Structural Change within the Service Sector and the Future of Baumol s Disease

Transcription

1 Srucural Change wihin he Service Secor and he Fuure of Baumol s Disease Georg Duernecker (Universiy of Munich, CEPR, and IZA) Berhold Herrendorf (Arizona Sae Universiy) Ákos Valeninyi (Universiy of Mancheser, CEPR, and CERS HAS) December 4, 2017 Absrac Srucural change in developed counries slows down aggregae produciviy growh by reallocaing producion o indusries wih low produciviy growh. We documen ha his so called Baumol s disease considerably reduced produciviy growh in he poswar U.S. We capure he effec of Baumol s disease on produciviy growh wih a novel model of srucural change ha disaggregaes he service secor ino services wih low and high produciviy growh. The daa imply ha he wo service subsecors are subsiues. We find ha his subsiuabiliy limis how imporan services wih low produciviy growh may become, which bounds he fuure effec of Baumol s disease. Keywords: Baumol s Disease; Produciviy Growh Slowdown; Service Secor; Srucural Change. JEL classificaion: O41; O47; O51. This paper incorporaes maerial from an earlier manuscrip, which was called Unbalanced Growh Slowdown. We are indebed o Richard Rogerson for deailed feedback. For helpful commens and suggesions, we hank Zsófia Bárány, Aspen Gorry, Mari Mesieri, Rachel Ngai, Michael Sposi, and Gusavo Venura, as well as he audiences of presenaions a ASU, he BEA, CEPR s ESSIM 2017, CERGE EI Prague, he Chrismas Meeing of he German Expa Economiss 2016, he Economic Growh and Flucuaions Group of he Barcelona Summer Forum 2017, Erasmus Universiy Roerdam, he European Moneary Forum 2016 a he Bank of England, he Federal Reserve Banks of Alana and S. Louis, he RIDGE Workshop on Growh and Developmen 2016, he SED Meeing 2017, Souhern Mehodis Universiy, he Universiies of Barcelona, Mancheser, Munich, Norh Carolina a Charloe, and Wesern Onario, he Vienna Macroeconomic Workshop, and he World Bank. Valeninyi hanks he Hungarian Naional Research, Developmen and Innovaion Office (Projec KJS K ). All errors are our own.

2 1 Inroducion Saring wih he seminal work of Baumol (1967), i has been recognized ha srucural change in developed economies slows down (aggregae) produciviy growh by reallocaing producion o indusries wih low produciviy growh; see for example Baumol e al. (1985) and Nordhaus (2008). This phenomenon is ofen referred o as cos disease or Baumol s disease. Baumol (1967) drew paricular aenion o he fac ha producion is even reallocaed o sagnan indusries of he service secor ha have no produciviy growh. Baumol s observaion raises he imporan quesion wheher he sagnan indusries will gradually ake over he economy in he fuure, which would drive aggregae produciviy growh down o zero. This quesion is paricularly relevan in he broader conex of he slowdown in produciviy growh ha has occurred since he 1970s in indusrialized economies like he U.S. and ha led o a lively debae abou wheher fuure produciviy growh will rebound or decline furher; see for example Fernald and Jones (2014) and Fernald (2016). The goal of his paper is o invesigae he effecs of Baumol s disease on pas and fuure U.S. produciviy growh. We define produciviy as he value added per human capial adjused hours ( efficiency unis ), eiher in a secor or a he aggregae level of he enire economy. Using efficiency unis is crucial in he conex of Baumol s disease, because i allows us o hink abou he implicaions for produciviy of reallocaing workers wih differen levels of human capial across secors. Our focus in his paper is on how changes in he secoral composiion of he economy affec produciviy growh, aking as exogenously given he processes for oal efficiency unis and secoral produciviy. 1 In oher words, we will no address he relaed quesions of how human capial or secoral produciviies may change in response o changes in he secoral composiion; see Herrendorf and Valeninyi (2015) for an analysis of he laer quesion. We firs documen ha Baumol s disease considerably reduced produciviy growh in he poswar U.S. Our preferred measure implies ha Baumol s disease accouns for a hird of he observed produciviy slowdown. We hen build a model ha capures he effec of Baumol s disease on pas produciviy growh and ha is a naural saring poin for invesigaing how imporan Baumol s disease will be in he fuure. The novel feaure of our model is ha i disaggregaes he service secor ino services wih high produciviy growh and services wih low produciviy growh. In conras, he lieraure on srucural change ypically absracs from he heerogeneiy among he service indusries and considers jus one broad service secor. Connecing our model o he poswar U.S. economy implies ha services wih high and low produciviy growh are subsiues. We find ha he subsiuabiliy beween he wo service subsecors implies ha he service secor wih low produciviy growh will no gradually ake 1 To be clear abou erminology, a secor is a collecion of indusries and an indusry is a group of esablishmens ha produce similar producs or provide similar services. 1

3 over he economy in he fuure. As a resul, our model predics ha in he nex 60 years he effec of Baumol s disease on produciviy growh will be less han half of wha i has been in he las 60 years. Turning now o he deails of our analysis, we firs esablish ha Baumol s disease considerably reduced produciviy growh in he pos war U.S. by comparing he average annual growh raes of produciviy during he weny year periods and We ake 20 year averages o smooh ou business cycle flucuaions and we sop in 2007 because his paper is no abou he Grea Recession. Our daa source is WORLD KLEMS because i has qualiy adjused hours ( efficiency unis ). We find ha in he poswar U.S., annual produciviy growh during was 0.9 percenage poins higher han during If he 1947 secoral composiion had remained unchanged while he secoral produciviy growh raes had been he observed ones, hen he difference beween he growh raes in he wo periods would have been 0.6 insead of 0.9 percenage poins. This means ha Baumol s disease caused a 0.3 percenage poins decline in produciviy growh, which is a hird of he oal decline. We conclude from his ha Baumol s disease has had a sizeable effec on poswar U.S. produciviy growh ha is oo large o ignore. Looking a he pas imporance of Baumol s disease also reveals ha in recen years virually all of he produciviy effecs of Baumol s disease have been due o srucural change from he goods secor o he service secor and wihin he service secor, insead of due o srucural change wihin he goods secor. This makes inuiive sense because he U.S. economy already wen hrough mos of he srucural change wihin he goods secor (mainly from agriculure o manufacuring). Moreover, he service secor is raher heerogeneous, conaining indusries ha have very high produciviy growh (e.g. air ransporaion) as well as indusries ha have very low produciviy growh (e.g. food services and drinking places). The implicaion of his observaion is ha he usual splis in he srucural change lieraure, which rea services as one broad secor and absrac from srucural change wihin he service secor, are no useful in our conex. 2 A naural firs sep for aking ino accoun he srucural change wihin he service secor is o disinguish beween service indusries wih high and low produciviy growh, defined as above and below he average produciviy growh in he service secor. We esablish ha his way of disaggregaing services capures almos all of he pas produciviy effecs resuling from srucural change wihin he service secor. In ligh of he evidence for he effec of Baumol s disease on pas produciviy growh, i is raher surprising ha he lieraure on srucural change has paid lile aenion o he produciviy slowdown ha resuls from Baumol s disease. For example, he review aricle of Herrendorf e al. (2014) does no discuss i a all. The likely reason for his is ha having an 2 An excepion is Duare and Resuccia (2016), who focused on final expendiure and spli services ino modern and radiional ones. Unforunaely, his spli is no applicable in our conex in which indusries produce value added. 2

4 aggregae balanced growh pah simplifies he analyical characerizaion of he equilibrium. In many models of srucural change, an aggregae balanced growh pah exiss if GDP in each period is expressed in erms of a numeraire from his period. Since produciviy growh is consan along aggregae balanced growh pahs, i seems naural o conclude ha Baumol s disease is no an issue in sandard models of srucural change. In a relaed paper, Duernecker e al. (2017), we show ha his conclusion is misleading: if we measure GDP hrough Fisher indexes as i is done in he Naional Income and Produc Accouns (NIPA), insead of in erms of a numeraire from he curren period, hen Baumol s disease can play an imporan role in oherwise sandard models of srucural change. In he curren paper, we ake his resul o hear and quanify he effecs of Baumol s disease on fuure produciviy growh in a novel model of srucural change in which GDP is measured as in he daa. Our model has hree secors ha produce goods, services wih high produciviy growh, and services wih low produciviy growh. The broad goods secor lumps agriculure ogeher wih consrucion, manufacuring, mining, and uiliies, because agriculure now plays a secondary role only. Our model generaes he usual srucural change beween he broad secors of goods and services as well as he lile sudied srucural change wihin he service secor. We keep hings as simple as possible and assume ha secoral value added is produced from labor under consan reurns and ha secoral produciviy and oal efficiency unis grow exogenously. We hen sudy how changes in he secoral composiion affec he growh of aggregae produciviy. Since our model does no have capial, all secoral value added is consumed and he uiliy funcion governs how producion is reallocaed in response o changes in he exogenous variables. Rogerson (2008) argued ha his a useful firs sep for undersanding he aggregae implicaions of srucural change if he uiliy funcion capures well he observed reallocaion of producion. We choose a specificaion ha mees his crierion. Herrendorf e al. (2017) sudy srucural change wihin he invesmen secor and derive condiions under which his is possible. We model preferences hrough a nesed version of he non homoheic CES funcion proposed by Comin, Mesieri, and Lashkari (2015). The ouer layer aggregaes he value added of he broad secors goods and services ino an aggregae consumpion index. The inner layer aggregaes he value added of he wo service subsecors ino he broad service secor. Our nesed specificaion allows he elasiciies of subsiuion and he income effecs o differ by layer. The parameer values of he elasiciies and he income effecs will be crucial for capuring he observed reallocaion of producion in response o exogenous produciviy growh a he secor level. Consisen wih he evidence provided by Boppar (2016) and Comin e al. (2015), our version of he non homoheic CES funcion implies persisen income effecs ha do no disappear in he limi. This will be crucial when we make predicion abou he disan fuure. We calibrae our model o capure salien feaures of srucural change and nominal and 3

5 real secoral produciviy growh in he poswar U.S. economy. For he ouer layer of our uiliy funcion, he calibraion yields ha goods are necessiies, services are luxuries, and goods and services are complemens. These feaures of our uiliy funcion are sandard; see for example Herrendorf e al. (2013). They imply ha he secor wih he low produciviy growh he service secor will ake over our economy in he limi. We emphasize ha his does no mean ha he service subsecor wih low produciviy growh will ake over, because he inner layer of our uiliy funcion generaes srucural change wihin he service secor. The calibraion for ha inner layer yields he novel feaures ha he services wih high produciviy growh are necessiies, he services wih low produciviy growh are luxuries, and he wo service subsecors are subsiues. The subsiuabiliy beween he wo service subsecors is going o be criical for he fuure imporance of Baumol s disease, because i works agains he income effecs and limis how imporan he service subsecor wih low produciviy growh can become. Assuming ha he recen growh of secoral labor produciviy and oal efficiency unis of labor coninues ino he fuure and simulaing our model forward, we find ha he fuure produciviy effecs of Baumol s disease will be limied. Specifically, over he nex 60 years, he reducion in produciviy growh ha resuls from Baumol s disease is less han half of wha i has been in he poswar period. The reason for his is ha he service secor wih low produciviy growh does no ake over he enire economy, because he subsiuabiliy beween he wo service subsecors consrains he fuure slowdown in produciviy growh. If he relaive price of services wih low produciviy growh increases wihou bound, hen households increasingly subsiue away from hem. As a resul, he economy reallocaes less and less producion o he service indusries ha have no produciviy growh. This feaure of our model is very robus o changing he deails of he forward simulaions and i markedly differs from he canonical model of srucural ransformaion which absrac from he subsiuabiliy wihin he service secor. 3 In he nex Secion, we discuss he closely relaed lieraure. Secion 3 presens evidence ha Baumol s disease has conribued o he slowdown in labor produciviy in he poswar U.S. In Secion 4, we develop our model. In Secion 5, we calibrae our model and use i o predic how much fuure slowdown in produciviy growh will resul from Baumol s disease. Secion 6 concludes. An Appendix conains background informaion for he daa work and he proofs of our resuls. 3 Sricly speaking, he previous saemen refers only o models of srucural change wihou capial. In conras, models of srucural change wih capial usually do no feaure srucural change wihin he invesmen secor, implying ha, in he limi of hese models, he secor wih he slowes produciviy growh akes over he consumpion secor, insead of he whole economy. An excepion o his saemen is he model of Herrendorf e al. (2017) which capures srucural change in he invesmen secor and he consumpion secor. 4

6 2 Relaed Lieraure Our work is closely relaed o a recen lieraure ha wonders wheher he pas slowdown in produciviy growh is a emporary or a permanen phenomenon; see Anolin-Diaz e al. (2017) for a saisical analysis. For example, Gordon (2016) argued ha we picked he low hanging frui (e.g., railroads, cars, and airplanes) during he special cenury and ha more recen innovaions pale in comparison. Bloom e al. (2016) provided evidence ha suppors his view. Fernald and Jones (2014) poined ou ha he engines of economic growh like educaion or research and developmen require he inpu of ime which canno be increased ad infinium. The endency in his lieraure is o conclude ha low produciviy growh raes may be he fuure norm. Our work adds an addiional reason for why fuure produciviy growh raes are no likely o reurn o pas ones: Baumol s disease. Our work is also relaed o aemps o measured cross counry gaps in secoral TFP or labor produciviy; see for example Duare and Resuccia (2010), Herrendorf and Valeninyi (2012), and Duare and Resuccia (2016). The mos closely relaed paper o ours is Duare and Resuccia (2016), who used he 2005 cross secion of he Inernaional Comparisons Program of he Penn World Table. Assuming ha secors produce final goods and disinguishing beween radiional and modern services, hey found ha he larges cross counry produciviy gaps are in goods and modern services and he smalles cross counry produciviy gaps are in radiional services. The main differences o our sudy are ha we are ineresed in he U.S. ime series, assume ha secors produce value added, and disinguish beween services wih high and low produciviy growh. Noneheless, if we used our model o generae a cross secion of counries wih differen levels of aggregae produciviy, hen i would generae a resul ha has he same flavor as ha of Duare and Resuccia (2016): he cross counry produciviy differences in he goods and he service secor wih high produciviy growh are larger han hose in he service secor wih low produciviy growh. Lasly, our work is relaed o several papers ha argued he usual hree secor spli ino agriculure, manufacuring, and services is no useful anymore in a rich counry like he U.S. where mos of producion is in he service secor. Since produciviy growh is raher heerogenous wihin he service secor, wih some indusries showing srong produciviy growh while ohers showing no produciviy growh, he effecs of reallocaion wihin he service secor are crucial when one seeks o undersand he aggregae implicaions of srucural change in rich counries [Baumol e al. (1985), Jorgenson and Timmer (2011), and Buera and Kaboski (2012)]. Since sudying Baumol s disease is jus one example where his poin is cenral, our model is likely o be useful beyond he narrow focus on Baumol s disease. 5

7 3 Evidence on Srucural Change wihin Services and Baumol s Disease We use daa from he March 2017 version of WORLD KLEMS, which offers informaion abou qualiy adjused hours ha ake ino accoun differences in human capial. We call hese efficiency unis of labor. Jorgenson e al. (2013) describe how he daa are consruced. Since we wan o sudy counerfacuals ha reallocae workers wih poenially differen levels of human capial across secors, conducing he analysis in erms of efficiency unis is crucial. The BEA does no provide ha informaion. 3.1 Baumol s disease To esablish ha Baumol s disease imporanly conribued o he produciviy growh slowdown in he poswar U.S., we sar wih he obvious exercise ha compares he acual growh raes of produciviy wih he counerfacual growh raes assuming ha here had no been srucural change among he 65 indusries of WORLD KLEMS. As always in his paper, produciviy is defined as real value added per efficiency uni. For he counerfacual, we fix he secoral composiion of 1947/8 and calculae he aggregae produciviy growh rae ha would have resuled from he acual growh raes of secoral produciviy wih he unchanged secoral composiion from 1947/8. Calculaing he counerfacual growh raes is no as sraighforward as one migh hink because WORLD KLEMS is buil around Törnqvis indexes ha are no addiive. In Appendix A below, we develop a produciviy accouning framework ha is similar o ha of Nordhaus (2002) and addresses he resuling complicaions. One implicaion of his mehod is ha o be consisen wih he way in which he Törnqvis indexes are consruced, we mus fix he secoral composiion in wo adjacen years. Tha is he reason why we wroe 1947/8 above. The upper panel of Table 1 repors he resuls. Wih he acual changes in he secoral composiion, he annual growh raes of produciviy fell by 0.86 percenage poins from 2.31% during o 1.45% during In conras, wih he secoral composiion held fixed a he 1947/8 values, he annual growh raes of produciviy would have fallen by only 0.58 percenage poins from 2.45% o 1.87%. The 0.28 percenage poin difference beween 0.86 and 0.58 implies ha Baumol s disease was responsible for one hird of he oal slowdown in produciviy growh. Noe ha we sopped our analysis in 2007 o avoid he effecs of he Grea Recession. While all resuls go hrough when we include he Grea Recession, he produciviy slowdown becomes a lo larger. Since ha has lile o do wih srucural change, we do no include i here. Nordhaus (2008) proposed an alernaive way o measure he effecs of srucural change on produciviy growh by comparing he counerfacual average growh raes over he period when he secoral composiion is fixed a is 1947/8 and 2006/7 values while he 6

8 Table 1: Acual and counerfacual average annual produciviy growh (in %) Secor composiion from Period daa 1947/8 2006/7 Baumol s disease % 2.45% % 1.87% difference = % 2.03% 1.44% = 0.59 secoral produciviy growh raes are kep a wha hey were in he daa. In addiion o being useful on is own, Nordhaus way of looking a he daa naurally conveys addiional informaion abou wha level of disaggregaion does bes a capuring he effecs of Baumol s disease a he beginning and he end of he sample. We firs calculae he Nordhaus counerfacuals for he 65 indusries from he daa. The resuls are conained he lower panel of Table 1. The able confirms he conclusion of he previous paragraph ha srucural ransformaion affeced aggregae produciviy growh in a quaniaively imporan way: if he composiion among he 65 indusries of WORLD KLEMS had been fixed a he 1947/8 (2006/7) values, hen he average aggregae produciviy growh rae would have been 2.03 (1.44) percen insead of he acual 1.74 percen in he daa. Given ha we build on he produciviy accouning mehod of Nordhaus, i is naural o compare our resuls wih his. Nordhaus (2008) finds ha if he secor composiion had no changed, hen he annual average growh rae would have been 0.37 percenage poins higher; he average growh rae wih he fixed iniial secor composiion is 0.64 percenage poins larger han he average growh rae wih he fixed final secor composiion. I is reassuring ha his numbers are in he same ballpark as our numbers. His numbers should no be expeced o be exacly he same as our numbers because here are wo imporan differences beween he wo sudies. Whereas we focus on and work wih WORLD KLEMS daa, Nordhaus focuses on he shorer ime period and worked wih BEA daa. Whereas we focus on produciviy per efficiency uni, Nordhaus focuses on oal facor produciviy. 3.2 Towards a new hree secor spli So far, we have measured he effec of Baumol s disease a he level of 65 disaggregae indusries. Now we develop a new hree secor spli ha capures he essence of he pas effecs of Baumol disease on aggregae produciviy in an analyically racable way and ha forms he foundaion of a model of srucural change ha can predic he fuure effecs of Baumol s disease on produciviy. Consisen wih he lieraure, we spli he economy ino he sandard broad secors of goods 7

9 Table 2: Counerfacual U.S. Produciviy Growh for Differen Secor Splis in % indusry 65 goods & 26 goods & goods & goods & goods & composiion indusries services goods & 39 high/low non/marke un/skilled from services services services services services 1947/ / difference and services. The goods secor comprises agriculure, consrucion, manufacuring, mining, and uiliies and he service secor comprises he remaining indusries. Table 2 shows ha his sandard spli does no work well in our conex. For he purpose of predicing he fuure effecs of Baumol s disease on produciviy growh, i is of firs order imporance o disaggregae he service secor, bu i is only of second order imporance o disaggregae he goods secor. To see why we are saying his, we sar wih he hird column. I shows ha for he usual wo secor spli beween goods and services he effec of Baumol s disease is only 0.30 compared o 0.59 for all 65 indusries. This implies ha he usual wo secor spli is no disaggregaed enough for our purpose here. The fourh column shows ha he 26 goods indusries ogeher wih he broad service secor do beer han he usual wo secor spli: he effec of Baumol s disease is now Moreover, he number for he counerfacual produciviy growh rae for he 1947/8 secor composiion is fairly close o ha for all 65 indusries (1.99 versus 2.03), bu he number for he 2006/7 secor composiion is off (1.56 versus 1.44). The fifh column shows ha he broad goods secor ogeher wih he 39 service indusries from he daa does beer han he previous wo splis: he effec of Baumol s disease is now 0.46, which ges closer o 0.59 for all 65 indusries. Moreover, he number for he 2007 secor composiion is now close (1.46 versus 1.44), bu he number for he 1947 secor composiion is off (1.92 versus 2.03). These findings sugges ha a he beginning of he sample, he reallocaion wihin he goods secor was crucial for he effecs of Baumol s disease whereas a he end of he sample he reallocaion wihin he service secor was crucial. The previous findings confirm ha if he focus is on he fuure produciviy effecs of Baumol s disease, hen we need o find an appropriae disaggregaion of service secor, because ha maers mos owards he end of he sample. We consider hree naural wo secor splis of services: services wih high versus low produciviy growh; marke versus non marke services; skilled versus unskilled as suggesed by Buera e al. (2015). The service subsecor wih high (low) produciviy growh comprises he service indusries ha have produciviy growh above (below) he average of 1.40% in he service secor. Marke (non marke) services are defined by he guidelines of he Sysem of Naional Accouns. Skilled (unskilled) service indusries as service indusries ha pay a higher (lower) share of labor compensaion o college graduae 8

10 han all service indusries do on average. 4 Table 3 liss all service indusries in declining order of heir average produciviy growh raes and in which oher wo secor splis hese service indusries belong. Table 9 in Appendix D liss he average annual produciviy growh raes, confirming he observaion of Baumol e al. (1985) ha he service secor conains some of he economies mos progressive aciviies as well as is mos sagnan. Table 2 shows ha goods and services wih high and low produciviy growh provide a very good approximaion o wha we ge for goods and he 39 service indusries from he daa, whereas he wo secor spli ino marke versus non marke services is fairly off. Coincidenally, he wo secor spli ino skilled and unskilled services generaes nearly he same numbers as ha ino high and low produciviy growh. We conclude from his ha using goods ogeher eiher wih services wih high and low produciviy growh or wih services wih high and low skills would work for sudying he fuure effecs of Baumol s disease on produciviy growh. In wha follows, we use he former because i seems more naural in our conex o consruc he disaggregaion of services according o he differences in secoral produciviy growh. 5 Anoher wo secor spli ha has been considered by Duare and Resuccia (2016) disinguishes beween modern vs. radiional services. We do no pursue his wo secor spli here because i is defined only for final expendiure whereas we are focused on value added. Figure 1 shows he behavior of our hree secors in he poswar U.S. economy. All figures use efficiency unis. The lef panel plos he sandard disaggregaion beween goods and services while he righ panel plos he new disaggregaion beween services wih high and low produciviy growh. The figures in he upper panel plo raios of secoral efficiency unis and secoral nominal expendiures. The upper lef figure shows he usual paerns for he raios of services o goods, which have boh increased. The upper righ figure shows he novel paern for he raios of services wih low o high produciviy growh, which boh increased unil he 1970s and hen flaened ou. The figures in he lower panel plo relaive labor produciviies and relaive prices. The lower lef figure shows he usual increases in he labor produciviy of goods relaive o services and in he price of services relaive o goods. The lower righ panel shows he novel paerns ha he labor produciviy of services wih high relaive o low produciviy growh and he price of services wih low relaive o high produciviy growh increased somewha unil he 1970s and srongly aferwards. There is some debae abou wheher he low produciviy growh of many service indusries comes in par from he fac ha qualiy improvemens in services are underesimaed. Triple and Bosworh (2003), for example, wroe ha perhaps he service indusries were never sick, i was jus, as Griliches (1994) has suggesed, ha he measuring hermomeer was wrong. In 4 We use he BEA BLS Indusry Level Producion Accoun, , for his calculaion, which yields 0.50% as he average labour compensaion share paid o college graduaes in he service secor. 5 We have conduced he analysis ha follows also for he oher wo secor splis. The resuls are qualiaively similar and are available upon reques. 9

11 Table 3: Definiions of Differen Two Secor Splis 39 Service Indusries in WORLD KLEMS Marke (1) vs. Unskilled (1) vs. (in declining order of produciviy) Non marke (2) Skilled (2) Service indusries wih high produciviy growh Pipeline Transporaion 1 1 Air Transporaion 1 1 Broadcasing and Telecommunicaions 1 2 Wholesale Trade 1 1 Securiies, Commodiy Conracs, and Invesmen1 1 2 Wase Managemen and Remediaion Services 1 1 Social Assisance 2 1 Railroad Transporaion 1 1 Publishing Indusries (includes Sofware) 1 2 Waer Transporaion 1 1 Adminisraive and Suppor Services 1 1 Renal and Leasing Services and Lessors of Inangible Asses 1 1 Truck Transporaion 1 1 Reail Trade 1 1 Insurance Carriers and Relaed Aciviies 1 2 Performing Ars, Specaor Spors, Museums, and Relaed Aciviies 1 2 Warehousing and Sorage 1 1 Moion Picure and Sound Recording Indusries 1 2 Service indusries wih low produciviy growh Managemen of Companies, and Enerprises 1 2 Miscellaneous Professional, Scienific, and Technical Services 1 2 Accommodaion 1 1 Federal General Governmen 2 1 Federal Reserve Banks, Credi Inermediaion, and Relaed Aciviies 1 2 Educaional Services 2 2 Real Esae 2 2 Legal Services 1 2 Federal Governmen Enerprises 2 2 Ambulaory Healh Care Services 2 2 Compuer Sysems Design and Relaed Services 1 2 Hospials, Nursing, and Residenial Care Faciliies 2 2 Oher Transporaion and Suppor Aciviies 1 1 Sae and Local Governmen Enerprises 2 2 Amusemens, Gambling, and Recreaion Indusries 1 1 Informaion and Daa Processing Services 1 2 Food Services and Drinking Places 1 1 Transi and Ground Passenger Transporaion 1 1 Sae and Local General Governmen 2 2 Oher Services, excep Governmen 1 1 Funds, Truss, and oher Financial Vehicles

12 conras, Byrne e al. (2016) and Syverson (2016) argued ha underesimaed qualiy improvemens are no likely o have played an imporan in he recen produciviy growh slowdown. Be ha as i may, i is undeniable ha if here were underesimaed qualiy improvemens in he poswar U.S., hen hey did ranslae ino an exaggeraed slowdown of aggregae produciviy growh. We will noneheless ake he numbers from WORLD KLEMS a face value and proceed under he assumpion ha here were no issues wih unmeasured qualiy improvemens. This way of proceeding is informaive in our conex because, as we will show below in Subsecion 5.3, our esimaes hen provide an upper bound of he effecs of Baumol s disease on produciviy growh. Since our key finding is ha he fuure effecs of Baumol s disease will remain limied, unmeasured qualiy improvemens canno overurn he main message of our findings. Figure 1: Poswar U.S. Srucural Transformaion Relaive nominal value added and efficiency unis Relaive nominal value added and efficiency unis Value added of services relaive o goods Efficiency unis of services relaive o goods Value added of services wih low relaive o high produciviy growh Efficiency unis of services wih low relaive o high produciviy growh Source: WORLD KLEMS, March 2017 release and own calculaions. Source: WORLD KLEMS, March 2017 release and own calculaions. 2.0 Relaive produciviies and prices relaive prices 1947=1 3.0 Relaive produciviies and prices relaive prices 1947= Price of services relaive o goods Real value added per efficiency uni of goods relaive o services Price of services wih low relaive o high produciviy growh Real value added per efficiency uni of services wih high relaive o low produciviy growh Source: WORLD KLEMS, March 2017 release and own calculaions. Source: WORLD KLEMS, March 2017 release and own calculaions. 3.3 Discussion Having esablished ha in he poswar U.S., srucural change wihin he service secor led o Baumol s disease and imporan reducions in produciviy growh, he quesion arises why he lieraure on srucural change has paid lile o no aenion o Baumol s disease. In Duernecker 11

13 e al. (2017), we argue ha he likely reason for his is ha he lieraure looks for an aggregae balanced growh pah because ha simplifies dramaically he analyical characerizaion of he equilibrium pah. In many models of srucural change, an aggregae balanced growh pah exiss if GDP growh is measured in a paricular way (in erms of numeraires ha change from period o period). Since produciviy growh is consan along any aggregae balanced growh pah, i seems naural o conclude ha Baumol s disease is no an issue in he sandard models of srucural change. In Duernecker e al. (2017), we show ha his conclusion is misleading: if we measure GDP growh as i is done in NIPA hrough a chain index, hen Baumol s disease does play a poenially imporan role along he balanced growh pah of he sandard models. 6 In wha follows, we will herefore make sure o measure GDP in he exac same way as i is done in he daa so as o give Baumol s disease a chance o affec produciviy growh. 7 We sar by building a simple model o capure he effecs of Baumol s disease on produciviy growh. Aferwards, we will calibrae he model and use i o assess by how much Baumol s disease will reduce fuure produciviy growh. 4 Model 4.1 Environmen There are hree secors producing goods, services wih high produciviy growh, and services wih low produciviy growh. We index he secors by g, h, and l. In each secor, value added is produced from labor: Y i = A i H i, i = g, h, l, (1) where Y i, A i, and H i denoe value added, oal facor produciviy, and efficiency unis of labor of secor i. The linear funcional form implies ha labor produciviy equals TFP, ha is, Y i /H i = A i. We use i because i is simple and because i capures well he essence of he role ha echnological progress plays for srucural ransformaion [Herrendorf e al. (2015)]. There is a measure one of idenical households. Each household is endowed wih a finie number of efficiency unis of labor ha are inelasically supplied and can be used in all secors. We will refer o GDP per efficiency uni as labor produciviy or produciviy for shor. Uiliy is described by wo nesed, non homoheic CES uiliy funcions. The uiliy from 6 In independen work, Leon-Ledesma and Moro (2017) also made some of hese poins. 7 In our applicaion ha means o measure GDP growh hrough a Törnqvis index because we use daa from WORLD KLEMS. Similar saemens as for chain indexes apply. 12

14 he consumpion of goods and (aggregae) services, C g and C s, is given by: 1 C = α σ c g ε g 1 σ C c σ c 1 σ C c g + α 1 ε s 1 σ c σ s C c C σ c 1 σ c s σ c σ c 1. (2a) Services are given by a non homoheic CES aggregaor of he consumpion from he wo service sub secors, C h and C l : C s = 1 α σ s h εh 1 C σ s σ s 1 σ C s h + α 1 ε l 1 σ s σ l C s C σ s 1 σ s l σ s σ s 1. (2b) α g, α s, α h, α l 0 are weighs; σ c, σ s 0 are he elasiciies of subsiuion; ε g, ε s, ε h, ε l > 0 capure income effecs. The non homoheic CES uiliy funcion (2) goes back o he work of Hanoch (1975) and Sao (1975) on implicily addiive uiliy and producion funcions. I has recenly been inroduced o he lieraure on srucural ransformaion by Comin e al. (2015). For ε i = 1, he expressions in (2) reduce o he sandard CES uiliy ha implies homoheic demand funcions for each consumpion good. For ε i 1, he level of consumpion affecs he relaive weigh ha is aached o he consumpion goods. Alhough in his case here is no closed form soluion for uiliy as a funcion of he consumpion goods, i urns ou ha he implied non homoheic demand funcions remain racable. In our conex, he mos imporan feaure of he non homoheic CES uiliy funcion (2) is ha he implied income effecs do no disappear in he limi as consumpion grows wihou bound. Boppar (2016) and Comin e al. (2015) esablished ha his is consisen wih he available evidence for he broad secors of goods and services ha are usually considered in he srucural ransformaion lieraure. Figure 2 esablishes ha his is also consisen wih he evidence for he wo service subsecors ha we consider here. Specifically, he figure esablishes ha he income effec on he relaive demand of he wo service secors does no sysemaically decline as he economy grows. Modelling persisen income effecs is imporan in our conex in which we are ineresed in he limi behavior of produciviy. A sandard Sone Geary uiliy specificaion would no capure persisen income effecs because, as consumpion grows wihou bound, i converges o a homoheic uiliy funcion. The non homoheic CES aggregaors make economic sense only if hey saisfy he usual regulariy condiions. To ensure ha his is he case, we resric he parameers as follows: Assumpion 1 σ c < min{ε g, ε s } or max{ε g, ε s } < σ c. σ s < min{ε h, ε l } or max{ε h, ε l } < σ s. 13

15 Figure 2: Persisen Income Effecs wihin Services Residuals of log difference of nominal value added of differen services Parial correlaion beween relaive value added wihin services and aggregae value added per efficiency uni Residuals of log of aggregae real value added per efficiency uni Residuals Linear fi Source: WORLD KLEMS, March 2017 release and own calculaions Noe: Residuals on he y-axis are from regressing he log difference of nominal value added of services wih low and high produciviy growh on he corresponding log difference of prices. Residuals on he x-axis are from regressing he log of aggregae real value added per efficiency uni on he same log differences of prices. Hanoch (1971,1975) showed ha his assumpion guaranees ha he uiliy funcion is monoonically increasing in each of is argumens and quasi concave. We complee he descripion of he environmen wih he resource consrains: C i Y i, i = g, h, l, (3a) H g + H s = H g + H h + H l H. (3b) 4.2 Compeiive equilibrium In he daa, he nominal labor produciviies per efficiency uni are no equalized across secors. I is poenially imporan o capure he resuling level differences in produciviy in our conex, because he effecs of srucural ransformaion on aggregae produciviy depend on he differences in boh he growh raes and he levels of secoral produciviy. A simple way of capuring hem is o inroduce a secor specific ax τ i ha firms pay per uni of wage paymens and ha is lump sum rebaed hrough a ransfer T = i=g,h,l τ i w H i o he households. Wih he ax, he problem of firm i = g, h, l becomes: The firs order condiions imply ha max H i P i A i H i (1 + τ i )w H i. P j P g = (1 + τ j)a g (1 + τ g )A j, j = h, l. (4) Using his and he specificaion of he producion funcion in (1), we obain ha he relaive 14

16 secoral labor produciviies equal he relaive axes: P j C j /H j P g C g /H g = 1 + τ j 1 + τ g, j = h, l. (5) As inended, he axes drive a wedge beween he nominal secoral labor produciviies which will allow us o mach differences in hem. To solve he household problem, we spli i ino wo layers. The inner layer of he problem is abou allocaing a given quaniy of service consumpion beween he consumpion of he wo services: min C h,c l P h C h + P l C l s.. 1 α σ s h εh 1 C σ s σ s 1 σ C s h + α 1 ε l 1 σ s σ l C s C σ s 1 σ s l σ s σ s 1 C s. Appendix B shows ha he firs order condiions imply ha P l C l = α ( ) 1 σs l Pl C ε l ε h, (6a) P h C h α h P h P s = ( α h C ε h 1 P 1 σ s h + α l C ε l 1 ) P 1 σ 1 s 1 σ s l. where P s is price index of services. The ouer layer of he problem is abou allocaing a given quaniy of oal consumpion beween he consumpion of goods and services: 8 (6b) min C g,c s P g C g + P s C s s.. 1 α σ c g ε g 1 σ C c σ c 1 σ C c g + α 1 ε s 1 σ c σ s C c C σ c 1 σ c s σ c σ c 1 C. Appendix B shows ha he firs order condiions imply P s C s P g C g = α s α g ( Ps P g P = ( α g C ε g 1 P 1 σ c g ) 1 σc C ε s ε g, (7a) + α s C ε s 1 where P is he aggregae price index and P C i=g,h,l P i C i. ) 1 P 1 σ c 1 σ c s. 8 The given quaniy of oal consumpion is deermined by he endowmen of labor and he echnology: C = A g /P. A paricular household akes A g /P as given because A g is exogenous and P is he aggregae price index ha is independen of is acions. (7b) 15

17 4.3 Equilibrium properies We now urn o he equilibrium properies of our model. Since i is impossible o solve for he equilibrium in closed form, we will resor o numerical simulaions o characerize he precise behavior of our model. Before we do so, i is noneheless useful o give he reader some idea abou how he model behaves qualiaively. We begin wih he srucural ransformaion beween goods and services. Dividing (7a) for periods + 1 and by each oher and denoing growh facors by has, we obain: ) ( Ps C ( ) 1 σ c s Ps = P g C g P Ĉ ε s ε g. (8) g The firs erm on he righ hand side is he relaive price effec and he second erm is he income effec. We make he sandard assumpion ha goods and aggregae services are complemens, goods are necessiies, and services are luxuries: 9 Assumpion 2 0 < σ c < 1 and ε g < ε s. Our calibraion below will generae parameer values ha are consisen wih hese assumpions. Expression (8) shows ha our model hen generaes he observed srucural ransformaion from goods o services if P s /P g and C boh grow. While in general his may or may no be he case for he non homoheic uiliy funcion (2), we will esablish below ha i is he case for he numerically relevan parameers ha our calibraion generaes. Before urning our aenion o he srucural change wihin he service secor, i is useful o draw he aenion o a feaure of (8) ha is going o become imporan in he quaniaive analysis following below. The righ hand side of he demand sysem depends only on he difference of ε s ε g, implying ha he wo ε i will no be separaely idenified. We herefore need o normalize one of hem. 10 We coninue wih he srucural ransformaion beween he wo service subsecors. Combining Equaions (5) and (6a), we obain: ) ( Pl C ( ) 1 σ s l Pl = P h C h P Ĉ ε l ε h. (9) h To fi he daa, we will need o assume ha he wo service subsecors are subsiues, services wih high produciviy growh are a necessiy, and services wih low produciviy growh are a luxury: Assumpion 3 1 < σ s and ε h < ε l. 9 See, for example, Kongsamu e al. (2001), Ngai and Pissarides (2007), and Herrendorf e al. (2013). 10 Sposi (2016) proceeds in a similar fashion. 16

18 Figure 3: Relaive Prices and Expendiures in Services 3.0 relaive prices 1947= Value added of services wih low relaive o high produciviy growh Price of services wih low relaive o high produciviy growh Source: WORLD KLEMS, March 2017 release and own calculaions. Our calibraion below will generae parameer values ha are consisen wih Assumpion 3. The relaive price effec, which is he firs erm on he righ hand side of Equaion (9), hen decreases he expendiure of services wih high produciviy growh relaive o he expendiure of services wih low produciviy growh. Moreover, he income effec, which is he second erm on he righ hand side, hen increases he expendiure raio of services wih low produciviy growh relaive o services wih high produciviy growh if C increases. The ne effec is analyically ambiguous. Assumpion 3 is required for our model o replicae he paerns of srucural ransformaion wihin he service secor as summarized by Figure 3. Unil around 1970 he price of services wih low produciviy growh relaive o services wih high produciviy growh increased along wih he corresponding expendiure raio. Afer 1970, he increase in he relaive price of services wih low produciviy growh acceleraed while he expendiure raio remained roughly consan. Since we assume ha services wih low produciviy growh are luxuries, he increases in consumpion expendiure increase heir share over he whole period. Since we assume ha he wo services are subsiues, he increases in he relaive price of services wih low produciviy growh decreases heir expendiure share over he whole period. Our model replicaes he observed paern by having he income effec dominae before 1970 and having he income and subsiuion effec offse each oher afer Alernaive parameer consellaions would no be able o generae he observed paerns. To see his, noe firs ha he income effecs do no change in 1970 bu work in he same direcions during he whole period. So he change in he relaive expendiure share paern mus be coming from he acceleraion in he relaive prices. If he services were complemens, hen he expendiure share of services wih low produciviy growh would have increased by more afer 1970 han before 1970, which is counerfacual. Given ha he wo services mus be subsiues, services wih low produciviy growh mus 17

19 be a luxury and services wih high produciviy growh mus be a necessiy. If he opposie was rue, hen he relaive expendiure of service wih high produciviy growh would have increased during he whole period, which again is counerfacual. I is imporan o realize ha he usual forces behind he reallocaion beween goods and services are very differen from he new forces behind he reallocaion of producion wihin he service secor. The usual forces imply ha he relaive price effec and he income effec boh work in he same direcion and increase he expendiure share of services relaive o goods. In conras, wihin he service secor he relaive price effec and he income effec work in opposie direcions: he increase in he relaive price decreases he relaive expendiure share of services wih low produciviy growh whereas he increases in oal consumpion increases hem. If he elasiciy of subsiuion is close o Cobb Douglas, hen he income effec will dominae; if he income effec is close o zero, hen he subsiuion effec will dominae. In inermediae cases, boh effecs will inerac wih each oher and i is impossible o say much more han ha hey work in opposie direcions. Consider, for example, he effec on he relaive expendiure share of an exogenous decline in he produciviy of he services wih low produciviy growh. Since he wo services are subsiues, he household will reac by subsiuing away from services wih low produciviy growh so srongly ha heir expendiure share declines. This will increase he produciviy of producing aggregae services, which in urn will increase aggregae produciviy and oal consumpion. Since services wih low produciviy growh are luxuries, he resuling income effec will increase he relaive expendiure of services wih low produciviy growh. The ne effec of he wo opposing effecs is ambiguous analyically. We emphasize ha using a uiliy funcion wih income effecs ha do no disappear in he long run is crucial for analyzing he effecs of srucural change wihin services. If, insead, we had used a sandard Sone Geary uiliy funcion wihou persisen income effecs, hen he subsiuion effec would have dominaed in he long run. In his case, he services wih high produciviy growh would have aken over he economy in he long run and here would have been no reason o worry abou he fuure effecs of Baumol disease. The siuaion is very differen for our uiliy funcion where he oucome is no clear and a serious quaniaive analysis becomes necessary. We urn o his ask now. 5 Quaniaive Analysis In his secion, we calibrae our model o mach salien feaures of he poswar U.S. economy, including he behavior of he relaive secoral prices, he relaive secoral labor produciviies, and he secoral composiion. We hen use he calibraed model o predic by how much Baumol s disease will affec produciviy growh. As before, produciviy is defined as he real value added per efficiency uni. 18

20 Before we urn o he deails of he quaniaive analysis, i is imporan o poin ou ha i is challenging o connec our model o he daa. The reason for his is ha in he model GDP growh is given by he change in he non homoheic CES uiliy index C, whereas in he WORLD KLEMS daa GDP growh is measured by he change in a Törnqvis index. Appendix A.2 shows ha hese wo indexes are compleely differen objecs when he uiliy is non homoheic, implying ha heir growh facors canno direcly be compared o each oher. Insead, one needs o consruc he Törnqvis index in he same way in he model from quaniies and prices of he model and as i was done in he daa and compare he wo Törnqvis indexes from he model and he daa wih each oher. We will carefully follow his procedure when we calibrae he model and when we compare he produciviy growh from he model wih he daa. 5.1 Calibraion We sar wih calibraing he secoral axes. Equaion (5) implies ha only relaive axes maer for he equilibrium. We herefore normalize he axes in he goods secor o zero for all years = 1947,..., 2007: τ g = 0. Defining nominal value added as VA j P j Y j and denoing observable variables by a ilde, Equaion (5) can hen be wrien as: 1 + τ j = ṼA j/ H j ṼA g / H g, j = h, l, = 1947,..., (10) This equaion uniquely deermines he values of he axes in secors h and l, because he righ hand side is he observable nominal labor produciviy per efficiency unis in secor j relaive o secor g. The upper lef panel of Figure 4 plos he resuling series for he disorions. We coninue wih calibraing he secoral TFPs. We normalize P g,1947 = P h,1947 = P l,1947 = A g,1947 = 1. We calibrae he TFPs in he goods secor by rewriing equaion (1) as follows: A g+1 A g = ṼA g+1/( P g+1 H g+1 ) ṼA g /( P g H g ), = 1947,..., (11) This equaion uniquely deermines he growh facor of TFP in he goods secor. We calibrae he oher secoral TFPs by rewriing Equaion (4) as: A j = P g P j (1 + τ j )A g, j = h, l = 1947,..., (12) We ake { P j } j=g,h,l, =1948,...,2007 from he daa. We have already normalized {P j,1947 } j=g,h,l and have calibraed he axes and he TFPs in he goods secor, implying ha all variables on he righ hand side are given. The upper righ panel of Figure 4 plos he implied secor TFPs. 19

21 Since only relaive prices maer in he model, we are free o choose {P g } =1948,...,2007 so as o mach he growh facors of he goods prices in he daa. The previous choices hen imply ha by consrucion we also mach he growh of nominal labor produciviy in he goods secor. Equaion (4) and he previous choices hen imply ha we also mach { P j } j=h,l, =1948,...,2007 and he growh of nominal labor produciviy in he oher secors by consrucion. In sum, he parameer choices ha we have made so far imply ha our model will mach he growh facors of nominal and real secoral labor produciviies and he growh facors of all prices. In addiion, our model also maches he iniial level differences beween he real secoral labor produciviies. Figure 4: Calibraion Implicaions 1.0 Disorions 5.0 Secor TFPs A g A h A l τ h τ l Toal consumpion and relaive price of services 3.5 C P s /P g This leaves en parameers o be calibraed: he four relaive weighs {α g, α s, α h, α l }, he wo elasiciies {σ s, σ c }, and he four parameers governing he income effecs {ε g, ε s, ε h, ε l }. As we menioned above already, ε s and ε g or ε l and ε h are no separaely idenified for he non homoheic CES funcional form ha we are using, because he expendiure sysem (6a) (7a) depends on he differences ε s ε g and ε l ε h. We are herefore free o se ε g and ε h o whaever is convenien. We choose ε g = 0.85 and ε h = 0.58, because he resuling parameers will saisfy Assumpion 1. We also impose ha α s = 1 α g and α l = 1 α h. This leaves he following six parameers o calibrae: {α g, α h, σ s, σ c, ε s, ε l }. 20