Does the United States have a productivity slowdown or a measurement problem?

Byrne, David M. ; Fernald, John G. ; Reinsdorf, Marshall B. 等

ABSTRACT After 2004, measured growth in labor productivity and total factor productivity slowed. We find little evidence that this slowdown arises from growing mismeasurement of the gains from innovation in information technology-related goods and services. First, the mismeasurement of information technology hardware is significant preceding the slowdown. Because the domestic production of these products has fallen, the quantitative effect on productivity was larger in the 1995-2004 period than since then, despite mismeasurement worsening for some types of information technology. Hence, our adjustments make the slowdown in labor productivity worse. The effect on total factor productivity is more muted. Second, many of the tremendous consumer benefits from the "new" economy such as smartphones, Google searches, and Facebook are, conceptually, nonmarket: Consumers are more productive in using their nonmarket time to produce services they value. These benefits raise consumer well-being but do not imply that market sector production functions are shifting out more rapidly than measured. Moreover, estimated gains in nonmarket production are too small to compensate for the loss in overall well-being from slower market sector productivity growth. In addition to information technology, other measurement issues that we can quantify (such as increasing globalization and fracking) are also quantitatively small relative to the slowdown.

The things at which Google and its peers excel, from Internet search to mobile software, are changing how we work, play and communicate, yet have had little discernible macroeconomic impact.... Transformative innovation really is happening on the Internet. It's just not happening elsewhere.

--Greg Ip (2015)

U.S. productivity data highlight the paradox at the heart of the quotation above. The fast pace of innovation related to information technology (IT) seems intuitive and obvious. Yet productivity growth has been modest, at best, since the early 2000s. In this paper, we examine the hypothesis that the U.S. economy has a growing measurement problem rather than a productivity slowdown (Aeppel 2015; Feldstein 2015; Hatzius and Dawsey 2015). Some components of real output, including the services provided by IT, are indeed poorly measured. Yet for mismeasurement to explain the productivity slowdown, growth must be mismeasured by more than in the past. Although we find considerable evidence of mismeasurement, we find no evidence that the biases have gotten worse since the early 2000s.

We focus especially on IT-related hardware and software, where mismeasurement is sizable, as well as on e-commerce and "free" digital services such as Facebook and Google. More broadly, we identify potential biases to productivity from intangible investment, globalization, and technical innovations in the production of oil and natural gas (for example, fracking). These are all areas where it is plausible that measurement has worsened since the early 2000s. But taken together, our adjustments turn out to make the post-2004 slowdown in labor productivity even larger than measured. The slowdown of business sector total factor productivity (TFP) growth is only modestly affected.

Figure 1 summarizes our quantitative analysis. The solid portions of the bars show the published data on average growth in U.S. business sector labor productivity, or output per hour. Growth was exceptional from 1995 through 2004, but the pace then slowed by more than about 1% percent a year. (1) Suppose productivity growth had continued at its 1995-2004 pace of 3 1/4 percent a year. Then, holding hours growth unchanged, business sector GDP would be $3 trillion (24 percent) larger by 2015 in inflation-adjusted 2009 dollars. (2)

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We find no evidence that growing mismeasurement related to IT or other factors can fill this gap. In section I, we explore the hypothesis that the slowdown reflects the growing importance of poorly measured industries with low productivity growth, such as health care and other services. These industries are indeed growing as a share of the economy, but holding weights fixed at their 1987 values would make little difference to the slowdown. That most industries show slowing growth matters more than changing weights.

We then turn to biases within specific sectors. Figure 1 shows our adjustments for various biases. We incorporate consistent measurement of quality-adjusted prices for computers and communications equipment; judgmental corrections to prices of specialized information-processing equipment and software; a broader measure of intangible investment than is used in the national accounts; and ballpark adjustments for other issues--Internet access, e-commerce, globalization, and fracking. These adjustments make labor productivity growth since 2004 look better. But the adjustments to account for mismeasurement matter even more in the 1995-2004 period. On balance, therefore, the labor productivity slowdown becomes modestly larger. (3)

In particular, although we find somewhat more mismeasurement of computer and communications equipment prices in the recent period than previously, domestic production of these products has plunged, making this mismeasurement less important for GDP. Although David Byrne, Stephen Oliner, and Daniel Sichel (2015) show that microprocessor (MPU) price declines are substantially understated, this has little immediate implication for productivity; because MPUs are not final products, they only affect GDP through net trade, which is roughly in balance for semiconductors.

The "other" adjustments in figure 1 include improved Internet quality (section III) and e-commerce (section IV), which together add about 5 basis points (bp) more in the post-2004 period than from 1995 to 2004. This adjustment is small, reflecting the conceptual challenges involved in bringing more of the services of Google, Facebook, and the like into market sector GDP. The major cost to consumers of these services is not broadband access, cell phone service, or the phone or computer; rather, it is the opportunity cost of time. This time cost is not consumption of market sector output. It is akin to the consumer surplus obtained from television (an old economy invention) or from playing soccer with one's children. Following Gary Becker (1965), activities that combine market products with the consumer's own time are properly thought of as nonmarket production that uses market goods and services as inputs. As we discuss, a small amount of market output could conceivably be included in final consumption, corresponding to online ad spending; this spending is relatively modest and has little effect on growth in output or productivity. Thus, though the digital services are valuable to households, the possible mismeasurement in these areas makes essentially no difference to market sector labor productivity and TFP growth. (4) That said, to the extent that the effect of innovation on the quality of leisure is outpacing the effect on market activities, market productivity growth might have become a less reliable measure of overall welfare.

These other adjustments also include effects from globalization and fracking (section V). Globalization was most intense in the late 1990s and early 2000s. That caused real import growth to be understated and, correspondingly, artificially boosted measured GDP growth by about 10 basis points (bp) per year during the period from 1995 to 2004. Hence, in figure 1 the "other" bar contributes negatively in the period. Fracking, on the other side, boosts productivity growth by about 5 bp after 2004. Together, these adjustments shave about 10 bp from growth in the 1995-2004 period, and add about 10 bp to growth thereafter.

For TFP, the adjustments are even smaller than for labor productivity. Adjusting equipment, software, and intangibles implies faster GDP growth, but also faster input growth (because effective capital services rise more quickly). After adjusting hardware and software, the aggregate TFP slowdown after 2004 is modestly worse. Adding a broader measure of intangibles--as is done by Carol Corrado, Charles Flulten, and Sichel (2009)--works modestly in the other direction, so our broadest adjustment for investment goods leaves the 114 percentage point slowdown in TFP a few basis points worse. The other (non-investment-good) adjustments we make pass directly into TFP; but, on balance, they still leave the slowdown in TFP only modestly attenuated.

In making these points, we draw on a large body of existing research. Before presuming that the measurement problems have gotten worse, it is worth remembering that in the 1990s and early 2000s, much research looked at missing quality improvement, the problem of new goods, and the fact that consumers had an explosion of new varieties. The biases were frequently estimated to be large. For example, VCRs, cell phones, and other similar products were added to the consumer price index (CPI) a decade or so after they appeared, and when their prices had already fallen by 80 percent or so (Gordon 2015; Hausman 1999). The explosion in consumer choice, and the possibilities for so-called mass customization, were documented in the 1990s. At about the same time, the Boskin Commission estimated that omitted quality change in new goods was worth at least 0.5 percent a year (Boskin and others 1998). (5) So again, the issue is not whether there is bias. The question is whether it is larger than it used to be.

The structure of the paper is as follows. Section I lays out motivating facts about the productivity slowdown, including a discussion of the changing industry composition of the U.S. economy. Section II discusses improved deflators for information technology and intangibles, and reworks the growth accounting with alternative capital deflators. We then turn to other issues in sections III, IV, and V that plausibly changed after 2004. Section VI concludes.

I. The Recent Rise and Fall of U.S. Productivity Growth

Three productivity facts frame our subsequent discussion. First, as measured, the growth in business sector labor productivity and TFP increases sharply in the mid-1990s but then slows down after about 2004. Second, the slowdown is broad-based across industries, including in relatively well-measured ones, such as wholesale and retail trade, manufacturing, and utilities. Third, the TFP slowdown is not caused by the rising share of slow-productivity-growth industries.

John Fernald (2015) interprets the slowdown as a "return to normal" following a period of exceptional, broad-based gains from the production and use of information technology. The remaining sections of this paper explore rising mismeasurement as an alternative explanation. (6)

We focus now on TFP, which is defined as a residual: output growth that is not explained (in a proximate sense) by growth in inputs of capital and labor. In the longer run, TFP growth mainly reflects innovation in a broad sense. The online appendix shows that changes in TFP growth have been the proximate driver of changes in labor productivity growth, as theory would suggest. TFP as well as labor productivity slow sharply in the 2004-07 period (before the Great Recession) relative to the late 1990s and early 2000s; the slowdown in growth is statistically significant in formal tests for a change in mean growth. (7)

Figure 2 shows the industry sources of the slowdown in business sector TFP growth from a Bureau of Labor Statistics (BLS) data set. Because of data availability, the subperiods shown are all between 1987 and 2013. We divide the private business economy into four mutually exclusive categories: IT-producing; wholesale and retail trade; other well-measured; and poorly measured. (8) All sectors show somewhat slower growth after 2004, but the slowdown is particularly pronounced for wholesale and retail trade and the other relatively well-measured sectors. After 2000, IT production adds less and less to TFP growth, a situation that we discuss in the next section. After 2004, wholesale and retail trade contribute negatively; this is noteworthy because IT provided a substantial boost to wholesale and retail trade in the preceding periods, in part through industry reorganization. Other (nontrade) well-measured industries contribute less after 2004. Thus, the slowdown is apparent even in areas such as trade and non-IT manufacturing, where measurement has traditionally been considered relatively good. (Of course, even in these industries, unmeasured gains from quality improvements and new goods may be occurring.) Finally, the poorly measured subgroup contributes negatively from 2004 to 2007, but then turns substantially positive from 2007 to 2013; quantitatively, the post-2007 shift reflects an increasingly positive contribution from finance and the elimination of a large negative contribution from construction.

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The slowdown is also not simply a matter of weights that have been shifting toward poorly measured industries with low TFP growth, such as services. Services have been growing as a share of the economy and are inherently challenging to measure in real terms (Griliches 1994; Triplett and Bosworth 2004). The top panel of figure 3 compares actual TFP growth with a counterfactual where nominal industry value added weights are held constant at their 1987 values. (9) During the periods shown, the growth rates of the two measures are within a few basis points. In other words, shifts in the industry composition of the economy play essentially no role in the productivity speedup in the mid-1990s or slowdown in the 2000s.

Why are the two series so similar? The value added share of services and other relatively poorly measured industries rises about 10 percentage points from 1987 to 2013. For the full sample, TFP growth in these poorly measured industries was about zero, compared with 2 percent annual growth for relatively well-measured industries (including IT hardware and trade). Hence, a back-of-the-envelope guess would be that, by the end of the sample, the fixed-weight index should grow about 20 bp faster, reflecting the annual difference of 2 percentage points in growth times the 10 percentage point shift in weights. Roughly half the shift in weights had occurred by 1998, so the expected effect on the post-2000s slowdown might be 10 bp.

In the top panel of figure 3, the differences are even smaller than this back-of-the-envelope calculation. First, within the groups of well-measured and poorly measured industries, weights shifted toward those with faster TFP growth. These shifts partially offset the broader shift toward services. Second, since 2007, "Baumol's cost disease" (Baumol and Bowen 1966) has reversed--TFP growth in poorly measured services has been faster than that in well-measured sectors.

The bottom panel of figure 3 makes this point about weights a different way by showing that the slowdown after the early 2000s is broad-based across industries. The figure shows the change in average annual industry value added TFP growth for 2004-13 relative to 1995-2004. About two-thirds of industries show a slowdown in measured TFP growth after 2004. We get a similar picture if we look at the change from 1995-2004 to 2004-07, so it is not simply a matter of the Great Recession affecting many industries. We also get a similar picture using labor productivity, so it is not something about capital measurement.

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Our results are consistent with previous studies that have found that the shrinking size of well-measured sectors was not a first-order explanation for previous swings in productivity (Baily and Gordon 1988; Sichel 1997).

Why did so many industries show a common slowdown after 2004? The economy plausibly received an exceptional boost from IT in the 1990s and early 2000s that hit many industries. However, by the mid-2000s, the low-hanging fruit of a wave of IT-based innovation (including associated reorganizations) had been plucked. For example, industries along the supply chain from factory to retailing had already been substantially reorganized to reduce inventory, waste, and headcount; and IT-supported efficiencies in middle management and administrative support had been exploited. It is possible that the latest waves of innovation will take time to bear fruit and that we are overlooking nascent IT-based productivity gains in service sectors such as health care and education. But here we sidestep this more challenging question and turn to an alternative hypothesis: that rising mismeasurement might explain the patterns in the data.

II. Growing Mismeasurement of Information Technology?

In this section, we document long-standing challenges in measuring information-processing equipment and software. (10) Correcting for the mismeasurement of these investment goods turns out to make the slowdown in labor productivity and TFP growth even worse after 2004. We also note a rise in uncertainty about these effects: Investment has shifted toward special-purpose information-processing equipment and intangibles, especially software--categories that have proven especially difficult to measure.

After moving roughly sideways in the postwar period through the late 1970s, the official IT investment price index turned downward as the personal computer (PC) era began, and then the rate of decline accelerated sharply, to 6 percent a year on average, during the IT boom of the 1990s and the early 2000s (table 1). Since 2004, the price declines have retreated to a modest rate of 1 percent, coinciding with the decrease in the contribution of IT production to TFP growth shown in figure 2. This flattening out has led to a revival of interest in measuring IT prices, and some recent studies find that official price statistics have substantially understated price declines in recent years. (11)

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Has worsening price mismeasurement caused a spurious slowdown in official estimates of output and real investment, distorting productivity estimates? Answering this question requires the construction of a fully consistent time series. We employ price indexes developed by Byrne and Corrado (2016), who review the full postwar history of IT price research and construct alternative price indexes for IT investment and production using research not only for recent years but also for earlier periods that may not have been incorporated into the National Income and Product Accounts (NIPA) that are issued by the Bureau of Economic Analysis (BEA).

We provide two alternative price indexes in figure 4. The first, a conservative index, is based solely on research studies that use detailed data sets for specific product classes. We extrapolate these results, as described in Byrne and Corrado (2016), for communications equipment and for computers and peripherals. For the second, liberal, index, we add plausible assumptions about the prices of IT products for which no direct studies are available, namely, other types of information-processing equipment and software. Overall, our alternative indexes suggest substantially faster price declines than those shown in the NIPA throughout the postwar period. For some categories (computers and communications equipment), price measurement appears to have worsened, but the importance of these categories in GDP has declined. On balance, the declining importance in GDP dominates, so the bias in GDP growth was larger in the past.

We discuss the component prices briefly here and compare them with the investment prices used in the NIPA.

II.A. Components of IT Investment

COMPUTERS AND PERIPHERALS The official investment price index for computers and peripherals reflects the results of internal BEA research (Cole and others 1986; Dulberger 1989), which led to the adoption of hedonic regression techniques to account for the rapid technological advances embodied in new models of computers and peripherals. (12) For the postwar period, through the early 1980s, BEA prices are consistent with outside studies (Gordon 1990; Triplett 1989). Beginning in the 1990s, the BLS adopted hedonics for computers (but not peripherals) as well, and the BEA now relies on BLS prices as inputs for the NIPA investment deflator (Grimm, Moulton, and Wasshausen 2005). Despite the commitment to quality adjustment in the official statistics, outside research indexes indicate somewhat different price trends beginning in the 1980s.

PERSONAL COMPUTERS Our alternative price index for computers and peripherals diverges from official prices beginning in 1984. For PCs, we adopt an aggregate of the indexes developed in a comprehensive study by Ernst Berndt and Neal Rappaport (2001, 2003), which exhibits declines that are 8 percentage points faster through the early 2000s. The documentation for the BLS hedonic models is not comprehensive enough to allow us to identify the source of the difference in results with confidence.

More recently (since 2004), the BEA index for PCs has slowed dramatically, and some aspects of the sources and methods used raise concerns about the accuracy of this development. The top panel of figure 5 shows the average unit price of PCs sold in the U.S. business market reported by IDC Corporation, which makes no adjustment for quality. The figure also shows the rate of change for the BEA investment price index for PCs. In the late 1990s and early 2000s, the gap between the two series indicates that quality improvements were contributing 15 to 20 percentage points to the fall in constant-quality PC prices. The gap has narrowed since that time, and since 2010 the two series have been almost identical, implying no improvement in PC quality, holding unit price constant, for the past five years.

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Three measurement problems appear to contribute to this implausible result. First, the BEA investment series is the aggregate of a domestic production price index and an import price index that are calculated independently from one another, using different source data (figure 5, bottom panel). As a result, any discount accruing to a business switching from domestically sourced to imported equipment is not reflected in the investment price index--a form of outlet substitution bias akin to omitting from a consumption price index the price savings associated with switching to shopping at Walmart (Reinsdorf 1993; Houseman and others 2011).

Second, the price index for imports falls markedly more slowly than the index for domestic production over a prolonged period--an average annual difference of 14 percentage points since its introduction in 1995. The implied continual rise in the relative price of imported computers is inconsistent with the increase in import penetration from 50 to 90 percent during the same period (Byrne and Pinto 2015). This contradiction suggests that the price mismeasurement is more severe for import prices than for domestic producer prices. Among the possible contributing factors to the relatively flat import price series is the heavy presence of intrafirm (transfer) prices in the index (more than 60 percent of the value of the basket in 2013). These prices may behave differently from arm's-length prices. This may be related to the finding by Emi Nakamura and Jon Steinsson (2012) that a surprisingly high proportion of the items in the import price index sample never experience a price change before exiting the index basket. Also, new models are generally linked into the import price index in a way that would not capture any decline in the quality-adjusted price of the item (Kim and Reinsdorf 2015).

This suggests the producer price index (PPI) would be a more appropriate deflator for investment, though the PPI itself has drawbacks. When quality-adjusting the computer PPIs, the BLS controls primarily for technical features, such as processor clock speed and features associated with changes in production costs (Holdway 2001). Design improvements not clearly tied to costs or not easily identified in technical specifications, such as circuits designed to work more effectively in parallel, may raise the value of the equipment to its user through superior performance without affecting the quality index. Thus, the approach used for quality adjustment in the PPI may lead to an understatement of quality improvements and an overstatement of inflation.

Although we are aware of no research studying computer prices directly in recent periods, Byrne, Oliner, and Sichel (2015) analyze prices for MPUs, the central analytical component of computers. When controls for direct measures of performance were used in their hedonic analysis of MPUs (benchmark scores on a battery of user tasks), their hedonic price index fell more than 20 percentage points faster than a hedonic index controlling for technical features during the 2000-13 period. We infer that the BLS hedonic index may be understating the annual rate of quality improvement for PCs by 4 percentage points--the (rounded) product of the bias in the MPU price index and the share of MPU inputs in the final value of PCs (15 percent). In our alternative index, we extend the Berndt-Rappaport index with the bias-adjusted PPI.

MULTIUSER COMPUTERS The BLS price index for multiuser computers (such as servers), which is used by the BEA, is quality-adjusted using a hedonic regression as well. Following the same logic used for PCs, we augment the BEA price index beginning in 1993 with an indicator of the average price per computer unit adjusted for MPU performance, which falls markedly faster than the PPI. The performance measure is an average of scores on a suite of benchmark tests developed by Systems Performance Evaluation Corporation (SPEC)--a consortium of industry representatives--to provide reliable comparisons across systems. We blend this price-performance indicator with the PPI, which controls for computer features not accounted for by the SPEC benchmark. We employ a weighted average of the PPI and the price-performance trend to deflate multiuser computers. This alternative index falls 10 percentage points faster than the official BEA price index.

STORAGE EQUIPMENT For storage equipment as well, the PPI that is the basis for the BEA investment price index appears out of alignment with price-performance trends in the industry. From its introduction in 1993 until 2014, the PPI fell 12 percent a year on average, in stark contrast to the price per gigabyte for hard disk drives, currently the dominant technology in the industry, which fell 35 percent per year on average (McCallum 2015). Recent research by Byrne (2015b), employing detailed model-level prices for storage equipment, developed prices that fell at nearly the rate of raw price-per-gigabyte series. We use the Byrne (2015b) index extended backward by the price-per-gigabyte series, with a 4 percentage point bias adjustment. (13)

All told, our alternative index for computers and peripherals falls faster than the NIPA index beginning in the early 1980s, and the gap between the two increases markedly, to 8 percentage points, between 1995 and 2004. The difference between the indexes has been even larger in recent years-an average of 12 percentage points (figure 6, top panel). This substantial gap suggests that additional research is needed to account well for computer investment in the NIPA, and the rising gap makes the issue increasingly important. However, the percentage point slowdown in the alternative index is still quite large and returns the rate of price decline to the pace seen before the IT boom of the 1990s.

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COMMUNICATIONS EQUIPMENT Official investment prices for communications equipment reflect both BLS producer and import price indexes, and internal BEA research (Grimm 1996). Outside research, including price indexes published by the Federal Reserve Board, is incorporated to some extent as well, and the investment index does fall faster than the PPI for the industry (figure 6, bottom panel). However, a substantial amount of research is not reflected in the NIPA (Byrne and Corrado 2015, 2016). This includes work on transmission and switching equipment in the early postwar era by Kenneth Flamm (1989), as consolidated and augmented by Gordon (1990), and satellite prices constructed by Byrne and Corrado (2015). For more recent years, the BEA investment price index appears inconsistent with new prices for cellular systems, data networking, and transmission developed in Byrne and Corrado (2015) and Mark Dorns (2000). Because subindexes are not published for communications equipment investment, it is impossible to analyze the sources of this difference. In any event, technological developments in the field suggest that careful attention needs to be given to account for quality changes, such as fourth-generation cellular systems now capable of delivering video.

Like the computer investment index, the Byrne and Corrado (2016) communications equipment investment index is carefully constructed to match the scope and weighting of the BEA index. All told, the difference between the BEA investment index and the alternative is noteworthy, and the gap is slightly larger in the 2004-14 period than in the 1995-2004 period. Unlike the index for computers and peripherals, the communications equipment index maintains roughly the same pace of decline as during the IT boom.

SPECIAL-PURPOSE ELECTRONICS The remaining components of the BEA's "other information-processing" equipment category form a diverse group of special-purpose types of equipment designed for use in medical, military, aerospace, laboratory, and industrial applications. (14) Examples include magnetic resonance imaging machines, electronic warfare countermeasure devices, and a wide variety of equipment used for monitoring and controlling industrial processes. Technological advances in recent years have been impressive. One well-known example is genomic sequencing, where specialized equipment has contributed to dramatic efficiency gains: The cost of sequencing a human genome has dropped from roughly $1 million in 2008 to $1,000 in 2015 (Wetterstrand 2016). (15)

Surprisingly, with the exception of electromedical equipment, which edges down modestly, the PPIs for these products have risen on average since the late 1990s. Differences in market structure (such as the smaller scale of production and the market power of military and medical customers) and the price trends of specialized inputs could cause prices for special-purpose electronics to behave differently from prices for general-purpose electronics like computers (Byrne 2015a). Yet these goods have electronic content comparable to computers, and one might expect the equipment prices to reflect the rapidly falling price of the electronic components used in their production. In our liberal alternative scenario, we remove roughly one-third of the difference between the trend price growth of special-purpose and of general-purpose (computer and communications) electronics.

SOFTWARE Investment in software is deflated in the NIPA by an aggregate of three subindexes: prepackaged, custom, and own-account software. BLS producer prices are available for prepackaged software, and research has been conducted at BEA and by outside researchers into quality-adjusted price trends (Parker and Grimm 2000; Copeland 2013). To deflate investment in prepackaged software, the BEA employs a BLS PPI, with an adjustment reflecting the average difference between the PPI and the BEA's research results. Because direct observation of prices for custom and own-account software has not been possible, investment in these categories of software is deflated by a blend of an input cost index for the industry and the prepackaged software index. In our liberal alternative scenario, we assume that price declines for the other components are understated and deflate own-account and custom software with an index created with one-third weight on prepackaged software and two-thirds weight on existing BEA deflators for the respective categories. (16)

IT INVESTMENT AS A WHOLE All told, declines for the official price index for information technology slow dramatically, from 6 percent a year for the period 1995-2004 to 1 percent a year for 2004-14. Although the alternative index consistently falls faster than the official price, it slows to a similar degree--from 9 percent a year for 1995-2004 to 4 percent a year for 2004-14. The liberal index accelerates as well, and provides essentially the same picture. Thus, on first examination, increasing mismeasurement does not appear to explain the slowdown in IT price declines when the available research from all periods is considered.

However, it bears emphasis that the composition of IT investment has shifted appreciably toward components for which measurement is more uncertain. Most notably, software investment has gone from 39 percent of IT investment for the period 1995-2004 to 48 percent for 2005-14. Also, special-purpose equipment's share has increased, bringing the share for which measurement is more uncertain to 68 percent. Thus, our confidence in the IT price indexes, even as amended in the alternative indexes, has deteriorated markedly because of compositional shifts.

II.B. Intangibles beyond the NIPA

Conceptually, capital investment represents the use of resources that "reduces current consumption in order to increase it in the future" (Corrado, Hulten, and Sichel 2009, p. 666). Tangible investments in equipment and structures clearly meet this definition. But much intangible spending by businesses and governments also meets this definition. The U.S. national accounts include some intangibles--R&D and artistic originals (history beginning in 1925; introduced in 2013) and software (history beginning in 1960; introduced in 1999)--as final fixed capital formation. However, businesses also undertake considerable other types of spending that have the same flavor--such as training, reorganizations, and advertising.

Corrado, Hulten, and Sichel (2009) and Ellen McGrattan and Edward Prescott (2012) argue that investment spending has increasingly shifted toward intangibles, including those that are not currently counted. Susanto Basu and others (2004) argue that reorganizations associated with IT can explain some of the dynamics of measured U.S. and U.K. aggregate TFP growth.

In the next subsection, we consider the effects of incorporating additional intangibles from Corrado and Kirsten Jager (2015). Their U.S. intangibles data run from 1997 to 2014. Ordered from largest to smallest estimated values in 2014, their data include investments in organizational capital; branding; training; design; and new finance and insurance products.

II.C. Capital Mismeasurement and TFP

To help interpret the counterfactuals in the next subsection, here we highlight the conceptual reason why capital mismeasurement is unlikely to explain the past slowdown in TFP growth: It affects inputs as well as output, in largely offsetting ways.

Consider a stylized example for a closed economy. Suppose that after some date in the past, we miss q percentage points of true investment growth. This miss could reflect an increase in unmeasured quality improvement (relative to whatever we were missing preceding that date) or an increase in the importance of unobserved intangible investment.

The growing mismeasurement implies that true output and true labor productivity grow at a rate [s.sub.I]q faster than measured, where [s.sub.I] is the investment share of output and, by assumption, the good is completely produced domestically. It also implies that true capital input grows more quickly than measured. In a steady state, the perpetual inventory formula implies that capital grows at the same rate as investment, so capital input also grows q percent a year faster.

Thus, the change in TFP growth is the extra output growth less the contribution of the additional capital growth. In a steady state, the change is ([s.sub.I] - [s.sub.K])q, where [s.sub.K] is capital's share in production. In the data (and consistent with dynamic efficiency), [s.sub.I] < [s.sub.K]. Hence, in a steady state, capital mismeasurement makes true TFP growth slower, not faster, than measured. (17)

Of course, this is a steady-state comparison. The initial effect is that output responds more quickly than capital input, so TFP temporarily increases. Also, some domestically produced capital goods are exported, and some goods used for investment are imported. Which effect dominates over particular time frames is thus an empirical question. (18)

II.D. Mismeasurement of Durables Worsens the Slowdown: Evidence from Simulations

We now assess the quantitative importance of the mismeasurement of durable goods. As discussed above, this mismeasurement was large in the past, as well--and domestic production was more important. As a result of both factors, the mismeasurement of productivity appears less important now than in the past. As a result, with consistent measurement, the labor productivity slowdown after 2004 becomes even larger than in the official data. For TFP, the adjustments are more modest, but the slowdown is also a touch larger than in the official data.

We begin narrowly, with areas that are most grounded in a consistent methodology over time. This first conservative simulation considers alternative deflators for two categories of equipment for which considerable recent research has been done: computers and peripherals; and communications equipment (see the discussion in section II.A). We also consider alternative deflators for semiconductors. Those are primarily an intermediate input into other types of electronic goods but, because of exports and imports, revised deflators modestly affect final output growth. We then add more speculative adjustments for specialized equipment (NAICS category 3345) and software. Finally, we add estimates of intangibles from Corrado and Jager (2015).

Given alternative deflators and measures of intangibles, we adjust both output and input (capital services). The online appendix describes the details. Output grows more quickly because of faster growth in domestically produced computers and other types of information-processing equipment. Of course, some of these products are sold to consumers. Hence, the output adjustment also captures the effect on real GDP of consumers' purchases of computers and communications equipment (such as mobile devices). Capital input grows more quickly because of the faster implied growth in investment in computers and other types of information-processing equipment (whether domestically produced or imported).

For semiconductors, the adjustment to output only matters for GDP through its effect on net exports. In a closed economy, an adjustment that raises the true output of semiconductors is exactly offset by higher true intermediate input usage of semiconductors--leaving GDP unchanged. However, in an open economy, semiconductors are exported and imported. We do not have separate adjusted prices for imported versus domestically produced semiconductors, so we assume that any adjustments are proportional.

Column 0 of table 2 shows our baseline from the published data. Measured labor productivity growth (top panel), capital deepening (middle panel), and TFP growth (bottom panel) sped up in the 1995-2004 period, but slowed thereafter. The slowdown in average annual labor productivity growth was about 1 3/4 percentage points. Some of this slowdown is explained by a reduced pace of capital deepening, leaving a slowdown in TFP growth of about 1 1/4 percentage points. Labor productivity growth is especially weak after 2010, though the growth accounting attributes this to the lack of capital growth relative to labor. Hence, TFP growth was about equally weak from 2004 to 2010 and from 2010 to 2014.

Column 1 of table 2 then shows how results change relative to this baseline from adjusting computers, communications equipment, and semiconductors. As the top panel shows, these adjustments do affect labor productivity in a noticeable way. But the increase in the labor productivity growth rate is most pronounced for the 1995-2004 period, at just under 0.3 percentage point. After 2004, the alternative deflators add only a little more than 0.1 percentage point to growth. This reduced effect is due to the declining importance of domestic IT production relative to imports. Domestic production of computer and communications equipment amounted to 2.9 percent of nominal business sector value added in the late 1990s, but only 0.5 percent by 2014. A given amount of mismeasurement of computer and communications equipment therefore would have had a larger effect in the 1990s than today.

The middle panel of the table shows that the adjustments also have a substantial effect on capital services growth. Again, the major adjustment is in the 1995-2004 period, when prices, by any measure, were falling rapidly. The bottom panel shows that the effect on TFP growth is small, but it goes in the direction of exacerbating the post-2004 TFP slowdown. The adjusted TFP is a little stronger than measured in the 1995-2004 period, but a little weaker after 2004.

Column 2 of the table adds more speculative adjustments for specialized equipment and software, as described above. The upward boost to labor productivity is a bit larger in each period than in column 1. But again, the upward boost is larger in the 1995-2004 period than in the post-2004 period this time by almost 0.2 percentage point. Adjusting capital goods, once again, turns out to exacerbate the slowdown in labor productivity growth. The bottom panel shows that the adjustments also modestly exacerbate the TFP slowdown.

Column 3 of the table adds intangibles from Corrado and Jager (2015). With intangibles, the adjustments to labor productivity are even larger--but, again, the effects are largest in the 1995-2004 period. Together, the adjustments in column 3 add about 0.5 percentage point to labor productivity relative to the published data for 1995-2004. From 2004 to 2014, the adjustments add only 0.2 percentage point. Thus, the slowdown in labor productivity growth after the adjustments in column 3 is about 0.3 percentage point larger. For labor productivity, then, the adjustments taken together make the productivity slowdown markedly worse.

Other approaches to measuring intangibles--such as the more model-based approach of McGrattan and Prescott (2012)--might yield different results. Still, the results in column 3 suggest that the intangibles route is unlikely to alter the productivity slowdown.

Of course, the slowdown in capital growth, in the middle panel, also becomes much larger. As a result, in the bottom panel, the slowdown of TFP growth is affected by only a few basis points relative to the measured baseline. In particular, the adjustment subtracts 8 bp from TFP growth in the 1995-2004 period but then 12 bp during the 2004-14 period. (19) The important takeaway is that correcting for capital goods mismeasurement does not resolve the post-2004 slowdown--if anything, it makes it worse.

We also experimented with an aggressive adjustment to software deflators after 2004, whereby true software prices are assumed to fall 5 percent a year faster than measured. This counterfactual captures the hypothesis that measurement has recently gotten worse, because only the post-2004 period is affected. Yet even this aggressive adjustment turns out to have relatively modest effects. The adjustment would add about 0.1 percentage point to labor productivity growth after 2004. Yet capital growth is also higher in this simulation, and TFP is little changed.

The alternative deflators in this section imply faster TFP growth for IT-producing industries, but slower TFP growth for IT-using industries (given that capital input grows more quickly without any adjustment in output growth). Nevertheless, as discussed in the appendix, the alternative deflators do not alter the broad-based nature of the TFP slowdown. With the alternative deflators, TFP growth for industries that produce IT and other types of investment goods slows sharply after 2004, as does TFP growth for other, non-investment-producing industries.

To summarize the takeaways from this section, prices for key capital goods are mismeasured, and this mismeasurement varies over time. However, the effects of mismeasurement on productivity have been less, rather than more, important since 2004. Including intangibles, our adjustments add about 30 bp to the slowdown in labor productivity but make the TFP slowdown only modestly larger.

Thus, if the productivity slowdown after the early 2000s indeed reflects mismeasurement, the source of this mismeasurement is not found in commonly studied IT durable goods. In the remainder of the paper, we find that the growing mismeasurement of Internet services, e-commerce, fracking, and globalization (shown as "other" in figure 1) can fill only a small part of the gap.

III. "Free" Digital Services

The benefits to consumer well-being from online information, entertainment, social connections, and the like are large (Goolsbee and Klenow 2006; Varian 2011; Brynjolfsson and Oh 2014). Nevertheless, these benefits do not change the fact that market sector TFP growth slowed broadly. Under long-standing national accounting conventions, the benefits are largely outside the scope of the market economy; as we discuss, given the small monetary size of the sector, it is very hard to bring many of the benefits inside the market boundary. The largest estimates of the gains are based on models of the time cost of using the Internet as an input into the home-based production of nonmarket services for one's own consumption. The gains from nonmarket production using the consumer's time are conceptually distinct from the gains in market sector output. And regardless of how they are treated, the nonmarket gains are not big enough to offset a significant fraction of the missing $3 trillion a year in business output from the productivity slowdown.

In the standard national accounts approach, none of the output of online service providers whose revenue comes from selling ads is included in the final consumption of households. Rather, their entire output is used for the intermediate consumption of the advertisers.

Drawing on an earlier body of literature on free broadcast television, Rachel Soloveichik (2015b) and Leonard Nakamura and Soloveichik (2015) propose an alternative approach that includes entertainment and information services supported by advertising in household final consumption. This approach prevents artificial changes in GDP when consumers switch between free and subscription-based media. The effect on the GDP growth rate turns out to be minuscule, however, because advertising tends to be a small and relatively stable share of GDP. Further, this alternative approach has no effect on the nominal value added of the business sector by construction, leaving little scope for an effect on business sector productivity. Our "other" category of adjustments in figure 1 therefore adds nothing to productivity growth in any of the periods for ad-supported digital services. Where we can get a small adjustment (about 1 bp from 1995 to 2004, and 4 bp from 2004 to 2014) is for the improved quality of Internet service providers (ISPs) that is not included in the official deflators.

III.A. The Time Cost Approach to Gains from Free Digital Services

The standard approach to measuring gains from new goods considers the difference between the amount of money that consumers would have been willing to pay and the amount that they actually had to pay. Yet the main cost to a user of, say, Facebook, YouTube, or TripAdvisor is the opportunity cost of the user's time. Hence, starting with Austan Goolsbee and Peter Klenow (2006), studies of the gains from free digital services have considered the time costs of using these services, and not only the money costs associated with accessing them.

Time costs are part of Becker's (1965) model of the allocation of time. Suppose the representative consumer has the following utility function:

U([Z.sub.I], [Z.sub.TV], [Z.sub.1],[Z.sub.2] ...).

Households benefit from the consumption of (possibly unpriced) services from the Internet, [Z.sub.I] from television, [Z.sub.TV], and from other activities, [Z.sub.i], i [subset] {l, 2, ...}. The elements of [Z.sub.i] include meals at home, meals at restaurants, having a clean house, playing soccer, skiing, and so forth.

In this Becker-style model, the [Z.sub.i] are not the direct purchases of market goods and services. Rather, households combine purchased market goods and services with their own time to generate the actual services they value. They buy a soccer ball (which is part of GDP), and they combine that market purchase with their (leisure) time, and their children's time, to obtain "soccer services." They combine a market purchase of a restaurant meal with several hours of their time. They combine gasoline and a car (both purchased in the market) with their time in order to go on a vacation that they enjoy. They combine a hotel room with their time to get a refreshing night of sleep during this vacation. Broadly, the services take the form

[Z.sub.i] = [Z.sub.i] ([C.sub.i], [T.sub.i], [Q.sub.i], i [subset] {I, TV, 1,2, ...}.

Thus, in the household's production function for combining the market purchase with time, playing soccer generates services from the market consumption of a soccer ball, [C.sub.i]; the time spent playing soccer, [T.sub.i]; and, possibly, technical change, [Q.sub.i].

Now consider a stylized problem that captures the key issues in valuing the Internet. Households seek to maximize their well-being subject to cash and time budget constraints:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

(2) s.t. [[SIGMA].sub.i][P.sub.i][C.sub.i] + [F.sub.I] + [F.sub.TV] = [WT.sub.work],

(3) [T.sub.work] + [T.sub.I] + [T.sub.TV] + [[SIGMA].sub.i] [T.sub.i] = 1.

In the cash budget constraint (equation 2), income is the wage, W, multiplied by time spent working, [T.sub.work]. Households purchase broadband access, [C.sub.I], via cable, mobile phone, or another means by paying a fixed or flat cost, [F.sub.I], each period. In the time budget constraint (equation 3), total time is normalized to 1; in other words, time spent working is time not spent engaged in other activities. The Internet services that they actually value then depend on the time they spend online, [T.sub.I], net of a flow "time tax," [[tau].sub.I], which is proportional to their use of the Internet. For example, they get "free" access to YouTube videos in exchange for spending a proportion of their time watching ads.

As Erik Brynjolfsson and Joo Hee Oh (2014) find, Internet content may get better over time, as captured in quality, [Q.sub.l]. The quality of Internet content may reflect the growing number of websites available, the number of videos available on YouTube, or whether one's friends are on Facebook. These are conceptually distinct from download speed or other characteristics of one's ISP. And these characteristics conceptually represent a larger quantity of [C.sub.I]. (As we discuss below, not all these characteristics are currently in the implicit deflator for Internet access.)

Television is similar to the Internet. One might pay a fixed cost for watching TV, [F.sub.TV], as well as paying a time tax, [[tau].sub.TV] again in the form of watching ads. Historically, in the United States, before the inception of cable TV, [F.sub.TV] = 0, the entire provision of broadcast TV service was paid for through watching ads. For other types of goods, [C.sub.I], the price is [P.sub.i].

This formulation illustrates the key issues, but it does make simplifications. For example, it ignores nonwage income, and also durable goods, such as computers, cell phones, TVs, and beds; it assumes that households are unconstrained in their time allocation, so that the marginal opportunity cost of time is the (fixed) wage; and it ignores any extra disutility associated with working or with other activities. Paul Schreyer and W. Erwin Diewert (2014) discuss extensions to Becker's (1965) framework.

It is useful to combine the money and time budget constraints as

(4) ([[summation].sub.i] [P.sub.i][C.sub.i] + [F.sub.l] + [F.sub.TV]) + W([T.sub.I] + [T.sub.TV] + [[summation].sub.i][T.sub.i]) = W.

"Full expenditure" in this formula is the sum of market expenditures (the first term in parentheses) and the monetary value of nonmarket expenditures of time (the second term). Some nonmarket expenditures could be on the home-based production of goods and services that are a close substitute for market goods and services, such as cooking and cleaning. Others are for leisure (surfing the Internet for personal reasons, watching TV, playing soccer, and so forth). Some are in the middle, such as Wikipedia, where unpaid content writers create and edit entries for their personal enjoyment, but it substitutes for market encyclopedia services. (20)

The core national accounts measure the prices and quantities that correspond to market activities, which show up in the first term in equation 4. Nevertheless, the importance of nonmarket activities, the second term, has long been recognized. After all, Americans ages 15 and older spend only 15 percent of their total time working, or 24 percent of the time not spent sleeping. (21) Katharine Abraham and Christopher Mackie (2005) and William Nordhaus (2006) discuss the need for nonmarket satellite accounts.

Based on increasing amounts of time spent online, Brynjolfsson and Oh (2014) estimate that the incremental consumer surplus from free digital services is sizable, averaging $25.2 billion for 2002-11, with larger effects in the years after 2005. (22) These incremental gains are the equivalent of adding about 0.3 percentage point a year to business sector output and productivity growth. Adding these gains is not appropriate, however, if the question is the productivity of the economy in producing market goods and services. The gains implied by changes in the allocation of consumers' time are linked to the home-based production of nonmarket services, not market output.

III.B. The Market Production of New Goods

In contrast to the time-based estimates of the value of free digital services, the standard approach used to define the theoretical measure of real GDP implies that only a small amount of extra digital service output is missed, mainly reflecting download speed and other characteristics that are not currently included in the deflators for Internet access and cell phone service.

Real household consumption and real GDP measure changes at the margin, not total amounts of consumer surplus. Hence, even if free digital services belonged in market sector GDP and provided a large amount of consumer surplus, the growth-rate effects would not necessarily be large. What would matter is the incremental consumer surplus from a change in the consumption of the digital services.

For existing goods, the BEA's chained Fisher index of real personal consumption expenditures correctly captures the change in the consumer surplus. (23) For an existing free good, the correct weight on any change in quantity is zero because consumers adjust the quantity consumed of each good (excluding those at a corner solution of zero) so that the value of the marginal unit consumed is proportional to the price.

Conversely, new goods bias can arise even if the good enters at a price of zero. The measurement theory for new goods imagines that the new good previously existed but was offered at the "virtual price" that just drove demand to zero. The area under the demand curve from the virtual price down to the actual price of the good after it entered gives the consumer surplus from the appearance of the new good. Some major free digital services--including Facebook, YouTube, and Google Maps--appeared after the start of the productivity slowdown.

However, because they require Internet access, free digital services are not costless to consume. The price of the required Internet access can be viewed as the price of a bundled commodity, where the free digital services are part of the bundle. With an assumption about the slope and curvature of the demand curve for the bundled commodity, increased spending on Internet access to enjoy the new free services could be used to estimate the gains from this newly available, bundled commodity.

We do not make such an estimate in the present paper, but an indication of its magnitude comes from estimates of welfare gains from Internet access. Shane Greenstein and Ryan McDevitt (2009), for example, use data on the replacement of dial-up Internet access with broadband, and estimate that the uptake of broadband generated an average of $0.3 billion a year in unmeasured consumer surplus for 1999-2003, and an annual average of just over $1 billion for 2004-06. Brynjolfsson and Oh (2014) extend Greenstein and McDevitt's (2009) analysis, adding an adjustment for increased consumption of services per hour, as measured by rising data usage patterns. They find that this "money measure" of the gains from improved ISP services (the part that would be appropriate to add to market sector output) are a little larger, but still small--averaging only $2.7 billion per year (2-3 bp of business output).

This analysis of the monetary mismeasurement applies only to Internet access at home, not mobile access. Using Brynjolfsson and Oh's (2014) data on the improved quality of Internet access, and assuming that the increase in the mobile share since 2004 reflects mobile data that are subject to the same unmeasured quality improvement, "true" output and productivity thus rise by 1 bp in the 1995-2004 period and by 4 bp after 2004. We include this adjustment in the "other" category in figure l. (24)

III.C. An Alternative Treatment of Advertiser-Supported Digital Services

Internet businesses make money in part by creating content that users value. Is it reasonable to exclude this entirely from GDP, just because it does not involve a monetary cost to households? We now consider an alternative that brings some of these otherwise-omitted, advertising-supported digital services into household consumption.

Some free digital services are, in fact, already included in GDP--namely, those provided by nonprofit institutions such as Wikipedia. But most free digital services are supported by advertising. (25) The national accounts treat advertisers as intermediate consumers of the services of a business whose revenue comes entirely from advertising. For example, broadcast television services have long been counted in the national accounts as an intermediate input: Companies buy advertising, so major broadcasting networks such as ABC or NBC are like advertising agencies. Many Internet services have that same treatment: Facebook and Google provide advertising services to businesses, not services consumed by households.

Nakamura and Soloveichik (2015) propose a framework for including ad-supported entertainment and information services in households' consumption that draws on an earlier body of literature on how to treat broadcast television in national accounts. They value the services given to households at their cost of production. This framework is based on the observation that consumers implicitly pay for TV entertainment and information by watching ads (or, in some cases, providing valuable personal information). The time taxes [[tau].sub.l] and [[tau].sub.TV] were not included in the cash budget constraint (equation 2) because they do not have an explicit price. But we can express [WT.sub.l] (the time value associated with the Internet in equation 4) as W[[tau].sub.i][T.sub.l] + S(1 - [[tau].sub.I])[T.sub.l], where the first term is part of a market-oriented barter transaction that can be imputed between households and firms. In this barter transaction, the time that consumers spend viewing ads is a service purchased from households by providing entertainment or information services.

When these "free" entertainment or information services are added to households' consumption, GDP goes up by the value of the extra household consumption. But the national accounts need to balance--someone needs to produce the extra value added. The TV networks or the providers of the digital services have the same inputs of capital and labor, and their measured value added does not change. Instead, on the production side, the rise in GDP can be traced to households' production of "ad-watching services." With no change in the output consumed by advertisers, recording output sold to households requires us to impute an equivalent amount of purchases of services from consumers who view the ads.

This approach is reasonable: It monetizes an implicit barter transaction that consumers undertake with Google and Facebook and other advertising-supported service providers, and it recognizes that consumers value the services they receive. Nonetheless, treating consumers as suppliers of ad-watching services and as consumers of free digital services does not change the business sector's nominal value added; the ad-watching services are outside the boundary of the business sector. (26) On one hand, if the deflators are the same, business sector TFP will also be unaffected because the intermediate inputs of the ad-watching services that are added on the input side of the productivity calculation will exactly offset the "free" entertainment and information services that are added on the output side. On the other hand, it is possible for the deflators to vary in a way that raises business TFP if ad viewing, and the delays caused by the time it takes to download the ads, take up a falling proportion of time spent consuming digital services.

III.D. The Significance of Free Digital Services for Productivity Measures

The effect on the level of GDP from allocating part of output of the providers of free entertainment and information services to household final consumption is limited because advertising is only a small share of GDP.

When services to households from traditional print and broadcast media are included along with digital services, the level of U.S. GDP shifts up by about 0.5 percent (Soloveichik 2015a). The effect on the growth rate of real GDP is smaller still. In Nakamura and Soloveichik (2015, table 3), real advertising services have an average growth rate of 2 percent from 2004 to 2013, while the real output of the business sector used in productivity measurement grows at just over 1.5 percent a year. Assuming that the real growth rate of the advertising-supported services was the same as the real growth rate of the advertising and using a share weight of 1.3 percent of business sector output implies an upward revision of less than 1 bp to productivity growth in the slowdown period. But the pre-slowdown adjustment is similar or larger, so this adjustment does not reduce the size of the productivity slowdown. In our benchmark set of "other" adjustments, we round the effect to zero.

How sensitive is this benchmark to the advertising deflator? This deflator may have a new goods bias caused by the emergence of online advertising, if that is a more efficient technology for delivering ads. Soloveichik's (2015a) estimate of the 2012 cost per viewer-hour of an online advertisement is 11 cents, compared with 54 cents for broadcast TV. The lower cost of attracting ad viewers by providing free digital services suggests that the substitution of online advertising for traditional media advertising may involve a productivity gain in ad delivery. Facebook, for example, does not have to pay to acquire content because consumers themselves create the content, making the cost of attracting users to the website quite low.

Suppose the quality-adjusted price for online advertising is half that of traditional media. A unit-value price index would capture the outlet substitution effect as ad buyers switch to online advertising. The market share of online advertising rose from 7 percent in 2004 to 27 percent in 2013 (Nakamura and Soloveichik 2015), implying an average annual growth rate adjustment of -1.9 percent. With a 1.3 percent weight of advertising in the output of business, the implied annual adjustment to productivity growth would be an increase of about 2.5 bp.

Finally, we note that some of the welfare benefits of free digital services involve better choices of where and what to buy. Information from TripAdvisor or Yelp may improve restaurant selection (and even have dynamic spillover effects as bad restaurants improve or exit). In addition, online information and online shopping have expanded the set of available varieties. Moreover, the Internet has also led to new markets for used goods through websites such as eBay and Craigslist. A cost-of-living index that measured the gains from the improved matching of products and product varieties to consumers' preferences and circumstances might show substantial gains (even beyond the e-commerce benefits discussed below). Making more efficient use of what we have raises welfare, but does not represent an outward shift in market output or even the production possibility frontier that is achievable with a given factor endowment. (27)

Divergences between welfare change and real GDP from IT-enabled shifts between market production and nonmarket production also arise in other contexts. For example, tax software has reduced reliance on paid tax preparers, and smartphone apps such as Skype and WhatsApp have reduced spending on phone calls and text messages. Yet it is worth remembering that welfare changes from substitution between nonmarket and market activity are not new. In the early 20th century, for example, paid domestic workers did many tasks that by mid-century had been taken over by the households themselves. Conversely, home appliances such as washing machines served as "engines of liberation" (Greenwood, Seshadri, and Yorukoglu 2005) that dramatically increased women's labor force participation.

Furthermore, though nonmarket and market production are somewhat substitutable in generating consumer welfare, many questions about economic growth require a concept of productivity that covers only the market sector's output and inputs. Imputations for nonmarket output would make the productivity measure more subjective and model-driven, as opposed to data-driven. Gains in nonmarket output and their contribution to welfare, though important, are best treated as a separate concept from productivity change.

IV. E-Commerce and Gains in Variety and Match Quality

E-commerce has grown rapidly in importance, both for business-to-business and business-to-consumer transactions. In this section, we estimate that the growing unmeasured benefits to consumers contribute about 2 bp to the productivity slowdown. Business-to-business e-commerce has made intermediate transactions more efficient, but in principle it does not directly cause the mismeasurement of aggregate productivity. Indirectly, however, it can complicate productivity measurement through its effects on outsourcing and the reorganization of production into global supply chains. The next section considers these effects in the context of globalization.

According to the Census Bureau's Monthly Retail Trade Report, the share of e-commerce in retail sales has risen about 0.5 percentage point a year since 2000--from 0.9 percent in 2000 to 2.1 percent in 2004, 5.3 percent in 2012, and 7.3 percent in 2015. (28) This steady shift in purchasing patterns reflects the gains to consumers in savings of time and transportation costs, as well as their ability to search over a much broader range of varieties.

For online books, Brynjolfsson, Yu Hu, and Michael Smith (2003) estimate the gains from increases in variety available on Amazon and other websites. They consider obscure book titles as new goods, because these would have been hard to find at brick-and-mortar stores. The compensating variation from a new good with a constant price elasticity of [alpha] < -1 can be approximated by dividing its post-entry sales by 1 + [alpha]. In 2000, out of $24.59 billion in total book sales, the authors estimate that $578 million were from online purchases of obscure titles. Depending on the assumed elasticity, the compensating variation was in the range of $731 million to $ 1.03 billion, or about 3 to 4 percent of total book sales that year.

This approach probably overestimates the gains by assuming a constant demand elasticity and by ignoring losses in consumer surplus from the disappearance of brick-and-mortar bookstores. Robert Feenstra (1994) derives a more conservative formula for the unmeasured gains from net variety growth based on a model with a constant elasticity of substitution [sigma] > 1. Let [[lambda].sub.t] equal 1 minus the share of expenditures in period t going to new varieties, and let [[lambda].sub.0] be 1 minus the share of expenditures in period 0 going to varieties that disappear in period 1. Then the welfare shift from changing the availability of varieties can be calculated by multiplying the constant elasticity of the substitution price index for the continuing varieties by a factor of [([[lambda].sub.t]/[[lambda].sub.0])).sup.1/([sigma]-1)]. The elasticity of substitution between different varieties of the same good is usually high. With [sigma] = 4 and an assumption of no variety disappearances, the 2.35 percent market share garnered by obscure book titles newly made accessible by the Internet implies a correction to the price index of-0.8 percent--though, with a relatively low assumption of [sigma] = 3, the bias becomes 1.2 percent. These gains accumulated during a period of several years, so the annual bias is smaller.

Books, of course, are just one type of good with an increased availability of varieties online. Suppose we view e-commerce itself as a sort of new variety. Using the Census shares and assuming [sigma] = 4, the correction factor to the price index for retail goods falls 15 bp a year from 2004 to 2014, compared with 8 bp a year from 1995 to 2004 (assuming the online share was zero in 1995). Personal consumption expenditures on goods amount to about 25 percent of the gross value added of business, excluding housing. Using this as a weight on the bias in the retail sales price index implies an upward correction of just under 4 bp a year in business sector productivity after 2004 and about 2 bp a year from 1995 to 2004. Thus, correcting for gains from e-commerce shaves perhaps 2 bp from the productivity slowdown.

V. Fracking and Globalization

Fracking and globalization are two areas where mismeasurement has plausibly contributed in a meaningful way to the slowdown in measured productivity growth. Fracking is a technological innovation that makes it profitable for drillers to access natural resources of an inferior "quality." A back-of-the-envelope calculation suggests that the unmeasured aspects of this innovation have raised true aggregate labor and TFP growth by about 5 bp a year since 2004. For globalization, import-price declines from offshoring and related changes in import sourcing are largely missed, so true import growth is understated in the late 1990s and early 2000s (the time of China's accession to the World Trade Organization); correspondingly, growth in GDP, labor productivity, and TFP are overstated. This globalization adjustment shows up as a negative contribution of about 10 bp from 1995 to 2004 and -2 bp from 2004 to 2014 for the "other" category in figure 1.

V.A. Technological Innovation in Oil and Natural Gas: The Tracking Revolution

In the industry TFP data discussed in section I, the extraction of oil and natural gas performed strongly in TFP during the 2007-13 period. Nevertheless, the standard measure of TFP for mining does not control for variation in the quality of the natural resources being extracted, so it is not a pure measure of technology. Technological innovations that made it possible to extract oil and natural gas from previously uneconomic geologic formations diffused rapidly in the 2000s. This type of technological change is unlikely to be fully reflected in the statistics. Hence, true growth in mining investment in infrastructural capital is almost surely faster than measured. At the same time, a key input (the subsoil reserves component of land) that is not included in the traditional approach to measuring mining productivity fell in quality.

[FIGURE 7 OMITTED]

Fracking--originally a cost-effective way to extract natural gas from shale, using horizontal drilling and hydraulic fracturing--was discovered in the late 1990s. During the next decade, this technique was improved and extended to the extraction of oil from shale and other types of low-permeability formations. As a result, the last half of the 2000s saw a remarkable resurgence in the production of oil and natural gas in the United States (figure 7). Import facilities for liquefied natural gas have been hastily repurposed as export facilities, and OPEC has changed its pricing strategy.

The fracked wells are like a new good whose benefits are not counted by conventional measures of TFP. Nordhaus and Edward Kokkelenberg (1999, pp. 63-64) observe that deposits of an exhaustible natural resource vary in their extraction costs. Above some cutoff level of rent (the difference between the extraction cost and the market price of output), extraction does not occur. Suppose that technological progress reduces the unit cost of extraction for all deposits. Now, 7t > 1 units can be extracted from any given deposit in period 1, with the same inputs of labor and capital that produced 1 unit in period 0. The output price is set on world markets and does not change, and neither does the cutoff level of rent for extraction to be undertaken. Deposits that were previously uneconomic now begin to be extracted. The level of productivity at the least productive establishment remains constant, though that of the most productive establishment rises from [[lambda].sup.max.sub.0] to [[lambda].sup.max.sub.1] = [pi] [[lambda].sup.max.sub.0]. Assuming productivity levels are uniformly distributed across establishments from 1 to [[lambda].sup.max.sub.0], and that all establishments are identical in size as measured by inputs, measured productivity growth for the industry, denoted by [??] - 1, is

[??] - 1 = [[1 + [pi][[lambda].sup.max.sub.0]]/[1 + [[lambda].sup.max.sub.0]]] - 1 = [[lambda].sup.max.sub.0]/[1 + [[lambda].sup.max.sub.0]] ([pi] - 1).

For example, if [[lambda].sup.max.sub.0] = 2, only two-thirds of true productivity gains would be measured.

A proper accounting for the quality of land as a factor of production would capture the gains. Deteriorating land quality would imply slower growth of inputs than in the official data, and TFP would grow faster. (29) Careful measurement of land services in mining--and elsewhere--is challenging. In the BLS productivity data, the extraction of oil and natural gas appears to use almost no land, because the value of rights to extract subsoil mineral deposits is included in the services of fixed capital assets (which consist largely of structures). Alternative productivity measures for Australian mining, published by the Australian Bureau of Statistics, imply that roughly half the conventionally measured services of fixed capital assets actually represent services of subsoil natural resources. (30) We assume that this relationship holds for the United States.

Accounting properly for technological progress in the oil and natural gas industries requires not only an assessment of land-quality changes but also quality-adjusting the fixed assets that embody the technological improvements. These consist primarily of oil and gas wells drilled for exploration or development purposes. The quality adjustment would reflect the cost reduction made possible by better technology while holding constant the mix of deposits being exploited.

In the post-2004 period, the average share of investment in oil and natural gas structures in the value added of business is about 0.9 percent. However, plausibly about half of that--or about 0.5 percent of business output--is the structure itself (which is improving more quickly than measured); the remainder is actually the subsoil asset (where the quality is getting worse). In terms of output (i.e., final investment), suppose there is a fairly large true-quality adjustment to the price index for oil and gas extraction structures of 10 percent a year after 2004. Multiplying this by the roughly 0.5 percent share of business value added implies that the true investment is about 5 bp faster. This goes directly into the other portion shown in figure 1 above, boosting true labor productivity in the post-2004 period. For TFP, the question is how much capital is improving and land is deteriorating. As a rough first pass, we assume that the two effects offset each other--leaving measured capital growth about right. In this case, the increment to labor productivity of 5 bp also passes through to aggregate TFP.