ACCOUNTING FOR GROWTH IN THE INFORMATION AGE by Dale W. Jorgenson

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ACCOUNTING FOR GROWTH IN THE INFORMATION AGE by Dale W. Jorgenson 1. The Information Age.

7 1.1. Introduction. The resurgence of the American economy since 1995 has outrun all but the most optimistic expectations.

Economic forecasting models have been seriously off track and growth projections have been revised repeatedly to reflect a more sanguine outlook 1 . It is not surprising that the unusual combination of more rapid growth and slower inflation touched off a strenuous debate about whether improvements in America's economic performance could be sustained. The starting point for the economic debate is the thesis that the 1990s are a mirror image of the 1970s, when an unfavorable series of "supply shocks" led to stagflation -- slower growth and higher inflation 2 .

In this view, the development of information technology (IT) is one of a series of positive, but 7 Department of Economics, Harvard University, 122 Littauer Center, Cambridge, MA 02138-3001. The Program on Technology and Economic Policy at Harvard University provided financial support. The Economic and Social Research Institute of the Cabinet Office of the Government of Japan supported the research reported in section 4 from its program for international collaboration through the Nomura Research Institute.

I am greatly ... more. less.

indebted to Jon Samuels for excellent research assistance, as well as useful comments. J. Steven Landefeld, Clinton McCully, and David Wasshausen of the Bureau of Economic Analysis provided valuable data on information technology in the U.S. Tom Hale, Mike Harper, Tom Nardone and Larry Rosenblum (BLS), Kurt Kunze (BEA), Eldon Ball (ERS), Mike Dove and Scott Segerman (DMDC) also provided data for the U.S. and helpful advice. I am grateful to John Baldwin and Tarek Harchaoui of Statistics Canada for data on Canada, Kazuyuki Motohashi and Koji Nomura for data on Japan, and Alessandra Colecchia, Marcel Timmer and Bart Van Ark for data on Europe. Colleagues far too numerous to mention have contributed useful suggestions. I am grateful to all of them but retain sole responsibility for any remaining deficiencies. 1 See Congressional Budget Office (2000) on official forecasts and Economics and Statistics Administration (2000), p. 60, on private forecasts. 2 Robert Gordon (1998, 2000); Barry Bosworth and Jack Triplett (2000). temporary , shocks. The competing perspective is that IT has produced a fundamental change in the U.S. economy, leading to a permanent improvement in growth prospects 3 . The resolution of this debate in favor of a permanent improvement has been the ckiller application d of a new framework for productivity measurement summarized in Paul Schreyer 9s (2001) OECD Manual, Measuring Productivity . A consensus has emerged that the development and deployment of information technology is the foundation of the American growth resurgence. A mantra of the "new economy" -- faster, better, cheaper -- captures the speed of technological change and product improvement in semiconductors and the precipitous and continuing fall in semiconductor prices. The price decline has been transmitted to the prices of products that rely heavily on semiconductor technology, like computers and telecommunications equipment. This technology has also helped to reduce the cost of aircraft, automobiles, scientific instruments, and a host of other products. Swiftly falling IT prices provide powerful economic incentives for the substitution of IT equipment for other forms of capital and for labor services. The rate of the IT price decline is a key component of the cost of capital, required for assessing the impacts of rapidly growing stocks of computers, communications equipment, and software. Constant quality price indexes are essential for identifying the change in price for a given level of performance. Accurate and timely computer prices have been part of the U.S. National Income and Product Accounts (NIPA) since 1985. Unfortunately, important information gaps remain, especially on trends in prices for closely related investments, such as software and communications equipment. Capital input has been the most important source of U.S. economic growth throughout the postwar period. More rapid substitution toward information 3 Alan Greenspan (2000). technology has given much additional weight to components of capital input with higher marginal products. The vaulting contribution of capital input since 1995 has boosted growth by close to a percentage point. The contribution of investment in IT accounts for more than half of this increase. Computers have been the predominant impetus to faster growth, but communications equipment and software have made important contributions as well. The accelerated information technology price decline signals faster productivity growth in IT-producing industries. In fact, these industries have been a rapidly rising source of aggregate productivity growth throughout the 1990s. The IT-producing industries generate less than five percent of gross domestic income, but have accounted for nearly half the surge in productivity growth since 1995. However, it is important to emphasize that faster productivity growth is not limited to these industries. The dramatic effects of information technology on capital and labor markets have already generated a substantial and growing economic literature, but many important issues remain to be resolved. For capital markets the relationship between equity valuations and growth prospects merits much further study. For labor markets more research is needed on investment in information technology and substitution among different types of labor. 1.2. Faster, Better, Cheaper. Modern information technology begins with the invention of the transistor , a semiconductor device that acts as an electrical switch and encodes information in binary form. A binary digit or bit takes the values zero and one, corresponding to the off and on positions of a switch. The first transistor, made of the semiconductor germanium, was constructed at Bell Labs in 1947 and won the Nobel Prize in Physics in 1956 for the inventors -- John Bardeen, Walter Brattain, and William Shockley 4 . The next major milestone in information technology was the co-invention of the integrated circuit by Jack Kilby of Texas Instruments in 1958 and Robert Noyce of Fairchild Semiconductor in 1959. An integrated circuit consists of many, even millions, of transistors that store and manipulate data in binary form. Integrated circuits were originally developed for data storage and retrieval and semiconductor storage devices became known as memory chips 5 . The first patent for the integrated circuit was granted to Noyce. This resulted in a decade of litigation over the intellectual property rights. The litigation and its outcome demonstrate the critical importance of intellectual property in the development of information technology. Kilby was awarded the Nobel Prize in Physics in 2000 for discovery of the integrated circuit; regrettably, Noyce died in 1990 6 . 1.2.1. Moore's Law. In 1965 Gordon Moore, then Research Director at Fairchild Semiconductor, made a prescient observation, later known as Moore's Law 7 . Plotting data on memory chips, he observed that each new chip contained roughly twice as many transistors as the previous chip and was released within 18-24 months of its predecessor. This implied exponential growth of chip capacity at 35-45 percent per year! Moore's prediction, made in the infancy of the semiconductor industry, has tracked chip capacity for thirty-five years. He recently extrapolated this trend for at least another decade 8 . 4 On Bardeen, Brattain, and Shockley, see: http://www.nobel.se/physics/laureates/1956/ . 5 Charles Petzold (2000) provides a general reference on computers and software. 6 On Kilby, see: http://www.nobel.se/physics/laureates/2000/ . On Noyce, see: Tom Wolfe (2000), pp. 17-65. 7 Moore (1965). Vernon Ruttan (2001), pp.316-367, provides a general reference on the economics of semiconductors and computers. On semiconductor technology, see: http://euler.berkeley.edu/~esrc/csm. 8 Moore (1997). In 1968 Moore and Noyce founded Intel Corporation to speed the commercialization of memory chips 9 . Integrated circuits gave rise to microprocessors with functions that can be programmed by software, known as logic chips . Intel's first general purpose microprocessor was developed for a calculator produced by Busicom, a Japanese firm. Intel retained the intellectual property rights and released the device commercially in 1971. The rapidly rising trends in the capacity of microprocessors and storage devices illustrate the exponential growth predicted by Moore's Law. The first logic chip in 1971 had 2,300 transistors, while the Pentium 4 released on November 20, 2000, had 42 million! Over this twenty-nine year period the number of transistors increased by thirty-four percent per year. The rate of productivity growth for the U.S. economy during this period was slower by two orders of magnitude. 1.2.2. Semiconductor Prices. Moore's Law captures the fact that successive generations of semiconductors are faster and better . The economics of semiconductors begins with the closely related observation that semiconductors have become cheaper at a truly staggering rate! Figure 1.1 gives semiconductor price indexes constructed by Bruce Grimm (1998) of the Bureau of Economic Analysis (BEA) and employed in the U.S. National Income and Product Accounts since 1996. These are divided between memory chips and logic chips. The underlying detail includes seven types of memory chips and two types of logic chips. Between 1974 and 1996 prices of memory chips decreased by a factor of 27,270 times or at 40.9 percent per year, while the implicit deflator for the gross domestic product (GDP) increased by almost 2.7 times or 4.6 percent per year! Prices of logic chips, available for the shorter period 1985 to 1996, decreased by a factor of 1,938 or 54.1 percent per year, while the GDP deflator 9 Moore (2003). increased by 1.3 times or 2.6 percent per year! Semiconductor price declines closely parallel Moore's Law on the growth of chip capacity, setting semiconductors apart from other products. Figure 1.1 also reveals a sharp acceleration in the decline of semiconductor prices in 1994 and 1995. The microprocessor price decline leapt to more than ninety percent per year as the semiconductor industry shifted from a three-year product cycle to a greatly accelerated two-year cycle. This is reflected in the 20003 Edition of the International Technology Road Map for Semiconductors 10 , prepared by a consortium of industry associations. Ana Aizcorbe, Stephen Oliner, and Daniel Sichel (2003) have identified and analyzed break points in prices of microprocessors and storage devices. 1.2.3. Constant Quality Price Indexes. The behavior of semiconductor prices is a severe test for the methods used in the official price statistics. The challenge is to separate observed price changes between changes in semiconductor performance and changes in price that hold performance constant. Achieving this objective has required a detailed understanding of the technology, the development of sophisticated measurement techniques, and the introduction of novel methods for assembling the requisite information. Ellen Dulberger (1993) introduced a "matched model" index for semiconductor prices. A matched model index combines price relatives for products with the same performance at different points of time. Dulberger presented constant quality price indexes based on index number formulas, including the Fisher (1922) ideal index used in the in the U.S. national accounts 11 . The Fisher index is the geometric average of the familiar Laspeyres and Paasche indexes. 10 On International Technology Roadmap for Semiconductors (2003), see: http://public.itrs.net/. 11 See Steven Landefeld and Robert Parker (1997). Erwin Diewert (1976) defined a superlative index number as an index that exactly replicates a flexible representation of the underlying technology (or preferences). A flexible representation provides a second-order approximation to an arbitrary technology (or preference system). A.A. Konus and S. S. Byushgens (1926) first showed that the Fisher ideal index is superlative in this sense. Laspeyres and Paasche indexes are not superlative and fail to capture substitutions among products in response to price changes accurately. Grimm (1998) combined matched model techniques with hedonic methods, based on an econometric model of semiconductor prices at different points of time. A hedonic model gives the price of a semiconductor product as a function of the characteristics that determine performance, such as speed of processing and storage capacity. A constant quality price index isolates the price change by holding these characteristics of semiconductors fixed. 12 Beginning in 1997, the Bureau of Labor Statistics (BLS) incorporated a matched model price index for semiconductors into the Producer Price Index (PPI) and since then the national accounts have relied on data from the PPI. Reflecting long-standing BLS policy, historical data were not revised backward. Semiconductor prices reported in the PPI prior to 1997 do not hold quality constant, failing to capture the rapid semiconductor price decline and the acceleration in 1995. 1.2.4. Computers. The introduction of the Personal Computer (PC) by IBM in 1981 was a watershed event in the deployment of information technology. The sale of Intel's 8086-8088 microprocessor to IBM in 1978 for incorporation into the PC was a major business breakthrough for Intel 13 . In 1981 IBM licensed the MS-DOS operating system from the Microsoft Corporation, founded by Bill Gates and Paul 12 Triplett (2003) has drafted a manual for the OECD on constructing constant quality price indexes for information technology and communications equipment and software. 13 See Moore (1996). Allen in 1975. The PC established an Intel/Microsoft relationship that has continued up to the present. In 1985 Microsoft released the first version of Windows, its signature operating system for the PC, giving rise to the Wintel (Windows-Intel) nomenclature for this ongoing collaboration. Mainframe computers, as well as PC's, have come to rely heavily on logic chips for central processing and memory chips for main memory. However, semiconductors account for less than half of computer costs and computer prices have fallen much less rapidly than semiconductor prices. Precise measures of computer prices that hold product quality constant were introduced into the NIPA in 1985 and the PPI during the 1990s. The national accounts now rely on PPI data, but historical data on computers from the PPI, like the PPI data on semiconductors, do not hold quality constant. Gregory Chow (1967) pioneered the use of hedonic techniques for constructing a constant quality index of computer prices in research conducted at IBM. Chow documented price declines at more than twenty percent per year during 1960-1965, providing an initial glimpse of the remarkable behavior of computer prices. In 1985 the Bureau of Economic Analysis incorporated constant quality price indexes for computers and peripheral equipment constructed by IBM into the NIPA. Jack Triplett 9s (1986) discussion of the economic interpretation of these indexes brought the rapid decline of computer prices to the attention of a very broad audience. The BEA-IBM constant quality price index for computers provoked a heated exchange between BEA and Edward Denison (1989), one of the founders of national accounting methodology in the 1950s and head of the national accounts at BEA from 1979 to 1982. Denison sharply attacked the BEA-IBM methodology and argued vigorously against the introduction of constant quality price indexes into the national accounts 14 . Allan Young (1989), then Director of BEA, reiterated BEA's 14 Denison cited his 1957 paper, "Theoretical Aspects of Quality Change, Capital rationale for introducing constant quality price indexes. Dulberger (1989) presented a more detailed report on her research on the prices of computer processors for the BEA-IBM project. Speed of processing and main memory played central roles in her model. Triplett (1989, 2003) has provided exhaustive surveys of research on hedonic price indexes for computers. Gordon (1989, 1990) gave an alternative model of computer prices and identified computers and communications equipment, along with commercial aircraft, as assets with the highest rates of price decline. Figure 1.2 gives BEA's constant quality index of prices of computers and peripheral equipment and its components, including mainframes, PC's, storage devices, other peripheral equipment, and terminals. The decline in computer prices follows the behavior of semiconductor prices presented in figure 1.1, but in much attenuated form. The 1995 acceleration in the computer price decline parallels the acceleration in the semiconductor price decline that resulted from the changeover from a three-year product cycle to a two-year cycle in 1995. 1.2.5. Communications Equipment and Software. Communications technology is crucial for the rapid development and diffusion of the Internet, perhaps the most striking manifestation of information technology in the American economy 15 . Kenneth Flamm (1989) was the first to compare the behavior of computer prices and the prices of communications equipment. He concluded that the communications equipment prices fell only a little more slowly than computer prices. Gordon (1990) compared Flamm's results with the official price indexes, revealing substantial bias in the official indexes. Consumption, and Net Capital Formation," as the definitive statement of the traditional BEA position . 15 General references on the economics of the Internet are Soon-Yong Choi and Andrew Whinston (2000) and Robert Hall (2002). On Internet indicators see: http://www.internetindicators.com/. Communications equipment is an important market for semiconductors, but constant quality price indexes cover only a portion of this equipment. Switching and terminal equipment rely heavily on semiconductor technology, so that product development reflects improvements in semiconductors. Grimm's (1997) constant quality price index for digital telephone switching equipment, given in figure 1.3, was incorporated into the national accounts in 1996. The output of communications services in the NIPA also incorporates a constant quality price index for cellular phones. Much communications investment takes the form of the transmission gear, connecting data, voice, and video terminals to switching equipment. Technologies such as fiber optics, microwave broadcasting, and communications satellites have progressed at rates that outrun even the dramatic pace of semiconductor development. An example is dense wavelength division multiplexing (DWDM), a technology that sends multiple signals over an optical fiber simultaneously. Installation of DWDM equipment, beginning in 1997, has doubled the transmission capacity of fiber optic cables every 6-12 months 16 . Mark Doms (2004) has provided comprehensive price indexes for terminals, switching gear, and transmission equipment. These have been incorporated into the Federal Reserve 9s Index of Industrial Production, as described by Carol Corrado (2003), but are not yet included in the U.S. National Income and Product Accounts. The analysis of the impact of information technology on the U.S. economy described below is based on the national accounts and remains incomplete. Both software and hardware are essential for information technology and this is reflected in the large volume of software expenditures. The eleventh comprehensive revision of the national accounts, released by BEA on October 27, 16 Rick Rashad (2000) characterizes this as the "demise" of Moore's Law. Jeff Hecht (1999) describes DWDM technology and provides a general reference on fiber optics. 1999, re-classified computer software as investment 17 . Before this important advance, business expenditures on software were treated as current outlays, while personal and government expenditures were treated as purchases of nondurable goods. Software investment is growing rapidly and is now much more important than investment in computer hardware. Parker and Grimm (2000) describe the new estimates of investment in software. BEA distinguishes among three types of software -- prepackaged, custom, and own-account software. Prepackaged software is sold or licensed in standardized form and is delivered in packages or electronic files downloaded from the Internet. Custom software is tailored to the specific application of the user and is delivered along with analysis, design, and programming services required for customization. Own-account software consists of software created for a specific application. However, only price indexes for prepackaged software hold performance constant. Parker and Grimm (2000) present a constant quality price index for prepackaged software, given in figure 1.3. This combines a hedonic model of prices for business applications software and a matched model index for spreadsheet and word processing programs developed by Oliner and Sichel (1994). Prepackaged software prices decline at more than ten percent per year over the period 1962-1998. Since 1998 the BEA has relied on a matched model price index for all prepackaged software from the PPI; prior to 1998 the PPI data do not hold quality constant. BEA's prices for own-account and custom software are based on programmer wage rates. This implicitly assumes no change in the productivity of computer programmers, even with growing investment in hardware and software to support the creation of new software. Custom and own-account software prices are a 17 Brent Moulton (2000) describes the 11 th comprehensive revision of NIPA and the 1999 update. weighted average of prepackaged software prices and programmer wage rates with arbitrary weights of 75 percent for programmer wage rates and 25 percent for prepackaged software. These price indexes do not hold the software performance constant and present a distorted picture of software prices, as well as software output and investment. 1.2.6. Research Opportunities. The official price indexes for computers and semiconductors provide the paradigm for economic measurement. These indexes capture the steady decline in IT prices and the recent acceleration in this decline. The official price indexes for central office switching equipment and prepackaged software also hold quality constant. BEA and BLS, the leading statistical agencies in price research, have carried out much of the best work in this area. However, a critical role has been played by price research at IBM, long the dominant firm in information technology 18 . It is important to emphasize that information technology is not limited to applications of semiconductors. Switching and terminal equipment for voice, data, and video communications have come to rely on semiconductor technology and the empirical evidence on prices of this equipment reflects this fact. Transmission gear employs technologies with rates of progress that far outstrip those of semiconductors. This important gap in our official price statistics has been filled by constant quality price indexes for all types of communications equipment constructed by Doms (2004), but these indexes have not been incorporated into the national accounts. Investment in software is more important than investment in hardware. This was essentially invisible until BEA introduced new measures of prepackaged, custom, and own-account software investment into the national accounts in 1999. This is a crucial step in understanding the role of information technology in 18 See Alfred Chandler (2000), Table 1.1, p. 26. the American economy. Unfortunately, software prices are a statistical blind spot with only prices of prepackaged software adequately represented in the official system of price statistics. The daunting challenge that lies ahead is to construct constant quality price indexes for custom and own-account software. 1.3. Impact of Information Technology. In section 2 I consider the ckiller application d of the new framework for productivity measurement 3 the impact of information technology on economic growth. Despite differences in methodology and data sources, a consensus has emerged that the remarkable behavior of IT prices provides the key to the surge in U.S. economic growth after 1995. The relentless decline in the prices of information technology equipment and software has steadily enhanced the role of IT investment. Productivity growth in IT-producing industries has risen in importance and a productivity revival is underway in the rest of the economy. A substantial acceleration in the IT price decline occurred in 1995, triggered by a much sharper acceleration in the price decline of semiconductors, the key component of modern information technology. Although the decline in semiconductor prices has been projected to continue for at least another decade, the recent acceleration may be temporary. This can be traced to a shift in the product cycle for semiconductors from three years to two years as a consequence of intensifying competition in markets for semiconductor products. In section 3 I show that the surge of IT investment in the United States after 1995 has counterparts in all other industrialized countries. It is essential to use comparable data and methodology in order to provide rigorous international comparisons. A crucial role is played by measurements of IT prices. The U.S. national accounts have incorporated measures of IT prices that hold performance constant since 1985. Schreyer (2000) has extended these measures to other industrialized countries by constructing cinternationally harmonized prices d. 19 I show that the acceleration in the IT price decline in 1995 triggered a burst of IT investment in all of the G7 nations 3 Canada, France, Germany, Italy, Japan, the United Kingdom, as well as the United States. These countries also experienced a rise in productivity growth in the IT-producing industries. However, differences in the relative importance of these industries have generated wide disparities in the impact of IT on economic growth. The role of the IT-producing industries is greatest in the United States, which leads the G7 in output per capita. Section 4 concludes. 2. Aggregate Growth Accounting. 2.1. The Role of Information Technology. At the aggregate level information technology is identified with the outputs of computers, communications equipment, and software. These products appear in the GDP as investments by businesses, households, and governments along with net exports to the rest of the world. The GDP also includes the services of IT products consumed by households and governments. A methodology for analyzing economic growth must capture the substitution of IT outputs for other outputs of goods and services. While semiconductor technology is the driving force behind the spread of IT, the impact of the relentless decline in semiconductor prices is transmitted through falling IT prices. Only net exports of semiconductors, defined as the difference between U.S. exports to the rest of the world and U.S. imports appear in the GDP. Sales of semiconductors to domestic manufacturers of IT products are precisely offset by purchases of semiconductors and are excluded from the GDP. 19 The measurement gap in IT prices between the U.S. and other OECD countries was first identified by Andrew Wyckoff (1995). Constant quality price indexes, like those reviewed in the previous section, are a key component of the methodology for analyzing the American growth resurgence. Computer prices were incorporated into the NIPA in 1985 and are now part of the PPI as well. Much more recently, semiconductor prices have been included in the NIPA and the PPI. The official price indexes for communications equipment do not yet reflect the important work of Doms (2004). Unfortunately, evidence on the price of software is seriously incomplete, so that the official price indexes are seriously misleading. 2.1.1. Output. The output data in table 2.1 are based on the most recent benchmark revision of the national accounts through 2000 20 . The output concept is similar, but not identical, to the concept of gross domestic product used by the BEA. Both measures include final outputs purchased by businesses, governments, households, and the rest of the world. Unlike the BEA concept, the output measure in table 2.1 also includes imputations for the service flows from durable goods, including IT products, employed in the household and government sectors. The imputations for services of IT equipment are based on the cost of capital for IT described in more detail below. The cost of capital is multiplied by the nominal value of IT capital stock to obtain the imputed service flow from IT products. In the business sector this accrues as capital income to the firms that employ these products as inputs. In the household and government sectors the flow of capital income must be imputed. This same type of imputation is used for housing in the NIPA. The rental value of renter-occupied housing accrues to real estate firms as capital income, while the rental value of owner-occupied housing is imputed to households. 20 See Jorgenson and Stiroh (2000b), Appendix A, for details on the estimates of output. Current dollar GDP in table 2.1 is $11.3 trillions in 2002, including imputations, and real output growth averaged 3.46 percent for the period 1948- 2002. These magnitudes can be compared to the current dollar value of $10.5 trillions in 2002 and the average real growth rate of 3.36 percent for period 1948-2002 for the official GDP. Table 2.1 presents the current dollar value and price indexes of the GDP and IT output. This includes outputs of investment goods in the form of computers, software, communications equipment, and non-IT investment goods. It also includes outputs of non-IT consumption goods and services as well as imputed IT capital service flows from households and governments. The most striking feature of the data in table 2.1 is the rapid price decline for computer investment, 15.8 percent per year from 1959 to 1995. Since 1995 this decline has increased to 31.0 percent per year. By contrast the relative price of software has been flat for much of the period and began to fall only in the 1980s. The price of communications equipment behaves similarly to the software price, while the consumption of capital services from computers and software by households and governments shows price declines similar to computer investment. The top panel of table 2.2 summarizes the growth rates of prices and quantities for major output categories for 1989-95 and 1995-2002. Business investments in computers, software, and communications equipment are the largest categories of IT spending. Households and governments have also spent sizable amounts on computers, software and communications equipment. Figure 2.1 shows that the share of software output in the GDP is largest, followed by the shares of communications equipment and computers. 2.1.2. Capital Services. This section presents capital estimates for the U.S. economy for the period 1948 to 2002 21 . These begin with BEA investment data; the perpetual inventory method generates estimates of capital stocks and these are aggregated, using service prices as weights. This approach, originated by Jorgenson and Zvi Griliches (1967), is based on the identification of service prices with marginal products of different types of capital. The service price estimates incorporate the cost of capital 22 . The cost of capital is an annualization factor that transforms the price of an asset into the price of the corresponding capital input. This includes the nominal rate of return, the rate of depreciation, and the rate of capital loss due to declining prices. The cost of capital is an essential concept for the economics of information technology 23 , due to the astonishing decline of IT prices given in tables 2.1 and 2.2. The cost of capital is important in many areas of economics, especially in modeling producer behavior, productivity measurement, and the economics of taxation 24 . Many of the important issues in measuring the cost of capital have been debated for decades. The first of these is incorporation of the rate of decline of asset prices into the cost of capital. The assumption of perfect foresight or rational expectations quickly emerged as the most appropriate formulation and has been used in almost all applications of the cost of capital 25 . 21 See Jorgenson and Stiroh (2000b), Appendix B, for details on the estimates of capital input. 22 Jorgenson and Kun-Young Yun (2001) present the model of capital input used in the estimates presented in this section. BLS (1983) describes the version of this model employed in the official productivity statistics. For a recent updates, see the BLS multifactor productivity website: http://www.bls.gov/mfp/home.htm . Charles Hulten (2001) surveys the literature. 23 Jorgenson and Stiroh (1995), pp. 300-303. 24 Lawrence Lau (2000) surveys applications of the cost of capital. 25 See, for example, Jorgenson, Gollop, and Fraumeni (1987), pp. 40-9, and Jorgenson and Griliches (1967). The second empirical issue is the measurement of economic depreciation. The stability of patterns of depreciation in the face of changes in tax policy and price shocks has been carefully documented. The depreciation rates presented by Jorgenson and Stiroh (2000b) summarize a large body of empirical research on the behavior of asset prices 26 . A third empirical issue is the description of the tax structure for capital income. This depends on the tax laws prevailing at each point of time. The resolution of these issues has cleared the way for detailed measurements of the cost of capital for all assets that appear in the national accounts, including information technology equipment and software 27 . The definition of capital includes all tangible assets in the U.S. economy, equipment and structures, as well as consumers 9 and government durables, land, and inventories. The capital service flows from durable goods employed by households and governments enter measures of both output and input. A steadily rising proportion of these service flows are associated with investments in IT. Investments in IT by business, household, and government sectors must be included in the GDP, along with household and government IT capital services, in order to capture the full impact of IT on the U.S. economy. Table 2.3 gives capital stocks for the business, household and government sectors from 1948 to 2002, as well as price indexes for total domestic tangible assets and IT assets -- computers, software, and communications equipment. The estimate of domestic tangible capital stock in table 2.3 is $45.9 trillions in 2002, considerably greater than the estimate by BEA. The most important differences reflect the inclusion of inventories and land in table 2.3. 26 Jorgenson and Stiroh (2000b), Table B4, pp. 196-7 give the depreciation rates employed in this section. Fraumeni (1997) describes depreciation rates used in the NIPA. Jorgenson (1996) surveys empirical studies of depreciation. 27 See Jorgenson and Yun (2001) for details on the U.S. tax structure for capital income. Diewert and Denis Lawrence (2000) survey measures of the price and quantity of capital input. Business IT investments, as well as purchases of computers, software, and communications equipment by households and governments, have grown spectacularly in recent years, but remain relatively small. The stocks of all IT assets combined account for only 3.79 percent of domestic tangible capital stock in 2002. Table 2.4 presents estimates of the flow of capital services from the business, household, and government sectors and corresponding price indexes for 1948-2002. The difference between growth in capital services and capital stock is the improvement in capital quality. This represents the substitution towards assets with higher marginal products. The shift toward IT increases the quality of capital, since computers, software, and communications equipment have relatively high marginal products. Capital stock estimates fail to account for this increase in quality and substantially underestimate the impact of IT investment on growth. Table 2.7 shows the growth of capital quality is near twenty percent of capital input growth for the period 1948-2002. However, improvements in capital quality have increased steadily in relative importance. These improvements jumped to 46 percent of total growth in capital input during the period 1995- 2002, reflecting very rapid restructuring of capital to take advantage of the sharp acceleration in the IT price decline. Capital stock has become progressively less accurate as a measure of capital input and is now seriously deficient. Figure 2.2 gives the IT capital service flows as a share of gross domestic income. The second panel of table 2.2 summarizes the growth rates of prices and quantities of capital inputs for 1989-1995 and 1995-2002. Growth of IT capital services jumps from 12.58 percent per year in 1989-1995 to 18.33 percent in 1995-2002, while growth of non-IT capital services increases from 1.91 percent to 3.01 percent. This reverses the trend toward slower capital growth through 1995. 2.1.3. Labor Services. This section presents estimates of labor input for the U.S. economy from 1948 to 2002. These incorporate individual data from the Censuses of Population for 1970, 1980, and 1990, as well as the annual Current Population Surveys. Constant quality indexes for the price and quantity of labor input account for the heterogeneity of the workforce across sex, employment class, age, and education levels. This follows the approach of Jorgenson, Gollop, and Fraumeni (1987) 28 . The distinction between labor input and labor hours is analogous to the distinction between capital services and capital stock. The growth in labor quality is the difference between the growth in labor input and hours worked. Labor quality reflects the substitution of workers with high marginal products for those with low marginal products. Table 2.5 presents estimates of labor input, hours worked, and labor quality. The value of labor expenditures in table 2.5 is $6.6 trillions in 2002, 58.3 percent of the value of output. This share accurately reflects the concept of gross domestic income, including imputations for the value of capital services in household and government sectors. As shown in table 2.7, the growth rate of labor input decelerated to 1.50 percent for 1995-2002 from 1.64 percent for 1989-1995. Growth in hours worked rose from 1.02 percent for 1989-1995 to 1.16 percent for 1995-2002 as labor force participation increased and unemployment rates declined. The growth of labor quality has declined considerably since 1995, dropping from 0.61 percent for 1989-1995 to 0.33 percent for 1995-2002. This slowdown captures well-known demographic trends in the composition of the work force, as well as exhaustion of the pool of available workers. Growth in hours worked does 28 See Jorgenson and Stiroh (2000b), Appendix C, for details on the estimates of labor input. Gollop (2000) discusses the measurement of labor quality. not capture these changes in labor quality growth and is a seriously misleading measure of labor input. 2.2. The American Growth Resurgence. The American economy has undergone a remarkable resurgence since the mid- 1990s with accelerating growth in output, labor productivity, and total factor productivity. The purpose of this section is to quantify the sources of growth for 1948-2002 and various sub-periods. An important objective is to account for the sharp acceleration in the growth rate since 1995 and, in particular, to document the role of information technology. The appropriate framework for analyzing the impact of information technology is the production possibility frontier, giving outputs of IT investment goods as well as inputs of IT capital services. An important advantage of this framework is that prices of IT outputs and inputs are linked through the price of IT capital services. This framework successfully captures the substitutions among outputs and inputs in response to the rapid deployment of IT. It also encompasses costs of adjustment, while allowing financial markets to be modeled independently. As a consequence of the swift advance of information technology, a number of the most familiar concepts in growth economics have been superseded. The aggregate production function heads this list. Capital stock as a measure of capital input is no longer adequate to capture the rising importance of IT. A stock measure completely obscures the restructuring of capital input that is such an important wellspring of the growth resurgence. Finally, hours worked must be replaced as a measure of labor input. 2.2.1. Production Possibility Frontier. The production possibility frontier describes efficient combinations of outputs and inputs for the economy as a whole. Aggregate output Y consists of outputs of investment goods and consumption goods. These outputs are produced from aggregate input X, consisting of capital services and labor services. Productivity is a "Hicks-neutral" augmentation of aggregate input. The production possibility frontier takes the form: (2.1) ) L , K , K , K , K ( f A ) Y , Y , Y , Y ( Y m s c n m s c n Å = where the outputs include non-IT output goods Y n and output of computers Y c , software Y s , and communications equipment Y m . Inputs include non-IT capital services K n and the services of computers K c , software K s , and telecommunications equipment K m , as well as labor input L. 29 Total factor productivity is denoted by A. The most important advantage of the production possibility frontier is the explicit role that it provides for constant quality prices of IT products. These are used as deflators for nominal expenditures on IT investments to obtain the quantities of IT outputs. Investments in IT are cumulated into stocks of IT capital. The flow of IT capital services is an aggregate of these stocks with service prices as weights. Similarly, constant quality prices of IT capital services are used in deflating the nominal values of consumption of these services. Another important advantage of the production possibility frontier is the incorporation of costs of adjustment. For example, an increase in the output of IT investment goods requires foregoing part of the output of consumption goods and non-IT investment goods, so that adjusting the rate of investment in IT is costly. However, costs of adjustment are external to the producing unit and are fully reflected in IT prices. These prices incorporate forward-looking expectations of the future prices of IT capital services. The aggregate production function employed, for example, by Simon Kuznets (1971) and Robert Solow (1957, 1960, 1970) and, more recently, by Jeremy Greenwood, Zvi Hercowitz, and Per Krusell (1997, 2000), Hercowitz (1998), and 29 Services of durable goods to governments and households are included in both inputs and outputs. Arnold Harberger (1998) is a competing methodology. The production function gives a single output as a function of capital and labor inputs. There is no role for separate prices of investment and consumption goods and, hence, no place for constant quality IT price indexes for outputs of IT investment goods. Another limitation of the aggregate production function is that it fails to incorporate costs of adjustment. Robert Lucas (1967) presented a production model with internal costs of adjustment. Fumio Hayashi (2000) shows how to identify these adjustment costs from James Tobin's (1969) Q-ratio, the ratio of the stock market value of the producing unit to the market value of the unit's assets. Implementation of this approach requires simultaneous modeling of production and asset valuation. If costs of adjustment are external, as in the production possibility frontier, asset valuation can be modeled separately from production 30 . 2.2.2. Sources of Growth. Under the assumption that product and factor markets are competitive producer equilibrium implies that the share-weighted growth of outputs is the sum of the share-weighted growth of inputs and growth in total factor productivity: (2.2) , ln ln ln ln ln ln ln , , , , , , , , A L v K v K v K v K v Y w Y w Y w Y w L m m K s s K c c K n n K m m Y s s Y c c Y n n Y + + + + + = + + + where w and v denote average value shares of the subscripted variable. The shares of outputs and inputs add to one under the additional assumption of constant returns, = + + + m , Y s , Y c , Y n , Y w w w w 1 = + + + + L m , K s , K c , K n , K v v v v v . The growth rate of output is a weighted average of growth rates of investment and consumption goods outputs. The contribution of each output is its weighted growth rate. Similarly, the growth rate of input is a weighted average 30 See, for example, John Campbell and Robert Shiller (1998). of growth rates of capital and labor services and the contribution of each input is its weighted growth rate. The contribution of total factor productivity, the growth rate of the augmentation Table 2.6 presents results of a growth accounting decomposition for the period 1948-2002 and various sub-periods, following Jorgenson and Stiroh (1999, 2000b). Economic growth is broken down by output and input categories, quantifying the contribution of information technology to outputs, as well as capital inputs. These estimates identify computer hardware, software, and communications equipment as distinct types of information technology. The results can also be presented in terms of average labor productivity (ALP), defined as H Y y / = , the ratio of output Y to hours worked H, and H K k / = is the ratio of capital services K to hours worked: ( ) A H L v k v y L K ln ln ln ln ln + 2 + = . This equation allocates ALP growth among three sources. The first is capital deepening, the growth in capital input per hour worked, and reflects the capital-labor substitution. The second is improvement in labor quality and captures the rising proportion of hours by workers with higher marginal products. The third is total factor productivity growth, which contributes point-for-point to ALP growth. Table 2.7 shows these estimates. 2.2.3. Contributions of IT Output. Figure 2.2 depicts the rapid increase in the importance of IT services, reflecting the accelerating pace of IT price declines. In 1995-2002 the capital service price for computers fell 26.09 percent per year, compared to an increase of 32.34 percent in capital input from computers. While the value of computer services grew, the current dollar value was only 1.44 percent of gross domestic income in 2002. The rapid accumulation of software appears to have different sources. The price of software services has fallen only 1.72 percent per year for 1995-2002. Nonetheless, firms have been accumulating software very rapidly, with real capital services growing 14.27 percent per year. A possible explanation is that firms respond to computer price declines by investing in complementary inputs like software. However, a more plausible explanation is that the price indexes used to deflate software investment fail to hold quality constant. This leads to an overstatement of inflation and an understatement of growth. Although the price decline for communications equipment during the period 1995-2002 is greater than that of software, investment in this equipment is more in line with prices. However, prices of communications equipment also fail to hold quality constant. The technology of switching equipment, for example, is similar to that of computers; investment in this category is deflated by a constant-quality price index developed by BEA. Conventional price deflators are employed for transmission gear, such as fiber-optic cables. This leads to an underestimate of the growth rates of investment, capital stock, capital services, and the GDP, as well as an overestimate of the rate of inflation. Figures 2.3 and 2.4 highlight the rising contributions IT outputs to U.S. economic growth. Figure 2.3 shows the breakdown between IT and non-IT outputs for sub-periods from 1948 to 2002, while figure 2.4 decomposes the contribution of IT into its components. Although the importance of IT has steadily increased, figure 2.3 shows that the recent investment and consumption surge nearly doubled the output contribution of IT. Figure 2.4 shows that computer investment is the largest single IT contributor after 1995, but that investments in software and communications equipment are becoming increasingly important. Table 2.2 reports IT input prices and figures 2.5 and 2.6 present a similar decomposition of IT inputs into production. The contribution of these inputs is rising even more dramatically. Figure 2.5 shows that the contribution of IT now accounts for more than 45.0 percent of the total contribution of capital input. Figure 2.6 reveals that computer hardware is the largest component of IT, reflecting the growing share and accelerating growth rate of computer investment in the late 1990s. Private business investment predominates in the output of IT, as shown by Jorgenson and Stiroh (2000b) and Oliner and Sichel (2000) 31 . Household purchases of IT equipment are next in importance. Government purchases of IT equipment and net exports of IT products must be included in order to provide a complete picture. Firms, consumers, governments, and purchasers of U.S. exports are responding to relative price changes, increasing the contributions of computers, software, and communications equipment. Table 2.2 shows that the price of computer investment fell by 31.00 percent per year, the price of software fell by 1.31 percent and the price of communications equipment dropped by 4.16 percent during the period 1995-2002, while non-IT investment goods prices rose 2.02 percent. In response to these price changes, firms, households, and governments have accumulated computers, software, and communications equipment much more rapidly than other forms of capital. 2.2.4. Total Factor Productivity. The price or "dual" approach to productivity measurement employed by Triplett (1996) makes it possible to identify the role of IT production as a source of total factor productivity growth at the industry level 32 . The rate of total factor productivity growth is measured as the decline in the price of output, plus a weighted average of the growth rates of input prices with value shares of the inputs as weights. For the computer industry this expression is dominated by two terms: the decline in the price of computers and the 31 Bosworth and Triplett (2000) and Martin Baily (2002) compare the results of Jorgenson and Stiroh with those of Oliner and Sichel, who incorporate data from the BLS measures of multifactor productivity. 32 The dual approach is presented by Jorgenson, Gollop, and Fraumeni (1987), pp. 53-63. contribution of the price of semiconductors. For the semiconductor industry the expression is dominated by the decline in the price of semiconductors 33 . Jorgenson, Gollop, and Fraumeni (1987) have employed Evsey Domar's (1961) model to trace aggregate productivity growth to its sources at the level of individual industries 34 . More recently, Harberger (1998), William Gullickson and Michael Harper (1999), and Jorgenson and Stiroh (2000a, 2000b) have used the model for similar purposes. Total factor productivity growth for each industry is weighted by the ratio of the gross output of the industry to GDP to estimate the industry contribution to aggregate productivity growth. If semiconductor output were only used to produce computers, then its contribution to computer industry productivity growth, weighted by computer industry output, would precisely offset its independent contribution to the growth of aggregate productivity. This is the ratio of the value of semiconductor output to GDP, multiplied by the rate of semiconductor price decline. In fact, semiconductors are used to produce telecommunications equipment and many other products. However, the value of semiconductor output is dominated by inputs into IT production. The Domar aggregation formula can be approximated by expressing the declines in prices of computers, communications equipment, and software relative to the price of gross domestic income, an aggregate of the prices of capital and labor services. The rates of relative IT price decline are weighted by ratios of the outputs of IT products to the GDP. Table 2.8 reports details of this decomposition of total factor productivity; the IT and non-IT contributions are presented in figure 2.7. Production of IT products contributes 0.47 percentage points to total factor 33 Models of the relationships between computer and semiconductor industries presented by Dulberger (1993), Triplett (1996), and Oliner and Sichel (2000) are special cases of the Domar (1961) aggregation scheme. 34 See Jorgenson, Gollop, and Fraumeni (1987), pp. 63-66, 301-322. productivity growth for 1995-2002, compared to 0.23 percentage points for 1989- 1995. This reflects the accelerating decline in relative price changes resulting from shortening the product cycle for semiconductors. 2.2.5. Output Growth. This section presents the sources of GDP growth for the entire period 1948 to 2002 as described in tables 2.6 and 2.7. Output grew 3.46 percent per year, as capital services contributed 1.75 percentage points, labor services 1.05 percentage points, and total factor productivity growth only 0.67 percentage points. Input growth is the source of nearly 80.6 percent of U.S. growth over the past half century, while productivity has accounted for 19.4 percent. Figure 2.8 shows the relatively modest contributions of productivity in all sub- periods. More than four-fifths of the contribution of capital reflects the accumulation of capital stock, while improvement in the quality of capital accounts for about one-fifth. Similarly, increased labor hours account for 68 percent of labor 9s contribution; the remainder is due to improvements in labor quality. Substitutions among capital and labor inputs in response to price changes are essential components of the sources of economic growth. A look at the U.S. economy before and after 1973 reveals familiar features of the historical record. After strong output and productivity growth in the 1950s, 1960s and early 1970s, the U.S. economy slowed markedly through 1989, with output growth falling from 3.99 percent to 2.97 percent and total factor productivity growth declining from 1.00 percent to 0.29 percent for 1973 to 1989. The contribution of capital input also slowed from 1.94 percent for 1948- 1973 to 1.53 percent for 1973-1989. This contributed to sluggish ALP growth -- 2.93 percent for 1948-1973 compared to 1.36 percent for 1973-1989. Relative to the period 1989-1995, output growth increased by 1.16 percent during 1995-2002. The contribution of IT production jumped by 0.27 percent, relative to 1989-1995, but still accounted for only 17.8 percent of the growth of output. Although the contribution of IT has increased steadily throughout the period 1948-2002, there has been a sharp response to the acceleration in the IT price decline in 1995. Nonetheless, more than eighty percent of the output growth can be attributed to non-IT products. Between 1989-1995 and 1995-2002 the contribution of capital input jumped by 0.80 percentage points, the contribution of labor input declined by 0.10 percent, and total factor productivity accelerated by 0.45 percent. Growth in ALP rose 1.03 percent as more rapid capital deepening and growth in total factor productivity offset slower improvement in labor quality. Growth in hours worked slowed as labor markets tightened considerably, even as labor force participation rates increased. 35 The contribution of capital input reflects the investment boom of the late 1990s as businesses, households, and governments poured resources into plant and equipment, especially computers, software, and communications equipment. The contribution of capital, predominantly IT, is considerably more important than the contribution of labor. The contribution of IT capital services has grown steadily throughout the period 1948-2002, but figure 2.6 reflects the impact of the accelerating decline in IT prices. After maintaining an average rate of 0.29 percent for the period 1973- 1989, total factor productivity growth declined to 0.26 percent for 1989-1995 and then increased to 0.71 percent per year for 1995-2002. This is an increasing source of growth in output and ALP for the U.S. economy (figures 2.8 and 2.9). Total factor productivity growth for 1995-2002 is still below the rate of 1948-1973 and the U.S. economy is recuperating from the anemic productivity growth of the past two decades. Slightly more than half of the acceleration in productivity from 1989-1995 to 1995-2002 can be attributed to IT 35 Lawrence Katz and Alan Krueger (1999) analyze the recent performance of the U.S. labor market. production, which is far greater than the 5.01 percent share of IT in the GDP in 2002. 2.2.6. Average Labor Productivity. Output growth is the sum of growth in hours and average labor productivity. Table 2.7 shows the breakdown between growth in hours and ALP for the same periods as in table 2.6. For the period 1948-2002, ALP growth predominated in output growth, increasing 2.23 percent per year, while hours worked increased 1.23 percent per year. As shown above, ALP growth depends on capital deepening, a labor quality effect, and overall productivity growth. Figure 2.9 reveals the well-known productivity slowdown of the 1970s and 1980s, emphasizing the sharp acceleration in labor productivity growth in the late 1990s. The slowdown through 1989 reflects reduced capital deepening, declining labor quality growth, and decelerating growth in total factor productivity. The growth of ALP recovered slightly during the early 1990s with a slump in capital deepening more than offset by a revival in labor quality growth. A slowdown in hours combined with middling ALP growth during 1989-1995 to produce a further slide in the growth of output. In previous cyclical recoveries during the postwar period, output growth accelerated during the recovery, powered by more rapid growth of hours and ALP. Accelerating output growth during 1995-2002 reflects modest growth in labor hours and a sharp increase in ALP growth 36 . Comparing 1989-1995 to 1995- 2002, the rate of output growth jumped by 1.16 percent -- due to an increase in hours worked of 0.14 percent and an upward bound in ALP growth of 1.03 percent. Figure 2.9 shows the acceleration in ALP growth is due to capital deepening as well as faster total factor productivity growth. Capital deepening contributed 36 Stiroh (2002) shows that ALP growth is concentrated in IT-producing and IT- using industries. 0.74 percentage points to the change, counterbalancing a negative contribution of labor quality of 0.16 percent. The acceleration in total factor productivity growth added 0.45 percentage points. 2.2.7. Research Opportunities. The use of computers, software, and communications equipment must be carefully distinguished from the production of IT 37 . Massive increases in computing power, like those experienced by the U.S. economy, have two effects on growth. First, as IT producers become more efficient, more IT equipment and software is produced from the same inputs. This raises total factor productivity in IT-producing industries and contributes to productivity growth for the economy as a whole. Labor productivity also grows at both industry and aggregate levels. Second, investment in information technology leads to growth of productive capacity in IT-using industries. Since labor is working with more and better equipment, this increases ALP through capital deepening. If the contributions to aggregate output are captured by capital deepening, aggregate total factor productivity growth is unaffected 38 . Increasing deployment of IT affects productivity growth only if there are spillovers from IT-producing industries to IT-using industries. Jorgenson, Ho, and Stiroh (2004) trace the increase in aggregate productivity growth to its sources in individual industries. Jorgenson and Stiroh (2000a, 2000b) present the appropriate methodology and preliminary results. Stiroh (2002) shows that aggregate ALP growth can be attributed to productivity growth in IT-producing and IT-using industries. 2.3. Demise of Traditional Growth Accounting. 2.3.1. Introduction. 37 Economics and Statistics Administration (2000), Table 3.1, p. 23, lists IT- producing industries. 38 Baily and Gordon (1988). The early 1970s marked the emergence of a rare professional consensus on economic growth, articulated in two strikingly dissimilar books. Kuznets summarized his decades of empirical research in Economic Growth of Nations (1971). " 39 Solow's book Economic Growth (1970), modestly subtitled "An Exposition", contained his 1969 Radcliffe Lectures at the University of Warwick. In these lectures Solow also summarized decades of theoretical research, initiated by the work of Roy Harrod (1939) and Domar (1946). 40 Let me first consider the indubitable strengths of the perspective on growth that emerged victorious over its many competitors in the early 1970s. Solow's neo-classical theory of economic growth, especially his analysis of steady states with constant rates of growth, provided conceptual clarity and sophistication. Kuznets generated persuasive empirical support by quantifying the long sweep of historical experience of the United States and thirteen other developed economies. He combined this with quantitative comparisons among a developed and developing economies during the postwar period. With the benefit of hindsight the most obvious deficiency of the traditional framework of Kuznets and Solow was the lack of a clear connection between the theoretical and the empirical components. This lacuna can be seen most starkly in the total absence of cross references between the key works of these two great economists. Yet they were working on the same topic, within the same framework, at virtually the same time, and in the very same geographical location-- Cambrid

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