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Interpreting dynamic space time panel data models

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Niveau: Supérieur, Doctorat, Bac+8
Interpreting dynamic space-time panel data models Nicolas Debarsy1 CERPE, University of Namur, Rempart de la vierge, 8, 5000 Namur, Belgium Cem Ertur LEO, Universite d'Orleans, Rue de Blois - BP 6739, 45067 Orleans Cedex 2, France James P. LeSage? Texas State University-San Marcos, Department of Finance & Economics, 601 University Drive, San Marcos, TX 78666, USA Abstract There is a great deal of literature regarding the asymptotic properties of various approaches to estimating simultaneous space-time panel models, but little attention has been paid to how the model estimates should be inter- preted. The motivation for use of space-time panel models is that they can provide us with information not available from cross-sectional spatial re- gressions. [8] show that cross-sectional simultaneous spatial autoregressive models can be viewed as a limiting outcome of a dynamic space-time autore- gressive process. A valuable aspect of dynamic space-time panel data models is that the own- and cross-partial derivatives that relate changes in the ex- planatory variables to those that arise in the dependent variable are explicit. This allows us to employ parameter estimates from these models to quantify dynamic responses over time and space as well as space-time diffusion im- pacts. We illustrate our approach using the demand for cigarettes over a 30 year period from 1963-1992, where the motivation for spatial dependence is a bootlegging effect where buyers of cigarettes near state borders purchase ?Corresponding author Email addresses: ndebarsy@fundp.

  • time panel

  • ?t ?t

  • dependent variable

  • dynamic space

  • cross-sectional spatial

  • over

  • space

  • partial derivatives


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Interpretingdynamicspace-timepaneldatamodelsNicolasDebarsy1CERPE,UniversityofNamur,Rempartdelavierge,8,5000Namur,BelgiumCemErturLEO,Universite´d’Orle´ans,RuedeBlois-BP6739,45067Orle´ansCedex2,FranceJamesP.LeSageTexasStateUniversity-SanMarcos,DepartmentofFinance&Economics,601UniversityDrive,SanMarcos,TX78666,USAAbstractThereisagreatdealofliteratureregardingtheasymptoticpropertiesofvariousapproachestoestimatingsimultaneousspace-timepanelmodels,butlittleattentionhasbeenpaidtohowthemodelestimatesshouldbeinter-preted.Themotivationforuseofspace-timepanelmodelsisthattheycanprovideuswithinformationnotavailablefromcross-sectionalspatialre-gressions.[8]showthatcross-sectionalsimultaneousspatialautoregressivemodelscanbeviewedasalimitingoutcomeofadynamicspace-timeautore-gressiveprocess.Avaluableaspectofdynamicspace-timepaneldatamodelsisthattheown-andcross-partialderivativesthatrelatechangesintheex-planatoryvariablestothosethatariseinthedependentvariableareexplicit.Thisallowsustoemployparameterestimatesfromthesemodelstoquantifydynamicresponsesovertimeandspaceaswellasspace-timediffusionim-pacts.Weillustrateourapproachusingthedemandforcigarettesovera30yearperiodfrom1963-1992,wherethemotivationforspatialdependenceisabootleggingeffectwherebuyersofcigarettesnearstateborderspurchaseCorrespondingauthorEmailaddresses:ndebarsy@fundp.ac.be(NicolasDebarsy),cem.ertur@univ-orleans.fr(CemErtur),jlesage@spatial-econometrics.com(JamesP.LeSage)1NicolasDebarsyisresearchfellowattheF.R.S-FNRSandgratefullyacknowledgestheirfinancialsupport.PreprintsubmittedtoStatisticalMethodologyAugust24,2010
inneighboringstatesifthereisapriceadvantagetodoingso.Keywords:Dynamicspace-timepaneldatamodel,MarkovChainMonteCarloestimation,dynamicresponsesovertimeandspace.1.IntroductionThereareobviouslinkagesbetweencross-sectionalanddynamicmod-els.[8]beginwiththerelationshipin(1),wherethetimelagofspatiallyweightedneighboringvaluesWyt1isintroduced,inadditiontoamatrixofexplanatoryvariablesXt.yt=ρWyt1+Xtβ+εt(1)TheN×NmatrixWisaspatialweightmatrixwhosei,jthelementtakessomepositivevalueifregionsiandjareneighborsandzerootherwise.Maindiagonalelementsaresettozeroandthematrixisnormalizedtohaverowsumsofunity.ThismeansthatthevectorWyt1representsalinearcom-binationofpreviousperiodvaluesfromneighboringregions.TheN×KmatrixXtontheright-hand-sideof(1)(whichmightincludeanintercept)isassumedtorepresentexplanatoryvariablesintherelationshipthatdonotchangeovertime(ormoregenerallyfollowsomedeterministictimepath).Recursivesubstitutionofyt1in(1)overqperiodsleadsto:yt=IN+ρW+ρ2W2+...+ρq1Wq1Xβ+ρqWqytq+ut(2)ut=εt+ρWεt1+ρ2W2εt2+...+ρq1Wq1εt(q1)(3)[8]showthatwhenqislarge,theexpectedvalueof(2),shownin(5),cor-respondstothemeanofthecross-sectionalsimultaneousspatiallagmodel,expressedin(4),whichcanbeviewedastheoutcomeofalong-runequilib-riumorsteadystate.y=ρWy+Xβ+(4)limE(y)=(INρW)1Xβ(5)qThemodelin(4)hasbeenlabeledaSARmodelinthespatialecono-metricsliteratureanditservesastheworkhorseofcross-sectionalspatial2