Must the growth rate decle? Baumol s ubalaced growth rested Ncholas Oulto Bak of Eglad, Threadeedle Street, Lodo, ECR 8AH. The ews expressed are those of the author, ot ecessarly those of the Bak of Eglad. I should lke to thak wthout mplcatg Wllam Baumol, Alec Chrystal, Roy Cromb, Adrew Gurey, DeAe Julus, Stephe Reddg, Paul Stoema, Joh Vckers, a aoymous referee ad other colleagues at the Bak of Eglad for helpful commets ad suggestos. Issued by the Bak of Eglad, Lodo, ECR 8AH, to whch requests for ddual copes should be addressed: eelopes should be marked for the atteto of Publcatos Group. (Telephoe 00 760 4030). Workg papers are also aalable o the Bak s Iteret ste at http://www.bakofeglad.co.uk/wplst.htm. Bak of Eglad 999 ISSN 368-556
Cotets Abstract 5 Itroducto 7. The stagatost argumet ad some facts about serces 7. The pla of the paper.3 A tute argumet 3 The stagatost argumet 5. The Baumol model whe all goods are fal 5. Relate prces ad put shares 8 3 The stagatost argumet whe some products are termedate 3. A alue-added model of productty growth 3. Two cocepts of sectoral TFP growth 3 4 A smple model of edogeous structural chage 8 4. The model 8 4. Dscusso 3 5 TFP growth the Uted Kgdom: a sectoral aalyss 34 5. Quatfyg the cotrbutos of each sector 34 5. The effects of structural chage the Uted Kgdom ad the Uted States 36 5.3 The effect of measuremet error 39 5.4 Outsourcg ad the relabellg of ecoomc acttes 4 6 Cocluso 4 Refereces 44 Appedx A: Based techcal progress 47 Appedx B: The measuremet of real alue-added 50 3
Abstract Accordg to Baumol s model of ubalaced growth, f resources are shftg towards dustres where productty s growg relately slowly, the aggregate productty growth rate wll slow dow. Ths cocluso s ofte appled to the adaced dustral ecoomes, where resources are deed shftg towards the relately stagat serce dustres. Howeer, I show that Baumol s cocluso oly follows f the stagat dustres produce fal products. Ths s mportat emprcally, sce the most rapdly expadg serce dustres are those such as facal ad busess serces, whch are large producers of termedate products. Ee f such dustres are stagat, I show that a moemet of resources to them may be assocated wth rsg, ot fallg, aggregate productty growth. JEL codes: O40, O47, D4, O5. Key words: Ubalaced growth, serces, productty. 5
Itroducto (). The stagatost argumet ad some facts about serces Suppose that productty s growg at dfferet rates dfferet dustres. Suppose too that resources are gradually shftg towards the dustres where productty s growg more slowly (the techologcally stagat dustres). The the aggregate growth rate of productty wll steadly fall to the rate prealg the stagat dustres. Ths s oe cocluso of the ubalaced growth model frst set out by Baumol (967) ad further deeloped Baumol (985) ad Baumol et al (989). () Ths stagatost argumet s thought to be partcularly applcable to the adaced dustral coutres. Productty growth serces (at least as coetoally measured) s typcally lower tha the rest of the ecoomy. The proportos of output costat prces ad of employmet accouted for by serces hae bee steadly rsg these coutres (Julus ad Butler (998)). So t mght seem that the growth rate of the adaced coutres s fated to decle. The respose to ths gloomy progostcato has usually bee to argue that ot all serce dustres hae low productty growth, that ee f they do ow t may rse the future, ad that ayway measuremet errors mea that growth s uderestmated (Rowthor ad Ramaswamy (997)). It s lkely that errors measurg serce sector output are qute large (see eg Grlches (99) ad (994)). But sce fxg the errors wll ot be easy, the stagatost argumet stll mples that the growth of measured output wll decle, uless ew techology ca be reled o to rase future serce sector growth, somethg t has so far faled to do (Stroh (998)). Whateer the merts of these resposes, they all accept the stagatost argumet as correct. Ths paper argues, to the cotrary, that ths cocluso of the ubalaced growth model may be correct as appled to the adaced coutres. The reaso s that the argumet s logcally correct () Ths paper has bee produced as part of the Bak of Eglad s research programme o the serce sector. The 998 Bak of Eglad Act requres the Bak to hae regard to the deelopmet of dfferet sectors of the ecoomy. Ths paper s offered as a small cotrbuto towards meetg that requremet. Oulto (999b), a compao paper to the preset oe, dscusses some of the same ssues from a growth theoretc ewpot. () The term techologcally stagat ad ts opposte techologcally progresse', are due to Baumol. 7
oly f all dustres produce fal goods. Qute a dfferet cocluso results f some of the dustres produce termedate goods. Ad ths could be the releat case practce, sce the serce dustres that hae bee expadg partcularly rapdly are those such as facal ad busess serces, whch are large producers of termedate puts. To set the scee for what follows, Table shows growth rates of output by sector from 973-96 fe leadg coutres: the Uted Kgdom, the Uted States, Frace, Germay ad Japa. We see mmedately that maufacturg has bee a relately slow-growg sector four out of the fe, the excepto beg Japa. The four serce sectors trasport ad commucatos, the dstrbute trades, face ad busess serces, ad mscellaeous persoal serces hae all bee growg more rapdly tha maufacturg the frst four coutres. I Japa, these sectors hae bee growg at about the same rate as maufacturg. Table shows the correspodg rates of growth of labour productty (alue-added costat prces per hour worked). I the Uted Kgdom, the Uted States ad Frace, labour productty has bee growg more slowly tha maufacturg three out of the four market serces (the excepto s trasport ad commucatos). I Japa, productty has bee growg more slowly two out of the four (face ad busess serces ad o-market serces). I Germay, t has bee growg more slowly the dstrbute trades. What has bee the cosequece of these dsparate growth rates for the allocato of resources betwee sectors? Chart shows the proporto of total hours worked that has bee absorbed by market serces (the aggregate of the four serce sectors Table ) oer the perod 950-96. I each of the fe coutres, there has bee a strog upward tred. More tha half of total hours worked s ow absorbed by market serces the Uted Kgdom, the Uted States ad Japa, wth somewhat lower proportos Frace ad Germay. I 950, as ow, the Uted States had the hghest share but the t was oly 40%. I the preset cotext, partcular terest attaches to the share of resources deoted to termedate producto. Wth market serces, ths may be proxed by face ad busess serces. (3) Chart shows that there has (3) The share of face ad busess serces s oly a proxy for termedate sales, because some face ad busess serces are sold to fal demad, cludg exports. 8
Table Growth rates of output selected sectors, 973-96 (per cet per aum) Sector UK US Frace Germay Japa Agrculture, forestry, ad fshg.35.60.7 0.5-0.5 Maufacturg 0.40.98.8 0.90 3.9 Utltes.47.5 4.9.8 4.3 Costructo 0.54 0.77-0.3-0.53.8 Trasport & commucatos.70 3.4 4.08 3.6 3.0 Dstrbute trades.63 3.5.55.80 3.83 Facal & busess serces 5.3 3.76. 5.04 4.09 Mscellaeous persoal serces 3.55 3.0.75 5.59 4. Note: Output s alue-added costat prces. Omtted sectors are mg ad o-market serces (health, educato, defece ad publc admstrato). Germay s Wester Germay. Source: Calculated from O Mahoy (999, Table A). Table Growth rates of labour productty selected sectors, 973-96 (per cet per aum) Sector UK US Frace Germay Japa Agrculture, forestry, ad fshg 3.66 3.93 6.03 5.05.87 Maufacturg 4.96.39 4..95.93 Utltes.60-0.77.37.04.07 Costructo 3.4. 3.65.93 4.47 Trasport & commucatos 3.88.0 3.95 4.3.66 Dstrbute trades.5.79.6.74 3.87 Facal & busess serces.07-0.08 0.6 3.06.87 Mscellaeous persoal serces.57 0.46 0.65 3.00.60 Note: Labour productty s alue-added costat prces per hour worked. Omtted sectors are mg ad o-market serces (health, educato, defece ad publc admstrato). Germay s Wester Germay. Source: Calculated from O Mahoy (999, Tables A, B ad C). 9
Chart Proporto of aggregate hours worked market serces, 950-96 (per cet) Uted Kgdom Uted States 5. 5..7 950 973 996.7 950 973 996 5. Frace 5. Germay (West).7 950 973 996.7 950 973 996 Japa 5..7 950 973 996 Note: Market serces comprse trasport ad commucatos, the dstrbute trades, face ad busess serces, ad mscellaeous persoal serces Source: Calculated from O Mahoy (999, Tables B ad C). 0
Chart Proporto of aggregate hours worked face ad busess serces, 950-96 (per cet) Uted Kgdom Uted States 3.0 3.0.7 950 973 996.7 950 973 996 3.0 Frace 3.0 Germay (West).7 950 973 996.7 950 973 996 Japa 3.0.7 950 973 996 Source: Calculated from O Mahoy (999, Tables B ad C).
bee a partcularly sharp crease the share of ths sector total hours worked. The share s ow aroud 3% the Uted States, the Uted Kgdom ad Frace, ad aroud 9% Germay ad Japa. The share was aroud 3%-4% 950, ad has bee rsg steadly for early 50 years. (4). The pla of the paper Secto of the paper sets out the ubalaced growth model whe all goods are fal. Followg Baumol, t shows the codtos uder whch, f output all dustres s growg at the same rate, resources wll shft to the stagat dustres, wth a cosequet slowg of the aggregate productty growth rate. Secto 3 explas how matters are chaged whe some dustres produce termedate products. A geeral result s dered, ad llustrated by meas of a smple, two-dustry example. Cetral to ths secto s the dstcto betwee two cocepts of productty growth at the dustry leel, oe based o gross output, the other o alue-added. The ma result s that, uder the assumpto of perfect competto, a rse the share of resources absorbed by a dustry producg termedate products rases the aggregate growth rate, proded oly that total factor productty (TFP) growth s poste ths dustry. Ths result has a paradoxcal corollary: a shft of resources towards ee a stagat dustry that produces termedate puts rases the growth rate. Secto 4 addresses the questo whe wll a shft resources towards dustres producg termedate products actually occur? A smple, two-dustry model s deeloped, whch the frst dustry supples a put to the secod; perfect competto s assumed. The aswer s show to deped o the elastcty of substtuto the secod dustry betwee the termedate put ad the prmary put. If ths elastcty exceeds oe, resources shft towards the frst dustry. Ths result requres oly that TFP growth the frst dustry be poste; t may be slower tha TFP growth the other dustry. (4) The same source shows that the proporto of aggregate hours worked absorbed by trasport ad commucatos has bee flat or fallg four of the fe coutres (Frace s the excepto). The share absorbed by the dstrbute trades has bee rsg except Japa; the share absorbed by other market serces has bee rsg all fe coutres. The share absorbed by o-market serces has also bee rsg all fe coutres, but output measures are meagless for ths sector.
Secto 5 quatfes the effect of structural chage o the UK growth rate oer the perod 973-95. It demostrates that the shft to face ad busess serces could hae rased the UK growth rate, ee though ths sector has low TFP growth. It also dscusses the effect of measuremet error o the estmates. Secto 6 cocludes..3 A tute argumet Much of the argumet to follow s rather techcal. So to assst tuto, the cetral pot of the paper wll be llustrated by the followg, orgorous argumet. Cosder frst the tuto behd the ubalaced growth model. For purposes of llustrato, suppose there are oly two dustres whch for cocreteess we label cars ad harcuts. Suppose that labour s the oly put. Assume that productty s rsg cars but ot harcuts. Icomes are rsg oer tme because there s productty growth oe sector ee f ot the other. Suppose that people s demad for the two products rses at a equal rate. (We shall see a momet that ths commo growth rate must be declg oer tme.) Assume that total employmet s costat. The sce people wat to hae ther har cut more frequetly as they grow rcher, more hardressers wll be employed. Sce total employmet s fxed, ths meas that fewer car workers wll be employed. Ths s possble sce the productty of car workers s rsg: the growg demad for cars ca be satsfed by progressely fewer car workers. As log as the assumptos cotue to apply, the proporto of the workforce employed hardressg wll go o rsg, approachg oe asymptotcally. Ge that total resources are fxed, the oerall growth rate of the ecoomy must slow dow. Ths s because aggregate productty growth s a weghted aerage of productty growth the two sectors, where the weghts are shares total employmet. (5) We hae already see that the employmet share of harcuts s rsg oer tme. So the sector wth zero productty growth gets a eer-creasg weght ad the oerall productty growth rate must therefore decle. Because total employmet s fxed, the growth rate of aggregate output must decle too. What s happeg to costs ad prces? Assume that wages the two dustres moe step wth each other. The sce t always requres the same amout of labour to cut someoe s har but progressely less labour (5) Ths s true because we are assumg equal growth rates of output the two sectors: see Secto below. 3
to produce a car, the relate prce of a harcut must be rsg. It follows that the proporto of cosumers expedture whch falls o harcuts must also be growg, approachg oe asymptotcally. Sce the product whch forms a eer larger share of expedture s subject to zero productty growth, the rate at whch the stadard of lg s rsg must be declg. More precsely, the growth rate of the stadard of lg s fallg asymptotcally to zero. Hag set out the argumet ts most basc form, we ca ow see a smple geeralsato. Suppose that productty growth harcuts s lower tha cars but greater tha zero. The the oerall growth rate of productty ad output wll stll slow dow, approachg ow the low rate foud harcuts. Now mage aother ecoomy where as before oe dustry produces cars but the other dustry supples a termedate put, say busess serces. That s, cars are produced by combg labour ad busess serces. Busess serces requre oly labour. Total employmet s costat as before. Productty growth cars s hgher tha busess serces, but sce the car dustry has two puts we must uderstad productty growth there to mea growth total factor productty. Sce busess serces use oly labour, labour productty ad TFP are detcal that dustry. At frst sght, ths chage of assumpto seems to make o dfferece ad the same argumet as aboe apples. But fact thgs are ery dfferet. At the aggregate leel, we care oly about the output of cars sce ths s the oly product demaded by cosumers. So the ssue s whether a rsg share of employmet busess serces wll be accompaed by a rsg or fallg growth rate of car output. There are two ways whch the ecoomy ca obta more cars, ge that total employmet s fxed. Oe s f TFP rses the car dustry, the other s f TFP rses busess serces. TFP growth the car dustry rases the productty of both the puts, labour ad busess serces: more cars ca be produced for a ge amout of labour drectly employed the car dustry ad drectly employed busess serces. I addto, TFP growth the busess serces dustry rases the productty of labour employed there. Ths meas that more busess serces ca be produced for a ge amout of labour. Hece TFP growth the busess serces dustry causes hgher car output, sce the car dustry buys busess serces. The hgher the proporto of the labour force employed busess serces, the bgger the mpact o car output of TFP growth 4
busess serces. Hece ee f productty growth s low busess serces, a shft of resources to ths dustry wll be accompaed by rsg, ot fallg, growth of car output. The reaso s that such a shft wll rase the cotrbuto to the aggregate comg from busess serces wthout reducg the cotrbuto comg from the car dustry. So for the cars/busess serces ecoomy we reach exactly the opposte cocluso to the oe for the cars/harcuts ecoomy. The argumet just stated prodes support for the more geeral proposto, that a shft resources to termedate-producg dustres rases the aggregate growth rate. As the paper wll make clear, the argumet depeds o the shft beg market-duced, as a result of proft-maxmsg behaour by producers, crcumstaces where exteraltes ad other market falures do ot uduly fluece outcomes. The stagatost argumet. The Baumol model whe all goods are fal Assume that all goods ad serces are fal, e there are o termedate puts. Let y deote the gross output of the th product ( =,...,), ad let y deote aggregate output. The growth rate of aggregate output ca be defed as a weghted aerage of the growth rates of the dustry outputs, where the weghts are the alue shares (s ) of the dustres the total alue of output: ˆ = ˆ,, p y y s y s s = () p y = = = Here, the p are the prces ad a hat (^) deotes a growth rate (logarthmc derate wth respect to tme, t). Also = p y py whch mplctly defes p as the aggregate prce dex. Let x be a dex of total put to the th dustry, ad let x be aggregate put the whole ecoomy. All puts are prmary. We ca thk of the x ether as a sgle put, say labour, or as a budle of prmary puts whose composto may well ary across dustres. The growth of aggregate 5
put may be defed as a weghted aerage of the growth rates of dustry puts: xˆ = r xˆ, r = = = where r s the proporto of aggregate put employed the th dustry. These proportos wll be defed more precsely below. Defe q y / x as productty the th dustry ad q y / x as aggregate productty. Productty growth the th dustry s the qˆ = yˆ xˆ () The dustry-leel productty growth rates are assumed to be exogeous. The growth rate of aggregate productty s: qˆ = yˆ xˆ = = = s yˆ = = r xˆ = r qˆ + ( s r ) yˆ (3) We see that aggregate productty growth s ot smply a weghted aerage of dustry productty growth rates, the frst term the equato, because of the presece of the secod term. The latter measures the effect of shfts the composto of output. There are two cases where the secod term equato (3) wll be zero. The frst case s the bechmark case cosdered by Baumol et al (989, Appedx to Chapter 6), where the composto of output s assumed costat, e output s growg at the same rate all dustres: ˆ ˆy, Sce the output ad put shares both add to oe, the secod term equato (3) s zero, ad so ths specal case y = all. 6
qˆ = r qˆ (4) = The secod case whch (3) reduces to (4) s whe there are costat returs to scale, ad perfect competto preals all markets, cludg the markets for puts. Uder these codtos, the prce of a ge put s the same all dustres, ad measures ts socal margal product. It s the approprate to aggregate the dustry puts usg put prces, e we ca defe the weghts as the alue shares: r w x / = w x, r = = (5) where w s the prce of the prmary put budle dustry. Also, the prce of aggregate put w s mplctly defed by the accoutg relatoshp: wx = w x = Uder perfect competto, log-ru equlbrum, the alue of output equals the cost of the puts (cludg a ormal retur o captal): p y = w x, =,..., py = wx Hece, ddg, s = r, all (6) ad aga (3) reduces to (4). These accoutg relatoshps mply that uder perfect competto the leel of productty curret prces s the same all dustres: p y / w x =, all. So the leels effect the aggregate productty growth equato (3) dsappears, rrespecte of the 7
growth rates of dustry outputs. Sce all dustres hae the same productty leel alue terms, there s o ga to reallocato. (6) Suppose that ether of these two cases apples, so that the aggregate growth rate s ge by (4). The f resources are shftg to dustres wth comparately low productty growth, the aggregate growth rate wll clearly decle. We may ote passg that f (4) holds, the growth rate of GDP s ge by yˆ = xˆ + = r qˆ So f the growth rate of aggregate put s take to be costat, fallg productty growth mples fallg GDP growth too. I fact, wth some addtoal assumptos, a stroger proposto apples. We show the ext sub-secto that f output s growg at the same rate all dustres, the the lower a sector s productty growth rate, the faster ts share of total put s rsg. The equato (4) mples that the aggregate productty growth rate wll fall mootocally, coergg o the growth rate of the most stagat sector: ˆ m{ qˆ } as t q Ths s the strog erso of the stagatost result.. Relate prces ad put shares So far derg the stagatost result we hae made two assumptos: frst, that output grows at the same rate all dustres, or alterately, that the ecoomy s compette; ad secod, that the share of resources gog to the stagat dustres s rsg. But f the ecoomy s compette, the secod assumpto ca be dered as a mplcato of the assumpto of equal output growth rates, proded that we make the further smplfyg assumpto that the prce of the prmary put budle s the same all (6) Ee a compette ecoomy, leels effects would stll arse f we chose to measure productty growth usg a fxed weght (eg Laspeyres) dex. But t s better to use a Dsa (cha) dex, as here. Leels effects ca also arse a compette ecoomy, f we are cosderg labour productty ad labour s ot the oly prmary put. 8
dustres. Ths last assumpto meas that there s effect oly oe prmary put. (7) Let us assume that w = w, all. The we hae ad r = x / x, r = = x = = x The accoutg relatoshp that the alue of output equals the cost of the puts ow becomes: p y = wx, =,..., (7) Rearragg ths relatoshp, p y x = p q = w, =,..., (8) e the leel of productty curret prces (the curret-prce alue of output per physcal ut of put) s the same all dustres, ee though the growth rate of productty may dffer betwee dustres. Ths s because a compette ecoomy, prces adjust to make ths so, as we ca see by logarthmcally dfferetatg the accoutg relatoshps wth respect to tme: (7) I geeral, the composto of the prmary put budle ares betwee dustres. Hece, ee f put markets are udstorted, so that the prce of a ge prmary put s the same all dustres, the w wll ot geeral be equal across dustres. It ca be show that the w wll be equal oly uder restrcte assumptos: ether f there s oly oe prmary put, or f relate put prces are always the same, or fally f put testes are the same all dustres, at ge put prces. The last codto amouts to assumg that all dustres hae the same producto fucto, up to a multplcate factor. 9
pˆ + qˆ = wˆ pˆ + qˆ = wˆ whece pˆ pˆ = qˆ ˆ (9) q e relate to the geeral prce leel, the prce of the th product rses by the dfferece betwee productty growth ad aggregate productty growth. (8) Note that ths result depeds crucally o the assumpto of oly oe (possbly composte) prmary put. If there were more tha oe prmary put, the the eoluto of relate product prces would also be flueced by the eoluto of relate put prces. For example, f the prce of labour s rsg relate to that of captal, the prce of a labour-tese product may be rsg too, ee f the dustry s techologcally progresse (Oulto (999a)). The tme-paths of the output ad resource shares come from logarthmcally dfferetatg the equato defg the output share () wth respect to tme, ad usg (6) ad (8): sˆ = rˆ = qˆ qˆ + yˆ yˆ Now cosder the bechmark case whch output grows at the same rate all dustres (e yˆ = yˆ, all ). The sˆ = rˆ = qˆ qˆ (0) That s, resources shft cotuously towards the relately stagat dustres. The slower productty growth s, the more rapd the shft. The stagatost argumet s therefore stregtheed. Uder the codtos assumed here, f output grows at the same rate all dustres, the aggregate productty growth wll slow dow asymptotcally to that of the (8) The equalty of productty leels dfferet sectors uder competto has bee dscussed by Baumol ad Wolff (984). 0
slowest dustry. If output growth s faster more stagat dustres, the slowdow wll be more rapd. 3 The stagatost argumet whe some products are termedate 3. A alue-added model of productty growth Suppose ow that some dustres produce products that are cosumed by other dustres. It mght be thought that ths would make lttle dfferece, f we adopt the usual alue-added approach. Let real alue-added dustry be, ad let omal alue-added be V. The growth of aggregate alue-added () or GDP s a weghted aerage of the growth rates of dustry-leel alue-added, where the weghts are each dustry s share (u ) aggregate omal alue added: ˆ = V ˆ u,, u u V = = = = () We ca defe a dustry-leel prce of alue-added prce of alue-added p from the accoutg relatoshps: p ad a aggregate V = p V = = p Idustry-leel productty growth ca be defed as: qˆ = ˆ xˆ () Note that we use a dfferet symbol here for productty growth from that used Secto. qˆ, ot qˆ sce these two symbols refer to dfferet cocepts. Preously, output was take to be gross output (compare equato ()), ow t s alue-added. We dscuss below the relatoshp betwee these two cocepts of productty growth at the dustry leel.
Aggregate productty growth ca ow be wrtte qˆ = ˆ xˆ = = = u ˆ = q + u = r r xˆ = ( r ) ˆ (3) At the aggregate leel, we use the same symbol for productty growth as Secto., qˆ, sce the growth of GDP ewed as a sum of alue-added must be the same prcple as the growth of GDP ewed as a sum of fal expedtures. Now cosder the specal case where alue-added s growg at the same rate all dustres: ˆ = ˆ, all. Now the leels effect s zero ad (3) becomes: qˆ = r qˆ (4) = Alterately, by assumg a compette ecoomy ad employg a exactly aalogous argumet to that of Secto., we ca proe that the output ad resource shares are equal: u = r, all. So (4) apples rrespecte of the alue-added growth rates. Ge competto ad equal alue-added growth rates, we ca also proe that the share of prmary puts deoted to a dustry wll rse faster, the slower ts productty growth rate ( qˆ ): uˆ = rˆ = qˆ qˆ (5) The stagatost argumet would thus seem to go through as before. If the share of puts gog to the stagat dustres s rsg, the the aggregate productty growth rate must fall mootocally to that of the most stagat dustry or at ay rate, so equato (4) seems to be sayg. Howeer, ths argumet cotas a hdde assumpto, amely that TFP growth rates the alue-added sese ( qˆ ) are parameters. I Secto. we assumed that TFP growth rates the gross output sese ( qˆ ) were
parameters. We ow show that these two assumptos are cosstet: f the qˆ are costats ad f the share of termedate puts s chagg, the the qˆ must be chagg too. 3. Two cocepts of sectoral TFP growth Let the gross output producto fucto be y = f ( x, m, t) (6) where m s a dex of termedate put (purchases from other dustres) dustry. The accoutg relatoshp s ow p y = w x + p m m m where p s the prce of termedate put. The, assumg competto so that put shares ca be equated to the elastcty of output wth respect to each put, TFP growth the gross output sese dustry s qˆ m w x p m = yˆ xˆ mˆ p y (7) p y We wat to fd the relatoshp betwee qˆ ad qˆ = ˆ xˆ (see equato ()). Assumg that the gross output producto fucto (6) s separable, we ca wrte t the form: where y = f, m ) (7 ) ( = g( x, t) (8) 3
ad g ( ) s the alue-added producto fucto. Dfferetatg (7 ) wth respect to tme ad stll assumg competto, we obta the growth rate of real alue-added: (9) ˆ m p y p m = yˆ mˆ w x (9) wx Substtutg ths to equato () ad usg (6), we obta: qˆ p y = qˆ w x (0) Or words, TFP growth gross output sese TFP growth alue-added sese = Share of alue-added gross output Clearly, TFP growth the alue-added sese ca eer be less tha ad wll usually be larger tha TFP growth the gross output sese. (0) Also f we take the qˆ as parameters, the the qˆ become arables, sce the alue-added share s determed by the relate prces of prmary ad termedate puts, ad wll ary oer tme. Hag establshed ths relatoshp betwee the two cocepts of productty growth at the dustry leel, equato (0), we ca ow substtute from ths to the equato for aggregate productty growth (4) to get: (9) Equato (9) s a cotuous-tme, Dsa-dex form of double deflato: see Appedx B for a comparso of double wth sgle deflato. A alterate way of derg (9) s to start wth the defto of omal alue-added dustry : p = p y p m. We ca the obta (9) by dfferetatg ths equato wth respect to tme, whle holdg prces costat. The treatmet the text has the adatage of showg how double deflato s cosstet wth producto theory. (0) The relatoshp betwee these two cocepts of TFP growth was dscussed Oulto ad O Mahoy (994), Chapters ad 6. 4 m
= p y qˆ q () = p Ths last result makes use of the fact that r = w x / w x = w x / = p. Equato () exemplfes what has bee called Domar aggregato (Oulto ad O Mahoy (994), Chapter 5, followg Domar (96)). The geeral prcple s that aggregate TFP growth s a weghted sum of the dustry-leel TFP growth rates. The Domar weghts are the rato of gross output each dustry to aggregate alue-added (total fal output). () Note that these weghts sum to more tha oe. Domar aggregato was ge a theoretcal justfcato by Hulte (978): o the assumpto of costat returs to scale ad compette markets, t measures the rate at whch the socal producto possblty froter s shftg out oer tme. The tuto behd Domar aggregato s that productty growth a dustry cotrbutes drectly to aggregate productty growth (a ts fal output), but also drectly whe t supples other dustres. Costs fall the purchasg dustres, ad ths effect s obously bgger the larger such purchases are. It s useful to splt the Domar weght to two, gross output for fal use ad gross output for termedate use, both expressed as a proporto of aggregate fal output: Itermedate sales of Fal sales of Domar weght of sector = + Total fal output Total fal output Note that the sum across dustres of the secod fracto, fal sales of dustry /total fal output, s oe. So f ths fracto rses for oe dustry, t must fall by a correspodg amout for oe or more other dustres. But the same s ot true of a rse the termedate part of the Domar weght. Ths frst fracto ca rse for oe dustry wthout a correspodg fall for ay other sector. For example, suppose that dustry has oly () I the most geeral case, the deomator of the Domar weghts s total fal output. I a closed ecoomy, total fal output equals omal GDP. I a ope ecoomy, t exceeds the latter by the amout of termedate mports, whch should also be cosdered a prmary put (Gollop 983). 5
termedate sales. Suppose that there are other dustres that sell oly to fal demad, ad that these ow purchase more of dustry s product, substtutg t for prmary put. The the Domar weght for dustry wll rse wthout ay correspodg fall ay other sector s weght. It follows that the oerall productty growth rate must rse too: see equato (0). To clarfy the argumet, recall that we hae dered two equatos for aggregate productty growth, repeated here for coeece. We also repeat the relatoshp betwee the two cocepts of productty growth: qˆ = r qˆ, r = w x / = p (4) = p y qˆ q () = p qˆ p y = qˆ w x (0) From the frst of these equatos, (4), t appears that a rse the resource share (r ) of a stagat dustry, couterbalaced by a fall the share of a progresse dustry, wll lower the aggregate productty growth rate, rrespecte of whether the stagat dustry supples termedate or fal goods. From the secod, (), a qute dfferet cocluso emerges. If there s a rse the Domar weght of a dustry supplyg a termedate product, the aggregate productty growth rate wll rse, ee f the dustry questo has lower-tha-aerage productty growth. More precsely, aggregate productty growth wll rse proded oly that TFP growth the dustry s poste. The resoluto of ths apparet cotradcto comes from takg accout of the thrd equato, (0). As the dustres supplyg fal goods purchase more from the oe supplyg termedate goods, so the formers alue-added shares decle. Cosequetly, ther TFP growth rates the alue-added sese qˆ ) rse. Ths ga more tha outweghs the loss ( from the reallocato of resources faour of the stagat dustry. 6
The argumet may also be llustrated by a smple case of a two-dustry ecoomy. Suppose that dustry produces a termedate product, whch t supples to dustry. Idustry supples a fal product oly. I ths ecoomy, total fal output equals the output of dustry p q = p ). Hece from (4), (0) ad () ˆ + ( r ˆ ˆ )ˆ q = r q + q ( qˆ = r q () where qˆ qˆ = ad qˆ = qˆ ( r ) Ths smple case makes clear that a shft towards dustry (a rse r ) rases the oerall productty growth rate proded oly that ˆq s poste. 7 A possble rposte, restatg the stagatost cocluso, s to tur the argumet aroud ad assume that the alue-added TFP growth rates ( qˆ ) are parameters, ad hece that the gross output TFP growth rates q ˆ ) wll ary wth alue-added shares. Ths seems a mplausble moe. The gross output producto fucto s the fudametal cocept. The alue-added producto fucto s dered from t as a tellectual costruct. Ideed, the latter does ot ee exst uless the gross output producto fucto s separable. For example, f the gross output producto fucto s a CES fucto of captal, labour ad materals, o alue-added producto fucto exsts. I summary, we hae show that f resources are shftg to dustres producg termedate puts, the aggregate productty growth rate wll rse, howeer low the TFP growth rates ( the gross output sese) are those dustres, proded oly that they are poste. We hae also show, wth some addtoal assumptos, that a shft of resources towards stagat dustres wll occur Baumol s bechmark case of equal growth rates of real alue-added all dustres. But f these dustres produce for termedate use, there wll be o slowdow aggregate growth, but rather a speed-up (proded aga that productty growth the stagat dustres s poste). (
The bechmark case of equal growth rates f aythg uderstates the obsered shft to serces, as we hae see (see Table ). Ee so, t mght be crtcsed as restg o a arbtrary assumpto. I the ext secto, therefore, we deelop the smple two-dustry model just troduced, order to explore the codtos uder whch the stagat dustry wll deed absorb a creasg share of resources, whle smultaeously the aggregate growth rate rses. 4 A smple model of edogeous structural chage 4. The model Cosder a ecoomy wth two dustres. As Secto 3, dustry supples a termedate put to dustry but produces o fal output. Idustry produces oly fal output. We assume that there s oly oe prmary put, labour, that there are costat returs to scale, ad that techcal progress s ubased (Hcks eutral). () The gross output producto fuctos are: y = f y, x ) exp( qˆ ) (3) ( t y = x exp( qˆ t) (4) where, as before, ˆq ad ˆq are the growth rates of TFP. We assume perfectly compette codtos, so the alue of output must equal the cost of the puts. Sce the wage must be the same both dustres, as we assume homogeeous labour ad compette labour markets, p = + (5) y py wx () Techcal progress s eutral the Hcksa sese f the margal rate of substtuto betwee the two puts (the slope of the soquats) at a ge put rato s uchaged. That s, TFP growth shfts the soquats wards radally. 8
p = (6) y wx whece p y = w( x + ) x or, atoal accoutg terms, fal expedture equals factor come. The share of dustry the total cost of dustry s p / = r y p y = wx / w( x + x ) ad the share of prmary put x the total cost of dustry s r =. r Totally dfferetatg the producto fuctos (3) ad (4) wth respect to tme, we obta the usual growth-accoutg expressos for TFP growth: qˆ = yˆ qˆ = yˆ xˆ ( r ) xˆ r yˆ (7) Here we rely o the fact that uder competto, the elastcty of output wth respect to ay put s equal to the share of that put total cost. Alterately, we ca calculate TFP growth usg prces rather tha quattes. By totally dfferetatg the accoutg relatoshps (5) ad (6), ad usg (7), we obta (3) qˆ = [ pˆ qˆ = [ pˆ wˆ ] r wˆ r pˆ ] (8) Note that we hae already dered the aggregate growth rate of productty: see equato () aboe. (3) Ths s the dual approach to growth accoutg, whch uses prces. It must yeld the same results as the prmal approach based o quattes, proded that the accoutg framework s cosstet (Jorgeso ad Grlches (967), Barro (998)). 9
For cocreteess, let us agree to call dustry busess serces ad dustry cars. Car producers must choose the proft-maxmsg put rato ther dustry, the rato of labour to busess serces x / ). ( y Sce there are oly two puts, they must be substtutes. The proft-maxmsg put rato depeds o the relate prce of the two puts, w / p. From (8), ths relate prce s rsg, proded that TFP growth busess serces s poste: wˆ pˆ qˆ =. Hece, t pays to substtute busess serces for labour drectly employed cars, e x / y s fallg. The argumet s llustrated Chart 3, whch shows the producto fucto for cars. Here the tal equlbrum s at R, where aa s the ut soquat, the slope of AB shows the tal relate prce of the two puts, ad the slope of OR shows the put rato. The the relate prce of labour terms of busess serces rses to a ew leel, ge by the slope of CD. Smultaeously, TFP growth cars causes the ut soquat to shft wards a radal fasho, owg due to eutral techcal progress. The ew equlbrum s at T o bb, wth a lower rato of labour to busess serces the car dustry. More precsely, the eoluto of the put rato cars s ge by: d log( x / y) d log( x / y) = dt d log( w / p ) = σ ( wˆ pˆ ) = σ ˆq d log( w / p) dt (9) where use s made of (8) ad σ s the elastcty of substtuto: d log( x / y) σ > 0 d log( w/ p ) Hece, the rato x /y s fallg at the rate σ ˆq. 30
Howeer, we are more terested the rato of labour the two dustres, x /x. The fact that x /y s fallg does ot ecessarly mea that x /x s fallg, e that less labour wll be employed cars ad more busess Chart 3 Producto fucto for cars Labour A a C R a b S b 0 D B Busess serces serces, sce fewer workers are ow requred to produce a ut of busess serces. Usg (7) ad (9), the eoluto of the labour rato s ge by: 3
d log( x dt / x ) d log( x / y) = + qö (30) dt = ( σ) q ö Fally, ote that sce r = x /(x + x ), the x x = ( r ) /, so / r d log( x / x ) dt r& = r ( r ) ad hece from (30) r& = r ( r )( σ ) qö (3) Hece r& > 0 f σ > ad qö > 0. The cocluso may be summed up a proposto: PROPOSITION I the model of equatos (3)-(6), suppose that (a) techcal progress dustry (busess serces) s poste ( q ö > 0), ad (b) the elastcty of substtuto dustry (cars) exceeds oe (σ > ). The resources wll shft to dustry so that r approaches asymptotcally ad aggregate TFP growth wll rse, approachg q ö = qö + qö. PROOF See the dscusso aboe, ad equatos () ad (3). Proposto assumes Hcks-eutral techcal progress. If techcal progress cars s based towards labour, the proposto s qualfed though ot reersed: see Appedx A. 4. Dscusso The tuto behd ths result s that what matters for ths ecoomy s a reducto the resources requred to produce a ge leel of y. Ths ca occur ether drectly dustry or drectly, through a reducto the resources requred to produce y. For example, suppose that busess serces are requred the producto of cars. A rse TFP busess serces wll ether allow the same amout of busess serces to be produced wth fewer resources, thus freeg some resources for drect employmet producg cars; or t wll allow a expaso of busess 3
serces wthout reducg resources drectly employed cars, thus drectly eablg more cars to be produced; or some optmal combato of these two optos ca be chose by proft-maxmsg producers. The more mportat y s the producto of y (the hgher r s), the for ge TFP growth rates the two dustres, the faster aggregate TFP wll grow. Ths result, that trasferrg resources to a actty wth low productty growth wll rase the aggregate growth rate, may seem ery paradoxcal. Does t mply that t would be a good dea to trasfer as may resources as possble to put-supplyg dustres ee f they hae low productty growth? No. Maxmsg the curret rate of productty growth s ot a sesble polcy objecte. The result has bee dered o the assumpto that the ecoomy s compette ad that market prces measure socal costs. So trasferrg more resources tha proft maxmsato would dcate would reduce the leel of output. The correct terpretato s ths: f such a ecoomy we obsere a shft of resources to dustres supplyg puts, ad f TFP growth rates the gross output sese are costat, the the aggregate rate of productty growth wll be rsg, ot fallg. Now let us compare the preset cars/busess serces model wth the correspodg case where there are two dustres producg fal goods oly, say cars ad harcuts. What s the essetal dfferece betwee the cars/harcuts ecoomy ad the cars/busess serces ecoomy? I the former, the crucal relate prce s that of cars for harcuts. Assumg that TFP growth s faster cars tha harcuts, ths relate prce falls cotuously: see equato (9). Hece, cosumers ted to reduce ther purchases of harcuts. But comes are rsg oer tme, owg to aggregate TFP growth, ad assumg that the come elastcty of demad for harcuts s poste, ths teds to push demad the opposte drecto. So whether aggregate TFP growth approaches asymptotcally the rate cars (hgh) or that harcuts (low) depeds o the relate stregth of these two forces. I the cars/busess serces ecoomy, f TFP growth s assumed to be faster cars tha busess serces, the here too the relate prce of cars wll fall oer tme, as ca be deduced from equatos (8). (4) But ths relate prce, p /p, does ot eter to ayoe s choces drectly. The mportat relate prce s that of the two puts to car maufacturg, amely labour ad busess serces (w/ p ). Ee though busess serces (4) Actually, the codto s somewhat weaker tha stated: p / p wll be fallg f qˆ > ( r ) qˆ. 33
are becomg more expese relate to cars, they are becomg cheaper relate to labour, ad ths s what dres the result. 5. TFP growth the Uted Kgdom: a sectoral aalyss I ths secto, we cosder the emprcal mportace of structural chage for the Uted Kgdom growth rate sce 973. 5. Quatfyg the cotrbutos of each sector I practce, all 3 dustres dstgushed the UK put-output tables supply both fal ad termedate output. Ee busess serces supply fal output, sce some of ther output s exported. So the extet to whch the shft to serces has reduced or creased aggregate growth remas a emprcal matter. It s ot possble to carry out the aalyss at the leel of detal of the Iput-Output tables, because data o puts are curretly lackg. Istead, we llustrate usg the estmates of TFP growth dered by O Mahoy (999) for te sectors coerg the whole ecoomy for the perod 973-95. These TFP estmates employed the alue-added approach. TFP growth s measured as the growth rate of real alue-added mus the growth rate of hours worked (weghted by labour s share alue-added) mus the growth rate of physcal captal (weghted by captal s share). The captal stock estmates dstgush betwee structures ad equpmet. These TFP growth rates appear Table 3. (5) Table 3 also shows the ratos of alue-added to gross output each dustry, whch eable us to coert TFP growth o the alue-added approach to the gross output approach. The latter ca the be aggregated, by weghtg each growth rate by the rato of gross output to total fal output (Domar aggregato). Total fal output s defed as aggregate alue-added plus termedate mports (the latter s 3.8% of the total). These ratos were calculated from the 995 put-output (IO) tables. Note that each sector cossts of a umber of IO (5) O Mahoy cautos agast takg the estmated TFP growth rate for o-market serces (whch s maly goermet serces) ery serously, because of the well-kow defceces the measuremet of output ths sector. 34
Table 3 TFP growth the Uted Kgdom, by sector, 973-95 Value-added/ gross output () () (3) (4) (5) (6) TFP growth (VA) TFP growth (GO) Gross output/ Total fal output Cotrbuto to aggregate TFP growth Sector Rato % pa % pa. Rato % pa % of total Agrculture, forestry, 0.54.9.50 0.09 0.04 4.6 ad fshg Mg ad ol 0.736 -.5 -.58 0.08-0.04-4.7 refg Utltes 0.499.87.43 0.039 0.06 6.0 Maufacturg 0.488.85 0.90 0.355 0.3 34. Costructo 0.490.5.05 0.085 0.09 9.5 Trasport & 0.587 3.06.80 0.3 0.0.5 commucatos Dstrbute trades 0.558 0.43 0.4 0.0 0.05 5.4 Facal & busess 0.69 0.98 0.68 0.98 0.3 4.3 serces Mscellaeous 0.606. 0.73 0.079 0.06 6. persoal serces No-market serces 0.788 0.7 0.3 0.6 0.03 3. Total.35 0.94 00.0 Note: No-market serces comprse health, educato, publc admstrato ad defece. Sources: Value-added/gross output ad gross output/total fal output ratos from 995 put-output tables, wth tra-sector sales etted out. Total fal output s aggregate gross alue-added at basc prces + termedate mports. TFP growth (VA) from O Mahoy (999), Table.9. TFP growth (GO), colum (3) s alue- added/gross output rato x TFP growth (VA) [colum () x colum ()]. Cotrbuto to aggregate TFP growth, colum (5), s colum (3) x colum (4).
groups or dustres. Gross output of a sector s ot the sum of gross outputs of the groups, but s et of tra-sector sales. (6) Some terestg facts emerge. Frst, TFP growth has deed bee lower most serces tha maufacturg, costructo ad the utltes. Ths s the case whether we employ the alue-added or the gross output approach. Howeer, trasport ad commucatos exhbt the hghest growth rate of all. The oerall TFP growth rate was 0.94% per aum oer 973-95. Secod, facal ad busess serces ad the dstrbute trades both recee a large weght the calculato of aggregate TFP growth (0.98 ad 0.0 respectely), secod oly to maufacturg (0.355). These weghts reflect both ther sze ad the extet of ther lks wth the rest of the ecoomy. By cotrast, the employmet shares of these two sectors are 3.4% ad.9% respectely, compared wth 8.7% for maufacturg. (7) But the cotrbuto of facal ad busess serces to oerall TFP growth was comparately small, 4.3% of the total compared wth 34.% from maufacturg. Arthmetcally, ths s because ts ow TFP growth rate was qute low. The cotrbuto of the dstrbute trades was stll smaller, 5.4%. 5. The effects of structural chage the Uted Kgdom ad the Uted States How much has the aggregate growth rate bee affected by the shft of resources to serces? To aswer ths questo, we should deally compare the Domar weghts of 973 wth those of 995. But the lmtatos of the put-output tables mea that the logest comparso that ca reasoably be made s for 979 wth 995. (8) Followg the aalyss of Secto 3., we splt the Domar weghts to two, termedate sales ad fal sales, both expressed as a proporto of aggregate fal output. Table 4 shows the extet of structural chage the Uted Kgdom betwee 979 ad 995. Oerall, there has bee a small rse the degree of ter-relatedess of the ecoomy. The sum of the Domar weghts was (6) The ettg-off was doe usg a upublshed domestc use table for 995, suppled by the ONS. O Mahoy s sectors may ot correspod exactly to the oes the IO table, sce she used SIC80 ad the IO tables use SIC9. Also, the calculato of aggregate TFP growth, t would be better to use a aerage of 973 ad 995 weghts, but the former are ot aalable. (7) O Mahoy (999), Table I.. (8) There are o tables for 973. There are tables for 974, but the treatmet of serces s too aggregated to be useful.
.35 995, up from.88 979, a crease of 5%. The Domar weghts of all sectors producg goods fell oer ths perod, whereas the weghts rose for all serce sectors except trasport ad commucatos. The crease for facal ad busess serces was partcularly strkg, percetage pots. If we look specfcally at the termedate part of the Domar weghts, two large chages stad out. Frst, the termedate mportace of maufacturg creased by 7 percetage pots. That s, UK maufacturg became a more mportat source of puts for the rest of the UK ecoomy. But UK maufacturg became a much less mportat source of fal output, so oerall, ts Domar weght fell by 3 percetage pots. The secod large chage o the termedate sde s the 0 percetage pot rse the weght for facal ad busess serces, whch accouts for early all the rse ts oerall Domar weght. If we calculate the aggregate TFP growth rate usg the 979 Domar weghts stead of the 995 oes, we fd t to be 0.85% per aum, lower by 0.09% per aum. Arthmetcally, the shft to facal ad busess serces rased the growth rate by 0.08% per aum. (9) Ths may seem a small amout, but recall that, o the coetoal argumet, the shft to ths sector would hae reduced the aggregate growth rate. These ratos ca also be calculated for the Uted States, usg the 977 ad 99 bechmark put-output tables (99 s the latest aalable). The results appear Table 5 for four sectors of terest: trade, face ad (9) The shft away from mg also rased the growth rate, ad by the same amout, 0.08% per aum. Ths s because TFP growth mg was egate. The faourable effect of the shft away from mg was couter-balaced by the ufaourable effects of the shft away from the other goods-producg sectors. 37
Table 4 Structural chage the Uted Kgdom, 979-95 Itermedate sales/total fal output Gross output/total fal output Sector 979 995 Chage 979 995 Chage Agrculture, forestry, ad fshg 0.03 0.04-0.08 0.04 0.09-0.03 Mg ad ol refg 0.04 0.03-0.07 0.079 0.08-0.05 Utltes 0.08 0.04-0.04 0.056 0.039-0.07 Maufacturg 0.06 0.087 0.07 0.38 0.355-0.07 Costructo 0.007 0.0 0.006 0.00 0.085-0.05 Trasport & commucatos 0.060 0.055-0.005 0.6 0.3-0.003 Dstrbute trades 0.034 0.0-0.03 0.00 0.0 0.00 Facal & busess serces 0.030 0.7 0.097 0.084 0.98 0.4 Mscellaeous persoal serces 0.040 0.007-0.033 0.069 0.079 0.00 No-market serces 0.000 0.00 0.00 0.6 0.6 0.055 Total 0.88 0.35 0.064.88.35 0.064 Note: Gross output ad termedate sales (sales to other UK sectors) are et of tra-sector sales. Total fal output s aggregate gross alue-added + aggregate termedate mports. (Gross alue-added cludes taxes less subsdes ad, 979, sales by fal buyers). Source: 979 ad 995 put-output tables. For 979, all calculatos use Table B of the 979 tables. For 995, both the combed use ad the (upublshed) domestc use matrx were employed. 979: Gross output s from row 07 of Table B, adjusted for tra-sectoral sales (sales by each of the dustres wth a sector to other dustres the same sector); tra-sectoral sales are the releat colum elemets of Table B. Itermedate sales are dered as a resdual: gross output mus sales to fal demad. Sales to fal demad s from colum 07 of Table B of the 979 tables. 995: Gross output s from row 30 of the combed use matrx (Table 3), adjusted for tra-sectoral sales. Itermedate sales are from colum 5 of the domestc use matrx, adjusted for tra-sectoral sales. Itra-sectoral sales are also from the domestc use matrx.
Table 5 Structural chage the Uted States, 977-9 Itermedate sales/total fal output Gross output/total fal output Sector 977 99 Chage 977 99 Chage Trade 0.054 0.048-0.006 0.93 0.7-0.00 Face ad surace 0.07 0.09 0.00 0.05 0.078 0.06 Busess serces 0.064 0.09 0.08 0.079 0.9 0.040 Real estate ad retal 0.03 0.045 0.03 0.3 0.55 0.0 Total (4 sectors) 0.66 0.03 0.037 0.457 0.54 0.067 Note: Trade s wholesale ad retal trade (row 69 of the tables). Face ad surace s row 70. Busess serces s row 73. Real estate (row 7) cludes the mputed ret of ower-occupers, whch was ot separately detfed 977. Gross output for termedate use s et of tra-sectoral sales. It was ot possble to remoe mports from the alue of sales, but these four sectors they are small. Total fal output s GDP at purchasers prces. Source: US put-output tables, 977 ad 99 (Surey of Curret Busess, May 984 ad Noember 997)..
surace, busess serces, ad real estate ad retal. (0) Rather surprsgly, the mportace of trade has shruk sce 977, both fal ad termedate output, though t stll gets the largest weght oerall (0.7). Face ad surace has grow mportace oer ths 5-year perod: ts Domar weght has grow by 49% to 0.078. A smlar crease appears busess serces. Its weght, three quarters of whch s termedate, has rse by 50% to 0.9. The termedate part has rse by 43%, from 0.064 to 0.09. Most of real estate ad retal s the mputed ret of ower-occupers, whch caot be separately detfed 977. The termedate part (mostly wholesale trade) has rse by 43%. The total Domar weght of these four sectors has rse by 5% to 0.54, ad the termedate part has rse to 0.03, or by %. Thus here too, structural chage seems to hae bee faourable to productty growth. () 5.3 The effect of measuremet error It s plausble that the output of facal ad busess serces s uderestmated, because of the rather crude methods of measuremet curretly used. () If output growth ths sector whe measured correctly tured out to be apprecably hgher, so that TFP growth was also hgher, what would be the effect o Table 3? Sce most of ths sector s output s sold to other domestc sectors, the probable effect would be a correspodg reducto of the TFP growth rates of other sectors, wth oly a small effect o the oerall TFP growth rate. Ths s because correcto of a error the, growth rate of gross output a termedate-producg sector wll, uder double deflato, cause chages the growth rates of alue-added other (0) We use GDP at purchasers prces to measure aggregate fal output, sce mports for termedate use are ot ge separately the Uted States put-output tables. These are probably a small proporto of GDP the Uted States, sce total mports of goods ad serces were oly 0% of GDP 99. The absece of formato o termedate mports does ot matter much for the four sectors Table 5, sce here mports (fal plus termedate) are small. But they may be more mportat other sectors, hece o calculatos are show for these. () But there s a qualfcato to ths cocluso. The most sophstcated calculatos of TFP growth at the sectoral leel are by Jorgeso et al (987). A updated erso of the dataset deeloped there (dow-loadable from Jorgeso s web page, lked to Harard Uersty, www.harard.edu) shows that TFP growth the face, surace ad real estate sector was egate oer the perod 977-9. It s possble, howeer, that output growth s uderestmated ths sector (see below). () Curret ONS methods are descrbed by Sharp (998) ad dscussed by Oulto (999c).
purchasg sectors (see equato (9)). The other sectors cotrbuto to the oerall rate would be lowered, whereas that of facal ad busess serces would rse. I the smple example of Secto 3., correcto of a error e measurg output growth dustry would lead to offsettg chages equato (): ˆq would rse by e, ad ˆq would fall by r e, leag qˆ uaffected. Howeer, ths assumes that alue-added s measured by double deflato. Ths ettg-off of errors wll ot occur f sgle deflato s employed, as curretly the UK atoal accouts. Uder sgle deflato, correcto of such measuremet errors wll lead to a spurous rse whole-ecoomy productty growth. See Appedx B for detals. The alterate way to calculate whole-ecoomy TFP growth s to use oly aggregate data, sce qˆ = ˆ xˆ (see equato (3)). GDP s a sum of fal expedtures as well as a sum of alue-added, so we ca use the expedture estmate of GDP ad thus aod ay errors measurg output dustres producg termedate goods. (I the smple example, the growth of GDP s smply the growth of gross output dustry, cars, ad s depedet of ay error measurg output dustry, busess serces.) Howeer, though ths ges the correct aswer at the aggregate leel, t fals to tell us the cotrbuto of each sector. (3) 5.4 Outsourcg ad the relabellg of ecoomc acttes There s a alterate ew of the rsg share of face ad busess serces. Accordg to ths ew, ecoomc acttes are smply beg relabelled. A actty such as cleag, oce doe wth, say, a maufacturg frm, s ow carred out by a cotract cleag frm located the serces sector. Why should such a relabellg of acttes hae ay effect o aggregate productty growth? Ths argumet may seem superfcally plausble. But t leaes uexplaed why there should be such a cosstet tedecy to relocate acttes to the serces sector. As Chart (3) Ths rases the ssue of the cosstecy of the costat prce estmates of GDP uder the output ad expedture approaches. The expedture estmates are largely uaffected by errors sectors such as facal ad busess serces, except sofar as these produce fal output. The curret practce the Uted Kgdom s to brg the aual output estmates to le wth the expedture estmates wheeer a serous dscrepacy occurs. (For the quarterly growth rate of GDP, the output estmates are cosdered more relable, ad so t s the expedture estmates that are adjusted). See Offce for Natoal Statstcs (998a), pages 37-38 ad (998b), Chapter. 4
has show, ths tedecy s logstadg. If acttes are smply beg relabelled, why do we ot see as may trasfers from serces to the producto sector as the other drecto? Ths argumet suggests that the relocato of acttes s respose to proft opportutes. To cotue the example, ee f the cleaers are the same people as before, the orgasato of ther work ad the maagemet of ther tme may ow be dfferet. Ad hgher profts may correspod to effcecy gas. Aother factor may also be at work. Oe reaso for outsourcg acttes preously doe wth the frm s that the wages pad the ew frm may be lower. Uo or sder power may hae pushed wages aboe the market leel the orgal frm. Ths possblty does ot arse the theoretcal framework used here, sce competto put markets s assumed. So there caot be ay dffereces betwee the wages pad by dfferet frms for the same type of labour. But ote that f outsourcg occurs, because the prce of the actty s lower outsde the frm tha wth t, there s stll scope for the kd of effcecy gas aalysed here a compette settg. If the prce s lower, more of the actty wll be demaded ad ths may lead to a crease TFP growth for the same reaso as the compette case. 6. Cocluso The ma cocluso of ths paper s a optmstc oe. Ee f resources are shftg towards dustres such as facal ad busess serces, whose productty s growg slowly, the aggregate growth rate of productty eed ot fall. Qute the cotrary: f resources shft towards ee stagat termedate dustres, aggregate productty growth may rse, ot fall. Of course, t s better stll f resources shft to sectors where productty growth s hgh. Thus, cotrary to the stagatost argumet, the shft to serce dustres the adaced dustral coutres may well be faourable, ot harmful, to productty growth. Oer the perod 973-95, TFP growth market serces the Uted Kgdom has mostly bee lower tha the producto sector. But the facal ad busess serces sector has curretly (wth dstrbuto) the secod-largest weght after maufacturg the calculato of aggregate 4
productty growth. Productty growth ths sector s therefore crucal to Brta s future ecoomc prospects. At the momet, the productty growth rate appears to be qute low ad ts cotrbuto to oerall growth s also comparately low. But structural chage has faoured ths sector both the Uted Kgdom ad the Uted States, so that ts cotrbuto s calculated to hae rased, ot lowered, aggregate growth. It s qute possble that TFP growth s uderestmated facal ad busess serces, owg to error measurg output. Correcto of ths error (f t s oe) would probably make ths sector appear ee more mportat for oerall growth, ad other sectors such as maufacturg less mportat. But t would ot lead to a apprecable upward reso the oerall productty growth rate. 43
Refereces Barro, R J (998), Notes o growth accoutg, NBER Workg Paper No 6654, Cambrdge, MA. Baumol, W J (967), Macroecoomcs of ubalaced growth: the aatomy of urba crss, Amerca Ecoomc Reew, 57, pages 45-6. Baumol, W J (985), Productty polcy ad the serce sector, Ima R P (ed), Maagg the Serce Ecoomy: Prospects ad Problems, Cambrdge: Cambrdge Uersty Press. Baumol, W J, Batey Blackma, S A ad Wolff, E N (989), Productty ad Amerca Leadershp, Cambrdge, MA: The MIT Press. Baumol, W J ad Wolff, E N (984), O terdustry dffereces absolute productty, Joural of Poltcal Ecoomy, 9 (December), pages,07-34. Domar, E D (96), O the measuremet of techologcal chage, Ecoomc Joural, LXXI, pages 709-9. Gollop, F M (983), Growth accoutg a ope ecoomy, Dogramac A (ed), Deelopmets Ecoometrc Aalyses of Productty, Bosto, MA: Klumer Njhoff. Grlches, Z (ed) (99), Output measuremet the serce sectors, NBER Studes Icome ad Wealth, Volume 56, Chcago ad Lodo: Uersty of Chcago Press. Grlches, Z (994), Productty, R&D, ad the data costrat, Amerca Ecoomc Reew, 84, pages -3. Hll, T P (97), The Measuremet of Real Product: A Theoretcal ad Emprcal Aalyss of the Growth Rates, For Dfferet Idustres ad Coutres, Pars: OECD. Hulte, C R (978), Growth accoutg wth termedate puts, Reew of Ecoomc Studes, 45, pages 5-8. 44
Jorgeso, D W, Gollop, F M ad Fraume, B M. (987), Productty ad US Ecoomc Growth, Cambrdge, MA: Harard Uersty Press. Jorgeso, D W ad Grlches, Z (967), The explaato of productty chage, Reew of Ecoomc Studes, 34, pages 49-83. Julus, D ad Butler, J (998), Iflato ad growth a serce ecoomy, Bak of Eglad Quarterly Bullet, Vol 38 (4), pages 338-46. Offce for Natoal Statstcs (998a), Uted Kgdom Natoal Accouts 998, Lodo. Offce for Natoal Statstcs (998b), Uted Kgdom Natoal Accouts: Cocepts, Sources ad Methods (998 edto), Lodo. O Mahoy, M (999), Brta s Productty Performace 950-996: A Iteratoal Perspecte, Lodo: Natoal Isttute of Ecoomc ad Socal Research. Oulto, N (999a), Treds relate prces: theory ad a accoutg framework, Bak of Eglad, mmeo. Oulto, N (999b), Rsg outsourcg as a ege of growth, Bak of Eglad, mmeo. Oulto, N (999c), The measuremet of output ad prces the serce sector, Bak of Eglad, mmeo. Oulto, N ad O Mahoy, M (994), Productty ad Growth: A Study of Brtsh Idustry 954-986, Cambrdge: Cambrdge Uersty Press. Rowthor, R ad Ramaswamy, R (997), Dedustralzato: causes ad mplcatos, Staff Studes for the World Ecoomc Outlook, Washgto, DC: Iteratoal Moetary Fud. Sharp, P (998), Gross Domestc Product: Output Methodologcal Gude, GSS Methodology Seres No 5, Lodo: Offce for Natoal Statstcs. 45
Stroh, K J (998), Computers, productty ad put substtuto, Ecoomc Iqury, XXXVI (Aprl), pages 75-9. Stoema, P ad Fracs, N (994), Double deflato ad the measuremet of productty growth UK maufacturg 979-89, Iteratoal Joural of the Ecoomcs of Busess, pages, 43-437. 46
APPENDIX A: BIASED TECHNICAL PROGRESS I Secto 4 t s assumed that techcal progress dustry s ubased. Ths appedx cosders the effect of relaxg ths assumpto ad allowg for factor augmetg techcal progress at possbly dfferet rates. For smplcty, we assume that the producto fucto for dustry s CES so equato (3) becomes: y λ t ρ λ t ρ / ρ = [( ye ) + ( xe ) ], ρ <, λ > 0, λ > λ = whch s of detcal form to (3) whe. Here λ ad λ are the rates of factor augmetg techcal progress. λ λ s a measure of the bas of techcal progress faour of labour the car dustry. The elastcty of substtuto s σ = /( ρ). λ Substtutg equato (4) to the last equato, we fd the aggregate relatoshp: y ( λ+ qˆ ) t ρ λ t ρ / ρ = [( xe ) + ( xe ) ] from whch we dere the aggregate growth rate of TFP: qˆ = r ( qˆ ( λ λ)) + λ (compare ()). Hece f r s rsg, qˆ wll be rsg too proded that 0 q ˆ > ( λ λ ) (A.) e TFP growth busess serces must exceed the bas of techcal progress towards labour cars. We ca fd the codtos uder whch rsg outsourcg wll actually occur the presece of based techcal progress by cosderg the codtos for proft maxmsato. Proft maxmsato the car dustry requres that the rato of the margal products should equal the rato of the put prces at all tmes: ρ( λ λ ) ρ ) e ( x / y = w / p 47
We ca use ths equato to fd the eoluto oer tme of the put rato x /y. Totally dfferetatg wth respect to tme ad usg (8), d log( x / y) = σqˆ + ( σ )( λ λ ) dt whch may be compared wth (9). We see that a suffcet degree of bas techcal progress towards labour λ > ) may result the ( λ labour/busess serces rato rsg the car dustry f σ >, despte the fact that labour s gettg more expese. The codto for the rato to fall as t does the ubased case s: σ > ( λ σ qˆ λ ) Preously (see equato (9)), the codto was just q ˆ > 0 to whch ths last equato reduces whe there s o bas ( λ = λ ). The relate growth rate of labour the two dustres s (usg (7)): d log( x / x ) = ( σ )[ qˆ ( λ λ )] dt (A.) whch may be compared wth (30). If σ >, the codto for rsg outsourcg to occur s ow: d log( x / x ) < 0 f qˆ > ( λ λ) ad σ > dt Of course f techcal progress s based towards busess serces ( λ < ) the ths codto s weaker tha the ubased case. I the λ presece of based techcal progress, rsg outsourcg ca occur ee f σ < : d log( x / x ) < 0 f qˆ < ( λ λ) ad σ < dt 48
So a combato of a low elastcty of substtuto ad a strog bas techcal progress towards labour cars ca lead to a rsg share of labour busess serces. Howeer ths case rsg outsourcg wll reduce the aggregate TFP growth rate: see equato (A.). I summary, based techcal progress qualfes rather tha oerturs the results of Secto 4. Rsg outsourcg wll occur ad wll rase the aggregate TFP growth rate f (a) as before, the elastcty of substtuto exceeds oe ad (b) TFP growth dustry exceeds the bas towards labour dustry, q > ( λ ), rather tha TFP growth dustry ˆ λ just beg poste. So f the bas s towards labour, the ma result of Secto 4 s qualfed though ot reersed. But f the bas s towards busess serces, the ma result s stregtheed. 49
APPENDIX B: THE MEASUREMENT OF REAL VALUE-ADDED Natoal come statstcas employ two ma methods of measurg alue-added costat prces, sgle deflato ad double-deflato. The double deflato method s as follows. We wrte omal alue added sector at tme t, showg explctly the depedece o tme, as: m p ( t) ( t) = p ( t) y ( t) p ( t) m ( t) where ( t), y( t), m ( t) are the quattes of alue added, gross output ad materal put respectely at tme t ad p ( t), p( t), p ( t) are the correspodg prces. Now deflate omal gross output, p ( t) y ( t), by the prce dex for gross output, p t) / p (0), ad omal termedate put, m ( p ( t) m( t), by the prce dex for termedate put, p ( t)/ p (0). The result s double-deflated alue-added costat (tme 0) prces: m p ( 0) ( t) = p (0) y ( t) p (0) m ( t) (B.) m m m Takg growth rates (B.), we get ( t) (0) p(0) y(0) y ( t) y(0) p = (0) p (0) (0) y(0) p m (0) m (0) m( t) m (0) (0) (0) m (0) (B.) Ths equato s aalogous to (9). There are two dffereces. Frst, (B.) uses a fxed base, tme zero, ad secod, t s dscrete ot cotuous tme. Sgle deflato measures the growth rate of real alue-added smply by the gross rate of real gross output: ( t) (0) = (0) y( t) y (0) y (0) (B.3) 50
It ca be see that double deflato ad sgle deflato wll produce the same aswer oly f gross output ad termedate put are growg at the same rate: y ( t) y(0) m ( t) m(0) = y (0) m (0) (B.4) Equaletly, the aswers wll be the same oly f the rato of termedate put to gross output costat prces s costat. Ths s clearly a hghly restrcte codto. Double deflato has two theoretcal adatages oer sgle deflato. Frst, t s cosstet wth the theory of producto, as show by the derato of (9). Secod, we wat the growth rate of real GDP from the expedture sde to equal the same growth rate measured from the output sde. Asde from errors ad omssos, double deflato satsfes ths codto but sgle deflato geeral does ot, as we ca llustrate wth the model of Secto 4.. From the expedture sde, the growth rate of real GDP s smply the growth rate of real expedture o the output of dustry : Growth of GDP(E) yˆ = (B.5) From the output sde, we would measure GDP growth as a weghted aerage of the growth rates of double-deflated alue-added the two dustres, the weghts beg each dustry s share of aggregate omal alue-added: Growth of GDP(O) Double wx wx = ˆ ˆ p y + p y (B.6) Usg (9) cojucto wth (5) ad (6), we fd the double-deflated alue-added growth rates to be: 5
ˆ = yˆ ˆ p y = wx yˆ py wx yˆ So substtutg to (B.6), we see that Growth of GDP(O) Double ˆ = y (B.7) agreemet wth the expedture-sde estmate, (B.5). Some statstcal ageces use sgle deflato for practcal reasos. If the patter of termedate put purchases s ot kow wth precso, t may be better to use sgle deflato, despte ts theoretcal dsadatages (Hll 97). I the Uted Kgdom, the Offce for Natoal Statstcs (ONS) uses double deflato oly for agrculture ad electrcty. For all other dustres, the ONS uses sgle deflato (Sharp 998). Stoema ad Fracs (994) hae estmated the measuremet error due to the use of sgle deflato UK maufacturg the 980s. There s aother effect of measuremet error that also deseres cosderato. Suppose there s a error e measurg the growth rate of the gross output of dustry. Measured growth s y ˆ + e, whereas true growth s ŷ. The GDP growth measured usg double deflato s uaffected. The error e dustry duces a error of p y / wx ) e ( the estmate of alue-added growth dustry. As ca be see from (B.6), these two errors cacel out at the aggregate leel. Suppose, howeer, that sgle deflato s employed. The Growth of GDP(O) Sgle wx = p y wx ˆ ( y e) + + p y So a poste error measurg output growth dustry wll rase the estmated growth rate of GDP, ad hece that of aggregate TFP as well. yˆ 5