NAMUR Choices of Wine Consumption Measure of Interaction Terms and Attributes

Transcription

1 NAMUR 009 Choics of Win Consumption Masur of Intraction Trms and Attributs Magali AUBERT, Véroniqu MEURIOT INRA, UMR 0 MOISA; CIRAD, UPR 88 ARENA; Montpllir, Franc vroniqu.muriot@cirad.fr Intrprting intraction trms in conomtric modlling is fussy. McFaddn 00 xplains th complxity of consumrs choic facd with complx attributs of good. H mphasizs th difficulty of conomtric modls to rval th psychologist procss which is most of th tim non dirctly obsrvabl, but inducs bhavioral ffcts. Th modls logit and probit ar th mor usd modlling consumrs choic. Howvr, thy omit th intraction ffcts among th xplanatory variabls during th procss of choic. Ths blndd ffcts ar howvr dclard in th modifications of th consumption dcision. Th difficulty is thn to intrprt th cofficints associatd with ths intraction variabls. Aï Norton 003 hav dmonstratd, in th cas of non linar modls, that ths cofficints could not b apprciat with a simpl t-tst. To solv this problm, w propos a dcision rul nforcabl whatvr th natur of th stimators and for ach kind of modls, linar and non-linar. W build a simpl rul dcision, which offrs an asy lctur and thn bcoms vry convnint. W carry out an application of this dcision rul to th choics of th win consumrs confrontd with incrasingly sophisticatd products: which arbitrations to raliz btwn th color, th dgr or th typ of win whn ths various attributs combin on th labls and on incrasingly broad rays? How to tak into account ths combinations of attributs for bttr undrstanding th procsss of choic of th consumrs? Using data from ONIVINS - Rcnsmnt xhaustif ds prmirs contrats d vnt non AOC d 987 `a 003 fctv03 - w giv an xprimntal rsult dscribing th arbitration of win consumrs btwn color, dgr and typ of Frnch win

2 Choics of win consumption : Msur of intraction trms and attributs Magali Aubrt Véroniqu Muriot Abstract : Intrprting intraction trms in conomtric modlling is fussy. McFaddn 00 xplains th complxity of consumrs choic facd with complx attributs of good. H mphasizs th difficulty of conomtric modls to rval th psychologic procss which is most of th tim non dirctly obsrvabl, but inducs bhavioural ffcts. Th modls logit and probit ar th mor usd modlling consumrs choic. Howvr, thy omit th intraction ffcts among th xplanatory variabls during th procss of choic. Ths blndd ffcts ar howvr dclard in th modifications of th consumption dcision. Th difficulty is thn to intrprt th cofficints associatd with ths intraction variabls. Aï & Norton 003 hav dmonstratd, in th cas of non linar modls, that ths cofficints could not b apprciat with a simpl t-tst. To solv this problm, w propos a dcision rul nforcabl whatvr th natur of th stimators and for ach kind of modls, linar and non-linar. W build a simpl rul dcision, wich offrs an asy lctur and thn bcoms vry convnint. W carry out an application of this dcision rul to th choics of th win consumrs confrontd with incrasingly sophisticatd products : which arbitrations to raliz btwn th color, th dgr or th typ of win whn ths various attributs combin on th labls and on incrasingly broad rays? How to tak into account ths combinations of attributs for bttr undrstanding th procsss of choic of th consumrs? Using data from ONIVINS Rcnsmnt xhaustif ds prmirs contrats d vnt non AOC d 987 à 003 fctv03, w giv an xprimntal rsult dscribing th arbitration of win consumrs btwn color, dgr and typ of frnch win. INRA, UMR 0 MOISA, F Montpllir, Franc CIRAD, UPR 88 ARENA, F Montpllir, Franc Addrss corrspondnc to Véroniqu Muriot, Tl : ; fax : Cntr d coopération intrnational n rchrch agronomiqu pour l dévloppmnt Cirad, Départmnt Environnmnts t Sociétés, Unité Propr d Rchrch ARENA, TA C-88/5, MONTPELLIER cdx 5, Franc addrss : vroniqu.muriot@cirad.fr

3 . Introduction Intraction ffcts ar vry sldom tratd in conomtrics. Th xplanation of a phnomnon is howvr snsitiv to this typ of information Ashr & Popkin, 984. In th consumr thory, for xampl, dcisions ar mad at th nd of an arbitration which is oftn badly prcivd by th standard conomtric modls. Intrprting dcisions of consumrs choic rquirs taking into account psychological factors which ar not always prcptibl in th stp of conomtric stimation. This complxity is notably rportd by McFaddn 00 whn h rlats a history of conomtric modllings in that contxt : Th charactrization of altrnativs in th [multinomial logit] modl in trms of thir hdonic attributs was natural for this problm, and followd th psychomtric tradition of dscribing altrnativs in trms of physical stimuli p.354. H spcifis a littl furthr that : [ ] most applications of th standard modl lav out dpndnc on xprinc, and much of th powr of this modl lis in its ability to xplain most pattrns of conomic bhaviour without having to account for xprinc or prcptions p.356. Nonlinar modls lik logit or probit ar th most usd modlling consumrs choic bcaus thy allow discrimination among dcisions. Nvrthlss, a waknss of ths modls, and of conomtric modls in thir standard us, is to omit intraction ffcts among xplanatory variabls in th choic procss. Ths blndd ffcts ar howvr dclard by th modifications of consumption dcision whn an individual must arbitrat btwn svral goods combining svral attributs but various ways. Th supply of consumption goods is today vr mor htrognous, vn complx, insofar as a sam good can associat various charactristics of singl goods. In most cass, th combination of attributs is not prcivd as purly additiv. Th association of attributs singly nhanciv is only xcptionally prcivd lik th xact addition of th utility providd by ach attribut takn sparatly. Rstoring this procss of consumrs choic rquirs th introduction of intraction ffcts in conomtric modls, that thy ar linar or not. Th way to introduc ths intractions is to add combinations of attributs to individual xplanatory variabls. Ths combinations ar introducd by th product of coupls of variabls. Th modl is incrasd in ths intraction ffcts, and ths ffcts ar stimatd as all th othrs variabls cofficints. Th difficulty is to intrprt cofficints associatd to ths intraction variabls. Unlik th natural 3 3 Th trm «natural» is rlatd to non blndd variabls.

4 xplanatory variabls whos cofficints signify lasticitis in linar modls or variations in rlation to a rfrnc in nonlinar modls, stimat cofficints of combinations of variabls ar much mor discrning. In linar modls th t-tst givs straight significanc of such a cofficint. Aï & Norton 003 provd that statistical significanc in nonlinar modls cannot b tstd with just a t-tst : thy ar conditiond by indpndnt variabls. In this cas, w must tak into account non unit modifications of th utility introducd by th natural variabls combination. In this papr, w discuss th significanc of intraction cofficints and suggst a dcision rul abl to arbitrat among svral valus of ths cofficints at th nd of th stimation procss, in linar and nonlinar modls. In a scond sction, w dvlop dfinition and implications of intraction trms according to modls usd, linar and non linar. In a third sction, w xplicit th dcision rul usful to intrprt intraction trms stimat. In a fourth sction, w carry out an application of this rul of dcision on a sgmnt of th Frnch win consumption markt. W conclud about usfulnss and prformanc of this dcision rul distinguishing procsss of consumrs choic whn thy ar confrontd with complx goods.. Dfining and intrprting intraction trms Thortical bass of conomtric modlling 4 advocat to dscrib a phnomnon th xplaind variabl starting from variabls xplanatory indpndnt btwn thm. This modlling xrcis is carrid in a contxt ctris paribus : th information containd in th slctd xplanatory variabls must provid th possibl bst stimat of th phnomnon on hav to xplain. Th standard modl is : whr a phnomnon to xplain, α a constant, i xplanatory variabls, i stimat cofficints, n α i i ε i ε stimat rror, rprsnting all th information not tak into account by th modl. 4 W mak rfrnc to th first probabilistic conomtric works of Haavlmo 940, 944.

5 Th prformanc of modling is thus closly rlatd to th informativ capacity of th xplanatory variabls. Howvr, most of th tim th conomtrician is out this framwork and must b satisfid with a rough stimat, apprciatd notably by th valu of th cofficint of dtrmination. On is ntitld to wondr whthr, whras th most rlvant variabls wr slctd, thr would not b an information rsidual in intraction trms btwn ths variabls. Bowls 970 indicats th absnc of thortical bass as th main difficulty. H mphasizs th rlvanc of intraction trms : [ ] Th crucial dficincy is not in th lack of th data but th absnc of a thory of larning to guid us in stablishing a modl for our stimation. On consqunc of this lack of thory has bn th tndncy of rsarchrs to ignor intraction ffcts of inputs. 970, p.3 Intraction trms inform about complmntary rlations among xplanatory variabls. On distinguishs straightforward ffcts xplanatory variabls cofficints and blndd ffcts intraction trms rlativ to combinations. Th phnomnon is bttr xplaind and th stimat rsidual,ε, is rducd. Ashr & Popkin 984 rval that omission of intraction ffcts can lads to wrong rsults. Thy prov that introducting intraction ffcts incrass th undrstanding of this discrpancy, whil thir omission maintains odd discrpncis. Th impact of th stimation of intraction trms is prgnant spcially for consumrs choic modls. Whn th consumr must xprss a choic fac to svral goods offring similar attributs, how appraising his dcision-making procsss? Th knowldg about intraction ffcts can b a rspons. Introducing intraction trms dpnds on som xplanatory variabls or on anothr ffct[3] 5. In th quantitativ cas, th modl is : α ε Th modl including intraction btwn two variabls and is : In th linar modl, marginal ffcts ar : α ε 3 5 Intraction trms do not introducd collinarity btwn variabls. Th formula for a collinarity rlationship is α α whil th intraction variabl is notd : α α : of th xplanatory variabls. S, for xampl, Fridrich 98.. It is basd on th wightd product

6 4 5 and th intraction marginal ffct is : 6 In th non linar modl, bcaus th form of th distribution function is rspctivly : Logit : F W w w w Probit : FW dt t w ² π So marginal ffcts ar for logit modl: 4 5 and th intraction marginal ffct, from 6, is : [ ] Thraftr, w dvlop only th linar modl argumnts can b transposabl to nonlinar modls from quations 4, 5 t 6. Nvrthlss, w obsrv that in th nonlinar cas th intraction trm is widr than th stimat cofficint producd by th stimat, but must b rcomputd using quation 6, as xplaind in Aï & Norton 003.

7 3. Dcision rul Th stimation of th intraction trm in th linar cas is dirctly prformd at th tim of th stimation of th modl. Its significanc is givn by a t-tst. Howvr, th intrprtation of this intraction cofficint is not so asy than thos of th natural xplanatory variabls. Bcaus convys a rsidual blndd ffct btwn xplanatory variabls, w must distinguish four possibl cass : Th combination contributs nothing ls : variabls ar indpndnt, Th combination ovrvalus attributs, Th combination lads to an undrvaluation of attributs, Th combination lads to disutility. Arbitration btwn ths cass diffrs according to th sign of and : Indpndanc Ovrvaluation Undrvaluation and > 0 and < 0 > 0 > < 0 with 0< < 0 ] [ ] 0 [ ;0 ; U ] [ ; with > > 0 and < 0 with > > ] ; 0[ U ] 0 [ ; Disutility < 0 with <0 ] [ ; Tabl Th dcision rul < Adaptation to nonlinar modls : this dcision rul also fits ovr nonlinar modls if on rspcts formulations of quations 4, 5 t 6 adaptd from Aï & Norton 003. For a straightforward us of th dcision rul, it is nough to writ : δ 7

8 δ 8 [ ] δ 9 and rplac, by, δ δ, δ., 4. Empirical xampl : th cas of Frnch win markt Th databas usd is a cnsus of all first mis n marché. Compltnss is guarantd by th compulsory natur of th qustionnair. This databas is implmntd by ONIVINS from 987 to 003. Th qustionnair is composd of thr parts: Th first on dscribs contractors charactristics. Th scond on dscribs products: quantity, quality, color, pric of dgr/hl Th third on dfins th contract financial trms. Anonymity must b guarantd. Th first part is so limitd to gnral information. W know nithr nam nor localisation at municipal lvl In a contract, w can hav svral diffrnt products xchangd. All charactristics rlativ to thos products ar dfind. For ach on, w hav pric, quantity All products ar distinguishd and that s why w work with th unity product. W stimat a linar modl basd on charactristics of Frnch win as : color : rd, othrs 0, dgr, typ : tabl win 0, country win Th dpndnt variabl,, is th pric of th hctolitr dgr, xprssd in uros. Th rsults ar :

9 W can obsrv that introducing intraction trms incrass th quality of th modl, basd on th R² valu. Using th dcision rul, w can conclud to th undr valuation for both of th combinations : Color and dgr W obsrv that and ar positivs but is ngativ : ; ; and < So, w ar in th cas of undrvaluation. Color and typ W obsrv that and ar positivs but is ngativ : ;.60 ; and < So, w ar in th cas of undrvaluation too. In both cass, w conclud that th combination of attributs dos not incras th utility of th win product. Consumrs do not pay much for a rd win with mor dgrs combination color / dgr which is oftn considrd as bad win that for rd country win combination color / typ which is not usually considrd as a good product. A good rd win must b an AOC, whil th worst is a rd tabl win in th consumrs practics. This is why th stimat rsult validats undrvaluation and not disutility. Ths combinations rval an undrvaluation of consumrs prfrncs within th Frnch win markt.

10 5. Conclusion Obsrving Aï & Norton advics, w hav built a dcision rul for intraction trms. Th arbitration btwn ths combind ffcts is oftn omittd in th xrciss of applid conomtrics bcaus it is complx. This dcision rul incrass not only th comprhnsion of consumrs prfrncs but also maks it possibl to qualify thir bhaviors. On of its advantags is to b vry simpl of us : onc th modl stimatd, it is nough to control th sign of th cofficints and to calculat thir sum ; thn, w apply th dcision rul as prsntd in tabl to qualify th contribution of intraction trms. Anothr advantag is that this dcision rul applis as wll to th linar modls with th nonlinar modls. Rfrncs Aï, C. & Norton, E.C., 003 Intraction trms in logit and probit modls, Economics Lttrs, 80, 3-9. Ashr, M.A., Popkin, J., 984. Th Effct of Gndr and Rac Diffrntials on Public- Privat Wag Comparisons: A Study of Postal Workrs, Industrial & Labor Rlations Rviw, 38, 6-5. Bowls, S., 970 Towards an Educational Production Function, in Education, Incom and Human Capital Ed. W. L Hansn, Nw ork : NBER, pp.3-4. Fridrich, R.J., 98 In Dfns of Multiplicativ Trms In Multipl Rgrssion Equations, Amrican Journal of Political Scinc, 6, McFaddn, D., 00 Economic Choics, Amrican Economic Rviw, 9, Piccolo, D., D Elia, A., 008 A nw approach for modlling consumrs prfrncs, Food Quality and Prfrnc, 9,