ICT Services and their Prices: What do they tell us about Productivity and Technology?

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. ICT Services and their Prices: What do they tell us about Productivity and Technology? David Byrne and Carol Corrado 2017-015 Please cite this paper as: Byrne, David, and Carol Corrado (2017). “ICT Services and their Prices: What do they tell us about Productivity and Technology?,” Finance and Economics Discussion Series 2017-015. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2017.015r1. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

ICT Services and their Prices: What do they tell us about Productivity and Technology? David Byrne∗ and Carol Corrado†‡§ May 16, 2016 (Revised, September 29, 2017) Abstract This paper reassesses the link between ICT prices, technology, and productivity. To understand how the ICT sector could come to the rescue of a whole economy, we extend a multi-sector model due to Oulton (2012) to include ICT services (e.g., cloud services) and use it to calibrate the steady-state contribution of the ICT sector to growth in aggregate U.S.laborproductivity. BecauseICTtechnologiesdiffusethroughtheeconomyincreasingly via purchases of cloud and data analytic services that are not fully accounted for in the standard narrative on ICT’s contribution to economic growth, the contribution of ICT to growth in output per hour going forward is found to be substantially larger than generally thought—1.4 percentage points per year. One reason why the estimated contribution is so large is that official ICT asset prices are found to substantially understate the productivity of the sector. The model developed in this paper also has implications for the relationship between prices for ICT services and prices for the capital stocks (i.e., ICT assets) used to supply them. In particular, ICT service prices may diverge from asset prices and capture productivity gains from ICT asset management by the sector. Keywords: ICT services; Cloud computing; Information and Communication Technology (ICT); Productivity; Technology; Price measurement. JEL codes: D24, E01, E22, L86, O41, O47 ∗Board of Governors of the Federal Reserve System, Washington, D.C. †The Conference Board and Center for Business and Public Policy, McDonough School of Business, Georgetown University. ‡Corresponding author: carol.corrado@tcb.org §Wethanktheeditorsofthisvolume,ananonymousreferee,BartvanArk,RalphBradley,NickOulton,participantsin theWorldKLEMSconference(Madrid)andworkshopsatKingsCollege(London)andtheFederalReserve(Washington, D.C.) for feedback on earlier drafts. This paper reflects the sole opinions of the authors and does not reflect opinions of the Board of Governors of the Federal Reserve System or other members of its staff.

Contents 1 Framework 4 1.1 Expanded two-sector model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 ICT services prices vs. ICT asset prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Quality change or productive externality? . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 ICT sector trends 11 2.1 Technology and R&D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 ICT services and software investment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Sector final output and capital income . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 ICT investment prices 21 3.1 New ICT product prices and implications for ICT services prices . . . . . . . . . . . . . 22 3.2 New ICT Investment Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4 Summary and conclusion 31 Appendix 37 A1 The steady-state solution of the two-sector model 37 A2 Nominal ICT investment deflators 40 i

ICT Prices and ICT Services: What do they tell us about Productivity and Technology? The importance of computers, computer microprocessors, and productivity-enhancing computer software in driving the step up in U.S. productivity growth in the mid-1990s is well established.1 But the Internet and mobile telephony—two of the 20th century’s greatest inventions—have been largely absent in the macroeconomic work on U.S productivity performance until recently. Our research on communications technology and communication equipment price measurement (Byrne and Corrado, 2015a,b) and its implications for interpreting U.S. productivity (Corrado, 2011; Corrado and J¨ager, 2014) puts these innovations front and center and offers a story in which communication and communication networks (as much as computing performance) drove productivity developments in the 1990s and early 2000s. Communication technology has continued to advance since the early 2000s, and rising connection speeds have made possible the cloud and mobile platforms that are transforming how organizations use computing resources and exploit data. But measured productivity growth has slowed dramatically. The deterioration in U.S. labor productivity growth is due in part to historically slow real investment ininformationandcommunicationtechnology(ICT)equipmentandsoftware,whichnolongerprovides an extra boost to overall output per hour.2 Indeed, not only has nominal ICT equipment and software (E&S) investment relative to GDP moved sideways since 2010 (figure 1a), relative ICT price change has posted extremely small declines of late, after having gradually lost force since 2004 (figure 1b). WhyisICTinvestmentsoweak? Andifdigitalinnovationsaresotransformative, whyaretheynot having a discernible impact on recent ICT prices (and labor productivity)? Google’s Hal Varian offers aviewfromSiliconValley, namely, thatU.S.productivityismis-measured.3 Anotherpossibilityisthat theICTsectorisinnovatingandprosperingbutistoosmalltocometotherescueofaneconomyfacing stiff supply-side headwinds that limit its productivity growth (Gordon, 2014a,b). As noted elsewhere (e.g., Brynjolfsson and Saunders, 2010) and by our calculations, the value added share of the U.S. 1In e.g., Jorgenson and Stiroh (2000); Oliner and Sichel (2000); Brynjolfsson and Hitt (2003). 2OutputperhourforthetotalU.S.economygrewanestimated1/2percentperyearfrom2010to2015—theslowest 5-year rate of change in the post WWII era based on The Conference Board’s Total Economy Database™ whose output per hour series for the U.S. total economy begins in 1950. 3See “Silicon Valley Doesn’t Believe U.S. Productivity is Down,” Wall Street Journal, July 16, 2015, by Timothy Aeppel.

Figure 1: ICT Equipment and Software Investment and Prices in the United States (a) Nominal ICT E&S Investment, percent of GDP (b) ICT Relative Price Change, annual rate Note: Private investment only. Source: Authors’ elaboration of data from U.S. BEA. The investment ratio for 2015 is based on partial year data. Nominal ICT investment and ICT price change are measured relative to nominal GDP and the GDP deflator, respectively, and exclude software R&D. ICT-producing sector (including ICT services production) has remained stable at about 6 percent of GDP since 2000, i.e., it has remained relatively small for an extended period of time. Thispapermakes, webelieve, threecontributionsthathelpaddressthisconundrum: First, amultisector growth model developed by Oulton (2012) is extended to include purchased ICT services (e.g., cloud or data analytic services). The amended model shows how ICT can be a driver of growth when ICT investment remains weak and suggests the balanced growth contribution of ICT to U.S. labor productivity growth is very large—1.4 percentage points per year. About 25 percent of this total ICT sector contribution owes to the diffusion of ICT technology via purchases of cloud and related ICT services.4 Second, themodelhighlightsthechannelsthroughwhichatransitiontocloudcomputingcanaffect productivity growth and sets out the determinants of ICT services price change during that transition and in balanced growth. The extended model implies and we further posit via a user cost (Jorgenson, 1963) approach that price change for marketed ICT services is proportional to price change for the 4NotethatthispaperbearsmostdirectlyoninterpretingtrendsinICTinvestmentandICTservicesuseviathetake up of cloud and related technologies by the producing sectors of the economy. Byrne and Corrado (2017a) assess the impact of digitization and take up of wireless technologies on the consumer sector. 2

productive assets used to produce them but that efficiency gains from rising ICT capital utilization may cause ICT services prices to diverge from ICT asset prices. Third, the paper puts official ICT product prices under a microscope and reviews the consistency of 14 new ICT research price indexes with the model’s implications. The new ICT product price indexes are based on our own prior work (Byrne and Corrado, 2015a,b) and new work reported in a companion paper to this paper (Byrne and Corrado, 2017b). They also draw upon the historical ICT price measurement literature (e.g., Berndt and Rappaport, 2001, 2003) and include prices for cellular and data networking equipment, enterprise software products, high-end computers/servers, PCs, and computer storage systems, which along with a high-speed broadband infrastructure, have spurred the growth of cloud computing, datacenter design services, and data analytics over the last decade. The companion paper documents how the new ICT product prices are folded into new estimates of national accounts-style investment price indexes that are then used in this paper. The new ICT asset prices suggest that long-term trends in official ICT prices suffer from substantial mismeasurement and that the relative productivity of the ICT sector remains strong and continues to provide an extra kick to labor productivity growth—unlike the implication of figure 1(b).5 We proceed as follows: Section 1 introduces the model, presents its solution, and discusses its implications for ICT services price change. Section 2 first shows how we measure the ICT vs the nonICTproducingsectorandreviewsselectedindicatorsofICTtechnicalchange, includingICTR&D. ThesectionalsodescribeshowthenewICTerainvolvestechnologiesdeliveredasservicesthatraisethe utilizationofICTcapital,andillustratesthetakeupofthesetechnologiesviapurchasesofICTservices by the nonICT-producing sector. Section 3 introduces the new ICT research product price indexes and reports and analyzes their implications for assessing ICT services price change and the relative productivity advantage of the ICT sector. Section 3 then uses the implied productivity differential along with Section 2’s information on income shares of ICT assets and ICT services to calibrate the model of Section 1. Because the results imply very weak productivity in the nonICT-producing sector, the paper discusses and then concludes with several hypotheses why this is both plausible and likely temporary. 5As discussed in Byrne, Fernald, and Reinsdorf (2016), ICT price mismeasurement has been with us for some time, andmismeasurementcanonlyexplainasmallportionofthe“missingoutput”fromtheproductivityslowdown(seealso Syverson 2016). The ICT equipment prices described in (Byrne and Corrado, 2017b) and used in this paper were used inByrneetal.(2016),whoconcludedthatmismeasurementofICTpricescannotexplaintherecentslowdown inoutput per hour. 3

1 Framework ICT plays a central role in modern economies, and quantitative assessments of longer-term economic growth prospects depend heavily on estimates of the contribution of ICT to productivity change for the years ahead. Oulton (2012) proposed an approach to making long-term growth projections based onatwo-sectormodelofanopeneconomywhereonesectorisanICT-producing/supplyingsector. His approachisinthespiritofthegrowthaccountingapproachtomakingeconomicprojections(Jorgenson, Ho, and Stiroh, 2004; Jorgenson and Vu, 2010; The Conference Board, 2015; Byrne, Oliner, and Sichel, 2013), in which one of the key drivers of economic growth is growth of total factor productivity (TFP) in the ICT-producing sector relative to the rest of the economy. BenefitstoeconomicgrowthaccruetofasterrelativegrowthofICTTFPbecausefasterrelativeICT TFPgrowthmanifests asfaster relativeICT pricedeclines, whichthen enablesfaster growth ofincome andconsumption. Oulton’smodelmakesthesefeaturesofaJorgenson-stylegrowthprojectionexplicit, along with its corollary that economies with little or no domestic ICT production derive benefits from faster TFP growth in ICT investment goods production elsewhere in the form of improving terms of trade. To account for the growth of cloud computing, data center design services and data analytics, this paper expands the Oulton model to include intermediate uses of ICT services. The expression for the steady state contribution of ICT to the growth of output per hour in the expanded model is unaffected by assuming a closed economy, as in the original Oulton model. Proceeding with a closed economy assumption for simplicity, the expanded model is set out below. 1.1 Expanded two-sector model Total final demand Y consists of investment (I) and consumption (C) produced in two sectors of the economy. The two producing sectors are (1) an ICT sector (denoted by the subscript T) and (2) a general business sector excluding ICT producers (denoted by the subscript N). Each sector produces investment and consumer goods and services for final use. Thus we have (1) Y = C +I = Y +Y ; Y = C +I ; Y = C +I ; T N T T T N N N and P Y T T (2) PY = P Y +P Y ; w = . T T N N T PY 4

where P is the price level, P and P are sector prices, and w represents the relative size of the ICT T N T sector in final demand in nominal terms. Withregardtointermediates, theICTsectorisassumedtosupplyservicesforitsownintermediate use, as well as for intermediate use by other producers. The general business sector is assumed to produce intermediates for its own use only; these intermediates are omitted from its production function to keep the exposition simple.6 With sector N producing for final demand only, and each sector’s output (production net of own use) denoted by Q and Q , respectively, sectoral production T N may be written in terms of the following outputs and inputs: (3) Q ≡ Y +SN = A FT(KT,KT,ST,LT) ; T T T T N T T Q ≡ Y = A FN(KN,KN,SN,LN) N N N N T T where Kj denotes sector j’s capital input from its stock of investment goods of type i (i = T,N) and i Sj is sector j’s intermediate use of ICT services. Lj = hHj is sector j’s labor input, Hj is hours T worked in the sector, and h is a labor composition index applicable to the economy as a whole. The value of each sector’s factor payments is given by (4) P Q = R Ki +R Ki +WHi+P Si , i = T,N , i i N N T T T T with relevant factor shares given by R (KT +KN) W(HN +HT) P SN (5) v = T T T ; v = ; ζ N = T T . KT PY L PY T PY In equation (4), R and R are the nominal rental prices of capital and W is the hourly wage, and in N T N (5), v and v are the shares of ICT capital and labor in total income, respectively, and ζ is ICT KT L T business services purchased by sector N relative to total income in the economy. ThemodelassumesthereisfastertechnicalprogressintheICTsector. Denotingtherateofgrowth in the Hicksian shifter (A ) in the sectoral production functions (3) as µ , this assumption is expressed i i as µ > µ . A major simplifying assumption is then employed to solve the model, namely, that the T N sectoral production functions exhibit constant returns and differ only by their A terms. This implies i 6The complications of chain weighting also are ignored. 5

factor shares and input quantities are the same in both sectors, in which case log differentiation of the factor payments equations (4) yields the result shown by Oulton that relative ICT price change equals (the negative of) relative ICT TFP growth. Defining the relative ICT price as p = P /P , this result T N is expressed as a steady-state rate of change in relative prices p˙ given by (6) p˙ = µ −µ < 0 . N T Asmaybeseen,relativeICTpricechangeisnegative,reflectingtheextenttowhichtherelativegrowth of productivity in the ICT sector exceeds the growth of productivity elsewhere in an economy. The expanded model’s solution for the contribution of ICT to the growth in GDP per hour (OP˙H) is given by (7) Contribution of ICT sector to OP˙H = N v +ζ KT T (−p˙) + w (−p˙) . T v L (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) Productioneffect Investment(use)andproductivity(diffusion)effects For details of this solution, see appendix A1. Equation (7) differs from the solution to the original N Oulton model due to the presence of the term ζ capturing the ICT services-using intensity of the T economy. The solution nonetheless aligns with the usual growth accounting approach in which the contribution of ICT capital to growth in output per hour is identified as flowing through two channels: ICT use and ICT production. It is typical to consider the ICT use effect as operating through services provided by producers’ own investment in ICT capital, i.e., via services generated by ICT assets that producers own themselves. In the expanded model, the channel also operates via nonICT producers’ purchases of ICT capital services, e.g., purchases of cloud services, that provide workers access to ICT technologies in essentially the same way.7 In steady-state growth, output and output per hour in the N sector grow less rapidly than output and output per hour in the T sector, the sector producing ICT goods and services. In fact, this growth 7ThecontributiontoproductivitygrowthisparticularlypowerfulwhenICTservicesaredomesticallyproduced—i.e., the effect shown in equation (7) includes the industry’s contribution to TFP growth via the standard Domar-Hulten channel whereby innovation in upstream industries has impacts on aggregate TFP growth via using industries. When purchased ICT services are imported, the technology diffusion channel (i.e, their capital deepening-like effect) is still there, but its salutary impact is partially offset by the negative effect of ICT services imports on w . Appendix A1 sets T outtheformulafortheDomar-HultencontributionoftheICTsectortoTFPgrowthintheICT-servicesamendedmodel. 6

differential is −p˙, a result that follows from equality of the marginal product of factors used in the two sectors, which follows from the assumption of perfect competition; see appendix A1 for further details. The model thus implies that, to the extent µ really is greater than µ , real ICT services prices fall T N (as they are on par with real ICT asset prices), and real ICT services output growth is faster than growth of real output of the general production sector, evidence for which shall be shown in section 3 below. 1.2 ICT services prices vs. ICT asset prices The ICT sector’s output price is a single price P by assumption in a two-sector model. The strictness T of this assumption may be readily relaxed, however, yielding the usual multiple sector framework with many relative prices and an aggregate production possibilities frontier that generates multiple types of C and I for final use (e.g., Jorgenson 1966; Jorgenson, Ho, and Stiroh 2005). In what follows, the user cost expression is used to set out the conditions under which a multiple sector framework generates essentially the same implication for ICT services prices as did the simple two-sector model. Consider the determinants of prices for two types of ICT services in a multiple sector setting. The first is where ICT services production is highly ICT-capital intensive, as in the production of “public” cloud services by the ICT sector for sale to the nonICT-producing sector (e.g., Amazon selling to GM). The secondis whereICT services arefor designing“private”cloud servicesfacilities withinfirms in the nonICT producing sector. In both cases, ICT services facilitate more efficient sharing of datacenter resources across users. PSTSN is the value of ICT services, where PST is a quality-adjusted price specific to each type T of service. PIT will denote the quality-adjusted price of ICT assets relevant to each case (i.e., it is an investment price index). These prices are expressed below as real prices pST, pIT, relative to, say, the PCE or GDP deflator, below. A steady state required real rate of return on assets ρ is defined consistently (i.e., the price change element is in the same relative terms). Case 1. Cloud providers deliver infrastructure, platforms, and software as a service. In this case, ICT services prices are per period charges for resources managed by the cloud provider. Assume that these services are priced as capital services provided to a capital owner and equal to a rental price 7

times the capital stock and a factor of proportionality: (8) pSTSN = [(ρ+δ )pITKT] λ . T T T The expression in brackets is the standard expression for capital services and λ is a factor of proportionality representing the efficiency of ICT service provision relative to in-house ICT. As previously indicated, ρ is the real net return to capital investment; δ is the depreciation rate of ICT capital.8 ρ T is constant in steady state growth by definition, and δ is constant by assumption. Thus, if the real T price of cloud services pST is falling rapidly in constant quality terms, equation (8) suggests that the driverofthatchangeiseitherfallingrealpricesofICTinvestmentgoodspIT orrisingefficiency(falling λ). Under what conditions might λ fall? One possibility is increasing returns, e.g., if ICT assets were more or less a large fixed cost that substantially inflated average costs relative to marginal costs (a huge server farm, say). Increased utilization of the relevant assets leads to declines in average costs, and if such declines are passed on to customers, declines in pST exceed those for pIT until steady state growth is achieved.9 In other words, from (8) we then have (9) p˙ST ≈ p˙IT +λ˙ T where, note, p˙ST,p˙IT, and λ˙ T are all < 0. λ˙ T reflects the drop in underutilization, which augments declines in cloud services prices relative to declines in prices of ICT assets according to equation (9).10 Cloud services prices that fall less than ICT asset prices suggest providers are retaining the efficiency gains for themselves. 8Appendix A1 sets out the four real rental prices in the two-sector model in a no-tax world where the terms in the nominal interest rate and the relevant relative asset price change are summarized by ρ. 9Note that equation (8) did not suggest or specify that ρ exhausted observed capital income, which is to say the nominalinterestrateinρisanexanterate. AsshownbyBerndtandFuss(1986),themarginalproductofcapitalvaries directly with capital utilization and is absorbed in capital income and attributed to capital rental prices only when ex post calculated rates of return are used. 10 Toseethis,letλ varywithcapitalutilization,e.g.,asinλ =1−dwheredisameasureoftheunderutilizationof T T ICTassets(andcanbecalculatedsoastoexhaustcapitalincome). Equation(8)thensuggeststhatimprovementsinthe utilization of ICT capital assets in the public cloud services-producing industry introduce a wedge λ˙ between changes T inobservedpricesforcloudservicesandpricesforICTassets. Suchwedgespresumablysurfaceforonlyperiodsoftime, as changes in utilization usually are a temporary phenomenon. 8

Case 2. System design services are purchased to improve the flow of ICT services produced within firms, and the services price is a fee proportional to the services-induced volume improvement in ownproduced ICT services.11 System design services may then be modeled as an increase in the efficiency of installed ICT asset stocks, an approach relevant to the spread and adoption of cloud technology, i.e., as in designing and installing a “private” cloud with significant server consolidation. Note first that the real price of ICT capital services rN and ICT capital owned within the nonICT T producingsectorK T N arethesubjectsofanalysis,andthatr T NK T N = [(ρ+δ T )pITK T N]istherealincome attributed to nonICT producers’ deployment of ICT capital. Consider next that producers will pay for system design services up to the point where fees do not exceed the present discounted value of per period benefits provided. Let α denote the proportional fee and −λ˙ the proportional improvement N in rN that is provided.12 Ignoring discounting, the effective decline in real ICT asset prices faced by T nonICT producers using system design services p˙eIT is given by (10) p˙eIT = p˙IT +λ˙ (1−α) N and industry revenues are expressed as (11) pSTSN = αrNKN (−λ˙ ) . T T T N Equation (10) suggests that ICT capital packs an extra punch to nonICT producers’ productivity, as the effective growth in real services will exceed real growth in stocks due to increases in utilization of the stocks. Equation (11) suggests that ICT services will grow relative to ICT capital income when substantial improvements are being made by providers (and the improvements they make are long-lived, not shown). All told, the λ˙’s represent efficiencies enjoyed by companies that move from a traditional IT datacenter to a cloud computing platform; for new firms, efficiencies represent lower capital required to start a business. Combined, these efficiencies have the potential to be large because cloud computing refers not only to shifts in workload location (from on-premises environments to the public cloud) but alsotoincreasedtakeupofcloudtechnologieswithinfirmsthatresultinmuchdenserworkload-to-ICT capital ratios. 11Note that in the very different case of ICT installation services, the price is simply a margin, i.e., an add-on to the purchasepriceofICTassetsthathasnoindependentimpactontheeffectivenessoftheinvestmentbeyondwhatisbuilt into a quality-adjusted investment price index. 12Where, as in footnote 10, there is an implicit term d capturing underutilization. 9

1.3 Quality change or productive externality? Fromamacroeconomicpointofview,increaseddemandforcloudcomputingleadstodecreaseddemand for computing hardware (for a given volume of ICT services) and increased demand for the software developersandsoftwareproductsthatenablemachinevirtualizationandapplicationcontainerization.13 Over time, the associated extra kick in effective ICT price declines implied by equation 10 would lead to greater computerization/digitization of an economy, which would then translate into a restoration of the share of computer hardware in the mix of ICT investment in the longer run. With regard to communication equipment, although high-speed broadband is a fundamental enabler of cloud services, we have not identified first order impacts of virtualization and its associated efficiencies on the demand for communication equipment beyond the fundamental need to support datacenter IP traffic. Before we go further, let us underscore that the server, storage, software product and computing servicespricesdevelopedandusedinsection3ofthispaperdonot treattheapplicationworkloadofIT capital, or the capability of software products or systems design services to enable cloud computing, as quality change. The macroeconomic impact of the adoption of cloud technology is via its contribution to productivity growth, as in network externalities (or spillovers to ICT capital in general). Cost savings due to virtualization, whether they accrue to cloud providers or to nonICT producers, thus are viewed as productive externalities.14 While this position is parallel to treating the productivityenhancing impacts of Internet platform business models as a (network) externality, virtualization as a computing technology is similar to multiplexing in communication where more and more signals are transmitted over physical networks (or spectrum), and where, to the extent possible, increases in capacity are built into quality-adjusted price indexes such as those developed for communications equipment in Byrne and Corrado (2015a,b). The adjustment of prices of servers, storage, systems software, and systems design services to consistently account for efficiencies due to virtualization and related cloud technologies is a similar challenge, but one well beyond the scope of this paper. 13These technologies are discussed below, in section 2.1. 14This is not to suggest that these effects cannot be isolated and quantified, as they have been in work that adds a separate channel to decompositions such as equation (7) to account for ICT to contributions to productivity growth beyond the direct capital contributions captured in growth accounting. For example, Corrado (2011) and Corrado and Ja¨ger(2014)showedthatnetworkexternalitieswereanoteworthycontributortoproductivitygrowthintheUnitedStates and8majorEuropeancountriesduringtheInternetandwirelessnetworkexpansioninthefirsthalfofthe2000s. Beyond broadband,however,spilloverstoICThavenotbeenfoundinmacroorindustry-leveldata(Stiroh,2002),despitealarge micro-basedliteraturesuggestingexternalitiestoITusebyindividualfirms. SeeCorradoandvanArk(2016)forfurther discussion. 10

Table 1: ICT-producing Industries NAICS 2007 Primary BEA industry code Description Use data code (1) (2) (3) (4) Manufacturing: 3341, 3344 Computers and semiconductors Final and 334 (pt) Intermediate 3342, 3343, 334511 Communication equipment Final 334 (pt) 3346 Magnetic and optical recording media Final 334 (pt) Services: 5112 Software publishing Final 511 (pt) 515 Broadcasting Final 513 (pt) 517 (pt) Telecommunications, excluding wireline Final and 513 (pt) telephony (but including internet access) Intermediate 5182 Data processing, hosting, and related Intermediate 514 (pt) 51913 Internet publishing and broadcasting Intermediate 514 (pt) and web search portals 541511 Custom computer programming Final 5415 541512 (pt) Computer systems design (integrators) Final 5415 541512 (pt) Computer systems design (consultants) Intermediate 5415 541513,9 Other computer related services Intermediate 5415 Note: (pt)afteranindustrycodesdenotesthatnotalloftheindustryconsistsofthecomponentbeingdescribed. 2 ICT sector trends Columns1and2oftable1definetheempiricalcounterparttosectorT oftheprevioussection. Column (1) is what we strive to measure, and column (2) indicates how close we come to achieving that using BEA’s annual Input-Output and Final Uses data. Using data for the T sector so defined, this section has three subsections that do the following: (a) examine indicators of ICT technologies, including ICT R&D, that suggest that the pace of change in the newer ICT technologies remains very fast, (b) examine the relative growth of ICT services (which also bears on the diffusion of ICT technologies) and relative pattern of ICT investment by major component, and (c) quantify the model’s parameters for the relative size of the ICT sector and N the diffusion of its technology in the economy, namely, w , v , and ζ . Relative ICT asset price T KT T change is presented in section 3, and quantitative implications of the model of section 1 are drawn there. 2.1 Technology and R&D Internet and wireless technologies. Faster relative growth of TFP in ICT production is usually attributed to the relatively rapid pace of advances in computing and semiconductor technology, espe- 11

cially in the speed of microprocessors (MPUs) used in computers (Jorgenson, 2001)—and, according to many accounts, such advances stepped down a notch in the first half-decade of the 2000s (Hilbert and L´opez, 2011; Pillai, 2011, 2013). By contrast, advances in communications technology, i.e., internet and wireless technologies, continue at a similar pace (Byrne and Corrado, 2015a,b). Figure 2: Global IP Traffic and U.S. Telecommunications Patents (a) Global IP Traffic, 1993 to 2019 (incl. forecast). (b) U.S. Wireless-related Telecom Patents, 1993 to 2014 Internet and wireless technologies are not single identifiable inventions, but rather a suite of communications technologies, protocols, and standards for networking computers and mobile devices.15 Advances in these technologies have been very rapid in the past 25 years and continue at blistering rates to this day. Without continued increases in internet technology and capacity from 2010 to 2015, the world could not have achieved the reported 29 percent per year increase in IP traffic and nearly 78percentperyearincreaseinwirelessdata trafficthatitdidduringthisperiod(figure2, leftpanel).16 Alltold, theinternetmarketsoftheG-20areprojectedtoreach$4.2trillionin2016—nearlydouble the size they were in 2010. Three out of four data center workloads are expected to be processed in the cloud by 2018, and Internet of Things (IoT) devices attached to the Internet—most of them wirelessly—are expected to increase more than 25 fold, from nearly 1 billion units in 2010 to 26 billion units by 2020 (IoT devices exclude PCs, tablets and smartphones).17 These estimates plus a 15This paraphrases (Greenstein, 2000, p. 391), who was describing internet technology. 16The calculations are based on the historical data and 2015 estimate reported in issues of Cisco’s Visual Networking Index and Global Mobile Data Forecast Update. 17The sources for these forecasts are Boston Consulting Group (http://www.marketwired.com/press-release/ g-20s-internet-economy-is-set-reach-42-trillion-2016-up-from-23-trillion-2010-as-nearly-1611718.htm), 12

continuation of the demand for mobility and hotspots cannot be realized without continued, rapid increases in communications capacity, especially wireless capacity. The panel on the right of figure 2 shows that by one measure (the rate at which wireless-related telecommunications patents are granted in the United States), the current pace of change in communications technology is more rapid than it was in the late 1990s. Cloud technologies. CloudserviceproviderssupplyICTresourcesovertheinternet.18 Servicesrange from simple data storage to full provision of software for “business intelligence” applications. Access is asubiquitousaswirelessandwirelinenetworks. Thefeasibilityandaffordabilityofcloudservicesisthe capstone of an ongoing series of networking innovations that have raised access speeds, lowered storage costs, and perhaps most importantly, enabled seamless and invisible sharing of computing resources across users. Cloud computing involves three major technologies that raise the utilization of computer resources andspeedsoftwaredevelopment: virtualization,gridcomputingandcontainerization. “Virtualization” provides each user with a distinct virtual machine with its own operating system kernel but allocates resources from actual individual machines to multiple users, enabling higher resource utilization in the data center. A complete history is beyond the scope of this paper, but virtualization has its roots in IBM mainframes of the 1970s, preceded by time sharing (simultaneous use of the same computer by multiple jobs) and complemented by grid computing (applying the resources of many computers in a network to a single job19). More recently “containerization” technology has allowed multiple platform environmentstooperateonthesamevirtualmachine, increasingthespeedofapplicationdevelopment, deployment, and scalability. Asshowninfigure3(a),theincreaseinspendingforcapacityexpansionamongmajorcloudvendors has been stunning: Nominal capital expenditures at Amazon, Microsoft, Google, and Apple increased 25 percent per year between 2003:Q1 and 2017:Q2. Firms that transition from traditional datacenters to a cloud platform (private or public) enjoy substantial hardware consolidation and cost savings. IT Gartner (http://www.gartner.com/newsroom/id/2636073), and Cisco’s Global Cloud Index (2013-2018) (http://www.cisco.com/c/en/us/solutions/service-provider/global-cloud-index-gci/index.html). 18According to the National Institute of Standards and Technology, “cloud computing is a model for enabling ubiquitous, convenient, on-demand network access to a shared pool of configurable computing resources that can be rapidly provisioned and released with minimal management effort or service provider interaction” (Mell and Grance, 2011). 19Gridcomputingwasfirstusedin1989tolinksupercomputersandthereaftergrewandevolvedalongwiththeInternet (De Roure, David, et al. 2003). 13

Figure 3: Cloud Providers’ Cap Ex and U.S. Server Application Workload (a) Cap Ex by Amazon, Microsoft, Google, and Apple (b) Application workload of U.S. server stock Sources. Panel (a): Quarterly financial reports. Panel (b): International Data Corporation (IDC). consultanciescommentedin2008thatservervirtualizationhadbecomethe“killerapp”forthebusiness datacenter and subsequently IDC estimated that the number of virtual machines (VM) per server in theUnitedStates—anindicatoroftheapplicationworkloadofadatacenterserverandplottedinfigure 3(b)—advanced 12 percent per year from 2007 to 2013.20 Companies historically ran one application workload per server (and many small and medium size firms still do). In terms of enterprise applications, it is very early on in the application of containerization.21 The consultancy IDC estimates that in 2016 only 1 percent of enterprise applications were running on containers that could readily be scaled. Within the ICT-producing sector, however, containerization and related microservices have been central to boosting the productivity new software development, i.e., boosting the productivity of software R&D investments. R&D investments in ICT. The conduct of ICT R&D as shown in figure 4 is consistent with a very brisk pace of change. Figure 4’s overall trajectory for ICT R&D is not a readily observ- 20IDC’s latest estimate is that the number of virtual machines per server is 10.6 (2016), suggesting the recent pace of change has slowed. 21Containerization—ascalableformofvirtualizationtechnology—generallywasnotwidelyunderstoodoutsidecertain cloudvendorsuntilthereleaseofopensourceLINUXformats(Docker1.0)inMarch2013. Dockertransformedcontainer technology to a product for enterprise use. 14

able component of the U.S. national accounts’ headline figure for R&D investment, however, but rather reflects (1) private R&D investment by the industries listed in table 1 as reported in the U.S. national accounts plus (2) soft- Figure 4: Private ICT R&D investment in the United ware products R&D presented as own- States account software investment. National accountants regard software products R&D as captured in own-account software investment. Consequently, they exclude software products R&D from the R&D source data when estimating private R&D investment. Most software products R&D is carried out in the ICT-producing industries listed in table 1. For the United States, estimates of software Source: Authors’ elaboration of BEA and NSF data. products R&D are derived from cross tabulations of the National Science Foundation’s R&D survey data by industry of funder and technological focus; figure 4 plots the time series for these estimates reported in table 2 of Crawford, Lee, Jankowski, and Moris (2014).22 For the analysis of the ICT sector, indeed for the analysis of R&D in general, including software products R&D with other R&D is a more logical presentation of the available data—and not doing so excludes an area where increases in R&D have been among the most rapid. The rate of investment in ICT R&D in recent years continues unabated in this presentation, suggesting that ICT innovation couldnothaveslowedforlackofinvestmentinthedevelopmentofnewICTtechnologiesandproducts. 2.2 ICT services and software investment Intermediate uses of ICT. ICT R&D historically has been oriented toward producing better and faster computers and more powerful productivity-enhancing computer software (installed locally) for 22Therelevantcross-tabulationofR&DsurveydatahasbeenpublishedbytheNationalScienceFoundation(NSF)for 2012(NSF,Business Research and Development and Innovation: 2012,table25,October2015). Thisrecentlypublished figureisconsistentwithestimatesreportedinCrawfordetal.(2014),whichincludedestimatesthrough2013. Thefigure plotted for 2014 is an extrapolation by the authors based on total private own-account software investment. 15

businesses and other organizations (i.e., investment goods). But with the locus of ICT R&D having shifted toward software apps and services enabled by high-speed communication and high performance computing systems, one should not be surprised to see an associated shift in ICT spending, too. Figure 5: Intermediate Uses of Information and Computer Services, percent of GDP (a) Data processing and related services (b) Computer systems design Note. Estimates are net of own sector, i.e, ICT-producing sector, use; see table 1 for industries comprising the ICT-producing sector. Figures are through 2014. Source: Authors’ elaboration of data from U.S. BEA. Privatedemandfordataprocessing, hosting, andrelatedinformationservices(NAICS5182, 51913) andforcomputersystemsdesignservicesandrelatedcomputerservices(NAICS54152,3,9)rosesharply relative to GDP in the United States in recent years (the solid blue shaded areas of the left and right panels of figure 5, respectively). These developments reflect both the growth of cloud services (which are in NAICS 5182 and has seen steady growth) and a remarkable surge in systems design services that likely also owes to the demand for cloud-based IT systems to the extent that systems design services are co-investments with the demand for cloud computing.23 All told, the analysis in section 1 suggested that the relative growth of ICT services industries would be strong if there were real gains to reconfiguring IT departments to capture cost savings due to cloud technologies. The prospective cost savings, along with a growing demand for data analytics and revenue momentum of the “subscription” 23 To be clear, spending on computer systems design is not counted as investment in national accounts even though in principle it would be included in expanded frameworks that recognize a portion of consulting services as long-lived investment in new business process design (e.g., as in Corrado, Hulten, and Sichel 2005, 2009). 16

business model that has been widely used to deliver ICT services, all underscore that the relative growth of ICT services since 2000 is unsurprising.24 Figure 6: Intermediate and Final Uses (PCE) of Telecommunications and Broadcasting Services, percent of GDP (a) Intermediate Telecom Use (b) Final Telecom and Broadcasting Use (PCE) Note. Estimates are net of own sector, i.e., ICT-producing sector, use; see table 1 for industries comprising the ICT-producing sector. Broadcasting is in the right panel only because intermediate uses of the output of this industry are essentially nil. Figures are through 2014. Source: Authors’ elaboration of data from U.S. BEA. Trends in intermediate and final uses of telecommunications and broadcasting services are shown in figure 6. Traditional wireline telephone services ideally would be excluded from this analysis, but a split of traditional vs. IP telephony and internet access services in data on intermediate purchases by industry is not available. As may be seen in panel (a), business demand for wireless services is robust, especially from 2010 on, whereas total private telecommunications services (which adds in wireline telecom and internet access services) has moved down since peaking in 2000. By contrast as shown in panel (b), consumer total telecom demand has not declined since 2000 but the relative pattern of consumer total telecom versus consumer wireless demand is similar to private industry. A breakdown of landline telephone and internet access services is available for consumers, and the detail shows, as expected, that wireline telephone services are a sharply declining component of total consumer NAICS 515,7 services spending whereas internet access is a growing component. 24For further discussion of the role of business models in ICT services provision, see OECD (2014), chapter 4, “The Digital Economy, New Business Models and Key Features.” 17

All told, information, computer, and wireless communication services supplied to private industries net of the ICT-producing sector’s own use has increased .06 percentage points per year relative to nominal GDP during the past 19 years, i.e., the ratio of such services to GDP rose from .7 percent in 1995 to 1.9 percent in 2014. To put this in perspective, consider again figure 1(a). This increase ICT business services use by other private producers is in fact a tad larger than the long-term increase in private spending on ICT investment goods (relative to GDP), i.e., the coefficient on time in the regression trend line plotted in figure 1(a) is .05. Final investment in software assets. Nearly 60 percent of total ICT investment in 2015 was for acquisition of new software assets, a dramatic turnabout from 1995 when 65 percent of total ICT investmentwasforequipmentandequipment-relatedcapitalizedservices(figure7,leftpanel). Between 1995and2005, thepureequipmentshareoftotalICTinvestmentdroppeddramatically(20percentage points). The computing equipment spending share has continued to trend down since 2005—it was only 14 percent in 2014—whereas the communication equipment share stopped dropping in the early 2000s has fluctuated between 21 and 22 percent since then.25 Figure 7: ICT and Software Investment Shares, 1959 to 2014 (a) ICT investment component shares (b) Software investment component shares Note. Excludes software products R&D. Source: Authors’ elaboration of data from U.S. BEA. 25NotethattheemergenceofthecloudbusinessmodelmayhaveledICTequipmentinvestmenttobeunderestimated. Byrne,Corrado,andSichel(2017a)calculatethatifelectroniccomponentspurchasedbytheICTservicessectorareused tobuildserver farms, totalICTequipmentinvestmentmaybeunderstatedbyasmuchas25percentin2015. Thisdoes not change the picture of weakness in nonICT producers’ ICT investment. 18

Within new software assets, purchases of marketed, standardized (prepackaged) software products are about 1/3 of total software, as illustrated by the dark blue shaded area in the right panel of figure 7. The lion’s share of software is custom produced, whether as purchased services or performed on own account. Price measures for these custom components do not exist (i.e., BLS does not produce prices indexes for NAICS 541511, or any part of 5415 for that matter); the BEA estimates them based in part on its price index for prepackaged software products. The companion paper reviews these prices, but suffice it to say BEA’s price indexes for software investment fall 2 percent per year, not the 15 to 20 percent that high-tech equipment prices do. All told, the dramatic shift in overall ICT investment from computing equipment toward software illustrated in figure 7 suggests that the rate of overall ICT investment price change should have slowed over time. 2.3 Sector final output and capital income ICT final output share. Consider first the ICT sector final output share w , which captures what T the domestic tech sector supplies to final investment and consumption. A substantial share of ICT investment and consumption goods are produced abroad and do not add much to the sector’s final output share. Note, too, that even though the overwhelming share of ICT intermediate services are domestically produced in the United States, services only enter w via final consumption and net T exports. Final consumption includes digitally-provided entertainment services as well as telecommunication services sold to consumers. The inclusion of digital entertainment services in ICT final output raises the question of whether investmentsindigitalentertainmentoriginals(EO)shouldalsobeconsideredpartofICTfinaloutput— and correspondingly, how to treat R&D investments in ICT. Our thinking is that EO assets are more akin to software assets than to the software original that is used to produce the software assets. The purchasers of software assets (software products) use the assets to generate (ICT) services for a period of time, just as the owners of entertainment originals use their assets to generate (entertainment) services for a period of years. EO investments are therefore included in ICT final output but R&D investmentsthatproducenewblueprintsororiginalcodeformanufacturing/reproducingICTequipment and software products are not. 19

The ICT final output share w T Figure 8: ICT Final Output Share and its major components are shown in figure 8. As may be seen, the share trended down in the early 2000s, but has been about flat at 5.6 percent of GDP for the past ten years (2004 to 2014). The ICT goods net exports component has been stable of late, whileICTfinalservices(PCEand net exports) has expanded to offset the downward drift in ICT final goods (PCEandPFIE&S,thedarkandlight blueshadedareas). NotethatifICTfi- Note: E&S is equipment and software. PFI = private fixed investment. nal PCE services and EO capital were PFI ICT E&S excludes software R&D. PCE ICT components include video and cellular equipment and exclude landline telecommunications. notincludedintheanalysis,theICTfi- Source: Authors’ elaboration of BEA’s NIPA data. naloutputsharewouldaverage2.6percent per year from 2004 to 2014—just a tad higher than the final output share of software over the same period (2.4 percent per year according to NIPA table 9.3U). ICT income and services shares Consider now the shares defined in equation (5): ICT and EO capital’s share of total income (v ), labor’ share (v ), and ICT services share net of sector own use KT L N (ζ ). Consistent with the pattern shown by the ICT investment rate, the share of capital income T earned by ICT (and EO) capital has edged down since the mid-2000s, after having climbed steadily over the 1990s (the blue shaded area in the left panel of figure 9). Capital income is the nominal value of the flow of services provided by capital assets owned and used in production, and it is typical to regard v as a basic indicator of the extent to which ICT has KT diffused via use in production in an economy. ICT business services also are inputs to production but maybemarketedversionsofthesameservicesprovidedviadirectownershipofICTcapital. Asmaybe seen, the trajectory of the total income generated by the use of ICT capital assets in the U.S. economy changes rather dramatically with the inclusion of marketed services, suggesting that v , alone, is an KT 20

Figure 9: ICT capital income and services shares Source: Authors’ elaboration of capital and labor income data from U.S. BLS productivity major sector and total economy systems and U.S. BEA input-output data. BLS capital income for software was adjusted to exclude software products R&D. insufficient indicator of ICT use in production. The right panel plots the capital income share relative to the labor share (a ratio of the compensations for ICT capital and labor). This combination of parameters is applied to the ICT productivity differential captured by the steady state rate of decline in real ICT asset prices (or effective asset prices) to determine the contribution of the ICT “use and diffusion” effect to OPH growth. The parameter combination averages 11.3 percent for the past 10 years, considerably higher than the 7.7 percent share implied by ICT capital ownership alone. 3 ICT investment prices Accurate ICT asset prices are required for the quantitative evaluation of equation (7). The strategy in this section is to present newly developed ICT product price measures, confirm their alignment with the trends in technology and R&D discussed in the previous section, and contrast them where relevant to official statistics. Then we examine new ICT investment research price indexes built from the new product price indexes. The new product price indexes reflect work that either (a) was conducted by the authors as part of writing this paper or (b) appears in the literature but has not yet been fully incorporated into BEA’s official ICT price statistics, e.g., Berndt and Rappaport (2003); Abel, Berndt, and White (2007); Copeland (2013); Byrne and Corrado (2015a). Further information on the sources and methods used to construct the new ICT product and investment price indexes are in our companion paper (Byrne and Corrado, 2017b). 21

3.1 New ICT product prices and implications for ICT services prices Table 2 reports prices for selected ICT products. More than a dozen new research price indexes are shown. Four are price indexes for the telecom products newly developed and analyzed in Byrne and Corrado (2015a,b); the computer storage device index was introduced in Byrne (2015). The remainder are price indexes newly developed for this paper and whose construction is discussed in the companion paper. Of these, the indexes for servers, enterprise software, enterprise wireline telecom services, along with telecom products, are particularly relevant for understanding developments in the last decade. Thefollowingobservationsemergefromtable2: First, pricesfortelecomequipmentproducts(lines 1to4)fallrelativelyrapidly—between12andabout18percentperyearduringthelastdecade(column 2). Although these are noteworthy rates of decline—especially for cellular networking equipment, the circleditemincolumn2—theyareslowerthanpricedeclinesestimatedforcomputingequipment(lines 5 to 7). Second, computer price declines have slowed in the past decade and the gap between rates of decline for computers and communications equipment has dwindled from about 20 to 10 percentage points. Third, the greatest computer declines, and the greatest gap, occurs in the 1994 to 2000 period, when MPU prices were falling especially fast (line 23). The post-2004 slowdown in MPU prices is not evident in servers (line 5) or PCs (line 7) until the 2008-2014 period however. Price declines for storage equipment also slowed in the post-2004 period as technical challenges emerged for advancing both the magnetic density of hard disk drives and the feature density of flash memory used in solid state drives (Byrne, 2015). Finally, and by contrast, prices for enterprise and other software products (which includes systems software as well as application software) maintained relatively strong declines through the most recent period (the circled items in line 10).26 From equation (9), prices for cloud computing and storage services are closely tied to the asset prices just discussed. However, imperfect competition and other fixed costs (in the form of nonICT assets)createpotentialforthesepricestodeviatefromthepricesoftheunderlyingICTassets. Services of nonICT capital assets (including land) are not an appreciable fraction of total capital income in the information processing services industry (16 percent), which includes cloud computing and storage 26The software products price measures were developed for use in this paper, and the new indexes are documented in our companion paper (Byrne and Corrado, 2017b). The inclusion of system software, whose prices are falling relatively rapidly, and the construction of an explicit component for enterprise software are the major innovations; the enterprise software price measure is an important anchor in our analysis of ICT services prices. 22

Table 2: Price Change for Selected High-tech Products, 1994 to 2014 (annual rate) 1994 to 2004 to 1994 to 2000 to 2004 to 2008 to 2004 2014 2000 2004 2008 2014 (1) (2) (3) (4) (5) (6) Research indexes: 1. Data networkinga -13.5 -12.1 -13.6 -13.0 -9.7 -13.6 2. Local loop transmission -18.4 -14.2 -13.8 -24.7 -14.4 -14.1 3. Cell networking -17.5 -18.4 -18.6 -15.8 -13.5 -21.5 4. Cell phones -19.4 -15.9 -17.7 -21.9 -15.3 -16.3 5. Computer servers -29.4 -26.1 -28.4 -30.7 -30.8 -22.8 6. Computer storage -49.2 -26.1 -54.5 -40.1 -30.1 -23.4 7. Personal computers -30.3 -23.7 -36.8 -19.3 -30.2 -19.1 8. Prepackaged software -9.6 -7.0 -10.3 -8.4 -6.8 -7.1 9. Desktop -5.8 -4.0 -5.3 -6.5 -3.9 -4.0 10. Enterprise and related -11.4 -8.4 -12.6 -9.4 -8.2 -8.5 11. Telecom services, wirelineb -1.5 -5.8 -2.2 -3.4 -5.6 -5.9 12. Enterprise onlyc – -8.2 – – -8.4 -8.1 13. A/V equipment -9.0 -16.3 -7.1 -11.8 -15.8 -16.7 Memo: 14. Computer mfg. industryd -25.2 -19.8 -30.7 -22.7 -26.3 -15.1 Official indexes: 15. Computer servers -22.2 -10.7 -24.8 -18.1 -17.9 -5.6 16. Computer storage -13.3 -4.7 -14.8 -11.1 -5.6 -4.0 17. Personal computers -25.1 -9.6 -29.0 -18.9 -16.9 -4.4 18. Prepackaged software -5.2 -2.5 -5.0 -5.4 -2.3 -2.7 19. Telecom services, wirelinee -1.8 1.5 -2.2 -1.3 1.8 1.3 20. A/V equipmentf -7.8 -13.2 -6.2 -10.3 -13.0 -13.3 Memo: 21. Computer mfg. industryd -17.4 -11.8 -23.8 -17.4 -19.6 -6.1 Performance measures (annual percent change): 22. MPUsg -59.9 -38.9 -64.2 -52.4 -36.9 -40.2 23. Smartphone storageh 23.9 – 16.5 49.5 90.9 – 24. Top500 computers (median)i 88.4 69.1 81.8 98.7 92.4 55.2 Sources: Byrne and Corrado (2015a,b, lines 1 to 4); this paper, lines 5 to 15, 23, 24 and 26, using McCallum (2002) and Byrne (2015) to inform line 6; Berndt and Rappaport (2001, 2003) to inform line 7; Abel et al. (2007) and Copeland (2013) to inform line 9; Gordon (1990) to inform line 14; and Grimm (1998), Byrne, Oliner, and Sichel (2015), Federal Reserve and BankofJapanestimatestoinformlines23and24. Thesourceforlines16to22isBEA.Thesourceforline25isHilbertand L´opez(2011). Notes: a. Column1isfromstartdateofseries(1986). b. Nonresidential. c. Columns2and5arefromstartdateofseries (2006). d. NAICS 334111. e. Nonresidential, calculated by authors. f. PCE index excluding recording media, calculated by authors. g.Quality-adjustedpriceindexusingperformancemeasuresfrom2000on. h.CapacityinMB.i.MFLOPSpersecond. 23

services, but they are more material (33 percent) for the broadcasting, telecom and internet access services industry.27 What direct evidence is available for ICT service prices? Press reports have highlighted declines of 20 to 30 percent per year at major cloud service providers.28 Silicon Valley’s Mark Andreessen, co-founder of Loudcloud, the first cloud computing company, wrote in the Wall Street Journal in 2011, “... the cost to a customer running a basic internet application [at Loudcloud] was approximately $ 150,000 per month [in 2000]. Running that same application today in Amazon’s cloud costs about $ 1,500 per month.” Andreessen’s figures imply a price drop of more than 40 percent per year during the first decade of the 2000s. Byrne, Corrado, and Sichel (2017b) construct price indexes for storage, computing, and database services offered by Amazon, Microsoft and Google from 2009 forward and find average prices declines on the order of 10 to 15 percent, with notable acceleration when Google and Microsoft achieved significant scale in the commercial market. We also examined prices for the enterprise segment of wireline telecom service using data from Telegeography, who report prices of individual service offerings for four groups of enterprise business services (virtual private network; dedicated internet access; IP private line, domestic; and IP private line, international) from 2006 on. The results of computing a matched model price index for enterprise wireline telecom services yields a price index that falls 8.2 percent per year from 2006 to 2014 (line 12 in the table; see also Byrne and Corrado, 2017b). The various results considered are on par or slightly faster than the results of the price index for enterprise software (line 10); the results are similar to the price indexes for the relevant telecom equipment (lines 1 and 2) and somewhat below the relevant computing equipment prices (lines 5 and 6). These comparative results suggest that the aggregate ICT asset price index might be a reasonable proxy for ICT services price change, consistent with the model and analysis in section 1. 3.2 New ICT Investment Prices To assess the macroeconomic implications of the ICT goods and services prices just discussed, the indexes must be folded into national accounts-style investment price indexes. Detailed components of 27NonICTcapitalincomeassetsharesarederivedfromthedetailedcapitalmeasuresfortheNAICS515,7andNAICS 518,9 industries from 2004 and 2014 as reflected in the BLS MFP database (accessed July 1, 2016). 28InMarch,2014,Googleannouncedpricecutsfor“virtuallyall”itscloudcomputingandstorageservicesof30percent, only to be followed in May, 2015, by further cuts in the 20 to 30 percent range (see Lardinois, h 25; Yegulalp, y 18). 24

the investment price indexes are reported in the appendix to this paper (table A1, page 40), where it may be seen that the results are largely presaged by the results presented in table 2. Figure10andtable3reportkeyresultsintermsusedtoassessthecourseoftherelativeproductivity differential of the ICT sector (p˙) and its current and historical misstatement. The real price of communication equipment (the red line in figure 10) falls below its simple long-term trend after 2000 and has remained there since then. The combined real Figure 10: Real ICT Investment Prices, 1959=1 price for computers and software (the dotted blue line) has not shown large deviations from trend, but note it did fall below trend beginning in the mid-1990s but returned to it by about 2004 and flattened further after that. The aggregate real ICT price index (the solid blue line) is spot on its long-termtrendin2014—11.5percentperyear(in log changes). Table 3 shows that while real ICT price declineshavegraduallyslowedoverthepast10years, at 9.9 percent per year from 2004 to 2014 (line 1, column 3), the recent experience is not all that Source— Nominal price change reported in appendix table A1 (page 40), whose construction is described in Byrne and far from the long-term trend shown in figure 10. Corrado (2017b) available here. Real prices are relative to From 2004 to 2014, the estimate of real ICT price BEA’s GDP deflator. change is 5.8 percentage points per year lower than suggested by official data (line 8, column 3). In terms of component contributions to real ICT price change (lines 5 to 7), the contribution of software from 1994 on is particularly noteworthy and owes, in part, to its growing share. But all told, in terms of differences relative to BEA (lines 9 to 11), all three components make similar contributions to the estimated nearly 6 percentage point per year understatement of overall ICT price declines in recent years (column 6). 25

Table 3: Real ICT Investment Price Change (annual rate) 1963 to 1987 to 2004 to 1994 to 2004 to 2008 to 1987 2004 2014 2004 2008 2014 (1) (2) (3) (4) (5) (6) 1. ICT investment -9.5 -12.7 -9.9 -14.1 -11.3 -8.9 2. Communications equipment -4.5 -9.4 -10.5 -10.7 -9.9 -11.0 3. Computers and peripherals -21.2 -23.0 -19.0 -25.4 -23.9 -15.6 4. Software -5.8 -6.6 -5.7 -7.3 -6.1 -5.5 Contributions to line 1: 5. Communications equipment -2.4 -3.1 -2.7 -3.4 -2.7 -2.7 6. Computers and peripherals -5.8 -7.0 -4.0 -7.6 -5.4 -3.0 7. Software -1.3 -2.6 -3.2 -3.1 -3.2 -3.2 Memos: Line 1 less BEA: 8. ICT investment -2.1 -4.2 -5.8 -4.8 -5.5 -5.9 Contributions to line 8: 9. Communications equipment -1.7 -1.4 -1.6 -1.3 -1.2 -1.8 10. Computers and peripherals -.1 -1.9 -2.2 -1.8 -2.3 -2.1 11. Software -.3 -.9 -2.0 -1.7 -2.0 -2.1 Note—Contributionsareinpercentagepoints. RealpricesarerelativetoBEA’sGDPdeflatorasofMay2016. Source—ThecorrespondingnominalpricesareshowninAppendixA2. TheirderivationissetoutinByrneandCorrado (2017b). 3.3 Implications Figure 11 updates the picture of real ICT price change in figure 1(b) to include the new estimate reported on line 1 of table 3. According to the new estimate real ICT price change is still estimated to have gradually lost force in recent years, but to a point that leaves the current pace of change in stronglynegativeterritory. Fromamacroeconomicperspectiveashighlightedbythetwo-sectormodel, this is the crucial result for continuing to regard ICT—either via investment, purchased services, or production—as a driver of economic growth in the future. Figure 11 further suggests that the newly estimatedpaceofrealICTpricechangefromthemid-1990sthroughtheearly2000swasextraordinary, and the experience likely is a poor indicator of relative ICT productivity going forward. A calibration of the solution to the two-sector model set out in equation (7) based on parameters drawn from themost recent ten-year periodimplies a still largecontribution of ICT tooutput per hour growth—1.4 percentage points per year. This of course assumes that these parameters are reasonable, which we shall detail in a moment. Regarding the assumption of balanced growth, empirics will be sensitive to the actual over-the-period changes in factor utilization and/or the cost of capital from 2004 to 2014, and these changed little on balance.29 The balanced growth assumption is in this sense 29See updated figures for the utilization adjustment in Fernald (2012) and stock market returns in Shiller (2000). 26

Figure 11: Real ICT Price Change, Redux not unreasonable, and we use calculations for the 2004 to 2014 period as indicative of what we might expect ICT to contribute to growth in total economy labor productivity growth going forward. Column 2 of table 4 shows the components of this estimated ICT contribution. (Column 1 of the table shows calculations for the prior ten-year period for reference only.) The first component of the contribution is the sum of the ICT use and diffusion effects, which is 1.1 percentage points per year (line 2, column 2). As shown on lines 2(a) and 2(b), this reflects the large income share for ICT assets and ICT services revenues (also shown in figure 9) multiplied by a productivity differential for ICT assets that is nearly 10 percentage points per year (taken from table 3, line 1, column 3). The secondcomponentistheproductioneffect—0.3percentagepointsperyear. Thisreflectsaproductivity differential for ICT production in the United States (software products, EO originals, and consumer ICT services) of 5-3/4 percentage points per year and a rather small final output share. Factory production of ICT equipment in the United States all but dried up during the past decade, and the software productivity differential is applied to other domestically-produced ICT components of final demand following the logic of the two-sector model. The memo items in table 4 shed light on why our calculation of the ICT contribution is so high. There are three reasons. First, the conventionally calculated contribution of ICT to labor productivity growth (i.e., via capital spending per worker) does not factor in business use of cloud computing; nor 27

Table 4: Contributions to Growth in Output Per Hour (percentage points, annual rate) 1994 to 2004 to 2004 2014 (1) (2) 1. Total ICT 1.8 1.4 of which: 2. ICT use and diffusion effect 1.2 1.1 (a) vKT +ζN T .085 .113 vL (b) −p˙ 14.0 9.9 3. ICT production effect .6 .3 (a) w .055 .056 T (b) −p˙ 10.6 5.8 Memos: 4. Line 2 excluding: (a) Diffusion effect .9 .8 (b) EO capital 1.0 .9 (c) Both diffusion and EO .7 .6 5. Effect of ICT price misstatement on: (a) OP˙H .27 .22 (b) Use effect .30 .44 Notes—Contributionsarebasedonequation(7)wherethediffusioneffectisthecontributionofICTbusinessservicestoproductivitygrowth. Lines2(a)and3(a)aresharesof grossdomesticincomeandlines2(b)and3(b)areestimatesofproductivitydifferentials inannualpercentagechanges. Line2(b)isthedifferentialforallICTassetswhereasline 3(b)isanestimateforfinalICTgoodsandservices. Inline5OP˙H =growthinoutput perhour. Source—Calculationsuseestimatesreportedintable4andfigure9. does it factor in purchases of ICT consulting services that capture design services for private clouds, and possibly data analytics and related AI services. Collectively, we call this the “ICT diffusion effect.” The channel is estimated to be .4 percentage points per year (after rounding) and is measured by an appropriate weight times the relative ICT productivity differential. A second reason why our calculationisoftheICTcontributionishighisourinclusionofEOcapital,whichisworth.2percentage points per year (after rounding). Together these sum to a tidy .5 percentage points per year. The third reason for our large estimated ICT contribution is the new estimates of ICT price change that imply that the growth rate of output per hour would be higher by .22 percentage points per year from 2004 to 2014 if official measures were adjusted to reflect the research reported in this paper (table 4, line 5(a), column 2).30 But as shown on line 5(b), the conventional use effect (or ICT capital 30The precise calculation is the 2004 to 2014 ICT final output share w reported on line 3 (a) (and shown in figure T 8) times 3.9 percentage points, which is this paper’s estimate of software asset price change from 2004 to 2014 (sign reversed, i.e., -3.8 percent per year less the change in BEA’s official index of .1 percent per year). This result is in the same ballpark as the findings reported in Byrne et al. (2016). 28

deepening) would be .44 percentage points higher—and this in turn implies that growth in total factor productivity(thedifferencebetweentheadjustmenttoOP˙H andtheadjustmenttocapitaldeepening) has been .2 percentage points more dismal than recorded in official estimates.31 Moreover, the implied contribution of the nonICT-producing sector to total factor productivity growth is unbelievably dismal after accounting for the ICT asset price misstatement and excluding the expected ICT diffusion effect via purchased services, -.18 percentage points per year. In the prior ten-year period, the comparably calculated contribution was .95 percentage points per year.32 Having suggested that comparing the 2004 to 2014 period with the preceding period was problematic, consider now temporary factors that may have disturbed productivity outcomes during recent years. In particular, from the discussion of macroeconomic implications in section 1.3 consider that: (a) computer demand is unlikely to remain as weak looking ahead as it has been during a period when firms have been adjusting to a cloud platform, and (b) weak demand and slow income growth during the Great Recession obscured nonICT producers’ cost savings from increased ICT capital utilization owing to adoption of cloud technologies. With regard to (a), the thin red line in figure 11 shows a counterfactual for real ICT price change in which the computer and software investment shares did not shift after 2000. The counterfactual closes the gap between the end point of the centered moving average of real ICT price change (about 9 percent) and the long-term trend used to determine the contribution of ICT to growth in output per hour (about 10 percent). We believe this mitigates the concern that ICT price change continued to slow over the 10 year period used to calibrate the model, i.e., that the calibrations are based on an adjustment phase during which growth in unit computer demand has been substantially diminished by the spread of cloud technologies, leading actual ICT price declines to have been unusually slow (per the discussion of the impact of declines in underutilization on effective prices in section 1.2). With regard to (b), figure 12 uses industry-level changes in total factor productivity growth before and after the Great Recession and relates them to the increase in intensity of ICT services use. The figure suggests that nonICT producers have not reaped the gains in productivity that should have 31AccordingtoBLSfiguresfor“outputperunitofcombinedinputs”intheirTotalEconomyProductionAccountTables dated March 24, 2016, TFP for the total U.S. economy grew 0.4 percent per year from 2004 to 2014, compared with 1.3 percentperyearfrom1994to2004. Thus,theICTpricemeasuresreportedinthispaper,givenexistingGDPinallother regards,implythatTFPforthetotalU.S.economylikelyedgeduponly.2percentagepointsperyearfrom2004to2014. 32See Byrne, Oliner and Sichel (2017) for discussion of the dismal pace of TFP growth in the nonICT sector. Braenstedder and Sichel (2017) point to several emerging technologies as potential sources of improving TFP. 29

Figure 12: TFP Acceleration and ICT Services Use Figure 13: Intangible Investment and ICT Services Use Notestofigures12and13: NonICTproducingindustriesonly. Relativeintensityistheuseorinvestment rateaveragedoverperiodindicatedrelativetoitstrendoverthepreviousdecade. Theratesarecalculated relativetothesumofvalueaddedpluspurchasedICTservices. Chartoutliersaresuppressed. 30

been enjoyed by the adoption of cloud platforms.33 And figure 13 suggests that the failure of nonICT producers to reap productivity gains did not owe to a lack of co-investments in the intangible assets that are especially crucial during the installation phase of new ICT platforms, e.g., investments in business process change and employer-specific training (Brynjolfsson, Hitt, and Yang, 2002). It is unclear why industries whose usage of ICT services increased the most after 2007 had weaker (or no greater) rates of change in productivity from 2010 to 2013 relative to prior performance despite their co-investments in ICT-related intangibles, but several possibilities are likely. First, the very swift pace of change in the ICT sector may have created adjustment costs that temporarily offset gains from adapting to the rapid pace of digital innovation.34 Second, it is possible some ICT spending may be defensive, e.g., in cyber security. Third, the Great Recession may have induced firms to “pull forward” their plans to adopt cloud-based ICT systems, and the savings from doing so may have only staunched losses that were particularly severe among adopters. All told, the “diffusion” portion of the model’s “use and diffusion” effect of 1.1 percentage points per year contribution of ICT to labor productivity growth seems to have not only shut down, but may even be temporarily generating negative productivity spillovers. Because it is common, even fundamental, to regard innovation in upstream sectors as diffusing to downstream sectors through intermediate use, and there is no reason to believe that this channel will not return in full force in the years ahead. 4 Summary and conclusion This paper set out a two-sector model that illustrated how the ICT sector can have an out-sized influence on economic growth via its relative productivity growth; the model, originally due to Oulton (2012), was expanded to include ICT services for improved relevancy. A central feature of the model is that relative ICT asset prices reflect the relative productivity of the sector. Official measures of ICT prices suggest that the relative productivity of ICT capital has been gradually eroding for 10 years and that its current advantage is close to nil. This paper found no evidence in support of this central implication of the current official ICT price measures. ThepaperfirstfoundthatICTR&Dhasnotonlybeenwell-maintained,butthatsoftwareproducts R&D has enjoying a stunning rise. If technical change in the ICT sector has ground to a halt, then 33Although this paper has shown a disturbing degree of price mismeasurement that would feed directly into the TFP estimates plotted in this figure, these concerns are somewhat ameliorated because the figure uses changes in the rate of productivity growth (i.e., double differences) and examines nonICT-producing industries only. 34Adjustment costs were used to analyze the Solow paradox and step-up in productivity growth in the 1990s (e.g., Greenwood and Yorukoglu, 1997; Basu, Fernald, and Shapiro, 2001; Hall, 2001; Kiley, 2001). 31

the return to software R&D must have fallen dramatically, which seems unlikely in the face of more than a decade of relative growth in investments in this area and the advent of cloud technologies that should have boosted productivity in the conduct of software R&D. Second, the model developed in this paper predicted strong growth in ICT services use and strong relative growth of ICT design services to the extent that cloud technologies has taken hold. The overt, first order macroeconomic effects of the transition to cloud technologies—weak computer hardware demand and increase in ICT capital utilization—are not easy to detect in macrodata. But strong relative growth in cloud services and systems design services (i.e., relative to GDP) is a key feature of the current ICT landscape and one sign that innovation is still driving the sector. All told, via the user cost relationship as well as the paper’s two-sector model, we also found that ICT services price change is driven by ICT asset price change; the alternative ICT asset price change measures reported in this paper—especially the 26 percent annual decline in real prices for servers and storage equipment (15 and 21 percentage points faster, respectively, than drops in official prices for these assets; see again table 2)—are consistent with press reports that suggest prices for cloud services are dropping rapidly. More broadly, the paper introduced new measures for ICT asset price change that incorporated availableresearchaswellasnewworkconductedexpresslyforthispaper. TheICTassetpricemeasures were based on more than a dozen new ICT product price indexes, and the new ICT investment price indexes for communication equipment, computers, and software were developed to be as coherent as possible with national accounts practices. The new results feature substantial innovations for total telecom equipment, computer servers, software products, and enterprise telecom services (wireline). AlthoughmuchnewevidenceonICTassetpricesandICTservicespriceswasmarshaledfortheanalysis reported in this paper, large gaps in evidence remain—enterprise software products and differentiated computer design services are notable examples of these holes. The paper’s primary conclusion that real ICT price declines remain squarely in negative territory suggests that the sector will continue to deliver an out-sized contribution to growth in output per hour—1.4percentagepointsperyearinbalancedgrowth. Thisfigureissubstantialinlightofhistorical average OPH growth of 2 percent, but it emerges from two sources documented in this paper: first, an ICT income share that has continued to expand along with the relative growth of ICT services, and second, a rate of real ICT price change that has declined more than 10 percent per year since 1959 and currently is understated by nearly 6 percentage points. Although the current weakness in output per 32

hourgrowthowesatleastinparttoheadwindsunrelatedtoICT,correlationsintheavailableindustrylevel data show that total factor productivity in nonICT producing industries has not been improving along with increased ICT services use. Additional research is needed to deepen our understanding of the linkages between measured productivity, firm performance and firm spending on ICT assets and ICT services. References Abel, J. R., E. R. Berndt, and A. G. White (2007). Price indexes for Microsoft’s personal computer software products. In E. R. Berndt and C. R. Hulten (Eds.), Hard-to-Measure Goods and Services, Volume 67 of NBER Studies in Income and Wealth, pp. 269–289. Chicago: University of Chicago Press. Andressen, M. (2011, August 20). Why software is eating the world. Wall Street Journal. Basu, S., J. G. Fernald, and M. D. Shapiro (2001). Productivity growth in the 1990s: Technology, utilization, or adjustment? Carnegie-Rochester Conference Series on Public Policy 55(1), 117–165. Berndt, E. R. and M. A. Fuss (1986). Productivity measurement with adjustments for variations in capacityutilizationandotherformsoftemporaryequilibrium. Journal of Econometrics 33(1), 7–29. Berndt,E.R.andN.J.Rappaport(2001). Priceandqualityofdesktopandmobilepersonalcomputers: A quarter-century historical overview. American Economic Review 91(2), 268–273. Berndt, E. R. and N. J. Rappaport (2003). Hedonics for personal computers: A reexamination of selected econometric issues. Presented at R&D, Education and Productivity, an international conference in memory of Zvi Griliches (1930–1999), August 25-27, Paris, France. Brynjolfsson, E. and L. M. Hitt (2003). Computing productivity: Firm-level evidence. Review of Economics and Statistics 85(4), 793–808. Brynjolfsson, E., L. M. Hitt, and S. Yang (2002). Intangible assets: Computers and organizational capital. Brookings Papers on Economic Activity 2002:1, 137–198. Brynjolfsson, E. and A. Saunders (2010). Wired for Innovation. MIT Press. Byrne, D., C. Corrado, and D. Sichel (2017a). Own-account IT equipment investment. Technical report, FEDS Note (September 29). Byrne, D., C. Corrado, and D. Sichel (2017b). The rise of cloud computing: Minding your P’s and Q’s (and K’s) Paper presented at the NBER/CRIW conference, Measuring and Accounting for Innovation in the 21st Century, held in Washington, D.C., March 10-11, 2017. Byrne, D. M. (2015). Prices for data storage equipment and the state of IT innovation. FEDS Notes (July 15), Federal Reserve Board, Washington, D.C. Byrne, D. M. and C. A. Corrado (2015a). Prices for communications equipment: Rewriting the record. FEDS Working Paper 2015-069 (September), Federal Reserve Board, Washington, D.C. 33

Byrne, D. M. and C. A. Corrado (2015b). Recent trends in communications equipment prices. FEDS Notes (September 29), Federal Reserve Board, Washington, D.C. Byrne, D. M. and C. A. Corrado (2017a). Accounting for Innovation in Consumer Digital Services: Implications for economic growth and consumer welfare. Paper presented at the NBER/CRIW conference, Measuring and Accounting for Innovation in the 21st Century, held in Washington, D.C., March 10-11, 2017. Byrne, D. M. and C. A. Corrado (2017b). ICT asset prices: Marshalling evidence into new measures. Finance and Economics Discussion Series 2017-016 (February), Board of Governors of the Federal Reserve System, Washington. Byrne, D. M., J. G. Fernald, and M. B. Reinsdorf (2016). Does the United States have a productivity slowdown or a measurement problem? Brookings Papers on Economic Activity (Spring). Byrne, D. M., S. D. Oliner, and D. E. Sichel (2013). Is the information technology revolution over? International Productivity Monitor (25), 20–36. Byrne, D. M., S. D. Oliner, and D. E. Sichel (2015). How fast are semiconductor prices falling? Working Paper 21074 (July), NBER, Cambridge, Mass. Copeland, A. (2013). Seasonality, consumer heterogeneity and price indexes: the case of prepackaged software. Journal of Productivity Analysis 39, 47–59. Corrado, C. (2011). Communication capital, Metcalfe’s law, and U.S. productivity growth. Economics Program Working Paper 11-01, The Conference Board, Inc., New York. Corrado, C., C. Hulten, and D. Sichel (2005). Measuring capital and technology: An expanded framework. In C. Corrado, J. Haltiwanger, and D. Sichel (Eds.), Measuring Capital in the New Economy, Volume 66 of NBER Studies in Income and Wealth, pp. 11–46. Chicago: University of Chicago Press. Corrado, C., C. Hulten, and D. Sichel (2009). Intangible capital and U.S. economic growth. Review of Income and Wealth 55(3), 661–685. Corrado, C. and K. J¨ager (2014). Communication networks, ICT, and productivity growth in Europe. Economics Program Working Paper 14-04, The Conference Board, Inc., New York. Corrado, C. A. and B. van Ark (2016). The Internet and productivity. In J. M. Bauer and M. Latzer (Eds.), Handbook on the Economics of the Internet, pp. 120–145. Northamption, Mass.: Edward Elgar Publishing, Inc. Crawford, M. J., J. Lee, J. E. Jankowski, and F. A. Moris (2014). Measuring R&D in the national economic accounting system. Survey of Current Business 94(11), 1–15. De Roure, D., M. A. Baker, N. R. Jennings, and N. R. Shadbolt (2003). The evolution of the grid. In F. Berman, G. C. Fox, and T. Hey (Eds.), Grid Computing: Making the Global Infrastructure A Reality, Wiley Series in Communications Networking and Distributed Systems, Chapter 3, pp. 65–100. Chichester, England: John Wiley & Sons, Ltd. Domar,E.D.(1961). Onthemeasurementoftechnologicalchange. TheEconomicJournal 71,709–729. Fernald, J. (2012). A quarterly, utilization-adjusted series on total factor productivity. Working Paper 2012-19, Federal Reserve Bank of San Francisco. 34

Gordon, R. J. (1990). The Measurement of Durable Goods Prices. Chicago: University of Chicago Press. Gordon, R. J. (2014a). The demise of U.S. economic growth: Restatement, rebuttal, and reflections. Working Paper 19895 (February), NBER, Cambridge, MA. Gordon, R. J. (2014b). A new method of estimating potential real GDP growth: Implications for the labor market and the debt/GDP ratio. Working Paper 20423 (August), NBER, Cambridge, MA. Greenstein, S. (2000). Building and delivering the virtual world: Commercializing services for internet access. Journal of Industrial Economics 48(4), 391–411. Greenwood, J. and M. Yorukoglu (1997). 1974. Carnegie-Rochester Conference Series on Public Policy 46(June), 49–95. Grimm, B. T. (1998). Price indexes for selected semiconductors. Survey of Current Business 78(2), 8–24. Hall, R. E. (2001). The stock market and capital accumulation. American Economic Review 91(5), 1185–1202. Hilbert, M. and P. L´opez (2011). The world’s technological capacity to store, communicate, and compute information. Science 332(6025), 60–65. Hulten, C. R. (1978). Growth accounting with intermediate inputs. The Review of Economic Studies 45(3), 511–518. Jorgenson, D. W. (1963). Capital theory and investment behavior. American Economic Review 53(2), 247–259. Jorgenson, D. W. (1966). The embodiment hypothesis. Journal of Political Economy 74(1), 1–17. Jorgenson, D. W. (2001). Information technology and the U.S. economy. American Economic Review 90(1), 1–32. Jorgenson, D. W., M. S. Ho, and K. J. Stiroh (2004). Will the U.S. productivity resurgence contine? Federal Reserve Bank of New York, Current Issues in Economics and Finance 10(3), 1–7. Jorgenson, D. W., M. S. Ho, and K. J. Stiroh (2005). Productivity, volume 3: Information technology and the american growth resurgence. MIT Press Books 3. Jorgenson, D. W. and K. J. Stiroh (2000). Raising the speed limit: U.S. economic growth in the information age. Brookings Papers on Economic Activity (1), 125–211. Jorgenson, D. W. and K. M. Vu (2010). Potential growth of the world economy. Journal of Policy Modeling 32(5), 615–631. Kiley, M. T. (2001). Computers and growth with frictions: Aggregate and disaaggregate evidence. Carnegie-Rochester Conference Series on Public Policy 55(1), 171–215. Lardinois, F. (2014, March 25). Google announces massive price drops for its cloud computing services and storage, Introduces sustained-use discounts. TechCrunch. McCallum, J. C. (2002). Price-performance of computer technology. In V. Oklobdzija (Ed.), The Computer Engineering Handbook, Chapter 4, pp. 4–1 to 4–18. CRC Press. 35

Mell, P. and T. Grance (2011). The NIST definition of cloud computing. OECD (2014). Addressing the Tax Challenges of the Digital Economy, OECD/G20 Base Erosion and Profit Shifting Project. Paris: OECD Publishing. Oliner, S. D. and D. E. Sichel (2000). The resurgence of growth in the late 1990’s: Is information technology the story? Journal of Economic Perspectives 14(4), 3–22. Oulton, N. (2012). Long term implications of the ICT revolution: Applying the lessons of growth accounting and growth theory. Economic Modelling 29(5), 1722–1736. Pillai, U. (2011). Technological progress in the microprocessor industry. Survey of Current Business 91(2), 13–16. Pillai, U. (2013). A model of technological progress in the microprocessor industry. The Journal of Industrial Economics 61(4), 877–912. Shiller, R. J. (2000). Irrational Exurberance. Princeton University Press. Stiroh,K.J.(2002). AreICTspilloversdrivingtheneweconomy? Review of Income and Wealth 48(1), 33–57. Syverson, C. (2016). Challenges to mismeasurement explanations for the U.S. productivity slowdown. Working Paper No. 21974 (February), NBER, Cambridge, Mass. The Conference Board (2015). The Conference Board Total Economy Database™ May 2015. The Conference Board. Yegulalp, S. (2015, May 18). Google one-downs Amazon with new cloud price cuts. InfoWorld. 36

Appendix A1 The steady-state solution of the two-sector model Model. Lower case variables are per hour versions of inputs and outputs introduced in the text, i.e., xj = Xj/Hj is the per hour form of variable X where i = T,N denotes type of good or service i i where relevant (i.e., ICT or other types), and j = T,N denotes sector of use (ICT-producers or other producers). As in the Oulton model, the sector production functions i are Cobb-Douglas and written here in per hour form as : (A1) q = A (kN) α (kN) β (sN) γ (h )1−α−β−γ N N T N T N and (A2) q = A (kT) α (kT) β (sT) γ (h )1−α−β−γ T T T N T T The functions for the two sectors are identical except for TFP (the Hicksian shifter) whose growth rates µ and µ are exogenous. T N The supply-use equations for the open economy version of the model are (A3) Y = C +I +X −M ; Y = Y +Y where T N Y = C +I −M −M ; Y = C +I +X +X . T T T C I N N N C I Imports M = M + M are imports of ICT goods, and exports X = X + X are exports of all C I C I other goods, i.e, the economy is an (net) importer of ICT and a (net) exporter of all other types of output. Next, we assume input supplies must equal demands, so that H = H +H and K = (cid:80) Kj, N T i j i j = T,N;i = T,N. Accumulation equations are given by (A4) K˙ = I −δ K N N N N (A5) K˙ = I −δ K T T T T Recalling that p = P /P , a steady state in this model is when trade is balanced X = pM and T N when the real interest rate r and proportions of total hours allocated to each sector H /H(i = T,N) i are constant. With sectoral hours shares constant in steady state growth, for sectoral and overall output per hour to grow at a constant rate it follows that the services share of ICT production must also be constant. This follows from the definitions: (A6) Q ≡ Y +SN and Q ≡ Y T T T N N where in the steady state, the growth rate Q and Y (and thus q and y ) are identical by definition. N N n n The growth rate of Q is a (constant) share-weighted average of the growth rates of Y and SN, which T T T grow at the same rate, and thus imply q˙ = y˙ in steady growth. T T Note also that with sectoral hours shares constant in steady state growth, output-per-hour (OPH) growth in the total economy is a share-weighted average of the growth rates of OPH growth in each of the sectors, i.e., accounting for “labor reallocation” due to shifts in hours shares is not needed. 37

Growth rate of relative ICT prices (p˙). Given the model’s assumption that production functions are the same up to a scalar multiple, it is easy to see that the rate of change in relative ICT prices p˙ (where recall p = PT ) is given by PN (A7) p˙ = µ −µ < 0 N T Equation A7 is proved by total differentiation of the payments equations, text equation (4), with respect to time. With µ and µ constant by assumption, so too is p˙. N T Growth rate of output per hour. To obtain the steady state growth rates of labor productivity, first differentiate equation (A1) and (A2) with respect to time, which gives (A8) q˙ = µ +αk˙N +βk˙N +γs˙N +(1−α−β−γ)h˙ N N N T T (A9) q˙ = µ +αk˙T +βk˙T +γs˙T +(1−α−β −γ)h˙ T T N T T where from (A6) we have (A10) q˙ = y˙ and q˙ = y˙ . N N T T ConsiderfirsttheN sector. Profitmaximizationrequiresthattherealusercostequalstherealmarginal product of capital, which for nonICT and ICT capital are given by q q N N (A11) (i+δ ) = α and (i+δ −p˙)p = β . N kN T kN N T where i is the nominal rate of interest and the real interest rate is the nominal rate minus the growth rate of the N sector price P , expressed in terms of the relative price p in (A11). N Insteadystatewheretherealinterestrateisconstantandfactorsarepaidtheirmarginalproducts, the solutions for sector N are then (A12) q˙ ∗ = y˙ ∗ = k˙N∗ N N N (A13) q˙ ∗ = y˙ ∗ = k˙N∗ +p˙ N N T where ∗ denotes a steady state solution (recall p˙ is constant by assumption). Consider now the T sector. Equality of the real marginal product of ICT capital in T sector production with real user cost implies q T (A14) (i+δ −p˙) = β T kT T Because the left hand side of (A14) is constant, it follows that q˙ = k˙T from which it follows: T T ∗ ∗ (A15) q˙ = y˙ −p˙ . T N In steady state growth, output per hour in sector T grows faster than output per hour in sector N. Finally, equality of the real marginal product of ICT intermediate services across the two sectors implies that ∂q q Y N N N (A16) = γ = γ ∂sN sN SN T T T 38

must be identical to ∂q q Y +SN (A17) T = γ T = γ T T ∂sT sT ST T T T Equation (A16) implies that s˙N is equal to y˙ in steady state growth but from (A15), we know that T N q , of which sN is a component, grows at a faster rate than y˙ . It is readily seen that the condition T T N q˙ = y˙ solves this dilemna and implies T T (A18) s˙N = y˙ −p˙ T N ∗ (A19) y˙ = y˙ −p˙ . T N Now substitute equations (A12), (A13), and (A18) into (A8), the expression for growth in output per hour in sector N: y˙ = µ +αy˙ +β(y˙ −p˙)+γ(y˙ −p˙)+(1−α−β−γ)h˙ N N N N N which after rearranging terms yields µ −(β+γ)p˙ (A20) y˙ = N +h˙ . N (1−α−β−γ) Define the steady state output share of the T sector as pY ∗ T (A21) ω = T Y +pY N T in which case the steady state OPH growth rate for the total economy may be written as ∗ ∗ ∗ ∗ y˙ = (1−ω )y˙ +ω y˙ T N T T ∗ ∗ ∗ ∗ (A22) = y˙ +ω (y˙ −y˙ ) . N T T N Substituting (A19) into (A22) yields ∗ ∗ ∗ y˙ = y˙ −ω p˙ N T and subsitituting (A20) into this expression and combining terms yields our final result, an expression for the contribution of the ICT sector to total OPH growth: µ −(β +γ)p˙ y˙ ∗ = N +h˙ −ω ∗ p˙ (1−α−β −γ) T µ (β+γ)(−p˙) (A23) = N +h˙ + +ω ∗ (−p˙) (1−α−β −γ) (1−α−β −γ) T (cid:124) (cid:123)(cid:122) (cid:125) Contribution of ICT to total OPH growth The final term in equation (A23) appears as text equation (7) where β,γ,(1−α−β−γ), and ω are T N replaced by their empirical counterparts v ,ζ ,v , and w . KT T L T Contribution of ICT to growth in TFP The amended model’s solution for aggregate TFP µ also is different than that implied by the original Oulton model. Under the usual neoclassical growth accounting assumptions in the presence of intermediates (e.g., Hulten 1978), the growth of aggregate 39

TFP is the sum of the growth of each sector’s TFP growth times its Domar-Hulten weight, which is the ratio of each sector’s sectoral production (gross output net of own use) to aggregate value added, P Q /PY. From (2) and (5), these weights are expressed as: i i P Q P Q T T N N N = w +ζ ; = 1−w PY T T PY T whose sum is greater than one by the relative size of ICT services supplied to nonICT producers. The growth of aggregate TFP µ is then given by N (A24) µ = (w + ζ )µ + (1−w )µ T T T T N (cid:124) (cid:123)(cid:122) (cid:125) Contribution of ICT sector The contribution of the ICT sector to overall TFP growth is larger than the sector’s share in final demand w to account for the diffusion of the sector’s innovation via use of ICT services (intermediate T inputs) by other producers in the economy. A2 Nominal ICT investment deflators The table below shows detailed components of the nominal national accounts-style price deflators calculated for the analysis in this paper. The methods used to construct these deflators are described in detail in our companion paper (Byrne and Corrado, 2017b). Table A1: Nominal ICT Investment Price Change (annual rate) 1963 to 1987 to 2004 to 1994 to 2004 to 2008 to 1987 2004 2015 2004 2008 2015 (1) (2) (3) (4) (5) (6) 1. ICT investment -4.9 -10.6 -8.0 -12.4 -8.9 -7.5 2. Communication equipment .4 -7.3 -8.7 -9.1 -7.4 -9.5 3. Telecom -.3 -11.7 -12.4 -14.3 -10.1 -13.7 4. Other equipment .4 -8.3 -9.3 -10.3 -8.1 -10.0 5. Capitalized services – 1.1 -3.7 -.1 -2.5 -4.3 6. Computers and peripherals -17.1 -21.2 -17.0 -24.0 -21.8 -14.1 7. Servers and storage -18.1 -25.2 -25.7 -31.0 -30.6 -22.7 8. PCs – -27.9 -23.4 -30.3 -30.2 -19.2 9. Other equipment -9.0 -9.3 -3.3 -8.8 -5.4 -2.0 10. Capitalized services – -2.0 -2.2 -3.1 -1.5 -2.6 11. Software -1.0 -4.4 -3.9 -5.5 -3.5 -4.1 12. Prepackaged -9.8 -9.0 -7.0 -9.6 -6.8 -7.2 13. Custom and own-account .0 -2.0 -2.2 -3.1 -1.5 -2.6 Memos: 14. ICT excluding PCs -4.5 -8.4 -6.5 -9.9 -6.6 -6.4 15. Computers excluding PCs -16.6 -17.1 -11.6 -19.8 -14.5 -9.9 16. BEA ICT -2.7 -6.4 -2.1 -7.5 -3.3 -1.4 17. BEA ICT excluding PCs -2.6 -4.5 -1.4 -5.2 -1.9 -1.2 18. Computers excluding PCs -16.6 -11.0 -3.6 -12.7 -6.6 -1.8 Note: Figuresreportedas“BEA”areauthors’calculationsbasedonBEAdata. 40