Effects of Terms of Trade Gains and Tariff Changes on the Measurement of U.S. Productivity Growth *

Transcription

1 Effecs of Terms of Trade Gans and Tarff Changes on he Measuremen of U.S. Producvy Growh * Rober C. Feensra Unversy of Calforna-Davs and NBER Benjamn R. Mandel Federal Reserve Bank of New York Marshall B. Rensdorf U.S. Bureau of Economc Analyss Mahew J. Slaugher Tuck School of Busness a Darmouh and NBER Augus 20 Absrac Afer 995, growh n roducvy n he Uned Saes acceleraed dramacally. Tha economywde growh s ofen arbued o declnng rces for nformaon echnology (IT) goods, and herefore enhanced roducvy growh n ha secor. In hs aer we nvesgae an alernave exlanaon for hese IT rce movemens and for he aaren acceleraon n U.S. roducvy: gans n he U.S. erms of rade and arff reducons, esecally for IT roducs. The globalzaon of he IT secor deeened afer 995 hanks o he Informaon Technology Agreemen of he WTO, whch elmnaed arffs worldwde n hundreds of IT roducs. We demonsrae ha hs agreemen led o magnfed reducon n IT rces. Furhermore, we argue ha convenonally measured mor and exor rces ndexes are unlkely o accuraely reflec hese rces declnes and hs msmeasuremen slls over no roducvy calculaons. From 995 hrough 2006, he average growh raes of our alernave rce ndexes for U.S. mors are.5% er year lower han he growh rae of offcal rce ndexes. I follows ha roerly measured erms-of-rade gan can accoun for close o 0.2 ercenage ons er year, whch s abou 20% of he aaren ncrease n roducvy growh for he U.S. economy. * We are graeful for Mke Harer s asssance wh he analyss of he roducvy measuremen mlcaons. We draw heavly uon Alerman, Dewer and Feensra (999), and he auhors are ndebed o Bll Alerman and Erwn Dewer for ha earler sudy whch we aly here o U.S. roducvy growh. For helful commens we hank semnar arcans a Columba, Harvard, Oxford, Sascs Canada and he NBER. For fnancal suor Feensra and Slaugher hank he Naonal Scence Foundaon. Fnally, he vews exressed n hs aer are hose of he auhors, no hose of he Bureau of Economc Analyss or of he Federal Reserve Bank of New York.

2 . Inroducon The sngle bes measure of a counry s average sandard of lvng s s roducvy: he value of ouu of goods and servces a counry roduces er un of facor nus. The more workers roduce, he more ncome hey receve and he more hey can consume. Hgher roducvy hus brngs hgher sandards of lvng. Undersandng he causes and roer measuremen of roducvy growh has long been a cenral research area n economcs. In he Uned Saes, snce 995 growh n aggregae labor roducvy aears o have acceleraed markedly. The U.S. Bureau of Labor Sascs (BLS) reors ha from 973 o 995, ouu er worker hour n he nonfarm busness secor grew on average a jus.37 ercen er year. From 995 hrough 200 hs rae acceleraed o an average of 2.69 ercen er year. If susaned, hs seed-u n U.S. roducvy growh wll carry dramac mlcaons for he U.S. economy. A he revous generaon s average annual growh rae of.37 ercen, average U.S. lvng sandards were akng 5 years o double. Should he more-recen average annual growh rae of 2.69 ercen erss, hen average U.S. lvng sandards would ake jus 26 years o double a generaon faser. A large leraure has n recen years analyzed hs mrovemen n U.S. roducvy growh. The declnng rces of nformaon echnology (IT) roducs, whch acceleraed n he lae 990s, are ofen creded wh key drec and ndrec roles n he roducvy seedu. For examle, Jorgenson (200,. 2) argues ha: The acceleraed nformaon echnology rce declne sgnals faser roducvy growh n IT-roducng ndusres. In fac, hese ndusres have been he source of mos of aggregae roducvy growh hroughou he 990s. 2 These calculaons are based on BLS daa seres #PRS , as reored a Smlar rends are evden n he BLS measures of mulfacor roducvy (MFP) for he rvae busness secor, whch we grah n Fgure. In , U.S. roducvy growh deceleraed agan, bu n 2009 resumed growng radly. 2 Smlarly, Olner and Schel (2000,. 7) sae ha, we have nerreed he shar declne n semconducor rces afer 995 as sgnalng a cku n ha secor s TFP growh. Oher romnen sudes of he U.S. roducvy acceleraon nclude Baly and Lawrence (200), Bosworh and Trle (2000), Gordon (2000, 2003), Jorgenson and Sroh (2000a,b), Nordhaus (200, 2005), and Olner and Schel (2000, 2002).

3 2 In hs aer, we argue ha ar of he aaren seed-u n U.S. roducvy growh acually reresened gans n he erms of rade and arff reducons, esecally for IT roducs. We frs demonsrae ha some of declne n IT rces was acually due o a mullaeral arff reducon under he World Trade Organzaon (WTO). Second, we argue ha erms of rade mrovemens were under-measured n U.S. mor and exor rce ndexes and ha arffs should be ncluded n mor rces for roducvy measuremen uroses. These correcons mly ha convenonally measured U.S. real ouu growh and roducvy growh were oversaed n he years afer The sarng on for our argumen s he observaon ha on many measures, he global engagemen of he U.S. IT ndusry deeened afer 995 recsely he erod of acceleraed IT rce declnes ha have been nerreed as oal facor roducvy (TFP). Parcularly moran was he Informaon Technology Agreemen, a comrehensve free-rade agreemen ha o dae remans he only such agreemen durng he lfe of he WTO. Rafed n 996 by dozens of counres accounng for nearly 95 ercen of world IT rade, he ITA elmnaed all world arffs on hundreds of IT roducs n four sages from early 997 hrough Ths mng suggess ha he ITA, dscussed n secon 2, layed an moran role n he os-995 rend n IT rces. In arcular, for IT roducs made n mulle counres, a mullaeral arff reducon wll lead o a magnfed declne n her rces. Usng daa on he U.S. mor rces of IT roducs, along wh U.S. and foregn arffs, we fnd srong evdence of such magnfed rce effecs. Ths resul s analogous o he magnfed mac of arff reducons on rade, as shown by Ke-Mu Y (2003, 200). Evdence for he second ar of our argumen aears n Fgure, whch los hree seres. The erms of rade based on ndexes reored by he BLS s calculaed as he rao of he U.S. 3 Relaed argumens abou how subsuon from domesc sources of suly o lower-rced mors can resul n an oversaemen of ouu and roducvy growh are made by Houseman (2007) and several of he aers summarzed n Houseman and Ryder (200), ncludng Houseman, Kurz, Lengermann and Mandel (200) and Rensdorf and Yuskavage (200). Tha s a dfferen effec from hose ha we examne n hs aer, however.

4 3 exor rce ndex o he non-eroleum (o exclude he ouszed role layed by flucuaons n ol rces) mor rce ndex. The Laseyres erms of rade ndex s based on Laseyres ndexes ha we consruced from he rce mcro-daa ha BLS colleced from morng and exorng frms for he erod of Seember 993 hrough December BLS uses a Laseyres formula for s ndexes, so our Laseyres ndexes relcae BLS mehods usng he mcro daa o whch we had access for he analyss reored n hs aer. 4 The hrd seres n Fgure, also from BLS, s U.S. mulfacor roducvy for he non-farm busness secor. Is sloe seeens n 996, reflecng he fac ha U.S. mulfacor roducvy growh rose from an average of 0.53 ercen er year durng o.4 ercen er year durng The ndex of U.S. erms of rade shows a declnng rend u unl 995 n Fgure. Bu snce 995 a recsely he me ha roducvy growh cked u U.S. erms of rade reversed and began rsng, wh a srng of sold gans from 995 hrough The average annual gan n he U.S. non-eroleum erms of rade from 995 hrough 2006 was.0%, mlyng a cumulave gan nearly as large as he 5% deeroraon n erms of rade from he eroleum rce shocks n and The fac ha U.S. erms of rade began o mrove recsely when roducvy acceleraed suggess a connecon beween he wo. Wha hs lnk mgh be, however, s no mmedaely clear from sandard heores of rade and growh. By defnon, drec, frs-order effecs from rce changes are excluded from he conce of roducvy change. Conssen wh hs, Kehoe and Ruhl (2008) have recenly argued ha changes n he erms of rade have no mac on roducvy when arffs are zero. When arffs are resen bu small, hen he mac of erms of rade shocks on roducvy s corresondngly small. In secon 3, we wll exend he analyss of Kehoe and Ruhl (2008) from a 4 Our Laseyres erms-of-rade ndex does no exacly mach he one consruced from ublshed BLS ndexes because we have ncomlee daa for some ndusres. Bu he dfference s mmaeral.

5 4 one-secor o a mul-secor model and smlarly consder arff reducons. In our mul-good seng, arff reducons and changes n he erms of rade have a second-order mac on GDP and roducvy. Ye f he erms of rade are msmeasured, he sory s crcally dfferen. Unmeasured changes n he erms of rade have a frs-order mac on convenonally measured roducvy growh. In arcular, f he reducon n mor rces s undersaed hen, oher hngs beng equal, convenonally measured roducvy growh wll be corresondngly oversaed. There are hree reasons why he U.S. erms of rade may be msmeasured for uroses of denfyng U.S. roducvy growh. Frs, as already noed, he BLS mor and exor rce ndexes use a Laseyres formula raher han a suerlave formula. Second, he BLS mor ndexes whch he Bureau of Economc Analyss (BEA) uses o deflae mors measure mor rces free of arffs, and mors are lkewse valued excludng dues n he calculaon of GDP. The relevan mor rces facng frms do, however, nclude hese rade barrers. And hrd, he BLS mor rce ndex does no accoun for ncreases n he varey of mors comng from new sulyng counres. As demonsraed by work ncludng Feensra (994), Hummels and Klenow (2006), and Broda and Wensen (2006), he economc mac of exandng varees s large and herefore crcal o accoun for. In secon 4 we consruc rce ndexes ha correc for all hree of hese errors. In erms of Fgure, hs key ar of our overall argumen s ha he acual mrovemen n U.S. erms of rade was even hgher han he mrovemen mled by he ndexes reored by BLS. To revew our man resuls, Fgure 2 shows several alernave erms-of-rade ndexes based on our calculaons n hs aer. We reea from Fgure he BLS and our comued Laseyres ndexes and hen show hree ohers: () an exac Törnqvs ndex for he erms of rade; () he

6 5 Törnqvs ndex ha also ncororaes arffs no he mor rces; () he Törnqvs ndex ha ncororaes boh arffs and mor varey. 5 The key message of Fgure 2 s ha, correced for hese hree measuremen errors, acual U.S. erms of rade were rsng much faser ha offcally reored. The cumulave mac of hese hree adjusmens means ha he rse o jus December 999 n he Törnqvs ndex ha ncororaes arffs and varey was nearly equal o he cumulave rse n he Laseyres ndex all he way o December 2006 (comare Fgures and 2). Whle he Laseyres erms of rade consruced from BLS exor and mor rce ndexes rose abou 0.9% er year over , he Törnqvs ndex ncororang arffs and mor varey rose more han wce as fas, a 2.2% er year over he same erod. The rue erms-of-rade gan for he Uned Saes snce 995 has been much hgher han ndcaed by offcal rce ndexes. The correced erms-of-rade ndexes n Fgure 2 canno, however, be used o nfer he amoun by whch unmeasured erms-of-rade gans have alered reored U.S. roducvy growh. They are correced versons of BLS s aggregae exor and mor ndexes, bu BEA s measures of real ouu growh whch drve he calculaons of roducvy growh use dealed ndusry exor and mor rce ndexes, rmarly he fve-dg Enduse ndexes roduced by BLS, o deflae dsaggregaed measures of exors and mors. To combne he dealed ndexes no a deflaor for GDP, BEA uses weghs based on he comoson of GDP and uses a chaned Fsher formula, no a Laseyres formula. Accordngly, o esmae he mac of msmeasured erms of rade on reored roducvy growh, n secon 5 we consruc comlee ses of correced Enduse exor and 5 The frs wo of hese ndexes are se equal o he Laseyres ndex n Seember 993, he begnnng of our samle erod, whereas he varey adjusmen (whch s annual) begns n 990. I s noeworhy ha mos of he varey adjusmen occurs n he erod afer 995, however, jus lke our oher wo adjusmens.

7 6 mor rce ndexes a he 5-dg level (or he 3-dg level n a few cases where he 5-dg level of deal s no ublshed by BLS). For exors, we consruc wo ses of dealed ndexes, one conanng Laseyres ndexes ha mmc offcal BLS ndexes (as a benchmark), and anoher conanng Törnqvs ndexes. For non-eroleum mors, we consruc four ses of dealed ndexes: Laseyres ndexes ha mmc offcal BLS ndexes; Törnqvs ndexes; Törnqvs ndexes ncludng arffs; and Törnqvs ndexes ncludng arffs and a correcon for ne enry of new varees. We hen use a chaned Fsher ndex formula o calculae wo alernave ndexes for exors and four alernave ndexes for non-eroleum mors. From hese ndexes, we calculae four versons of he deflaor for GDP, a benchmark verson based on our dealed Laseyres ndexes and hree alernave versons based on he dealed Törnqvs ndexes. 6 Also, because he governmen comonen of GDP s excluded from offcal measures of roducvy, we calculae he deflaor for a subse of GDP ha excludes governmen, gross value added of rvae busness. 7 Correcons o deflaors for GDP and s subses mly correcons o measures of real ouu growh, whch, n urn, mly correcons o measures of roducvy growh. By comarng roducvy growh calculaed from our hree alernave correced rce ndexes wh ha obaned wh our reconsruced offcal BLS ndexes, we hus can esmae he oron of convenonally reored U.S. roducvy growh ha was acually due o unmeasured gans n erms of rade and declnes n arffs. Our correced rce deflaors rse faser han he offcal deflaor, and so our correced real ouu and roducvy growh are lower. Our referred 6 As exlaned n Dewer (978), Fsher ndexes lack he roery of conssency n aggregaon n an exac sense, bu hey are aroxmaely conssen n aggregaon. Ths means ha Fsher ndex for GDP s nearly, bu no recsely, equal o a combnaon of he Fsher ndexes for each of he md-level aggregaes of C, I, G, X and M. 7 In analyzng TFP for a secor, he conceually correc measure of ouu s he secor s gross sales ousde he secor, whch equal s value added lus s urchases of nermedae nus from ousde he secor. The ouu conce for he rvae busness secor ough herefore o equal s value added lus mored nermedae nus, and mored nermedaes ough o be ncluded n nus. BLS measures he ouu of rvae busness by s value added because ncludng mored nermedaes n nus nsead of neng hem ou of he ouu was found o have lle effec on he TFP esmaes.(gullkson and Harer, 999,. 50 and fn 29).

8 7 esmaes are ha roerly measured erms-of-rade gans and arff reducons accoun for close o 0.2 ercenage ons abou 20% of he reored ncrease n U.S. roducvy growh. Secon 6 concludes. 2. The Informaon Technology Agreemen Under he ausces of he World Trade Organzaon (WTO), he Informaon Technology Agreemen (ITA) commed sgnaory counres o elmnae all arffs on a wde range of nearly 200 IT roducs. These roducs covered boh fnshed and nermedae goods such as comuers and neworkng and erheral equmen; crcu boards and oher assve/acve comonens; semconducors and her manufacurng equmen; sofware roducs and meda; and elecommuncaons equmen. The orgnal Mnseral Declaraon on Trade n Informaon Technology Producs was concluded n December 996 a he frs WTO Mnseral n Sngaore. Ths declaraon sulaed ha for he ITA o ake effec, sgnaory counres would have o collecvely reresen a leas 90% of world rade n he covered roducs. The 29 orgnal sgnaores accouned for only abou 83% of covered rade. Bu by Arl 997 many more counres had sgned on o ush he share over 90%, and he agreemen enered no force n July 997. Ulmaely here were more han 50 ITA sgnaores ha accouned for more han 95% of world rade n he covered ITA roducs. All ITA sgnaores agreed o reduce o zero her arffs for all covered ITA roducs n four equal-rae reducons sarng n 997 and endng no laer han he sar of Some develong counres were graned ermsson o exend rae cus beyond 2000, bu no laer han The overarchng goal of he ITA was o elmnae world arffs n a wde range of IT roducs. Thanks o he number and commmen of sgnaory counres, vrually acheved ha goal.

9 8 The arff reducons over exerenced by a number of U.S. IT ndusres are shown n Table. The ITA arff cus are defned a he 8-dg level of he Harmonzed Sysem (HS) sysem, used o rack mor commodes. In Table, we ndcae he ercenage of mor value whn each ndusry ha s covered by ITA commodes. For comuers, erherals and semconducors, 00% of mors were ncluded n he ITA arff cus. In he smaller ndusry of blank aes for audo and vsual use, 90% of he mors were covered by he ITA, and n he large secor of elecommuncaon equmen, 80% of he mor value was covered by he ITA. Table also ncludes he nformaon for several oher ndusres where more han 50% of mor value was covered by he ITA, and ndusres such as busness machnes and equmen, and measurng, esng, and conrol nsrumens, where less han 50% of he mor value was affeced by he ITA agreemen. 9 In Table we also show he average arffs a he begnnng of 997, before he ITA was mlemened, and n 2000, when was concluded. Clearly, U.S. arffs n hese ndusres even before he ITA agreemen were low: average arffs were beween and 4% n all ndusres, and zero or nearly so n comuer accessores and semconducors. Ths means ha he ITA arff cus for he Uned Saes were corresondngly small. Bu remember ha he ITA was a mullaeral agreemen, so ha arff cus n he U.S. could be mached by equal or larger arff cus abroad. For frms sourcng her IT roducs from overseas locaons, he arffs cus whn he ITA could herefore have had a mulled mac on lowerng her mor rces and coss. Y (2003, 200) formally models how rade-barrer reducons can rgger magnfed resonses n rade volumes n he resence of cross-border roducon neworks lke hose so cenral o IT. We nvesgae he analogous effec 8 The four arff cus for he U.S. occurred n July 997, January 998, January 999, and for a small number of commodes, January Omed from Table are ndusres where less han 0% of mors are covered by he ITA.

10 9 for mor rces n he followng secon, and ndeed, we fnd ha he esmaed effec of he ITA agreemen on U.S. mor rces s much larger han ha of he drec decrease n arffs. Imac of he ITA on Imor Prces To deermne how he arffs cus under he ITA affeced mor rces, we consruc a geomerc ndex for arffs n ndusry, denoed by Tar,, as: where and mj, + τ j Tar =, j J + τ j τ j denoes he ad valorem U.S. arff rae for roduc comng from counry j n monh, w mj denoes he share of mor exendure for good on counry j. In racce we use annual daa for mors so ha w w mj dffers by year raher han by monh. In addon, we consruc a geomerc ndex of exchange raes n Enduse ndusry, Exch,, as a weghed average of he exchange rae mes he roducer rce ndexes (PPI) for U.S. radng arners. These are combned wh Laseyres monh-o-monh ndexes of mor and exor rces,, P xl, P ml,, whose consrucon mmcs ha used by he BLS (as dscussed n secon 4) exce ha he mor rce ndexes are arff-nclusve. 0, P ml, These ndexes are cumulaed from Seember 993 hrough December 2006 o oban 0, P xl, 0, Tar and 0, ln P ml = 0, Exch. We use hem n he followng ass-hrough regresson: 3 6 0, 0, 0 k k lntar ln Exch l l Z k= l = 0 α + α δ +β + β +γ +ε where: α 0 s a fxed-effec for each ndusry, ITA (.e. July 997, January 998 and January 999) and δ k are hree ndcaor varables for he sages of he, Z denoes addonal conrol varables. The rces of comeng roducs belong n regressons of hs ye, so our frs conrol varable s

11 0 he U.S. exor rce ndex for ndusry, P 0, xl. In addon, Bergn and Feensra (2007) have recenly shown ha he share of mors comng from counres wh fxed exchange raes, and s neracon wh he exchange rae, add exlanaory ower o ass-hrough regressons for he U.S., so we nclude hose as conrol varables oo. Fnally, we add conrols for he mac of mulsage nernaonal roducon on U.S. mor rces. Y (2003, 200) demonsraes he morance of nernaonal vercal roducon lnkages for exlanng why observed nernaonal rade flows are subsanally larger han wha sandard heory would redc. Here we exend hs reasonng o aly o rade rces; goods crossng borders mulle mes a sequenal sages of roducon wll amlfy he mac of a mullaeral lberalzaon by reducng he cos of mored nermedae nus for downsream frms. Ths resul s shown from equaons (5) and (6) n Y (200). In a wo-sage roducon rocess where nermedaes are exored and fnal goods mored, he ass-hrough of a symmerc ceberg rade cos, (+τ), o mor rces s (+θ)(+τ) log ons, where θ ndexes he share of mored nermedaes n fnal good roducon. If a hrd sage s resen, he asshrough muller for rade coss rses o (+θ+θ 2 ). Therefore, as he number of sages grows large, he ass-hrough muller for vercal negraon aroaches /(-θ). 0 To caure hese deas n our ass-hrough regresson, we frs nclude foregn arffs n he same ndusry whn he ass-hrough regresson. The resuls are shown n columns () (3) of Table 2, whch uses 0, Tar as he U.S. arff and a weghed average of foregn arffs. The frs regresson n s run over hose ndusres where 00% of he mor commodes are covered by 0 Incdenally, hs muller looks smlar o he border effec n he wo-sage model of (+θ)/(-θ) derved by Y (200), bu arses for a dfferen reason. We use he MFN ad-valorem aled arff raes for U.S. radng arners from TRAINS, aggregaed annually from he 6-dg HS schedule o 5-dg Enduse ndusres and across U.S. rade arners. For he ITA ndusres, he arffs avalable on he WTO webage were more accurae and were used n lace of he TRAINS arffs.

12 he ITA (denoed by ITA = ); from Table, hese ndusres are comuers, erherals and semconducors. The second regresson s run over hose ndusres where 99% of he mor value covered by he ITA (0 < ITA < ), and he hrd regresson s run over a conrol grou of ndusres ha nclude no ITA commodes (ITA=0). 2 Lookng frs a he regresson for ITA =, he ndcaor varables for he ITA arff cus (July 997, January 998 and January 999) are all negave, ndcang a dro n rces ha s no accouned for by he arff varable. The cumulave dro due o he ndcaor varables s nearly 20%. The arff varable self has a ass-hrough coeffcen of 3.3, whch s exremely large comared o wha s normally found and ndcaes ha he arff declnes have a hghly magnfed effec on lowerng he mor rces. 3 The foregn arff has a coeffcen of 4.5, whch s also very large. Our execaon from he wo-sage roducon model of Y, dscussed above, s ha he oal ass-hrough of a symmerc arff cu of one ercenage on would be (+θ) ercenage ons, whch we can searae as coeffcens of on he U.S. arff and θ on he foregn arff. Obvously, our resuls n column () ndcae a much larger mac of he ITA arff cus. Column (2) of Table 2 reors he ass-hrough regresson run over ndusres wh nermedae levels of mor value covered by ITA roducs (.e., 0 < ITA < ). Ths regresson ndcaes a U.S. arff ass-hrough coeffcen of 2.4, and 0.32 for he foregn arff. These esmaes are sll larger han, hough more n lne wh, Y s wo-sage model (.e. coeffcens of on he U.S. arff and θ on he foregn arff agan). Column (3) reors he ass-hrough regresson for a conrol grou of rmarly caal and consumer goods ndusres ha do no nclude any commodes affeced by he ITA arff cus. For hese ndusres, we fnd a U.S. arff coeffcen 2 The conrol grou of ndusres used n he fnal regressons ncludes caal goods (Enduse 2), auomobles and ars (Enduse 3), consumer goods (Enduse 4) and chemcals (Enduse 2). 3 In he absence of he foregn counry conrol varable, he coeffcen on he arff varable s 9.4.

13 2 of 0.99, whch s nsgnfcanly dfferen from uny, whle he foregn arff s no sgnfcan a all. 4 One reason ha he ass-hrough coeffcens for he ITA= ndusres are so hgh may be ha hese goods are subjec o more sages of nernaonal roducon han wo: comonens mgh cross borders mulle mes. If so, a ercen symmerc arff cu would have a cumulave mac on he rce of /( θ) ercen, where θ s he share of mored nermedae nus. The coeffcen θ ales o he foregn counry n Y s model, bu he varable avalable o us s he share of mored nermedae nus for he U.S. descrbed n Feensra and Hanson (999). Recognzng ha a θ comued wh U.S. daa s no necessarly alcable o foregn counres, we do an analogous calculaon of θ usng he 2000 Chnese nu-ouu able, whch dsngushes ordnary and rocessng mors o Chna. Our referred secfcaon, reored n columns (4) (6), uses a weghed average of he Chnese and U.S. values of θ (usng he U.S. mor shares of ordnary and rocessed Chnese goods, and non-chnese goods, by ndusry), and mulles boh he U.S. arff and he foregn arff by /( θ) n each Enduse ndusry. The resuls for he ITA= ndusres n column (4) show ha he ass-hough coeffcen of U.S. arffs comes down o.5, whle he coeffcen on he foregn arff s 0.7 (boh hese arffs are mulled by /( θ)). These are much more reasonable values for ass-hrough coeffcens, wh he coeffcen on he U.S. arff nsgnfcanly dfferen from uny. For he oher ITA ndusres n column (5), we fnd a ass-hough of he U.S. arff of almos exacly uny, and a very small effec for he foregn arff. Fnally, for he conrol grou of ndusres n column (6), 4 We have also esmaed he rce regresson for subses of he conrol grou. For auomobles and ars (Enduse 3), and for consumer goods (Enduse 4), he lnear combnaon of he arff coeffcen and arner arff coeffcen s nsgnfcanly dfferen from uny. For caal goods, ha lnear combnaon s nsgnfcanly dfferen from.5; hs ass-hrough would be exacly he redcon of he Y model wh θ =0.5. The only Enduse caegory ousde he ITA ndusres ha shows conssenly hgher arff and arner arff coeffcens s Enduse 2500, whch s chemcals. However, no ncludng chemcals n he conrol grou has only slgh effecs on he arff coeffcen.

14 3 he ass-hrough from he U.S. arff s 0.72, whch s somewha lower han execed bu no ha unusual and, agan, we fnd very small foregn arff effecs. Thus, by conrollng for many sages of roducon usng /( θ) we oban very reasonable esmaes for he ITA= ndusres, whou affecng he oher ndusres oo much. These fndngs suor our hyohess ha he mul-sage naure of roducon n hgh-ech ndusres s resonsble for he magnfed mac of he arff cus n reducng mor rces. Dese he fac ha U.S. arffs were low, he global naure of he ITA resuled n sgnfcan reducons n U.S. hgh-ech rces. Ths resul s shown n las column of Table, where we have comued he mled change n U.S. mor rces for hgh-ech roducs due o he ITA. We do so by comarng acual mor rces wh an esmae of counerfacual rces had he ITA no occurred, wha we call a non-ita rce ndex. Ths laer seres s consruced usng he asshrough coeffcens n columns () and (2) of Table 2 and by holdng he arff-relaed varables consan a her re-ita levels. 5 The resulng redced values are our bes esmae of he counerfacual mor rces ha would have exsed had he ITA no been mlemened. 6 The las column of Table reors he ercenage dfference a he end of our samle erod beween he ublshed mor rces and our calculaed hyohecal non-ita mor rces. Tarffs layed a key role n lowerng U.S. mor rces for hgh-ech goods: he ITA conrbued 6 and 24 ercen, resecvely, o he declne n comuer and comuer accessory rces, and large amouns o several oher Enduse ndusres. 3. Measuremen of Producvy Growh wh Inernaonal Trade 5 To faclae comarson wh he BLS ublshed seres, we se he non-ita seres equal o he BLS mor rces u unl June 997 and use he redced values of he ass-hrough regresson o exend he ndex hereafer. 6 An alernave formulaon of hs counerfacual would use columns (4) and (5) nsead of columns () and (2). However, he dfference beween hose wo seres urns ou o be small and does no maerally affec our resuls.

15 4 We have seen n he revous secon ha arffs on mored IT roducs fell durng he erod covered by he ITA. In hs secon we descrbe how o accoun for such declnes n arffs n he measuremen of oal facor roducvy (TFP) a an economy-wde level, and we consder addonal sources of msmeasuremen of TFP arsng from he deflaors for exors and mors. In our exoson of he heory, we assume ha roducvy s measured for GDP as a whole even hough, n racce, he avalable nformaon only erms he rvae busness oron of GDP o be ncluded n he broad measure of roducvy growh. Our heorecal model exends he model of nernaonal rade and roducvy of Dewer and Morrson (986), whch reas mors as nermedae nus no he economy s GDP funcon. To oulne he noaon, suose here are =,,M fnal goods, wh quanes q > 0 and rces > 0. In addon, here are =,,N exored ouus, wh quanes x > 0 and nernaonal rces x > 0. For smlcy, we gnore axes or subsdes on exors. Fnally, here are also =,,N mored nermedae nus, bu each of hese come n j =,,C varees ndexed by he counry of orgn. So he mor quanes are m j > 0, wh nernaonal rces mj > 0, ad valorem arffs j mj τ, and domesc rces ( + τ ). j The vecor of fnal goods and free-rade rces s denoed by P = (,, x m ), and he quanes of hese goods are y = (q, x, m ) > 0. Furher, he mor arffs are n he vecor τ. Then he revenue funcon for he economy s: R (P, τ, v ) M N + N C max q x ( + τ )m y S (v ) x mj j j () y 0 = = = j=

16 5 where S (v ) s a convex echnology se ha deends on he counry s endowmen of rmary facors v. We assume ha S (v ) s srcly convex, so he maxmum n () s well-defned. The suerscr on he revenue funcon ndcaes ha he echnology can change over me. The revenue funcon equals he oal value added of all ndusres wh arffs ncluded n nermedae nu coss, whch s he roducon aroach measure of he economy s ouu. 7 In conras, arffs are excluded from he cos of mors n he defnon of GDP because he arff revenue remans whn he morng counry. Le X = = xx denoe he value of exors and le N C M = m denoe he value of mors a duy-free rces. Usng = j = mj he exendure aroach, nomnal GDP s measured by: j M GDP q + (X M ). (2) Subsung for X and M, we can re-wre nomnal GDP as he funcon: = N G (P, τ, v ) = R (P, τ, v ) + N C = j= mj j j τ m, (3) where he equaly s obaned usng he defnon of he revenue funcon R (P, τ, v ). Equaon (3) saes ha nomnal GDP equals he aggregae ouu R (P, τ, v ) lus arff revenue. To analyze he effec of arff changes on he measure of nomnal GDP, we use he GDP funcon n (3) o oban he famlar omaly of free rade n a small oen economy: Prooson Holdng fxed P and v, he value of GDP n (3) s maxmzed a τ = 0. 7 Assumng ha arffs are he only ax on roducs, R (P +T, v ) s he measure of aggregae ouu known as gross value added a basc rces n he nernaonal gudelnes for naonal accouns n he Sysem of Naonal Accouns or SNA and equaon (3) s he roducon aroach measure of GDP (Uned Naons e al., 993, aragrahs and ) Followng he SNA, we refer o R (P +T, v ) as he economy s oal valued added. In conras, BEA defnes oal gross value-added o nclude arffs and oher axes on roducs, makng he same as GDP.

17 6 Proof: Because he dervave of he revenue funcon wh resec o τ j s mj m j, follows ha he frs dervave of he GDP funcon wh resec o j j = τ s zero evaluaed a τ 0. The second dervave s negave sem-defne because he revenue funcon s concave n mor rces. I follows ha τ = 0 s a maxmum. QED Ths famlar resul shows he omaly of zero arffs n a small counry, and has a very moran mlcaon for he measuremen of roducvy. Dewer (2006,. 30), cng Jorgenson and Grlches (972), observes ha arffs and smlar axes on nermedae nus (such as excse axes) should be ncluded n nu rces when measurng roducvy change. The revenue funcon allows us o do hs because uses arff-nclusve rces. We wll show ha even f rue roducvy change s zero, hen oal facor roducvy as s commonly measured wll be osve when arffs are reduced. To show hs resul, we begn by defnng rue roducvy. A very general formulaon of roducvy change, due orgnally o Caves, Chrsensen and Dewer (982) and aled o an oen economy seng by Dewer and Morrson (986), Kohl (990, 2004, 2005, 2006) and Dewer (2008), comes from defnng roducvy as he shf n he economy s revenue funcon whle holdng rces and facor endowmens fxed. Deendng on whch erod s rces and endowmens are chosen, roducvy growh s defned as eher: A, τ, v R (P R (P, τ, v ), or ) A R (P, τ, v ). (4) R (P, τ, v ) These conces of roducvy change are no measurable because boh he numeraor of A - and he denomnaor of A are unobservable. Ye her geomerc mean can be measured, once we assume a secfc form for he revenue funcon. In arcular, suose ha he revenue

18 7 funcon akes a nesed form. In he frs sage, for mored varees j J {,...,C}, we suose ha he revenue funcon n () s a CES funcon wh elascy σ, /( ) ~ m = ( ) j J b j ( mj ( j )) σ σ +τ, =,,N. (5) In he nex secon we wll show how he mor rces can be aggregaed over sulyng counres, obanng ~ m, bu for now suose ha hese aggregae mor rces are avalable, and ~ x m denoe he vecor of rces by P (,, ~ ). Then n he second sage, across goods and facors, we suose ha revenue s a ranslog funcon over he rces ~ P and endowmens. We furher assume ha he arameers mullyng hese rces n he ranslog revenue funcon are sable over me, bu he coeffcens mullyng endowmens are allowed o change over me, reflecng echnologcal change. I follows from Dewer and Morrson (986) ha: ( A ) / 2 A = R R ~ / [P T ( P ~ -, P,y,y ) QT (v -,v,w -,w )], (6) ~ where P T ( P ~ -, P,y,y ) s a Törnqvs rce ndex over fnal goods, exors and mors, and Q T (w -,w,v -,v ) s a Törnqvs quany ndex over rmary facors, wh rces w - and w. Equaon (6) saes ha roducvy growh can be measured by deflang he change n nomnal revenue R by s rce deflaor P T, hen comarng he esmae of real revenue growh o he growh n rmary facors Q T. The Törnqvs rce ndex aearng n (6) s defned as: ~ ln P T ( P ~ -, P,y,y ) M = 2 R q q + R ln + N = 2 R x x xx + R ln x x

19 8 N = 2 C j= mj ( R + τj )m j + C j= mj R j ( + τ )m j ~ ln ~ m m. (7) Noe ha he weghs used o sum over domesc goods, exors and mors n (7) add u o uny, and ha mors receve a negave wegh because hey are nus. We can now comare rue roducvy growh n (6) o wha s ycally measured. The reamen of arffs n convenonal esmaes of aggregae TFP dffers from her reamen n (5) because nomnal ouu s measured by GDP, no R, and because mor rces are measured whou arffs n he ndex used o deflae mors. Tha s, convenonal esmaes of aggregae TFP are comued as: TFP G G / [P E (P -,P,y -,y ) Q E (w -,w,v -,v )], (8) where G G (P, τ, v ) s nomnal GDP, P E (P -,P,y -,y ) s an exac GDP deflaor over rces of fnal domesc demand, exors, and duy-free mors, and Q E (w -,w,v -,v ) s an exac quany ndex of rmary facors. If he funconal form for hese ndexes s exac for he underlyng revenue funcon (as s he case for he Törnqvs ndex, whch s exac for he ranslog revenue funcon), and f arffs are zero, hen convenonally measured TFP n (8) s dencal o rue roducvy growh n (6). However, measured TFP wll dffer from rue roducvy when arffs are non-zero or when he rce ndexes used n (8) are no exac for he underlyng revenue funcon, as s he case for he U.S. In arcular, he GDP rce deflaor P E (P -,P,y -,y ) aearng n (8) s consruced by he BEA as a Fsher Ideal ndex usng comonens of he CPI, PPI and exor and mor rce ndexes obaned from BLS. The exor and mor comonen ndexes are Laseyres ndexes and are duy-free.

20 9 To undersand he mac of arffs on he dfference beween rue and measured TFP, noce ha rue roducvy n (6) has arffs aearng n boh he numeraor (as argumens of he revenue funcon) and he denomnaor (he Törnqvs rce ndex s arff-nclusve). In conras, measured TFP n (8) excludes arffs from boh he numeraor (hnk of GDP as C+I+G+X M, wh mors measured a duy-free rces) and he denomnaor (snce he rces n he mor ndexes from BLS are duy-free). Ye even hough he consrucon of convenonal TFP n (8) s conssen n s reamen of arffs, s affeced by arffs because he quanes of ouus and nus are chosen a arff-dsored rces n (8) and hence resond o changes n arffs. The mac of hese quany resonses s shown by he followng resul: Prooson 2 Assume ha echnology, rces and endowmens do no change beween erods, so ha S - = S, P - = P, and v - = v. Then reducng arffs from τ - 0 o τ = 0 wll lead o TFP > n (8), / 2 even hough (A A ) = n (6), ndcang ha here s no rue roducvy change. / 2 Proof: The assumon ha S - = S mles (A A ) = n (6). Furher assumng ha P - = P and v - = v means ha P E = Q E =. From hese assumons we have G - (P -, τ -, v - ) = G (P, τ -, v ), whch s no beng maxmzed because τ - 0. From Prooson, reducng arffs o zero rases GDP, so G (P, 0, v ) > G (P, τ -, v ) and TFP > n (8). QED Prooson 2 saes ha he effcency gan from elmnang arffs whch s a movemen around he roducon ossbles froner wll ncorrecly be arbued o TFP growh as measured by (8). Bu, n addon o changes n arffs, he level of arffs can also nerac wh changes n rces o cause msmeasuremen of roducvy change. In arcular, n he resence of arffs, quany resonses o changes n he erms of rade can resul effcency gans or losses ha are measured as changes n TFP. Ths s shown by he nex rooson:

21 20 Prooson 3 Assume ha echnology and endowmens do no change, so ha A - = A n (4). Then τ - 0 or τ 0 s a necessary condon for a change n rces o resul n TFP n (8). The roof s mmedae, snce when τ - = τ = 0, hen measured TFP n (8) s dencal o rue roducvy n (6), whch s uny regardless of any change n rce. Thus, a change n he erms of rade has an mac on measured TFP only f arffs are non-zero. The effecs of arffs on he measuremen of roducvy arse because he ouu conce ha s measured by GDP uses arff-free rces, whle he ouu conce ha s bes-sued for measurng roducvy change uses arff-nclusve rces. For he Uned Saes and oher ndusral counres, arffs and changes n arffs such as occurred under he ITA are low. Thus, f he reamen of arffs were he only roblem n he measuremen of roducvy, we would exec he mac of he ITA on measured TFP o be small. Ye when he rce ndex P E (P -,P,y -,y ) s msmeasured, addonal measuremen errors n TFP arse besdes he omsson of arffs, and hese need no be small. In arcular, unmeasured changes n he erms of rade have a frs-order mac on convenonally measured roducvy growh. The U.S. mor and exor rce ndexes are subjec o wo sources of measuremen error. Frs, as already noed, he ndusry-level BLS mor and exor rces ndexes are Laseyres ndexes, so hey are vulnerable o subsuon bas. And second, he BLS mor rce ndex does no accoun for ncreases n he varey of mors comng from new sulyng counres. Provded ha he new counres are sulyng dfferenaed roducs, he resulng fall n he CES ndexes of mor rces leads o a msmeasuremen of TFP ha s frs-order. 8 8 These frs-order gans from mor varey, as measured by Broda and Wensen (2006), arse n he model of Krugman (980) where an ncrease n mor varey does no lead o any reducon n domesc varey. Bu n he

22 2 The BEA uses a Fsher formula o aggregae dealed ndexes from BLS o oban he GDP deflaor n (8). The dfference beween he Fsher and he Törnqvs formulas s neglgble, so for convenence we wll wre he GDP deflaor as he Törnqvs formula over he domesc rces and Laseyres exor and mor ndexes. Denong he Laseyres exor and mor ndexes from BLS by, xl P and, ml P, he deflaor for GDP s: ln P E (P -,P,y -,y ) = + + M ln G q G q 2 = + N, xl x x P ln G x G x 2 = + = = N, ml j mj j mj ln P G m G m 2 C j C j. (9) For convenence, we also suose ha a Törnqvs formula s used for Q E (w -,w,v -,v ) n (8), whch s he quany ndex of rmary facors, jus as n (6). Comarng (6)-(7) wh (8)-(9), he dfference beween measured and rue TFP growh s: ln TFP ( ) 2 / A A ln = R G ln R G ln + = + + N, xl x x x x x x P ln G x G x 2 ln R x R x 2 = τ τ = = N m m j j mj j j mj ~ ~ ln R )m ( R )m ( 2 C j C j, ml j mj j mj N ln P G m G m 2 C j C j = + + = =. (0) Melz (2003) model, Feensra (200) shows ha he welfare gan from he ncrease n mor varey exacly cancels wh he welfare loss from he reducon n domesc varey. There s, however, sll a frs-order welfare gan from he mroved selecon of more roducve frms no exorng.

23 22 To nerre he frs lne of (0), noce ha G and R dffer only by arff revenue, as n (3). For he U.S. economy as a whole, arff revenue relave o GDP s very small, and so s he dfference beween G and R, so he erm on he frs lne of (0) s small. The erm on he second lne of (0) deends on he dfference beween he rue ndex of exor rces ( / ) x x and he Laseyres ndex of exor rces. If he Laseyres ndex oversaes he rue ndex, as we shall fnd, ha ends o make measured TFP less han he rue roducvy ndex. The reverse occurs on he mor sde, where uward bas n he Laseyres rce ndex, P ml as comared o he rue rce ndex ( ~ / ~ ) leads o an uward bas n measured TFP. We fnd n he followng m m secons ha he dfferences beween he rue mor rce ndex ( ~ / ~ ) m m and he Laseyres ndex can be subsanal, esecally for IT roducs, whle he dfferences on he exor sde are no as large; as a resul, he combned effec s an uward bas n he measuremen of TFP. 4. Measuremen of Inernaonal Prces The Inernaonal Prce Program (IPP) of he BLS uses monhly rces for mors and exors colleced from frms o consruc mor and exor rces ndexes by means of a Laseyres formula. We have he dealed monhly rces for Seember 993 December 2006, ogeher wh an (ncomlee) se of he value weghs used n he BLS ndexes, as dscussed n he Aendx. From hese daa we relcae he consrucon of BLS s Laseyres ndexes, and hen mrove on hese mehods by consrucng varous Törnqvs rce ndexes. Suose ha whn Enduse ndusry and monh, a se he revous secon we used J of rce quoes s avalable. In J o denoe counres exorng good o he U.S., bu more generally hs se denoes all avalable rces by counry, frm, and em-level roducs whn he ndusry. The Laseyres mor rce ndex consruced by BLS s hen:

24 23 P mj, () 0 mj 0, 0 ml w m j J where m s he duy-free rce of mor n monh ; 0 m 0 m s he rce of em n a base year 0, and w s he annual mor share s a base year 0, wh w. Snce () refers o he 0 m = cumulave rce ncrease from he base erod 0 o monh, he monh-o-monh rce change s obaned as he rao of such long-erm ndexes: P, ml 0, ml 0, ml P / P, (2) Analogous formulas aly on he exor sde. Consder now he rue mor rces ~ m. In he revous secon we assumed ha he revenue funcon was CES across he se of counres sellng each good. In ha case, he mor rces ~ m should be obaned usng an ndex formula ha s exac for he CES funcon. To develo ha ndex, suose frs ha he se of counres j sellng good does no change, and denoe ha se by j J. Then he rao of CES rce aggregaes can be exressed as: P, mg w mj mj( + τj), j J ( ) (3) mj + τj where, P mg s he geomerc ndex due o Sao (977) and Vara (977), and uses he weghs w mj whch are he logarhmc mean of he mor shares n erods - and, for good and counry j, consruced from he exendure shares: s mj = mj J mj j j j ( + τ )m ( + τ )m j, wh w mj s s s s mj mj mj mj. (4) ln smj ln s mj J ln smj ln s mj Tha s, he Sao-Vara ndex s a geomerc mean over he mor rce raos, comued over he counres ha are sulyng he mor good n boh erods.

25 24 As new sulyng counres may sell good or oher sulyng counres may ex, we need o exend he Sao-Vara formula o accoun for effecs of new and dsaearng counres. A formula o do hs s derved n Feensra (994) for he CES model wh >. Suose ha he se of counres sulyng roduc n erod, j J, has a non-emy nersecon wh a base erod 0 se, 0 J. We denoe hs nersecon by 0 J J J. Then defne he erm λ m as he value of mors n erod from counres also sulyng roduc n erod 0, relave o he oal mors of roduc n erod : λ m j J j J mj mj m m j j. (5) The erm λ m can be nerreed as he erod exendure on he goods n he se J relave o oal mor exendure on good. Alernavely, λ m can be nerreed as one mnus he share of erod exendure on new sellng counres (no n he se J ). The greaer he marke share of he new sellng counres n erod, he lower he value of λ m. The corresondng erm for erod -, λ m, equals erod - exendure on he goods n J relave o he oal exendure, or one mnus he share of exendure on new counres. Then he rao of CES rce aggregaes ha ncludes he effec of ne enry of new sulyng counres can be exressed as: ~ ~ m m = P, mg λ λ m m /( σ), (6) where, P mg s agan he Sao-Vara geomerc ndex. As new sulyng counres sell more, he effecve rce n (6) falls by an amoun ha deends on σ.

26 25 In alyng equaons (3) (6) o he BLS rce daa, several ssues arse. Frs, a rue monhly Sao-Vara rce ndex, P mg would requre he use of monhly rade weghs for mors. In racce he monhly rade weghs are oo volale o be relable, so we have nsead used annual rade weghs combned wh monhly daa on he mor and exor rces, o consruc geomerc ndexes. The formula for he mor ndex, P mg s sll gven by (3)-(4), bu now w mj reflecs he annual mor shares for Enduse ndusry, whch do no vary across monhs. The geomerc ndexes consruced n hs way could equally well be called Törnqvs ndexes as we shall do snce wh annual daa here s no dfference beween he consan monhly values for mj s = s mj and he weghs w mj n (4). 9 Second, he mor values used o consruc he λ-values n (5) are also annual, and are aken from Harmonzed Sysem (HS) rade daa. To aly hese annual HS daa o equaons (5) and (20), le h denoe a 0-dg HS good and J h denoe he se of counres exorng ha good o he U.S. n any monh whn he year. Then 0 h h h J J J s he nersecon of ha se over year and a base year 0, whch s he frs year ha a HS code aears beween 989 and We consruc he λ-raos n wo ses: (a) we use (5) o consruc ( λ / λ ) for each HS roduc h, and rase hese o he ower /(σ h ) o reflec he elascy of subsuon beween varees (from Broda and Wensen, 2006); () hen we ake he geomerc mean across roducs mh mh h H whn an Enduse ndusry : m ( λ wmh /( σh ) / ) mh λ mh h H Λ. (7) 9 Normally he Törnqvs ndex uses he smle averages (smj + smj) / 2 for weghs, bu s mj = s mj when usng annual daa. Then leng smj smj n (20), we have wmj smj, as can be shown usng L Hoals rule. 20 Tha s, for HS sysem codes ha exs n 989 we use ha year as he base for consrucng roduc varey. There was a major revson o he HS sysem n 996, so for codes nroduced beween 990 and 996, we use he frs year he code aeared as he base for consrucng roduc varey. HS codes nroduced afer 996 are no used.

27 26 Noe ha (7) s an nverse measure of mor varey, because havng new sulyng counres wll lead o a lower value n (7). Fnally, n (6) he Törnqvs ndex o oban he rce ndex correced for varey., P mg s mulled by Λ m Thrd, s moran o recognze ha he measure of roduc varey we oban s no nvaran o he choce of base year, whch we have assumed s he frs year ha an HS code aears beween 989 and 996. Tha choce wll ensure ha all counres who frs suly n an HS caegory afer 989 wll be ncluded n he erm λ mh every year, and are herefore beng reaed as havng enrely new roducs every year. As exlaned by Feensra (994, Pro. ), hese counres can have shfng ase arameers or shfng qualy for her roducs every year, and our consrucon of he CES ndex s sll exac. Allowng for shfng qualy n hs way s esecally moran for IT roducs. In conras, he counres who are already sulyng n an HS caegory n he frs year aears are assumed o have consan ase arameers and qualy. By choosng an early base year we are herefore allowng for he mos counres o have changng qualy for her roducs, whch was also he aroach aken by Broda and Wensen (2006). 2 Havng obaned he mor rce ndexes for each 5-dg Enduse ndusry, we do he same for exors, bu hs me here s no correcon for varey. 22 We denoe he Törnqvs exor rce, P xg x ndexes by, whch are used n lace of ( / ) x n (0). The mor and exor rce ndexes are consruced for all 5-dg Enduse ndusres from Seember 993 December In Fgures and 2 we dslayed he erms of rade consruced from he Laseyres and Törnqvs 2 Broda and Wensen used 972 as he base year for he Tarff Schedule of he U.S. (TSUSA) sysem, and 990 for he Harmonzed sysem, whle omng 989 due o he unfcaon of Germany n ha year. 22 Feensra and Kee (2008) and Feensra (200) argue ha new exor varees should be modeled as havng a rse n her rce from a low rce, where suly s zero, o a hgher rce. Therefore, adjusng exor rces for ncreased varey leads o an ncrease n he effecve exor rce ndex and an ncrease n he mled erms of rade. However, hs resul assumes ha he enry of new exor varees s drven by shfs n foregn demand, no domesc

28 27 ndexes for aggregae exor and mor rce ndexes. In Fgure 3 0 we show he mor and exor ndexes for he varous IT ndusres, normalzed o 00 n Seember 993 (exce for comuers, whch begns n 994). In Fgure 3 we show he BLS, Laseyres, non-ita Laseyres (as defned n Secon 2), and Törnqvs ndexes (wh adjusmens for arffs and varey) for mors of Comuers, Enduse Our Laseyres ndex dffers only slghly from he ublshed BLS rce ndex, due o mssng daa and concordances ha are no fully accurae, bu he dfferences seem small enough o roceed. The non-ita seres, whch rojecs a ah for mor rces holdng arff varables consan afer June 997, les well above he ublshed seres; hs ga demonsraes he morance he ITA layed n lowerng hgh-ech rces relave o he hyohecal world wh no ITA. The arff-nclusve Törnqvs ndex s abou 7 ercenage ons below he Laseyres by he end of he samle, hough snce acual arff declnes were small, he vas majory of he dfference s accouned for by he alernave ndex formula. The mac of varey s o reduce he rce ndex by a modes % hrough On he exor sde, n Fgure 4 he BLS ndex, Laseyres and Törnqvs are all very close, devang only slghly over he samle erod. The greaer uward bas of he Laseyres ndex n he case of mors can be exlaned by he dfference beween he way ha subsuon behavor affecs he mor ndex and he way ha affecs he exor ndex. For mors, cos-mnmzng behavor by U.S. buyers ends o rase he relave quanes of he ems wh he smalles rce ndexes, causng he suerlave Törnqvs ndex o be below he Laseyres ndex. For exors, revenue-maxmzng behavor of U.S. roducers resondng o shocks n foregn demand ends o rase he relave quanes of he ems roducvy gans. Because domesc roducvy gans are clearly an moran drver of new exor varees, we do no ursue he adjusmen for exor varees here.

29 28 wh he larges rce ncreases, rasng he relave oson of he Törnqvs ndex. 23 Indeed, f shocks o foregn demand and fallng foregn arffs were he only drvers of changes n he comoson of U.S. exors, we could exec o fnd he Laseyres exor ndex o be below s Törnqvs counerar, bu he resence of oher facors, ncludng shocks o domesc suly, means ha roducer subsuon behavor jus makes he dfference beween he Laseyres ndex and he Törnqvs ndex smaller whou reversng s sgn. In Fgure 5 we show he mor rce ndexes for Comuer Accessores (Enduse 230). In hs case, he non-ita Laseyres ndex les 24 ercenage ons above he Laseyres by he end of he samle, whle he arff-nclusve Törnqvs ndex s abou 9 ercenage ons below he Laseyres. Furher adjusmen for varey s small, so ha he Törnqvs ndex nclusve of arffs and varey s ercenage ons below he Laseyres by December For exors n Fgure 6, he Törnqvs ndex has a relavely large dro n June 998, whch aears much more mued n he BLS ndex and he Laseyres because hose ndexes are usng base-erod weghs raher and curren weghs, and use an arhmec mean formula () raher han he geomerc mean (9). Turnng o Semconducors (Enduse 320) n Fgures 7 and 8, for mors we agan see ha he arff-nclusve Törnqvs ndex s abou 3 ercenage ons below he Laseyres by he end of he erod. Though he effecs of he ITA are more modes han for comuers, he mac of varey s sgnfcan, reducng he rce ndex by 5 ercenage ons over he course of he samle. For exors, we see ha he Törnqvs ndex les subsanally below he Laseyres ndex. In hs case, aears ha he convenonal demand-sde uward bas of he Laseyres ndex domnaes, as buyers of U.S. exors subsue away from goods whose relave rces have gone 23 Varan (984) resens he heory of he reverse drecon of subsuon bas n a roducer s ndex from he more famlar subsuon bas of a consumer s ndex, whch s covered n Varan (982).