A Two-Step Approach to Estimating State-to-State Commodity Trade Flows *

Transcription

1 A wo-step Approach to Estmatng State-to-State Commoty rae Flows * JYoung Park Von Klensm Center 382 School o Polcy, Plannng, an Development nversty o Southern Calorna Los Angeles, CA Emal: youngp@usc.eu Phone: (213) Peter Goron Ralph & Goly Lews Hall 321 School o Polcy, Plannng, an Development nversty o Southern Calorna Los Angeles, CA Emal: pgoron@usc.eu Phone: (213) James E. Moore II Ethel Percy Anrus Center McClntock Avenue, nversty o Southern Calorna Los Angeles, CA Emal: moore@usc.eu Phone: (213) Harry W. Rcharson Ralph & Goly Lews Hall 212 School o Polcy, Plannng, an Development nversty o Southern Calorna Los Angeles, CA Emal: pgoron@usc.eu Phone: (213) * An earler verson o ths paper was presente at the 2004 Natonal IMPLAN ser s Conerence, Shepherstown, West Vrgna, SA, October 6-8. hs research was supporte by the nte States Department o Homelan Securty through the Center or Rsk an Economc Analyss o errorsm Events (CREAE) uner grant number N However, any opnons, nngs, an conclusons or recommenatons n ths ocument are those o the authors an o not necessarly relect vews o the nte States Department o Homelan Securty.

2 A wo-step Approach to Estmatng State-to-State Commoty rae Flows ABSRAC A maor problem n evelopng nterregonal-nternustry moels, nclung multregonal nput-output (MRIO) moels, s how to combne seemngly ncompatble atabases. hs research ams to estmate state-to-state commoty trae low tables by maor nustral sectors or the.s. useul or creatng an MRIO-type moel, the Natonal Interstate Economc Moel (NIEMO). he moel s base on IMPLAN an relate ata or Constructng NIEMO was challengng because o the lmte avalablty o commoty reght shpment ata between the states. hs helps to explan why a Chenery-Moses-type moel such as NIEMO has not been evelope n recent years. wo basc sets o are necessary to construct NIEMO. Interregonal trae tables to estmate trae coecents by states an nustry ha been avalable rom the.s. Commoty ransportaton Survey Data snce 1977, but reportng was scontnue or some years. For the years snce 1993, ths ata ect can be met to some extent wth the recent (CFS) ata rom the Bureau o ransportaton Statstcs (BS). Avalable snce 1993, the CFS ata are wely use, but they have several nherent problems. Recent attempts to estmate nterregonal trae lows usng ata rom the 1997 Commoty Flow Survey (CFS), base on IMPLAN ata mae ths clear to us. hs stuy suggests a new approach to estmatng the trae tables between all 50 States plus D.C. an the rest o the worl. hese tables are assemble va a two-step metho, to aust or ncomplete reporte trae lows, an to upate the auste trae lows by estmatng values va a Fratar Moel base on the 1997 Commoty Flow Survey (CFS) ata. Reconclaton o the IMPLAN an CFS atabases present varous problems that are aresse n ths paper. Keywors: Interstate trae lows; auste low moel; oubly constrane Fratar moel JEL classcatons: C61, C63, F17

3 I. Introucton Input-output moels are among the most wely use tools or the evaluaton o economc mpacts. In aton, recent economc sruptons rom natural or man-mae sasters have prompte economsts to evaluate these events economc mpacts. Analysts have starte to conser the possblty o sruptons that may or may not nvolve many ataltes but that coul cause enormous economc losses. Concerns lke ths have also recently rsen to the top o many government agency s research agenas. Generally, natonal IO moels aggregate over large numbers o verse regons. However, the sasters uner scusson shoul be stue by tracng eects va nter-regonal commoty lows as well as nter-connecte nustres, because the economc mpacts have an nevtable spatal ncence. hs suggests ang spatal etal to tratonal IO approaches. Frst, poltcal representatves have an obvous nterest n ther own consttuency an urscton. Secon, subnatonal mpacts can cancel each other n the aggregate, causng natonal measures to obscure key mensons o the event. Mult-regonal nputoutput moels (MRIO) suggest an attempt at regonal saggregaton but these are cult to construct: Sub-natonal trae ata are har to evelop even though commoty low ata between regons an states o the.s. are publshe every ve years. An ntegrate moel o losses throughout the.s. economy requres that spatal connectons between states be accounte or. A maor problem n evelopng ntegrate nterregonal-nterternustry moels s how to combne not easly compatble atabases. Although Chenery (1953) an Moses (1955) ormulate an nterregonal ramework base on the early scusson o Isar (1951), ata problems stll styme applcatons. hs explans why an operatonal Chenery-Moses moel has not been ormulate n the nterval ollowng Polenske s (1980) an Jack Faucett Assocates (1983) ntal contrbutons. Also,.S. Commoty ransportaton Survey reports on nter-regonal trae lows snce 1977 have been scontnue. he earth o ata can be met to some extent wth the Commoty Flow Survey (CFS) rom the Bureau o ransportaton Statstcs (BS), but currently avalable CFS ata are ncomplete wth respect to nterstate lows. he prmary purpose o ths stuy s, thereore, to suggest a useul way to create trae lows between.s. states as the bass or a new MRIO, the Natonal Interstate Economc Moel (NIEMO), or the.s. Drect economc mpacts are relatvely easly estmate n the atermath o a saster or attack. I plausble scenaros or the tme-prole o reuce shppng acltes are avalable, spatally etale nrect an nuce economc eects can be estmate wth a NIEMO-type moel. Stanar applcatons o IO etermne nrect an nuce mpacts that typcally o not nclue nteractons among nustres an states. o estmate such short-term mpacts, mult-regonal moels consstng o two sets o tables, regonal coecents tables an trae coecents tables, are approprate (Mller an Blar, 1985). hese Chenery-Moses-type moels can be use to estmate nter-state nustry eects as well as nter-nustry 1

4 mpacts n each state. o procee ths way, t s necessary to calculate mult-regonal nustry coecents among.s. states; the regonal tables that gve us ntra-regonal nustry coecents by state an the nterregonal trae tables to gve us trae coecents by nustry. hs paper, thereore, suggests a sequence o computatonal steps or estmatng nter-state trae lows requre to mplement such a moel. o construct trae tables between all 50 states plus D.C. an the rest o the worl, we apple an Auste Flow Moel (AFM) an a Doubly-Constrane Fratar Moel( DFM) that s base on 1997 CFS an 2001 IMPLAN ata. Due to the erent nustral coe systems that characterze the two ata sources, however, reconclaton o the IMPLAN an CFS atabases presente several problems that are scusse n the next secton. here we escrbe the SC (reconcle) Sectors, whch are evelope to enable a mappng between the two coe systems use n the North Amercan Inustry Classcaton System (NAICS), the Bureau o Economc Analyss (BEA), an the new 509-sector IMPLAN moel. he thr secton o ths paper explans two ata mprovement methoologes, the Auste Flow Moel an the Doubly-Constrane Fratar Moel. We show the estmate results n the ourth secton. II. Backgroun As Lahr (1993) ha note, a maor problem n evelopng a MRIO-type moel stems rom the act that t s cult to obtan ata representng.s. trae lows between the states, not to menton the problem o ata reconclaton. Actually, the.s. Commoty ransportaton Survey Data on nterregonal trae lows ha been avalable snce 1977, but reportng was scontnue or some years. For the years snce 1993, ths ata ect can be met to some extent wth the recent Commoty Flow Survey (CFS) ata rom the Bureau o ransportaton Statstcs (BS). Whle the CFS ata have been wely use, they have several nherent problems (Erlbaum an Holgun-Veras, 2005:3). he most serous one among them s that the CFS ata o not nclue trae lows below the state level but also these are not complete trae lows, even between the states. For these reasons, there has been no comprehensve nventory o lows snce the test moels prove by Polenske (1980) an Faucett Assocates (1983). he exstence o many unreporte values requres relyng on other ata sources or completeness. Harrgan et al (1981) compare ol methoologes to estmate nterregonal trae lows an showe more normaton, better results base on 1973 Scotlan ata;: All o ther technques are smple ratobase methoologes. A smlar eort to estmate trae nlows below the state-level usng the CFS, Lu an Vlan s (2004) locaton quotents requre very restrctve assumptons, resultng n szable errors n the estmates. Base on the approach o Wlson (1970) an Batten (1982), Cannng an Wang (2005) suggeste a new metho or estmatng nterregonal trae lows or MRIO an IRIO moels, along wth an emprcal test o perormance. Recently, larger scale eorts to overcome the shortcomngs n CFS have 2

5 been conucte by FHWA/S DO, by combnng other ata sources usng a log-lnear moel. he new Freght Analyss Framework (FAF) s a comprehensve atabase or polcy analyss or 2000 (SDO, FHWA, 2002): It not only proves more comprehensve normaton on reght lows by moe, usng the same sector coes as the CFS, but t also orecasts uture reght actvtes. he contnuous eorts to mprove the FAF ata set mae t possble to release the latest verson o FAF 2.2 n November 2006 (SDO, FHWA, 2006). Yet, these ata stll have screpances relatve to other ata sources ue to the ncluson o servce sector values n the commoty sectors. he two recent stues use the CFS an IMPLAN ata as ther basc ata set. Jackson et al. (2007) use IMPLAN ata to aust ncomplete CFS normaton prmarly by aoptng a Box-Cox transormaton as well as ouble-log stance-ecay unctons. Also, because there are no trae ata or servce sectors n CFS, the authors use the average coecents or all other servces, but each servce nustry may have very erent coecents rom the average (Park, 2006). Further, accorng to the CFS entons, oregn mports that are transporte rom port o entry to the estnaton state have been nclue n the CFS nter-state commoty low. 1 However, n the IMPLAN ata, oregn mports reer to the mports whch are consume n the local area. he oregn mports that are not consume n the local area an transporte to other state(s) are exclue rom the state or county-level IMPLAN ata (Park et al, 2007; Gulano et al, 2006). hereore, t s necessary to aust or the gaps between the two approaches. he secon attempt nvolves usng a oubly-constrane gravty moel base on county-level ata rom IMPLAN an ton-mle ata rom CFS (Lnall et al, 2005; or the moel, see Lee, 1973). hese authors use three ata sets or ths estmaton: Oak Rge Natonal Labs (ORNL) or county-to-county stances by moe o transportaton, CFS or ton-mles by sector, an IMPLAN ata or total supply an eman by county. he ORNL ata support an mpeance nex as a combnaton o stance, tme, an cost act (Lnall et al, 2005: 4) when entyng employment centros. he CFS ata are use or a crteron nex to etermne whether the average o the estmate ton-mles s matche to the CFS tonmles or not. However, there may be three problems when usng the CFS ata. Frst, t s stll not clear whether Lnall et al constructe a compatble ata brge between the CFS an IMPLAN ata. Secon, though the IMPLAN ata only support ollar values wthout tonnage normaton, the authors not report on a mechansm to convert IMPLAN estmates, whch are ollar values, to ton values to compare estmates o average ton-mles. Fnally, IMPLAN ata are not shpments but transacton values, so the 1 An anonymous reeree, who we thank, ponte to the nature o the problem. he CFS oes not nclue mporte goos whch are out o the survey's scope. But some mports o enter CFS nter-state movements (nclung nonlocal ones) they are hanle once they arrve n the S. However, the extent o ths eect s unknown. I an mport s not shppe omestcally by a.s. shpper (ater transer o ownershp) who s also wthn the scope o the CFS sample rame, then these goos are not capture by the CFS. Hence, the reconclaton wth the IMPLAN mport values may stll be problematc. Conceptually, they are thereore not truly reconcle. Our eorts reman an approxmaton. 3

6 ata must be auste by ollowng the CFS entons, as mentone above. Further, Lnall et al set the exponent n ther gravty unctons to a value o two or non-servce sectors. However, they seemngly set these values hgh (though not reprote explctly) or the servce sectors nuce lower volumes n these sectors traes. In the servce sector cases, because there s no ton-mle normaton n the CFS, t s stll unclear how they estmate trae lows or servce sectors. Although they nclue many caveats, ther results may be the rst attempt to estmate trae lows at the county level. he common problem wth all o these attempts s that there s no clear scusson o how to estmate trae lows base on elaborate reconclatons between IMPLAN s sectors an the SCG sectors o the CFS. Also, t may be unorme to accept such low levels o trae or the servce sectors, an ths mportant assumpton mght prouce storte results. III. Data Reconclaton Basc ata or our stuy are obtane rom the 1997 CFS an 2001 verson o IMPLAN. he 1997 CFS reports trae lows between.s. states, although the low ata are not complete because o hgh samplng varablty or sclosure lmts on nvual company status. Yet, these ata can be a useul base-lne to upate to 2001 usng 2001 IMPLAN ata. However, ncompatblty between erent coe systems rom erent ata sources s especally problematc. here s no stanarze an teste converson brge. o estmate 2001 trae lows rom the 1997 CFS, thereore, requre varous ntermeate converson steps between the SCG coe system use n the 1997 CFS an the IMPLAN system o sectors, because there are not always one-to-one matche pars between BEA an NAICS coes. Our approach ollowe the ata reconclaton process suggeste by Park et al (2006) so as to create a SCG-IMPLAN converson brge enablng aggregaton o 509 IMPLAN sectors to 43 SCG sectors. he varous matches are shown n Appenx 1. Another reconclaton task between IMPLAN an CFS ata concerns basc concepts. For example, base on CFS entons, oregn mports that are transporte rom a port o entry to the estnaton state are nclue n CFS nter-state commoty low. However, n the IMPLAN ata, oregn mports reer to mports that are consume n the local area. hose oregn mports that are not consume n the local area an transporte to other state(s) are exclue rom the state or county-level IMPLAN ata. o make the concept o nter-state commoty low consstent wthn these two ata sources, Foregn Imports n the IMPLAN ata ( IM I ) are auste by vng by ratos that enote the proportons o Foregn Imports summe over every state s. oregn mport or 29 SC commoty sectors. Auste oregn mports ( a I ), thereore, wll nclue the oregn mports consume n other states ( c I ) as well as the oregn mports consume n the local area corresponng to the port o entry ( IM I ). 4

7 able 1. Reconclaton o 2001 IMPLAN Data wth 1997/2002 CFS Proucer Prces by SC Sector Sectors 2001 IMPLAN 2002 CFS_Revse 1997 CFS_Revse 2002 Rato 1997 Rato SC V1* P1** V4 P4 V5 P5 V1/V4 P1/P4 V1/V5 P1/P5 SC01 192, % 171, % 153, % SC02 130, % 131, % 115, % SC03 45, % 41, % 50, % SC04 86, % 86, % 79, % SC05 302, % 263, % 252, % SC06 80, % 76, % 58, % SC07 54, % 49, % 36, % SC08 20, % 19, % 17, % SC09 11, % 14, % 11, % SC10 480, % 270, % 253, % SC11 104, % 120, % 126, % SC12 174, % 300, % 158, % SC13 22, % 29, % 23, % SC14 159, % 172, % 154, % SC15 231, % 248, % 201, % SC16 122, % 115, % 113, % SC17 154, % 160, % 158, % SC18 133, % 106, % 202, % SC19 292, % 316, % 236, % SC20 113, % 114, % 87, % SC21 169, % 213, % 240, % SC22 200, % 199, % 193, % SC23 433, % 424, % 347, % SC24 844, % 799, % 733, % SC25 654, % 620, % 481, % SC26 143, % 157, % 124, % SC27 160, % 166, % 118, % SC28 92, % 82, % 59, % SC29 436, % 404, % 295, % otal 6,047, % 5,880, % 5,085, % * nt: (mllon$) ** {(Each SCG sector value)x100}/ (otal). Wth ths reconclaton, some mnor manual austments are stll requre on the bass o ugment. Sector names o 5-gt SCG sectors an 6-gt NAICS sectors are use to aust even proportons (the eault assumpton) assocate wth aggregaton n cases nvolvng mappng sngle or multple sectors to multple sectors. Also, a proucer/purchaser ollar value austment was mplemente because the IMPLAN ata nclue proucer values, whle CFS ata are base on purchaser values that nclue transportaton cost, wholesale markup, an retal markup beses the proucer values. he steps nvolve n ata reconclaton, the enton o SC Sectors, an the qualty o results are escrbe n Appenx 2. Base on the the two Appenx ables 2e an 2 an the SC Sectors ene n Appenx able 2g [***HERE IS NO 2.G], able 1 shows the nal 2001 IMPLAN reconclaton wth 1997 an 2002 CFS ata expresse n proucer prces by SC Sector. he value ratos (=V1/V4) between the 2001 IMPLAN ata an the 2002 CFS ata are nearly one across the SC Sectors. 5

8 IV. Moel A two-step approach va an Auste Flow Moel (AFM) an a Doubly-Constrane Fratar Moel (DFM) was evelope base on the ata brges to reconcle erent ata coe systems. Estmates o 2001 commoty trae lows among all 50 states plus Washngton, D.C. an the rest o the worl were evelope rom the orgnal 1997 CFS ata or the 29 SC Commoty Sectors. he rst step n applyng the DFM s to estmate unreporte values or a varety o commotes n the 1997 CFS. hese nclue some margnal values such as total shpments orgnatng n each state, total shpments estne or each state, an the matrx o cells representng commoty trae lows between varous pars o states. he 2001 IMPLAN ata report total commoty orgn an estnaton values by state. Hence, the 2001 commoty trae lows can be estmate by usng a Fratar moel to upate the (complete) 1997 CFS low. Ater suggestng notatons o key-varables n Secton IV-1, the proceures or estmatng mssng values are escrbe n the Secton IV-2 an upate estmates appear n Secton IV-3. IV-1. Descrpton o Varables Auste Flow Moel: O (or D ) Reporte total orgn (or estnaton) values o state (or ) rom CFS. O (or IM O (or IM D ) D ) nreporte total orgn (or estnaton) value o state (or ) rom CFS IMPLAN total orgn (or estnaton) value o state (or ). mv 1997 CFS reporte total value o each SC Sector m. IM S otal supply commoty. IM N (= IM N ) IMPLAN net omestc proucts o state, where =. IM E Domestc exports rom state. IM E Foregn exports rom state. IM I IMPLAN oregn mports to state that reman n each state. c I Foregn mports to state that are consume n other states. a I Auste oregn mports to state. IM I Domestc mports to state obtane rom IMPLAN ata. V rae low values between states an that are unreporte n the CFS. R p (or R ) otal unreporte CFS resuals or states (or ). p 6

9 Doubly-Constrane Fratar Moel: Ô (or Dˆ ) otal orgn (or estnaton) value or state (or ) reporte n the 1997 CFS or the values estmate usng the AFM. IM ND Net agonal entres n a trae matrx or state. IM NO (or NO (or NO (or IM ND ) IMPLAN net total orgnatng (estne) values n state (or ). ND ) ND ) Net values o outputs IM ND. IM NO (or Net values o Ô (or Dˆ IM ND. IM ND ) ater exclung the corresponng agonal ) ater exclung the corresponng agonal outputs IV-2. wo-step Approach: Auste Flow Moel (AFM) otal orgn an total estnaton values must be xe to calculate the unreporte trae lows between the states. Let reporte total orgn an estnaton values rom CFS be calculate unreporte total orgn (output) value o state (= O O an D respectvely. o ), the rato o 2001 IMPLAN total orgn o state (= IM O ) to the sum an 1997 CFS reporte total value o each SC Sector m (= mv O O m ) ( D D ) m a specc SC Sector m. (, m 1,..., 29 ) s use as shown n equaton (1), base on O = IM IM O O V, (1) All these are supporte by IMPLAN ata. Also, IM O = IM S + a I. (2) where IM S = IM N + IM E + IM E, enotng total commoty supply, IM N s net omestc proucts (= IM E s omestc export, an IM E s oregn export. IM N, ), 7

10 hence the IM O shown n equaton (2) can be rewrtten as, IM O = IM N + IM E + IM E + a I. (3) hs s because oregn mports shoul be counte n the trae lows n.s. omestc trae, or (IMPLAN oregn mports to state, that remans n each state) plus IM I c I (oregn mports to state that are consume n other states), once commotes are mporte. Hence, auste oregn mports are shown as, a I = IM I + c I, (4) although IMPLAN ata nclue only values IM I. Also, oregn mports are more closely relate to regonal economc contons than oregn exports ( IM E ). hereore, values IM E nclue no trae lows to other states because ) there s no way to separate what quanttes rom each state go rectly to the rest o worl an what quanttes go outboun to omestc locatons an then on to the rest o worl, an ) once they are prouce, they are economcally relate to only the transportaton servces sector. Smlarly, the IMPLAN values or total estnaton lows IM D to state can be calculate as, IM D = IM N + IM I + a I, (5) where IM N s the sum o net omestc proucts rom state, IM I s omestc mports to state obtane rom IMPLAN ata, an a I s auste oregn mports to state. For a specc SC Sector m, unreporte total estnaton (nput) values o state, as, D are calbrate D = IM D IM D V (6) 8

11 nreporte trae low values between states an ( V ) rom the estmate an orgnal total orgn/estnaton values can be ae to the matrx. In ths computaton, the cross-eects o orgn an estnaton values are consere to estmate any unreporte cell values. For nstance, the cell value compute or an unreporte estnaton can be calculate rom total unreporte resuals R = p D ( ) - p p V, (7) by multplyng the portons o total orgn corresponng to unpublshe cells sector V as shown n equaton (8.1). Smlarly, cells compute rom an unreporte orgn are compute as n equaton (8.2). However, because two matrces ( D an O ) are auste base only on total orgn [*** total orgn WHA? FLOWS?] or total estnaton [*** total estnaton WHA? FLOWS?] rom the two equatons o (8.1) an (8.2), we take the mean value o the two n equatons (8.3). hs yels the auste values o each cell. D = O = O ( ) k R p O ( ) k k D ( ) k R p D ( ) k k (8.1), (8.2), V = D O 2 (8.3). where, subscrpts p an p ncate publshe ata cells, an hence V p or V enty reporte or 0 p values o each cell n the trae matrx. Also, subscrpt k n O ) k ( or D ) k ( ncates the cells n O ) k ( or D ) k ( that correspon to the unreporte cells V, rrespectve o the estmate value O k (or D k ) or the known value O (or D ). 2 k k 2 Each CFS trae matrx nclues numercal values along wth a coe symbol. he symbol has our realzatons; 0 (or ), 1, 2, an 3, where 0 entes a reporte value, 1 means zero value, an 2 an 3 are values elberately unreporte ue to some specc reason (Bureau o ransportaton Statstcs an.s. Census Bureau, 2000). 9

12 o obtan the optmal tv, where subscrpt t enotes t th teraton, equatons (8.) shoul be terate as shown n (9.), where the startng values or unreporte ata are obtane rom the equatons (1), (6), an (7). t D = t O 1 (9.1), ( ) t 1 k R p t O ( ) 1 k k t O = t D 1 (9.2), ( ) t 1 k R p t D ( ) 1 k k tv = t D 2 t O (9.3). hereore, the optmal value satses the ollowng crtera: tv n the th t teraton maxmzes n equaton (10) (= MV ) an MV = MAX (10) tv subect to 1) t V t V V m, or 2) V V t 1 t 1 Note that the optmal value 1997 CFS reporte total value o each SC Sector m (or m MV or SC Sector m rom ths moel s the closest value to the an orgn/supply eects wthout accountng or stance ecay nluences. V m ), but only consers estnaton/attracton 10

13 IV-3. wo-step Approach: Doubly-Constrane Fratar Moel Fratar moels are useul or estmatng upate commoty trae lows. he startng matrces nclue numerous estmate values or mssng entres n the CFS ata. However, the tratonal Fratar moel calbrates only o-agonal nterregonal cells. In ths applcaton, new agonal values accountng or ntrastate trae lows also ha to be estmate. For ths, we evelope the Doubly-Constrane Fratar moel (DFM), a new ormulaton that upates the agonal values n the CFS matrx, along wth the tratonal Fratar moel to estmate the o-agonal values. he DFM teratvely estmates all the upate CFS values smultaneously an consstently. he estmate values or each SC Sector are the startng values or the next teratve step o the DFM. Dene Ô an Dˆ as the total orgn (output) value or state an the total estnaton (nput) values or state, respectvely. hat s, O ) ( an D ) ( respectvely enote the observe values reporte n the 1997 CFS or the mssng values estmate usng the AFM. hese estmates are prove by the proceure use to estmate mssng values n the 1997 CFS ata wth the AFM. Also, ene IM ND (= IM N + IM I ) as the net agonal entres n a matrx consstng o IMPLAN s net omestc proucts ( IM N ) plus the remanng IMPLAN oregn mports or each state ( IM I ). IMPLAN net total orgnatng values (outputs) n state, IM NO, are ene n equatons (11.) IM NO = IM O IM E (11.1) = ( IM N + IM E + IM E + a I ) IM E (11.2) = ( IM N + IM E + IM E + IM I + c I ) IM E (11.3) = IM N + IM E + IM I + c I (11.4) IM ND + IM E + c I (11.5) = Smlarly, IMPLAN s net total estne values (nputs) or state, IM ND, are ene as, IM ND = IM D c I (12.1) = ( IM N + IM I + a I ) c I (12.2) = ( IM N + IM I + IM I + c I ) c I (12.3) = IM N + IM I + IM I (12.4) 11

14 IM ND + IM I (12.5) = Here, by exclung the corresponng agonal outputs IM ND or IM ND, net values ( NO an ND ) o IM NO an IM ND can be obtane as, NO = IM NO IM ND (13.1) = IM E + a I, (13.2) an ND = IM ND IM ND (14.1) = IM I (14.2) Also, by exclung corresponng agonal outputs ( NO an ND ) o Ô an Dˆ can be obtane as, IM ND or IM ND respectvely, net values NO = Ô IM ND, (15) an ND = Dˆ IM ND. (16) he growth actors or orgn states an estnaton states, G ang, are calculate rom equatons (17) an (18), NO G, (17) NO 12

15 an ND G. (18) ND hese growth actors are substtute nto equatons (19) an (20) to obtan balance actors whch are use to upate o-agonal CFS entres teratvely. Let cell values rom the AFM an rom state to state. L an L, MV be the observe an estmate 1FV be the startng values to estmate the 2001 CFS o-agonal lows L = NO ( MV G, (19) ) an L = ND ( MV G ) (20) hs s a stanar applcaton o the tratonal Fratar moel that reles on the calbrate actors prove by equatons (17) to (20). 1 FV = ( L L ) MV G G or all. (21) 2 Equatons (22) to (23) ene DG an DG, agonal entry growth actors or orgn state to estnaton state. IM NO DG, (22) O 13

16 an IM ND DG. (23) D Smlarly, equatons (24) an (25) ene DL an DL, the agonal entry balance actors use to teratvely upate the agonal (ntrastate) entres o the CFS matrx. DL = O ( MV DG, (24) ) an DL = D ( MV. (25) DG ) DV Estmate Dagonal Values ( 1 ) are calculate va equaton (26), whch enes a secon Fratar moel estmatng trae lows wthn each state. hese results also account or new oregn mports remanng wthn each state. 1 DV = ( DL DL ) MV DG DG or all =. (26) 2 hese ntal estmates o the upate agonal values, 1, the agonal entry growth actors, DG an DG, an the agonal entry balance actors, DV DL an equaton (27) untl they converge to consstent values across equatons (22) to (26). DL, are all upate teratvely va t DV = t ( t 1DL t 1DL ) DV t 1DG t 1DG or all =. (27)

17 he t DV replaces IM ND an only t DV > IM ND, an hence, the nal, terate agonal values at t tmes t DV replace the agonal values t 1 DV n the CFS matrx an only t DV > t 1 DV. Note the CFS totals or each state are reuce by the erence between the corresponng values t DV an the orgnal agonal values IM ND, an hence, sum o o-agonal lows (or resuals) or the corresponng state wll be ecrease. he ntal estmates o the upate o-agonal CFS lows, 1 FV, the growth actors or orgn states an estnaton states, G ang, an the balance actors, L an L are all upate teratvely va equaton (28) untl they converge to consstent values across equatons (17) to (20). t FV = t 1 ( t 1L t 1L ) FV t 1G t 1G or all. (28) 2 he stoppng rule to enty the optmal values o equaton (29). he stoppng conton s met by maxmzng. t FV or equatons (27) an (28) s shown n MAX t FV (29) subect to < ( <( < IM NO / IM ND / FV t 1 / t FV ) < 1.001, an (30.1) t FV ) < 1.001; or, alternatvely, (30.2) t FV ) < (30.3) rae n servces between states cannot be estmate wth our current methos ue to the avalablty o only lmte normaton concernng nterstate trae n servce nustres. Another approach evelope n Park (2006) wll aress ths shortcomng o the two-step approach. 15

18 V. Results he 2001 trae lows between the.s. states or 29 SC commotes are estmate an upate va to the AFM an DFM. In able 2 an able 3, we show a summary o the estmate trae low matrces or SC Sector 15 (Plastcs an Rubber) as examples, gvng the AFM an DFM outputs, respectvely. Values n able 2 are roune o to the nearest nteger. Only unreporte values are subect to estmaton,.e, those cell entres coe n the 1997 CFS wth the symbol 2. hs estmaton s execute wthout mocaton to the publshe values shown n Appenx 3. he total estmate value or SC Sector 15 s $278,797-mllon, gvng a erence o only $35-mllon relatve to the 1997 CFS, suggestng a hgh levelo accuracy. For the results o each state, the ratos, V / O (or V / D ), are very nearly Although the AFM oes not conser the eects o stance n these low estmatons, the results o not appear to volate any stance eects when the estmate matrx s compare to the raw matrx or the 1997 CFS. Fgure 1 shows the estmate trae lows usng the Auste Flow Moel only or the ncomplete 1997 CFS trae lows,.e., those represente by the symbol 2 n Appenx 3. Fgure 1 summarzes the state-to-state trae lows. he largest value estmate or an unreporte trae low or ths sector s $911 mllon, the low rom rom Illnos to Inana. hese gures emonstrates that the AFM approach estmates unreporte trae lows wthout moyng any o the publshe quanttes n the CFS 3 here exst reporte total values or all estnatons an reporte total values or almost all orgns except D.C. an Wyomng. See Appenx 3. Snce the unreporte total values such as D.C. an Wyomng are auste rst by equaton (1), the estmates prove by the AFM show larger error ratos or these values than or the reporte values. Also, smaller total values lea to larger ratos erent rom 1 across V (or V ) an O (or D ). 16

19 able 2. Summary o 1997 rae Flows between.s. States Estmate by the Auste Flow Moel or SC Sector 15, Plastcs an Rubber ($M.) State O V ( V )/ O D V ( V )/ D Alabama Alaska Arzona Arkansas Calorna Colorao Connectcut Delaware Dstrct o Columba Flora Georga Hawa Iaho Illnos Inana Iowa Kansas Kentucky Lousana Mane Marylan Massachusetts Mchgan Mnnesota Msssspp Mssour Montana Nebraska Nevaa New Hampshre New Jersey New Mexco New York North Carolna North Dakota Oho Oklahoma Oregon Pennsylvana Rhoe Islan South Carolna South Dakota ennessee exas tah Vermont Vrgna Washngton West Vrgna Wsconsn Wyomng OAL Note: V=Value, O = otal Orgn (Output) value o State, D = otal Destnaton (Input) value o State. 17

20 Fgure 1..S. rae Flows or SC Sector 15, Plastcs an Rubber, Estmate by the Auste Flow Moel are Restrcte to nreporte Flows n the 1997 Commoty Flow Survey Note: Orer o States ollows the orer shown n able 1. he DFM was use to estmate 2001 trae lows between the states base on the 1997 trae lows matrx complete va applcaton o AFM. he summary o the estmaton s shown n able 3. he wthn-state trae lows are llustrate n Fgure 2-1 or SC Sector 15, Plastc an Rubber. State-tostate trae lows absent agonal movements are shown n Fgure 2-2. he largest wthn-state trae lows or 2001 occurrs n Calorna, at $13 bllon, whle exas accounte or the largest outboun low to Calorna, $1,119 mllon n current ollars. 18

21 able 3. Summary o 2001 rae Flows between.s. States Estmate by the Doubly-Constrane Fratar Moel or SC Sector 15, Plastcs an Rubber ($M.) State a I V IM ND Sale_VD IM E V IM NO Sale_VO Alabama Alaska Arzona Arkansas Calorna Colorao Connectcut Delaware Dstrct o Columba Flora Georga Hawa Iaho Illnos Inana Iowa Kansas Kentucky Lousana Mane Marylan Massachusetts Mchgan Mnnesota Msssspp Mssour Montana Nebraska Nevaa New Hampshre New Jersey New Mexco New York North Carolna North Dakota Oho Oklahoma Oregon Pennsylvana Rhoe Islan South Carolna South Dakota ennessee exas tah Vermont Vrgna Washngton West Vrgna Wsconsn Wyomng OAL Note: Sale_VO={( V + IM E )/0.72}, Sale_VD= ( V + a I )/0.72} o assess the accuracy o the estmate values, we show n able 3 the sum o trae low between states ( V or V ) an the IMPLAN total values ( IM O or IM D ) an compare the ratos o the two. hese are very close to 1.00 or every state. Foregn exports an oregn mports are suggeste as the trae lows to/rom the Rest o Worl. Foregn mports are alreay nclue n omestc trae lows between the states. 19

22 Fgure Wthn-State rae Flows Estmate va the Doubly-Constrane Fratar Moel Note: Orer o States ollows the orer shown n able 1. Fgure State-to-state rae Flows (Absent Dagonal Movements) Estmate va the Doubly- Constrane Fratar Moel Note: Orer o States ollows the orer shown n able 1. Because the values n the trae matrx upate prove by the DFM are proucer values, vng by the proucer/purchaser rato or SC Sector 15 (0.72) gves the sales value or each low. hs enables comparsons wth the raw CFS trae lows or the trae lows matrx estmate va the AFM. For nstance, because the estmate proucer value or Calorna-to-Calorna shpments n 2001 s $12,944-mllon, 20

23 about 43 percent (=100*(12,944/ ,557)/ 12,557), ncreasng rom 1997 total orgn value (=$12,557 mllon) n current ollars. Smlarly, all other values n able 3 can be compare wth those n able 2. However, because our current estmate values o trae lows n the states wth ports o not nclue oregn exports, the values n able 3 mght be overestmate IM E s ae to the agonal value n trae lows an compare wth the CFS, whch counts oregn exports as omestc lows. Also, Sale_VO or Sale_VD, meanng {( V + IM E )/0.72} or {( V + a I )/0.72}, respectvely, are prove n able 3 or comparson to total values n able 2. For nstance, the sum o orgn lows rom Calorna s ncrease by 30 percent (=100*(25,424-19,953)/19,953) n 2001 as the nomnal value, whle the total sum o the estmate trae lows s erent by 15.7 percent rom the total sum n able 2 (=100*(322, ,797)/ 278,797). VI. Senstvty ests We teste our approach by comparng BEA s use IO tables or 2002 an 2005 as shown n able 4-1 an 4-2, respectvely [*** HERE IS AN ERROR. HE CONENS OF 4-1 AND 4-2 ARE IDENICAL.]. hese ata sets escrbe use o commotes-by-nustres (pror to reenton [***OF WHA BY WHO?] at the natonal level or 2002 an hese ata are avalable onlne at We selecte the eault aggregate 15 sectors an estmate the 2005 values. Because (unlke the 1997 CFS) those values are complete or 2002, we nee apply only the DFM approach to estmate 2005 values base on these 2002 values. As shown n able 7, our results usng the DFM ncate that our approach can prouce goo estmates, showng a 96 percent relablty (base on auste R-square values) an a 0.98 correlaton coecent. More etale, sector-by-sector results are shown n ables 5, where we see that some sectoral estmates have relatvely large erences. However, when these erences are normalze relatve to the column sums o the 2005 BEA ata, the relatve erences are trval. See able 6. he relatonshp between the actual 2005 BEA ata an the 2005 estmates generate usng the DFM can be assesse vsually n Fgure 3. Note that our approach oes not aress any varance n lows resultng rom structural changes n economc contons over tme: We can only aspre to saty ceters parbus contons. 21

24 able 4-1. he se o 2002 Commotes by Inustres (Pror to Reentons, $M). IOCoe SM SM Source: We examne only the rs t15 eault aggregate sectors an strke column an row sums. able 4-2. he se o 2005 Commotes by Inustres (Pror to Reentons, $M). IOCoe SM SM Source: We examne only the rs t15 eault aggregate sectors an strke column an row sums. 22

25 able 5. he Estmate se o 2005 Commotes by Inustres Base on 2002 Values an the DFM (Pror to Reentons, $M). IOCoe SM SM able 6. he Normalze Derences between 2005 Actual an Estmate BEA Values Relatve to Column Sums. IOCoe SM SM

26 able 7. Statstcal Results or the Actual an Estmate BEA Data, 2002 an 2005 ($M). BEA 2005 (Dep.) an Estmate 2005 (In.) BEA 2002 (Dep.) an BEA 2005(In.) BEA 2002 (Dep.) an Estmate 2005(In.) Coe. S.E. Coe. S.E. Coe. S.E. In. Var *** *** *** Correlaton R_sq A_R_sq Note: 1. Dep.=Depenent varable an In.=Inepenent varable. 2. *** p< Fgure 3. Lne Ft Plot between 2005 BEA an 2005 Estmates usng DFM ($M). 2005BEA Estmates Lne Ft Plot Est mat es Note: he 45-egree lne ncates a perect relatonshp between the actual 2005 BEA ata an the 2005 estmates prove by the DFM VII. Conclusons Analysts have to work wth the ata they have access to, mperect though t s. hey are oten n the poston o havng to close gaps to exten the value o publshe ata. We ha to aress ths problem 24

27 beore we coul move on to the next steps n our research. Our real nterest stemme rom the act that athough a large varety o IO moels have been evelope, the constructon o multregonal IO moels ha remane a challengng task that we wante to aress. In ths paper, we suggest how trae lows between the.s. states can be estmate an upate usng seconary ata, as a bass on whch to bul a multregonal IO moel or the.s. We apple a two-step metho, base on ncomplete 1997 CFS trae low ata between states an IMPLAN regonal commoty balance ata. Beore creatng any estmates, we evelope several kns o converson tables to reconcle erent nustral coe systems. Wth the auste low moel, ncomplete trae lows or 1997 CFS are lle out. Base on ths trae lows matrx, nclung oregn mports/exports n the.s. trae lows, we estmate the 2001 trae lows matrx, but nclung oregn mports usng a Doubly-Constrane Fratar Moel. hese 2001 trae lows are constructe or 29 SC commoty sectors n the nal step. As an example, SC Sector 15 s hghlghte n the results secton, where we very that our moel an estmatons are acceptable at a reasonable level o accuracy. However, our 2001 moel s base on 1997 ata, an has some lmtatons. Lmte ata on the sources o servce trae lows keeps us rom reportng the economc nterrelatonshps o the servces sectors between regons. he rap ncreases n telecommuncatons, especally web-base nustres, however, requre us to nvestgate the amount o servce traes between regons. Although there are some suggestons on how to estmate servce trae lows, these stll requre strong assumptons. Atonal methoologcal evelopments are stll neee to overcome these lmtatons. Reerences Batten, D.F., 1982, he Interregonal Lnkages Between Natonal an Regonal Input-Output Moels. Internatonal Regonal Scence Revew 7:53-67 Cannng, P. an Wang, Z., 2005, A Flexble Mathematcal Programmng Moel to Estmate Interregonal Input-Output Accounts. Journal o Regonal Scence 45(3): Chenery, H.B., 1953, Regonal Analyss, n he Structure an Growth o the Italan Economy, ete by H.B. Chenery, P.G. Clark an V.C. Pnna,.S. Mutual Securty Agency, Rome: Erlbaum, N. an J. Holgun-Veras, 2005, Some Suggestons or Improvng CFS Data Proucts, Paper presente at Commoty Flow Survey (CFS) Conerence, Boston Seaport Hotel & Worl rae Center, Boston, Massachusetts, Jul. 8~9. Gulano, G., P. Goron, Q. Pan, J.Y. Park, an L. Wang, 2006, Estmatng Freght Flows or Metropoltan Area Hghway Networks sng Seconary Data Sources, Paper presente at Natonal rban Freght Conerence, Long Beach, CA, Feb. 1~3. 25