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 Marshall B. Rensdorf U.S. Bureau of Economc Analyss Mahew J. Slaugher Tuck School of Busness a Darmouh and NBER July 2008 Absrac Snce 995, growh n roducvy n he Uned Saes has acceleraed dramacally, due n large ar o he nformaon echnology secor. In hs aer we argue ha ar of he aaren seedu n roducvy growh acually reresens gans n he erms of rade and arff reducons, esecally for hgh-ech roducs. Unmeasured gans n he erms of rade and declnes n arffs cause real ouu growh and roducvy growh o be oversaed. Buldng on he GDP funcon aroach of Dewer and Morrson, we develo mehods for measurng hese effecs. The growh raes of our alernave rce ndexes for U.S. mors are as much as 2% er year lower han he growh rae of rce ndexes calculaed usng offcal mehods. Because non-eroleum mors amoun o around 0% of GDP durng he lae 990s, he erod we sudy, hs erms-of-rade gan can accoun for close o 0.2 ercenage ons er year, or abou 20% of he aaren ncrease n roducvy growh for he U.S. economy. Deflaors for domesc absoron are beyond he scoe of he research n hs aer, and s ossble ha bases n he domesc rce ndexes offse some of he effecs of he bases n he exor and mor ndexes on he measuremen of ouu and roducvy growh. * 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 Harvard, Oxford, and he Naonal Bureau of Economc Research. 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.

2 . Inroducon Snce 995, growh n aggregae labor roducvy n he Uned Saes 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.40 ercen er year. From 995 hrough 2007 hs rae acceleraed o an average of 2.55 ercen er year. Ths seed-u n U.S. roducvy growh would, f susaned, carry dramac mlcaons for he U.S. economy. A he revous generaon s average annual growh rae of.40 ercen, average U.S. lvng sandards were akng 50 years o double. Should he more-recen average annual growh rae of 2.55 ercen erss, hen average U.S. lvng sandards would ake jus 28 years o double or a generaon faser. Wha are he exlanaons for hs mrovemen n roducvy growh? Among ohers, he declnng rces of nformaon echnology (IT) roducs, whch acceleraed n he lae 990s, are ofen creded wh key drec and ndrec roles n hs roducvy seedu. 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 In hs aer we advance a relaed, bu new hyohess: ha nernaonal rade, and n arcular he ncreased globalzaon of he IT secor, accouns for an moran ar of he seed-u n roducvy growh. 3 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. Snce 2002, however, U.S. roducvy growh aears o have deceleraed agan. 2 Smlarly, Olner and Schel (2000,. 7) sae ha, In accord wh he dual framework descrbed above, we have nerreed he shar declne n semconducor rces afer 995 as sgnalng a cku n ha secor s TFP growh. On he ndrec role of IT n he roducvy seedu, Jorgenson (200,. 22) fnds ha, In resonse o hese [IT] rce changes, frms, households, and governmens have accumulaed comuers, sofware, and communcaons equmen much more radly han oher forms of caal. 3 See also Mann (2003), who exresses a smlar vewon.

3 2 On many measures, he global engagemen of U.S. IT frms deeened afer 995 recsely he erod of acceleraed IT rce declnes ha have been nerreed as oal facor roducvy (TFP). An moran facor n hs rce declne s ha IT has been he only ndusry o have a mullaeral rade lberalzaon under he World Trade Organzaon. As we dscuss n secon 2, he Informaon Technology Agreemen (ITA) was rafed n 996 by dozens of counres accounng for nearly 95 ercen of world IT rade, and he elmnaed all world arffs on hundreds of IT roducs n four sages from early 997 hrough Ths mng suggess ha he ITA may have layed an moran role n he os-995 rends n IT rces. To rovde some suggesve evdence for hs hyohess, n Fgure we grah he U.S. erms of rade (he rao of he exor rce ndex o he mor rce ndex) snce 989, ogeher wh mulfacor roducvy from BLS. U.S. nonfarm mulfacor roducvy growh rose from 0.53 ercen er year durng o.4 ercen er year durng The overall erms of rade are heavly nfluenced by ol mors, so o avod ha nfluence we use he overall exor rce dvded by he non-eroleum mor rce, boh from he BLS. Ths ndex of U.S. erms of rade shows a declnng rend u unl 995 n Fgure. Snce 995 a recsely he me ha roducvy growh cked u s behavor changed, wh a srng of sold gans n he non-eroleum erms of rade ndex from 995 hrough The average annual gan n he BLS non-eroleum erms of rade from 995 o 2007 s.0 ercen, so he cumulave gan was nearly as large as he deeroraon n erms of rade from he eroleum rce shocks n and , whch oaled around 5%. The BLS uses a Laseyres formula o consruc rce ndexes for mors and exors based on rce quoes collecs from morng and exorng frms. We have hs rce daa for Seember 993 hrough December 999, so we are able o reconsruc he Laseyres rce

4 3 ndexes of BLS for ha me erod. The rao of our Laseyres exor rce ndex o our Laseyres non-eroleum mor rce ndex s also shown n Fgure. Our Laseyres erms-ofrade ndex does no exacly mach he one consruced from ublshed BLS ndexes due o mssng daa for some ndusres, bu he dfference s mmaeral. The fndng ha he U.S. erms of rade began o mrove a recsely he me of he roducvy seedu, as shown n Fgure, suggess ha here could be some connecon beween he wo. Ye here are srong heorecal reasons o hnk ha changes n he erms of rade have no effec on roducvy growh. Kehoe and Ruhl (2007) 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 (2007) from a one-secor o a mul-secor model and also consder arff reducons. We show ha arff reducons and changes n he erms of rade have only a second-order mac on GDP and roducvy. If he erms of rade are msmeasured, however, he sory s dfferen. Unmeasured changes n he erms of rade have a frs-order mac on reored roducvy growh. In arcular, f he reducon n mor rces s undersaed, roducvy growh wll be corresondngly oversaed. There are hree reasons o exec ha he U.S. erms of rade are msmeasured: () as already noed, he mor and exor rces ndexes ublshed by he BLS are Laseyres ndexes, raher han a suerlave formula; () n he calculaon of GDP, mors exclude dues, and he BLS mor ndexes whch he Bureau of Economc Analyss (BEA) uses o deflae mors also measure mor rces free of arffs; () he BLS mor rce ndex does no accoun for ncreases n he varey of mors comng from new sulyng counres, as analyzed by Feensra (994) and Broda and Wensen (2006). In secon 4 we

5 4 consruc rce ndexes ha correc for hese hree feaures, and n secon 5 we analyze he mac of he ITA on he rces and varey of hgh-echnology roducs. We fnd ha hgh-ech roducs are mos affeced by hese sources of msmeasuremen. In erms of Fgure, our cenral argumen s ha he mrovemen n he erms of rade was even hgher han dslayed here. To revew our man resuls, several alernave erms-ofrade ndexes based on he calculaons n hs aer are shown n Fgure 2. We reea he BLS and our comued Laseyres erms of rade ndexes from Fgure, and also show: () an exac Törnqvs ndex for he erms of rade; () he Törnqvs ndex ha also ncororaes arffs no he mors rces; () he Törnqvs ndex ha ncororaes arffs and also mor varey. 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 snce 995, however, jus lke our oher adjusmens. The cumulave mac of hese hree adjusmens o he erms of rade means ha he rse n he Törnqvs ndex, ncororang arffs and varey, o December 999 s nearly equal o he cumulave rse n he BLS ndex o December 2007 (comare Fgures and 2). Whle he BLS ndex rses.0 ercen er year over , he Törnqvs ndex ncororang arffs and mor varey rses wce as fas, a 2. ercen er year over Evdenly, he erms-of-rade gan for he Uned Saes snce 995 has been much hgher han suggesed by offcal rce ndexes. From our aggregae erms-of-rade ndexes n Fgure 2, however, we canno nfer how unmeasured erms of rade gans mac reored U.S. roducvy growh. The reason s ha BLS s aggregae exor and mor ndexes have no role n BEA s measures of real ouu growh, whch drve he calculaons of roducvy growh. Raher, BEA consrucs GDP

6 5 deflaors from dealed ndusry exor and mor rce ndexes, generally he fve-dg Enduse ndexes roduced by BLS, usng a chaned Fsher formula and GDP weghs. To esmae he mac of msmeasured erms of rade on reored roducvy growh, we consruc alernave rce ndexes a he 5-dg (or, f arorae, 3-dg) Enduse level of deal. We hen aggregae hese dealed ndexes usng a chaned Fsher ndex formula wh weghs ha reflec her morance n GDP. The effecs of he alernave dealed rce ndexes on he measure of roducvy growh are generally he same as he ones ha we calculae for real ouu growh. 4 The alernave dealed ndexes ha we consder are: Laseyres ndexes ha mmc he BLS ndexes; Törnqvs ndexes; Törnqvs ndexes ncludng arffs; and Törnqvs ndexes ncludng arffs and a correcon for new and dsaearng varees. These alernave 5- dg ndexes are used o consruc deflaors for GDP and for he subse of GDP ha excludes governmen, he gross value added of rvae busness. 5 By comarng roducvy growh calculaed from our correced ndexes wh ha obaned wh he reconsruced BLS ndexes, n secon 6, we esmae he oron of reored U.S. roducvy growh 990s ha was acually due o unmeasured gans n erms of rade. Our cenral esmaes are ha roerly measured erms-of-rade gans can accoun for close o 0.2 ercenage ons of he os-995 ncrease n roducvy growh for he U.S. economy. Comarng ha amoun o he ncrease n labor or mulfacor roducvy, he erms of rade accouns for abou 20% of he seedu n roducvy growh. Secon 7 concludes. 4 Exce ha, as we noe below, nus of caal servces used o esmae TFP are sensve o he rce ndexes for mored caal goods. 5 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. However, ncludng mored nermedaes n nus nsead of neng hem ou of he ouu measure was found o have lle effec on TFP esmaes, so BLS measures he ouu of rvae busness by s value added. See Gullkson and Harer (999,. 50 and fn 29).

7 6 2. Globalzaon of he Informaon Technology Indusry To gauge he role of nernaonal rade n he roducon of IT goods and servces, a sensble sarng on s o resen rade flows for some secfc ndusres. Take, for examle, comuers, erherals and semconducors (Enduse caegory 23) and elecommuncaon equmen (Enduse 24). 6 These secors nclude some of he mos hgh-rofle nformaon and communcaon echnology (ICT) ndusres. Table reors curren-dollar rade flows n hese wo secors for hree years sannng mos of he 990s 992, 996, and The boom of Table also reors he share of economy-wde exors and mors flows accouned for by hese ndusres. Over he 990s exors n hese secors have been rsng faser han he naonal oal, such ha her share of ha oal rose from 0.7 % o 5.4 %. Bu a more srkng feaure s he even hgher level of mors n hese secors. Over he 990s her naonal mor share rose from 2 % o 6 %. Ths means ha hese wo cenral ICT secors are subsanal ne morers whose rade mbalance wdened durng he decade. Whn hese secors, comuers and semconducors show ha smalles rade defcs, whle comuer accessores and elecommuncaon equmen have he larges defcs. By 2000 he combned rade defc n hese ICT secors was $57 bllon, or fully 7 ercen of he non-ol U.S. rade defc ha year. Table 2 offers some addonal evdence on he rade nensy of IT ndusres, defned as rade flows as a share of ouu. For 997, Table 2 shows exors, mors, and ne exors, all as a share of ouu for wo IT ndusres comuers and erheral equmen, and semconducors and elecronc comonens. (These wo IT ndusres dffer from he Enduse classfcaons used n Table.) The key message of Table 2 s ha IT ndusres are much more rade nensve han he overall U.S. economy. In hese ndusres boh exors and mors as a share of ouu range 6 The Enduse ndusry classfcaon s used by he BEA for measurng GDP, so we also use here. Trade daa for Enduse ndusres comes from Bureau of he Census,

8 7 beween 9 and 38%. These measures of rade nensy are hgher han manufacurng ndusres n general, for whch exors and mors were jus 4 2% of ouu. Taken ogeher, Tables and 2 ndcae ha many of he cenral IT ndusres n he Uned Saes are more rade-nensve han s he res of he economy, and are subsanal ne morers. There are many facors ha conrbue o he ncreasng globalzaon of he IT ndusry, ncludng he creaon and sread of global roducon neworks. Bu n he second-half of he 990 s, one even n he global economy was of arcular morance. Under he ausces of he World Trade Organzaon (WTO), an Informaon Technology Agreemen (ITA) commed sgnaory counres o elmnae all arffs on a wde range of nearly 200 ICT 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 Also, an ITA 7 The four arff cus for he U.S. occurred n July 997, January 998, January 999, and for a small number of commodes, January 2000.

9 8 Revew Commee was esablshed o monor comlance. 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, has vrually acheved ha goal. The arff reducons over exerenced by a number of U.S. ICT ndusres are shown n Table 3. The ITA arff cus are defned a he 8-dg level of he Harmonzed Sysem (HS) sysem, used o rack mor commodes. In he second column of Table 3, we ndcae he ercenage of mor value whn each ndusry ha are 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 3 also ncludes he nformaon for several oher ndusres where more han 50% of mor value was covered by he ITA, and ndusres such as ndusres such as busness machnes and equmen, and measurng, esng, and conrol nsrumens, where less han 50% of he mor value was maced by he ITA agreemen. 8 In Table 3 we show he average arffs a he begnnng of 997, before he ITA was mlemened, and n 2000, when was concluded. I s aaren ha U.S. arffs n hese ndusres even before he ITA agreemen were low: average arffs are beween one and four ercen 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 8 Omed from Table 3 are ndusres where less han 0% of mors are covered by he ITA.

10 9 could herefore have a mulled mac on lowerng her mor rces and coss, as we wll argue n secon 5. In addon o her oenal mac on rces, mullaeral arff cus under he ITA could exand he range of sulyng counres, rovdng dfferenaed varees of IT roducs. Recen leraure has shown how o measure he roduc varey of mors or he exensve margn of rade (Feensra, 994; Hummels and Klenow, 2005; Broda and Wensen, 2006). In he fnal column of Table 3 we show he growh n mor varees for each 5-dg Enduse caegory, reflecng he ncreasng number of sulyng counres. The formula for mor varey wll be dscussed n he followng secons, bu we noe here ha he ncreases n mor varey for he ITA roducs was above ha for all oher U.S. mors, suggesng ha he mullaeral cus under he ITA were effecve n ncreasng he range of sulyng counres. 3. Measuremen of Producvy Growh wh Inernaonal Trade We have seen n he revous secon ha arffs on mored ICT roducs fell durng he erod covered by he ITA. In hs secon we descrbe how such declnes n arffs are ncororaed no he measuremen of oal facor roducvy (TFP) a an economy-wde level. 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. Though such a unform reamen for all mors mgh aear o gnore he sgnfcan reresenaon of fnshed goods n U.S. mors, Dewer and Morrson argue ha

11 0 mors can all be reaed as nermedae nus n he GDP funcon because even fnshed good mors generally requre domescally roduced dsrbuon servces o ge o fnal consumers. Modelng all mors as nermedae nus no he GDP funcon s also reasonable for our uroses, because mored fnshed consumer goods are reaed n jus he same way as mored nermedaes n he mor rce ndexes, and any bas n hose ndexes have he same mac on he measuremen of real GDP growh. 9 Le here be =,,M fnal goods, wh quanesq > 0 and rces here are =,,N exored ouus, wh quanes x > 0 and nernaonal rces > 0. In addon, 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, and domesc rces ( + ). 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. Then he revenue funcon for he economy s: R (P,, v ) y M N + N C q x ( + )m y S (v ) x mj j j () 0 = = = j= max 9 However nvesmen goods ha are mored drecly by her fnal urchaser are deflaed dencally when hey are ar of mors (M n he equaon GDP = C+I+G+X M) and when hey are ar of nvesmen (I), so he effecs on M are canceled by he effecs on I n calculaons of real GDP. Therefore, ncludng mored nvesmen goods (such as an Arbus arcraf) as nermedae nus n he GDP funcon causes a slgh oversaemen of he effec of msmeasured mors on esmaes of real GDP. The oversaemen of he effec on TFP caused by hs reamen of mored nvesmen goods s neglgble, however, because over-esmaon of real nvesmen causes an overesmaon of caal servces on he nu sde of he real TFP calculaon.

12 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. 0 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,, v ) = R (P,, v ) + N C = j= mj j j m, (3) where he equaly s obaned usng he defnon of he revenue funcon R (P,, v ). Equaon (3) saes ha nomnal GDP equals he aggregae ouu R (P,, 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 = 0. 0 Assumng ha arffs are he only ax on roducs, R (P +T, v ) s he recommended measure of aggregae ouu and equaon (3) below s he recommended roducon aroach measure of GDP n he Sysem of Naonal Accouns or SNA (Uned Naons e al., 993, aragrahs ) We use he SNA defnon of valued added, no he BEA one. BEA defnes oal gross value-added o nclude arffs and oher axes on roducs.

13 2 Proof: Because he dervave of he revenue funcon wh resec o j s mj m j, follows ha he frs dervave of he GDP funcon wh resec o j j = s zero evaluaed a 0. The second dervave s negave sem-defne because he revenue funcon s concave n mor rces. I follows ha = 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,, v R (P R (P,, v ), or ) A R (P,, v ). (4) R (P,, 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

14 3 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, /( ) ~ m = ( ) b j J jmj( j) +, =,,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, ~ x m and denoe he vecor of rces by P (,, ~ ). Then n he second sage, across goods and facors, we suose ha he revenue funcon 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 ) The coeffcens mullyng boh rces and endowmens are also allowed o change. The key resrcon mosed ~ by hs assumon s ha he coeffcens j ha aear n j j ln P ~ ln P j, whch s one comonen of he ranslog revenue funcon, canno change over me.

15 4 = + + M ln R q R q 2 = + N x x x x ln R x R x 2 = = = N m m j j mj j j mj ~ ~ ln R )m ( R )m ( 2 C j C j. (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 snce 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,, v ) s nomnal GDP, and P E (P -,P,y -,y ) s an exac GDP deflaor over rces of fnal domesc demand, exors, and duy-free mors. Noce ha f he funconal form for hese rce 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 aggregae TFP n (8) s dencal o rue roducvy growh n (6). However, 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 over comonens of he CPI, PPI and exor and mor rce ndexes obaned from BLS. The exor and mor rces are Laseyres ndexes a he 5-dg Enduse level, whch are duy-free.

16 5 To undersand he mac of arffs on rue versus 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). So he consrucon of convenonal TFP n (8) seems o be conssen n s reamen of arffs. Bu dese hs aaren conssency, he quanes of ouus and nus are chosen a arff-dsored rces n (8) and wll 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 - 0 o = 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 -, -, v - ) = G (P, -, v ), whch s no beng maxmzed because - 0. From Prooson, reducng arffs o zero rases GDP, so G (P, 0, v ) > G (P, -, v ) and TFP > n (8). QED Prooson 2 saes ha he effcency gan from elmnang arff whch s a movemen around he roducon ossbles froner wll ncorrecly be arbued o TFP growh as measured by (8). The msmeasuremen n TFP due o arff reducons s of he secondorder, snce he effcency gan from elmnang arffs s of he second-order. The followng rooson shows ha a smlar resul holds for changes n he erms of rade n he resence of arffs:

17 6 Prooson 3 Assume ha echnology and endowmens do no change beween erods, so ha S - = S and (A A / 2 ) = n (6). Then TFP n (8) due o changng rces only f - 0 or 0. The roof s mmedae, snce when - = = 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. Bu f arffs are small, hen hs mac s corresondngly small. Ths resul confrms he same fndng by Km and Ruhl (2007) for a one-secor economy. For he Uned Saes and oher ndusral counres, arffs and changes n arffs such as occurred under he ITA are low. Thus, we mgh exec ha he mac of he ITA and oher arff reducons on measured TFP s small. However, an ndrec effec of elmnang arffs under he ITA s he enry of new counres no sulyng ICT roducs. 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 no second-order. Furhermore, he formula bas from aggregang exor and mor rces wh Laseyres ndex formulas could also sgnfcanly dsor measured TFP. As noed above, he BEA uses 5-dg Enduse exor and mor rces ndexes ha obans from BLS. These are Laseyres ndexes, so we denoe hem by, P xl and, P ml. 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: 2 2 Noe ha we are gnorng any ssue ha arse from he CPI comonens used n he GDP rce deflaor.

18 7 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), we see ha 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 = = = 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) 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 hese frs erms are small. The second brackeed erm deends on he dfference beween he rue exor rces ) / ( x x and Laseyres ndex of exor rces. If he Laseyres ndex oversaes he exor rces, as we shall fnd, ha ends o make measured TFP less han rue roducvy. The reverse occurs on he mor sde, where

19 8 uward bas n he Laseyres mor rces as comared o he rue rces ( ~ / ~ ) leads o an uward bas n measured TFP. We show n he followng secons ha he dfferences beween m m he rue rces ( ~ / ~ ) m m and he Laseyres ndexes can be subsanal, esecally for ICT roducs, whle he dfferences on he exor sde s 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 999, 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 Törnqvs rce ndexes. Suose ha whn Enduse ndusry and monh, a se In he revous secon we used J of rce quoes s avalable. 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: where 0, 0 mj P ml w m, () 0 mj j J 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:

20 9 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: ~ ~ m m w mj, mj( j) = PmG, j J ( ) + (3) mj + j 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 ( + )m ( + )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. As new sulyng counres sell good, we need o exend he Sao-Vara formula o ncororae he new (and also any dsaearng) counres. Tha formula s avalable from Feensra (994). Suose ha he se of counres sulyng roduc n erod, j J, has a non-emy nersecon wh erod -, J J J. Then defne he erms m and m as he value of mors n erods - and from counres sulyng roduc n boh hese erods, relave o he oal mors of roduc n each erod:

21 20 m j J j J mj mj m m j j. (5) The erms m < can be nerreed as he erod exendure on he goods n he se J relave o oal mor exendure on good. Alernavely, hs can be nerreed as one mnus he share of erod exendure on new sellng counres (no n he se J ). When here s a greaer number of new sellng counres n erod, hs wll lower he value of m. Then he rao of CES rce aggregaes can be exressed as: ~ ~ m m = P, mg m m /( ), (6) where, P mg s agan he geomerc ndex due o Sao (977) and Vara (977). As new sulyng counres sell more, hen amoun ha deends on he elascy of subsuon. m falls and so does he effecve rce n (6), by an When 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, mg P 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 was are consrucng could equally well be called Törnqvs as we shall do snce wh annual daa here s no dfference beween he consan monhly values

22 2 for mj s = s mj and he weghs w mj n (4). 3 Second, he mor values used o consruc he -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 (6), 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 J h 989 h h J J s he nersecon of ha se over year and 989, whch we use as he base year. We consruc he -raos n wo ses: (a) we use mh mh (5) o consruc ( / ) for each HS roduc h, rasng hese o he ower /( h ), o reflec he elascy of subsuon beween varees comng from dfferen counres; 4 () hen we ake he geomerc mean across roducs m h H whn an Enduse ndusry : wmh /( h ) ( mh / mh). (7) hh Noe ha (7) s an nverse measure of mor varey, because havng new sulyng counres wll lead o a lower value n (7). In Table 3 we reored he negave of he log growh rae of m, whch s he growh n mor varey adjused by he elasces of subsuon for each 5-dg Enduse ndusry. Fnally, n (6) he Törnqvs ndex he rce ndex correced for varey., P mg s mulled by m o oban Havng obaned he mor rce ndexes for each 5-dg Enduse ndusry, we do he same for exors, bu n ha case here s no correcon for varey. We denoe he Törnqvs exor rce ndexes by, xg x P, 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 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 (6), we have wmj smj, as can be shown usng L Hoals rule. 4 We use he elasces of subsuon esmaed by Broda and Wensen (2006).

23 22 December 999. In Fgures and 2 we dslayed he erms of rade consruced from he Laseyres and Törnqvs ndexes for aggregae exor and mor rce ndexes. In Fgure 3 0 we show he mor and exor ndexes for he varous ICT ndusres, normalzed o 00 n Seember 993 (exce for he varey adjusmen, whch begns n 990). Snce he rce ndexes are very close n he early ar of our samle, we sar hese grahs a January 996. In Fgure 3 we show he BLS, Laseyres and Törnqvs ndexes for mors of Comuers (Enduse 2300), wh he adjusmens for arffs and varey. Our Laseyres ndexes dffers only slghly from he ublshed BLS rce ndexes, due o mssng daa and concordances ha are no fully accurae, bu he dfferences seem small enough o roceed. 5 The Törnqvs ndex n abou 0 ercenage ons below he Laseyres by he end of he samle, and furher adjusmens for arffs are very small. The mac of varey s o reduce he rce ndex by a facor of 0.99 n 996 and 0.92 n 999, for a 7% declne n he rce ndex beween hose years. 6 On he exor sde, n Fgure 4 he BLS ndex, Laseyres and Törnqvs are all very close, devang only slghly durng 997. In Fgure 5 we show he mor rce ndexes for Comuer Accessores (Enduse 230). In hs case he Törnqvs ndex n abou 5 ercenage ons below he Laseyres by he end of he samle. Whle furher adjusmen for arffs are very small, here s a sgnfcan mac of varey on he mor rce ndex, so ha he Törnqvs ndex nclusve of arffs and varey s 0 5 As noed n he Aendx, wo daases were rovded by BLS: Seember 993 December 996 and January 997 December 999. Whle our Laseyres ndexes are very close o he BLS ndex n he frs erod, we canno dulcae BLS rocedures afer 997 for several reasons. Frs, he rces n he second daase had o be re-based o mach he frs daase, and we could no dulcae he BLS s re-basng because he classfcaon grou numbers used o rack commodes changed beween he daases. Second, he concordance beween he classfcaon grou and Harmonzed sysem (HS) numbers, used o oban he curren rade weghs for he Törnqvs ndexes, were ncomlee due o changes n HS numbers afer 997. Ths led o some omed commodes n he Törnqvs ndexes. Thrd, n a few nsances we dd no have he Laseyres weghs used by he BLS afer 997. To mgae hese roblems, we consruc he Laseyres and Törnqvs ndexes over exacly he same se of commodes n each ndusry (whch mgh dffer slghly from he se used by BLS), so ha dfferences beween he Laseyres and Törnqvs ndexes are due solely o her weghs and formulas, no he commodes used.

24 23 ercenage ons below he Laseyres by December 999. For exors n Fgure 6, he Törnqvs ndex has a noceable dro n June 998, whch 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 (5). Turnng o Semconducors (Enduse 320) n Fgures 7 and 8, for mors we agan see ha he Törnqvs ndex s abou 0 ercenage ons below he Laseyres by he end of he erod. The mac of varey s o reduce he rce ndex by a facor of 0.97 n 996 and 0.95 n 999, so here s only slgh growh n varey. 7 For exors, we see ha he Törnqvs ndex les subsanally he Laseyres ndex. Ths rankng of exor rce ndexes was also found n Alerman, Dewer and Feensra (999). As hey exlan, can be undersood as resulng from echnologcal mrovemen n he suly of exors, leadng o hgher quanes and fallng rces along he foregn demand curve. So he exor rce ndex reflecs subsuon along foregn demand curves, and herefore he Laseyres ndex oversaes he ncrease n rces, jus as he mor rce ndex reflecs subsuon along U.S. demand curves. Fnally, n Fgures 9 and 0 we show he ndexes for Telecommuncaons (Enduse 2400). In hs case here was a sgnfcan fall n arffs over The varey adjusmen s subsanal, leadng o a reducon n he Törnqvs ndex by a facor of 0.93 n boh 996 and 999. So varey grew from s comarson year of 989, bu dd no change over hese hree years. On he exor sde we see ha he Törnqvs ndex s below he Laseyres, whch s he same aern ha occurred by Semconducors. 6 In Table 3 we reor a 9% rse n mor varey for Comuers from 996 o 200. Therefore, an addonal 2% growh n varey occurs n 2000 and In Table 3 we reor a 9% rse n mor varey for Semconducors from 996 o 200. Snce only 2% of ha occurs beween 996 and 999, he remanng 7% occurs n 2000 and 200.

25 24 To summarze he resuls from hese four ICT ndusres, n every case he Törnqvs ndex for mors s consderably below he Laseyres by he end of he samle erod, whereas for exors he ndexes dffered sgnfcanly n only wo cases. Tha means he mac of he msmeasuremen of mor rces wll have a greaer mac on TFP leadng o an uward bas han he msmeasuremen of exor rces. In addon, here s a furher mac of fallng arffs and rsng varey on reducng he mor rce ndex. These addonal macs aear o be small n he Fgures, bu as we show n he nex secon, even small reducons n arffs under he ITA have consderable mac on boh rces and varey. Snce hese varables connue o fall beyond 999 (whch was our samle erod for he dsaggregae BLS rce daa used o consruc he Törnqvs ndexes), when nvesgang he mac of arffs n he nex secon we exend he samle o 2006, usng he ublshed BLS Laseyres ndexes or mor varey consruced from he HS mor daa. 5. Imac of he ITA on Imor Prces and Varey To deermne how he arffs cus under he ITA affeced mor rces, we consruc a arff ndex for ndusry, denoed by Tar,, as: w mj, + j Tar =. (8) j J + j In addon, we also consruc a geomerc ndex of exchange raes n Enduse ndusry, Exch,, whch s a weghed average of he exchange rae mes he roducer rce ndexes (PPI) for U.S. radng arners. In hs ndex we sar wh nomnal exchange raes mes he PPI for each counry, average hese across source counres for U.S. mors (usng mor counry weghs), and hen aggregae hese across commodes agan usng he geomerc formula (wh mor commody weghs).

26 25 The varous cumulaed ndexes are denoed by 0, P mg, 0, xg 0, P, Tar and 0, Exch. As noed above, o exend hese varables beyond December 999, we use he ublshed Laseyres mor and exors rce from BLS o exend P 0, mg and we run he followng ass-hrough regresson: P 0, xg o December Usng hese ndexes, 0, P mg 3 0, 0,l ln = j0 + kk + ln Tar + l ln Exch + Z +, (9) k= where: 0 s a fxed-effec for each ndusry, and 6 l= 0 of he ITA (.e. July 997, January 998 and January 999) and k are hree ndcaor varables for he sages Z denoes addonal conrol varables. The rces of comeng roducs also belong n regressons of hs ye, and we nclude he U.S. exor rces 0, P xg n ndusry for hs urose, whch s he frs conrol. 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 varables oo. The resuls from hs ass-hrough regresson are shown n Table 4. The frs regresson s run over hose ndusres where 00% of he mor commodes are covered by he ITA (denoed by ITA = ); from Table 3, hese ndusres are comuers, erherals and semconducors. The second regresson s run over hose ndusres where 50 99% of he mor value covered by he ITA (0.5 < ITA < ), and he hrd regresson s run over hose ndusres where 49% of he mor value s covered by he ITA (0 < ITA < 0.5). The fourh regresson s run over a conrol grou of ndusres ha nclude no ITA commodes. 9 8 Runnng he ass-hrough regresson (9) usng he hybrd Törnqvs (before 2000) and Laseyres (afer 2000) rce ndexes, as comared o usng Laseyres ndexes hroughou, makes only mnor dfferences rovded ha he samle of ndusres used s held consan. 9 The conrol grou of ndusres used n he fnal regressons nclude caal goods (Enduse 2), auomobles and ars (Enduse 3), and consumer goods (Enduse 4).

27 26 Lookng frs a he regresson for ITA =, whch ncludes comuers, erherals and semconducors, 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 exceeds 20%. The arff varable self has a ass-hrough coeffcen of 22.6, whch s exremely larger han normally found and ndcaes ha he arff declnes have a hghly magnfed effec on lowerng he mor rces. Admedly, he arffs hemselves are very low n hese ndusres (see Table 3), so even wh he very large ass-hough coeffcen, he mac of he arff cus on mor rces s sll modes. The exchange rae coeffcens reored are he sum of coeffcens on he curren and sx lagged values. These esmaes show ha a 0% ermanen arecaon of foregn currences resuls n a 3.5% ncrease n U.S. mor rces. Turnng o he nex regresson (2), hs s run over ndusres wh 50 99% of he mor value covered by ITA roducs, or 0.5 < ITA <. Ths regresson ndcaes a arff ass-hrough coeffcen of 2.5, so agan, here s a magnfed mac of he ITA arff cus on he mor rces. Our exlanaon for hese resuls s ha he ITA was a mullaeral arff reducon, wh U.S. arff cus mached by hose abroad, so wh mors beng rocessed n mulle counres her rces can easly fall by more han he dro n U.S. arffs. The hrd regresson ncludes ndusres where 49% of he mor value s covered by he ITA, and now has a arff asshrough of uny. In boh of hese regressons, he ITA ndcaor varables are much smaller han found wh ITA =, so ha mos of he mac of he ITA s hrough he arff cus. The fnal regressons n Table 4 are for a conrol grou of caal and consumer goods ndusres ha do no nclude any commodes affeced by he ITA arff cus. For hese ndusres, we fnd a arff coeffcen of 0.86 for OLS, bu hs s nsgnfcanly dfferen from

28 27 uny. 20 The fac ha hs conrol grou rovde he small counry resul for arff ass-hrough gves us confdence ha he magnfed arff effecs found for ndusres wh ITA > 0.5 shows ha hose arff cus really do reflec he mullaeral naure of he ITA. In addon o OLS, we have also esmaed he regressons wh ooled mean grou (PMG), whch accouns for un-roos n he me seres and s maxmum lkelhood for conegraed anels. 2 In hs case, we combne he ndusres wh ITA > 0 n regresson (5), whle he conrol grou wh ITA = 0 s shown n regresson (6). The PMG esmae of he arff coeffcen for he ITA > 0 samle s 4.9, whch s sll sgnfcanly greaer han uny and ndcaed a magnfed mac of he arff cus. In conras, he conrol grou has a arff coeffcen of exacly uny, whch s he small counry resul. We have also nvesgaed he mac of he ITA on mor varey, usng daa from 989 o 2006 on all 5-dg Enduse ndusres. Raher han aem o srucurally model he growh n mor varey, we erform a smle dfference-n-dfference es o evaluae he mac of he ITA. We use he nverse of (7) o measure mor varey on an annual bass, and secfy he dfference-n-dfference es as: ln m = (ITA = ) (Year 997) + (0.5 ITA < ) (Year 997) (20) + (0 < ITA < 0.5) (Year 997) + Indusry andyear fxedeffecs where () are ndcaor varables reurnng a value of uny when he saemen () s rue, and zero oherwse. In addon o he secfcaon (20), we also exermen wh a sngle ndcaor varable for ndusres wh any ercenage of commodes maced by he ITA (.e. ITA > 0), 20 We have also esmaed he rce regresson for subses of he conrol grou, whch nclude caal goods (Enduse 2), auomobles and ars (Enduse 3), and consumer goods (Enduse 4). In each of hese hree caegores, he arff coeffcen s nsgnfcanly dfferen from uny. The only Enduse caegory besdes he ITA ndusres ha conssenly show a arff coeffcen greaer han uny s Enduse 2500, whch s chemcals. 2 The PMG esmaor, coded by Blackburne and Frank (2007), s avalable n STATA as he xmg command. The me-seres roeres of he daa s nvesgaed n Bergn and Feensra (2007).

29 28 whch s sll neraced wh he daes afer he ITA was n effec (.e. Year > 997). In he frs anel of Table 5, we use all Enduse ndusres, ncludng agrculure, raw maerals, caal goods, auos, and consumer goods. In he second anel we dro agrculure and raw maerals, focusng on Enduse 2 4 (caal, auos and consumer goods). The frs regresson reored n Table 5 uses OLS, along wh all Enduse ndusres. Two ou of hree neracon erms n (20) beween he ITA ndusres and he me of he ITA agreemens are sgnfcan n ha case. In he second regresson we wegh he regressons by he value of mors, and n ha case all hree neracon erms are sgnfcan, wh an ncrease n mor varey of 4.2% for he ndusres covered enrely by he agreemen,.e. comuers, erherals and semconducors. If we om agrculural goods and raw maerals, n eher he OLS or WLS regressons n he rgh anel of Table 5, hen we fnd nearly a 6% ncrease n varey for hose ITA ndusres covered fully by he agreemens, wh smaller ncreases for hose ndusres arally covered by he agreemen. Furhermore, here s an average 4.5% ncrease n varey over all ndusres maced by he ITA (n he fnal regresson). 22 We urn now o he queson of how he dro n rces and ncrease n mor varey due o he ITA has nfluenced he measuremen of roducvy growh n he Uned Saes. 6. Terms of Trade and Producvy Growh for he Uned Saes To nvesgae he sensvy of esmaes of roducvy growh o unmeasured gans n erms of rade, we calculae alernave versons of he deflaors of exors and mors on whch he esmaes of roducvy deend. The Major Secor Producvy and Coss Program n BLS s Offce of Producvy and Technology uses measures of he ouu of rvae busness and

30 29 nonfarm rvae busness from BEA. 23 Therefore he relevan deflaors are he ones calculaed by BEA usng weghs from he Naonal Income and Produc Accouns (NIPAs) and rce ndexes for dealed ems from BLS. In he case of exors and mors, he dealed rce ndexes are generally he 5-dg Enduse level ndexes from he Inernaonal Prce Program. We frs relcae BLS s Laseyres rce ndexes for 5-dg Enduse exors and mors o oban a baselne for our comarsons. To oban he buldng blocks for our correced deflaors, we consruc arallel exor and mor rce ndexes usng a Törnqvs ndex formula, and for mors we calculae addonal ses of Törnqvs ndexes ha nclude arffs and varey effecs, as descrbed n secon 4. We hen aggregae he varous versons of he 5-dg Enduse ndexes usng he Fsher ndex formula rce wh weghs from he NIPAs o oban deflaors for merchandse exors and for non-eroleum merchandse mors. Table 6 reors he resuls for our Törnqvs exor rce ndexes and he hree knds of mor rce ndexes: he Törnqvs, he arff-nclusve Törnqvs, and he arff-nclusve Törnqvs adjused for varey effecs. Unsurrsngly, relacng he Laseyres ndex wh he Törnqvs ndex has a smaller effec when a Fsher ndex s used for hgher-level aggregaon han dd when a Laseyres ndex was used a all sages of aggregaon (as shown n Fgure ). Usng he Törnqvs formula o calculae he dealed ndexes reduces he growh rae of our aggregae Fsher exor ndex by 0.6 o 0.66% er year, wh a subsanal oron of hs effec comng from ICT goods. The Törnqvs formula also reduces he growh rae of he aggregae mor rce ndex by 0.35 o 0.72% er year. From 996 o 999, he effec on he growh rae 22 I s worh emhaszng ha because we are ncororang he elascy of subsuon /( h ) no he defnon of varey n (7), he acual ncrease n varey s larger han ndcaed by hese regresson coeffcens, e.g. wce as hgh for h = 3, or hree mes as hgh for h = BLS revously made a mnor adjusmen o BEA s ouu measure (Fraumen e al.,. 379), bu hs s no longer necessary.