Parameter Estimation and Measures of Fit in a Global, General Equilibrium Model. Liu, Jing. Arndt, Channing. Hertel, Thomas

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1 Paamee Esmaon and Measues of F n a Global, Geneal Equlbum Model B Lu, Jng And, Channng Heel, Thomas GTAP Wokng Pape No Publshed n: Jounal of Economc Inegaon, 19(3):66-649

2 Paamee Esmaon and Measues of F n A Global, Geneal Equlbum Model Absac: Compuable Geneal Equlbum (CGE) models have been wdel used fo quanave analss of global economc ssues. Howeve, CGE models ae fequenl cczed fo esng on weak empcal foundaons. Ths pape bulds on ecen wok n maco-economec esmaon, developng an appoach o paamee esmaon fo a wdel emploed global CGE model, he Global Tade Analss Pojec (GTAP) model. An appoxmae lkelhood funcon s developed and he se of opmum elasc values s obaned b maxmzng hs appoxmae lkelhood funcon n he conex of a back casng execse. In addon, wo sascal ess ae pefomed. The fs of hese ess compaes he sandad GTAP elasc veco wh he esmaed ade elasc veco. I ejecs he null hpohess of equal beween he wo ses of ade elasces. The second es examnes he wdel mananed hpohess known as he ule of wo, b whch he elasc of subsuon acoss mpos b souces s se equal o wce he elasc of subsuon beween domesc goods and mpos. We fal o ejec hs common ule of humb. We conclude ha hee s much o be ganed b nesng CGE models whn an esmaon famewok as hs opens he wa fo fomal evaluaon of model pefomance and paameezaon. JEL classfcaons: C3, D5, F1. 1

3 Paamee Esmaon and Measues of F n A Global, Geneal Equlbum Model Jng Lu Channng And Thomas W. Heel I. INTRODUCTION Compuable Geneal Equlbum (CGE) models have been wdel used fo quanave analss of global and egonal economc ssues. In he Decembe, 001 ssue of he Jounal of Economc Inegaon alone, hee wee hee acles emplong a mul-coun CGE appoach o examne ade elaed ssues. Despe he popula, CGE models ae fequenl cczed fo esng on weak empcal foundaons (e.g., Hansen and Heckman, 1996; Jogenson, 1984; Sngleon, 1988; Hoove, 1995; and McKck, 1998). The use of appaenl aba values fo behavoal paamees and a lack of model valdaon ae wo fequenl cczed aspecs. Fo example, CGE modeles fequenl assume ha commodes ae dffeenaed b ogn. (Ths Amngon assumpon s emploed n all of he papes menoned above). Elasces of subsuon mus hen be specfed beween mpos and domesc goods. These Amngon elasces of subsuon have been shown o be mpoan deemnans of model esuls, paculal fo ade elaed applcaons (And, Heel, Dmaanan, Huff, and McDougall, 1997; Robes, 1994). Despe (o pehaps because of) he mpoance of hese paamees, debae ove appopae values emans conenous. In addon, supsngl lle s known abou he capac of egonal o global CGE models o epoduce he hsocal ecod. Ths pape pesens a geneal appoach o paamee esmaon and develops goodness-of-f measues fo egonal and global CGE models. The mehod s appled o esmaon of Amngon subsuon elasces n a elavel sandad global model focused on Eas Asan ade. We pose, and aemp o answe, wo quesons. Fs: wha ae he mos sensble values fo hese ade elasces, gven he calbaed sucue of he model and he hsocal ecod? Second: how well does he model ack hsocal expeence, paculal wh espec o ade flows? To do hs, he CGE model s lnked o an economec model wheen a sochasc eo s noduced o movae he goodness-of-f measues. An appoxmae lkelhood funcon s emploed o measue he sze of sochasc eos beween seleced pedced values fom he model and he hsocal daa. The se of opmum elasc values s obaned b maxmzng he appoxmae lkelhood funcon n he conex of a backcasng execse. Ths appoach enables us o dscmnae among alenave ses of paamee values, as well as geneang measues of model f o he hsocal daa. I. A Leaue Revew I.A.1 Bef Revew of CGE Model Paamee Esmaon and Calbaon A vae of appoaches have been used o oban paamees fo CGE models. B fa he mos common appoach s o specf fal pasmonous funconal foms, oban necessa behavoal paamees fom he mco-economec leaue (o ohe souces), and hen calbae he emanng paamees such ha he model pefecl epoduces a base ea daa se. Ths appoach has he dsnc advanage of no 1

4 equng me sees daa and leavng esmaon ssues o he economecans. Neveheless, ohe, moe ambous, appoaches o paamee esmaon and/o model valdaon have been aemped. Fo example, dec economec appoaches o esmang he paamees of seleced equaons appeang n CGE models have been used (Jogenson, 1984; Jogenson and Slesnck, 1997; McKck, 1998). Tpcall, ade, demand, and suppl paamees ae esmaed sepaael. Whle hs appoach s pefeable o smple calbaon based on he (nvaabl spo) mcoeconomecs leaue, And, Robnson, and Tap (fohcomng) pon o a sees of dffcules assocaed wh he dec economec appoach. These nclude: subsanal daa demands, he lengh of un of he elasces obaned (usuall annual when CGE models pcall consde longe adjusmen me fames), he song lkelhood of sucual changes dung he esmaon peod, whch s dffcul o accoun fo whou a sucual model, and falue o mpose he full se of geneal equlbum consans. Gven hese dawbacks, ohe CGE eseaches have expanded he calbaon mehod o emplo wo pons n me. In hs appoach, he eseache uns he model ove an hsocal peod and compaes esuls fo some vaables wh he hsocal ecod. These compasons can povde an nfomal bass fo evsng esmaes of some mpoan paamees. Examples of hs appoach nclude Gehlha (1994); Kehoe, Polo, and Sancho (1995); Dxon, Pamene, and Rmme (1997); and Abego and Whalle (00). Ths appoach has he advanage of mposng he full se of geneal equlbum consans. On he ohe hand, makes lmed use of he hsocal ecod and povdes no sascal bass fo judgng he obusness of esmaed paamees. And, Robnson, and Tap (fohcomng) combne he wo mehods descbed above. The use an enop-based mec o measue he capac of he model o ack elevan hsocal daa ove seveal pons n me. B endogenzng ke behavoal paamees, he paamee values ha pem he model o bes ack he hsocal ecod can be esmaed b mnmzng he enop dsance of pedced values fom hsocal ages. The enop appoach s movaed b nfomaon heo, whch deals explcl wh cases whee nfomaon s scaeed, ncomplee, o even nconssen. Ths makes he appoach aacve, paculal n he conex of developng counes. And, Robnson, and Tap pon ou a numbe of advanages of he appoach. The also pon ou lmaons. Fo example, whle he appoach pems hpohess esng hough an enop ao sasc, he sasc s known o have weak powe. In addon, And, Robnson, and Tap do no consde he exensve leaue ha has evolved assocaed wh paameezng eal busness ccle models. Ths leaue, and some of he poenal lnks o CGE model calbaon, s dscussed n Dawkns, Snvasan and Whalle (000). We now un o a evew of elevan aspecs of he eal busness ccle leaue o se he sage fo ou subsequen economec specfcaon. I.A. The Real Busness Ccle Leaue Macoeconomc, dnamc, sochasc geneal equlbum (DSGE) models can be vewed as a speces of he genus CGE model (Hoove, 1995). Thus, s useful o consde he empcal foundaons of DSGE models n he seach fo was o mpove he empcal foundaons of CGE models. DSGE models ae well epesened n he eal-busness-ccle leaue. In he followng, we evew hee sudes n he

5 busness-ccle leaue. In pacula, we consde he semnal wok of Kdland and Pesco as well as lae woks b Alug and Wason. 1 Kdland and Pesco pesen a compeve equlbum gowh model of cclcal vaances fo a se of quael economc daa fom 1950 o 1979 fo he Uned Saes. The model s a one seco, calbaed, opmal-gowh model whee he onl dvng foce n he econom s exogenous echnologcal change. Shocks o echnolog ae assumed o follow a sochasc pocess wh a deemnsc componen and a andom componen. The vaance of he andom componen s se o exacl mach he vaance of oupu n he poswa US econom. Mos paamees n hs model ae pese wh a vew o boh mcoeconomc sudes and sead sae values fo ke model oupus. Remanng fee paamees ae deemned hough a gd ach ove he sensble doman of paamee values so ha cclcal covaances n model oupus ae nea hose obseved. No explc mec s defned o fomall judge he goodness of f of he model (e.g., he exac defnon of nea ). Alug uses maxmum lkelhood mehods o esmae some ke paamees and es he assumpons undelng a evsed Kdland-Pesco model. Hs model esablshes he lnkage beween he paamees of nees, he nnovaon o he echnolog shock, and he laws of moon descbng he evoluon of equlbum quanes. Quael daa on fve maco vaables fom ae colleced and used o consuc a sample of obsevaons on he saona sochasc pocess, fom whch he lkelhood funcon can be appoxmaed. The dscepances beween obseved and model-pedced values ae egaded as measuemen eos fo each sees. The eos ae assumed uncoelaed ove me bu coelaed among sees. Mulvaae nomal s mplcl assumed fo he eo see s. The vaances of he andom componen of echnolog shocks ae endogenousl deemned n hs model. Bascall, hs sud es o answe he followng quesons: Wha s he opmum combnaon of a subse of he paamee alues n he model? And, wha s he magnude of andom echnolog shocks equed such ha a jon measue of he second momens of measuemen eos fo hose fve vaables s mnmzed? Wason suggess a new pocedue fo assessng he pefomance of he ognal Kdland-Pesco model. Unlke he maxmum lkelhood appoach of Alug, Wason abandons he null hpohess ha hs economc model s well specfed. Rahe, he model s eaed as an appoxmaon of eal whee he eo epesens he degee of absacon of he model fom he daa (p. 101). Wh msspecfcaon of he model assumed a po, he esos o devsng a measue of goodness of f fo he model. Ths measue povdes a moe fomalzed means fo judgng nea (a lacunae n he ognal wok of Kdland and Pesco, 198). Wason geneaes measues of f fo a DSGE wh a gven se of paamee values. He does no seek o esmae paamee values; howeve, he does pon ou ha hs poposed measue of f could be used as a ceon fo esmang paamees of nees. Whle quanave sudes n he dnamc macoeconomcs leaue povde a ch souce of deas, hee ae some mpoan dffeences beween macoeconomc models and mul-seco CGE models. Fs, pcal eal-busness-ccle models lke he Kdland-Pesco model ae one-good, one-agen models and have fa fewe paamees han pcal CGE models (Hoove, 1995). Second, he gowh models n he eal-busness-ccle leaue ae based on me sees whle man CGE models eman fundamenall compaave sac n naue. Ths has mpoan mplcaons fo ou pape. In he fome case, nfomaon s manl deved fom me sees daa fo evaluang model pefomance. In he lae case, nfomaon ma be deved fom muldmensonal longudnal daa (e.g., a panel of esuls acoss commodes, egons, and/o me) fo he same pupose. Thd, man macoeconomc models ae sochasc models whee he dvng foces of he econom conan andom componens and he sees beng acked (such as GDP, consumpon, nvesmen) ae non-saona and co negaed. CGE 1 We should also menon ha he woks b Sms and Sngleon ae addonal useful souces o exploe he deas of evaluang he pefomance of CGE models. 3

6 models, on he ohe hand, ae ofen sac and deemnsc. Despe hese dffeences, we beleve ha makes good sense o appl some of he deas fom he eal busness ccle leaue o he esmaon of paamees and he developmen of goodness of f measues fo CGE models. Geneal Appoach The mehod adoped b hs sud s smla o ha emploed b Alug who ulzed a sngle lkelhood ndex o esmae ccal DSGE model paamee values. In hs pape, we develop an appoxmae lkelhood appoach ha focuses on dscepances beween model pedcons and avalable daa hough me, acoss nduses and acoss egons. Hpohess ess can hen be conduced based on he concep of he lkelhood ao. The esmaon pocedue s heefoe esablshed b lnkng he CGE model wh an economec model. Followng And, Robnson, and Tap, he sucue of ou CGE model ma be descbed as a nonlnea smulaneous squae ssem of equaons: F( E, Z, C, β, δ ) = 0 T (1) whee F s a funcon geneang an I-dmensonal veco of eal values and s he me subscp, E s an I-dmensonal veco of endogenous vaables such as pces and quanes, Z s a veco of exogenous vaables ncludng faco endowmens and polc nsumens, C s he veco of coeffcens ehe compued b a calbaon execse o pese, β s he paamee veco of nees (e.g. subsuon elasces n ade), and δ s a veco of me-vaan shf paamees. CGE analss pcall poceeds b changng he veco of exogenous vaables Z, and examnng he esulng veco of endogenous vaables, E, whch sasfes he above ssem. If he exogenous vaables, Z, ae se o mach values obseved n hsocal me peods (fo faco endowmens and polc nsumens fo example), he soluon o he CGE model could be vewed as a pedced hsocal me pah fo seleced vaables of nees (such as ade shaes). The economec appoach poceeds b compang he acual hsoc me pahs fo ke vaables wh he pedced values n he followng manne: Y = G ( E, Z, C, β, δ ) + e () whee Y s an N dmensonal veco of hsocal ages, G s a funcon poducng he veco of model pedced values fo he ages Yˆ, and e s an N dmensonal veco epesenng he dscepanc beween hsocal ages and pedced values. The veco of paamees of nees, β, s endogenous and s chosen subjec o he esmaon ceon pesened n secon 4. Calbaed paamees, elemens of C, ae also endogenous wh equaons focng pefec eplcaon of he benchmak daa fo an economcall coheen veco β. Ths endogenous calbaon o he base ea mples ha e =0 n he base ea. Fo eas ohe han he base ea, he elemens of C ae effecvel exogenous and Yˆ wll n geneal dffe fom he obseved Y. O U In eal, Z ma be paoned no wo pas as {Z } = { } { Z } Z whee { Z O } ae obsevable and Z } unobsevable. Fo ease of noaon, he unobseved vaables { Z U } ae assumed consan ove me hencefoh excep whee explcl noed. { U ae 4

7 The followng secons povde moe deal on he CGE model emploed n ou sud as well as he undelng socal accounng max, he hsocal daa and he esmaon appoach. II. THE CGE MODEL We emplo a modfed veson of a sandad, global CGE model developed b Ruhefod (1998) and nck-named "GTAP n GAMS." As such, s closel elaed o man of he global CGE sudes epoed n eale volumes of hs jounal. Modfcaons o he model sucue focus on he Cobb-Douglas epesenaons of pefeences and echnolog. These ae eplaced wh Lnea Expendue Ssem (LES) pefeence sucues, and Consan Elasc of Subsuon (CES) poducon funcons. In addon, a me ndex s added o eve vaable n he model. The addon of he me subscp essenall ceaes a sees of CGE models (one fo eve elemen of he me ndex) ha ae no lnked n an wa (no explc dnamc elemens). Ths pems he model o be smulaneousl solved fo a sees of sac equlba -- each coespondng o a dffeen peod n me. The emanng feaues of hs model ae elavel sandad. Invesmen, savng, and govenmen expendue ae exogenous. Faco endowmens ae combned n a CES funcon o poduce value added. Value added combnes wh nemedae npus n a Leonef fashon o poduce fnal goods. Poducs ae dffeenaed b ogn, and mpoed and domesc goods ae combned n a nesed CES funcon n he adon of Amngon (1969) o poduce a compose good ha s ulzed domescall b fms, govenmen and he sngle pvae household. A a lowe nes, mpos fom dffeen egons ae aggegaed o fom a compose mpo commod. The elasc of subsuon acoss souces of mpos s labeled σ M. In he uppe level nes, compose mpos and domesc poducon fo each commod ae combned wh elasc of subsuon σ D. The fnal demands n each egon ae deemned b a epesenave egonal household, whch s endowed wh pma facos, ax evenue, and an exogenousl specfed ne ansfe fom ohe egons. Toal ncome s allocaed o savngs, publc demand and pvae demand. Invesmen s exogenous whle pvae and publc demand fo commodes s deemned b ul maxmzng behavo epesened b a Lnea Expendue Ssem (LES) and a Cobb-Douglas ul funcon, especvel. Inenaonal anspoaon npus ae popoonal o ade and ae defned b a Cobb-Douglas aggegae of nenaonal anspo npus suppled b dffeen counes. As wh man global models, goods poduced fo expos subsue pefecl wh goods poduced fo domesc consumpon, bu mpefecl wh expos fom ohe egons (e.g., Heel o McKbbn and Wlcoxen). III. THE SOCIAL ACCOUNTING MATRIX AND THE HISTORICAL DATA III. A 1 The Socal Accounng Max All vaables n he model, E, ae nall calbaed o he veson 4 GTAP daabase (McDougall, Elbeh, and Tuong, 1998). GTAP veson 4 povdes a full econcled pcue of he global econom n 1995 boken no 45 secos and 40 egons. Compuaonal budens peven use of he full dsaggegaed daase. Theefoe, we emplo a 10-egon b 10-seco aggegaon saeg (shown n Table 1) ha s que smla o he aggegaon saeg emplo ed b Gehlha (1994) n hs eale wo-peod calbaon execse usng he GTAP model. The emphass n he aggegaon s on Eas Asa. These economes wee among he mos dnamc dung he peod of nees n hs sud. The song shfs n ade and poducon sucue ove he esmaon peod should help o denf he undelng paamees of nees. 5

8 Table 1 Secos and Regons n he Sud Secos Regons AGR Agculue USC USA and Canada PAG Pocessed Foods MEX Mexco FMN Fuels And Mneals JPN Japan CTX Clohng And Texles KOR Koea OLT Ohe Lgh Manufacues TWN Tawan CHM Chemcals THA Thaland MEV Machne-Equpmen-Vehcles IDN Indonesa BAM Basc Manufacues CHN Chna NSV Non-aded Sevces REA Ohe Eas Asa TSV Taded Sevces ROW Res of Wold III.A. The Hsocal Daa Exenal daa sees ma be classfed no wo caegoes. The fs caego ncludes all exogenous vaables (elemens of Z ), whch ae used o shock he model backwad n me. Ths caego ncludes nvesmen, govenmen expendue, aff equvalens, ne capal nflow, and faco endowmens n fou caegoes 3 : agculual land, sklled labo, unsklled labo, and capal socks. The second caego of daa ncludes GDP, expos b commod, and mpos b commod a he egonal level. These daa seve as hsocal ages ( Y ) fo he endogenous vaables n he model. As noed above, he base ea fo he GTAP v4 daa s The eas seleced as hsocal ages ae 1986, 1989, and 199. We adop hee-ea nevals n ecognon of he medum-em naue of hs CGE model. Land, labo, capal and naonal accouns daa wee deved fom a vae of souces. Deals on he souces fo hese me sees (as well as geae deal on he daa dscussed below) can be found n Lu (001). Tme-sees ade daa wee pepaed b Mak Gehlha (1998). These daa ecod econcled blaeal mechandse ade a FOB values. Table epos he aos of 1986 o 1995 values fo hese ke vaables. Capal nflow daa wee obaned fom he Inenaonal Monea Fund. The poecon daa used n hs sud wee obaned fom UNCTAD (Cole e al.). Thee ae man lmaons n he me sees poecon daa. The mos sevee of hese lmaons s he poblem posed b non-aff baes (NTBs). The UNCTAD daa povdes us wh a coveage ao (CR) fo NTBs and we combne hs wh he aveage aff(tf) o oban a compose aff (CTF) usng he followng fomula: CTF = TF/(1-CR). Thus, a ve hgh levels of NTB coveage, he compose aff becomes que hgh. Snce we ae pmal neesed n he ao of poecon n wo peods, s changes n CR ha wll be mos sgnfcan. The mos damac changes n NTBs ove hs peod occued n agculue, beween 199 and Dung hs peod, NTBs wee conveed o affs as a esul of he Uugua Round Ageemen o sucue. Snce he objecve of hs execse was o esmae a aff equvalen fo he NTBs and hen conve he NTB o a aff equvalen, we have avoded usng a fomula fo CTF n hs case and nsead we have smpl assumed ha agculual poecon, as measued b he compose aff, was unchanged ove hs peod. A summa of he esmaed compose aff aos (1986/1995) s epoed n Table 3. Whee he en n hs able s geae han one, some lbealzaon s pesumed o have occued. Whee s less han 3 Tme sees daa se fo naual esouce (he ffh faco endowmen n GTAP veson 4) s no avalable and s assumed unchanged ove me. 6

9 one poecon s esmaed o have nceased. The mos skng esul n hs Table s he ncease n CTF fo Chna's mpos of manufacues. Ths does no appea o be epesenave of wha happened n Chna dung hs peod. The dscepanc s lkel due o he noducon of "du dawbacks" n he 1990's o pomoe manufacung expos (Ianchovchna and Man, 001). As a esul, aff collecons ae onl a small facon of ha pedced b Chna's sauo affs. Ths s bu one of man lmaons n ou poecon daa. Anohe s he absence of blaeal affs and hence aff pefeences. Ths affecs Mexco, n pacula, whch joned NAFTA ove hs peod. Unfounael, global me sees fo effecvel appled affs ae no cuenl avalable. TABLE : Summa fo Ke Vaables n 1986 (1995=1) Exogenous Vaables Tages Land Unsklle Sklled Capal Invesm Gov. GDP Impos Expos USC 101% d 94% 77% 80% en 75% Esp. 94% 81% 71% 59% MEX 91% 78% 68% 8% 89% 95% 87% 40% 44% JPN 108% 97% 76% 66% 69% 85% 77% 48% 70% KOR 108% 87% 56% 39% 36% 58% 48% 33% 40% TWN 10% 89% 59% 46% 38% 6% 53% 9% 40% THA 98% 85% 71% 41% 6% 68% 43% 19% 6% IDN 96% 79% 71% 43% 3% 68% 5% 39% 46% CHN 101% 87% 80% 43% 43% 65% 4% 3% 17% REA 89% 83% 55% 57% 43% 60% 56% 30% 38% ROW 98% 88% 67% 83% % 8% 65% 65% Table 3 Compose Taff Raos of 1986 o 1995 SECTOR USC a MEX JPN KOR/TWN CHN THA/IDN/REA ROW b AGR PAG FMN/BAM CTX OLT CHM/MEV a These aff aos efe o he Uned Saes b These aff aos efe o Wesen Euope 7

10 VI. VI.A.1 THE ECONOMETRIC MODEL Paamees o be Esmaed The focus of mos global o egonal geneal equlbum models s on nenaonal ade, and values fo Amngon paamees ae ke deemnans of model pedcons fo ade flows. Esmaon hus focuses on choosng values fo Amngon ade elasces ha allow he model o f hsocal ade paens as closel as possble (based on he mec pesened below). Whle he focus s on choosng Amngon paamees ha accuael pedc ade shaes, ohe unobsevable paamees mus also be esmaed n ode o geneae a vable epesenaon of he global econom. In pacula, aes of echncal change b acv and he endenc fo ade o consue a lage shae of economc acv mus be accouned fo. Befoe pesenng he esmao, hese wo ssues ae dscussed. Technologcal pogess s elavel eas o accoun fo. Dung he peod of hs sud, economc gowh (measued b GDP) n he Eas Asan egon canno be explaned b faco accumulaon o ohe obsevable souces of gowh (such as polc shfs ha enhance he effcenc wh whch exsng esouces ae used). Technologcal change s vewed as he emanng souce of gowh. To mplemen hs dea, Hcks-neual echnologcal pogess vaables ae noduced no he model. These vaables ae me- and egon-specfc, bu seco-genec. Accodngl, hese vaables allow he model o exacl h he GDP ages fo each egon and me peod. Accounng fo he gowh of ade as a shae of GDP s moe challengng. Snce Wold Wa II, nenaonal ade has gown much moe apdl han global GDP. A numbe of facos, such as educed affs, nceased qual and melness of anspo, and mpoved communcaons, have seved o spu he gowh of ade. Howeve, paculal ove he esmaon peod, hese facos canno explan he apd gowh n ade ha has been obseved (see Table ). One explanaon ha has been poposed s he eoson of home pefeence bases, whch McCallum (1995) and ohes have found o be ve lage, even beween he Uned Saes and Canada. Unde hs heo, mpoes have laen demand bu lle expeence wh man of he poducs avalable on nenaonal makes. The pefeences ae hus based owads home-poduced goods wh whch he have pevous expeence. Howeve, as expeence wh mpoed goods nceases, hese home pefeence bases (HPB) eode. In hs analss, we assume ha eoson of HPB accouns fo he esdual gowh n ade ha canno be accouned fo hough ohe facos (such as changes n affs and anspo coss). To mplemen hs, we add a new vaable, δ, o he CES Amngon mpo aggegao funcons. I s ndexed ove me as well as fo wo egonal goupngs he developed counes (DC) and he less developed counes (LDC). Ths new vaable acs a shfe of he CES mpo aggegao funcons. So, lookng backwad n me, fo an gven pce ao beween aggegae mpos and domesc supples (δ enes he op nes ha combnes aggegae mpos and domesc supples), δ shfs he ndffeence cuves such ha fewe mpos ae demanded. The values of he elemens of he veco δ ae consaned such ha he model pedced oal ade volumes fo DC and LDC h he ages exacl. IV.A. Economec Specfcaon We now un ou aenon o he economec model. Le (, = ( m, x (, ae mpos and expos of seco a egon a me, we ma vew ) = { ) whee m and x (, } as sacked N x N 8

11 mulvaae and we have N xn obsevaons, whee: N, N, N, and N ae he numbe of egons, secos, ages, and pons n me, especvel. The economec model has he fom: Log( / (, 95 ˆ ˆ95 ) ) ) = Log( / ) + ε (3) whee, ) = ae he calbaed mulvaae a he benchmak ea 1995; 95 ˆ95, (, ˆ ε ae he empcal sampled mulvaae, model pedced mulvaae, and mulvaae esdual, especvel. Denoe ε ~ ={ m x m x m x x m ε }=( ε, ε ) = ( ε 9, ε 9, ε 89, ε89, ε86, ε 86)' as he sacked N xn mulvaae esduals. Ou esmaon s caed ou b assumng ε ~ s mulvaae nomal wh mean veco zeo and vaance-covaance max Ω. In hs sud, ε ~ has N xn =*3=6 dmenson and oal numbe of obsevaon ε ~ (, ) s N x N =10*8=80. Snce, b consucon, oal pedced ade volumes ae equal o acual ade volumes, equaon 3 has an equvalen fom n ems of shaes: Log( S / S 95(, ) = Log( Sˆ / S 95(, ) + ε. (4) Equaon 4 focuses on he shae aos whle equaon 3 focuses on he volume aos. Theefoe, ε (, = Log( / ˆ ) = Log( ˆ S / S ). (, Ou objecve s o selec a ansfomaon funcon f such ha ε = f( ) / ) appeas as ndependenl and dencall dsbued (d) fo all nduses and egons. Once hs has been obaned, and gven he vaance and covaance max Ω of he mulvaae esduals ε ~, he appoxmae lkelhood funcon s eas o deve b followng Gallan and Holl (1980) and Alug (1989). The condonal dens fo ε gven Ω has he fom: ˆ, and 1/ ' 1 P( ε Ω )=(π ) (de Ω) exp[ ( ε ) Ω ε / ]. N N / (5) Ths apples, egadless of he exac lnkage beween he ages, he paamees of nees β, and he sae paamees of HPB and echnologcal pogess: δ ={ ς, ς, ech }. In hs sud, Ω needs o be esmaed and he concenaed log-lkelhood funcon fo paamees β, as a funcon of all obsevedε and z log L E { β, δ, Ω } = log{p( ε = Consan ( N z, β, δ, Ω)} DC ' 1 N /) * log (de Ω) - { ε Ω ε / } = Consan ( N, Hee de(ω ) s he deemnan of Ω, ( Ω LDC δ and Ω can be expessed 1 ' N /) * log (de Ω) - ( Ω ) { ε ε / }. (6) 1, ) he ace of max a posve scala. The lkelhood ao es s based on he sasc 1 ' Ω, and { ε / }, ε s k T = - [log L ( σ ~, β ~,Ω ~ k )- log L ( σˆ, βˆ, Ωˆ )] (7) E n E n 9

12 whee he fs em nsde he paenheses s he esced log-lkelhood and he second em he unesced log-lkelhood. Ou appoach movaes wo ses of valuable sascs. The log-lkelhood ao sasc n equaon 7 can be used fo hpohess ess. In addon, he vaance of he appoxmae eos n equaons 3 and 4 can be used o consuc pseudo R measues fo each vaable of he mulvaae n a manne smla o a sandad egesson model. The R sascs ma be used o compae he oveall fs unde alenave scenaos. To esmae Ω, we fs esc s sucue n ode o peseve degees of feedom. Specfcall, we adop a nesed coelaon sucue n whch he coelaon coeffcens beween mpo m x esduals ε and expo esduals ε ae assumed o be of he fom: ρ = ρ. Ths s a sensble assumpon snce hs coelaon s lagel deemned b he model sucue. The veac of hs assumpon s also confmed b pos-esmaon esdual analss. Auocoelaon s assumed o be he same fo expos and mpos m ρ _j = x _ j ρ fo all me pas (, j ). Heeoscedasc s assumed o be me-specfc. Ths s a ve easonable assumpon eflecng boh he deceasng pedcve powe of he model and he educon n daa qual as one moves backwad n me. We ae now n a poson o e-sack he mulvaae as ε ~ x = ε, ε, ε } ={( ε m,ε ), ( ε m,ε x ), 1 1 x ( ε m,ε )} wh pa-wse coelaon 3 3 ρ = ρ 1, Heeoscedasc Va( ε m ) = Va( ε x ) = addon, E( ε m ) = E( ε x ) poduc as: Ω = σ ( ( σ A ) whle 9 { 1 3 auocoelaon m ρ _j = x _ j ρ = ρ j, j and A s nomalzed and fxed as una. In =0. These assumpons ma be expessed usng o denoe he Konecke R _ A R ) M X p 89 p ρ 9 89 R M _ X =, R = ρ 1 p89 1 p86, and A = 0 0 A 89. (8) 9 89 p86 p A 86 The hee maces above epesen: he pa-wse coelaon max beween mpos and expos (R m_x ), he auocoelaon max (R ), and he nomalzed heeoscedasc max (A ), especvel. In hs sud, he elaonshps beween he esduals and he elemens of Ω ae mplemened as a se of consans. The whole CGE model s also conveed no a se of consans. The appoxmae loglkelhood funcon (equaon 6) s he objecve funcon of he esulng opmzaon poblem. The objecve ma be expessed as a eal valued funcon of esduals and elemens of Ω, whch ae ulmael elaed o he ade elasces. We now un o he esmaon of elemens n Ω = σ ( A R ) R M _ X. Geene (1993, p ) pesens a lengh dscusson of hs ssue. Due o space consans, we appeal hee o he eade's nuon. We fs esablsh he lnkages beween he elemens of Ω and esduals b means of he lnea ' 1/ ' ansfomaon ε =ε. Ω whee ansfomed esduals ε ae ndependen of each ohe (Geene, 1/ p36). In so dong, we can ehe compue Ω o decl lnk he elemens of Ω wh esduals. To educe he compuaonal buden, we use a sep-b-sep esdual ansfomaon appoach. The heeoscedasc acoss me A s saghfowad o esmae as: 10

13 A = 9 m A * (, )) +, m x [( ε ( ε (, )) ]/ [( ε (, )) + ( ε (, )) (9) x, 9 9 ]. Nex, we oban he ansfomed esdual 1 1m 1x ε =( ε, ε )= ε / A whch s fee of heeoscedasc. The nex ansfomaon nvolves coecng fo he coelaon beween expos and mpos: ρ = {,, ε ( m (, ) ε )( A Snce he coelaon max x m x (, ) ε (, ) ε (, ) 1/ ) }/{( ( ) ) *( ( ) )}. A A A M X,,,, R _ s posve defne, P = ( R 1/ M _ X ) (10) s guaaneed o exs. Tansfomng he heeoscedasc-fee esdual 1 ' ε ) b pe-mulplng P, we have ε = P. 1 ' m ' x ' ε, whch s coelaon-fee beween ε and ε, wh expeced vaance Va ( ε )= σ. The same appoach s appled fo esmang auocoelaon as: m m ρ = ' (, ). ε ' (, ) + 1, ( ε ε /( N x x 1 ε ' 1 (, ). ' (, )) R. Hee, he coeffcens 1 ρ ae esmaed N N σ ). (11) ' " 1/ ' Tansfomng ε esuls n new esdual ε = ( R ) ε, whch s fee of coelaon, " auocoelaon, and heeoscedasc. We have expeced vaance Va ( ε )= σ. In addon, " m x ε s dsbued nomall snce ε and ε ae b assumpon nomall dsbued and all ansfomaons ae lnea. " Fnall, he followng elaonshp beween he esmaed σ and ε ma be esablshed: σ =,, [ε ] /( N N N N ). (1) " " 1/ Fuhemoe, ma be shown ha ε = Ω ε and he log-lkelhood funcon coespondng o equaon 7 s: log L = N N E N [log( π ) + ln σ ] N N ln A + ε N N [log ( R )]/ + M _ X " " N N N [log ( R ) ] / -{[ e ] [ e ]}/ σ (13) " " whee e s he gaheng of all sacked ε. The objecve funcon s -log L E and equaons 8-11 " " ae mposed as consans. The onl paccal dffcul s o se up he em {[ e ] [ e ]}/ σ. A fs 1/ glance, seems ha we need o compue he squae oos of he nveses of [ R and ( Howeve, onl [ R and 1 M _ X ] 1/ 1/ funcon nvolve ehe [ R o ( R ). M _ X ] ( M _ X ] 1/ R ). 1 R ) ae equed, snce nehe consans: 8-1, no he objecve 11

14 A fnal se of consans mposed on he esmaon pocedue elaes o he elave magnudes of Amngon elasces n he uppe and lowe ness. Recall ha he lowe nes (wh assocaed elasc paamee σ M ) aggegaes mpos acoss souces fo a gven commod whle he uppe nes (wh assocaed elasc paamee σ D ) combnes hs mpo compose wh domesc goods. Global models commonl assume ha σ M = σ D. Ths assumpon daes back o he wok of Jomn e.al (1991) undeaken n suppo of he SALTER model of global ade. In he compehensve evew of economc eseach on ade ela sces, Jomn e.al fnd ha mos sudes focused on esmang he uppe level obsucon elasc, σ d, wh elavel few esmaes of σ m. Fo hs eason, he sough a "ule of humb" lnkng hese wo paamees. Usng eale esmaes of boh σ D and σ m b Coado and de Melo (1983) as a jusfcaon, he adoped he "ule of wo": σ m = * σ D. In hs pape, we fs mpose hs escon and lae es s vald. IV: IV.A.1 RESULTS Paamee Esmaon Table 4 dsplas he esmaed esuls. I s neesng o compae he esmaed values o hose paamee values assocaed wh he GTAP veson 4 global daabase, whch ae also pesened n Table 4. 4 Based on hs compason, he GTAP elasces seem o be oo small fo pocessed food (PAG) and moo vehcles and eleconc machne (MEV), and oo lage fo agculue (AGR), Clohng and Texle poducs (CTX), Fuels and Mneals (FMN), and Basc Manufacues (BAM). The GTAP elasces ae que close o he esmaed values fo ohe lgh manufacues (OLM), and Chemcals (CHM). Table 4 Cuen and Esmaed Tade Elasces Indus GTAP Esmaed Indus GTAP Esmaed AGR * OLT.15.3 PAG CHM FMN MEV CTX BAM The esmaes LS ae obaned fom Table 5.5 of las chape *Ths value s a s lowe bound Table 5 dsplas he esmaes of he home bas pefeence paamee values ς and DC ς LDC. Ths paamee has been scaled o ndcae he popoonal educon n mpo volumes ha would occu, a consan pces and ncomes, as one moves backwad n me fom 1995 o 199, 1989 and The eoson n home pefeence bases has been apd, paculal n LDCs. The mos apd ae of HPB shf seems o occu n he peod fom 1986 o 1989 fo boh DC and LDC egons. Table 5 Home Pefeence Bases Shf Paamees (1995=1) Developed Counes Less Developed Counes GTAP elasc values have been emploed b a lage numbe (hundeds) of sudes of global ade. In ode o oban a samplng of hese sudes, go o and selec Resouce Cene Applcaons. 1

15 Table 6 dsplas he esmaes of he paamees n he covaance max Ω. 5 Thee s evdence of auocoelaon, heeoscedasc, and coelaon beween expos and mpos. The eo ems ae especall hghl coelaed beween 1989 and 199. Exsence of song coelaon beween daa sees ends o dscoun he nfomaon conen. In effec, we have less nfomaon han would be he case whee all obsevaons ndependen. The hgh value of heeoscedasc efleced n he value of A 86 heavl dscouns he 1986 ages n he penal funcon, pung nsead a lage wegh on moe ecen daa. Ths pobabl makes good sense, gven he dffcul nvolved n consucng he hsocal me sees. Table 6 Esmaed Covaance Max Ω ρ 9 ρ 89 9 ρ ρ Α 86 9 Α 89 Α V.A. Measues of F As noed above, ou appoach movaes wo ses of descpve sascs fo he global CGE model. In hs secon, we focus on he pseudo R-squae sascs o measue he goodness-of-f fo he CGE model. In a smple, lnea egesson model wh a consan em, he R value based on leas squaes esmaon s an mpoan measue fo evaluang he f of he egesson. The R s calculaed as 1- SSR/SST whee SSR s he sum of squaed esduals and SST s he sum of squaed devaons of he dependen vaable. In hs case, he R value s nepeed as he popoon of vaaon explaned b he ndependen vaables. If he egesson does no conan a consan em, we can oban an analogous, pseudo-r value, whou compung he devaons fom means (Geene, p155). The compuaon of a pseudo-r n ou case s smla o ha fo a egesson model whou consan em. Consde he model defned n equaon 4. 6 We defne SSR and SST as: SSR = [ε, ] SST = [log( S / S95 )] (14), Ths defnon has some meanngful mplcaons n he CGE conex. As we know, he R measues ae nall nended o evaluae he conbuon of ndependen vaables n a lnea egesson model o educng he vaaon of he dependen vaable, measued as SST. In a smple lnea egesson model wh consan em j = α + β x j, SST = [ j ]. The em eflecs a naïve guess fo he j value of j n he absence of he model; and SST s he sum of squaed devaons of he dependen vaable fom hs naïve guess. Analogousl, we ma defne n CGE conex: 5 We have conduced an analss of he esduals o es he assumpons of nomal as well as he andomness of specfcaon on Ω. These esuls sugges ha ou economec model s well-defned. ε, and he 6 Please noe ha R-Squae values wll change f we use anohe model (e.g. equaon 3). 13

16 SST = [ Log( S / S95 ) Log( S& / S95 )] (15), whee, S& denoes he bes guess whou he CGE model. Aguabl, he bes naïve guess s o assume he shae sucue a me emans he same as he benchmaked shae sucue, o S& = S ). Theefoe, Log( S& / S95 ) = 0 and we have equaon Table 8 dsplas he Analss of Vaance (ANOVA) able fo ou model. We fnd ha ou model explans abou 30-65% of oal vaaon. I s no supse ha hese R-squaes ae elavel low. Ths s due o he naue of hs sud whee coss secons of ndvdual daa ae analzed and he model s a damac smplfcaon of eal. We also noe ha he R values fo mpos n 199 and 1989 ae lowe han ha fo he ea 1986 whle he evese s he case wh espec o expos. Table 7 also pesens esuls usng he sandad GTAP elasc values. Calculaon of he opmal elasces pmal mpoves he f of he model wh espec o expos. Measues of f wh espec o mpos change onl magnall. Table 7 Analss of Vaance* Impos Expos Opmum Tade Elasces Toal Vaaon Explaned Vaaon Resdual Vaaon Pseudo-R 8.9% 4.5% 65.6% 44.3% 3.9% 38.0% Cuen Tade Elasces Toal Vaaon Explaned Vaaon Resdual Vaaon Pseudo-R 30.4% 41.0% 64.6% 35.6% 4.9% 33.5% * ˆ Log S / S = Log( S / S ) + ε ) ( V.A.3 Hpohess Tess The second use of he descpve sascs geneaed b ou appoach o esmaon s hpohess esng based on he lkelhood ao es usng equaon 7. The fs es we consde nvolves explong whehe k he opmum esmaes of ade paamees σˆ, sgnfcanl mpove he model s pefomance wh he k k cuen GTAP elasces, σ 0. The null hpohess s: H 0 : σ = σ k 0. Table 8 dsplas he esuls of he es. The fs wo columns show he values of he log-lkelhood, fs unesced and hen wh he escons assocaed wh he null hpohess. The hd column consucs he log-ao sasc. 7 The 7 In lgh of he fac ha one of he esmaed paamees eaches he lowe bound n he unesced model (Table 4), hpohess es s acuall a consevave one, snce he log-lkelhood ao whou bounda escon would be lage. 14

17 fouh column shows he pobabl of he null hpohess gven he sasc n column hee. Accodngl, we ejec he null hpohess. Theefoe, he cuen GTAP elasces ae assocaed wh a sgnfcanl pooe f of he hsocal ade shaes, compaed wh he esmaed elasces. TABLE 8: Resuls of Fs Hpohess: GTAP Paamees Imposed Log-Rao Mec log( L ˆ U ) log( L ˆ R ) C = log( Lˆ / ˆ R L ) P( λ 8 c) u In he second hpohess es, we examne he elaonshp σ M =σ D : he so-called "ule of wo." So fa, hs has been a mananed hpohess. To es he escon, we le σ M =ω σ D n he unesced model. The esced model s he fomel unesced model shown n he fs column of Table 8. The null hpohess s H 0 : ω =, and he pobabl of hs null hpohess, gven he log ao sasc n column hee s Accodngl, he null hpohess s no ejeced. Table 9 Resuls of Second hpohess: Rule of wo Log-Rao Mec log( L ˆ U ) log( L ˆ R ) C = - log( L ˆ / ˆ R Lu ) P( λ 8 c) ωˆ VI. CONCLUSIONS AND FUTURE DIRECTIONS FOR RESEARCH Global CGE models ae wdel used fo economc eseach and analss of ade polc quesons. Howeve, hese models ae wdel cczed fo esng on weak empcal foundaons. Specfcall, ke paamees ae ofen gleaned fom unelaed economc sudes, and CGE modeles ael valdae he models agans he hsocal ecod. In esponse o hs defcenc, he pesen pape develops an economecall based appoach o paamee esmaon fo a vaan of he wdel used GTAP model of global ade. Ths appoach bulds on an appoxmae lkelhood funcon nsped b he ecen leaue o dnamc, maco-economecs. The se of opmum ade elasces s obaned b maxmzng hs lkelhood funcon n he conex of a model backcasng execse ove he peod 1995 o The appoxmae lkelhood funcon also pems us o develop a fomal famewok fo hpohess esng whch s used o es wo null hpoheses abou he ade elasces n ou model. The fs of hese s he hpohess ha he ue elasces ae equal o he ade elasces cuenl n he GTAP paamee fle. Ths s ejeced. We fnd ha he wo ses of elasces dffe mos fo pma agculue and fuels and mneal poducs (GTAP values ae oo lage), wheeas he GTAP esmaes fo pocessed food poducs, moo vehcles and eleccal machne ae oo small. The second null hpohess esed s he wdel emploed "ule of wo", wheeb he elasc of subsuon among mpos fom dffeen souces fo a gven poduc s se equal o wce he value of he domesc-mpo subsuon elasc. We fal o ejec hs hpohess, heeb lendng addonal cedence o hs ule of humb. Fnall, we develop a goodness of f measue, whch s analogous o he pseudo-r used n egesson analss. Ths pems us o assess how well he fed model pedcs hsocal behavo, compang he 15

18 "goodness-of-f" of alenave model specfcaons whn he same boad economec model. An neesng exenson of hs measue would be o use o evaluae he ndvdual conbuons of he dffeen exogenous shocks (e.g., aff educons, endowmen shocks, ec.) n a manne analogous o faco decomposon analses n egesson models. In summa, we beleve ha hee s much o be ganed b followng he lead of he dnamc macoecomecans n nesng CGE models whn an economec famewok ha adms eos due o model specfcaon and measuemen poblems. Whle such effos ae exemel me-consumng - no leas due o he challenge of obanng hsocal me sees fo he model shocks and ages -- he also pomse o bea consdeable fu. I s onl b pedcng he pas ha CGE models wll gane cedbl fo analss of he fuue. 16

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