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

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 introduce a simple model that sets out the steady-state contribution of the sector to the growth in U.S. labor productivity. The model extends Oulton (2012) to include ICT services and draws conclusions about the relationship between prices for ICT services and prices for the capital stocks (i.e., ICT assets) used to supply them. ICT asset prices are then put under a microscope, and official prices are found to substantially understate ICT price declines. And because ICT capital continues to grow and penetrate the economy—increasingly via cloud services which 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 calibrated to be substantially larger than it has been in the past.


Contents
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 Jäger, 2014) puts these innovations front and center and offers a story in which communication and communication networks (more than computer microprocessors) drove productivity developments in the 1990s and the 2000s. An overarching story of productivity performance for nearly 25 years is all to the good, but it begs the question of why the recent performance of U.S. productivity has been so dismal, given that advances in information and communications technology (ICT) have continued to be strong to this day.
The deterioration in U.S. productivity, as measured in the official statistics, is due in part to the fact that real ICT equipment and software (E&S) investment spurred by rapidly falling relative prices no longer provides an extra boost to the rate of growth in output per hour. Not only has nominal ICT E&S investment relative to GDP moved sideways since 2010 (figure 1a), relative ICT price change has posted historically very small declines of late, after having gradually lost force since 2005 (figure 1b).
As a result, measured labor productivity growth has been extraordinarily weak: Output per hour for the total economy grew an estimated 1/2 percent per year from 2010 to 2015-the slowest 5-year rate of change in the post WWII era. 2 The digital transformation of the U.S. economy is highly visible in the plentiful supply of new software apps, powerful wireless devices, and widespread access to high-speed broadband. Why, then, is ICT investment so weak? And if digital innovations are so transformative, why are they not having a discernible impact on ICT prices (and labor productivity)? Google's Hal Varian offers a view from Silicon Valley, namely, that U.S. productivity is mis-measured. 3 It is of course possible that the ICT sector-about 6 percent of the economy in value added terms-is innovating and prospering while the overall economy continues to suffer from weak demand in the aftermath of the Great Recession and/or demographic and other headwinds as argued by Gordon (2014a,b). Nevertheless, Varian's comments suggest a conundrum, which this paper addresses.
Recent ICT developments are a new era in which mobile and cloud platforms, enabled by highspeed broadband, are transforming the means organizations use to interact with both customers and employees. Some prominent technologies in this transformation enable server and storage consolidation (virtualization) and more efficient development and deployment of apps (containers). 4 The standard narrative used to analyze the diffusion of ICT technology in economies does not capture the uptake of these technologies, and the activities touched most directly by them are not very evident in official statistics. To remedy this situation, this paper introduces new ICT asset prices and incorporates ICT services (i.e., cloud computing and related services) in the modeling and quantitative analysis of the contribution of ICT to labor productivity growth.
We proceed as follows: First, to understand how a small sector can be a driver of growth in an economy, we extend a simple two-sector model, originally due to Oulton (2012), to include ICT services.
In the extended model, as in Oulton's original model, the pace of decline in relative ICT prices is an indicator of productivity change in the ICT sector relative to the rest of the economy. The extended model implies, and we further posit via the user cost framework, that price change for marketed ICT services is proportional to price change for the productive assets used to produce them; thus the model implies that purchases of certain ICT services are similar to services provided via direct ownership of ICT capital. Second, the model is used to set out the contribution of ICT technology to total economy labor productivity growth in the medium-to long-term. This involves documenting the growing role of ICT services in the United States, the growing intensity of ICT R&D, and assessing the extent to which official measures of ICT price change are capturing all that is going on.
In our review of ICT price measures, we introduce a new, quality-adjusted price index for communications equipment investment that draws upon our own prior work on the measurement of telecommunications and networking equipment. We also introduce new price indexes for enterprise software products, high-end computers and computer storage systems, which, along with high-speed broadband, have made the growth of cloud computing and data analytics possible, i.e., they reflect prices of assets used to generate these ICT services. All told, our findings suggest that ongoing ICT technological change potentially contributes as much as 1.4 percentage points per year to labor productivity growth in the United States and that trends in official ICT prices suffer from substantial mismeasurement, especially recently, and especially in software, which accounts for more than half of ICT investment.
It should be underscored that the assessment conducted in this paper keeps the scope of GDP as in official statistics and addresses the measurement of technology via ICT prices included in existing national accounts. The paper thus bears most directly on interpreting recent trends in ICT investment and ICT services use by the producing sectors of the economy. Subsequent work (under way) uses the framework developed in this paper to address the impact of digitization on the consumer sector and the scope of its measured activity.

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 on a two-sector model of an open economy where one sector is an ICT-producing/supplying sector. His approach is in the spirit of the growth accounting approach to making economic projections (Jorgenson, Ho, and Stiroh, 2004;Jorgenson and Vu, 2010;The Conference Board, 2015), 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.
Benefits to economic growth accrue to faster relative growth of ICT TFP because faster relative ICT TFP growth manifests as faster relative ICT price declines, which then enables faster growth of income and consumption per hour. Oulton's model makes these features of a Jorgenson-style growth projection explicit, 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 and popularity of cloud services enabled by high-speed broadband, 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 OPH 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.

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 ). Thus we have Each sector produces investment and consumer goods and services for final use. With regard to intermediates, the ICT sector is assumed to supply services for its own intermediate 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. 5 With sector N producing for final demand only, and each sector's output (production net of own use) denoted by Q T and Q N , respectively, sectoral production may be written in terms of the following outputs and inputs where K j i denotes sector j's capital input from its stock of investment goods of type i (i = T, N ) and S j T is sector j's intermediate use of ICT services. L j = hH j is sector j's labor input, H j is hours 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 with relevant factor shares given by In equation (4), R N and R T are the nominal rental prices of capital and W is the hourly wage, and in (5), v K T and v L are the shares of ICT capital and labor in total income, respectively, and ζ N T is ICT business services purchased by sector N relative to total income in the economy.
The model assumes there is faster technical progress in the ICT sector. Denoting the rate of growth in the Hicksian shifter (A i ) in the sectoral production functions (3) as µ i , this assumption is expressed as µ T > µ N . A major simplifying assumption is then employed to solve the model, namely, that the sectoral production functions exhibit constant returns and differ only by their A i terms. This implies 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 T /P N , this result 5 The complications of chain weighting also are ignored.
is expressed as a steady-state rate of change in relative pricesṗ given bẏ As may be seen, relative ICT price change is negative, reflecting the extent to which the relative growth 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 (ȮP H) is given by Investment (use) and diffusion (productivity) effects For details of this solution, see appendix A1. Equation (7) differs from the solution to the original Oulton model due to the presence of the term ζ N T capturing the ICT services-using intensity of the 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, however, the channel also operates via the contribution of producers' purchases of ICT services, e.g., purchases of computing, storage, and software services generated by ICT assets owned by ICT services producers, to total factor productivity.
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 differential is −ṗ, 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 T really is greater than µ N , real ICT services prices fall (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.

ICT services prices vs. ICT asset prices
The ICT sector's output price is a single price P T by assumption in a two-sector model. The strictness 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. The second is where ICT services are for designing "private" cloud services facilities within firms in the nonICT producing sector, e.g., services for transitioning from traditional uses of IT datacenter assets to one based on virtualization.
In each case, the value of the produced ICT services will be denoted as P S T S N T , where P S T is a quality-adjusted price specific to each type of service. P I T 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 p S T , p I T , 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 services prices are per period charges for ICT capital services (i.e., an asset rental price) and production of such services is highly ICT-capital intensive. Assume then that the services produced are proportional to the flow of services generated by the ICT assets, where the expression in brackets on the RHS is the real rental price of ICT capital and λ is the factor of proportionality. (Appendix A1 sets out the four real rental prices in the two-sector model, where, note, δ T is the depreciation rate of ICT capital). λ and δ T are constant by assumption, and ρ is constant in steady state growth by definition. Now, if the real price of cloud services p S T is falling rapidly in constant quality terms, equation (8) suggests that the driver of that change is falling real prices of ICT investment goods p I T .
Under what conditions might these prices not be in sync? One possibility is when λ is not constant, as would be the case in the presence of 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 p S T exceed those for p I T until steady state growth is achieved. 6 In other words, from (8) we then haveṗ where, note,ṗ S T ,ṗ I T , andλ 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 used by the vendors of cloud services. 7 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. 8 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 r N T and ICT capital owned within the nonICT producing sector K N T are the subjects of analysis, and that r N is the real income 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 6 Note that equation (8) did not suggest or specify that ρ exhausted observed capital income, which is to say the nominal interest rate in ρ is an ex ante rate. As shown by Berndt and Fuss (1986), the marginal product of capital varies 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.
7 To see this, let λT vary with capital utilization, e.g., as in λT = 1 − d where d is a measure of the underutilization of ICT assets (and can be calculated so as to exhaust capital income). Equation (8) then suggests that improvements in the utilization of ICT capital assets in the public cloud services-producing industry introduce a wedgeλT between changes in observed prices for cloud services and prices for ICT assets. Such wedges presumably surface for only periods of time, as changes in utilization usually are a temporary phenomenon.
8 Note that in the very different case of ICT installation services, the price is simply a margin, i.e., an add-on to the purchase price of ICT assets that has no independent impact on the effectiveness of the investment beyond what is built into a quality-adjusted investment price index. period benefits provided. Let α denote the proportional fee and −λ N the proportional improvement in r N T that is provided. 9 Ignoring discounting, the effective decline in real ICT asset prices faced by nonICT producers using system design servicesṗ eI T is given bẏ and industry revenues are expressed as 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, theλ's represent efficiencies enjoyed by companies that move from a traditional IT datacenter to a public or private 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 also to increased take up of many IT technologies-server virtualization, containers, and grid computing-all of which result in much denser workload-to-IT capital ratios.

Quality change or productive externality?
From a macroeconomic point of view, increased demand for cloud computing leads to decreased demand for computing hardware (for a given volume of ICT services) and increased demand for the software developers and software products that enable machine virtualization and application containerization. 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, virtualization and its associated efficiencies do not have first order impacts 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 services prices developed and used in section 3 of this paper do not treat the application workload of IT 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 rather is via its contribution to productivity growth, much as is done when analyzing network externalities (or spillovers to ICT capital in general). 10 Cost savings due to virtualization, whether via direct purchases of cloud services or via lower user costs of IT capital in the nonICT-producing sector, thus are viewed as productive externalities, not part of the contribution of ICT capital to growth in output per hour.
While this position may have parallels to treating the productivity enhancing impacts of Internetplatform 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).
Comparable work on prices of servers, storage, software products, and systems design services to consistently account for virtualization and other aspects of cloud technologies is a related challenge, but one well beyond the scope of this paper.

ICT sector trends
This section reviews indicators that support the model of the previous section. This requires (a) defining the ICT sector, which is done in in columns 1 and 2 of table 1 below, (b) examining indicators that suggest ICT technology continues to increase at a relatively fast pace, (c) pinning down the relative growth of ICT services (which also bears on the diffusion of cloud technologies), and (d) examining the relative pattern of ICT investment by major component.
The section concludes with an explicit quantification of the model's parameters reflecting the relative size of the ICT sector and the diffusion of its technology in the economy, namely, w T , v K T , and ζ N T . Relative ICT asset price change is presented in section 3, and quantitative implications of the model are drawn there.
10 In this work, a separate channel is added to decompositions such as equation (7) to account for the contribution of ICT to productivity growth beyond the direct capital contributions captured in growth accounting. For example, Corrado (2011) and Corrado and Jäger (2014) showed that network externalities were a noteworthy contributor to productivity growth in the United States and 8 major European countries during the Internet and wireless network expansion in the first half of the 2000s. Beyond broadband, however, spillovers to ICT have not been found in macro or industry-level data (Stiroh, 2002), despite a large micro-based literature suggesting externalities to IT use by individual firms. See Corrado and van Ark (2016) for further discussion. Other computer related services Intermediate 5415 Note: (pt) after an industry codes denotes that not all of the industry consists of ICT production.

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, especially in the speed of microprocessors (MPUs) used in personal computers (Jorgenson, 2001)-and, according to many accounts, such advances stepped down a notch in the first half-decade of the 2000s (Hilbert and López, 2011;Pillai, 2011Pillai, , 2013. By contrast, advances in communications technology, i.e., internet and wireless technologies, continue to be rapid (Byrne and Corrado, 2015a,b).
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. 11 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, Newer cloud technologies such as containers aim to speed software application development, deployment, and scalability, thereby boosting productivity of software R&D investments. In terms of enterprise applications, it is very early on in the application of containerization. 14 The consultancy IDC estimates that only 1 percent of enterprise applications are running on containers that can readily be scaled. in ICT R&D in recent years continues unabated in this presentation, suggesting that ICT innovation could not have slowed for lack of investment in the development of new ICT technologies and products.

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 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. Private demand for data processing, hosting, and related information services (NAICS 5182, 51913) and for computer systems design services and related computer services (NAICS 54152,3,9) rose sharply 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 the 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. 16 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" business model that has been widely used to deliver ICT services, all underscore that the relative growth of ICT services since 2000 is unsurprising. 17 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.
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. 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 on part on the price index for prepackaged software products. The paper reviews these prices in a subsequent section, 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. 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 investments in digital entertainment originals (EO) should also be considered part of ICT final output.
The thinking is that EO assets are more akin to software assets than to the software original used to produce software assets. In other words, software originals are used to generate produced capital assets (software products) that in turn yield services (over a period of years) to the owner/purchaser of the asset whereas entertainment originals are assets whose owners generate services for sale in the service marketplace. Accordingly to this reasoning, EO investments should be included in ICT final output but R&D investments that produce new blueprints or original code for manufacturing/reproducing ICT equipment and software products should not.  ICT income and services shares Consider now the shares defined in equation (5): ICT and EO capital's share of total income (v K T ), labor' share (v L ), and ICT services share net of sector own use (ζ N T ). Consistent with the pattern shown by the ICT investment rate, the share of capital income 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 right 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 K T as a basic indicator of the extent to which ICT has diffused via use in production in an economy. ICT business services also are inputs to production but may be marketed versions of the same services provided via direct ownership of ICT capital. As may be 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 K T , alone, is an 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 left 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. 18

ICT investment prices
Relative ICT investment prices are used to evaluate the model's implication for ICT's contribution to productivity growth. In this section, we first examine price change for selected ICT products, in part to confirm the basic trends in technology and R&D discussed in the previous section, but also to examine nuances and developments revealed by the newly developed price statistics themselves. The strategy is to present results of new price research and contrast those results with official statistics.
Second, the new ICT product price indexes are used to build a new research price index for ICT assets. This index is then used to ascertain (a) the most likely contribution of ICT to growth in output per hour in balanced growth and (b) the impact of ICT investment price mismeasurement on recent macro-productivity growth statistics for the United States.
The new price results presented in this section reflects work that (a) was conducted by the authors as part of writing this paper or (b) appears in the literature but has not been 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 and details may be found in a separate, supplemental paper available here. 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 detailed in the supplemental paper. Of these, the indexes for servers, enterprise software, enterprise wireline telecom services, along with telecom products, are notable in that their results are particularly relevant to understanding developments in the last decade.

New ICT product prices
Key features of the new price indexes for software and telecom services are presented below shortly.
With regard to servers, the new price index extends BEA's index from 1996 on based on the BLS PPI and unit prices from IDC and Gartner adjusted by performance scores from System Performance Evaluation Corporation (SPEC) and Hilbert and López (2011). 19 Price/performance trends of IBM mainframes show a trend similar to the new server index, as discussed in the supplemental paper.
Regarding table 2, the following observations emerge: First, prices for telecom equipment products (lines 1 to 4) fall relatively rapidly-between 12 and about 18 percent per year during the last decade (column 2). Although these are noteworthy rates of decline-especially for cellular networking equipment, the red circled item in column 2-they are slower than price declines estimated for computing equipment (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 19 The new PC price index was constructed in a similar fashion. Results for laptops and desktops from Berndt and Rappaport (2003) from 1983 to 2002 are combined and extended by the BLS PPI adjusted for the contribution of performance (relative to clockspeed) based on results from Byrne, Oliner, and Sichel (2015).  (2002) and Byrne (2015) to inform line 6; Rappaport (2001, 2003) to inform line 7; Abel et al. (2007) and Copeland (2013) to inform line 9; Gordon (1990)   Prices for storage equipment-a product based on a magnetic density, not semiconductors-also slow during the same period. Finally, and by contrast, prices for enterprise and other software products (which includes systems software as well as application software) maintain relatively strong declines through the most recent period (the red circled items in line 10).
More broadly, when we think of digitization and connectivity of the economy, and specifically of enablers of growth in cloud computing and other online services, computing capacity and data/content storage capacity emerge as important factors (along with broadband capacity, discussed previously).
Declines in the research price indexes for servers and storage shown in the table 2 (the red circled items in column 2, lines 5 and 6) are fairly close to the rate of decline in cloud services prices implied in press reports-about 30 percent per year. 20 From equation (9), prices for cloud computing and storage services cannot plausibly be falling so rapidly unless prices of the large-scale equipment and software assets that enable the provision of these services-load-balancing routers, multiple servers, and storage systems for handling data for multiple sessions across servers, etc.-are falling rapidly too, as we find. By contrast, official ICT price measures (lines 15 and 16, column 2) suggest a gap of 20 to 25 percentage points between price change for ICT equipment and ICT cloud computing and storage services.
Consider further prices of telecom and internet access services in light of the analysis in section 1.
Imperfect competition and large fixed costs (in the form of nonICT assets) clearly create potential for these prices to deviate from the prediction that changes in ICT services prices should align with changes in prices for the underlying ICT assets used to produce them. Services of nonICT capital assets (including land) are a substantial fraction (51 percent) of total capital income in the telecom and internet access services industry, whereas such assets play a less material role (16 percent) in the capital of the information processing services industry, which includes cloud computing and storage services, suggesting the potential for substantial deviation. 21 We focus on the enterprise segment of wireline telecom services using data from Telegeography, who report prices of individual service offerings for four groups of enterprise business services ( 1 and 2). Although the enterprise wireline segment of telecom and internet access services is not necessarily representative of the total industry (see again figure 6), the fact that enterprise wireline telecom prices fall about as fast as software assets (i,e., an ICT asset) but not less than 1/2 the declines seen for telecom equipment is very relevant to the arguments put forth in this paper. 22 Desktop and portable device software a 4.

New Software Prices
Enterprise, networking, database, tools/languages, and other software 5.
Game software products a. Covers both application and system software products.
As suggested by table 2 and illustrated in table 3 shown on the right, the new software products price index has two major "end-use" components, desktop 22 Note further that when the new enterprise services index is folded into an overall nonresidential price index for wireline services, the result falls substantially faster (7.3 percentage points) than its counterpart in official data (line 19, column 2). The construction of this index is detailed in the supplemental paper. its enterprise component), but we were able to make sufficient headway to inform the measurement and analysis of recent price change for software investment for this paper. The most important new source of information that has been incorporated is our own inference of recent trends in prices for system software based on the PPI for overall software publishing relative to certain of its components.
Without going into details, what has been done can be understood from the following: (1) prices for system software are collected by the BLS, but a PPI component for systems software is unpublished because estimates do not meet standards for disclosure; (2) the PPI for application software is the primary source data for U.S. national accounts estimates of software investment prices, and (3) recent trends in BLS prices for application software (a published index) and systems software (our inference) diverge substantially, imparting a notable bias in the BEA's software investment price index. Software, except games and other receipts 3.
Application software publishing 4.
Desktop and portable device apps 5.
Enterprise and other apps 6.
Systems software publishing 7.
Other receipts 8. Game software publishing Note: Indexes for items in red are not disclosed. In short the BEA has been using the dark blue line shown in figure 10 to drive its software investment price index from 1998 on, whereas this paper uses the dashed red line. There are numerous other features of the software products and software investment price indexes developed for this paper, including the folding in of research available in the literature but not reflected in BEA's current methodology and an effort to align our new work to BEA's history so that figures are comparable over time. (The supplement to this paper includes these details.) It is important to underscore that most existing research on software prices, and essentially all of the work that informed BEA's software price methodology reported in Parker and Grimm (2000), pertains to PC desktop application software. 23 Greenstein and Nagle (2014) looked at the economic benefits of Apache, a widely-used open source software system used to manage e-commerce transactions in the 1990s, and found substantial benefits even after accounting for substitution with priced products.
This suggests there could be large price declines in the systems software in wide use today, but we cannot really know without additional research. The implied systems software component in the PPI in fact drops relatively rapidly, and while its incorporation in an ICT asset price index is a major  figure 10). Many new products in the data analytics/business intelligence and marketing/management of customer relationships space have been introduced in recent yearsconsistent with the strong software products R&D shown in the previous section. All told, additional research is badly needed to assess/further improve the price measures for enterprise software (apps and systems/infrastructure) reported in this paper.

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 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. The procedures used for constructing the new investment price indexes are detailed in the supplement to this paper. 23 One study available to Parker and Grimm (Harhoff and Moch, 1997) covered a PC database platform for business applications, but prices for PC desktop operating systems were not studied until much later (Abel et al., 2007;Copeland, 2013). As discussed in the supplemental paper, systems software includes enterprise databases as well as operating systems.   Table 4 shows that while real ICT price declines have gradually slowed over the past 10 years, at 9.9 percent per year from 2004 to 2014 (line 1, column 3), the recent experience is not all that far from the long-term trend shown in figure 11. From 2004 to 2014, the estimate of real ICT price 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).

Implications
The two-sector model employed in this paper, specifically equation (7), implies that the contribution of ICT to output per hour growth could be as large as 1.4 percentage points per year if the trends established during the most recent ten-year period (2004 to 2014) continue to hold in the medium-term and conditions approximate balanced growth. This is a substantial contribution. 1. ICT investment -9.5 -12.7 -9.9 -14.1 -11.3 -8.9 2.
Computers and peripherals -21. The balanced growth contribution is based on two components. The first reflects the ICT use and diffusion effects that together sum to 1.1 percentage points per year. This large component stems from (1) a productivity differential for ICT assets that is nearly 10 percentage points per year, in combination with (2) the large relative income share for ICT assets and ICT services revenues that was shown in figure 9. The second component of the balanced growth contribution is a relatively small production effect-0.3 percentage points per year. This reflects a productivity differential for ICT production in the United States (software products, EO originals, and consumer ICT services)  of ICT to labor productivity growth (i.e., via capital spending per worker) also would be higher-by .4 to .6 percentage points per year depending on whether EO capital is included (the high estimate) or excluded (the low estimate) from the analysis. 26 All told, these impacts imply that growth in total factor productivity has been even more dismal than recorded in official estimates. 27 Finally, figure 12 updates the picture of real ICT prices introduced at the start of this paper. As previously noted, 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 strongly negative territory. From a macroeconomic perspective, as highlighted by the two-sector model, 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. From a historical perspective, figure 12 further shows that, according to the new price indexes assembled in this paper, the pace of real ICT price change during the late 1990s was extraordinary. The ten-year trends used to calibrate and draw implications from the two-sector model do not incorporate the experience of the late 1990s. 26 The precise calculation is the relevant share from figure 9 times 5.9 percentage points, where 5.9 is the difference between the ICT asset price measures reported in this paper and the official estimates of change from 2004 to 2014.
27 According to BLS figures for "output per unit of combined inputs" in their Total Economy Production Account Tables  dated March 24 That said, a balanced growth calculation does not incorporate temporary factors that might disturb productivity outcomes, and the last ten years witnessed a major financial crisis. Although a thorough review of influences on productivity growth during this period is beyond the scope of this paper, it is possible to close the loop on the central macroeconomic implications of the paper's two-sector model discussed in section 1.3. Consider (a) that computer demand is unlikely to remain as weak in the medium term as it has been during a period of adjusting to a cloud platform, and (b) that weak demand and slow income growth and/or costs of adjusting to a new ICT platform have obscured nonICT producers' gains from increased ICT capital utilization due to the adoption of cloud technologies.
With regard to (a), the thin red line in figure 12 shows a counterfactual for real ICT price change in which the computer and software 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). This then 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 suggests the last 10 years of actual ICT price declines were unusually slow.
With regard to (b), figure 13 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 been enjoyed by the adoption of cloud platforms. 28 And figure 14 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 crucial during the installation phase of new ICT platforms, e.g., investments in business process change and employer-specific training.
It is unclear why industries whose usage of ICT services increased the most after 2007 had weaker rates of change in productivity from 2010 to 2013 relative to prior performance despite their coinvestments in ICT-related intangibles, but several possibilities are likely. First, the very swift pace  In figures 13 and 14, relative intensity is the use or investment rate averaged over period indicated relative to its trend over the previous decade. The rates are calculated relative to the sum of value added plus purchased ICT services. Chart outliers are suppressed.
of change in the ICT sector may have created adjustment costs that temporarily offset gains from adapting to the rapid pace of digital innovation. 29 Second, it is possible some ICT spending may be defensive, e.g., in cyber security. On the other hand, 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 a negative productivity spillovers.
Nearly 1/3 of the "use and diffusion" effect is due to diffusion via intermediate use. It is of course common to regard innovation in upstream sectors as diffusing to downstream sectors through intermediate use (Domar, 1961), and there is no reason to believe that this channel will not return in full force in the years ahead.

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.
The paper first found that ICT R&D has not only been well-maintained, but that software products R&D has enjoying a stunning rise. If technical change in the ICT sector has ground to a halt, then 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 the productivity of the conduct 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 had 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 is a key feature of the current ICT landscape and one of the most relevant signs that innovation is still driving the sector. All told, via the user cost relationship as well as the paper's two-sector model, ICT services price change is driven by ICT asset price change, and while cloud services providers enjoy scale and perhaps unique abilities to harness advanced technologies, it seems unlikely that cloud computing and storage services prices which reportedly are dropping about 30 percent per year, could be dropping so much faster (20 to 25 percentage points!) than official prices for the equipment deployed in the delivery of these services.
Finally, the paper introduced new measures of relative ICT price change that incorporated available research as well as new work conducted expressly for this paper. More than a dozen new ICT product price indexes were introduced, and new ICT investment price indexes for communication equipment, computers, and software were developed. The new results feature substantial innovations for total telecom equipment, computer servers, software products, and enterprise telecom services (wireline).
Although much new evidence on ICT asset prices and ICT services prices was marshaled for the analysis 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 is that real ICT price declines remain squarely in negative territory and suggest that the sector will continue to deliver an out-sized contribution to growth in output per hour in balanced growth-1.4 percentage points per year. This figure is substantial in light of historical 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 hour growth owes at least in part to headwinds unrelated to ICT, correlations in the available industrylevel 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.

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., x j i = X j i /H j is the per hour form of variable X where i = T, N denotes type of good or service 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 : The functions for the two sectors are identical except for TFP, whose growth rates µ T and µ N are exogenous.
The supply-use equations for the open economy version of the model are Imports M = M C + M I are imports of ICT goods, and exports X = X C + X I are exports of all 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 N + H T and K i = j K j i , j = T, N ; i = T, N . Accumulation equations are given bẏ Recalling that p = P T /P N , a steady state in this model is when trade is balanced X = pM and when the real interest rate r and proportions of total hours allocated to each sector H i /H (i = T, N ) 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: where in the steady state, the growth rate Q N and Y N (and thus q n and y n ) are identical by definition. The growth rate of Q T is a (constant) share-weighted average of the growth rates of Y T and S N T , which grow at the same rate, and thus implyq T =ẏ T in steady growth.
Note also that with sectoral hours shares constant in steady state growth, 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.
Growth rate of relative ICT prices (ṗ). 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 is given byṗ = µ N − µ T < 0 (A7) which as stated in the text is proved by total differentiation of the payments equations (4) with respect to time. With µ N and µ T constant by assumption, so too isṗ.
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 giveṡ where from (A6) we haveq Consider first the N sector. Profit maximization requires that the real user cost equal the real marginal product of capital, which for nonICT and ICT capital are given by 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 N , expressed in terms of the relative price p in (A11).
In steady state where the real interest rate is constant and factors are paid their products, the solutions for sector N are thenq * where * denotes a steady state solution (recallṗ is constant by assumption). Equality of the real marginal product of ICT capital in T sector production with real user cost implies Because the left hand of the (A14) is constant, it follows thatq T =k T T from which it follows: 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 Equation (A16) implies thatṡ T N is equal toẏ N in steady state growth but from (A15), we know that q T , of which s N T is a component, grows at a faster rate thanẏ N . It is readily seen that the conditioṅ q T =ẏ T solves this dilemna and impliesṡ Now substitute equations (A12), (A13), and (A18) into (A8), the expression for growth in output per hour in sector N :ẏ N = µ N + αẏ N + β(ẏ N −ṗ) + γ(ẏ N −ṗ) + (1 − α − β − γ)ḣ which after rearranging terms yieldsẏ Define the steady state output share of the T sector as in which case the steady state OPH growth rate for the total economy may be written aṡ Substituting (A19) into (A22) yieldsẏ * =ẏ * N − ω * Tṗ and subsitituting (A20) into this expression and simplifying yields our result, an expression for the contribution of the ICT sector to total OPH growth: Contribution of ICT to total OPH growth (A23) The final term in equation (A23) appears as text equation (7) where β, γ, (1 − α − β − γ), and ω T are replaced by their empirical counterparts v K T , ζ N T , v L , and w 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 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, (2) and (5), these weights are expressed as: 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 µ = (w T + ζ N T )µ T

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 T to account for the diffusion of the sectorn's innovation via use of ICT services (intermediate 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 a supplemental document available here. Other equipment -9.0 -9.3 -3.3 -8.8 -5.4 -2.0 10.