Investment-Specific Technical Change in the US (1947-2000): Measurement and Macroeconomic Consequences

Investment-Speci(cid:222)c Technical Change in the US (1947(cid:151)2000): Measurement and Macroeconomic Consequences ∗ Jason G. Cummins Giovanni L. Violante Federal Reserve Board University College London, CEPR jason.g.cummins@frb.gov g.violante@ucl.ac.uk January 24, 2002 Abstract By extrapolating Gordon(cid:146)s (1990) measures of the quality-bias in the official priceindexes,weconstructquality-adjustedpriceindexesfor24typesofequipmentandsoftware(E&S)from1947to2000andusethemtomeasuretechnical change at the aggregate and at the industry level. Technological improvement in E&S accounts for an important fraction of postwar GDP growth and plays a key role in the productivity resurgence of the 1990s. Driving this(cid:222)nding is 4 percent annual growth in the quality of E&S in the postwar period and more than 6 percent annual growth in the 1990s. The acceleration in the 1990s occurred in every industry, consistent with the idea that information technology represents a general purpose technology. Furthermore, we measure for the aggregateeconomyanddifferentsectorsthe(cid:147)technologicalgap(cid:148): howmuchmore productive new machines are compared tothe average machine. We show that the technological gap explains the dynamics of investment in new technologies and the returns to human capital, consistent with Nelson and Phelps(cid:146) (1966) conjecture. Since the technological gap continues to increase (cid:150) it more than doubled in the past 20 years (cid:150) our evidence supports the view that at least some of the recent increase in productivity growth is sustainable. JEL Classi(cid:222)cation: D24, O47. Keywords: Quality-Adjusted Prices, Growth Accounting, Skill Premium. ∗We owe a special debt to Boyan Jovanovic who provided guidance from start to (cid:222)nish. We are especially grateful to Dan Sichel and Karl Whelan for their comments and suggestions. We thankSteveBond,DarrelCohen,DaleJorgenson,DavidLebow,CostasMeghir,SteveOliner,Nick Oulton, Jeremy Rudd, Kevin Stiroh, and seminar participants at the Bank of England, Federal ReserveBoard,InstituteofFiscalStudies,andtheconference(cid:147)ProductivityGrowth: ANewEra(cid:148) at the New York Fed for additional comments and suggestions. Bruce Grimm and Brent Moulton kindlyhelpedwiththeBEAdata. MarcoCozziprovidedoutstandingresearchassistanceandJulie Stephensassistedinpreparingthedataset. Theviewspresentedaresolelythoseoftheauthorsand do not necessarily represent those of the Federal Reserve Board or its staff. The data used in this paper are available from theauthors upon request.

1 Introduction Technological improvement in equipment and software in the postwar period has been remarkable. In the (cid:222)eld of microelectronics the advances have been spectacular, owing mainly to progress in the manufacture of semiconductors. In the semiconductor industry, Moore(cid:146)s Law (cid:150) which predicts that the number of transistors per integrated circuit doubles every 18 months (cid:150) seems to suggest that technical progressis aninexorable process. In fact, progress proceedsapace because (cid:222)rms reap productive bene(cid:222)ts by investing in the latest technologies.1 Investment in microelectronics has been especially widespread so that microelectronics are now the key components in all kinds of goods, resulting in improvements in quality that were once unimaginable. Advances in other technologies like miniaturization have been impressive as well. Moreover, experimental technologies, such as fusion, hightemperature superconductors and quantum computing, hold the promise of even more rapid technical change in the future. The extent to which such rapid technical change is an engine of growth and a source of interesting macroeconomic dynamics is a quantitative question that can be approached using measures of constant-quality price indexes for capital goods.2 Building on Gordon(cid:146)s (1990) systematic measurement of quality-adjusted prices for differenttypesofproducers(cid:146)durableequipment,Hulten(1992)andGreenwood,Hercowitz, andKrusell(1997)(GHK)measure thecontributionofequipment-embodied technical change to aggregate growth using a Solow (1960) vintage model. Because Gordon(cid:146)s data cover the postwar period until 1983, Hulten(cid:146)s analysis is limited to that period, while GHK extend the aggregate constant-quality price index to 1992 1Intelandothersemiconductormanufacturersarenoexception. In thelast20yearsIntelalone spentonaveragemorethantwobillion peryearin constant 1996dollarsonplant,equipment,and R&D. 2Productionfunctionestimationisanalternativeapproachtomeasuringtechnicalchange. Bakh and Gort (1993), Gort, Bahk and Wall (1993) and Sakellaris and Wilson (2000) focus on estimating the effect of investment-speci(cid:222)c technical change while Stiroh (2001) is a recent entry in the voluminous literature pursuing the more traditional approach which ascribes technical change to theresidualsfromestimation. Inaddition,Hobijn(2000)suggestsanapproachbasedonstructural estimation of an Euler equation forinvestment. 1

by applying a constant adjustment factor to the National Income and Product Accounts (NIPA) official price index. We (cid:222)ll this gap by estimating for each type of equipment the rate of quality improvement since 1983. Starting with Gordon(cid:146)s quality-adjusted price indexes for 1947(cid:151)83, we estimate the quality bias implicit in the NIPA price indexes for that period. Using the NIPA series, we then extrapolate the quality bias from 1984 to 2000. From this we construct constant-quality price indexes for the capital goods that make up equipment and software (E&S). We view this approach as a sensiblealbeitcrudealternativetothepreferableapproachthatwouldquality-adjust every asset in E&S using hedonic techniques, a monumental effort that Bureau of Economic Analysis (BEA) is implementing piecemeal. The speed of technical change for each capital good in E&S can be measured as the difference between the growth rate of constant-quality consumption and the growthrateofthegood(cid:146)squality-adjustedprice. Excludingcomputersandsoftware, forwhichNIPAprice series seem preferable tothe onesgeneratedbyour alternative approach, we conclude that the greatest technical change occurred in communications equipment (9 percent per year), aircraft (8 percent per year), and instruments (6 percent per year). Using these asset-speci(cid:222)c constant-quality price indexes we buildanaggregateindexofinvestment-speci(cid:222)ctechnicalchangefortheUSeconomy. This index grows at an average annual rate of 4 percent in the postwar period, with asharpaccelerationinthe1980sthatleadstoanaverageannualgrowthrateofmore than 6 percent in the 1990s. Most of the acceleration is due to a shift in investment expenditures towards computers, software, and communications equipment. We also construct measures of investment-speci(cid:222)c technical change at the twodigit and (cid:222)ner industry level using BEA(cid:146)s detailed estimates of E&S investment by industryandtype ofasset, whichare basedonavarietyofsourcematerialincluding the input-output tables. It comes as no surprise that there are big differences in the rate of technical change at the industry level. For example, the growth rates of the 90th and the 10th percentile of the distribution differ by more than 5 percentage 2

points in each year. What is perhaps surprising given the diversity of industries is that the distribution has remained stable in the postwar period. In particular, the rate of growth accelerates in the 1990s by a similar amount in virtually every industry, demonstrating that information technology affects productivity in a general way. This result as well as others we present support the idea that information technology is a (cid:147)general purpose(cid:148) technology. Previous empirical studies using quality-adjusted measures of investment constructed the productive capital stock with economic depreciation rates from BEA or from Bureau of Labor Statistics. Economic depreciation incorporates the effect of productive decay and obsolescence. We remove the obsolescence component from BEA economic depreciation using our estimates of asset-speci(cid:222)c quality improvement. Using these corrected depreciation rates and our quality-adjusted investment price indexes, we construct a measure of the aggregate capital stock for E&S that grows at an annual rate of 8.8 percent in the postwar period. This growth rate is 3 percentage points greater than growth rate of the capital stock constructed using the official depreciation rates and price indexes. With our estimates of the quality-adjusted productive capital stock, we perform a statistical and an equilibrium growth accounting exercise. Regardless of how real GDP is quality-adjusted, improvement in the quality of E&S explains about 20 percent of growth in the US in the postwar period and about 30 percent of growth in the 1990s. During the 1990s, quality improvement outside of high-tech categories is more important than quality improvement inside high-tech categories (cid:150) a (cid:222)nding that is underappreciated by those who focus on the role of information technology in the growth resurgence. This explains why our results differ somewhat comparedtoJorgensonandStiroh(2000a) andOlinerandSichel (2000), whichtake the official statistics more or less at face value. Although each of these studies (cid:222)nd that information technology plays a leading role in the resurgence of GDP growth in the 1990s, they also (cid:222)nd that a large part of GDP growth is left unexplained. According to our calculations, the growth rate of this residual (cid:150) called total factor 3

productivity(TFP)(cid:150)is0.4percentagepointinthe1990s, abouthalfthesizeofthe (cid:222)gures inJorgensonand Stirohand in Olinerand Sichel. This suggests at least part ofgrowthattributedtoTFPbythoseresearchersrepresentstheunmeasuredquality of capital that our approach identi(cid:222)es. When we embed this growth accounting exercise in a structural equilibrium model along the lines suggested by GHK, we (cid:222)nd that 60 percent of labor productivity growth in the postwar period comes from technological advances in E&S. Since a substantial increase in the quality of E&S was largely responsible for the growth resurgence in the 1990s, it may be reasonable to suspect that such gains are unsustainable. However, our results show that there is a great deal of potential productivity improvement that remains to be done. Based on our calculations, the technological gap between the productivity of the best technology and the productivity of the average practice in the economy was 15 percent in 1975. In 2000, the (cid:222)gure had jumped to 40 percent. The technological gap actually increased by 5 percentage points in the 1990s, despite the boom in capital spending. According to Nelson and Phelps (1966), the improvement of the average productivity of capital depends on the technological gap between the best and average technology and on (cid:147)adaptable(cid:148) labor which de(cid:222)nes human capital. We estimate an adoption equation based on this idea using aggregate data and (cid:222)nd that it (cid:222)ts very well. The growth rate of the average practice moves nearly one-for-one with the technological gap and is correlated with measures of adaptable labor (such as the shares in the labor force of college graduates and of young workers). AnotherimplicationoftheNelsonandPhelpsmodelisthatthereturnstoadaptability increase with the technological gap. We con(cid:222)rm this by showing that the returnstoeducationandthetechnologicalgapmoveinlock-stepduringthe postwar period. In particular, the technological gap stopped growing in the 1970s, the only period in which wage inequality moderated. When the gap increased in the 1980s and 1990s, wage inequality increased as well. This suggests the technological gap may be a key determinant of wage inequality. Perhaps then rising wage inequality 4

is a persistent feature of economies experiencing rapid technological improvement. Therestofthepaperisorganizedasfollows. Section2presentsasimpletheoretical model in which prices are used to measure investment-speci(cid:222)c technical change, outlinestheeconometricmethodologyweusetoconstructtheconstant-qualityprice indexes, and describes the estimation results. In section 3, we use the estimates to construct measures of technical change at the aggregate, asset, and industry levels. In section 4, we examine the implications of technical change for postwar growth. Section 5 shows that the technological gap has been growing and that it determines the speed of adoption of new technology and the skill premium. In section 6, we consider the robustness of our results to generalizations of our benchmark model. Inthe (cid:222)nal section, we summarize ourmajor (cid:222)ndingsandrelate themtoeachother. 2 Methodology 2.1 Measuring Investment-Speci(cid:222)c Technical Change Using Prices Quality improvement in investment goods is pervasive, especially in high-tech categories. For example, a new PC may have the same price today as a new PC had (cid:222)ve years ago, but if it provides 10 times as much computing power as before, in effect the constant-quality price of the new PC is one-tenth the price of the old PC. The opportunity cost of innovating (cid:150) whether it is in producing PCs or tractors (cid:150) is foregone consumption. Intuition therefore suggests that a comparison of constant-quality investment prices with a constant-quality consumption price is an informative measure of technical change. We formalize this idea in a very simple two-sector model in which an investment good and (cid:222)nal goods are produced competitively. Final goods x are produced competitively with some constant returns to scale t combination of capital and labor. They can be used for consumption or in the productionofefficiency-unitsofinvestment goodsi , accordingtothe lineartechnology ∗t i =q x , (1) ∗t t t 5

where q is a Hicks-neutral index of the state of technology used to produce investt ment goods.3 The price of investment goods in efficiency units is pi ∗ and the price t of constant-quality consumption goods is pc ∗. Competition in the investment goods t sector implies pi t ∗i ∗t =pc t ∗x t . (2) Using equations (1) and (2) we can measure investment-speci(cid:222)c technical change using prices as pi ∗ 1 pc t t ∗ = q t ⇒ ∆q t =∆pc t ∗ − ∆pi t ∗, (3) where ∆ denotes the growth rate.4 In section 6, we consider how generalizations of this basic approach (cid:150) such as mismeasurement, mark-ups and changing factor shares (cid:150) affect our (cid:222)ndings. 2.2 Data Sources Outside of computers and software, items for which BEAprovides some of the most reliableconstant-qualitypriceindexes, ourprimarysourceforconstant-qualityprice indexes is Gordon (1990). Gordon collected detailed information on prices and goods(cid:146) characteristics from sources ranging from mail-order catalogs to articles in specialized magazines like Consumer Reports and Computerworld. Using hedonic techniques as well as more conventional matched-model methods, Gordon constructed quality-adjusted price indexes that offer an alternative to the NIPA price indexes. The result is a set of quality-adjusted chain-weighted price indexes for 22 different categories of producer(cid:146)s durable equipment, covering the period 1947-83. The goods included in Gordon(cid:146)s calculations were classi(cid:222)ed into four groups: 1. Industrial equipment: Electrical transmission, distribution, and industrial apparatus; Engines and turbines; Fabricated metal products; General industrial 3Inthissimplemodel,itisirrelevantwhetherwecallq(cid:147)disembodied(cid:148)or(cid:147)embodied(cid:148)technology. Aspointed out originally by Hall (1968), in this type of model the embodied and the disembodied components are not identi(cid:222)ed separately. Following the bulk of the literature, we refer to changes in q asinvestment-speci(cid:222)c technical change. 4GHK,HornsteinandKrusell(1996),andHercowitz(1998)arriveatthesameequationinsimilar setups. 6

(including materials handling) equipment; Metalworking machinery; Special industry machinery. 2. Transportation equipment: Autos; Aircraft; Railroad equipment; Ships and boats; Trucks, buses, and truck trailers. 3. Otherequipment: Agriculturalmachinery(excepttractors); Constructionmachinery(excepttractors);Electricalequipment;Furnitureand(cid:222)xtures;Mining and oil(cid:222)eld machinery; Other equipment; Service industry machinery; Tractors. 4. Office information processing: Office, computers and accounting machinery; Communication equipment; Instruments, photocopy, and related equipment. This taxonomy of goods re(cid:223)ected the NIPA classi(cid:222)cation at the time when Gordon was writing. Luckily, the current NIPA classi(cid:222)cation is similar except for the last group of goods. BEA now distinguishes explicitly among computers and peripherals and other office and accounting machinery. Moreover, since 1999 software is recorded as investment.5 This last group of goods is now called information processing equipment and software (IPES) and the entire set of 24 investment goods is called nonresidential private (cid:222)xed investment in equipment and software (E&S). 2.3 Econometric Model We use simple forecasting methods to extrapolate for the period 1984-2000 the quality-bias implicit in some of the NIPA price series. We use as a benchmark Gordon(cid:146)s computations, which covered the period 1947-83. In addition to providing a longersample periodforstatistical analysis, we cansee whetherthere has been an acceleration in technical change in the past two decades that may help explain the surge in the growth rates of GDP and average labor productivity in the late-1990s. 5Previously,onlysoftwareembeddedinequipmentbytheproducerofthatgoodwascountedas investment. Thattypeofsoftwareisstillcountedashardware(e.g.,Microsoft(cid:146)sWindowsoperating system already installed on new PCs). 7

To construct the extended quality-adjusted price series, we update and improve upon the analysis in Krusell, Ohanian, Rios-Rull, and Violante (2000). The key idea exploits the fact that we have a long time series (1947-83) of Gordon(cid:146)s qualityadjusted and of NIPA price indexes. Using these pairs of price indexes, we estimate for each type of asset j an econometric model of Gordon(cid:146)s quality-adjusted price index as a function of a time trend and a cyclical indicator, augmented with the current and lagged values of the NIPA price series of the type: log p i ∗j =c+β t+β log p ij +β log p ij +β ∆y +εj, (4) t 1 2 t 3 t 1 4 t 1 t ! " # $ # − $ − i where p∗j is Gordon(cid:146)s quality-adjusted price index for asset category j, c is the t constant, t is the linear time trend, p ijand p ij are, respectively, the current and t t 1 − j laggedvalueoftheNIPApriceindex,∆y isthegrowthrateoflaggedGDPandε t 1 t − is the disturbance. Usingthe coefficientestimates, we canextrapolate for1984-2000 the quality-adjusted price level for each asset from the original sample. Anumberofeconometricissuesariseinthechoice ofthemodelspeci(cid:222)cation. To begin with, we had to choose the order of integration of the series. We (cid:222)rst tested for a unit root in the quality-adjusted and NIPA price index using Augmented Dickey Fuller and Phillips-Perron tests. We could not reject the null hypothesis of a unit root for any of the series.6 Next, we tested for cointegration between the quality-adjusted and NIPA price series using the Johansen test. For almost all assets we could not reject the null of cointegration at the 10 percent level and for most assets we could not reject at the 5 percent level. From this battery of tests we concluded that the quality-adjusted and the NIPA price series are I(1) and cointegrated. Hence, estimation in levels exploits the long-run comovements of the series and generates a more informative forecast compared to a speci(cid:222)cation in (cid:222)rst-differences.7 6Structuralbreakscouldbepresentinsomeoftheseries(e.g.,aircraft). Itiswellknownthatthe existenceofbreaksbiasesunitroottestsagainstrejectingthenullhypothesis. Inthemostobvious cases,wejudgmentallysplitthesampleintwoandtestedforaunitrootineachsubsample. There wereno major changes in the results. 7Wedidplentyofsensitivityanalysisonthepriceseriesforwhichtheevidenceoncointegration 8

Weuseatimetrend,laggedGDPgrowth,andlagsoftheNIPApriceindexinthe speci(cid:222)cation.8 Analternativespeci(cid:222)cationwithlagsofthedependentvariablewould have necessitated multi-step forecasting methods in which the computed forecast of thelaggeddependentvariableisusedrecursively. Giventhe16-yearspanoverwhich we need to predict our series, we prefer to anchor our forecast only to actual data. Our procedure explicitly accounts for the fact that BEA has upgraded its measurementofqualityovertime. Hence, wedonotnaivelyextrapolatethequality-bias in the NIPA price indexes from earlier to later periods. However, the admittedly disputable assumption for the accuracy of our approach is that the data generating process for the quality-bias in the NIPA price indexes has not changed since 1983. For this reason, we do not implement this procedure for most of the goods included in the IPES category, in particular computers and peripherals since BEA provides a reliable constant-quality price index for this category. We also cannot apply our methodology to software, as data on software investment were unavailable to Gordon. Instead, forsoftwareweusetheNIPApriceindexes. Byproceedinginthisway we minimize the bias that arises if the key assumption underlying our estimation and forecasting methodology is violated.9 Finally,theintroductionofcurrentandlaggedvaluesoftheNIPApricevariables in our regression implies a trade-off between accuracy in forecasting and a potential endogeneity problem. Our estimates are biased insofar as shocks to quality not controlled for in the regression affect the unadjusted price level. To assess this was weaker. Notably, we used different speci(cid:222)cations of the model in (cid:222)rst-differences with very littlechangein the extrapolated series. 8We followed a mixture of Akaike and Schwartz criteria to select the optimal order lag in each equation. In the three case in which more than one lag was statistically signi(cid:222)cant, we report in Table 1 only the most precisely estimated lag to economizeon the presentation. 9It is somewhat comforting that extrapolation isalso used byBEA and otherresearchers when bettersourcesofdataareunavailable. Forexample,theNIPApriceindexforpre-packagedsoftware (which is quality-adjusted) is back-cast from 1985 using a time series equal to 60 percent of the annual change in the NIPA price index for computers and peripherals, which corresponds to the average difference from 1985-97 between the annual rate of change in the computer price index and the pre-packaged software price index. Moreover, some authors such as Jorgenson and Stiroh (2000a)havedrawnfromtheexistingempiricalresultsofmicrostudiesonqualityimprovementsin switchinggearequipmentandspreadsheetstoconstructconstant-qualityindexesinordertode(cid:223)ate softwareand communicationsinvestment. 9

endogeneityproblem, we forecastedGordon(cid:146)s qualitybiasusingonlyaconstant and a trend. When we tried this alternative, our results were not appreciably different for most assets, suggesting such endogeneity is a secondary concern. 2.4 Quality-AdjustedPriceIndexesfor IndustrialEquipment, Transportation Equipment, and Other Equipment For the 19 goods in these categories we gather the corresponding quality-adjusted priceindexconstructedbyGordon(1990,AppendixB)fortheperiod1947-83. Then we collect the NIPA price indexes of the investment goods for the period 1947-2000 (Table 7.8, Survey of Current Business). For each category of good j, we select data from the (cid:222)rst part of the sample (1947-83) and we estimate an econometric relationship between Gordon(cid:146)s series and the NIPA series, using the model in (4) Table1containstheestimatesforeachcategoryofgoodsinindustrialequipment, transportation equipment, and other equipment. In the (cid:222)rst row, the coefficient on the linear time trend determines the extent of the quality-bias in the NIPA price index. Theestimatedtrendisstatisticallysigni(cid:222)cantfor15of19assets. Thequalitybias is largest for aircraft (15 percent), engines and turbines (6 percent), service industrymachinery(about 6percent), andspecialindustrymachinery(alsoabout 6 percent). For metalworking machinery (column 5), agricultural machinery (column 12), electric equipment (column 14), and tractors (column 19) the estimated trend was statistically insigni(cid:222)cant indicating that quality-bias in the NIPA price index is unimportant. For these assets, we suppressed the trend and used the estimates reported to extrapolate the series. 2.5 Quality-Adjusted Price Indexes for IPES Information processing equipment and software (IPES) contains the assets with the fastest rising nominal investment shares and most rapid price declines. To construct a quality-adjusted price index for computers and peripherals, we combine twodatasources. First,Gordonprovidesaquality-adjustedindexforcomputersand peripherals for 1947-83 (Table 6.12, column 2). Second, in 1985 BEA introduced 10

hedonic-basedquality-adjusted price indexes forcomputers andperipherals starting from 1958 (Table 7.8, SCB).10 We combine these two sources, using Gordon(cid:146)s index from 1947-57 and the NIPA index from 1958 onward.11 We exploit the 1999 comprehensive revision of the NIPA that provides price indexes beginning in 1959 for prepackaged software sold commercially, own-account software (software developed internally by (cid:222)rms themselves), and custom software (software tailored to the speci(cid:222)cations of (cid:222)rms and purchased externally by these (cid:222)rms). The series for prepackaged software is computed using both matched-model methods and hedonic techniques; the price index for own-account software is based on compensation rates for computer programmers and system analysts and on the costoftheintermediateinputsassociatedwiththeirwork;thepriceindexforcustom software is computed as a weighted average of the (cid:222)rst two indexes.12 The price of pre-packaged software has been falling at the fastest rate (11 percent per year). This rapiddecline has contributedto the slowdownin the rise of the overall qualityadjusted price of software: from 2 percent in the period 1959-78 to virtually zero since then.13 There are a few studies that can be used to check the adjustment BEA makes for prepackaged software. Brynjolfsson and Kemerer (1996) report that the qualityadjusted price of spreadsheets falls at an annual rate of 16 percent from 1987 to 10Evenbefore1985BEAtriedtomeasurequalitychangeinanumberofwaysusing,forexample, (cid:147)matched-model(cid:148)methods. Matched-modelmethodswouldseeminadequatewhenproductvariety expands rapidly. However, Aizcorbe, Corrado and Doms (2000) (cid:222)nd that matched-model and hedonic price techniquesshow very similar price declines for computers from 1994 to 1998. 11Kruselletal. (2000)exploitthelargeempiricalliteratureonthederivationofquality-adjusted price indexes for computers and peripherals to extend the Gordon series to 1992. As an alternative, we also constructed a constant-quality index for computers and peripherals using Gordon(cid:146)s price series until 1983 and the Krusell et al. series thereafter. The resulting price index and our benchmark index are similar in the (cid:222)rst half of the sample: for both series the average decline rate of the quality-adjusted price is around 16 percent from 1947 to 1973. However, in the second part of the sample, the benchmark series declines at an annual average of 17 percent whereas the Gordon-Krusell series declines at an annual average of 20 percent. The difference is concentrated in the late-1980s and the early-1990s. Overall, our benchmark price index provides a conservative estimate of quality improvement in computers and peripherals. 12The methodology used to construct these indexes is described in detail in Parker and Grimm (1998). 13TheaggregatepriceseriesforsoftwareinvestmentistheTornquistaggregateofthethreeprice series using theirrespectivenominal investment shares as weights. 11

1992. This is slightly faster than the 15 percent decline estimated by Gandal (1994) for 1986-91. The average rate of change of the BEA price index for prepackaged softwareis13percentperyearinthecomparableperiod,suggestingthatthequalityadjustment in the NIPA data may be fairly accurate.14 Nevertheless, the fact remains that prices for the other two categories of software are almost certainly overstated substantially. In the absence of a comprehensive alternative, we take a conservative approach and use the NIPA price index for software. Communications equipment and instruments are the other goods for which we would expect rapid price declines. Unfortunately, systematic studies of the qualitybias in the BEA price index have yet to be done: BEA has adopted a constantquality index only for digital switching equipment which is a subcategory of communications equipment (Grimm, 1997). However, the quality of other fast-growing types of telecommunications equipment has improved vastly (e.g., (cid:222)ber-optic cables). Therefore, we use the same forecasting procedure we applied to the goods outside IPES and report in Table 1 the results for communications (column 20) and instruments (column 21). Our estimated constant-quality price indexes for communications equipment and for instruments decline at an annual rate of nearly 7 percent and nearly 5 percent, respectively. By contrast, their NIPA counterparts re(cid:223)ect very little change. Finally, since Gordon(cid:146)s work does not contain a quality-adjusted series for office and accounting equipment goods other than computers, for this set of goods we simplyuse the NIPAseries(Table 7.8, SCB). It isclearthat thisconservative choice will have only a small effect since this type of investment accounts for a tiny and shrinking share of nominal E&S outlays. 14ThefactthattheBEAnumberisslightlylowermaybeattributabletothefactthatprepackaged software does not include only spreadsheets. Oliner and Sichel (1994) estimate a 3 percent annual price decline during an earlier period for a bundle of prepackaged software programs including spreadsheets, word processors and databases. Hence, evidence suggests that the price decline for softwareother than spreadsheets has been slower. 12

2.6 Quality-Adjusted Price Index for Consumption We rely entirely on the NIPAs for a constant-quality price index for consumption. Our preferred price index is constructed with the prices of nondurable goods (excluding energy expenditures which can be exogenously affected by (cid:223)uctuations in the price of petroleum) and non-housing services (from Table 7.5, SCB), weighted bytheirrespective shares (fromTable 2.2, SCB)throughaTornquist procedure. As a very basic way to assess the robustness of our results, we compared our preferred priceindextoothersthatinclude,inturn,energyexpenditures,housingservicesand residential structures. Despite our concern, the movement of these various price indexes is remarkably similar and they all grow at an annual rate of just less than 4 percent. 3 Empirical Results 3.1 Quality-Adjusted Price Index for E&S We use the Tornquist procedure to aggregate the asset-level price indexes into a quality-adjusted price index for E&S. We (cid:222)rst compute the nominal investment shares of each asset for each year. The share of asset j is the ratio of the current dollar value of investment in asset j and the current dollar value of total private nonresidential E&S investments (Table 5.8, SCB). Let s ij be the nominal share for t i investment good j 1,2,...,24 and let p∗j be the corresponding quality-adjusted t ∈{ } price index for investment of type j. Then the change in the aggregate qualityadjusted price index for E&S is 24 p i ∗j s ij +s ij ∆p i ∗e = log t t t 1 , (5) t j % =1  p i t ∗j 1  2 −   −   and the level of the price index is recovered recursively i i i p∗e =p∗e exp(∆p∗e). t t 1 t − By comparing the growth rate of the quality-adjusted price index for E&S in equation (5) to the NIPA price index for E&S we can compute the quality-bias in 13

the NIPA price index. Recall that this bias arises because we use for 21 of the 24 categories of E&S constant-quality price indexes that decline more rapidly than the comparable NIPA price indexes. According to our estimates, the average annual quality-bias is about 2.5 percent over the sample period. Perhaps surprisingly, the quality-bias is about the same in the 1980s and 1990s when computers and software (cid:150)forwhichwerelyontheNIPAde(cid:223)ators(cid:150)areagrowingshareofinvestment. The reasonisthatthereisagreatdealofquality-biasinsomefast-growingcategorieslike communications equipment. This effect approximately offsets the smaller qualitybias stemming from an increase in the share of computers and software. 3.1.1 Robustness Check Our methodology explained Section 2 is silent about the mechanism that generates quality improvement. In this volume, Wilson argues that R&D determines the rate of quality improvement. As a robustness check, we replaced the time trend in equation (4) with the log of the R&D capital stock for 10 different types of equipment from 1957(cid:151)97.15 In the bottom panel of Table 1, we also report results using the overlapping sample of Gordon(cid:146)s quality-adjusted price data and Wilson(cid:146)s R&D data. The coefficient estimates on the log of the stock of R&D is statistically signi(cid:222)cant for 8 of the 11 types of equipment. Usingtheestimatesfromthisalternativespeci(cid:222)cation,weextrapolatethequalityadjusted price until 1997 and aggregate the asset-speci(cid:222)c price indexes using the Tornquist procedure described in equation (5). The annual rate of decline for the resulting price index is 2.2 percent in the period 1984-97, which compares to a decline of 2.5 percent from our baseline estimation. Severe trend breaks in the R&D series for transportation equipment goods (cid:150) the stock of R&D for aircraft falls by almost 10percent peryearbetween1993and 1997and the stock of R&D for trucks, buses, and truck trailers falls by 15 percent per year from 1987 to 1997 (cid:150) account 15 We thank Dan Wilson for providing us with the data. The reader should refer to Wilson(cid:146)s article for a detailed description of the R&D data and the mapping between product (cid:222)elds and BEA asset categories. 14

for the slower growth rate. Hopefully, additional research will isolate the source of these sudden plunges in the R&D capital stock data. 3.2 Indexes of Investment-Speci(cid:222)c Technical Change 3.2.1 Aggregate Index Our aggregate index of the state of technology for E&S is pc ∗ qe = t , (6) t i p∗e t where pc ∗ is the consumption price index. In Figure 1, we plot the aggregate rate of t investment-speci(cid:222)c technical change ∆qe as the solid line. Two important (cid:222)ndings t emerge: (cid:222)rst, technical change grows rapidly (cid:150) at an annual average of 4 percent (cid:150) in the postwar period; second, since the mid-1970s the pace of technological improvement has accelerated: the index grows at an annual rate of about 3 percent until 1975 and at an annual rate of 5 percent thereafter.16 In the 1990s the growth has been spectacularly high, reaching an average annual rate in excess of 6 percent. We postpone discussing the dashed line in Figure 1 (cid:150) an alternative measure of technical change that adjusts for factor share bias (cid:150) until section 6. Not surprisingly, our baseline estimate of the annual growth rate of technical change is similar to Hulten(cid:146)s (1992) estimate of 3.4 percent for the comparable period, 1949-83. Hobijn (2000) calculates the rate of embodied technical change by calibrating a vintage capital model. According to his computations, the average annual growth rate of embodied technical change in equipment and structures is 2.5 percent. When we include structures in our index and assume conservatively that structureshavenoqualityimprovement,ourcomparableestimateofthegrowthrate is 2.6percent: not only are the annual averagesvery similar, the time pattern of the two series is similar as well. The production function approach used for example by 16We have excluded the 1975 outlier from both sub-samples. This outlier is present even in the original Gordon(cid:146)s data and, to a large extent, is attributable to the fact that some of his data sources for 1974 were still affected by price and wage controls, lifted a few months later. In the absence of better information on prices, we have left this entry unchanged, but the reader should be awarethat the sharp drop in the series in 1975 does not re(cid:223)ect (negative) technical change. 15

Bahk and Gort (1993) and Sakellaris and Wilson (2000) on plant-level data yields estimates of the growth rate of capital-embodied technical change between 12 and 18 percent per year, much larger than our estimate. 3.2.2 Asset Indexes The index of the state of technology for a speci(cid:222)c asset j is constructed as qj = pc t ∗ . (7) t i p∗j t Table 2 reports the pace of technical change in each of the 24 asset categories as well as for the components of software. Not surprisingly, the largest gains are in IPES: productivity improvements for computers increased at an annual average of 23.5 percent, with a peak growth rate of 26.5 percent in the 1960s and in the 1970s. Technical change in prepackaged software also advanced at a swift pace, increasing at an annual average of 15 percent over the period, with a peak growth rate of 18 percent in the 1970s. Interestingly, for both computers and software there was a slight decelerationinthe pace of growthinthe1980sandthe 1990scomparedtothe previous decade. The productivity level of communication equipment advanced at an annual average of 9 percent in the postwar period. In contrast to computers and software, the 1990s witnessed a sharp acceleration in the rate of growth for communications, reaching 13 percent. The productivity level of aircraft also advanced rapidly,atanannualrateof9percentand11percentinthelasttwodecades. Atthe sametime, therearecategorieswithverylittletechnicalchange, suchasagricultural machinery, metalworking equipment, and own-account software.17 A careful review of Table 2 shows that in most categories outside IPES productivity growth accelerated only in the 1990s. One possible interpretation of this pattern is that in a (cid:222)rst phase (1970s and 1980s) productivity advancements were concentrated in IPES goods, while later (in the 1990s) the new technologies started 17Asexplainedearlier,forown-accountsoftwareweusetheNIPApriceindexwhichisnotqualityadjusted. 16

to be applied to a much wider range of goods beyond IPES, fully displaying the (cid:147)general purpose(cid:148) nature of the new technology. 3.2.3 Industry Indexes We also construct measures of technical change at the two-digit and (cid:222)ner industry level using BEA(cid:146)s detailed estimates of E&S investment by industry and type of asset, which are based on a variety of source material including the input-output tables.18 Our industry-level measures of technical change are obtained through the same Tornquist aggregation procedure we adopt for the economy-wide index in equation (5), where each asset-speci(cid:222)c constant-quality price index is weighted by the industry-level nominal expenditure shares for that asset.19 These indexes measure the rate of technological improvement in the typical mix of investment goods used in production by each industry. Table 3 documents the growth rates of technical change for 11 major industries by decade. Wide variation in the growth rates is apparent: quality improvements in investment goods used in the communications industry advanced at an 8 percent annual rate during the postwar period, while agriculture, forestry and (cid:222)shing experienced a relatively dismal 1 percent annual growth rate.20 To appreciate such heterogeneity, in Figure 2 we plot the annual distribution of technical change (cid:150) 90th percentile, median, mean and10th percentile (cid:150)usingthe most detailed classi- (cid:222)cation of 62 industries available using our data. Each industry-year observation is weighted by the nominal industry investment share that year. Two (cid:222)ndings stand outfromFigure 2: (cid:222)rst, thereisalot ofheterogeneityacrossindustriesasevidenced by the 6 percentage point annual average difference between the 90th and 10th percentiles of the distribution; second, over the years this differential has remained 18The data are available fromwww.bea.doc.gov/bea/dn/faweb/Details/Index.html. 19The implicit assumption in this procedure is that the bulk of the variation in rates of technologicalchangeacross industriescan beattributed tothedifferent mixofinvestment goodsbetween our 24 categories rather than within each category. 20ThenegativeestimateforAgriculture,Forestry,and Fishinginthe1970sre(cid:223)ectsintensiveuse oftractors,whichareestimatedtohavenegativeratesoftechnicalchangeforanumberofyearsin the1970s. 17

quite stable and has moved in tune with the mean which suggests that the IPESled technological acceleration that began in the mid 1970s had a general impact, reaching virtually every industry in the economy. As another way to assess the general impact of IPES, we calculated the transition probability for industries within the distribution. In the last two decades, the persistence of an industry(cid:146)s relative position in the distribution has increased signi(cid:222)cantly.21 This suggests that productivity improvements in the best-practice technology are more the result of an aggregate shock, rather than industry-speci(cid:222)c shocks. Taken together, our (cid:222)ndings con(cid:222)rm the idea that IPES is a (cid:147)general purpose(cid:148) technology. 3.3 Quality-Adjusted E&S Capital Stock We create a quality-adjusted investment series i by dividing nominal E&S invest- ∗et i ment by the quality-adjusted price index p∗e. Then we construct the aggregate t quality-adjusted productive capital stock of E&S k using the perpetual inventory e∗t method and a constant geometric rate of depreciation: k =(1 δe)k +i , (8) e∗t t e∗,t 1 ∗et − − where δe is the time-varying physical depreciation rate. t As Oliner (1993), Gort and Wall (1998) and Whelan (2001) show, physical depreciation must be used to construct the quality-adjusted productive capital stock when investment is measured in efficiency units. Largely as a result of Oliner(cid:146)s research, BEA began to construct its capital stocks correctly, but only for the assets Oliner studied, mainframes and peripherals. For every other type of asset, BEA continues to construct capital stocks using economic depreciation. This causes the capital stock to be mismeasured, especially for the types of assets that are subject to rapid quality improvement over time, such as PCs, prepackaged software and 21If we divide the cross-industry distribution of technical change into quartiles and weight each industry by its nominal investment share, the diagonal elements of the transition matrix are on average0.45 during the postwar period, rising to 0.70 during the1990s. 18

communication equipment.22 BEA reports economic depreciation rates by asset dj (Tables A-B-C in BEA, t 1999). Parker and Grimm (2000) report the depreciation rates BEA uses for software: 55 percent for pre-packaged software and 33 percent for own-account and custom software. Fraumeni (1997) describes the methodology for calculating these depreciation rates: in most cases, BEA still uses the numbers created by Hulten and Wykoff (1981), which include both physical decay and obsolescence. Economic depreciation for an asset of type j is de(cid:222)ned and measured by BEA as the change in the value of an asset associated with the ageing process, so it consists of a pure age effect and a time effect. The age effect captures physical decay δj due to wear t and tear and the time effect captures obsolescence due to the change in the relative price of the asset in the period, qj/qj . Thus, t t 1 − qj dj =1 1 δj t 1. (9) t − − t q −j # $ t Obviously, when there is no technical change, economic and physical depreciation are identical. However, when technology improves, economic depreciation exceeds physical depreciation. Using the identity in equation (9), we separate the physical decay component δj from the BEA measures of d to appropriately construct the t t aggregate series for k . e∗t For each asset category j, we use the official depreciation rates and equation (9) (cid:150) where we measure qj from equation (7) (cid:150) to back out the actual physical t decay rate δj. As suggested by Whelan (2000), we then aggregate these physical t depreciation rates in each year using the nominal capital shares of each asset in the totalE&Scapitalstockskj (wecompute these nominal capital sharesfromthe BEA Fixed Assets Tables), in order to obtain a series for the physical depreciation rate 22The Bureau of Labor Statistics (BLS) measures of the productive capital stock suffer from a similarproblemandsodothecapitalstocksconstructedbyresearcherswhofollowtheleadofBEA andBLS.AlthoughBLSusesahyperbolicdepreciationrateratherthanageometricone,theytune the hyperbolic pro(cid:222)le so that it is consistent with BEA(cid:146)s geometric rate of economic depreciation. To understand how wrong the calculations may be, keep in mind that BEA and BLS construct their capital stocksof prepackaged software based on a 55 percent depreciation rate. 19

in E&S δe, t 24 δe = δjskj. t t j=1 % Figure 3 plots three series: the official economic depreciation rate de, our comt puted series for physical depreciation δe, and a polynomial-smoothed version of our t series.23 The BEA rate of economic depreciation rises from 12 percent in the 1950s to over 15 percent at the end of the sample, while our estimated series, although very volatile because of the variability implicit in our measures of technical change, looks trendless at 10 percent. Hence, the gap between economic depreciation and physical depreciation that opened up inthe mid-1970s canbe attributed to losses in the value of assets because of faster obsolescence. The rise in the importance of the obsolescence component over time is principally due to the increasing share of IPES in the capital stock. To parallel the practice of the BEA of using constant depreciation rates, even for long periods, in what follows we always use our smoothed series. Perhapssurprisingly,wefoundthatourquantitativeresultswerelittleaffectedusing the non-smoothed physical depreciation rates. In Table 4 we compare the growth rates of our quality-adjusted capital stock ∆k and the BEA capital stock ∆kBEA. Our capital stock of E&S, which is based e∗ e on quality-adjusted investment (cid:223)ows and physical depreciation, grew at an annual average rate of 8.8 percent in the postwar period. By contrast, the BEA capital stock, which is based on quality-adjusted investment (cid:223)ows for a subset of assets and economic depreciation, grew at an annual average of 5.8 percent in the postwar period. About80percentofthedifferencebetweenthegrowthratesisduetomissing quality-adjustment in the BEA price indexes. The residual is due to the presence of obsolescence in the official depreciation rates.24 23Wedonot(cid:222)lterouttheobsolescencecomponentfrommainframesandperipherals,astheBEA depreciation rates for these goods are net of this component (see Oliner 1993 for details). For autos and PCs, BEA does not report a geometric depreciation rate, but rather an age-dependent depreciation schedule. We approximate these with a constant geometric rate of 25 percent and 40 percent per year, respectively. 24We also computed the difference between the growth rate of our series and the growth rate of a series constructed using investment valued in terms of consumption and economic depreciation. The overall difference between the annual growth rate of our series and this alternative series is 20

Given the emphasis on the role of IPES capital in explaining US growth in the pastdecade,itisinterestingtocomputethedynamicsoftheIPEScapitalstock. Asa by-product, we can use this quality-adjusted IPES capital stock as a separate factor of production in our growth decomposition. In order to compute a rate of physical decay for the stock of IPES goods, we repeat the same procedure outlined above. Our estimated depreciation rate is substantially lower than the NIPA series (the difference is 5 percentage points at the beginning of the sample and 7 percentage points at the end of the sample); moreover, our implied rate of physical decay displays a rise at the beginning of the 1980s (from 13 to 16 percent), consistent with BEA(cid:146)s claim that the physical depreciation rate for computers and peripherals increasedfrom27percent to31percent after1978.25 Theresultingquality-adjusted productive capital stock for IPES reported in Table 3 grows at an annual average of 16.3 percent over the sample, compared to an annual growth rate of the BEA series of 12.3 percent. The decomposition of this differential between quality-adjustment of the investment (cid:223)ows (namely communications and instruments, as for all other IPES goods we have used BEA data) and the presence of obsolescence in economic depreciation yields about the same 80-20 split as the decomposition for aggregate E&S. 3.4 Structures Capital Stock For growth accounting, we need to integrate the structures capital stock into our framework. To de(cid:223)ate nominal investment in structures, we use the NIPA price indexes for 19 different categories of structures. On aggregate, this price index for structures grew just a little faster than the price index for consumption in the 3.7 percent. Gort and Wall (1998) show that if both the physical decay rate δe and the rate of obsolescence∆q (technicalchange)areconstant,thenthedifferencebetweenthetwoseriesshould beexactly∆q,whichis4percentforourseries. Thus,giventhatδeisabout(cid:223)at,the0.3percentage t point differential is fromthe large variation of ∆q . t 25Although computers and software have very high depreciation rates, the overall depreciation rate (even before accounting for obsolescence) for IPES is much lower because computers and softwarerepresent asmallshareofthecapitalstock: untiltheearly-1990scomputers andsoftware constituted less than one-third of the total stock of IPES goods. 21

postwarperiod, whichimpliesthat there wasnoappreciablequalityimprovementin structures. However, according to Gort, Greenwood and Rupert (1999), structuresembodied technical change advanced at an annual rate of 1 percent in the postwar period. Hence, we might underestimate the growth rate of structures by using the NIPA price indexes. Nevertheless, in keeping with our conservative approach, we use the NIPA price indexes. Creating an aggregate stock of equipment and structures in efficiency units (k ) t∗ takes three steps. First, we construct a price index for total business (cid:222)xed investment by weighting the two price indexes for E&S and structures by their nominal investment shares. Second, we calculate a physical depreciation rate for business (cid:222)xed investment. In doing so, we compute an average depreciation rate for structures of about 3 percent per year.26 Finally, we construct the aggregate capital stock using the perpetual inventory method and a constant geometric rate of physical depreciation. 4 Growth Accounting 4.1 (cid:147)Statistical(cid:148) Growth Accounting Using statistical growth accounting we can attribute the growth in real GDP to the share-weighted growth in inputs and, in particular, to quality improvement in capital goods. It is straightforward to show that our simple theoretical model in Section 2.1, together with equation (8) can be interpreted as a one-sector growth model with an aggregate production function. In our accounting framework, we use a Cobb-Douglas speci(cid:222)cationfor the production function and we measure real GDP in constant-quality consumption units. We focus on the domestic private business sector of the US economy. A standard computation yields a labor share with an average value of 0.64 for the period 1947-2000. We measure real GDP growth in the 26Wecomputethisnumberbyaggregatingasset-speci(cid:222)cBEAdepreciationrateswiththeirnominal capitalstockshares. Gort,Greenwood andRupert separate theobsolescencecomponent from economic depreciation and estimate a physical rate of decay of about 2 percent per year. This is consistent with ournumber, given Gort, Greenwood and Rupert(cid:146)s estimate that thereis1 percent unmeasured technicalchangeembodied in structures. 22

private business sector directly from NIPA (Table 1.8, SCB). When decomposing the sources of real GDP growth, we distinguish between the contribution made by the quality of capital (Q ) and by the quantity of capital t k(cid:152) . The quantity of capital is measured in terms of constant-quality consumption t #unit$s. The quality of capital is measured as the ratio of the quality-adjusted capital stock(k )andthecapitalstockmeasuredintermsofconstant-qualityconsumption: t∗ Q = k /k(cid:152) . Hence, the quality of capital isolates the contribution to real GDP t t∗ t growth from our quality-adjusted investment price indexes.27 To measure labor input l , we use the quality-adjusted index created by Ho and Jorgenson (1999, t Table 5) which allows us to distinguish between quantity of labor (hours worked n ) t and quality of labor (h ), with l =h n .28 t t t t Our statistical growth accounting is based on decomposing real GDP growth ∆y into the share-weighted growth in inputs t ∆y =(1 α)∆h +(1 α)∆n +α∆k(cid:152) +α∆Q +z , t t t t t t − − where αdenotesthecapitalshare. InTable5, we reporttheresultsofthestatistical growthaccountingforavarietyofperiods.29 Inthepostwarperiod, thetotal contribution of capital to real GDP growth is nearly 54 percent, whereas the contribution of labor input is 32 percent. TFP growth accounts for the remaining 14 percent of growth. The contributions of both capital and labor grow steadily over the sample periodattheexpenseofTFP,whichhasanegativecontributioninthelast20years. Out of the 54 percent average contribution of capital, about 20 percent is due to quality improvement in total capital. In the 1990s the contribution jumps to more 27Noticethatthequalityofcapitalwemeasureisnottheusualone,de(cid:222)nedasthedifferencebetweencapitalservicesandcapitalstockscreatedwithNIPApriceindexes. Thatdifferencemeasures the composition effect of moving toward assets with short service lives and, hence, high estimated productivity during each year of service. In future research, we plan to combine approaches by constructing thecapital services of our quality-adjusted capital stock. 28Ho and Jorgenson(cid:146)s index is constructed for total private sector, including business sector, private households and non-pro(cid:222)t institutions. Private households are not a major source of employment,butthereremainsaslight discrepancybetweenouroutputmeasureandthelaborindex due to the non-pro(cid:222)t sector. 29We begin in 1948 and end in 1999 because the labor index constructed by Ho and Jorgenson spans that period. 23

than 30 percent. Since the contribution of every other factor falls or is about (cid:223)at in the 1990s, our (cid:222)ndings indicate that the jump in the quality of capital in the 1990s explains the resurgence in real GDP growth. As we would expect, the contribution of productivity improvement in IPES capital grows enormously over the sample, from just 1 percent in the 1950s to over12percent inthe 1990s, averaging6 percent in the postwar period.30 By contrast, the contribution of worker quality was very high in the 1950s, but it falls sharply in the 1980s and the 1990s, possibly because of the entry of the baby-boom cohorts in the late 1970s and because the strong labor market of the 1990s absorbed predominantly workers from the lower part of the skills distribution. A number of authors (e.g., Hulten, 1992, Jorgenson and Stiroh, 2000a, 2000b) argue that GDP should be quality-adjusted in proportion to the division between consumption and investment. For comparability, we create a Tornquist price index from personal consumption expenditures (Table 10.1, SCB) and from business (cid:222)xed investment, where we use our quality-adjusted price index for the lattercomponent. Real GDP growth computed in this way is on average 0.3 percentage points greater than GDP measured in constant-quality consumption units, but this difference is twice as large in the 1990s. As a result, we (cid:222)nd that the contribution of capital and labor is smaller in the 1990s, implying a larger contribution of TFP, which is no longer negative. The TFP contribution remains positive in the 1980s and increases substantially in the 1990s. We analyze the effect of this pick-up on labor productivity in the late-1990s in more detail in Section 4.3. Hulten (1992) found that embodied technical change explained 20 percent of growth in manufacturing sector output from 1949-83. Our comparable estimate for the whole economy is much higher, nearly 40 percent in the same period. Jorgenson 30To identify the contribution of growth in IPES goods for the growth of the aggregate capital stock between timet and t", we use the Tornquist decomposition ∆k = s k t ipes+s k t! ipes ∆k + sk t other +sk t! other ∆k t − t! # 2 $ ipes,t − t! 2 other,t − t! * + where s denotes thenominal share in the total capital stock at time t. t 24

andStiroh(2000a, Table 2) report the contributions of various inputsforthe period 1959-98: intheircalculations the quantityof capital contributes36percent, capitalembodied quality improvement contributes 13 percent, and labor input contributes 34 percent. This implies TFP accounts for 17 percent of growth. Despite the fact that we (cid:222)nd a similar contribution for capital in efficiency units, our estimates suggest that amuch larger fractionis due toquality. We also compute the contribution of labor to be roughly 3 percentage points smaller, which boosts up by the same amount our estimate of the share of TFP growth. 4.2 (cid:147)Equilibrium(cid:148) growth accounting One disadvantage of statistical growth accounting is that it does not isolate the underlying sources for capital accumulation. As a result, such growth accounting is silent about whether, for example, the quantity of capital increased because there were advances in the productivity of new investment goods or because of TFP. By contrast, a structural equilibrium model can be used to solve for the optimal investment policy rule as a function of the underlying sources of growth of the economy. Our economy displays three sources of growth in per capita income (or labor productivity y /n ): technical change in producing capital q , quality improvement t t t in labor h , and total factor productivity z . Assuming that all three sources of t t growth are exogenous, it is a simple exercise to use the solution of an equilibrium model to attribute income per capita growth entirely to the three sources.31 We (cid:222)nd that technological advance in producing capital dwarfs the other two sources of growth: 60 percent of growth from 1948-99 is explained by quality improvement the production of capital, 25 percent is due to improvements in the quality of labor (essentially linked to the rising educational attainment of the population), and the residual 15 percent is due to neutral technical change. Our results are in line with the equilibrium growthaccounting exercise ofGHK whoquanti(cid:222)edthe contribution 31In a mathematical appendix available from the authors we derive the model we use for the calculations. 25

of q for the whole economy to be 58 percent from 1954(cid:151)90.32 t 4.3 Productivity Surge in Late-1990s: Cycle or Trend? The performance of the US economy in the second half of the 1990s has been remarkable. According to our calculations, real GDP growth in the private sector averaged 5.2 percent per year from 1995 to 1999, while the average in the preceding two decades was just below 3.5 percent. This large acceleration in real GDP growth hasgeneratedadebateamongeconomistsabout(1)whetherIPESinvestmentdrives the acceleration, and (2) whether the upturn is cyclical or structural. Jorgenson and Stiroh (2000a) and Oliner and Sichel (2000) suggest that IPES investment is key to the productivity acceleration of the late 1990s. For example, OlinerandSichelcomputethatover40percentofthelaborproductivityacceleration of the late-1990s compared to the 1973-95 period is due to capital deepening from IPES investment. Jorgenson and Stiroh(cid:146)s computations imply a somewhat smaller (cid:222)gure, around 35 percent. In both calculations, TFP accounts for the remaining growth, with labor quality playing a very small role.33 Both studies document that the TFP acceleration is large even in industries that do not use IPES intensively. However, neither study attempts to disentangle the cyclical and structural components of the upswing. Gordon (2000) offers a more skeptical view about the role of IPES investment. According to Gordon, more than one-third of the labor productivityresurgence ofthe late 1990sis acyclicalphenomenon. Moreover, he (cid:222)ndsthat the bulk of disembodied productivity acceleration is concentrated in IPES-intensive industries, with other industries gaining little if anything from the (cid:147)IT revolution(cid:148). InTable6,wereportourowndecompositionoftheincreaseinthegrwothrateof labor productivity in the late-1990s. For this exercise, we use real GDP constructed with a price index that includes our constant-quality investment price index, as in 32Ourdataimplythatthecontributionofq intheGHKsampleperiodisslightlylowerofwhat t they found, around 54 percent. We attribute a much smaller role to the residual component z , t because they did not account for quality improvementsin labor input. 33Both studies report that capital deepening outside of IPES categories has decelerated and therefore hascontributed negatively. 26

the right panel of Table 5. We distinguish among capital deepening, labor quality changes, and TFP. According to our calculations, the growth rate of labor productivity increased from an annual rate of 1.77 percent in 1973-94 to an annual rate of 2.64 percent in 1995-99, a pick-up of 0.87 percentage point. This is a somewhat smaller increase than reported by Gordon (2000) and by Oliner and Sichel (2000), but closer to Jorgenson and Stiroh (2000a) and BLS. The (cid:222)rst column con(cid:222)rms that capital deepening helps drive the recent increase, contributing over 42 percent. This number hides a difference with the previous studies: in our calculations, IPES accounts for only 25 percent of the total productivity surge whereas other investment goods contribute the rest. It is worth noting that the entire surge in capital deepening is due to quality improvement, with the quantity of capital measured in consumption units contributing negatively. Consistent with other studies, we (cid:222)nd that the dominant force in the increase in labor productivity growth is TFP. To analyze whether the increase is temporary or permanent, we split each component of labor productivity into cycle and trend using a Hodrick-Prescott (cid:222)lter. The commonly used smoothing parameter for annual data is λ = 100, but recently Ravn and Uhlig (2001) argue that the best choice is λ = 6.25 which implies a more volatile trend component. Thus, with a lower λ we would expect to obtain a lower bound for the cyclical component. We (cid:222)nd that the cyclical component of the increase in labor productivity growth is bounded between 30 percent and 90 percent. Hence, Gordon(cid:146)s estimate of one-third could well be conservative.34 From Table 6, we also conclude that the deceleration in labor quality is mostly a cyclical phenomenon (probably associated with a strong labor market that drew from the bottomtail ofthe skillsdistribution), while the acceleration inthe qualityofcapital is a structural phenomenon. The large gap between the upper and lower bound in the estimation of the cyclical component is linked to TFP: the data cannot disen- 34Thisisthecyclicalcomponentfortheperiod1995-99extracted(cid:222)lteringthewholeseriesforthe period1948-99. Therearetworeasonswhythiscouldbeaninaccurateestimate: (cid:222)rst,thebusiness cycle was not completed in 1999 because real GDP had not reached a turning point; second, any (cid:222)lter tends to bemore imprecise at end-points. 27

tanglewhetherthe surgeinTFPbelongstothecycleortothetrend. Theanswerto thisquestionwillhelpdeterminewhetherthestronglaborproductivityperformance of the US economy will extend beyond the typical length of an expansion. 5 Technological Gap and Its Effects 5.1 Technological Gap Between Productivity of New Vintages and Average Practice Hulten (1992) shows that quality-adjusted price indexes can be used to measure the (cid:147)technological gap(cid:148) between the productivity of new vintages and the average practice in the economy. Let the average efficiency level of E&S be Qe = k /k , t e∗t et where k is the quality-adjusted stock of E&S and k is the stock of E&S measured e∗t et , in constant-quality consumption units. Then the technological gap is given by the , following expression qe Qe Γe = t − t. (10) t Qe t The dynamics of this index are determined by the speed of the leading edge technology relative to the pace of investment growth.35 Figure 4 plots the evolution of Γ separately for E&S and for IPES. The techt nological gap for E&S was about 10 percent in the 1950s, rising to 20 percent in the 1960s. After holding steady in the 1970s, the gap rises again in the 1980s and 1990s, when it reaches 40 percent. This represents a truly amazing upsurge in the average technological gap in the economy.36 Interestingly, although the gap for IPES is always greater than that for E&S, the difference between the two opens up dramatically from the mid-1970s to the mid-1980s. The difference evaporates in the 1990s when the technological gap in IPES remains about constant. This pattern can be explained by the substitution between different types of E&S following 35Hulten calls this measure the (cid:147)elasticity of embodiment(cid:148) because it also measures how investment in the frontiertechnology feeds back into the growth rateof the averagelevelof efficiency. 36Hulten(1992)computedestimatesofΓ foronlythemanufacturingsector. Hereportsanavert agevalue of 23 percent fortheperiod 1949-83,and 22 percent for the sub-period 1974-83. Forthe samesampleperiods,ourestimatesare17percentand20percent,respectively. Thedifferencescan beattributedtomanyfactors: includingupdatedestimatesforcomputerandsoftwareinvestment, sectoral differences, different rates of depreciation used to construct the capital stock. 28

the sharp changes in their relative quality-adjusted prices. The period 1975-85 witnessed phenomenal technological advances in IPES, but these technologies were not yet widespread in the workplace. Firms started substituting to IPES from other equipment, thus investment in IPES started to grow rapidly. As a consequence, the technological gap for IPES closes down gradually. Figure 5 plots the distribution of the technological gap for E&S in our 62 industries. Although the increase in technological gap for the economy depicted in Figure 4 is evident at every quantile of the industry distribution, Figure 5 shows a rise in the difference between the 90th and 10th quantile over time. In 1968, the technological gap of the 90th percentile was 30 percent and the technological gap of the 10th percentile was 10 percent. Thirty years later, these two numbers are 55 percent and 20 percent, respectively. Given that the productivity of new vintages accelerated at about the same rate across all 62 industries (see Figure 2), this latter (cid:222)nding suggests that the speed of adoption of new technologies has been very different across industries. This is con(cid:222)rmed by comparing the technological gaps by 11 major industries in Table 7. In the 1990s, for example, the technological gap in communications was 60 percentage points greater than in agriculture, forestry and (cid:222)shing. 5.2 Adoption of New Technologies and Returns to Human Capital Althoughathoroughexaminationofthedifferentpatternsofadoptionacrosssectors isbeyondthescopeofthispaper, adeeperlookattheaggregatedataisauseful(cid:222)rst step. In their in(cid:223)uential paper, Nelson and Phelps (1966) conjecture that (cid:147)[T]he rate at which the latest, theoretical technology is realized in improved technological practice depends upon educational attainment and upon the gap between the theoretical level of technology and the level of technology in practice(cid:148) (p. 73). In terms of our notation, the discrete-time version of theirequation(8) at the aggregate level is ∆Q =φ(h )Γθ , (11) t t 1 t 1 − − 29

where φ(h ) is an increasing function of human capital stock in period t 1 and t 1 − − ∆Q is the growth rate in the average practice between period t 1 and period t.37 t − Given that we have data on Q , Γ , and human capital we can estimate equation t t (11) using OLS by taking logs and appending a stochastic error term, which we assume is orthogonal to the regressors. Ho andJorgenson (1999) construct anindex of the quality of the labor force in the US in the postwar period based on several dimensions: age, education, gender, and occupation. When we estimate equation (11), we enter each of these different measures of human capital: age is proxied by the share of young workers aged 16-24, education by the share of college graduates, gender by the share of female workers, occupation by the share of self-employed. The results of the estimation are reported in Table 8. The coefficient on Γ in column (5) is about 0.7 and statistically signi(cid:222)cant t 1 − fromzero. Byitselfourmeasureofthetechnologicalgapcapturesroughly85percent of the variation in the growth rate of the average practice over time (column (1)). The residual 2 percent is explained by human capital: the shares of young workers, and college educated workers are positively associated with more rapid adoption of new technology, while the fraction of self-employed workers is not statisitically signi(cid:222)cant. Hence,certainobservablemeasuresof(cid:147)adaptability(cid:148)dodeterminewhether newtechnologyisadopted,buttheydonotexplainalargefractionofthetime-series variation. Nevertheless, the coefficient on the skilled share is remarkably high: a 1 percentage point increase in the share of college-educated workers induces a 10 percent acceleration in the speed of adoption (i.e., the growth rate of Q rises by t 10 percent). More puzzling at (cid:222)rst is the negative and signi(cid:222)cant estimate on the share ofwomeninthelaborforce. Laborforceparticipationofwomenhasincreased massively: in1950womenaccounted forless thanone-thirdofthe laborforce, while in 1999 the share of women was close to 50 percent. Many models of labor force participation imply that the rise in participation rates takes place from the top of 37We slightly generalize the adoption equation by introducing the parameter θ which measures the elasticity of the growth in average practice to the technological gap. In Nelson and Phelps(cid:146) originalformulation θ isrestricted to equal 1. 30

the ability distribution. Thus, the share of women is negatively correlated with the average level of unobserved ability among women and therefore in the workforce. According tothis interpretation, the negative sign in the regression picks up the fall in unobserved ability and suggests that the latter is an important determinant of technology adoption.38 Since our (cid:222)rst pass at the aggregate data is so encouraging, in future research we plan to estimate the adoption equation at the industry level. Another implication of Nelson and Phelps(cid:146) adoption equation (11) is that a larger technological gap increases the marginal productivity of skilled workers and hencetheirrelative wage. The time-seriesbehaviorofthe technological gapforE&S squares with the well-known facts on wage inequality. The gap increases steadily except when it levels off during the 1970s, which is the only decade in the postwar period during which the education premium fell. In Figure 6, we compare the returns to college education from Goldin and Katz (1999) and a smoothed version ofthetechnologicalgapforE&SplottedinFigure4.39 Thetwoseriesmovetogether at low frequencies, consistent with the idea that the technological gap may be an important force driving the skill premium. 6 Robustness Ourbasicapproachabstractsfromanumberofpotentiallyimportantconsiderations. Paramount among these is how our measures of technical change would be affected by changing factor shares, mismeasurement of constant-quality consumption, and ignoring mark-ups. 38Whenweexcludetheshareofwomenfromtheregression,seee.g. column(2),theestimateon thecollegesharevariablebecomes insigni(cid:222)cant. This is consistent with our interpretation because the large rise in college enrollment (the bulk of which is explained, again, by women) is likely to have taken placefrom the top of theunobserved ability distribution. 39Goldin and Katz (2000) report the returns to college computed through the decennial Census starting from 1940. To obtain a continuous time series, we interpolate linearly between successive decades. 31

6.1 Factor Shares The one-to-one mapping between the change in the relative price and the rate of technical change may break down when the shares of capital in the consumption and investment goods producing sectors differ. In such a model, with competitive markets and free factor mobility, it is simple to establish that the change in the relative price consists of two components ∆pc t ∗ ∆pi t ∗ =∆q t αc αi ∆κ t , − − − # $ where αc and αi are the capital shares in the consumption and investment sectors, respectively, and ∆κ is the growth rate of the economy-wide capital-labor ratio. t We can assess the extent of the share-bias by constructing sector-speci(cid:222)c capital shares and the capital-labor ratio. De(cid:222)ne the investment goods sector as durable goods manufacturing and business services, which is dominated by software manufacturers, withthe consumption goods sector consisting of the remaining industries. Such abreak-down is not perfect, mostly because durable goods manufacturers produce at least some consumption goods. Nevertheless, classi(cid:222)cation errors do not affect the (cid:222)nding that the consumption goods sector is considerably more capital intensive than the investment goods sector. According to our calculations (cid:150) based on data since 1948 when full-time equivalent worker data at the industry level are (cid:222)rst available (cid:150) αc = 0.45 and αi = 0.26. Since the capital-labor ratio was growing at about a 4.5 percent annual rate, our baseline measure of technical change underestimates actual growth by nearly 0.85 percentage point annually since 1948. Moreover, this number is larger in the second part of the sample, suggesting that the acceleration of the 1980(cid:146)s could be slightly larger. In Figure 1, we plot as a dashed line the bias-corrected series for technical change. 6.2 Mismeasurement Our measure of investment-speci(cid:222)c technical change is biased upward when quality improvementinconsumptionisneglected. SupposeNIPAconsumptionpriceindexes 32

pc understate quality by a factor uc so that pc = ucpc ∗. Using this relation with t t t t t equation (3), we conclude that the change in the price of investment relative to consumption overestimates technical change when ∆uc >0. t The similarity we discussed in section 2.6 between various consumption price indexes gives us some con(cid:222)dence that our measure is not seriously distorted. Nevertheless, it would be preferable to construct a constant-quality consumption price index using the sort of approach we adopt for measuring constant-quality investment. Unfortunately, the dataforsuch an exercise are simply not available. Indeed, there are no studies documenting by how much the personal consumption expenditures de(cid:223)ator (PCE) neglects quality improvement over the period we consider. We can get some idea from Moulton (2001), who documents the expanding role of hedonic methods in the official statistics: currently, almost 20 percent of (cid:222)nal expenditures is de(cid:223)ated through hedonic price indexes. Much of the adjustment is in durable consumption goods (e.g., PCs, apparel, audio and video equipment, refrigerators, and microwave ovens). Among services, only housing rents are adjusted for quality. Although BEA has consistently upgraded its methods of accounting for quality improvement, most commentators express the view that quality adjustment for many goods is still insufficient (see, Wilcox and Shapiro 1996 and Lebow and Rudd 2001). It is tempting to conclude that the bias has increased over time due to increased expenditures on high-tech durables. But this would be incorrect because, as argued above, methods for accounting for quality have also improved. Moreover, a discussion about whether the bias is, say, zero or 1 percentage point is secondary in our application. The quality bias in investment goods that we correct for is so large as to swamp even the largest estimates of the quality bias in PCE. 6.3 Mark-ups Finally, in our simple model we assumed that goods markets are competitive. The presenceofmark-upsinthe investment andinthe consumptiongoodssectorswould 33

also change our key equation (3). Recall that we measure technical change in terms of growth rates, so constant mark-ups would leave our results unaffected.40 Timevarying mark-ups do pose a problem since we would attribute changes in markups to changes in the state of technology. In particular, slower-growing (or faster declining) mark-ups in the investment good sector would bias upward our measure of investment-speci(cid:222)c technical change. Ourindustry-leveldataenable ustogetafeelforhowmark-upsintheconsumption and investment sectors have evolved.41 Denote the non-competitive price as p t so that p = (1+(cid:181) )p , where p is the competitive price and (cid:181) is the mark-up. t t t t t , From the de(cid:222)nition of pro(cid:222)ts, Π = p y c , where y is output and c is the cost t t t t t t , − of production. From the relation p y =c , it follows that (cid:181) =π /(1 π ) where π t t t t t t t , − is the pro(cid:222)t rate, i.e. π = Π /(p y ), which can be calculated for the consumption t t t t and investment good sectors using our data. , Two conclusions emerge from these calculations. First, mark-ups have been falling in both sectors: in the investment (consumption) sector mark-ups decline from 23 (13) percent in the 1950s to 7 (8) percent in the early 1980s, and then they remain steady until 2000.42 Although this suggests that the growth in our aggregate index of investment-speci(cid:222)c technical change could be overestimated by 0.25 percentage point per year, quantitatively this bias is very small. Second, mark-ups in the investment goods sector are growing faster than mark-ups in the consumption goods sector since the 1980s. This bias leads to an underestimate of the recent technological acceleration. 40Different models of imperfect competition, such as the one Hobijn (2001) develops, do not necessarily lead to the same conclusion. 41Weclassifytheconsumptionandinvestmentgoodssectorsinthesamemannerasdescribedin Section 6.1. 42Domowitz, Hubbard and Petersen (1986) estimate largerprice-cost margins in the US (on the order of 26 percent in both sectors) between 1958-81. However, in acompanion paper (Domowitz, Hubbard and Petersen, 1988) theymodify theircomputation andessentially calculatepro(cid:222)t rates, as we do (Table 5, page 64). This adjustment reduces their estimate by 10 percentage points on average, leading to estimates of mark-ups in line with our numbers. 34

7 Conclusion The quantitative importance of productivity improvement in investment goods is a central issue in a number of macroeconomic debates (on rising wage inequality, the productivity slowdown and resurgence, and the dynamics of the stockmarket, just to cite a few). In this paper, we use a price-based approach to measure technical change at the asset, industry, and aggregate level in the US from 1947 to 2000. Whenever we faced a choice in constructing the data, we opted for the conservative alternative that understates the importance of quality improvement. Nevertheless, ouraggregateandindustry-level(cid:222)ndingssuggestthattechnicalchangeinequipment and software in the postwar period has been large and was instrumental in the growth resurgence in the 1990s. We show that the rate of technical change has accelerated in the past two decades. Most of the initial acceleration is due to a shift in investment toward computers, software, and communications equipment. However, later the growth rate of the leading edge technology accelerated for virtually every investment good and in every industry, demonstrating that information technology may cause generalized productivity improvements. The fact that the productivity of new vintages advanced at about the same rate for every industry does not imply that the average practice did too, and indeed it did not. Certain industries kept up with the fast pace of technical change better than others, as demonstrated by our (cid:222)nding of a widening of the cross-sectional distribution of the technological gap. Perhaps surprisingly, the gap was largest in industries like communications in which investment has been robust. The explanation is simply that technical change in these industries has outpaced even the rapid pace of investment. Whyisthereasubsetofindustriesthatexploittechnologicalprogressfasterthan others by investing heavily in new vintages of equipment and software? The (cid:222)rst encouraginglead comesfrom Hobijn andJovanovic (2001, Figure 8), whoshowthat 35

small (cid:222)rms outperformedlarge (cid:222)rms inthe stock market from 1973to1982.43 After that period, large (cid:222)rmsoutperformedsmall (cid:222)rms. One interpretationof this(cid:222)nding is that small (cid:222)rms (cid:222)rst adopted information technologies, boosting their expected pro(cid:222)ts and their share prices. Adecade later, large (cid:222)rms started toinvest massively in computers, software, and communications equipment, regaining their dominant position. This interpretation matches the behavior of the technological gap for IPES(Figure 4), which increased quickly in the 1970s and leveled-off in the last two decades once large (cid:222)rms shifted investment to IPES from other equipment.44 Second, at the aggregate level, we con(cid:222)rm Nelson and Phelps(cid:146) hypothesis that the speed of adoption of new technology is determined by the gap between the average and best practice, and by speci(cid:222)c features of the workforce. In particular, we (cid:222)nd aggregate evidence that younger, more able, and better-educated workers were the catalysts for adoption. Moreover, the increase in the college skill premium appears to re(cid:223)ect the premium to (cid:147)adaptability(cid:148) during periods of rapid technological progress and expanding technological gap, where the demand for adaptable labor was especially strong. To conclude, although at this stage of our research we cannot identify precisely the distinctive features of those organizations that led the adoption of the new technologies in the postwar US economy, two promising candidates are the size of (cid:222)rms and the (cid:147)adaptability(cid:148) of the workforce. 43Mitchell (2001) develops a theoretical model consistent with this (cid:222)nding. Within a simple industryequilibriummodel,heshowsthattheoptimalscaleofproductionissmallerwhentherate of embodied technical change increases. 44It is also consistent with the fact that aggregate nominal expenditure shares in IPES show a remarkable acceleration fromtheearly-1980(cid:146)s (Table5.8, SCB). 36

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Percent Change, Annual Rate 8 6 4 2 0 -2 Technical Change Technical Change -4 with BiasAdjustment -6 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 1: Price-BasedAggregate Measures of Investment-Specific Technical Change

Percent Change, Annual Rate 15 10 5 0 -5 90th Percentile Median Mean -10 10th Percentile 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 2: Distribution of Price-Based Measure of Investment-Specific Technical Change by 62 Industry Groups

Percent, Annual Rate Economic Depreciation Physical Depreciation 17.5 Physical Depreciation (Polynomial Fitted) 15 12.5 10 7.5 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 3: Economic and Physical Depreciation for Equipment and Software

Percent 50 45 Technological Gap for E&S 40 Technological Gap for IPES 35 30 25 20 15 10 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 4: Technological Gap Between Productivity of New Vintages andAverage Practice

Percent 50 90th Percentile Median 40 Mean 10th Percentile 30 20 10 0 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 5: Distribution of Technological Gap Between Productivity of New Vintages and Average Practice for Equipment and Software by 62 Industry Groups

TechnologicalGap ReturnstoEducation (Percent) (Percent) 50 14 13 Technological Gap 40 Returns to Education 12 30 10 9 20 8 10 7 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 Figure 6: Returns to Education and Smoothed Technological Gap Between Productivity of New Vintages andAverage Practice for Equipment and Software

Table1:OLSEstimatesofQuality-BiasinNIPAPriceIndexesforEquipmentandSoftware(1947-1983) IndustrialEquipment TransportationEquipment OtherEquipment IPES Elec Engn& Fabr Gnrl Metl Spcl Air Auto Rail Ship& Trck Agrc Cnst Elec Furn Mine Othr Srvc Trctr Comm Inst& Tran Turbn Metl Eqp Mach Mach Boats &Bus Mach Mach Eqp &Oil Eqp Mach Eqp Photo Variable (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) Trend*100 -3.30 -6.06 -3.13 -1.08 — -4.58 -15.0 -0.85 -0.82 -3.16 -3.65 — -1.91 — -0.91 -0.85 -1.37 -4.64 — -6.65 -4.57 (0.35) (0.77) (0.35) (0.27) (0.28) (1.26) (0.25) (0.15) (0.17) (0.25) (0.19) (0.18) (0.21) (0.31) (0.16) (0.42) (1.37) (cid:1) (cid:2) log p ij 1.40 1.48 1.23 0.76 0.72 0.99 2.37 0.84 0.86 1.51 1.15 1.71 0.95 1.23 0.60 0.73 1.10 1.22 1.25 1.68 -0.57 t (0.16) (0.10) (0.08) (0.06) (0.23) (0.05) (0.28) (0.17) (0.03) (0.18) (0.25) (0.12) (0.04) (0.15) (0.20) (0.04) (0.11) (0.05) (0.18) (0.16) (0.24) (cid:1) (cid:2) log p ij -0.49 — — — -0.74 — — 0.42 — -0.88 — -0.69 — — 0.42 — — —- -0.55 — 1.36 t−m (0.19) (0.24) (0.19) (0.21) (0.13) (0.20) (0.20) (0.56) ∆yt−n — — -0.01 -0.01 -0.01 — — — — — — — -0.01 — -0.01 -0.01 — — 0.01 0.01 — (0.005) (0.003) (0.003) (0.004) (0.003) (0.005) (0.003) (0.006) R¯2 0.87 0.77 0.93 0.98 0.99 0.91 0.89 0.79 0.99 0.99 0.91 0.99 0.99 0.95 0.99 0.98 0.86 0.96 0.98 0.91 0.77 EstimatesofQuality-BiasUsingR&DCapitalStock(1957–83) log(R&Dt) -0.27 -0.30 -0.08 -0.05 -0.05 -0.04 -0.83 — NA NA -0.30 — NA NA NA NA NA NA NA NA -0.44 (0.10) (0.07) (0.02) (0.02) (0.02) (0.01) (0.12) (0.06) (0.07) (cid:1) (cid:2) log p ij 0.87 1.17 0.91 0.73 0.86 0.96 1.11 0.45 0.90 1.45 -2.40 t (0.24) (0.12) (0.05) (0.04) (0.04) (0.06) (0.22) (0.12) (0.06) (0.17) (0.43) (cid:1) (cid:2) log p ij — — — — — — — 0.72 — -0.56 2.79 t−m (0.16) (0.19) (0.55) ∆yt−n — -0.02 -0.01 -0.01 -0.01 — — — — — — (0.008) (0.003) (0.003) (0.005) R¯2 0.44 0.93 0.97 0.99 0.99 0.94 0.68 0.93 0.95 0.99 0.91 (cid:1) (cid:2) i∗ Eachcolumncontainsestimatesofaseparateequationinwhichthedependentvariableislog pj . t Theorderofthelagsmandnischosentoassurethebestfit. Inthethreecasesinwhichmorethanonelagwasstatisticallysignificant,we reportonlythemostpreciselyestimatedlagtosimplifythepresentation. Standarderrorsoncoefficientsareinparentheses.

Table2:Price-BasedMeasureofInvestment-SpecificTechnicalChangebyAsset (PercentChange,AnnualRate) 1948–2000 1948–59 1960–69 1970–79 1980–89 1990–2000 Equipmentandsoftware 4.0 2.3 3.6 3.6 4.6 6.3 IPES 9.7 4.5 7.3 11.7 9.4 10.6 Computersandperipheral 23.5† — 26.6 26.5 18.2 22.5 equipment Prepackagedsoftware 15.3† — 15.7 18.1 15.8 9.9 Customsoftware 3.8† — 4.0 4.4 3.6 2.6 Own-accountsoftware 0.2† — 0.5 0.3 0.1 0.3 Communicationequipment 8.7 9.6 5.1 7.3 8.5 12.9 Instruments,photocopy, 5.6 1.7 3.4 13.5 5.0 5.4 andrelatedequipment Officeandaccounting 2.4 0.0 2.1 5.3 3.1 2.4 equipment IndustrialEquipment 2.3 1.9 2.8 1.3 2.1 3.6 Electricaltransmission, 2.6 1.8 4.1 2.5 0.7 4.4 distribution,and industrialapparatus Enginesandturbines 3.2 4.4 3.7 1.7 3.4 5.9 Fabricatedmetal 2.7 2.8 3.1 1.2 4.4 4.7 products Generalindustrial 1.6 0.4 1.8 2.2 1.3 2.6 equipment Metalworkingmachinery 0.9 0.5 1.1 0.9 0.8 1.6 Specialindustry 3.8 3.2 4.2 2.7 3.6 5.2 machinery TransportationEquipment 3.2 2.5 4.2 2.0 3.0 4.3 Aircraft 7.9 8.1 8.4 3.5 9.1 10.6 Autos 2.5 2.9 3.2 3.0 0.6 2.6 Railroadequipment 1.0 1.3 2.3 0.6 3.1 2.3 Shipsandboats 2.1 1.5 2.6 0.3 3.0 3.4 Trucks,buses,and 3.3 3.0 4.5 1.5 3.3 4.0 trucktrailers OtherEquipment 1.7 1.5 1.9 0.5 2.0 2.5 Agriculturalmachinery 0.1 0.5 0.7 3.0 1.6 0.9 Constructionmachinery 1.3 0.5 1.6 0.5 1.6 2.6 Electricalequipment 2.0 1.4 2.7 1.1 2.4 3.0 Furnitureandfixtures 1.1 0.9 1.4 0.6 0.8 2.0 Miningandoilfield 1.4 0.5 1.6 0.5 2.4 2.1 machinery Otherequipment 2.4 3.4 2.0 2.1 1.9 2.3 Serviceindustry 4.9 5.3 6.0 3.6 4.6 5.1 machinery Tractors 0.3 2.2 0.9 0.1 2.0 1.8 Each entry is the annual average during the period. The price-based measure of investmentspecific technical change is calculated as the difference between the growth rate of constantqualityconsumptionandthegrowthrateofthequality-adjustedpriceofassetj. The† denotestheannualaverageisfortheperiod1960-2000.

Table3:Price-BasedMeasureofInvestment-SpecificTechnicalChange(PercentChange,AnnualRate) andNominalEquipmentandSoftwareInvestmentSharesbyMajorIndustry 1948–2000 1948–59 1960–69 1970–79 1980–89 1990–2000 Technical Nominal Technical Nominal Technical Nominal Technical Nominal Technical Nominal Technical Nominal Change Share Change Share Change Share Change Share Change Share Change Share Agriculture,Forestry 1.1 8.0 0.8 12.4 1.1 8.7 -0.8 8.4 2.3 4.4 2.4 4.3 andFishing Mining,Oiland 2.4 3.3 0.9 3.0 2.4 3.2 1.5 3.9 3.5 4.0 4.4 2.2 GasExtraction Construction 2.2 3.7 1.1 5.2 2.4 4.7 1.0 3.7 2.7 2.0 4.5 2.4 DurableGoods 3.5 13.9 1.3 14.8 3.2 15.5 3.9 14.5 4.1 12.9 5.7 11.5 Manufacturing NondurableGoods 3.9 11.9 2.4 12.9 3.9 12.7 4.0 12.1 4.1 10.7 5.6 10.8 Manufacturing Transporation 4.0 15.6 2.3 18.4 4.9 16.2 2.2 15.5 4.6 14.3 6.7 12.3 andUtilities Communications 7.7 7.9 7.6 6.2 5.2 8.6 7.3 8.6 8.1 8.2 10.9 8.5 WholesaleTrade 5.5 5.8 2.6 3.5 4.8 4.5 6.0 5.4 6.4 8.0 8.8 8.6 RetailTrade 4.3 5.7 3.3 6.7 4.3 5.6 3.8 5.0 4.9 5.6 5.9 5.4 Finance,Insurance, 5.6 13.1 3.4 8.8 4.8 9.7 7.0 11.7 5.8 17.7 8.0 19.5 andRealEstate OtherServices 5.0 11.1 2.9 8.1 4.6 10.6 5.3 11.1 6.2 12.1 6.8 14.5 Eachentryistheannualaverageduringtheperiod. Theprice-basedmeasureofinvestment-specifictechnicalchangeiscalculatedasthe differencebetweenthegrowthrateofconstant-qualityconsumptionandthegrowthrateofthequality-adjustedpriceofassetj.

Table4:Quality-AdjustedandBEACapitalStocks(PercentChange,AnnualRate) 1948–2000 1948–59 1960–69 1970–79 1980–89 1990–2000 1. k∗ 8.8 9.1 8.9 8.7 7.5 10.0 e 2. kBEA 5.8 5.6 5.9 6.1 4.6 6.8 e Difference(1-2) 3.0 3.5 3.0 2.6 2.9 3.2 3. k∗ 16.3 13.7 16.5 17.9 17.2 16.3 ipes 4. kBEA 12.3 8.6 13.2 13.7 13.2 13.3 ipes Difference(3-4) 4.0 5.1 3.3 4.2 4.0 3.0

Table5:StatisticalGrowthAccounting(1948–1999) RealGDPCalculatedUsingConstant-Quality RealGDPCalculatedUsingConstant-Quality ConsumptionPriceIndex ConsumptionandInvestmentPriceIndexes 1948–99 1948–59 1960–69 1970–79 1980–89 1990–99 1948–99 1948–59 1960–69 1970–79 1980–89 1990–99 RealGDP(PercentChange,AnnualRate) 3.72 3.68 4.34 3.64 3.39 3.53 4.01 3.69 4.82 3.89 3.60 4.15 ContributionofCapital(k∗=Qk(cid:3)) 53.6 41.1 48.7 59.7 60.2 64.2 49.7 41.0 43.8 55.8 56.8 54.7 QualityofCapital(Q) 21.1 18.2 18.1 16.9 24.1 31.0 19.6 18.1 16.3 15.8 22.7 26.4 IPESCapital(QIPES) 6.0 1.4 2.7 6.2 9.0 12.4 5.6 1.4 2.4 5.8 8.5 10.6 OtherCapital(Q ) 15.1 16.8 15.4 10.7 15.1 18.6 14.0 16.7 13.9 10.0 14.2 15.8 Other QuantityofCapital(k(cid:3)) 32.5 22.9 30.6 42.8 36.1 33.2 30.1 22.8 27.5 40.0 34.1 28.3 IPESCapital(k(cid:3) IPES) 5.5 2.6 3.9 4.9 6.0 4.9 5.1 2.6 3.5 4.6 5.7 4.2 OtherCapital(k(cid:3) ) 27.0 20.3 26.7 37.9 30.1 28.3 25.0 20.2 24.0 35.4 28.4 24.1 Other ContributionofLabor(l=hn) 32.3 20.0 29.0 34.2 41.3 41.9 29.9 20.0 26.1 32.0 38.9 35.7 QualityofLabor(h) 10.4 17.1 13.2 15.6 6.2 7.4 9.6 17.0 11.9 14.6 5.8 6.3 QuantityofLabor(n) 21.9 2.9 15.8 18.6 35.1 34.5 20.3 2.9 14.2 17.4 33.1 29.4 ContributionofTFP(z) 14.1 38.9 22.4 6.1 -1.5 -6.1 20.4 39.0 30.1 12.2 4.0 9.6 Thecontributionofeachinputistheratiooftheshare-weightedrealgrowthrateoftheinputandrealGDPgrowth. Theaggregateshareof labor(capital)is0.64(0.36)overthesampleperiod.

Table6:DecompositionofIncreaseinGrowthRateofLaborProductivityin1995-1999 Ravn-Uhlig Hodrick-Prescott (λ=6.25) (λ=100) Contribution Cycle Trend Cycle Trend IncreaseinGrowthRate 31.5 68.5 88.9 11.1 ofLaborProductivity ContributionofCapital 42.3 17.0 25.3 43.3 -10.0 QualityofCapital 66.1 9.3 56.8 30.8 35.3 IPESCapital 28.6 5.8 22.8 20.4 8.2 OtherCapital 37.5 3.5 34.0 10.4 27.1 QuantityofCapital -23.8 7.7 -31.5 12.5 -36.6 IPESCapital -4.0 5.1 -9.0 13.6 -17.5 OtherCapital -19.9 2.6 -22.5 -0.9 -18.8 ContributionofLaborQuality -29.7 -12.4 -17.3 -29.4 -0.3 ContributionofTFP 87.5 27.0 60.5 75.0 12.5 Thegrowthrateoflaborproductivityincreasedfromanannualrateof1.77percentin1973–94 toanannualrateof2.64percentin1995–99. Thecyclicalcomponentoftheincreaseisextracted from each series using the Hodrick-Prescott filter. We use filtering parameters suggested for annual data by Ravn and Uhlig and Hodrick and Prescott. The contribution of each input is theratiobetweentheshare-weightedrealgrowthrateoftheinputandthegrowthrateoflabor productivity. Theaggregateshareoflabor(capital)is0.64(0.36)overthesampleperiod.

Table7:TechnologicalGapBetweenProductivityofNewVintagesandAveragePractice byMajorIndustry 1948–2000 1948–59 1960–69 1970–79 1980–89 1990–2000 Agriculture,Forestry, 5.1 1.5 6.7 -0.8 6.4 13.4 andFishing Mining,Oiland 11.8 2.7 9.7 7.5 14.2 29.5 GasExtraction Construction 9.4 3.1 9.8 6.4 10.3 20.3 DurableGoods 17.7 4.2 12.9 17.3 24.5 35.5 Manufacturing NondurableGoods 22.8 8.8 21.9 24.0 27.2 37.9 Manufacturing Transportation 28.3 5.6 32.0 28.0 30.1 55.6 andUtilities Communications 41.0 24.0 31.9 27.4 56.8 73.4 WholesaleTrade 18.3 6.9 15.4 18.8 23.0 32.0 RetailTrade 18.5 9.2 20.6 17.7 21.3 27.3 Finance,Insurance, 20.0 8.4 17.9 24.2 23.3 30.9 andRealEstate OtherServices 18.2 5.9 16.1 21.1 24.7 28.0

Table8:OLSEstimatesofNelson-PhelpsAdoptionEquation(1948–99) Variable (1) (2) (3) (4) (5) log(Γ ) 0.84 0.84 0.72 0.66 0.67 t−1 (0.05) (0.05) (0.12) (0.12) (0.14) ShareofYoungWorkers — 0.46 0.67 2.75 2.83 (ages16-24) (0.85) (0.87) (1.23) (1.35) ShareofCollegeGraduates — — 0.93 10.9 11.0 (0.84) (4.44) (4.49) ShareofFemaleWorkers — — — -10.5 -10.4 (4.57) (4.62) ShareofSelf-employed — — — — 0.27 (1.82) Durbin-Watson 1.59 1.62 1.53 1.49 1.50 R¯2 0.85 0.85 0.85 0.87 0.87 Each column contains estimates of a separate equation in which the dependent variable is log(∆Q ). t Standarderrorsoncoefficientsareinparentheses.