NBER WORKING PAPER SERIES THE RISE OF THE SERVICE ECONOMY. Francisco J. Buera Joseph P. Kaboski. Working Paper

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1 NBER WORKING PAPER SERIES THE RISE OF THE SERVICE ECONOMY Francisco J. Buera Josep P. Kaboski Working Paper 4822 ttp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 5 Massacusetts Avenue Cambridge, MA 238 Marc 29 We ave benefited from epfu comments of te editor, tree anonymous referres. We aso tank Fernando Avarez, Gary Becker, Bob Ha, Bob Lucas, and Ivan Werning as we as seminar participants at various paces. Te views expressed erein are tose of te autor(s) and do not necessariy refect te views of te Nationa Bureau of Economic Researc. 29 by Francisco J. Buera and Josep P. Kaboski. A rigts reserved. Sort sections of text, not to exceed two paragraps, may be quoted witout expicit permission provided tat fu credit, incuding notice, is given to te source.

2 Te Rise of te Service Economy Francisco J. Buera and Josep P. Kaboski NBER Working Paper No Marc 29 JEL No. D3,J22,J24,O4 ABSTRACT Tis paper anayzes te roe of speciaized ig-skied abor in te growt of te service sector as a sare of te tota economy. Empiricay, we empasize tat te growt as been driven by te consumption of services. Rater tan being driven by ow-ski jobs, te importance of ski-intensive services as risen, and tis as coincided wit a period of rising reative wages and quantities of ig-skied abor. We deveop a teory were demand sifts toward ever more ski-intensive output as income rises, and because skis are igy speciaized tis owers te importance of ome production reative to market services. Te teory is aso consistent wit a rising eve of ski and ski premium, a rising reative price of services tat is inked to tis ski premium, and ric product cyces between ome and market, a of wic are observed in te data. Francisco J. Buera Department of Economics University of Caifornia, Los Angees 8283 Bunce Ha Office 8357 Mai Stop: 4773 Los Angees, CA 995 and NBER fjbuera@econ.uca.edu Josep P. Kaboski Te Oio State University 4 Arps Ha 945 Nort Hig Street Coumbus, OH 432 kaboski.@osu.edu

3 Te Rise of te Service Economy Francisco J. Buera y and Josep P. Kaboski z Marc 24, 29 Abstract Tis paper anayzes te roe of speciaized ig-skied abor in te growt of te service sector as a sare of te tota economy. Empiricay, we empasize tat te growt as been driven by te consumption of services. Rater tan being driven by ow-ski jobs, te importance of ski-intensive services as risen, and tis as coincided wit a period of rising reative wages and quantities of ig-skied abor. We deveop a teory were demand sifts toward ever more ski-intensive output as income rises, and because skis are igy speciaized tis owers te importance of ome production reative to market services. Te teory is aso consistent wit a rising eve of ski and ski premium, a rising reative price of services tat is inked to tis ski premium, and ric product cyces between ome and market, a of wic are observed in te data. Introduction Two of te most saient, interesting trends in te post-95 U.S. economy ave been te rising importance of te service sector and te growt in te premium to ski despite a arge expansion in te reative suppy of ig-skied workers. Te growt of te service sector and te reative demand for ig-skied workers ave been we-studied independenty, but teorists ave not formay inked te two penomena. Lacking teory, poitica retoric and aarmist concerns We ave bene ted from epfu comments of te editor, tree anonymous referres. We aso tank Fernando Avarez, Gary Becker, Bob Ha, Bob Lucas, and Ivan Werning as we as seminar participants at Brown University, Forida Internationa University, Harvard University, Massacusetts Institute of Tecnoogy, Micigan State University, Nortwestern University, Oio State University, Pennsyvania State University, Princeton University, University of Caifornia Los Angees, University of Cicago, University of Pennsyvania, University of Rocester, University of Soutern Caifornia, University of Texas Austin, Wasington University, te IMF, te Federa Reserve Banks of Cicago, Ceveand, and Piadepia, SED meetings at Vancouver, EFG summer meeting, and te Minnesota Worksop in Macroeconomic Teory. y UCLA, fjbuera@econ.uca.edu z Oio State University, kaboski.@osu.edu

4 tat te rise of te service economy as repaced industria work wit owski, ow-paying services (e.g., "McJobs") ave arisen. Tis paper addresses tese concerns, and compements te two existing strands of iterature, by bot documenting te reevant facts and providing a teoretica framework for understanding te connection between ski accumuation and te growt of te service sector. Contrary to te conventiona view, we argue tat te growt in services is driven by te movement of consumption into more ski-intensive output. Severa empirica trends invoving services and skis motivate our anaysis. Te sare of te service sector in vaue-added as grown steadiy from 6 percent in 95 to 8 percent in 98, and tis increase is expained by te growt in te consumption of services. Tis twenty percentage point increase is aso expained entirey by te growt of ski-intensive services, and is contemporaneous wit an increasing reative quantity of ig-skied abor and a rising ski premium: Te output of ig-ski industries increases by more tan twenty- ve percent, wie te sare of ow-ski industries actuay decines. Over te same period, te wages of coege-educated workers rose from 25 percent to more tan twice te wage of ig scoo-educated workers, and te fraction of workers wo were coege-educated rose from just fteen percent to over sixty percent. Finay, te growt in coege-educated abor, te ski premium, te reative size of ski-intensive services, and te sare of te service sector a acceerate around 95. Our key teoretica idea inking tese tree penonomena is tat skis are speciaized, and speciaization pays an important roe in te decision between ome and market provision of services. Genera skis increase te productivity of workers equay in a activities. In contrast, speciaized workers are igy productive on te market, but ess productive in oter work, incuding amost every potentia ome production activity. Tus, service output for wic speciaized abor is reativey productive wi tend to be market purcased by a consumers. Moreover, given te iger opportunity cost of teir time, speciaized workers wi tend to purcase a wider range of services on te market. We incorporate tis idea into a growt mode. Agents face tree stages of decisions. First, tey decide weter or not to become ig-skied. Since te acquisition of any particuar ski entais paying a xed cost, eac agent cooses to attain speciaized skis in at most one service. Te margina cost of attaining ski is increasing in te fraction of agents wo become ig-skied so tat tere is an upward soping suppy of ig-skied workers. Second, agents ave preferences over a continuum of individua services, eac of wic is satiabe. Tey order teir wants, and satiate tese desires sequentiay, starting wit te east compex, and terefore ceapest, rst. Eac want is produced using intermediate manufactured inputs and abor in a na stage. We refer to tis na stage as te production of services. Finay, for eac want tat tey satisfy, agents furter decide weter to ome produce or market purcase te service. Market production as potentia cost advantages due to te use of more productive speciaized skis, but ome production is more customized and terefore provides more utiity. 2

5 Te driving force of growt in te mode is exogenous tecnica cange, but tis tecnica cange is bot ski- and sector-neutra. Instead, te canging margin between ome production and market services arises from te movement toward te consumption of services for wic ig-skied abor as a arger reative productivity advantage. As abor productivity grows, income rises, and te consumption set expands to ever more compex (costy) services. For te more necessity services consumed at ow incomes, ig-skied workers od a stabe absoute advantage in production. In tis initia stage, te ski premium, te fraction of workers becoming ig-skied, and te sare of services are terefore stabe. Eventuay, owever, demand begins sifting continuay toward services for wic ig-skied workers od an ever arger productivity advantage. Te increased importance of speciaized ig-skied abor eads to te rise of te service economy. We identify four reated forces eading to te rising importance of services. Te rst two combine to sift te rea consumption bundes of individua agents toward market services. First, for xed reative prices and wages, iger income sifts consumption towards services in wic ig-skied abor as a comparative advantage. Tese ski-intensive market services ave a arger cost advantage over teir ome production counterparts, and so te sare of market services in consumption rises for every agent. Second, an increase in te demand for ig-skied abor tends to increase te reative wage of ig-skied agents, wic increases teir opportunity cost of ome production, reinforcing teir sift toward market consumption. A tird force tat eads to te growt in rea services is a compositiona e ect. As more agents become ig-skied, tota consumption can sift toward ig-skied workers wo consume a iger sare of market services. Finay, a rising reative wage of ig-skied workers increases te reative price of services, wic increases teir current-vaue sare. Te non-omoteticity toward ski-intensive output is consistent wit te observed compositiona sift toward ski-intensive services. Our story as additiona impications, owever, wic we examine. First, in te mode, te sift in demand manifests itsef as an increase in bot te reative price and reative quantity of services. In te data, te growt in te reative sares of services is indeed driven by bot quantities and prices. Second, in te mode, te reative price of services rises because of te rising reative price of a scarce resource, ig-skied abor. We sow tat tere is a strong, positive time-series reationsip between te ski premium and te reative price of services. Te mode as aso ric impications on te nature of product cyces of activities from market to ome, and from ome to market production. As income rises, individua purcase new market produced services. At te same time, as te cost advantage of market services decines wit neutra productivity growt, te ost utiity from market services becomes more important and so previousy market-produced services become ome-produced. Recent exampes of market to ome product cyces incude medica acticivities ike cecking bood sugar/ pressure or ome diaysis. At te same time, te ome production of oter services move into te market as generations of ow-skied workers are repaced by ig-skied workers wit ig opportunity costs, and consumption 3

6 basket weigted toward market services. Toug poicy evauation is not te focus of tis paper, we conjecture tat te mode woud ave di erent impications tan existing teories in severa areas, incuding te easticity of abor suppy and productivity growt. Te ome-market decision makes abor suppy more eastic tan oterwise, but tis easticity may fa as market production becomes more ski-intensive. Tis woud ave impications for te wefare costs of distortions to abor suppy or te service sector (reative to Rogerson, 28). Te mode aso iustrates tat service sector growt need not rey on sower productivity growt in te service sector. Hence, our teory as no Baumo s disease impications of sower ong run growt prospects (Baumo, 967). Te rest of te paper is organized as foows. We concude tis introduction wit a review of reated iterature. Section 2 ten estabises te facts tat motivate our anaysis. Te mode and teoretica resuts are presented in Section 3. We evauate testabe impications of te mode vis-a-vis te data in Section 4, and Section 5 concudes.. Reated Literature Our paper is reated to a vast existing iterature on structura cange, for wic we provide a (very) incompete summary in order to deineate our reative contribution. Earier discussions of te facts and expanations for te canges in te structure of production incude Cark (94), Stiger (956), Kuznets (957), Baumo (967), Cenery and Syrquin (975), Fucs (968), Kravis et. a. (984), and Maddison (987). Tey observed an eary growt of te empoyment sare of te service sector, and posited tat a combination of biased productivity rates and non-omotetic preferences and were important in expaining abor sifts across sectors. A recent iterature as adapted tese ideas to expain ong run structura cange witin modes tat are consistent wit Kador facts (e.g., Kongsamut, Rebeo and Xie, 2, Acemogu and Guerrieri, 28, and Ngai and Pissarides, 27). We compement tis iterature by studying te roe uman capita as a driving force of structura cange. Tis approac eps address a series of empirica observations, incuding te ate rise of te sare of services in vaue-added, te ski composition of services, and te joint movement of reative prices and quantities. We aso focus on output and consumption rater tan te aocation of raw abor. Tere is aso an existing iterature on te roe of te ome vs. market production. Ngai and Pissarides (28) and Rogerson (28) are two recent contributions examining te roe of ome production in expaining te abor market sift toward services. Tey mode di erentia rates of productivity growt across market and ome production sectors in order to expain abor movements. Greenwood et a. (25) aso empasize tecnoogica cange in A reated iterature as empasized te roe of ome production in ess deveoped economies, incuding an empasis on structura cange out of agricuture (e.g., Goin, et a, 24, Buera and Kaboski, 28). 4

7 te ome, but teir focus is on te te growt of te femae abor force rater tan te service sector. Buera and Kaboski (28) argue tat a rising optima scae of production as caused structura reaocations across ome and market, and broad sectors of te economy. Locay (99) anayzes te roe of customization and scae in te ome vs. market decision. Finay, te work by de Vries (994) empasizes te canges between ome and market production over deveopment, incuding te importance of two-way movements, wit market production rising in te eary stages of te industrious revoution, and ome production gaining importance wit te decine in femae market abor in te atter pases of te industria revoution. Tis paper compements tese papers by anayzing te reationsip between ome-production, uman capita acquisition, and te service sector. Our anaysis of uman capita is reated to severa oter papers, owever. Becker and Murpy (27) examine te e ect of genera, rater tan speciaized, uman capita on non-market productivity. Casei and Coeman (2) use uman capita accumuation to expain discrepancies in abor and output trends in te decine of agricuture. Kaboski (29) sows tat uman capita investments are often reated to reaocations of abor across industries. Our paper s empasis on te roe of speciaization, ome vs. market-production, and te feedback on services is unique. Our particuar non-omotetic preferences buid on tose of Matsuyama (2, 22), Murpy, Seifer, and Visny (989), and Zweimueer (2) in teir work on structura cange. Tese preferences ave sown to be a tractabe way of modeing non-omoteticities over dissagregated components of consumption. Our twist is to introduce a decision between ome and market production. Ha and Jones (27) provide an important contribution in expaining te underying non-omoteticity for one important area of consumption: eatcare. Our mode of disaggregated activities and non-omotetic preferences is aso cosey reated to Foemi and Zweimueer (25). Teir anaysis posits a direct preference expanation in wic ierarcica wants are satis ed rst as agricuture, ten industry, and nay services. Our mode as no direct exogenous non-omoteticity toward services, but we empasize ow tis can arise endogenousy troug te ome production margin and a non-omotetic sift toward ski-intensive wants. Finay, given our focus on te consumption of eterogeneous services, wit more compex, newer ones contributing to te rise of te service economy, our paper reates to te earier work by Katouzian (97). 2 Empirics Tis section provides empirica motivation for our anaysis of te ink between ski accumuation and te growt in te reative size of te service sector. 2 We review evidence on te deayed acceeration in services, extend tis evidence by 2 Our data, source documentation and cacuations are avaiabe at ttp://kaboski.econ.oiostate.edu/servicesdataappendix_aerrevision.xs. 5

8 sowing tat growt in services is accounted for by growt in te consumption of services, and estabis tat tis acceeration occurs at a particuar income tresod. 3 We ten estabis tat growt in te service sare subsists amost excusivey in ski-intensive services, and ten discuss te fact tat te timing of te growt in services coincides wit two we-known trends in te iterature: te spread of coege-education and te rising return to ski. Figure sows a strong mid-century break in te current-vaue sares of services in consumption and vaue-added in te United States. Consumption data is based on na output purcases by consumers. Data is rst avaiabe from Lebergott (996) in 9, wie te data post-929 are based on nationa income and product (NIPA) accounts. Te vaue-added data is from Martin (939) from 869 to 92, te ony source to give vaue-added in current vaues for te fu service sector, and from NIPA accounts after 929. For te vaueadded data, we sow a broad measure of services (incuding tose provided by government, pubic utiities and transportation), but te same substantia trend exists in more narrow concept of services as we. Te 25 percentage point di erence in te eves of te series is a resut of consumption services excuding government services and distribution services (i.e., retai, woesae and transportation services) on goods, bot of wic are incuded in services in te vaue-added data. Te two series are rougy parae but consumption actuay exibits te arger absoute increase from 95 to 2. Our mode is a mode of te consumption of services and te ome production margin, so we stress tat growt in services is accounted for by growt in teir consumption. 4 Te break point after wic growt in sare of services acceerates is common to many countries. In te U.S., tis breakpoint coincides wit te year 95, but across countries te break is more strongy tied to income per capita tan cronoogica year. We sow tis using Buera and Kaboski (28) s pane data assembed for 3 countries spanning six continents and constituting two-tirds of te word s popuation and eigty percent of goba output. 5 In 95, te U.S. ad an income per capita of $92, in Geary-Kamis 99 internationa doars. We divide te sampe of country-year observations using tis $92 3 Kuznets (957) noted te ate acceeration in te vaue-added sare of services for a sma sampe of countries, but it as neverteess been overooked in te iterature (e.g., Maddison, 987), probaby because raw abor numbers tend to be more readiy avaiabe. 4 Government services are 2 percent in 2, wie transportation, woesae and retai togeter account for 6 percent in 2. Anoter di erence between te two series is te treatment of non-distribution intermediates. Te consumption of goods incudes vaue-added from te service sector, and te consumption of services incudes vaue-added from te goods sector. Te magnitudes and canges in tese intermediates approximatey net out, owever. 5 Tese countries incude Argentina, Austraia, Austria, Brazi, Canada, Cie, Cina, Coombia, Denmark, Egypt, France, Germany, India, Indonesia, Israe, Itay, Japan, Korea, Mexico, Neterands, Norway, Pakistan/Bangades, Spain, Sri Lanka, Sweden, Switzerand, United Kingdom, United States, and Taiand. Based on Maddison (26), our data covers: 68 percent of word popuation and 8 percent of word GDP in 2; 7 percent and 75 percent, respectivey, in 95; and 4 percent and 6 percent, respectivey in 9. Atoug te numbers are ower for 9, since te onger time series incude Western Europe and its o soots, we cover a muc arger sare of te popuation and economic activity undergoing arge structura cange at te time. 6

9 tresod, and ten run te foowing regressions on te ow- and ig-income sampes: services sare of vaue-added i;t i + n y i;t + e i;t () were n y i;t is og per capita income of country i at time t. i is a country i xed e ect. (We incude to contro for eve di erences in te series, some of wic are te resut of di erences in measurement across countries. 6 ) Here ^ captures te e ect of te witin country variation of income on te service sare. Beyond te $92 tresod income, te services sare is strongy reated to income. Wie te estimated coe cient on og income is positive and signi cant in bot sampes, te coe cient ^ increases more tan tree-fod from just.6 (std. error of.) for te <$92 sampe to.22 (.2) for >$92 sampe. In contrast, spitting te sampe by te year 95 yieds simiar coe cients of.8 (.) before 95 and. (.) from 95 on. 7 Tus, an acceeration of te sare of services in consumption and vaueadded at iger incomes appears to a be a common feature of structura transformation. Tis paper is about growt in te consumption of services, but we soud note tat in contrast to te deayed acceeration of services observed for consumption and vaue-added, te sare of abor in services increases muc more graduay wit income per capita, bot over time in te U.S. (Ngai and Pissarides, 28) and in te cross-section of countries (Kuznets, 957). 8 Tese numbers impy arge di erences in output per worker across sectors in te earier period for te U.S (Casei and Coeman, 2; Buera and Kaboski, 29). If ski eves di er across sectors, te numbers may re ect arge discrepancies between raw abor and e ective abor. Raw abor numbers may not be as informative for our purposes, especiay given our empasis on uman capita. Sti, te reason for te discrepancy between sectora output and abor aocations pre-95 is an open question, and not one tat our teory wi expain. Our teory associates te increase in te consumption of market services wit an income e ect toward ski-intensive output, and indeed te growt in services as been toward ski-intensive services. Figure 2 separates te growt in services into te contributions of ig- and ow-ski industries. We rank industries according to teir ski intensity as measured by te fraction of workers coege-educated in 94 (te ast avaiabe data preceding te acceeration) and divide te vaue-added of te service sector in af in 95. Hig-ski industries are terefore industries wit at east 2.5 percent of abor-coege educated in 6 For exampe, in severa countries utiities cannot be separated from mining and so are excuded from services. Countries aso di er to te extent tat sma-scae andicrafts are cassi ed as services or manufacturing. Anoter interesting exampe is Cina wose istorica data sow an extremey ow sare of services, probaby because services were not viewed as producing vaue under Marxist ideoogy. After te Economic Census of 24, te service sare was revised upwards by nine percentage points in te current o cia data. 7 Tat is, te growt in services appears to be a feature of deveopment rater tan driven by a common sock to te word economy suc as a commony avaiabe new tecnoogy or adoption of a common poicy. 8 Te di erence between te abor and vaue-added trends in a sma sampe of deveoped countries was noticed quite eary by Kuznets (957). 7

10 94. 9 We appy te same tresod to map disaggregated components of service consumption into ig- and ow-ski. We again see a breakpoint at 95, and te rise of te service economy as been ceary driven by ig-ski industries. Te importance of ow-ski service industries in vaue-added as actuay decined, toug it as remained rougy constant for consumption. Again, distribution costs account for te discrepancy between consumption and te oter measures. In any case, growt patterns ceary di er across ski-intensity. We can ook at a more disaggregate eve, if we focus on abor compensation data. Labor compensation numbers are neary identica to vaue-added numbers in Figures and 2, but are avaiabe at a more detaied eve. Figure 3 sows tat tere are many quantitativey important industries in te growt of ig-ski services. It pots te absoute cange in te sare of di erent service industries in tota abor compensation between 95 and 2 against te ski-intensity of te industry (measured as te fraction of workers wit coege-education in 94). Again, given avaiabe data, tis positive reationsip appears to be particuar to ony te ig income, post-95 period. Te absoute importance of eac industry to te tota growt in services is its vertica distance from te zero growt ine. Te growing ig-ski services incude education (especiay iger education), ega services, banking, rea estate and accounting, broadcasting and teevision, air transportation, and eat care. We empasize tat te growt in services is a broad increase in te demand for output tat is intensive in speciaized skis. Of course, two important industries are eat care and education, wose growt may be driven at east in part by growt in government subsidies or oter poicies. Wie important, owever, tese industries are simpy not te fu story. For exampe, eat and ospitas togeter account for an amost 8 percentage point increase, but tey constitute ess tan one-quarter of te tota rise in ig-ski services, and te ve percentage point increase in education constitutes ess tan one- ft. Moreover, te trends we igigt are robust to te excusion of eat care, education, and government from te data. Namey, te remaining service industries do not rise unti after 95, but ten rise 6 percentage points tereafter, and growt of te remaining ig-ski services (9 percentage points) again exceeds service growt overa. Te remaining consumption categories grow substantiay too, toug witout eat care and education, te increase is now 8 percentage points, or about af of te growt in vaue-added. 9 Tese rankings are remarkaby stabe over time. We coud ave produced identica resuts if we ad used data in 2 to rank industries, but we woud need a cuto of 5 percent. Output and consumption sare cannot be merged precisey wit workforce education data at tis detaied eve. Te detaied industry and education data comes from IPUMS census. After 95, census abor and compensation numbers cosey mirror NIPA numbers, except tat census compensation does not incude bene ts. Using manours instead of abor compensation yieds a very simiar picture. Atoug ony a singe decade of data are avaiabe, census data sow absoutey no reationsip between ski-intensity and growt in te sare of disaggregated services from 94 to 95. At an even more disaggregate eve, it is cear tat many ig-ski services were simpy not consumed in earier periods. 8

11 More generay, we empasize tat our teory invoves not ony wat is being demanded, but ow it is being deivered. Indeed, even witin te categories of eat care and education, tere as been a rise in te service economy. Heat care is provided as bot services (medica services, ospitas) and commodities (medica equipment, parmaceuticas), but te sare of services in eat care consumption rose from 77 percent in 95 to 84 percent in 2. Simiary, if we combine educationa services and books togeter, we see tat te sare of services in tis broad educationa consumption category increases from 73 percent in 95 to 83 percent in 2. Te broad increase in te demand for ski-intensive output tat we propose soud manifest itsef in te market for ig-skied abor. We terefore view te growt in services as reated to te we-known post-95 increase in te demand for a broad range of ig-skied workers (see Jun, Pierce, and Murpy, 993). Using coege-educated workers as a proxy for ig-skied workers, Figure 4 sows te growt in te reative price and reative quantity of services. Te average wage of coege-educated workers rose from 25 percent of te average ig scoo-graduate wage in 95 to over 2 percent by 2. At te same time, te ratio of coege- to ig scoo-educated abor in te workforce rose from about fteen percent to sixty percent. Te rising disparity between igand ow-ski workers is of great poicy interest. Poicy makers and journaists often argue paradoxicay tat te faing reative wage of ow ski workers is a resut of te growing prevaence of ow ski service jobs, but we stress tat te growt in services is a resut of te growt in ig-ski services. Based on avaiabe evidence for te U.S., te timing of trends invoving te service economy and te market for ig-skied abor correspond. Tat is, te year 95, or te $92 tresod, appears to be a turning point in terms of trends reated to te scedue for te excess demand for ski. Wage and education questions were rst introduced in te 94 census, and so representative data are scant before tat. Tere was a sarp decrease in premiums to ski, incuding te coege-premium between 94 and 95. Broader returns to education, and oter proxies for te ski-premium suc as wite coar-bue coar occupation di erentias, did not increase and most ikey decined before 94 (see Godin and Katz, 999). Leves of education and oter measures of ski increased we prior to tis, and te growt in skis in te abor force is ceary part of a more continuous process. Sti, we mode ski dicotomousy, and coege education appears to be a convenient measure of te eve of skis associated wit te rise of te service economy. 2 Te coege boom is overwemingy a post-95 penomenon, since coege educated workers accounted for just percent of te abor force in te 94 U.S. census. Te coege boom aso coincides wit te $92 tresod 2 Empiricay, an increase in eementary and ig-scoo education precedes te coege boom. Tis took pace in a time of faing ski premia, suggesting tat it coud ave been, at east partiay driven by an increase in te suppy of skis, (see Godin and Katz, 999, Kaboski, 24). From te point of view of a more genera mode wit mutipe eves of igski, tese ower eves of education coud be viewed as aowing individuas to be speciaized in te production of ess compex output, were ski as merey an absoute advantage. 9

12 in oter countries as we. Using Coen and Soto (27) data, te fraction of te adut (25+) popuation of a country tat as some coege-education averages just.8 (std. dev. of.3) at rea incomes near $92. Spit-sampe regressions anaogous to equation () but were te service sare is repaced wit te fraction of coege-educated aduts, yied a ve-fod increase in te coe cient on og income between te ow- and ig-income sampes, from.4 (<$92) to.23 (>$92). 3 Tat is, bot growt in te service economy and investment in coege education coincide wit an income per capita of $92. 3 Mode In tis section, we deveop a mode of speciaized ski accumuation tat eads to te rise (acceeration) of te service economy. Speci cay, we mode an economy wit a continuum of di erentiated manufactured goods and a continuum of di erentiated services, bot indexed by teir compexity, z 2 R +. Manufactured goods are inputs into te production of services, and services are wat individuas utimatey consume. Services can be produced eiter in te market or at ome. In te atter case, ouseods directy purcase manufactured goods to ome produce services. In our teory, we posit a utiity advantage in consuming ome-produced services, re ecting te ouseod s gains from customizing services to its own need. On te oter and, te production of services in te market can be more cost e ective. Labor is te one resource in te economy and is eiter genera ow-skied abor or speciaized ig-skied abor. Given a xed time cost of becoming ig-skied in te production of eac di erentiated service, z 2 R +, individuas coose to speciaize in at most one service. Te ome production of amost a services wi terefore use ow-skied abor. Exogenous productivity improvement is te ony source of growt in te economy. For simpicity, we assume tat agents are in nitesimay-ived, and so te mode is static except for tis tecnica cange. 3. Tecnoogies Te tecnoogy for producing type-z service output y s (z; t) requires abor and type-z manufactured goods as intermediates, y m (z; t). Production is Leontie in intermediates and abor vaue-added, were ig-skied abor s (z; t) and ow-skied abor s (z; t) are perfect substitutes in producing tis vaue-added: y s (z; t) min fa (z; t) s (z; t) + (z; t) s (z; t) ; qy m (z; t)g 3 For eac country, we use a countries wit a year of income between $85-$95 and coose te year cosest to $92. In comparison, at tis income eve, primary education is neary compete (te fraction of te adut popuation averages.97), wie secondary scooing is we underway (.37).

13 Te eves of productivity of ig- and ow-skied workers, A (z; t) and (z; t), respectivey, are speci c to te production of service z. We make severa assumptions regarding tese functions: First, z indexes compexity, so we assume tat productivity is decreasing in < <. Second, for a t, A (z; t) > (z; t); so tat ig-skied abor is more productive. Sti, since ski is speciaized, A (z; t) is speci c to one particuar z (te agent s speciaty), so te ig-skied agent as te ow-skied productivity (z ; t) for a oter output z 6 z, wit A (z; t) (z; t) for a z and t. Finay, ig-skied abor as a (weak) comparative advantage in te production of more compex services, (z;t) > (). Tis tecnoogy can be used to produce services by competitive rms in te market, or at ome by individua ouseods. In te case of ome-production, ig-skied abor can ony be used to produce a particuar service z if te ouseod is speciaized in te production of tat service (e.g., ony accountants use ig-skied abor to process teir own taxes). For simpicity we abstract from te use of intermediates in te production of manufactured goods, and te output of manufactured goods y m (z; t) is simpy inear in abor: y m (z; t) A (z; t) m (z; t) + (z; t) m (z; t) Te production of manufactures can ony be done in te market Firms Probem Given wages, free entry of service and manufacturing rms impies tat rms wi price at average cost: w (t) p m (z; t) min A (z; t) ; (2) (z; t) and w (t) p s (z; t) qp m (z; t) + min A (z; t) ; (z; t) 4 See Buera and Kaboski (28) for an extension of tis mode in wic manufactures are produced, as is true in te data, using tecnoogies requiring arge xed costs and aving a arge e cient scae. In tis extension, it is not cost-e ective to produce manufactured goods at te very sma scae of ome-production. (3)

14 3.3 Preferences Agents od preferences over te continuum of discrete, satiabe wants indexed by te service tat satis es tem, z. Tus, na consumption takes te form of services, wie manufactured goods are purcase as inputs in te omeproduction of services. 5 Let te function C (z) : R +! f; g indicate weter a particuar want is being satis ed. Wants can eiter be satis ed by procuring te service directy from te market, or by purcasing te required manufactured goods and producing te service at ome. De ne te function H (z) : R +! f; g to take te vaue if want z is satis ed by ome production and oterwise. Togeter te set of indicator functions mapping R + into f; g 2 de- nes te consumption set. Preferences over wants and te metod of satisfying tose wants, i.e., over indicator functions C (z) and H (z), are represented by te foowing utiity function: u (C; H) Z [H (z) + ( H (z))] C (z) were H (z) C (z). Te parameter 2 (; ) re ects te utiity of market consumption, wic is ess tan te utiity of ome-produced consumption because it is not as customized (e.g., driving precisey wen and were you want rater tan riding te bus on xed scedues). Tese preferences, toug somewat non-standard, ave certain advantages. First, te continuum of satiabe wants is simpe way of modeing disaggregate non-omoteticities tat as been used in te existing iterature on structura transformation. 6 Tis disaggregation is not witout content and we sow, in Section 4, te extent to wic tey can be represented in a more standard form, as preferences over tota consumption of goods and services. Aso, Matsuyama (23) as sown tat tey can be easiy generaized to aow for asymmetries in te utiity provided by satiating di erent wants, in wic case our cost of satisfying a particuar want can be interpreted as a cost per unit of utiity. In any case, we view te preferences as a simpe abstraction capturing sifting demand patterns and te ome production decisions associated wit tem. As suc, te preferences may be reduced form for a ost of idiosyncratic expanations for canges in disaggregate demand patterns. For exampe, te growt in demand for eat-reated goods and services may stem from a desire to invest in eat capita (as in Ha and Jones, 27). 7 Our empasis wi be on te importance of ski-intensity in determining weter tese are ome or market produced, and tese preferences wi give parsimonious framework for anayzing a common dimension to a wide set of micro penomena. 5 One coud easiy introduce a second continuum of wants tat are directy satis ed by manufactured goods, but it woud contribute itte to te anaysis. 6 See Murpy et a (989), Zweimueer (2), and Matsuyama (2,23), for exampe. 7 Indeed, increases in te demand for eat-, education-, and nance-reated coud a be driven by exogenous increases in ife expectancy. 2

15 3.4 Scooing Individuas make a dicotomous education decision e 2 f; g ; but becoming speciaized ig-skied workers, e, requires spending a fraction of teir time endowment acquiring skis. 8 Tis cost of becoming educated is a continuous increasing function of f, te fraction of workers wo decides to acquire education, i.e., (f) >. We assume tat (), in order to ensure f >, and () <. Te (f) function is a simpe way of generating an upward soping suppy curve for education witout introducing underying eterogeneity. One can motivate tis in te typica way, were individua agents draw after coosing teir ski eve, but are competey insured against teir draw. Tus, ig- and ow-skied agents a receive te same utiity in equiibrium. In tis interpretation, (f) is te average cost of education as a function of te fraction of individuas tat decide to acquire education. In principe, agents coud acquire skis for mutipe z in order to increase teir productivity in ome production, but tis woud never be optima. Since te time cost is stricty positive for any stricty positive fraction of agents acquiring skis (i.e., (f) > for any f > ); in any aocation wit positive ig-skied workers, individuas can acquire speciaized skis for at most a - nite number of services. Given tat individuas consume a continuum of tem, tis nite number woud constitute a measure zero of ome-produced services. Terefore, individuas wi acquire skis in at most one service, and te omeproduction of a (but a measure zero of) services wi be done wit ow-skied productivity. 3.5 Consumer s Probem Te demand for market services and manufactured goods of an individua wit ski e, soves: V e s.t. Z Z + max H(z)C(z) [H (z) + ( H (z))] C (z) [C(z)H(z)qp m (z; t) + C(z) [ H(z)] p s (z; t) {z } {z } C m Z Z w e (f)i (e) C(z)H(z) (z; t) {z } abor suppy C s (4) 8 Te key assumption in our anaysis of te growt of services wi be tat te comparative advantage of ig-skied abor is increasing after a tresod compexity, n A (z; t)@z > for z >. An aternative modeing coice tat woud ave aowed for mutipe (a continuum of) ski eves, and assignment of skis to te production of want of di erent compexity. If skis and compexity are compementary, and equiibrium woud exibit positive sorting. We coose to abstract from mutipe eves of ski and postuate a dicotomous set of skis as tis assumption greaty simpi es te anaysis. 3

16 Market expenditures are on te eft-and side of te budget constraint, wit te rst term in te integra capturing expenditures on goods used in ome production (C m ), and te second term capturing expenditures on market services (C s ). Te rigt-and side of te budget constraint is abor income. Labor income is te product of te wage w e and abor suppied to te market, bot of wic depend on te educationa decision e. Labor suppy is net of te amount of time used for scooing (f)i (e), were I (e) is an indicator function tat equas one if e and zero oterwise. Market abor suppy is aso net of ome production time. Note tat ome production is performed using te ow-skied productivity, regardess of educationa decision e: Given a margina utiity of consumption, for eac z, te consumer decides to satisfy it (i.e., C(z) ) i : p s (z) and/or qp m (z) + w e (5) (z; t) were te eft inequaity reates to te decision to market consume and te rigt inequaity is te decision to ome produce. Using our knowedge of equiibrium prices from equations (3) and (2), any z tat wi be satis ed, wi be ome produced i : we (z; t) min (z; t) ; w (6) A (z; t) Te rigt-and side of expression (6) above captures te di erence in te cost (in utiity terms) of producing te service at ome or purcasing on te market. Tis di erence is iger for more compex (i.e., ig z) services, especiay tose tat are more e cienty produced on te market using ig-skied abor, and for agents wit ig opportunity cost of ome production time w e. Tus, a want wi be ome-produced if te gains from customizing our consumption exceed te productivity gains from market production. Reca tat wants enter utiity symetricay, and production costs, as we as te additiona costs of ome production, are increasing in z. Terefore, consumers wi satisfy and ome produce te east compex wants rst, and te consumer s probem can be simpi ed to te coice over te restricted consumption set de ned by step functions of te type: if z ze C (z) if z > z e and H (z) if z ze if z > z e were z e denotes te most compex want tat is satis ed, and z e denotes te most compex want tat is ome-produced. Preferences over te restricted consumption set can ten be represented as a utiity function over two tresods z e and z e : 4

17 u (z e ; z e ) ( ) z e + z e wit z e z e. On te margin, agents can increase utiity in two ways: by satisfying an additiona not-yet-satiated want (i.e., increasing z e ) or by moving te east expensive market-satis ed want into ome production (i.e., increasing z e ). Since te main interest of te paper is te service economy, we focus on parameters in wic market services are purcased in equiibrium. Te foowing assumption guarantees z < z, i.e., ig-skied workers consume some market services. > ( + q) A (;) (;). (7) Intuitivey, to ensure market services are used, we need te utiity of market services and cost bene ts of market services, governed by te minimum reative productivity of ig-skied workers, to be su cienty ig. Te su ciency of tis condition foows from ig-ski workers aving a comparative advantage in te production of more compex services, [A (z; t) (z; and productivity growt being neutra. An agent cooses to be ig-skied if V > V, and vice-versa. Given our assumptions on (f), ony an interior f 2 (; ) can be an equiibrium, wic wi require agent indi erence: V ( ) z + z ( ) z + z V (8) Atoug ig- and ow-skied workers earn te same utiity in equiibrium, teir consumption bundes di er. A iger w e in te rst-order condition (6) above makes te reative cost of ome production iger for ig-skied workers tan for ow-skied workers. Substitution eads ig-skied workers to omeproduce fewer services and market consume more services. Moreover, since agents are indi erent to being ig- or ow-skied, te iger wage captures a pure substitution e ect (see condition 8). Terefore, since a consumers prefer ome-produced services, ig-skied workers consume fewer ome-produced services but remain indi erent to being ow-skied because tey consume a arger range of services overa. Proposition Hig-ski workers consume some market services tat ow-ski workers do not consume; z > z, ome produce a smaer range of services z < z. De ning C (C ), C s (C s), and c s c s as te market consumption, market consumption of services, and te services sare of market consumption of igskied (ow-skied) agents 9, we state te foowing coroary: Coroary 2 Hig-skied workers spend a arger fraction of teir income in services, c s C s C > C sc c s. 9 Speci cay, Cs e R z e z p e s(z), Cm e R z e p m(z), C e Cs e + Ce m, and ce s Ce s Ce : 5

18 3.6 Competitive equiibrium A competitive equiibrium is given by price functions p m (z; t), p s (z; t), w (t), a fraction of peope wo attain scooing f, quantities of manufactured goods and market services determined by z (t), z (t), z (; t), z (; t), and abor aocations suc tat consumers demands and scooing decisions sove (4); prices sove zero pro ts conditions (2) and (3); and abor markets cear. 4 Growt of Services Te dynamics of te mode are fuy driven by te functions A (z; t) and (z; t): In tis section, we anayze speci cations of tese functions tat ead to an initia baanced pase foowed by a pase wit growt in te sare of services, te fraction of ig-skied workers, and te ski premium. First, we caracterize restrictions on tese functions tat are consistent wit baanced growt as te resut of neutra tecnica cange. We ten study a variation in wic neutra tecnica cange sifts demand toward wants in wic ig-skied workers ave iger reative productivity. Tis variation eads to growt in services and as additiona impications about te ski composition, te rising reative price of services, and product cyces, wic we ater evauate reative to te data. 4. Baanced Growt We begin by sowing tat given our assumptions on A (z; t) and (z; t), a power parameterization of tese functions is necessary and su cient to generate baanced growt wit a constant sare of services in consumption. Wie te focus of te paper is te rise of te service economy, we restrict our anaysis to variations on tis power parameterization of productivity, since we are interested in modes tat can aso reconcie te reativey constant sare of services in output and consumption in te pre-95 data. Proposition 3 Consider te consumer s probem for workers parameterized by constants q and and a stricty positive and stricty decreasing function ~ A (z), so tat A (z; t) ~ A (z) e gt and A (z; t) ~ A (z) A e gt, and w A >. Ten, te sare of service in consumption c s (t) C s (t) [C s (t) + C m (t)] is a constant for a q and if and ony if ~ A (z) z. Proof. See Appendix Proposition 3 states tat te reative wage is set at te reative productivity of ig- and ow-skied workers, wic is common across z. Hence, a rms are indi erent between using ig- and ow-skied workers. (See te cost minimization in equations (3) and (2).) In tis case, te cost of ome producing services for ow-skied workers is te same as te cost of market purcasing services, but since <, consumers get more utiity from ome production. Terefore, 6

19 ow-skied workers consume no market services. 2 Hig-skied workers face iger costs to ome produce, owever, since teir wage is iger but not teir productivity in ome production, and assumption (7) ensures tat tey indeed consume positive market services. A roug intuition for te above resut is tat te power function as a memoryess sape, wic keeps te rst-order conditions for te margina z and z constant, even as tese margins increase ineary. Indeed, one can rewrite te consumer s probem for te ig-skied agents into a probem wit omotetic quasi-preferences over tota expenditures on services and manufactured goods, Cs and Cm respectivey: max C m + 2 C Cm s + 3 C m (9) ;C s s:t: p mc m + C s we gt ( ) We ca tese quasi -preferences because te preference parameters, 2, 3 and depend on underying preference and tecnoogy, wie te price on manufacturing expenditures p m is a function of te (constant equiibrium) wage. 2 It is straigtforward to see tat te above preferences are omotetic, owever, and so te sare of services remains constant as income grows. Wie te preferences are omotetic wit respect to income, consumption patterns noneteess vary wit respect to te wage/opportunity cost of time troug its e ect on p m. Tat is, a pure weat e ect (i.e., an increase in income as t increases) does not a ect te reative sares of service and manufactured goods consumption, but a iger wage wi ave a substitution e ect away from manufactured goods (wic are inputs into ome production) and toward services. Product Cyces We concude tis section by igigting an interesting impication of tis baanced mode for product cyces between ome and market production. As productivity grows, individuas consume new services. In te case of ig-ski workers, tey start purcasing tese services on te market, since production of te margina services is particuary time-consuming, and te opportunity cost of ig-ski workers time is too ig to be used in ow-ski ome-production. Eventuay, abor productivity increases enoug making te absoute cost advantage of market-production smaer, and eading individuas to ome produce customized versions of tese services wic yied iger utiity. (See te rst-order equation (6).) Tat is, tere is a cear product cyce of services being rst market produced and ater ome produced. Tis foows naturay from te assumption of a preference for ome production, a cost bene t 2 Tis resut is done for simpicity but is not particuary necessary. Low-skied workers coud consume services if some wants ad > or if tecnoogies were caracterized by e cient scaes greater tan te ome production scae as in Buera and Kaboski (28). 2 In particuar, ( + ), ( ) ( + ) q (+), 2 [( + ) ( + q)] (+), 3 ( + q) q and p m + wq. 7

20 to market production, and neutra productivity growt. Te foowing remark formaizes tis discussion: Remark: In an economy wit neutra productivity growt were A e (z; t) A e z e gt, e ;, te tresods de ning te demand of ow- and ig-ski individuas grow at te constant rate g ( + ), wit z (t) < z (t) z (t) < z (t). For ig-ski workers, for any particuar z, te mode yieds a product cyce from not consumed, to purcased on te market, and nay ome-produced. In te variation of te mode we discuss in te foowing section, a ricer set of product cyces arises Comparative Advantage of Ski in More Compex Output In tis section, we study te growt of te service economy, wic arises from agents satisfying more compex and ski-intensive wants as incomes grow. Higskied abor as a comparative advantage in satisfying tese wants, ence more of tese services are produced on te market, and te demand for ig-skied abor increases. We proceed by estabising four reated e ects tat a contribute to te growt in services. Te eading e ect, wic drives te oters, comes directy from ig-skied workers aving a greater comparative advantage in more compex output, wic we ca te ig-ski advantage e ect. Two oter e ects, te opportunity cost e ect and ski-deepening e ect, come troug te e ect of comparative advantage on te demand for ig-skied abor. We ten sow ow comparative advantage-drive sorting eads to growt in ski-intensive services, and aso growt in te reative price of services, te reative price effect, wic aso contributes to te growt in te sare of services. Finay, we combine tese resuts, and sow tat over time tese forces ead to growt in te aggregate sare of services in te economy. Te underying assumption tat gives rise to a growing sare of services is tat ig-skied abor as a comparative advantage in te more compex goods and services, wic wi rst be consumed at a ater date given teir ig cost of production. Speci cay, over a range of ess compex (i.e., z < ) production, productivity fas wit z at a rate for bot ow- and ig-skied workers aike. For te range of more compex output (i.e., z > ), te productivity fas more sowy for ig-skied workers tan for ow-skied workers. Speci cay, we assume: (z; t) e gt z () A (z; t) A e gt max z ; z wit <. Given tese productivity assumptions, consumption eventuay moves into te z > region were ig-skied workers od a stronger productivity advan- 22 See aso Buera and Kaboski (28) for an anaysis of ricer, e cient scae-driven product cyces tat are important in te eary pase of deveopment. 8