AJAE appendix for Is Exchange Rate Pass-Through in Pork Meat Export Prices Constrained by the Supply of Live Hogs?

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1 AJAE ppendix for Is Exchnge Re Pss-Through in Por Me Expor Prices Consrined by he Supply of Live Hogs? Jen-Philippe Gervis Cnd Reserch Chir in Agri-indusries nd Inernionl Trde Cener for Reserch in he Economics of Agri-food (CREA), Lvl Universiy Nceur Khrief Grdue Reserch Assisn, CREA, Lvl Universiy Jnury 19, 27 Noe: The Meril conined herein is supplemenry o he ricle nmed in he ile nd published in he Americn Journl of Agriculurl Economics.

2 Comprive sic Le D nd b D represen he slope of he demnd funcion in mres nd b respecively. Equions (1), (11) nd (12) in Gervis nd Khrief (27) cn be rewrien in mrix form s: (1) 2e D e D dp D 2 p D de 2e D e D dp D 2 p D de e D b b d b b b b b b b b b b e D dq p D de p D de p b b b Using Crmer s rule, he mrginl impc on he expor price in counry of chnge in he exchnge re beween he domesic nd mre s currencies is: (2) dp 2 p e D e D e D de 2e e D b b e D b b b b In conrs, he exchnge re pss-hrough effec defined in equion (9) of Gervis nd Khrief (27) in he cse in which cpciy consrins re no binding cn be wrien s (under he ssumpion of liner demnd funcion, D ): (3) p 2 p r p r e 2e e 2e p p In he simples cse in which he slope of he wo demnd funcions re equl b D D D, (2) cn be rewrien s: b dp p e (4) b de e 2 e e The mrginl pss-hrough effecs in (3) nd (4) re similr bu he second erm on he righ hnd-side of he equions illusres he min differences. When hog producion 1

3 hs no impc on pricing decisions, he chnge in he expor price following chnge in he exchnge re is funcion of he mr-up over mrginl cos (mesured by p r ) s profi mximizing behviour implies sbilizion of he price in he imporing counry s currency. When here re cpciy consrins, he price response is funcion of he degree o which predeermined hog supplies re binding nd of he relive vlue of he currencies in boh mres. I is hus difficul o generlize he comprison beween he exchnge re pss-hrough effecs even in he simples cse in which he demnd slopes in ech mre re idenicl. Uni roo esing The sndrd Augmened Dicey-Fuller (ADF) es is performed o ssess he degree of inegrion of he vribles. The vribles used in Gervis nd Khrief (27) re expor uni vlues (denoed by jm, p ; j QB, MB, ON nd m US, JP ), he exchnge re m weighed by he food price index for ech desinion e ; m US, JP, he hog price in j ech province r ; j QC, MB, ON nd ol hogs slughered in ech province j Q ; j QC, MB, ON. The ADF es involves esiming he equion (Hmilon, 1994): (5) y y 1 j y j ; 1,, T ; j 1 where is ime rend, T is he smple lengh nd mesures he lengh of he lg in he dependen vrible. The selecion of his prmeer is crried ou using Ng nd Perron (21) modified Aie Informion Crierion (MAIC). The objecive is o minimize: MAIC ln ˆ 2 2 T mx ; where 2 ˆ is he vrince esimor nd mx is defined 2

4 s he mximum degree of ugmenion in (5) nd is se o.25 mx in 12 T 1 14 (Coo nd Mnning, 24). Visul inspecion of he series deermines wheher ime rend is included in (5) or if i is esimed wih he resricion. The criicl vlues of he ADF uni roo ess re provided in McKinnon (1991). Tble 1 presens he ADF es resuls. Two vribles ou of he 14 vribles used in he empiricl nlysis hve sisic h exceeds he criicl vlue of he es he 5% significnce level. I is however noorious h uni roo ess suffer from low power nd end o under-rejec he null hypohesis of uni roo (Mddl nd Kim, 1998). Hence, ble 1 lso repors he sionriy es of Kwiowsi e l. (KPSS, 1992). The KPSS esing procedure differs from sndrd uni roo ess since he null hypohesis is h of sionriy in he level of series. The KPSS es involves esiming he equion: (6) y ; 1 u ; u iid, 2 u The null hypohesis of rend sionriy is bou he vlidiy of zero resricion on 2 u. Tesing he null of level sionriy insed of rend sionriy involves regressing he series on consn insed of rend vrible. The KPSS es is compued using he Brle ernel o ccoun for he poenil correlion of he residuls wih bndwidh seleced using he procedure suggesed by KPSS; i.e..25 l runc 4.1T. The KPSS es rejecs he null hypohesis of sionriy for 1 ou of he 14 possible cses. There re conflicing resuls beween he wo ess in some insnces; conclusion h is no unusul for his ype of Confirmory D Anlysis (CDA). Ambiguiy bou he degree of inegrion in ech vrible exiss for 6 of he 14 vribles. Crrion-i- 3

5 Sylvesre, Snso-i-Rossello nd Oruno (21) buled differen ses of criicl vlues o ccoun for he joinness in he disribuion of he wo es sisics under he CDA pproch. Their procedure yields more powerful uni roo invesigion hn sndrd uni roo esing. Their se of criicl vlues resolves mbiguiy for wo vribles. Hence he join hypohesis of uni roo cnno be rejeced for 1 of he 14 vribles. Residul-Bsed Coinegrion Tess I is imporn o es for pre-coinegrion mong he vribles of ech equion o void he well-nown spurious regression problem (Mddl nd Kim, 1998). The Phillips- Ouliris Z nd Z sisics (Hmilon, 1994) re compued o es he null hypohesis of no-coinegrion using he residuls genered by he OLS esimion of equion (14) in Gervis nd Khrief (27). Tble 2 presens he Z nd Z es sisics for ech equion of boh sysems. The criicl vlues re repored below he ble. Boh ess srongly rejecs he null hypohesis h here is uni roo in he residuls; hus rejecing he null hypohesis of no-coinegrion. Boosrp Becuse sisicl inference in coinegred sysems cn exhibi significn bis in smll smples (Li nd Mddl, 1997), we lso invesiged poenil improvemens in he sisicl inference hrough boosrp mehods. The boosrp procedure mus ccoun for he poenil endogeneiy of he regressors in he curren conex nd he poenil uocorrelion in he residuls. We followed he suggesion of Li nd Mddl (1997) nd implemened he sionry boosrp of Poliis nd Romno (1994). Their ide is o smple blocs of residuls whose lengh is rndomly seleced using geomeric 4

6 disribuion. 1 Consider he sysem of ERPT equions for mre m nd he ssocied rndom wls: (7) p e e Q r z QC, m QC QC, US US QC, JP JP QC QC QC QC QC p e e Q r z MB, m MB MB, US US MB, JP JP MB ON MB MB MB p e e Q r z ON, m ON ON, US US ON, JP JP ON MB ON ON ON (8) e u, US US e u, JP JP r v, Q w ; QC, MB, ON The sregy is o use he residuls of he MDE esimes of (7) o obin z ˆ. Using he definiions in (8), we cn bloc-boosrp from he se V ˆ m zˆ QC, zˆ MB, zˆ ON, uˆ US, uˆ JP, vˆ, wˆ, 1,, T. This boosrpping preserves he conemporneous correlion beween he differen residuls due o he poenil endogeneiy of he regressors while lso ccouning for he uocorrelion in he residuls. Le V be he firs residul vecor smpled from he se V ˆ m such h m. The second observion in he boosrp smple will be he vecor m m V 2 V 1 m m V1 V wih probbiliy 1 p or vecor drwn from he whole disribuion of V ˆ m wih m m probbiliy p; i.e. V 2 V. Hence, he verge bloc lengh is 1 p, where he prmeer p is se.1. 2 Using he residuls of he boosrp smple nd he cul vlues of he righ hnd-side vribles in (7), expor price ime series re consruced under he null QC hypohesis of ineres (e.g., ). The MDE esimes re compued nd he es sisic of ineres is sored in vecor. This procedure ws repeed 2, imes o obin he empiricl disribuion of he es sisic. Tble 3 repors he boosrp p-vlues of he es sisics ssocied wih he cpciy consrin in he ERPT equions. The resuls re consisen wih he inference bsed on sympoic heory repored in bles 2 5

7 nd 3 in Gervis nd Khrief (27), excep perhps in he cse of he coefficien MB in he Jpnese expor sysem. The p-vlue is lrger hn he sympoic p-vlue which is lower hn.5. Thus, he boosrp inference yields greer evidence h hog cpciy hs no significn impc on expor price decisions of Mniob por exporers. The boosrp p-vlues of he join ess do no modify he quliive nure of he conclusions reched in Gervis nd Khrief (27). References Andrews, D. W. K. 24. The Bloc-Bloc Boosrp: Improved Asympoic Refinemens, Economeric 72: Crrion-i-Silvesre, J. L., A. Snso-i-Rossello nd M. A. Oruno. 21. Uni Roo nd Sionriy Tess Wedding. Economics Leers 7: 1-8. Coo, S., nd N. Mnning. 24. Lg Opimision nd Finie-Smple Size Disorion of Uni Roo Tess. Economics Leers 84: Gervis, J-P. nd N. Khrief. 27. Is Exchnge Re Pss-Through in Por Expor Prices Consrined by he Supply of Live Hogs? Forhcoming in he Americn Journl of Agriculurl Economics. Hmilon, J. D Time Series Anlysis. Princeon, NJ: Princeon Universiy Press. Kwiowsi, D., P. C. B. Phillips, P. Schmid nd Y. Shin Tesing he Hypohesis of Sionriy gins he Alernive of Uni Roo: How Sure re we h Economic Time Series Hve Uni Roo? Journl of Economerics 54: Lhiri, S. N Theoreicl Comprisons of Bloc Boosrp Mehods, Annls of Sisics 27:

8 Li, H., nd G. S. Mddl Boosrpping Coinegring Regressions, Journl of Economerics 8: McKinnon, J. G "Criicl Vlues for Coinegrion Tess". Ch.13 in Long-run Economic Relionships: Reding in Coinegrion, (eds) R.F. Engle nd C.W.J. Grnger, Oxford, Oxford Universiy Press. Mddl, G. S., nd I-M. Kim Uni Roos, Coinegrion nd Srucurl Chnge, Cmbridge Universiy Press. Ng, S., nd P. Perron. 21. Lg Lengh Selecion nd he Consrucion of Uni Roo Tess wih Good Size nd Power. Economeric 69: Poliis, D. N., nd J-P. Romno The Sionry Boosrp, Journl of Americn Sisicl Associion 89: Poliis, D. N., nd H. Whie. 24. Auomic Bloc-lengh Selecion for he Dependen Boosrp, Economeric Reviews 23:

9 Tble 1. Uni Roo nd Sionriy Tess ADF KPSS Join confirmion of uni roo Vribles Deerminisic specificion Lgs Tes vlue Tes vlue he 5% significnce level US e T Yes JP e T No QC Q T Yes MB Q T Yes ON Q T Yes QC, US p NT Yes MB, US p NT No ON, US p NT Yes QC, JP p NT Yes MB, JP p NT Yes ON, JP p NT Yes QC r NT Yes MB r NT No ON r NT No Noe: Criicl vlues for he ADF es wihou rend re: , nd he 1%, 5% nd 1% significnce levels respecively. Criicl vlues for he ADF es wih rend re: -4.11, nd he 1%, 5% nd 1% significnce levels respecively. Criicl vlues for he KPSS sionriy es wihou rend re:.739,.463 nd.347 he 1%, 5% nd 1% significnce levels respecively. Criicl vlues for he KPSS sionriy es wih rend re:.216,.146 nd.119 he 1%, 5% nd 1% significnce levels respecively. Finlly, he join criicl vlues of he ADF nd KPSS ess o perform he confirmory nlysis he 5% significnce level re respecively nd.171 when here is no rend nd nd.73 when here is rend. Finlly, T nd NT snd respecively for rend nd no rend in he uni roo es specified in (5). 8

10 Tble 2. Coinegrion Tess Equion Z Z U.S. sysem Quebec Onrio Mniob Jpn sysem Quebec Onrio Mniob Noe: Criicl vlues for he Z es sisic re: , nd he 5%, 1% nd 15% significnce levels respecively (McKinnon, 1991). Criicl vlues for he Z es sisic re: , nd he 5%, 1% nd 15% significnce levels respecively (McKinnon, 1991). 9

11 Tble 3. Boosrp Inference Null hypohesis for he U.S. sysem p-vlue QC.7 MB.794 ON.18 QC, JP QC.1 MB, JP MB.358 ON, JP ON.7 Null hypohesis for he Jpn sysem QC. MB.139 ON.2 QC, US QC. MB, US MB. ON, US ON. 1

12 Endnoes 1 Obviously, he independence beween he blocs does no fully mimic he dependence srucure in he iniil smple (Andrews, 24). Lhiri (1999) rgues h boosrp mehods wih fixed bloc lengh re relively more efficien h he sionry bloc boosrp. This ws chllenged by Poliis nd Whie (24) who rgue h he resuls in Lhiri (1999) re driven by he ssumpion h he opiml lengh of he blocs is nown. Moreover, one of he dvnges of he sionry boosrp is h he series genered re sionry unlie hose from moving bloc boosrp which consiss of smpling blocs of residuls (overlpping or non-overlpping) of fixed lengh. 2 Poliis nd Whie (24) recenly proposed n lgorihm o opimlly selec he lengh of he bloc boosrp bsed on he uoregressive coefficien nd smple lengh. In our cse, modifying he vlue of p did no produce significnly differen resuls. 11