefore the producton approach to mport demand analyss s used n ths study. The Dfferental Input Demand Model The dfferental nput demand model (Latnen 1980; Thel 1980ab) begns wth the tradtonal producton problem of choosng a bundle onputs that (1) Mn C ' p x s.t.: z ' h(x) where C s total cost p and x are the prce and quantty for the th nput z s output whch s held constant and x s a vector of n nput quanttes. The frst-order condtons are solved [equaton (1)] for the nput demand equatons x ' x (p 1... p n ; z). The dervaton of the dfferental nput demand model s an approxmaton of ths set onput demand equatons whch results n the dfferental nput demand system and s represented by:

4 20 Sprng 2007 Journal of Agrbusness (2) dln(x ) ' θ dln(x) & π ) where ' p x /C s the share of total cost from nput dln(x ) s the change n the th nput θ ' M(p x /Mz)/(MC/Mz) s the th nput s share of margnal cost dln(x) ' dln(x ) s the Dvsa volume ndex and π s the Slutsky coeffcent. Equaton (2) s the th dfferental demand equaton of the frm whch ndcates that changes n the decson to purchase the th nput are dependent upon the changes n the total amount onputs obtaned and changes n nput prces. Gven data wth suffcent varablty n nput prces and quanttes varables are constructed for dln(x ) dln(x) and dln( p ) and the coeffcents for θ and π are estmated. The restrctons on the nput demand equaton (2) are: addng-up: θ ' 1 π homogenety: π Slutsky symmetry: π ' π and the curvature condton s (xnbx) $ 0. Equaton (2) also results n own- and crosscompensated prce elastctes and the Dvsa volume elastcty s g xp ' dln(x ) ) '&π g xx ' dln(x ) dln(x) ' θ. The Producton AIDS Model Instead of havng expendture as a functon of utlty and prces for a consumer as n Deaton and Muellbauer s (1980) consumer AIDS model the producton AIDS model specfes cost as a functon of output and prces onputs for a frm as follows: (3) where ln c(p z) ' (1 & z)ln a(p) % zln b(p) ln a(p) ' a 0 % a ln( p ) % ½ γ * ln( p )ln(p ) and ln b(p) ' ln a(p) % β 0 k p β.

5 Lu Klmer and Lee Canadan OJ Imports and Producton Level Import Demand 21 Total cost s denoted by c p s a vector of n nput prces and z s output. When there s no producton z and ln(c(p z)) ' ln(a(p)) whch s the frm s fxed cost. The consumer AIDS model n dfferental form (Barten 1993) s wrtten as the producton AIDS model: (4) d ' β dln(x) % γ ). Ths model s smlar on the rght-hand sde to the dfferental nput demand model [equaton (2)]; however the dependent varables are dfferent on the left-hand sde. The producton AIDS model explans the change n nput s share of total cost whle the dfferental nput demand model s concerned wth the change n nput quantty. Followng Lee Brown and Seale s (1994) verson of the consumer AIDS model the producton AIDS model s wrtten as: (5) dln(x ) ' (β % )dln(x) & (γ & % f ) ) where s Kronecker s delta equal to unty ' and zero otherwse. The AIDS model [equaton (5)] and the dfferental nput demand model [equaton (2)] have the same dependent varable. Ths wll allow the use of Barten s (1993) synthetc model to emprcally test for the approprate functonal form. The restrctons on the producton AIDS model are: addng-up: β γ homogenety: γ Slutsky symmetry: γ ' γ and the curvature condton s (xnbx) $ 0 where the matrx B s composed of the elements π ' γ & % f. Equaton (5) results n the own- and cross-compensated prce elastctes equalng and the Dvsa volume elastcty s The Producton CBS Model g xp ' dln(x ) ) '&γ & % f g xx ' dln(x ) dln(x) ' β %. Keller and van Drel (1985) developed the Dutch Central Bureau of Statstcs (CBS) consumer demand model. The producton CBS model wrtten n dfferental form s:

6 22 Sprng 2007 Journal of Agrbusness (6) dln(x ) & dln(x) ' β dln(x) & π ). Followng Lee Brown and Seale s (1994) verson of the consumer CBS model and rearrangng equaton (6) the producton CBS model s wrtten as: (7) dln(x ) ' (β % )dln(x) & π ) whch s another representaton of the producton CBS model and Barten s (1993) synthetc model s used to emprcally test for the approprate functonal form. Ths model has the producton AIDS model s volume coeffcents β [equaton (5)] and the dfferental nput demand model s prce coeffcents π [equaton (2)]. It shares wth these two models the addng-up homogenety and symmetry condtons. The constrants on the producton CBS model are: addng-up: β π homogenety: π Slutsky symmetry: π ' π and the curvature condton s (xnbx) $ 0. Equaton (7) results n the own- and crosscompensated prce elastctes and the Dvsa volume elastcty s g xp ' dln(x ) ) '&π g xx ' dln(x ) dln(x) ' β %. The Producton NBR Model Neves (1994) developed the NBR consumer allocaton model. The producton NBR model wrtten n dfferental form s: (8) d % dln(x) ' θ dln(x) & γ ). Followng Lee Brown and Seale s (1994) verson of the consumer NBR model the producton NBR model s expressed as: (9) dln(x ) ' θ dln(x) & (γ & % f ) ).

7 Lu Klmer and Lee Canadan OJ Imports and Producton Level Import Demand 23 Ths model has the dfferental nput demand model s volume coeffcent θ [equaton (2)] and the producton AIDS model s prce coeffcents γ [equaton (5)]. The constrants are: addng-up: θ ' 1 γ homogenety: γ Slutsky symmetry: γ ' γ and the curvature condton s (xnbx) $ 0 where the matrx B s composed of the elements π ' γ & % f. Equaton (9) results n the own- and cross-compen- sated prce elastctes (10) and the Dvsa volume elastcty s (11) The Synthetc Input Demand Model g xp ' dln(x ) ) '&γ & % f g xx ' dln(x ) dln(x) ' θ. A synthetc model contanng all four nput demand models was developed by Barten (1993). The synthetc system s employed to assess and compare the emprcal performance of each of the four condtonal demand systems. Followng Lee Brown and Seale s (1994) verson of Barten s synthetc model Barten s synthetc producton model s wrtten as: (12) dln(x ) ' (g % δ 1 )dln(x) & e & δ 2 ( & f ) ) where g ' δ 1 β % (1 & δ 1 )θ ande ' δ 2 γ % (1 & δ 2 )π. Equaton (12) becomes the dfferental nput demand model when δ 1 ' δ 2 ' 0; the producton CBS model when δ 1 ' 1 and δ 2 ' 0; the producton AIDS model when δ 1 ' δ 2 ' 1; and the producton NBR model when δ 1 ' 0 and δ 2 ' 1. The demand restrctons on (12) are: addng-up: g ' 1 & δ 1 e homogenety: e Slutsky symmetry: e ' e and the curvature condton s (xnbx) $ 0 where the matrx B s composed of the elements π or π ' γ & % f. For applcaton to dscrete data the specfcatons

8 24 Sprng 2007 Journal of Agrbusness are approxmated by replacng wth ( t % t&1 )/2 dln(x ) wth log(x t /x t&1 ) and d ln( p ) wth log(p t /p t&1 ) where the subscrpt t ndcates tme. Data Statstcs Canada provded the data used n ths study. The target market s the Canadan orange uce mportng market. Sem-annual mport data from the frst half of 1990 through the second half of 2005 provde detals on the orange uce mport quanttes and value from dfferent orgns: the Unted States (U.S.) Mexco Brazl and rest of the world (ROW). Imported quanttes from each of the three countres and ROW are n sngle strength equvalent (SSE) gallons (uce n drnkable form) and value s n Canadan dollars. Commodty prces are calculated by dvdng the value of orange uce mported by the quantty whch results n unt cost per SSE gallon. Table 1 shows the budget or expendture shares and the average prces of the mports from the four orgns for 1990 the sample mean and The largest mport expendture share was for the OJ mported from the U.S. and the lowest was for mports from the ROW. The mport expendture share for the OJ from the U.S. ncreased from 44.3% n 1990 to 69.1% n 2005 whle the mport expendture shares for Brazl Mexco and ROW decreased durng the same perod. The average prces for the OJ from Brazl and Mexco are smlar. Import prces of U.S. OJ are hgher than the OJ mported from other countres and ncreased over tme an ndcaton that more non-concentrated OJ and consumer packaged OJ were mported from the Unted States. Results Snce all four competng models and the general system satsfy the addng-up condtons only three equatons were estmated for the four-good system (the ROW equaton was not ncluded; see Barten 1969). The parameters for the omtted equaton are recovered from the estmates of the other equatons usng the addng-up condtons. Homogenety symmetry and frst-order autocorrelaton (Berndt and Savn 1975) were mposed and the models were estmated by the teratve seemngly unrelated regresson (ITSUR) procedure. Ths method s performed usng the LSQ procedure n the Tme Seres Processor (Hall and Cummns 1998). For the four competng models and the synthetc system the estmated frst-order autocorrelaton coeffcent was at least two tmes greater than ts asymptotc standard error. Log-lkelhood values and correspondng test statstcs for each of the systems are presented n table 2. The frst numerc column of table 2 reports the log lkelhoods and the second column gves the log-lkelhood rato test statstcs for model selecton. The test results show that the synthetc system reects the dfferental nput demand the producton AIDS and the producton CBS. Only the producton NBR s not reected by the synthetc system mplyng the producton NBR fts the data

9 Lu Klmer and Lee Canadan OJ Imports and Producton Level Import Demand 25 Table 2. Test Results for the Producton Dfferental AIDS CBS and NBR Models wth Frst-Order Autocorrelaton Imposed Model Log Lkelhood LLR Test Statstc 2[L(θ * ) L(θ)] a Producton Input Demand *** Producton AIDS *** Producton CBS *** Producton NBR Producton Synthetc b Note: Frst-order autocorrelaton coeffcent (Berndt and Savn 1975) s at least twce as large as ts asymptotc standard error. a The table value for χ 2 [2] ' 9.21 at the α ' 0.01 level. b The estmates for δ 1 and δ 2 are and wth standard errors and respectvely. better compared to the other three models. Accordngly only results based on the producton NBR corrected for autocorrelaton are reported and dscussed further n the followng sectons. The NBR coeffcent estmates for equaton (9) are presented n panel A of table 3; estmates for the demand parameters θ and π are presented n panel B; and the demand elastcty estmates [see equatons (10) and (11)] calculated at sample mean budget shares are presented n panel C. The property of postve sem-defnteness s verfed by nspecton of the egenvalues of the Slutsky matrx. Ths property s valdated when all egenvalues are postve except one whch s zero. The egenvalues for the NBR Slutsky matrx are! ! and ndcatng that the mport frms behave n an optmal manner. Dvsa Elastctes As reported n table 3 (panel C) the Dvsa mport elastctes for the U.S. Brazl Mexco and ROW are and respectvely. All are sgnfcant except for ROW. Among the sgnfcant Dvsa mport elastctes only those for the U.S. and Mexco exceeded unty; the Dvsa mport elastcty for Brazl s less than unty. These fndngs ndcate that as total mports of orange uce nto Canada ncrease by 1% ceters parbus mports from the U.S. and Mexco would ncrease more than 1% mports from Brazl would ncrease by less than 1% and mports from ROW would not change. Own-Prce Elastctes From table 3 (panel C) the respectve own-prce elastctes for the U.S. Brazl Mexco and ROW are!0.1744!0.1774! and! The own-prce

10 26 Sprng 2007 Journal of Agrbusness Table 3. Parameter and Elastcty Estmates of the Producton NBR Model PANEL A. Coeffcent Estmates Equaton θ U.S. Brazl Mexco ROW γ U.S **!0.1342** (0.0616) a (0.0347) Brazl ** (0.0704) Mexco * (0.0278) ROW (0.0129) ** (0.0388)!0.1685** (0.0503)! (0.0139) (0.0197)! (0.0116)! (0.0071)! (0.0065)! (0.0030) (0.0050) PANEL B. Demand Parameter Estmates b Equaton θ U.S. Brazl Mexco ROW π U.S ** (0.0616) Brazl ** (0.0704) Mexco * (0.0278) ROW (0.0129) ** (0.0347)!0.0805** (0.0388) * (0.0503)! (0.0139) (0.0197) (0.0116)! (0.0071)! (0.0065) (0.0030) ** (0.0050) PANEL C. Demand Elastcty Estmates cd Prce Elastcty Dvsa Equaton Elastcty U.S. Brazl Mexco ROW U.S ** (0.1021) Brazl ** (0.1825) Mexco * (3.9181) ROW (3.0777)!0.1744** (0.0575) ** (0.1007) (1.9619) (1.6971) ** (0.0644)!0.1774* (0.1305)! (2.7776) (1.5515) (0.0230)! (0.0510)! (1.6317)! (0.7175) (0.0118) (0.0168)! (0.4236)!2.6380** (1.1899) Note: Sngle and double astersks (*) denote statstcally dfferent from zero at the α = 0.10 and 0.05 levels respectvely. a Numbers n parentheses are asymptotc standard errors. b The egenvalues for the Slutsky matrx are! ! and c Estmated at sample mean budget shares. d Standard errors were estmated usng the delta method.

11 Lu Klmer and Lee Canadan OJ Imports and Producton Level Import Demand 27 elastctes for the U.S. Brazl and ROW are sgnfcantly dfferent from zero. These fndngs reveal that the mport demands for the U.S. and Brazl are nelastc meanng that quantty s less responsve to prce changes wth the demand for U.S. orange uce beng the most nelastc and the least responsve to prce change. In contrast mport demand quantty for ROW orange uce s prce elastc. If prces were decreased Canadan frms would ncrease ther purchases of ROW orange uce. Cross-Prce Elastctes Of the sx cross-prce demand parameter estmates only one was statstcally dfferent from zero.e. between the U.S. and Brazl (table 3). The cross-prce elastcty estmates between the U.S. and Brazl are sgnfcant and postve (nput substtutes). Results show that f the prce of Brazlan OJ s ncreased by 1% the mport demand for U.S. OJ would ncrease by 0.13%. On the other hand f the prce of U.S. OJ s ncreased by 1% the mport demand for Brazlan OJ would ncrease by 0.21%. As shown n table 1 the mport dollar shares of the OJ mported from Mexco and ROW are small less than 1%; therefore the nfluence of ther prces on the demand for U.S. and Brazl OJ was nsgnfcant. Summary Ths analyss used producton nput demand models to estmate mport demands. Past studes have attempted ths type of analyss utlzng consumer demand allocaton models as a means of obtanng mport demand estmates and elastctes. However gven the nature onternatonal trade where mported goods are used n domestc producton processes or go through a number of domestc channels before reachng the consumer a domestc value s added to mported goods before the fnal product reaches the consumer. Furthermore the mported nputs are typcally reported n bulk quanttes and values at docksde. Consequently the producton approach to mport demand analyss used here s approprate. The consumer AIDS CBS and NBR demand models were adapted nto the frm s versons of the AIDS CBS and NBR models. Barten s (1993) synthetc model was used to emprcally test for the best performng model among the three plus Latnen (1980) and Thel s (1980ab) dfferental nput demand model. The functonal form test showed that the producton NBR model was the best model to use for estmatng the Canadan orange uce mport demand. Fndngs reveal that the own-prce elastctes for the U.S. Brazl Mexco and ROW are all negatve. All the absolute values are less than unty except for ROW ndcatng the mport demands for orange uce from the U.S. and Brazl are prce nelastc and relatvely unresponsve to prce changes. The mport demand for orange uce from ROW s elastc and responsve to prce changes; however the quanttes mported from ROW are mnuscule. Results also show that U.S. and Brazl OJ exports to Canada are substtutes and compete wth each other.

12 28 Sprng 2007 Journal of Agrbusness Of these four orange uce nputs only the U.S. and Mexco Dvsa mport elastctes are greater than unty and those for Brazl and ROW are less than unty. All are sgnfcant except the mport elastcty for ROW. These results suggest that as total mports of orange uce nto Canada ncrease by 1% orange uce mported from the U.S. and Mexco would ncrease by more than 1% and orange uce mported from Brazl and ROW would ncrease less than 1%. The marketng strategy for the U.S. s clear. An expanson of total Canadan orange uce mport gallons usng advertsng favors the U.S. much more than t does the other three orgns (Brazl Mexco and ROW). A 1% ncrease n mported gallons of orange uce due to advertsng wll ncrease U.S. mports by 1.20% and Brazl s gallons by 0.60% thereby ncreasng the gallon share of the U.S. relatve to Brazl. References Barten A. P. (1964). Famly composton prces and expendture pattern. In P. E. Hart G. Mlls and J. K. Whtaker (eds.) Econometrc Analyss for Natonal Economc Plannng. London: Butterworths.. (1969). Maxmum lkelhood estmaton of a complete system of demand equatons. European Economcs Revew 1 7S73.. (1993). Consumer allocaton models: Choce of functonal form. Emprcal Economcs S158. Berndt R. R. and N. E. Savn. (1975). Estmaton and hypothess testng n sngular equaton systems wth autoregressve dsturbances. Econometrca S956. Deaton A. and J. Muellbauer. (1980). An almost deal demand system. Amercan Economc Revew 3 312S326. Dewert W. E. and C. J. Morrson. (1989). Export supply and mport demand functons: A producton theory approach. In R. C. Feenstra (ed.) Emprcal Methods for Internatonal Trade. Cambrdge MA: The MIT Press. Hall B. H. and C. Cummns. (1998). Tme Seres Processor Reference Manual Verson 4.5. Palo Alto CA: TSP Internatonal. Keller W. J. and J. van Drel. (1985). Dfferentable consumer demand systems. European Economcs Revew S390. Kohl U. R. (1978). A gross natonal product functon and the derved demand for mports and supply of exports. Canadan Journal of Economcs S182. Latnen K. (1980). Theory of the Multproduct Frm. Amsterdam: North-Holland Publshng Co. Lee J.-Y. M. G. Brown and J. L. Seale Jr. (1992). Demand relatonshps among fresh frut and uces n Canada. Revew of Agrcultural Economcs S262.. (1994). Model choce and consumer analyss: Tawan 1970S89. Amercan Journal of Agrcultural Economcs S512. Lee J.-Y. J. L. Seale Jr. and P. A. Jerwryapant. (1990). Do trade agreements help U.S. exports? A study of the Japanese ctrus ndustry. Agrbusness: An Internatonal Journal 6 505S514.

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