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Is Automation Labor Share-Displacing? Productivity Growth, Employment, and the Labor Share.

It is a widely held view that recent and incipient breakthroughs in artificial intelligence and dexterous, adaptive robotics are profoundly shifting the terms of human-versus-machine comparative advantage. In light of these advances, numerous scholars and popular writers anticipate the wholesale elimination of a vast set of currently labor-intensive and cognitively demanding tasks, leaving an ever-diminishing set of activities in which labor adds significant value (Brynjolfsson and McAfee 2014; Ford 2015; Frey and Osborne 2017). The displacement of labor from production could take (at least) two forms: employment displacement, meaning the elimination of aggregate employment; or labor share displacement, meaning the erosion of labor's share of value added in the economy.

Whether technological progress ultimately proves employment-displacing or labor share-displacing depends proximately on two factors: how technological innovations shape employment and labor's share of value added directly in the industries where they occur; and how these direct effects are augmented or offset by employment and labor share changes elsewhere in the economy that are indirectly spurred by these same technological forces. The first of these phenomena--the direct effect of technological progress on employment and labor share in the specific settings in which it occurs--is often readily observable, and we suspect that observation of these direct labor share-displacing effects shapes theoretical and empirical study of the aggregate impact of technological progress. The indirect effects of technological progress on these same outcomes, however, are likely more challenging to observe and quantify, and hence may receive short shrift in economic analysis and in the wider public debate. (1)

To see the challenge this creates, consider the two panels of figure 1, which reports bivariate scatters of the relationship between industry-level total factor productivity (TFP) growth over the 1970-2007 period and contemporaneous industry-level log employment growth (the top panel) and industry-level changes in log labor share (the bottom panel), defined as the log ratio of the wage bill to value added. (2) Both panels reveal a well-determined downward slope: Industries experiencing faster measured TFP growth on average exhibit steep relative declines in employment and labor share over this period. It would be tempting to infer from these figures that technological advances (captured by TFP growth) erode aggregate employment and labor's share of national income.

But theory makes clear that there is no direct mapping between the evolution of productivity and labor demand at the industry level and the evolution of labor demand in the aggregate (Foster and others 2017). A long-standing body of literature, starting with research by William Baumol (1967), has considered reallocation mechanisms for employment, showing that labor moves from technologically advancing to technologically lagging sectors if the outputs of these sectors are not close substitutes. Further, Rachel Ngai and Christopher Pissarides (2007) and Daron Acemoglu and Veronica Guerrieri (2008) show that such ongoing unbalanced productivity growth across sectors can nevertheless yield a balanced growth path for labor and capital shares. Indeed, one of the central stylized facts of modern macroeconomics, immortalized by Nicholas Kaldor (1961), is that during a century of unprecedented technological advancement in transportation, production, and communication, labor's share of national income remained roughly constant (Jones and Romer 2010). This empirical regularity, which John Maynard Keynes (1939) deemed "a bit of a miracle," has provided economists--though not the lay public--with grounds for optimism that, despite seemingly limitless possibilities for labor-saving technological progress, automation need not displace labor as a factor of production.

Table 1 confirms the broad relevance of these theoretical observations. Aggregate employment grew dramatically in all countries from 1970 to 2007, even as relative employment fell in the industries experiencing the fastest productivity growth. Yet, conversely, labor's share of value added was steady or rising in the 1970s, declined modestly in the 1980s and 1990s, and then fell steeply in the 2000s in many countries. These facts thus highlight the pitfalls of extrapolating from direct, first-order technological relationships (here, observed at the industry level) to labor market outcomes in the aggregate, because the latter incorporate both direct and indirect consequences of technological progress (as well as many non-technological factors).

This paper applies harmonized cross-country and cross-industry data to explore the relationship between technological change and labor market outcomes over four decades. A first contribution of the paper is to attempt to overcome the tension, endemic to this area of work, of using micro-economic variation to afford identification while attempting to speak to macroeconomic outcomes. This tension arises here because we study the relationship between productivity growth, innovation, and labor displacement at the country-industry level. As figure 1 underscores, naively extrapolating from industry-level to aggregate-level relationships is potentially fallacious. The alternative--directly estimating effects at the macro level--often suffers from underidentification and low statistical power, and furthermore is silent on the microeconomic channels through which aggregate effects come about.

To overcome these pitfalls, we empirically model three micro-macro linkages that, in combination with the industry-level estimates, allow us to make broader inferences about aggregate labor displacement effects. (3) The first link uses harmonized data from the World Input--Output Database (Timmer and others 2015), enumerating cross-industry input--output linkages to trace the effects of productivity growth in each industry to outcomes occurring in customer industries and in supplier industries--that is, industries for which, respectively, the originating industry is upstream or downstream in the production chain. (4) The second link connects aggregate economic growth and sectoral labor demands. Recognizing that productivity growth in each industry augments aggregate income and hence indirectly raises final demand, we estimate the elasticity of sectoral demand emanating from aggregate income growth and then apply our TFP estimates to infer the indirect contribution of each industry's productivity growth to final demand. Third, our analytic framework recognizes that uneven productivity growth across industries yields shifts in industry shares of value added, which in turn potentially alter labor's share of aggregate value added. (5)

Our net estimates of the impact of productivity growth and innovation on aggregate outcomes of interest therefore sum over (i) direct industry-level effects; (ii) indirect customer and supplier effects in linked sectors; (iii) final demand effects accruing through the effect of productivity growth on aggregate value added; and (iv) composition effects accruing through productivity-induced changes in industry shares of value added. We believe that this simple accounting framework can be usefully applied to other data sets and sources of variation.

Distinct from earlier work that focuses on specific measures of technological adoption or susceptibility (for example, robotics and routine task replacement), a second contribution of the analysis is to employ TFP--which is an omnibus measure of technological progress (Solow 1956). Using TFP as our baseline measure potentially overcomes the challenge for consistent measurement posed by the vast heterogeneity of innovation across sectors and periods. TFP is also applicable to our analysis for a second reason: Because all margins of technological progress ultimately induce a rise in TFP--either by increasing the efficiency of capital or labor in production or by reallocating tasks from labor to capital or vice versa--our empirical approach is not predicated on a specific mechanism through which technological progress affects outcomes of interest. But the flip side of this agnosticism is that merely observing a change in TFP in any industry or time period does not tell us which channel (augmentation, reallocation) is operative. Using information on output, employment, earnings, and labor's share of value added, however, we can infer these channels. Specifically, we study how changes in industry-level TFP affect output (value added) quantities and prices, employment, earnings, and labor's share of value added economy-wide, to draw inferences on both industry-level and aggregate labor-augmenting and labor share-displacing effects of technological progress.

It is well understood that estimates of TFP may also be confounded with business cycle effects, industry trends, and cross-industry differences in cyclical sensitivity (Basu and Fernald 2001). We confront these issues directly. We purge the simultaneity between an industry's estimated TFP growth and changes in other industry-level measures that serve as inputs into the TFP calculation (for example, output, wage bill, and employment) by replacing own-country-industry TFP with the mean TFP of the corresponding industry observed in other countries in the same year. (6) We purge the potential cyclicality of TFP by including a set of distributed lags as well as country-business cycle indicators, which absorb business cycle variation in productivity measures. We address the opaqueness of TFP as a measure of technological progress by complementing it with an alternative, directly observable measure of industry-level technological advancement: patent awards by industry and country (Autor and others 2017a). Patent awards--and even more so, patent citations--prove to be strong predictors of industry-level TFP growth. Using patent awards in place of TFP growth, we obtain strongly comparable estimates of the relationships between technological progress, employment, wage bill, and value added, which we view as useful corroborative evidence.

TFP's virtue as an omnibus technology measure is also its shortcoming as a specific technology measure. Because TFP incorporates productivity growth arising from all sources, our analysis cannot directly answer the question of whether recent or specific technologies--such as industrial robotics or artificial intelligence--are more or less labor-complementing or labor share-displacing than earlier generations of technology. By the same token, our analysis cannot distinguish between the effects of automation-based versus non-automation-based sources of TFP growth, which may in turn have distinct (or even countervailing) effects on either employment or on labor's share of value added. We refer readers to recent studies focusing on specific technological advances for this evidence (Graetz and Michaels, forthcoming; Acemoglu and Restrepo 2017; Dauth and others 2017; Chiacchio, Petropoulos, and Pichler 2018).

Our work builds on an active, recent body of literature that questions the optimistic implications of the long-standing Kaldor facts by offering models where aggregate labor displacement is a potential consequence of advancing technology. Acemoglu and Pascual Restrepo (2018, forthcoming) consider models in which two countervailing economic forces determine the evolution of labor's share of income: the march of technological progress, which gradually replaces "old" labor-using tasks, reducing labor's share of output and possibly diminishing real wages; and endogenous technological progress that generates novel labor-demanding tasks, potentially reinstating labor's share. The interplay of these forces need not necessarily yield a balanced growth path; that is, labor's share may decline. Daniel Susskind (2017) develops a model in which labor is ultimately immiserated by the asymptotic encroachment of automation into the full spectrum of work tasks--contrary to Acemoglu and Restrepo (forthcoming), labor immiseration is guaranteed because falling labor scarcity does not spur the endogenous creation of new labor-using tasks or labor-complementing technologies. (7)

A central empirical regularity that underscores the relevance of this recent work is that labor's share of national income has indeed fallen in many nations in recent decades, a trend that may have become more pronounced in the 2000s (Elsby, Hobijn, and Sahin 2013; Karabarbounis and Neiman 2013; Piketty 2014; Barkai 2017; Autor and others 2017b; Dao and others 2017; Gutierrez and Philippon 2017). Reviewing an array of within- and cross-country evidence, Loukas Karabarbounis and Brent Neiman (2014) argue that labor's falling share of value added is caused by a steep drop in the quality-adjusted equipment prices of information and communication technology relative to labor. Though Karabarbounis and Neiman's work is controversial, in that it implies an aggregate capital/labor substitution in excess of 1--which is a nonstandard assumption in this literature--their work has lent empirical weight to the hypothesis that computerization may erode labor demand. Related work by Maya Eden and Paul Gaggl (2018) calibrates an aggregate production function, and similarly attributes part of the decline in the U.S. labor share to a rise in the share of income paid to information and communication technology capital.

A growing microeconometric literature presents a mixed set of findings on whether such erosion has occurred recently or in the past. Focusing on the first half of the twentieth century, Michelle Alexopoulos and Jon Cohen (2016) find that positive technology shocks raised productivity and lowered unemployment in the United States between 1909 and 1949. Using contemporary European data, Terry Gregory, Anna Salomons, and Ulrich Zierahn (2016) test whether routine-replacing technical change has reduced employment overall across Europe, and they find that though this type of change has reduced middle-skill employment, this reduction has been more than offset by compensatory product demand and local demand spillovers. In work closely related to ours, Mai Chi Dao and others (2017) analyze sources of the trend decline in labor share in a panel of 49 emerging and industrialized countries. Using cross-country and cross-sector variation in the prevalence of occupations potentially susceptible to automation (a la Autor and Dorn 2013), Dao and others find that countries and sectors initially more specialized in routine-intensive activities have seen a larger decline in labor share, consistent with the possibility of labor displacement. (8)

Concentrating on industrial robotics, arguably the leading edge of workplace automation, Georg Graetz and Guy Michaels (forthcoming) conclude that industry-level adoption of industrial robots has raised labor productivity, increased value added, augmented workers' wages, had no measurable effect on overall labor hours, and modestly shifted employment in favor of high-skill workers within countries that belong to the European Union. Conversely, using the same underlying industry-level robotics data but applying a cross-city design within the United States, Acemoglu and Restrepo (2017) present evidence that U.S. local labor markets that were relatively exposed to industrial robotics experienced differential falls in employment and wage levels between 1990 and 2007. (9)

Our analysis proceeds as follows. Section I summarizes the data and measurement framework and presents the simple shift-share decomposition that undergirds our accounting framework. Section II presents our estimates for the direct effects of productivity growth (measured initially by TFP, in subsection II.A; and by patents in subsection II.B) on labor input, value added, and labor's share of value added, across a range of model specifications. Section III then presents our main results accounting for both direct ("own-industry") effects, and for indirect effects operating through input-output linkages and final demand. Section IV quantifies the aggregate implications of these direct and indirect effect estimates for employment, hours worked, and labor's share of value added to assess whether technological progress has, on net, been either augmenting or displacing of the aggregate employment or labor share. We also consider in this section whether our accounting approach can explain cross-industry patterns of employment change and aggregate, time-series changes in the evolution of the labor share between and within industries.

To briefly summarize our results, automation (as embodied in TFP growth) has been employment-augmenting yet labor share-displacing over the last four decades. As implied by the scatter plot in figure 1 (top panel), industries with persistent gains in relative productivity secularly contract as a share of aggregate employment, meaning that the direct effect of rising productivity has been to reduce labor input in the sectors where it originates. But this direct effect is more than fully offset by two indirect effects: First, rising TFP within supplier industries catalyzes strong, offsetting employment gains among their downstream customer industries; and second, TFP growth in each sector contributes to aggregate growth in real value added and hence rising final demand, which in turn spurs further employment growth across all sectors.

Conversely, we find that productivity growth is directly labor share-displacing in the industries where it originates; and it is particularly important that this direct effect is not offset by indirect effects spurred by input-output linkages, compositional shifts, or final demand increases. Thus, we conclude that productivity growth has contributed to an erosion of labor's share of value added. Notably, this labor share-eroding effect was not present in the first decade of our sample, the 1970s, but then became strongly evident thereafter. Our analysis therefore broadly supports the hypothesis that the decline in the labor share since the 1980s is consistent with a shift toward more labor-displacing technology commencing in the 1980s. But the acceleration in the labor share decline observed during the 2000s is left unaccounted for by this mechanism.

In section V, we briefly consider the interpretation of our findings, focusing in particular on the relationship between the industry-level and aggregate outcomes observed in our data, and the underlying unobserved firm-level dynamics that may contribute to these outcomes.

I. Data and Measurement

Our analysis draws on EU KLEMS, an industry-level panel database covering the countries that belong to the Organization for Economic Cooperation and Development since 1970 (O'Mahony and Timmer 2009). We use the 2008 release of EU KLEMS, supplemented with data from the 2007 and 2011 releases to maximize data coverage. Our primary analytic sample covers the period 1970-2007. We limit our analysis to the 19 developed countries of the European Union, excluding its Eastern European members; and we also include Australia, Canada, Japan, South Korea, and the United States. These countries and their years of data coverage are listed in online appendix table A1. (10) The EU KLEMS database contains detailed data for 32 industries in both the market and nonmarket economies, as summarized in online appendix table A2. We focus on nonfarm employment, and we omit the poorly measured private household sector, and public administration, defense, and extraterritorial organizations, which are almost entirely nonmarket sectors. (11) The end year of our analysis is dictated by major revisions to the industry definitions in EU KLEMS that were implemented from the 2013 release onward. These definitional changes inhibit us from extending our consistent 1970-2007 analysis through to the present, though we analyze 2000-15 separately using the 2017 release of EU KLEMS for a smaller subset of countries for which these data are available. (12)

Table 1 summarizes trends in aggregate hours of labor input and labor's share of value added by decade for the 19 countries in our analysis. As with all analyses in the paper, these statistics are calculated using the 28 market industries that constitute our analytic sample and are annualized to account for the fact that years of data coverage differ by country. With very few exceptions, aggregate labor hours rise in all countries and time periods. The growth rate of labor hours is most rapid in the 1980s, slower in the 1990s, and slower still in the 2000s. Distinct from aggregate labor hours, trends in labor's share of value added differ by country and time period. On average, the aggregate labor share rises in the 1970s and then falls during the subsequent three decades, with by far the sharpest annual rate of decline in the 2000s.

Table 2 reports analogous statistics for trends in hours of labor input and labor's share of value added among the 28 industries in our sample. There is a substantial diversity of experiences among industries. Employment fell steeply in mining and quarrying, textiles and related products, and refining, while growing rapidly in many business and personal services. Labor's share of value added declined in the majority of sectors, with the steepest fall in heavy industry. TFP growth, meanwhile, was most rapid in manufacturing and was negative in several service industries.

Table 3 summarizes trends in employment, hours, wages, value added, labor share, and TFP by industry over the four decades of our sample. We quantify these trends overall, by broad sector, and by decade by estimating regression models for the change in country-industry-year outcomes (multiplied by 100). In this table, and throughout the paper, regression models are weighted by time-averaged shares of the relevant weighting variable--employment, hours, or value added--within countries multiplied by time-varying country shares of the weighting variable. As such, we weight by country size in our main estimates, and we show in the online appendixes that our main results are not sensitive to this choice.

The top row of table 3 reports estimates for all industries and time periods. The middle rows report these relationships separately by decade, and the bottom rows report them separately for five broad sectors encompassing the 28 industries in our analysis. As detailed in online appendix table A2, these sectors are: mining, utilities, and construction; manufacturing; education and health; low-tech services (including personal services, retail, wholesale, and real estate); and high-tech services (including post and telecommunications, finance, and other business services). The reported regression coefficients, which correspond to within-industry changes, reflect a number of key trends in the data. Employment growth, measured in workers or hours, is positive in all decades but slows substantially across consecutive decades. Employment growth is negative in manufacturing; modestly positive in mining, utilities, and construction; and strongly positive in services--with the most rapid growth evident in high-tech services, followed by education and health, and finally low-tech services. Like employment, the growth of real hourly wages is positive in all periods but is secularly slowing.

Consistent with results reported in much recent work (Elsby, Hobijn, and Sahin 2013; Karabarbounis and Neiman 2014; Autor and others 2017b), trends in the labor share of value added vary across the decades. Labor's share of value added trends modestly upward in the 1970s, then falls in each decade of the 1980s, 1990s, and 2000s. This trend is most pronounced in manufacturing and in mining, utilities, and construction. It is modest in high-tech services, and in the education and health sector, and it is absent in the low-tech services sector.

The descriptive statistics given in table 3 focus on within-industry changes in the labor share of value added and its components. But of course, changes in the aggregate labor share may stem from both (i) within-industry shifts in labor's share of value added; and (ii) changes in the share of value added accounted for by industries that differ in their labor shares. Our analysis assesses the contribution of technological change to both margins. To quantify the importance of within- versus between-industry shifts, we implement a simple shift-share decomposition, as follows. Let [[bar.L].sub.c,t] = [[SIGMA].sub.i][[omega].sub.i,c,t][l.sub.i,c,t] equal the aggregate log labor share of value added in country c in year t, defined as the weighted sum of log labor shares [l.sub.i,c,t], in each industry i, where weights [[omega].sub.i,c,t] correspond to industry i's share in value added in its respective country and year. (13) Let [DELTA][[bar.L].sub.c,[tau]] equal the change in aggregate log labor share in country c over time interval [tau]--equal to 1970-80, 1980-90, 1990-2000, or 2000-07--where [DELTA] is the first-difference operator. Finally, let [mathematical expression not reproducible] and [mathematical expression not reproducible]. We can then decompose the observed labor share change in each decade as

(1) [DELTA][[bar.L].sub.c,[tau]] = [summation over (i)][[??].sub.i,c,[tau]][DELTA][[??].sub.i,c,[tau]] + [summation over (i)][[??].sub.i,c,[tau]][DELTA][[omega].sub.i,c,[tau]],

where the first term to the right of the equals sign is the contribution of within-industry changes in labor share to the aggregate change, and the second term is the contribution to the aggregate change due to shifts in value-added shares across industries.

The results of this decomposition, reported in table 4, indicate that the majority, but not the entirety, of the change in aggregate labor share of value added in each decade is accounted for by within-industry shifts. Focusing first on the country size-weighted calculations (the left columns), we find that more than all of the rise in labor share in the 1970s is due to within-industry changes, whereas between 51 and 72 percent of the fall in the labor share in the subsequent three decades is accounted for by within-industry declines. If we instead weight each country equally in the shift-share decomposition, we reach similar conclusions about the importance of within-industry labor share movements (the right columns). Further, if we decompose the change in the mean level of labor share rather than the mean log level (online appendix table A3), we find a similar time pattern as for the log labor share and a similarly outsized role played by within-industry changes.

These decomposition results suggest that the within-industry determinants of changes in the aggregate labor share are of greater analytic interest compared with the between-industry drivers, though we explore both margins below. The 2000s stand out, however, for having a roughly even distribution of the aggregate labor share changes into within-industry and between-industry components. Consistent with the observations of Matthew Rognlie (2015) and German Gutierrez (2017), this pattern reflects the outsized growth of the real estate industry's value added in numerous countries--particularly during the 2000s--and this industry has an extremely low share of labor in value added (see online appendix table A4). If we eliminate real estate from the analysis, however, we find that the fall in the aggregate labor share in the 2000s is reduced by less than one quarter (from -0.86 to -0.64 per year); the within-industry component of the labor share decline explains no less than 90 percent of the total in each decade; and the annual rate of decline in the labor share during the 2000s is still more than twice as rapid as in the 1990s. (14) Thus, the rising share of real estate in value added is not the primary driver of the falling labor share.

Figure 2 adds country-level detail to these calculations by plotting the evolution of the aggregate labor share of value added for all the countries in our sample. Each panel contains two series: In the first series, industry shares are permitted to vary by year; the second series holds these shares constant at their within-country, over-time averages. The fact that these series closely correspond for almost all countries reinforces the inferences from the decomposition that most of the aggregate changes in the labor share observed in the data stem from within-industry movements in this share.

II. Main Estimates

Before making estimates, we tackle two remaining issues: simultaneity and timing. The simultaneity issue arises because labor's share of value added features in the construction of TFP, inducing a mechanical correlation between TFP growth and shifts in the labor share. (15) To overcome this pitfall, we construct industry-level TFP growth for each industry-country pair as the leave-out mean of industry-level TFP growth in all other countries in the sample. This approach eliminates the mechanical correlation between TFP and labor share and arguably exploits movements in the technology frontier that are common among industrialized economies. Confirming the utility of this strategy, we show in online appendix table A5 that other-country, same-industry TFP is a strong predictor of own-country-industry TFP: In a set of regressions of own-country-industry TFP on other-country-industry TFP that includes a large number of country, year, sector, and business cycle main effects, we obtain a prediction coefficient that ranges from 0.32 to 0.57, with a t value above 5 in all specifications. Based on this reasoning and evidence, we employ the leave-out TFP measure in place of own-industry TFP in all the analyses given below.

The second issue, timing, arises because contemporaneous productivity innovations are unlikely to induce their steady-state effects immediately, meaning that a lag structure is needed for estimating the relationship between TFP and outcomes of interest (Ramey 2016). To explore a suitable structure, we estimate simple local projection models in the spirit of Oscar Jorda (2005), which involve regressing a series of first differences of increasing length of the outcome variable of interest on the explanatory variable of interest (here, TFP growth) and a set of controls. We estimate

(2) [mathematical expression not reproducible]

where ln [Y.sub.i,c,t+K] denotes the log outcome of interest in industry i, country c, and year t; and K denotes the time horizon for the local projection. The dependent variables therefore reflect the log change in outcome Y from base year t - 1 up to year t+K. The impulse variable is the log change in other-country-industry TFP between years t - 2 and t - 1, [DELTA] ln [TFP.sub.i,c[not equal to]c(i),t-1]. These effects are estimated while controlling for lagged values of both TFP growth ([DELTA] ln [TFP.sub.i,c[not equal to]c(i),t-2]) and of outcome variable growth ([DELTA] ln [Y.sub.i,c,t-2])--that is, conditional on the lagged history of both TFP and outcome growth at the path start time. This allows for feedback dynamics within the system and controls for them through the inclusion of the lagged variables. Each model further controls for a set of country-year fixed effects ([[alpha].sub.c,t]), as well as fixed effects for five broad sectors ([[gamma].sub.s], as outlined in online appendix table A2). Following the approach of Coen Teulings and Nikolay Zubanov (2014), we also control for subsequent TFP innovations occurring between t = 0 and t = K, which reduce the influence of serial correlation in TFP innovations on estimates of [[beta].sub.1]. Finally, standard errors are clustered by country-industry.

Figure 3 reports local projection estimates and confidence intervals for the relationship between a TFP innovation shock, measured as an increase in TFP of 1 standard deviation, occurring between periods t = -1 and t = 0, and ensuing industry-level changes [[DELTA].sub.k] ln [Y.sub.i,c,] [equivalent to] ln [Y.sub.i,c,t+k] - ln [Y.sub.i,c,t-1] for K [member of] {0,..., 5). (16) For all the outcome variables considered (employment, hours, wage bill, value added, and labor share), the local projection estimates indicate that TFP growth predicts small or negligible contemporaneous changes in the outcomes of interest that cumulate in ensuing years. In all cases, however, these effects plateau after three years, implying that no more than four lags of the independent variable are needed to capture the impulse response of a contemporaneous shock. For completeness, we include five lags in our main specifications, though we shorten the lag structure when analyzing subintervals of the data.

II.A. Within-industry Direct Effects: Own-Industry TFP and Own-Industry Outcomes

Our initial estimates, reported in table 5, consider the within-industry "direct" effects of TFP growth on own-industry outcomes. We fit ordinary least squares, first-difference models of the form

(3) [mathematical expression not reproducible]

where [DELTA] ln [Y.sub.i,c,t], is an outcome of interest and, as above, i indexes industries, c indexes countries, and t indexes years; and the log change in TFP (contemporaneous plus five distributed lags) is the explanatory variable of interest. Because equation 3 is a first-difference specification estimated at the industry-country-time level, it implicitly eliminates industry-country effects. We additionally include country and year indicator variables, which correspond to linear country and time trends in the first-difference model; country-time interaction terms, which allow country trends to accelerate or decelerate over the sample interval; and country-specific cyclical peak and trough indicators interacted with country indicators to account for country-specific business cycle effects. All models are weighted by industries' time-averaged shares of the relevant weighting variable--employment, hours, or value added--within countries, multiplied by time-varying country shares of the weighting variable, and standard errors are clustered at the level of country-industry pairs.

The top left panel of table 5 presents estimates for industry-level employment, measured as the log number of workers (encompassing both employees and the self-employed). We estimate that industries experiencing relative gains in productivity exhibit relative declines in employment. The point estimate of -2.07 in column 1, corresponding to the sum of the six [[beta].sup.k.sub.1] coefficients, implies that an increase of 1 standard deviation in own-industry TFP (2.58 log points) predicts a fall in own-industry employment of approximately 2 log points. This estimate implies that the estimated elasticity of employment to TFP growth is below 1 (0.80 = 2.07 / 2.58)--that is, there is a partial industry-level demand offset (compare with Bessen 2017).

Columns 2 and 3 of table 5 stress-test this estimate by adding five major sector group fixed effects, and by replacing the country-trend and country-business cycle controls with an exhaustive set of country-year indicator variables. The inclusion of sector group trends reduces the point estimate from -2.07 to -1.13, and increases precision. This pattern suggests that TFP innovations may spill over across industries within a sector. We subsequently model these spillovers in the next section, when we add input-output linkages to the regression model; meanwhile, we add sector group dummies (reflecting sector group trends in the log-level models) to all subsequent models, so our primary identification comes from within-sector, between-industry comparisons. Conditional on the inclusion of these sector group trends, the addition of a full set of country-year dummies in column 3 has almost no impact on the magnitude or precision of the point estimates. This insensitivity is worth bearing in mind because we do not include exhaustive country-year dummies in our main models; these dummies would interfere with the identification of input-output linkages, which have much lower country-year variability than own-industry TFP.

The top middle panel of table 5, which reports analogous estimates for log hours of labor input, finds an almost identical slope as for employment, indicating that most of the employment adjustment to productivity changes occurs on the extensive margin. The top right panel explores the relationship between TFP and nominal industry wage bill changes. These point estimates are also similar to those for hours and employment, suggesting that industry (relative) nominal wages are not much affected by TFP changes; rather, the industry-level relationship between TFP and wage bill changes stems from employment shifts.

We turn to output measures in the bottom left and bottom middle panels of table 5. Rising industry TFP predicts significant relative declines in industry-level nominal value added (bottom left panel) and significant relative rises in real industry value added (bottom middle panel), implying (logically) that rising industry productivity lowers industry prices.

Comparing the estimates in the bottom left and bottom middle panels of table 5 reveals that a rise in industry TFP predicts a smaller (less negative) change in nominal value added than in the wage bill. This suggests that rising TFP predicts a relative fall in labor's share of industry value added. (17) The bottom right panel of the table confirms this implication: A rise in TFP of 1 standard deviation predicts a fall in an industry's labor share of value added of about 0.55 percentage point over a five-year horizon.

We have implemented a large number of tests of the robustness of these estimates, which are reported in table 6. These include weighting all countries equally rather than by their value-added shares (top rows); eliminating the contemporaneous TFP term from the distributed lag model (second group of rows); eliminating the self-employed from our employment, wage bill, and labor share models (third group of rows); imputing zeros to the TFP measures in cases where the reported values are negative (fourth group of rows); (18) estimating equation 3 using five-year-long first differences in place of annual first differences (fifth group of rows); (19) and using data from the 2000-15 period from the 2017 release of the EU KLEMS data (van Ark and Jager 2017), thus adding eight additional outcome years at the cost of dropping prior decades and several countries (bottom rows). (20) Results are remarkably stable across these many sets of estimates, though precision is much lower for models fitted using the short 2000-15 panel.

The robust negative industry-level relationships between TFP and both employment and labor's share of value added seen in tables 5 and 6 are central inputs into our subsequent analysis. We stress that these findings do not by themselves imply that productivity growth depresses either employment or the labor share in the aggregate. Indeed, these direct within-industry relationships do not at present incorporate any of the potentially countervailing effects operating through other channels, including input-output linkages, compositional shifts, and final demand effects. Before incorporating these links in the next section, we perform a validity test on our main technology measure.

II.B. Applying Direct Measures of Technological Progress

Our omnibus measure of productivity-augmenting technological change, TFP, has the advantage of not being bound to a specific set of technologies or their associated measurement challenges. But TFP's strength is also its weakness. Because it is an accounting residual, one can only speculate on the underlying sources of technological progress that contribute to rising TFP. To partially address this concern, we test whether our key results above hold when we focus on a specific margin of technological advancement: industry-level patenting flows (Acemoglu, Akcigit, and Kerr 2016).

Using data from Autor and others (2017a), who match patent grants to their respective corporate owners, and then to industry codes based on corporate owners' industry affiliations, we construct counts of patent grants and patent citations by year for patents granted to both U.S. and non-U.S. inventors using data from the U.S. Patent and Trademark Office that use U.S. Standard Industrial Classification codes, cross-walked to the EU KLEMS industry level. Aggregate summary statistics for standardized patent counts and patent citations are reported in online appendix table A6, while online appendix table A7 reports the mean log number of patent grants and patent citations by industry and by inventor nationality (U.S. versus non-U.S.), and online appendix table A8 summarizes industry-level trends by decade and sector. These tables highlight the substantial heterogeneity in patent flows across industries and over time, with the highest levels of patenting occurring in chemicals and electrical equipment, and the lowest occurring in education. Patent grants rise across the decades while citations fall in the most recent decade, reflecting the substantial lag between patent grants and patent citations. Although citations are likely a better measure of innovation than the raw count of patent grants (Trajtenberg 1990), citations may understate innovation in the final years of the sample because they arrive with a lag. In what follows, we report results using both measures of patenting activity.

Given that patenting activity is an input into the industry-level innovation and automation process, it should predict TFP growth. To verify this supposition, we estimate industry-level descriptive regressions of the form

(4) [mathematical expression not reproducible]

where [DELTA] ln [TFP.sub.i,c,t] is the measured change in industry-level TFP, and In [PAT.sub.i,c[not equal to]c(i),t] is the log count of industry-level patents, which are normalized to have a standard deviation of 1. Paralleling the specifications given above, we include both contemporaneous patenting activity and a set of annually distributed lags. Analogous to our strategy of using other-country ("leave out") TFP growth by industry, we use patenting activity by non-U.S. inventors as predictors of U.S. TFP growth and, similarly, use patenting activity by U.S. inventors as predictors of non-U.S. TFP growth.

The estimates of equation 4, reported for patent counts in the upper rows of table 7 and for patent citations in the lower rows, confirm that patent flows are a strong predictor of industry TFP growth. A rate of industry patents or patent citations that is 1 standard deviation higher predicts about 0.6 log point faster industry TFP growth (t = 2.9). This relationship is robust; adding year effects (column 2), country-business cycle effects (column 3), and country-year effects (column 4) to these first-difference models has almost no impact on the magnitude or precision of the predictive relationship.

Table 8 explores the relationship between patenting activity and the evolution of industry-level labor input, value added, and factor payments. Following the template of the tables presented above, we report regressions of industry-level first differences in outcome variables on log industry patent counts or patent citations--contemporaneous and five annually distributed lags--and the full set of controls used in table 7. (21) Comparable to the pattern of results for TFP, we find that industry-level patent citation flows predict a fall in own-industry employment and hours, a decline in nominal value added, a rise in real value added, and, most important, a fall in own-industry labor share. (22) These findings hold for both measures of patenting activity--patent counts and patent citations. Though precision is far lower for the patent-based estimates than TFP-based estimates--likely because we effectively have patenting data for only two countries, U.S. and non-U.S.--we view these findings as supportive of our main results.

III. Linking Micro to Macro

As underscored by the top panel of figure 1, it would be erroneous to conclude that because relative employment declines in industries experiencing rising productivity, aggregate employment falls as productivity rises. To move from this cautionary observation to a rigorous quantification of how industry-level productivity growth affects the aggregate employment and labor share, we next add three micro-macro linkages to our estimation and accounting framework: customer-supplier linkages; final demand effects; and composition effects.

III.A. Accounting for Customer-Supplier Linkages

The effect of productivity growth occurring in an industry is unlikely to be confined to the sector in which it originates. Industries facing lower input prices or higher-quality inputs from their suppliers may increase purchases; similarly, industries whose customers are experiencing rising productivity may face rising or falling output demands. We account for these input-output linkages by adding two terms to equation 3:

(5) [mathematical expression not reproducible]

These additional terms, [[??].sup.SUP.sub.j[not equal to]i,c,t] and [[??].sup.CUST.sub.j[not equal to]i,c,t], measure the weighted sum of TFP growth in all other domestic industries j [not equal to] i, which are, respectively, the suppliers and customers of industry i: (23)

(6) [DELTA]ln [[??].sup.L.sub.j[not equal to]i,c,t] = [J.summation over (j=1)] weight.sup.L.sub.j[not equal to]i,c] x [DELTA]ln [TFP.sup.L.sub.j[not equal to]i,c,t], [for all] L [member of] {SUP, CUST}.

The supplier and customer weights used for this calculation are obtained from input-output coefficients from the World Input-Output Database and are averaged over the period 1995-2007. The supplier weights are equal to each domestic supplier industry j's value added as a share of the value added of industry i, capturing the importance of supplier industries j in the production of industry i's output. Analogously, the customer weights are the shares of value added of each industry i that are used in domestic industry j's final products, capturing the importance of industries j as end consumers of industry i's output. (24) These weights account not only for shocks to an industry's immediate domestic suppliers or buyers but also for the full set of input-output relationships among all connected domestic industries (that is, the Leontief inverse). We renormalize both the customer and supplier TFP terms to have a standard deviation of 1, with summary statistics reported in online appendix table A6. As with our main (direct) measure of TFP, these supplier and customer TFP linkage terms are calculated using industry-level, leave-out means of TFP growth in all other countries in the sample.

The estimates of equation 5, reported in the top half of table 9, indicate that productivity growth emanating from supplier industries predicts steep increases in the employment and hours of labor input of customer industries (though not in their nominal wage bill, value added, or labor share). Specifically, the point estimate of 0.97 on the supplier-industry TFP term in column 1 indicates that a rise of 1 standard deviation in an industry's supplier productivity predicts an employment gain of 97 log points. This effect is almost identical in magnitude but opposite in sign to the estimated direct effect of TFP growth of -0.95 on own-industry employment. Thus, this input-output linkage reveals a first channel by which direct effects of productivity growth on own-industry outcomes may be offset by effects accruing outside the originating sector.

Conversely, productivity growth emanating from customer industries (the third row of the top half of table 9) generally has negligible and always insignificant estimated effects on employment, hours, wage bill, value added, and labor share in supplier industries. This result is consistent with the simple Cobb-Douglas input-output framework developed by Acemoglu, Ufuk Akcigit, and William Kerr (2016), where productivity-innovations in a given industry lead to output gain in its customer industries--those benefiting from its price declines--but have no net effect on its supplier sectors, where price and quantity effects are offsetting.

A third important pattern revealed by table 9 is that our earlier estimates of the relationship between TFP growth and own-industry outcomes are essentially unaffected by the inclusion of the customer and supplier terms (compare the point estimates in tables 5 and 9). Thus, our initial findings for the relationship between TFP growth and own-industry employment and labor share are unaltered.

III.B. Accounting for Final Demand Effects

The lower half of table 9 adds a third channel of response: final demand effects accruing through the contribution of productivity growth to aggregate value added. To capture these final demand effects, we estimate the relationship between country-specific aggregate economic growth (contemporaneous and five distributed lags) and industry-specific inputs using the following specification:

(7) [DELTA] ln [Y.sub.i,c,t] = [[lambda].sub.0] + [5.summation over (k=0)] [[lambda].sup.k.sub.1] [DELTA] ln V[A.sub.j[not equal to]i,c,t-k] + [[alpha].sub.s] + [[epsilon].sub.i,c,t].

The explanatory variable of interest in this equation, [DELTA] In V[A.sub.j[not equal to]i,c,t], is the growth of own-country real or nominal value added, where the subscript j [not equal to] i highlights that we exclude own-industry output from the explanatory measure for each industry to eliminate any mechanical correlation between agregate growth and industry outcomes. These stacked first-difference regression models drop the country, year, trend, and business cycle indicators used in equation 5, so that identification largely arises from country and year time series. Because these are first-difference models, however, they implicitly eliminate industry-country effects.

The estimates of equation 7, reported in the lower half of table 9, document a second countervailing effect of industry-specific productivity innovations on aggregate outcomes: Each log point gain in country-level real value added predicts an approximately 0.6 log point rise in same-country, other-industry employment and hours. Similarly, each log point gain in country-level nominal value added predicts essentially a one-for-one rise in same-country, other-industry wage bill and nominal value added, as well as a very modest but statistically significant rise in same-country, other-industry labor share (the estimated elasticity is 0.071). Because TFP growth emanating from any one sector raises the real aggregate value added in the country where it occurs, these estimates imply that each industry's productivity growth contributes to aggregate labor demand across all other sectors. (25)

III.C. Accounting for Compositional (Between-Sector) Effects

The estimates given in table 9 reveal one further mechanism by which sectoral productivity gains affect the aggregate labor share: by shifting relative sector sizes. Column 4, in the top half of table 9, shows that a rise in own-industry TFP growth predicts a fall in industry-level nominal value added with an elasticity of -0.58. This finding implies that sectors with rising productivity will tend to shrink as a share of nominal value added. Figure 4 confirms this intuition by depicting a scatter plot of the bivariate relationship between industry-level TFP growth and the change in industries' log shares of own-country nominal value added (averaged over years and across countries). On average, industries that experience 1 log point faster TFP growth than the economy-wide average lose about 0.6 log point as a share of nominal economy-wide value added.

Applying this observation to the Oaxaca decomposition equation above (equation 1), it is immediately clear that uneven productivity growth across industries will shift the aggregate labor share through changes in relative sector sizes. If rapid productivity growth occurs in industries with relatively low labor shares (for example, manufacturing industries), this will indirectly raise the aggregate labor share; conversely, relatively rapid productivity growth in labor-intensive sectors (for example, education and health) will have the opposite effect. (26)

IV. Quantitative Implications

With these estimates in hand, we now quantify the implied contribution of TFP growth to the evolution of the aggregate employment and labor shares accruing through the four channels outlined above: own-industry, supplier and customer, final demand, and composition. We start with employment and hours, then turn to the labor share.

IV.A. Aggregate Employment and Hours Effects

The effect of TFP growth on employment and hours combines the first three of these effects: the own-industry (or "direct") effect, the supplier and customer effects, and the final demand effect. The first (own-industry) effect is equal to the sum of the [[beta].sup.k.sub.1] coefficients in equation 5 multiplied by their corresponding [DELTA] ln [TFP.sub.i,c[not equal to]c(i),t] terms, and aggregated by weighting these industry-level predictions by the time-averaged share of each industry in total employment or hours:

(8) [DELTA] ln [Y.sup.OWN.sub.c,t] [equivalent to] [[partial derivative] ln [Y.sub.c,t]/[partial derivative] ln [TFP.sub.i,c[not equal to]c(i),t]] = [5.summation over (k=0)][[beta].sup.k.sub.1] x [1.summation over (i=1)][[omega].sub.ic] x [DELTA] ln [TFP.sub.i,c[not equal to]c(i),t].

Here, In [Y.sub.c,t] is log employment or hours in country c in year t; [5.summation over (k=0)][[beta].sup.k.sub.1] is the sum of coefficients in equation 5; [[omega].sub.i,c]. is the time-averaged employment or hours share of industry i in its respective country; and [DELTA] ln [TFP.sub.i,c[not equal to]c(i),t] is own-industry TFP growth.

The supplier and customer effects are, analogously, equal to the sum of the [[beta].sup.k.sub.2] and [[beta].sup.k.sub.3] coefficients multiplied by their corresponding [[??].sup.SUP.sub.j[not equal to]i,c,t] and [[??].sup.CUST.sub.j[not equal to]i,c,t] terms, and then aggregated to the national level by weighting each by its time-averaged industry employment or hours shares ([[omega].sub.i,c]):

(9) [DELTA] ln [Y.sup.SUP.sub.c,t] [equivalent to] [[partial derivative] ln [Y.sub.c,t]/[partial derivative] ln [[??].sup.SUP.sub.j[not equal to]i,c,t]] = [5.summation over (k=0)][[beta].sup.k.sub.1] x [1.summation over (i=1)][[omega].sub.i,c] x [DELTA] ln [[??].sup.SUP.sub.j[not equal to]i,c,t]],

and

[DELTA] ln [Y.sup.CUST.sub.c,t] [equivalent to] [[partial derivative] ln [Y.sub.c,t]/[partial derivative] ln [[??].sup.CUST.sub.j[not equal to]i,c,t]] = [5.summation over (k=0)][[beta].sup.k.sub.3] x [1.summation over (i=1)][[omega].sub.i,c] x [DELTA] ln [[??].sup.CUST.sub.j[not equal to]i,c,t]].

The third component that we calculate is the final demand effect of TFP growth in each industry on employment or hours economy-wide, [DELTA][Y.sup.FD.sub.c,t]. For any one industry, this contribution is equal to the product of four terms: (i) the effect of TFP growth in i on i's real value added ([[SIGMA].sup.5.sub.k=0][[beta].sup.k.sub.1,VA]); (ii) the effect of growth in i's real value added on total value added ([[phi].sub.i,c]); (iii) the effect of growth in real value added on employment or hours in each industry j [not equal to] i ([[SIGMA].sup.5.sub.k=0][[lambda].sup.k.sub.1]); and (iv) the size of industry j relative to overall employment or hours in the economy ([[omega].sub.i,c]). (27) To obtain the aggregate effect (summing across industries), we calculate:

(10) [mathematical expression not reproducible]

In this expression, In [Y.sub.c,t] is log employment or hours in country c in year t as before; ([[SIGMA].sup.5.sub.k=0][[lambda].sup.k.sub.1]) is the estimated effect of the aggregate real value added on outcome Y from equation 7 reported in column 5 of the lower half of table 9; [[SIGMA].sup.5.sub.k=0][[beta].sup.k.sub.1,VA] is the estimated direct effect of [DELTA] ln TFP in equation 5 on own-industry real value added (reported in column 5 in the lower half of table 9); [[omega].sub.i,c] is the time-averaged employment or hours share of industry i in its respective country; and [[phi].sub.i,c] is the time-averaged value-added share of industry i in country c. (28)

Figure 5 displays the results of these calculations for overall employment and hours of labor input, respectively. The first bar in the top panel of figure 5 corresponds to the direct effect of TFP growth on own-industry employment. Its height of -0.22 implies that, on average, productivity growth reduced own-industry employment by approximately 8.2 percent over the full 37-year period (0.22 x 37). The second bar (supplier effect), with a height of 0.35, indicates that the countervailing effect of rising supplier productivity on employment in customer industries more than offset this direct effect. The third bar (customer effect), with a height of 0.05, indicates that rising productivity in customer industries exerted a very modest positive employment effect in supplier industries. The fourth bar, with a height of 0.30, reflects the substantial contribution of rising productivity to overall employment operating through final demand. The fifth bar (net effect) sums these four components to estimate a net positive effect of productivity gains on aggregate employment, totaling about 18 log points (0.48 x 37 = 17.8) over the outcome period.

The bottom panel of figure 5 reports the analogous exercise for hours of labor input rather than employment. We find comparable effects on this outcome: Although rising productivity reduces relative employment in the sectors in which it occurs, it augments employment in (downstream) customer sectors (as captured by the supplier effect) and boosts aggregate demand through its contribution to overall value added. As with employment, the net effect on hours is strongly positive.

To provide insight into how rising TFP spurs relative employment declines in directly affected industries while simultaneously generating rising employment in the aggregate, online appendix tables All and A12 report the contributions to employment growth by industry operating through each channel estimated above: direct effects, input-output linkages, and final demand effects. These contributions, underlying the aggregate employment growth predictions in figure 5, can be analyzed from two complementary perspectives. The first, reported in online appendix table All, calculates the contribution of TFP growth originating in each industry to the predicted aggregate change in employment. The second, reported in online appendix table A12, enumerates the predicted effect of TFP growth originating throughout the economy on predicted employment growth in each destination industry, scaled by that industry's weight in aggregate employment. (29)
Figure 5. Predicted Effects of Total Factor Productivity Growth on
Aggregate Employment and Hours of Labor Input, 1970-2007 (a)

                        Employment

Direct effect          -0.222
Supplier effect         0.353
Customer effect         0.051
Final demand effect     0.301
Net effect              0.482

                       Hours of labor input

Direct effect          -0.215
Supplier effect         0.398
Customer effect         0.085
Final demand effect     0.268
Net effect              0.537

Source: Authors' calculations, based on table 9.
(a.) The units are the predicted annual change in the outcome variable
expressed in log points. See the notes to table 9.

Note: Table made from bar graph.


For the direct effect, the contributions to employment in the originating and destination industry are the same by definition because these direct effects operate only within industries. As shown in online appendix tables All and A12, the negative direct effects that we estimate for employment originate in industries that have experienced strong TFP growth (such as electrical and optical equipment, and transportation and storage), or industries that make up a large share of total value added (such as retail), or both.

Conversely, TFP growth originating in supplier and customer industries leads to employment and hours growth elsewhere in the economy through input-output linkages. The supplier/customer contribution of any given industry to aggregate employment depends on three terms: the industry's rate of TFP growth; the weight that industry has as a supplier or customer of other industries; and, in turn, the weight that those customer and supplier industries have in aggregate employment. Industries such as post and telecommunications, wholesale trade, financial intermediation, and transportation and storage produce important positive employment spillovers to other industries, in part because they are suppliers to a variety of service industries, which are themselves a large share of total employment. These industries highlight the potential of productivity growth in service industries to induce sizable positive employment spillovers. Conversely, other business activities--an important supplier industry--exhibits declining productivity, and thus contributes a meaningful negative employment spillover. Finally, manufacturing industries--such as chemicals, basic and fabricated metals, and electrical and optical equipment--make a large indirect contribution to employment in customer industries, due to their rapid productivity growth. (30)

Finally, each industry's TFP growth potentially contributes to employment via its effect on final demand. This effect depends on two terms: the originating industry's rate of TFP growth, and its share in national value added. Hence, productivity growth in industries that make up a large share of value added has a larger effect on overall income. Manufacture of electrical and optical equipment (codes 30-33); post and telecommunications (code 64); financial intermediation (code J); manufacture of motor vehicles and transportation equipment (codes 34-35); manufacture of chemicals and chemical products (code 24); and wholesale trade, excluding motor vehicles (code 51) are the largest contributors by TFP source to final demand, reflecting their rapid productivity growth and substantial weight in aggregate value added. (31)

How successful is our approach in capturing the evolution of employment observed in the data? Figure 6 answers this question by comparing the industry-level employment predictions of our statistical model to observed employment changes, averaged across country-years. In each panel, employment growth predictions, obtained by summing across all channels in the model, are reported on the horizontal axis, while observed employment growth is reported on the vertical axis. The top panel of figure 6 plots the predicted versus observed log employment change by industry, while the bottom panel plots the predicted versus observed contribution that each industry makes to aggregate employment growth. (32) This figure makes evident that our model can account for a substantial part of the variation in employment growth by industry (the top panel), and the extent to which these industry effects contribute to aggregate job growth (the bottom panel). Each of the three channels featured in the model contributes to its predictive power. A regression of the observed contribution of each industry to aggregate employment growth on its predicted value based only on the direct (own-industry) effect yields an [R.sup.2] of .34. Adding customer and supplier effects to this prediction raises this [R.sup.2] to .45. Incorporating the final demand effect raises it further to .61. Given that the model exclusively uses variation in TFP across industries to form predictions, we consider this as strong confirmation of the utility of our accounting framework.

IV.B. Aggregate Labor Share Effects

We now perform the analogous exercise for the implied effect of rising TFP on labor's share of value added. In this calculation, the own-industry, interindustry, and final demand effects are obtained analogously to those for employment and hours. (33) However, the labor share calculation includes a fourth channel: TFP-induced compositional shifts in value-added shares across industries. This between-industry composition effect is calculated as

(11) [mathematical expression not reproducible]

Here, [DELTA][[??].sub.i,c] is the predicted change in the value-added share of industry i in country c, and [[??].sub.i,c] is the time-averaged log labor share in industry i in country c. The terms [[omega].sub.i,c] and [[beta].sup.k.sub.1,VA]are defined as in equation 10, again adjusted for the labor share model: The time-averaged weights [[omega].sub.i,c] are shares of nominal value added rather than shares of employment or hours worked, and the coefficients [[beta].sup.k.sub.1,VA] reflect nominal rather than real value-added coefficients (shown in column 4 of table 9). Concretely, this prediction reflects the sum of induced shifts in each industry's share of own-country nominal value added ([DELTA][[omega].sub.i,c], the expression in braces) multiplied by that industry's labor share. (34)

We report quantitative implications for labor's share of value added in figure 7. The first bar reflects the labor share effect associated within own-industry productivity growth. Its height of -0.14 suggests that, on average, own-industry productivity growth reduced the labor share by some 5.2 percent over the 37-year period (0.14 x 37). Unlike employment and hours worked, however, there are no positive countervailing effects from interindustry linkages or final demand; rather, these additional channels also serve to decrease the aggregate labor share, albeit by small amounts compared with the direct effect (-0.01, -0.06, and -0.02 log point annually for, respectively, the supplier, customer, and final demand effects). Finally, industry composition shifts resulting from a reallocation of value added across industries also predict a small net labor share decline: This effect amounts to about 1.7 percent over the entire period (0.046 x 37).
Figure 7. Predicted Effects of Total Factor Productivity Growth on the
Aggregate Labor Share, 1970-2007 (a)

Log points

Direct effect         -0.141
Supplier effect       -0.010
Customer effect       -0.060
Final demand effect   -0.015   -0.046
Net effect            -0.271

Source: Authors' calculations, based on table 9.
(a.) The units are the predicted annual change in the outcome variable
expressed in log points. See the notes to table 9.

Note: Table made from bar graph.


Taken together, all four channels operating on the labor share--direct, supplier/customer, final demand, and composition--predict a decline of -0.27 log point annually, or about 10 percent over the entire period (0.27 x 37). Most of this effect stems from the direct labor share--displacing effect operating within industries, combined with an absence of countervailing effects operating within industries. Compositional shifts modestly reinforce this trend. Given an initial average labor share of about 67 percent in our 19 countries (table 1), this corresponds to a nonnegligible predicted decline of 6 percentage points over the period 1970-2007, of which the large majority (0.225 log point annually--that is, 8.3 percent, or about 5.5 percentage points, over the entire period) is predicted to occur within industries.

Table 10 reports the separate industry-level contributions made to these overall predictions. (35) The first column shows each industry's contribution to the total predicted within-industry effects (that is, the predicted effects for own-industry TFP growth, interindustry linkages, and final demand taken together, which are largely driven by the own-industry effect). The second column analogously shows the contribution of each industry to the predicted between-industry effect shown in figure 7. Table 10 highlights that most industries experience a negative within-industry labor share effect. Predictably, some of the largest contributions are made by industries that have witnessed strong productivity growth, such as electrical and optical equipment, chemicals, basic and fabricated metals, and post and telecommunications. However, industries with more modest productivity growth but comprising relatively large shares of value added--such as wholesale trade, and transportation and storage--also contribute substantially to the aggregate within-industry effect. Real estate and other business activities are the only industries that contribute a small countervailing effect; here, positive within-industry labor share changes are predicted because these sectors have experienced negative TFP growth on average. Finally, several (public) services--such as education, health and social work, and other personal services--contribute almost nothing to the predicted aggregate labor share decline, because they have experienced virtually no measured productivity growth.

Table 10 also shows that the industry-specific contributions to the composition (that is, between-industry) effect are quite heterogeneous. In general, the predicted shift away from capital-intensive mining, utilities, and manufacturing industries tends to increase labor's share: In isolation, these industries contribute a predicted increase in the labor share of about 1.6 percent cumulated over the period (0.036 x 37). This is reinforced by contributions from (mostly high-tech) services, such as post and telecommunications, financial intermediation, and transportation and storage. However, real estate single-handedly contributes a large negative compositional effect of, on average, 0.086 log point annually, or over 3 percent across the entire period. This prediction is consistent with the aggregate labor decomposition reported in table 4 and stems from three distinctive features of the real estate industry: a very low labor share relative to the economy-wide average, a rising share of value added, and zero or negative TFP growth.

IV.C. Why Has the Fall in Labor Share Accelerated?

Our results imply that technological progress, broadly construed, has been employment-augmenting but labor share-displacing--that is, generating net employment gains while serving to reallocate value added away from labor and toward other factors. But this observation raises a puzzle: If automation has been consistently labor share-displacing, why has the evolution of labor's share differed so sharply across the decades--rising during the 1970s, declining in the 1980s and 1990s, and then falling more steeply in the 2000s? We briefly take up this question here.

Table 11 reports our baseline model's predictions separately by decade. The first three columns report the observed annual log labor share change in each decade, both within and between industries, while the last three columns report the changes predicted by our baseline model. This table highlights the fact that, although our baseline approach explains a substantial part of the aggregate labor share fall observed since the 1980s, it fails to match two key features of the decade-specific patterns: the positive sign of the within-industry effect operating in the 1970s, and the observed acceleration of the within-industry log labor share decline in the 2000s. The proximate reason for both mismatches is clear: The bulk of the model's explanatory power for the labor share derives from the so-called direct effect--the differential decline of the labor share in industries with faster TFP growth; thus, for the baseline approach to explain the time pattern of rising and then falling labor share across the decades, it would need to be the case that TFP growth was negative in the 1970s, became positive in the 1980s and 1990s, and then accelerated in the 2000s. This does not match the time pattern of TFP growth, however (see table 3). The model does slightly better at capturing the time pattern of between-industry effects--predicting larger compositional shifts in the 1970s and 2000s, which is approximately consistent with the data--but our explanatory power is limited here as well. (36)

Our empirical framework admits several mechanisms through which the effect of technological progress on the labor share may differ over time. One mechanism is that an acceleration of TFP growth will lead to a more rapid fall in the labor share. But as noted above, this explanation is a nonstarter because TFP growth decelerated in the 2000s, even as the fall in the labor share accelerated. Second, the locus of productivity growth may be differently distributed among industries in different eras. To the extent that industries experiencing rapid TFP gains are more (or less) labor-intensive or make up a larger (or smaller) share of the total economy, the aggregate labor share will decline more (or less) strongly through, respectively, compositional effects and within-industry effects. But table 11 suggests that these explanations have a limited bite. Allowing the sources of TFP growth to differ across decades, as we do in the table, does not explain the sharp decadal differences in the between- and within-industry contributions to the fall in the labor share.

A third possibility is that, all else being equal, a given amount of overall productivity growth might have different effects in different eras if the source of that productivity growth is changing--for example, if productivity growth increasingly stems from technologies that are relatively less labor-augmenting and relatively more labor share-displacing. Figure 8 suggests that this explanation has some promise. Akin to figure 1 above, figure 8 presents bivariate scatters of the relationship between industry-level TFP growth and changes in, respectively, industry-level log employment (the top panel) and industry-level log labor share (the bottom panel). Distinct from earlier figures, figure 8 depicts separate slopes by decade. The top panel shows a consistently stable, downward-sloping relationship between industry-level TFP growth and relative declines in employment, with a somewhat steepening slope after the 1970s. By contrast, the bottom panel shows a much more noticeable shift in the relationship between productivity and labor's share over time. During the 1970s, there is no appreciable link between industries' productivity growth and their labor share changes. A clear negative relationship emerges in the 1980s, however, and remains in place during the 1990s and 2000s. This pattern suggests that a shift toward more labor share-displacing productivity growth is a possible explanation for the fall in the labor share commencing in the 1980s.

To explore this possibility more rigorously, we estimate a set of distributed lag models where the own-industry impact of TFP growth is allowed to vary by decade. Across a range of specifications, we find that the 1970s stand out as a period when own-industry TFP growth had a less negative effect on labor's share. We do not find much evidence of statistically significant heterogeneity in coefficients for the decades thereafter, consistent with the broad patterns shown in the bottom panel of figure 8. Table 12 provides estimates of the direct effect of TFP growth on our range of outcomes, estimated separately for the 1970s and the three subsequent decades. As shown in columns 11 and 12, there is a statistically insignificant positive relationship between own-industry TFP growth and own-industry labor share changes during the 1970s, which turns statistically significant and negative for the three more recent decades. Online appendix table A13 provides additional detail by estimating these models separately by decade, applying a five-year lagged long-difference specification. (37)

To assess the quantitative importance of these decadal differences, table 13 reports a set of decade-specific predictions based on table 12. These predictions are constructed by allowing the [[beta].sup.k.sub.1] coefficients in equation 8 and the [[beta].sup.k.sub.1,VA] coefficients in equation 11 to be different in the 1970s compared with the other three decades, thereby allowing both the effect of TFP growth on the within-industry and between-industry components of the aggregate labor share to change over time. (38) A drawback of performing predictions with these estimates is that, relative to our main estimates, the estimated TFP slopes are shallower across all periods, likely because identification of the distributed lag terms is weak in short panels. Nevertheless, the predicted within-industry pattern now qualitatively matches the turnaround after the 1970s: Productivity growth is predicted to modestly increase labor's share during the 1970s and to decrease it thereafter.

The model is also somewhat successful at predicting the increase in the between-industry component of the falling labor share in the 2000s. The model is not successful, however, in explaining the acceleration of the within-industry fall in the labor share in the 2000s.

Summarizing, our analysis broadly supports the hypothesis that the decline in the labor share since the 1980s is consistent with a shift toward more labor share-displacing technology commencing in the 1980s. But the acceleration in the labor share decline observed during the 2000s is left unaccounted for by this mechanism. We hypothesize that a closer study of specific technologies may yield additional insights into these periods. At the same time, we do not assume that technological factors are the sole contributor to the changing secular pattern of the labor share decline or its recent deceleration. Instead, what our findings make clear is that technological progress has been broadly employment-augmenting and labor share-displacing for at least three decades. The consistency of the evidence, rather than its over-time acceleration or deceleration, is what gives us confidence in the utility of our approach for tracing through the within-industry, between-industry, and aggregate consequences of productivity growth originating in all industries.

V. Concluding Remarks

Theory makes clear that there is no direct mapping between the evolution of productivity and labor demand at the industry level and the evolution of labor demand in the aggregate. Theory gives less guidance about how to draw this indirect mapping. We present an empirical approach for mapping the industry-level effects of technological progress on aggregate employment and labor share outcomes, taking into account both the direct effects of productivity growth in advancing industries and the indirect effects of interindustry demand linkages, between-industry compositional change, and increases in final demand. Our findings indicate that these indirect effects are sizable and are countervailing for employment. We find that technological progress is broadly employment-augmenting in the aggregate. But this is not so for labor's share of value added, where direct labor share-displacing effects dominate. Our simple framework can account for a substantial fraction of both the reallocation of employment across industries and the aggregate fall in the labor share over the last three decades. It does not, however, explain why the share of labor in value added fell more rapidly during the 2000s than in prior decades. Nor can it distinguish between the contributions of automation-based versus non-automation-based sources of productivity growth, which may plausibly exert distinct effects on either employment or on labor's share of value added.

Although our empirical exploration of labor displacement has linked effects at the industry level to aggregate outcomes, this high-level representation is consistent with a variety of within- and between-firm adjustments. At one extreme, every firm in an industry undergoing technological progress might substitute capital for labor in a subset of tasks. Alternatively, absent any within-firm change in task allocation, a technological advance might spur an increase in industry market share among relatively capital-intensive firms, and a concomitant decline among relatively labor-intensive firms. (39) Under either scenario, labor's share in industry value added would fall. Our analysis cannot speak to these within-firm versus between-firm dynamics. Nevertheless, we believe that the scope of the evidence presented here complements more granular, but narrower, firm-level and establishment-level studies.

ACKNOWLEDGMENTS We are deeply grateful to discussants John Haltiwanger and Richard Rogerson. We thank Daron Acemoglu, Jim Bessen, Uwe Blien, Janice Eberly, Maarten Goos, Pascual Restrepo, James Stock, Coen Teulings, John Van Reenen, and Xianjia Ye, whose valuable input improved the paper. We are grateful to Pian Shu for sharing data on approved patent applications and citations by industry, year, and country.

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DAVID ALITOR

Massachusetts Institute of Technology

ANNA SALOMONS

Utrecht University

Conflict of Interest Disclosure: David Autor is a trustee and board member for the Urban Institute, and codirector of the Labor Studies Program at the National Bureau of Economic Research. He received financial support for this work from the IBM Open Collaboration Research award program, the Schmidt Family Foundation, and the Smith Richardson Foundation. Anna Salomons received financial support for this work from the Netherlands Organization for Scientific Research through the Innovational Research Incentives Scheme Veni research grant program. With the exception of the aforementioned, the authors did not receive financial support from any firm or person for this paper or from any firm or person with a financial or political interest in this paper. With the exception of the aforementioned, they are currently not officers, directors, or board members of any organization with an interest in this paper. No outside party had the right to review this paper before publication.

(1.) Caselli and Manning (forthcoming) observe that many recent analyses of the potential impact of new technology on workers implicitly rely on models that omit general equilibrium effects.

(2.) Our data sources and methods are documented in detail in section I. The figures above average across the 19 developed countries in our sample encompassing 28 market industries. Each industry is weighted by its own-country average share of employment (the top panel of figure 1) or value added (the bottom panel of figure 1) over the full time interval. Patterns are similar when instead using decadal changes in employment or labor's share and previous-decade TFP growth starting in the 1980s.

(3.) Our approach here builds on our earlier work (Autor and Salomons 2017), in which we incorporate only one of these linkages.

(4.) Our analysis follows many recent works exploiting these linkages to study the propagation of trade and technology shocks (Acemoglu and others 2016; Pierce and Schott 2016; Acemoglu, Akcigit, and Kerr 2016).

(5.) This mechanism is akin to skill-biased structural change in the framework developed by Buera. Kaboski, and Rogerson (2015). though here we focus on labor share rather than skill composition.

(6.) This strategy leverages the fact that changes in other-country, same-industry TFP are highly predictive of the evolution of own-country-industry TFP but are not intrinsically correlated with its evolution.

(7.) The conceptual frameworks of both papers build on the work of Zeira (1998), Autor, Levy, and Murnane (2003), and Acemoglu and Autor (2011), who offer models in which advancing automation reduces labor's share by substituting machines (or computers) for workers in a subset of activities (which Autor, Levy, and Murnane designate as "tasks"). Other labor-displacement mechanisms are given by Sachs and Kotl!koff (2012) and Berg. Buffie, and Zanna (2018), who develop overlapping-generation models in which rapid labor-saving technological advances generate short-run gains for skilled workers and capital owners, but in the longer run, immiserate those who are not able to invest in physical or human capital. Stansbury and Summers (2017) present time-series evidence that productivity growth and wage growth are positively correlated.

(8.) Using an analogous approach, Michaels, Natraj, and Van Reenen (2014) find that information and communication technology adoption is predictive of within-sector occupational polarization in a country-industry panel sourced from EU KLEMS covering 11 countries observed over 25 years.

(9.) Dauth and others (2017) and Chiacchio, Petropoulos, and Pichler (2018) apply the Acemoglu--Restrepo approach to German and EU-wide data, respectively. Dauth and others find that robot adoption leads to worker reallocation but has no net impact on employment or wages. Chiacchio, Petropoulos, and Pichler affirm the Acemoglu--Restrepo results for employment though not for wages.

(10.) The online appendixes for this and all other papers in this volume may be found at the Brookings Papers web page, www.brookings.edu/bpea. under "Past BPEA Editions."

(11.) Although EU KLEMS classifies health care and education as nonmarket sectors, they are a substantial and growing part of GDP across the developed world; and in many countries (for example, the United States), they also encompass a large private sector component. We therefore choose to retain these sectors in our analysis.

(12.) This subset includes Austria, Belgium, Denmark, Finland, France, Germany, Italy, the Netherlands, Spain. Sweden, the United Kingdom, and the United States.

(13.) Per our convention, this calculation includes only the 28 market industries featured in our analysis.

(14.) Supplemental tables are available upon request from the authors.

(15.) In EU KLEMS, TFP growth is calculated as the log change in industry value added minus the log change in labor and capital inputs, weighted by the average start and end period of their respective factor shares (Timmer and others 2007). In a regression of the change in labor share on TFP growth, the change in labor share used in the TFP calculation enters the right-hand side of the equation, leading to a mechanical relationship.

(16.) The standard deviation of TFP growth is 2.6 log points, as reported in online appendix table A6.

(17.) Because the wage bill regression is weighted by hours shares and the value-added regression by value-added shares, the precise impact of TFP growth on the labor share cannot be directly inferred from a comparison of these two columns.

(18.) Thirty-six percent of all country-industry-year TFP growth observations are negative. This is most frequently the case for renting of machinery and equipment, computer and related activities, research and development, and other business activities (codes 71-74): other community, social, and personal service activities (code O): hotels and restaurants (code H); and real estate activities (code 70). But it occurs in all industries to some extent. The likely cause is that annual frequency TFP calculations incorporate a fair amount of measurement error, leading to short-run intervals where nominal value added rises less rapidly than the share-weighted growth of labor and capital inputs.

(19.) These estimates are obtained from full-length five-year intervals (1970-75, 1975-80,..., 2000-05) only; and the reported coefficients reflect the effect of TFP growth occurring over the previous five-year interval.

(20.) More recent EU KLEMS releases cover a smaller set of countries and rely on back-casting data preceding 1995. We use a balanced panel of 12 countries--Austria, Belgium, Denmark, Finland, France, Germany, Italy, the Netherlands, Spain, Sweden, the United Kingdom, and the United States--over the period 2000-15.

(21.) Since the majority of variation in patenting reflects stable, cross-industry differences rather than over-time, within-industry fluctuations, we exclude sector-specific indicators from these models (which would otherwise absorb most identifying variation). Due to this limited variation, we confine our patent analysis to direct (own-industry) effects.

(22.) Due to the differences in underlying units, the magnitude of coefficients cannot be directly compared between the TFP and patents models.

(23.) We eliminate the on-diagonal (own-industry) term from the input-output measures because these are captured by the direct TFP terms ([[beta].sup.k.sub.1]).

(24.) Although every industry is potentially both a customer and supplier to every other industry, the terms "customer" and "supplier" refer to the direction of flows of inputs and outputs: Suppliers produce outputs that are purchased by (downstream) customers; and customers purchase inputs produced by (upstream) suppliers.

(25.) We report a pure stacked country-level time series version of these estimates in online appendix table A9, in which we eliminate industry-level variation entirely and instead use only country-year observations. These point estimates are similar to those used in the bottom half of table 9, which we prefer because they eliminate the mechanical relationship between own-industry and country-level aggregate outcomes.

(26.) The upstream and downstream linkages estimated in equation 5 can also contribute to the between-industry component of the labor share change through their effects on industry nominal output shares, though we estimate these effects to be comparatively small and statistically insignificant.

(27.) In calculating [DELTA][Y.sup.FD.sub.c,t], we also include the customer and supplier TFP effects estimated in equation 5, though we suppress those terms above to conserve notation.

(28.) This last term, [[phi].sub.i,c], is derived by differentiating the sum of industry log value added at the country level with respect to the log value added of industry i in country c, which is simply equal to i's share in country c's value added. Note that the sum of industry shares is less than 1, because we exclude nonmarket industries from the analysis, though they are logically included in aggregate national value added.

(29.) We do not separately report contributions for hours worked because they are nearly identical to those for employment.

(30.) The indirect employment contribution made by productivity gains in customer industries is much smaller than the corresponding effect of productivity gains in supplier industries, and it is primarily driven by TFP growth in electrical and optical equipment, transportation equipment, and machinery.

(31.) Observe that the contribution of final demand growth to employment and hours worked in destination industries reported in online appendix table A12 is directly proportional to the size of the industry in total employment.

(32.) The predicted versus observed employment contribution (the bottom panel of figure 6) depends on the proportional growth in each industry multiplied by its weight in overall employment, whereas the predicted versus observed employment change (the top panel of figure 6) depends on only the first of these terms.

(33.) The weights ([[omega].sub.i,c]) used in equations 8, 9, and 10 are now time-averaged, industry value-added shares rather than employment or hours shares; and the final demand effect is calculated using aggregate increases in nominal rather than real value added. Hence, the coefficients [[SIGMA].sup.5.sub.k=0][[lambda].sup.k.sub.1] and [[SIGMA].sup.5.sub.k=0][[beta].sup.k.sub.1,VA] in equation 10 are taken from column 4 (rather than column 5) of, respectively, the lower and upper rows of table 9.

(34.) As with prior calculations, we incorporate customer and supplier TFP effects into this calculation but suppress them from the equation for simplicity. We have also estimated models that allow the aggregate income elasticities, estimated in the lower half of table 9, to vary by broad sector (thereby potentially admitting nonhomotheticities). This has negligible effects on the predicted composition changes, and we therefore do not report these specifications.

(35.) Unlike for employment and hours, most effects for the labor share are driven by the direct effect. As a result, there is no need to separately consider the industry contributions by source of TFP growth.

(36.) The substantial between-industry component of the falling labor share in the 2000s is, as above, due to the rapid growth of the real estate industry in value added, a phenomenon that is unlikely to be attributable to technological progress.

(37.) We are severely limited in our ability to estimate distributed lag models for the decade of the 1970s because no country enters the EU KLEMS data before 1970, and several enter later (see online appendix table A1).

(38.) We restrict our attention here to the direct effect because we find this to be the main driver of aggregate labor share changes, irrespective of the time period under consideration.

(39.) For further explorations of the linkage between firm-level dynamics and aggregate productivity, see Decker and others (2017), Autor and others (2017b). and Foster and others (2017, 2018).
Table 1. Trends in Hours Worked and Labor Share by Country and Decade,
1970-2007

                Average across years                        100 x
                                                         annualized
                                                            change
                                                         in log hours
                            Labor   Value-added           worked (a)
Country         Log hours   share   share        1970s   1980s  1990s

Australia        9.41       0.648   0.020         1.77    2.48   2.32
Austria          8.61       0.672   0.009         0.52    0.48   1.42
Belgium          8.50       0.641   0.011        -0.96    0.23   1.82
Canada           9.82       0.594   0.028         2.59    2.38   1.82
Denmark          8.20       0.676   0.007        -0.07    0.18   1.18
Finland          8.10       0.683   0.006         0.26    1.34  -0.30
France          10.36       0.679   0.063         0.04    0.37   1.07
Germany         10.82       0.666   0.093        -0.60    0.29   1.13
Ireland          7.77       0.559   0.007                 3.71   5.32
Italy           10.39       0.682   0.052         1.20    1.21   0.84
Japan           11.57       0.566   0.196         1.17    0.80  -0.27
Luxembourg       5.82       0.554   0.001                 3.52   4.86
Netherlands      9.06       0.683   0.017        -0.59    1.26   3.26
Portugal         8.87       0.594   0.004         1.43   -1.23   0.76
South Korea     10.33       0.695   0.017         6.46    3.43   1.82
Spain            9.85       0.628   0.027         0.81    1.28   2.72
Sweden           8.72       0.679   0.015                 1.50   0.29
United          10.65       0.705   0.059         0.11    1.46   0.92
Kingdom
United States   12.08       0.637   0.366         2.39    2.70   2.50
Weighted                                          1.424   1.699  1.553
average

                               100 x
                            annualized
                              change
                            in log labor
                             share (b)
Country         2000s  1970s   1980s   1990s    2000s

Australia       3.03   -0.22   -1.07    0.01    -0.27
Austria         1.95   -0.72   -1.12   -0.79    -1.16
Belgium         1.79    0.92   -1.27    0.22     2.52
Canada          2.55   -0.40   -0.02   -1.13     0.42
Denmark         2.02    0.14   -0.37   -0.96     0.59
Finland         2.17   -0.10    0.35   -2.53     0.17
France          1.80   -0.37   -1.07   -0.81    -0.44
Germany         0.80    0.42   -1.18    0.15    -1.52
Ireland         4.37            0.17   -2.15     0.78
Italy           1.94    0.54   -0.52   -1.82    -0.53
Japan           0.97    2.38   -0.43   -0.76    -0.71
Luxembourg      3.99            1.21   -0.84    -0.08
Netherlands     1.77   -1.73   -0.47    0.09    -0.85
Portugal        0.88    3.01    2.26   -0.56    -0.55
South Korea     1.56   -0.07    0.44   -1.22     0.93
Spain           4.06    0.10   -0.11    0.31    -0.94
Sweden          1.30           -0.61   -0.91     0.40
United          2.38   -0.34    0.36   -0.91     0.32
Kingdom
United States   0.70    0.12   -0.38    0.36    -1.46
Weighted        1.350   0.513  -0.459  -0.263   -0.861
average

Sources: EU KLEMS; authors' calculations.
(a.) Changes are annualized log differences by decade weighted by
time-averaged hours-worked shares.
(b.) Changes are annualized log differences by decade weighted by
time-averaged value-added shares.

Table 2. Trends in Hours Worked, Labor Share, and Total Factor
Productivity, by Industry, 1970-2007

ISIC                                                 100 x annual
code                              Time-averaged       log change
(rev.    Description              value            Hours        Labor
3)                                added          worked (a)   share (b)
                                  share

C        Mining and quarrying     0.015           -2.45        -1.22
15-16    Manufacture of food,     0.026           -0.52        -0.08
         beverages, and
         tobacco products
17-19    Manufacture of           0.012           -3.96         0.18
         textiles, apparel,
         leather, and
         related products
20       Manufacture of wood      0.005           -1.34        -0.32
         and wood products,
         excluding furniture
21-22    Manufacture of paper     0.022           -0.25        -0.19
         and paper products,
         printing, and
         publishing
23       Manufacture of coke,     0.006           -1.54        -1.60
         refined petroleum
         products, and
         nuclear fuel
24       Manufacture of           0.022           -0.78        -0.44
         chemicals and
         chemical products
25       Manufacture of           0.010            0.67         0.21
         rubber and
         plastics products
26       Manufacture of other     0.009           -1.33        -0.18
         nonmetallic mineral
         products
27-28    Manufacture of basic     0.029           -0.87        -0.22
         and fabricated
         metals
29       Manufacture of           0.023           -0.60         0.03
         machinery and
         equipment not
         elsewhere
         classified
30-33    Manufacture of           0.033           -0.28        -0.10
         electrical and
         optical equipment
34-35    Manufacture of motor     0.024           -0.12        -0.27
         vehicles and
         transportation
         equipment
36-37    Manufacture of           0.008           -0.58        -0.03
         furniture and
         manufacturing not
         elsewhere classified;
         recycling
E        Electricity, gas,
         and water supply         0.025           -0.28        -0.65
F        Construction             0.068            0.94         0.04
50       Sale, maintenance,       0.014            0.95        -0.05
         and repair of motor
         vehicles and fuel
51       Wholesale trade,         0.064            0.67        -0.28
         excluding motor
         vehicles
52       Retail trade,            0.052            0.73        -0.16
         excluding motor
         vehicles; repair
         of personal and
         household goods
H        Hotels and
         restaurants              0.028            1.80        -0.09
60-63    Transportation
         activities of travel     0.045            0.91        -0.17
         agencies
64       Post and                 0.025            0.52        -1.18
         telecommunications
J        Financial
         intermediation           0.064            1.70        -0.46
70       Real estate
         activities               0.113            3.08         0.70
71-74    Renting of machinery     0.098            4.63         0.68
         and equipment;
         computer and related
         activities;
         research and
         development; and
         other
         business
         activities
M        Education                0.057            1.67        -0.01
N        Health and social
         work                     0.066            2.89         0.05
O        Other community,
         social,                  0.040            2.16         0.11
         and personal
         service
         activities

                                  100 x annual
ISIC                              log change
code
(rev.    Description                Total factor
3)                                 productivity (b)

C        Mining and quarrying       0.29
15-16    Manufacture of food,       0.72
         beverages, and
         tobacco products
17-19    Manufacture of             2.07
         textiles, apparel,
         leather, and
         related products
20       Manufacture of wood        2.12
         and wood products,
         excluding furniture
21-22    Manufacture of paper       1.10
         and paper products,
         printing, and
         publishing
23       Manufacture of coke,      -0.49
         refined petroleum
         products, and
         nuclear fuel
24       Manufacture of             3.19
         chemicals and
         chemical products
25       Manufacture of             2.56
         rubber and
         plastics products
26       Manufacture of other       1.68
         nonmetallic mineral
         products
27-28    Manufacture of basic       1.72
         and fabricated
         metals
29       Manufacture of             1.86
         machinery and
         equipment not
         elsewhere
         classified
30-33    Manufacture of             4.49
         electrical and
         optical equipment
34-35    Manufacture of motor       2.42
         vehicles and
         transportation
         equipment
36-37    Manufacture of             1.09
         furniture and
         manufacturing not
         elsewhere classified;
         recycling
E        Electricity, gas,
         and water supply           1.29
F        Construction               0.20
50       Sale, maintenance,         0.11
         and repair of motor
         vehicles and fuel
51       Wholesale trade,           1.07
         excluding motor
         vehicles
52       Retail trade,              1.18
         excluding motor
         vehicles; repair
         of personal and
         household goods
H        Hotels and
         restaurants               -0.88
60-63    Transportation
         activities of travel       1.24
         agencies
64       Post and                   3.04
         telecommunications
J        Financial
         intermediation             0.95
70       Real estate
         activities                -0.66
71-74    Renting of machinery      -1.65
         and equipment;
         computer and related
         activities;
         research and
         development; and
         other
         business
         activities
M        Education                 -0.14
N        Health and social
         work                      -0.22
O        Other community,
         social,                   -1.02
         and personal
         service
         activities

Sources: EU KLEMS; authors' calculations.
(a.) Changes are annualized log differences weighted by country size
and hours-worked shares.
(b.) Changes are annualized log differences weighted by country size
and value-added shares.

Table 3. Within-Industry Trends in Key Variables Used in the Analysis,
1970-2007 (a)

                                 100 x mean annual log change
                        Employment        Hours worked        Nominal
                                                            hourly wage

Overall                  1.337 (***)       1.001 (***)       6.472 (***)
                        (0.166)           (0.171)           (0.171)
1970s                    2.035 (***)       1.572 (***)      11.556 (***)
                        (0.204)           (0.210)           (0.401)
1980s                    1.661 (***)       1.365 (***)       6.550 (***)
                        (0.198)           (0.214)           (0.238)
1990s                    0.996 (***)       0.656 (***)       3.815 (***)
                        (0.190)           (0.220)           (0.178)
2000s                    0.382 (**)        0.174             3.043 (***)
                        (0.190)           (0.210)           (0.226)
Mining,                  0.625             0.521             6.441 (***)
utilities,
and
construction            (0.393)           (0.443)           (0.809)
Manufacturing           -0.810 (***)      -0.984 (***)       7.068 (***)
                        (0.170)           (0.182)           (0.266)
Education                2.566 (***)       2.351 (***)       6.422 (***)
and health
                        (0.203)           (0.196)           (0.412)
Low-tech                 1.676 (***)       1.227 (***)       6.158 (***)
services
                        (0.148)           (0.168)           (0.251)
High-tech                3.286 (***)       3.091 (***)       6.324 (***)
services
                        (0.379)           (0.379)           (0.380)
No. of              18,062            18,062            18,062
observations (b)
Weights                 Employment        Hours             Hours

                                100 x mean annual log change
                       Real hourly-       Nominal value     Labor share
                       wage               added

Overall                 1.700 (***)        7.058 (***)      -0.051
                       (0.116)            (0.188)           (0.104)
1970s                   2.472 (***)       11.643 (**)        0.503 (**)
                       (0.261)            (0.270)           (0.217)
1980s                  1 728 (***)         7.689 (***)      -0.265 (**)
                       (0.170)            (0.294)           (0.123)
1990s                  1 3i9 (***)         4.135 (***)      -0.141
                       (0.157)            (0.253)           (0.171)
2000s                  ] ]27 (***)         3.876 (***)      -0.395 (***)
                       (0.176)            (0.293)           (0.152)
Mining,                 1.641 (***)        6.523 (***)      -0.391 (*)
utilities,
and
construction           (0.573)            (0.550)           (0.223)
Manufacturing           2.246 (***)        5.484 (***)      -0.157 (**)
                       (0.160)            (0.236)           (0.080)
Education               1.664 (***)        8.306 (***)      -0.058
and health
                       (0.245)            (0.430)           (0.089)
Low-tech                1.403 (***)        7.164 (***)       0.162
services
                       (0.168)            (0.254)           (0.237)
High-tech               1.608 (***)        8.688 (***)      -0.095
services
                       (0.274)            (0.360)           (0.222)
No. of             18,062             18,062            18,062
observations (b)
Weights                Hours              Value added       Value added

                    100 x mean annual log change
                       Total factor
                       productivity

Overall                 0.619 (***)
                       (0.150)
1970s                   0.440 (**)
                       (0.201)
1980s                   0.994 (***)
                       (0.168)
1990s                   0.603 (***)
                       (0.154)
2000s                   0.360 (***)
                       (0.133)
Mining,                 0.405 (***)
utilities,
and
construction           (0.114)
Manufacturing           2.185 (***)
                       (0.180)
Education              -0.190 (***)
and health
                       (0.023)
Low-tech                0.150
services
                       (0.193)
High-tech              -0.022
services
                       (0.452)
No. of             18,062
observations (b)
Weights                Value added

Sources: EU KLEMS; authors' calculations.
(a.) The data are for all sectors of the economy, excluding
agriculture, public administration, private households, and
extraterritorial organizations. All models are weighted by
time-averaged industry shares of the weighting variable within
countries, multiplied by time-varying country shares in the total
annual value of the weighting variable. Standard errors clustered by
country-industry are in parentheses. Statistical significance is
indicated at the (*) 10 percent, (**) 5 percent, and (***) 1 percent
levels.
(b.) The number of observations is the number of country-industry cells
multiplied by the number of years.

Table 4. Shift-Share Analysis of the Changes in Labor Share by Decadea

         Weighted by county size            Unweighted
                 Between    Within              Between      Within
Decade   Mean    industry   industry   Mean     industry     industry

1970s     0.513   -0.187     0.700      0.230    -0.146       0.376
                 (-0.36)    (1.36)              (-0.63)      (1.63)
1980s    -0.459   -0.183    -0.276     -0.201    -0.121      -0.080
                  (0.40)    (0.60)               (0.60)      (0.40)
1990s    -0.263   -0.075    -0.188     -0.750    -0.304      -0.446
                  (0.28)    (0.72)               (0.41)      (0.59)
2000s    -0.861   -0.425    -0.436     -0.126    -0.018      -0.104
                  (0.49)    (0.51)               (0.17)      (0.83)

Sources: EU KLEMS; authors' calculations.
(a.) The units are 100 x annualized decadal log changes in labor share
by country. The values in parentheses are the shares explained by
between-industry or within-industry shifts.

Table 5. Estimates of the Relationship between Total Factor
Productivity Growth and Industry-Level Outcomes, 1970-2007 (a)

                                         Annual change
                                        in log outcome
                                          variable by
                                        country-industry
                                          Employment
                           (1)        (2)           (3)         (4)

[SIGMA][DELTA]ln(own
-industry                  -2.073     -1.132        -1.117      -1.989
[TFP.sub.i,c,t-k])          (***)      (***)        (***)        (***)
                           (0.172)    (0.144)       (0.147)     (0.187)
[R.sup.2]                   0.223      0.271         0.359       0.203

Model weights                             Employment
                                      Nominal value added

                           (10)       (11)          (12)        (13)
[SIGMA][DELTA]ln(own
-industry                  -1.332     -0.629        -0.609       0.641
[TFP.sub.i,c,t-k])          (***)      (***)         (***)
                           (0.221)    (0.180)       (0.191)     (0.494)
[R.sup.2]                   0.299      0.313         0.368       0.105

Model weights                         Nominal value added

Fixed effects
  Country                     Yes          Yes      Yes       Yes
  Year                        Yes          Yes      Yes       Yes
  Sector                      No           Yes      Yes       No
  Country x                   Yes          Yes      No        Yes
time trend
  Country x                   Yes          Yes      No        Yes
business
    cycle
  Country x                   No           No       Yes       No
year
No. of                     15,520       15,520    15,520    15,520
observations (b)

                                           Annual change
                                          in log outcome
                                            variable by
                                          country-industry
                                    Hours                  Wage bill
                               (5)            (6)            (7)

[SIGMA][DELTA]ln(own
-industry                      -1.048         -1.028         -1.848
[TFP.sub.i,c,t-k])              (***)         (***)           (***)
                               (0.160)        (0.162)        (0.272)
[R.sup.2]                       0.239          0.359          0.414

Model weights                            Hours
                                   Real value added        Labor share

                               (14)           (15)           (16)
[SIGMA][DELTA]ln(own
-industry                       1.214          1.238         -0.504
[TFP.sub.i,c,t-k])              (***)          (***)         (***)
                               (0.401)        (0.405)        (0.128)
[R.sup.2]                       0.137          0.183          0.063

Model weights                            Nominal value added

Fixed effects
  Country                     Yes        Yes         Yes        Yes
  Year                        Yes        Yes         Yes        Yes
  Sector                      Yes        Yes         No         Yes
  Country x                   Yes        No          Yes        Yes
time trend
  Country x                   Yes        No          Yes        Yes
business
    cycle
  Country x                   No         Yes         No         No
year
No. of                      15,520     15,520      15,520     15,520
observations (b)

                                  Annual change
                                  in log outcome
                                    variable by
                                 country-industry
                                     Wage bill
                             (8)               (9)

[SIGMA][DELTA]ln(own
-industry                    -1.078 (***)      -1.29
[TFP.sub.i,c,t-k])                              (***)
                             (0.220)           (0.225)
[R.sup.2]                     0.426             0.530

Model weights                         Hours
                                   Labor share

                             (17)              (18)
[SIGMA][DELTA]ln(own
-industry                    -0.571            -0.541
[TFP.sub.i,c,t-k])            (***)             (***)
                             (0.148)           (0.152)
[R.sup.2]                     0.064             0.147

Model weights            Nominal value added

Fixed effects
  Country                        Yes
  Year                           Yes
  Sector                         Yes
  Country x                      No
time trend
  Country x                      No
business
    cycle
  Country x                      Yes
year
No. of                         15,520
observations (b)

Sources: EU KLEMS; authors' calculations.
(a.) The dependent variable is the annual change in the log of the
outcome variable by country-industry. TFP is other-country,
within-industry TFP, and is rescaled to have a standard deviation of 1.
The estimates shown are the sum of coefficients for the contemporaneous
effect and five annually distributed lags. Standard errors clustered by
country-industry are in parentheses. Statistical significance is
indicated at the (*) 10 percent, (**) 5 percent, and (***) 1 percent
levels.
(b.) The number of observations is equal to the number of
country-industry cells multiplied by the number of years.

Table 6. Robustness Tests for Estimates in Table 5a

                          Annual change in log outcome variable by
                                     country-industry
                        Employment        Hours             Wage bill
                        (1)               (2)               (3)

All
countries
given
equal
weight
(b,c)
[SIGMA]
[DELTA]lnlown
-industry               -1.038 (***)      -0.996 (***)      -0.888 (***)
[TFP.sub.i,
c,t-k])
                        (0.123)           (0.125)           (0.146)
[R.sup.2]                0.331             0.335             0.565
No. of
observations        15,520            15,520            15,520
Excluding
contemporaneous
effect (c,d)
[SIGMA]
[DELTA]ln(own
-industry               -1.038 (***)      -0.985 (***)      -1.039 (***)
[TFP.sub.i,
c,t-k])
                        (0.142)           (0.153)           (0.198)
[R.sup.2]                0.358             0.358             0.530
No. of
observations        15,520            15,520            15,520
Excluding
self-employed
(b,c)
[SIGMA]
[DELTA]ln(own
-industry               -1.156 (***)      -1.056 (***)      -0.996 (***)
[TFP.sub.i,
c,t-k])
                        (0.156)           (0.163)           (0.218)
[R.sup.2]                0.384             0.386             0.580
No. of
observations        15,520            15,520            15,520
Setting
negative TFP
growth to
zero (b,c)
[SIGMA]
[DELTA]ln(own
-industry               -1.109 (***)      -0.962 (***)      -0.880 (***)
[TFP.sub.i,c,
t-k])
                        (0.223)           (0.234)           (0.309)
[R.sup.2]                0.350             0.352             0.528
No. of
observations        15,520            15,520            15,520
Five-year-long
first
differences
(c,e)
[SIGMA]
[DELTA]ln(own
-industry               -0.683 (***)      -0.636 (***)      -0.713 (***)
[TFP.sub.i,c,
t-k])
                        (0.090)           (0.097)           (0.119)
[R.sub.2]                0.505             0.490             0.787
No. of
observations         2,820             2,820             2,820
EU KLEMS
2000-15
data (b)
[SIGMA]
[DELTA]ln(own
-industry               -1.194 (***)      -0.943 (***)      -0.904 (**)
[TFP.sub.i,
c,t-k])
                        (0.304)           (0.310)           (0.359)
[R.sub.2]                0.365             0.492             0.331
No. of
observations         3,148             3,148             3,148
Model weights           Employment        Hours             Hours

                          Annual change in log outcome variable by
                                     country-industry
                        Nominal value     Real value       Labor share
                        added             added            (6)
                        (4)               (5)
All
countries
given
equal
weight
(b,c)
[SIGMA]
[DELTA]lnlown
-industry               -0.603 (***)       1.040 (***)     -0.426 (***)
[TFP.sub.i,
c,t-k])
                        (0.147)           (0.182)          (0.108)
[R.sup.2]                0.395             0.218            0.104
No. of
observations        15,520            15,520           15,520
Excluding
contemporaneous
effect (c,d)
[SIGMA]
[DELTA]ln(own
-industry               -0.719 (***)       0.947 (**)      -0.423 (***)
[TFP.sub.i,
c,t-k])
                        (0.157)           (0.367)          (0.145)
[R.sup.2]                0.367             0.174            0.146
No. of
observations        15,520            15,520           15,520
Excluding
self-employed
(b,c)
[SIGMA]
[DELTA]ln(own
-industry               -0.609 (***)       1.238 (***)     -0.528 (***)
[TFP.sub.i,c,
t-k])
                        (0.191)           (0.405)          (0.142)
[R.sup.2]                0.368             0.183            0.147
No. of
observations        15,520            15,520           15,520
Setting
negative TFP
growth to
zero (b,c)
[SIGMA]
[DELTA]ln(own
-industry               -0.490 (**)        1.880 (***)     -0.690 (***)
[TFP.sub.i,c,
t-k])
                        (0.228)           (0.575)          (0.186)
[R.sup.2]                0.367             0.186            0.145
No. of
observations        15,520            15,520           15,520
Five-year-long
first
differences
(c,e)
[SIGMA]
[DELTA]ln(own
-industry               -0.472 (***)       0.631 (***)     -0.348 (***)
[TFP.sub.i,
c,t-k])
                        (0.115)           (0.231)          (0.104)
[R.sub.2]                0.687             0.263            0.119
No. of
observations         2,820             2,820            2,820
EU KLEMS
2000-15
data (b)
[SIGMA]
[DELTA]ln(own
-industry                0.070             0.896           -0.633*
[TFP.sub.i,
c,t-k])
                        (0.286)           (0.562)          (0.368)
[R.sub.2]                0.272             0.304            0.094
No. of
observations         3,148             3,148            3,148
Model weights           Value added       Value added      Value added

Sources: EU KLEMS; authors calculations.
(a.) TFP is other-country, within-industry TFP, and is rescaled to have
a standard deviation of 1. All estimates include country, year, and
country-year fixed effects. Standard errors clustered by country
industry are in parentheses. Statistical significance is indicated at
the (*) 10 percent, (**) 5 percent, and (***) 1 percent levels.
(b.) The estimates shown are the sum of coefficients for the
contemporaneous effect and five annually distributed lags.
(c.) These panels contain sector fixed effects.
(d.) The estimates shown are the sum of coefficients for five annually
distributed lags.
(e.) This panel contains country, year, and country-year fixed effects,
but the years are defined as five-year intervals.

Table 7. Predictive Relationships between Industry Patenting Activity
and Total Factor Productivity Growth, 1970-2007 (a)

                              100 x annual change in log TFP by
                                     country-industry
                                 (1)               (2)

[summation]ln
([patents.sub.i,c,t-k])           0.574 (***)       0.602 (***)
                                 (0.197)           (0.202)
[R.sup.2]                         0.061             0.137
No. of observations (b)      16,518            16,518
[summation]ln(patent              0.608 (***)       0.647 (***)
[citations.sub.i,c,t-k])
                                 (0.208)           (0.229)
[R.sup.2]                         0.054             0.139
No. of observations (b)      16,479            16,479
Fixed effects
  Country                        Yes               Yes
  Year                           No                Yes
  Country x time trend           No                No
  Country x                      No                No
  business cycle
  Country x year                 No                No

                             100 x annual change in log TFP by
                                    country-industry
                                (3)               (4)

[summation]ln
([patents.sub.i,c,t-k])          0.602 (***)       0.603 (***)
                                (0.202)           (0.204)
[R.sup.2]                        0.138             0.142
No. of observations (b)     16,518            16,518
[summation]ln(patent             0.648 (***)       0.649 (***)
[citations.sub.i,c,t-k])
                                (0.230)           (0.233)
[R.sup.2]                        0.140             0.143
No. of observations (b)     16,479            16,479
Fixed effects
  Country                       Yes               Yes
  Year                          Yes               Yes
  Country x time trend          Yes               No
  Country x                     Yes               No
  business cycle
  Country x year                No                Yes

Sources: EU KLEMS; U.S. Patent and Trade Office; authors' calculations.
(a.) Log patents and log patent citations are rescaled to have a
standard deviation of 1. The estimates shown are the sum of
coefficients for the contemporaneous effect and three annually
distributed lags. Standard errors clustered by country-industry are in
parentheses. Statistical significance is indicated at the (*) 10
percent, (**) 5 percent, and percent levels.
(b.) The number of observations is equal to the number of
country-industry cells multiplied by the number of years.

Table 8. The Relationship between Patenting and Industry-Level
Outcomes, 1970-2007 (a)

                               100 x annual change in log outcome
                                  ariable by country-industry
                                           Employment
                            (1)                   (2)            (3)

[summation]ln
([patents.sub.i,
c,t-k])                     -0.328 (*)            -0.261         -0.267
                            (0.187)               (0.197)        (0.201
                             0.036                 0.130          0.223
No. of
observations            15,456                15,456         15,456
[summation]ln(patent        -0.327                -0.239         -0.246
[citations.sub.i,
c,t-k])
                            (0.208)               (0.230)        (0.235
[R.sup.2]                    0.089                 0.280          0.336
No. of
observations            15,417                15,417         15,417

Model weights                             Employment
                                       Nominal value added
                            (10)                  (11)           (12)

[summation]ln
([patents.sub.i,
c,t-k])                     -0.437 (*)            -0.133         -0.135
                            (0.230)               (0.209)        (0.210
[R.sup.2]                    0.089                 0.280          0.336
No. of
observations            15,456                15,456         15.456
[summation]ln(patent        -0.729 (***)          -0.099         -0.121
[citations.sub.i,
c,t-k])
                            (0.259)               (0.215)        (0.217
[R.sup.2]                    0.116                 0.284          0.341
No. of
observations            15,417                15,417         15,417

Model weights               Nominal value
                            added

Fixed effects
  Country                   Yes                   Yes            Yes
  Year                      No                    Yes            Yes
  Country x time
  trend                     No                    Yes            No
  Country x
  business cycle            No                    Yes            No
  Country x year            No                    No             Yes

                               100 x annual change in log outcome
                                  variable by country-industry
                                              Hours
                         (4)              (5)                (6)

[summation]ln
([patents.sub.i,
c,t-k])                  -0.303           -0.243             -0.243
                         (0.192)          (0.205)            (0.209)
                          0.032            0.137              0.261
No. of
observations         15,456           15,456             15,456
[summation]ln
(patent                  -0.338           -0.206             -0.211
[citations.sub.i,
c,t-k])
                         (0.213)          (0.239)            (0.244)
[R.sup.2]                 0.023            0.104              0.150
No. of
observations         15,417           15,417             15,417

Model weights                 Hours
                                      Real value added
                         (13)             (14)               (15)

[summation]ln
([patents.sub.i,
c,t-k])                   0.607 (**)       0.678 (***)        0.672 (**)
                         (0.250)          (0.256)            (0.261)
[R.sup.2]                 0.023            0.104              0.150
No. of
observations         15,456           15,456             15,456
[summation]l
(patent                   0.553 (**)       0.738 (***)        0.731 (**)
[citations.sub.i,
c,t-k])
                         (0.272)          (0.285)            (0.291)
[R.sup.2]                 0.021            0.106              0.152
No. of
observations         15,417           15,417             15,417

Model weights            Nominal value aded

Fixed effects
  Country                Yes              Yes                Yes
  Year                   No               Yes                Yes
  Country x time
  trend                  No               Yes                No
  Country x
  business cycle         No               Yes                No
  Country x year         No               No                 Yes

                             100 x annual change in log outcome
                             variable by country-industry
                              Wage bill
                         (7)                  (8)             (9)

[summation]ln
([patents.sub.i,
c,t-k])                  -0.420 (*)            0.039           0.029
                         (0.219)              (0.222)         (0.226)
                          0.117                0.387           0.492
No. of
observations         15,456               15,456          15,456
[summation]ln
(patent                  -0.769 (***)          0.097           0.087
[citations.sub.i,
c,t-k])
                         (0.272)              (0.263)         (0.269)
[R.sup.2]                 0.006                0.062           0.147
No. of
observations         15,417               15,417          15,417

Model weights                Hours
                                    Labor share
                        (16)                 (17)              (18)

[summation]ln
([patents.sub.i,
c,t-k])                  -0.263 (**)          -0.213 (*)      -0.222
                         (0.133)              (0.129)         (0.135)
[R.sup.2]                 0.006                0.062           0.147
No. of
observations         15,456               15,456          15,456
[summation]l
(patent                  -0.329 (**)          -0.242 (*)      -0.235 (*)
[citations.sub.i,
c,t-k])
                         (0.145)              (0.141)         (0.142)
[R.sup.2]                 0.008                0.066           0.153
No. of
observations         15,417               15,417          15,417

Model weights            Nominal value added

Fixed effects
  Country                Yes                  Yes             Yes
  Year                   No                   Yes             Yes
  Country x time
  trend                  No                   Yes             No
  Country x
  business cycle         No                   Yes             No
  Country x year         No                   No              Yes

Sources: EU KLEMS; U.S. Patent and Trade Office; authors' calculations.
(a.) Log patents and log patent citations are rescaled to have a
standard deviation of 1. The estimates shown are the sum of
coefficients for the contemporaneous effect and five annually
distributed lags. Standard errors clustered by country-industry are in
parentheses. Statistical significance is indicated at the (*) 10
percent, (**) 5 percent, and (***) 1 percent levels.

Table 9. Estimates of the Relationship between Total Factor
Productivity Growth and Industry-Level Outcomes, 1970-2007 (a)

                                    Annual change in log outcome
                                    variable by country-industry
                                    Employment        Hours
                                    (1)               (2)

Industry effects
[SIGMA][DELTA]ln
(own-industry                       -0.951 (***)      -0.869 (***)
[TFP.sub.i,c,t-k])
                                    (0.144)           (0.160)
[SIGMA][DELTA]
ln(supplier-industry                 0.971 (***)       1.028 (***)
[TFP.sub.j[not equal to]i,
c,t-k])
                                    (0.223)           (0.237)
[SIGMA][DELTA]
ln(customer-industry                 0.097             0.159
[TFP.sub.j[not equal to]i,
c,t-k]))
                                    (0.128)           (0.152)
Fixed effects
  Year                              Yes               Yes
  Sector                            Yes               Yes
  Country x time
  trend                             Yes               Yes
  Country x business
  cycle                              Yes               Yes
[R.sup.2]                            0.280             0.252
No. of observations (b)         15,520            15,520
Model weights                       Employment        Hours
Aggregate
elasticities
[SIGMA][DELTA]
ln(aggregate real                    0.633 (***)       0.558 (***)
V[A.sub.j[not equal to]i,
c,t-k])
                                    (0.073)           (0.083)
[SIGMA][DELTA]
ln(aggregate nominal
V[A.sub.j[not equal to]i,
c,t-k])
Sector fixed
effects                              Yes               Yes
[R.sup.2]                            0.227             0.194
No. of observations (b)         15,520            15,520

Model weights                       Employment        Hours
                                                    Nominal
                                                    value
                                   Wage bill        added
                                   (3)              (4)

Industry effects
[SIGMA][DELTA]ln
(own-industry                      -1.052 (***)     -0.579 (***)
[TFP.sub.i,c,t-k])
                                   (0.233)          (0.201)
[SIGMA][DELTA]
ln(supplier-industry                0.196            0.376
[TFP.sub.j[not equal to]i,
c,t-k])
                                   (0.313)          (0.291)
[SIGMA][DELTA]
ln(customer-industry               -0.121           -0.410 (*)
[TFP.sub.j[not equal to]i,
c,t-k]))
                                   (0.202)          (0.243)
Fixed effects
  Year                             Yes              Yes
  Sector                           Yes              Yes
  Country x time
  trend                            Yes              Yes
  Country x business
  cycle                             Yes              Yes
[R.sup.2]                           0.428            0.317
No. of observations (b)        15,520           15,520
Model weights                      Hours            Value added
Aggregate
elasticities
[SIGMA][DELTA]
ln(aggregate real
V[A.sub.j[not equal to]i,
c,t-k])
[SIGMA][DELTA]
ln(aggregate nominal                1.083 (***)      1.030 (***)
V[A.sub.j[not equal to]i,
c,t-k])
                                   (0.026)          (0.024)
Sector fixed
effects                             Yes              Yes
[R.sup.2]                           0.414            0.300
No. of observations (b)        15,520           15,520

Model weights                      Hours            Value added
                                  Real
                                 value
                                   added             Labor share
                                   (5)               (6)

Industry effects
[SIGMA][DELTA]ln
(own-industry                       1.243 (***)       -0.584 (***)
[TFP.sub.i,c,t-k])
                                   (0.398)           (0.171)
[SIGMA][DELTA]
ln(supplier-industry                0.269            -0.029
[TFP.sub.j[not equal to]i,
c,t-k])
                                   (0.426)           (0.269)
[SIGMA][DELTA]
ln(customer-industry                0.253            -0.110
[TFP.sub.j[not equal to]i,
c,t-k]))
                                   (0.221)           (0.178)
Fixed effects
  Year                             Yes               Yes
  Sector                           Yes               Yes
  Country x time
  trend                            Yes               Yes
  Country x business
  cycle                             Yes               Yes
[R.sup.2]                           0.142             0.069
No. of observations (b)        15,520            15,520
Model weights                      Value added       Value added
Aggregate
elasticities
[SIGMA][DELTA]
ln(aggregate real                   0.907 (***)
V[A.sub.j[not equal to]i,
c,t-k])
                                   (0.084)
[SIGMA][DELTA]
ln(aggregate nominal                                  0.071 (***)
V[A.sub.j[not equal to]i,
c,t-k])
                                                     (0.025)
Sector fixed
effects                             Yes               Yes
[R.sup.2]                           0.110             0.006
No. of observations (b)        15,520            15,520
Model weights                        Value added       Value added

Sources: EU KLEMS; World Input-Output Database; authors' calculations.
(a.) TFP is other-country TFP. and is rescaled to have a standard
deviation of 1. The estimates shown are the sum of coefficients for the
contemporaneous effect and five annually distributed lags. Standard
errors clustered by country-industry are in parentheses. Statistical
significance is indicated at the (*) 10 percent, (**) 5 percent, and
(***) 1 percent levels.
(b.) The number of observations is equal to the number of
country-industry cells multiplied by the number of years.

Table 10. Industry-Level Contributions to Predicted Within- and
Between-lndustry Components of the Change in Aggregate Labor Share,
1970-2007

ISIC code                                       Within     Between
(rev. 3)    Description                         industry   industry

C           Mining and quarrying                -0.003      0.001
15-16       Manufacture of food,
            beverages,                          -0.006     -0.005
            and tobacco
            products
17-19       Manufacture of textiles,            -0.009      0.001
            apparel, leather,
            and related products
20          Manufacture of wood and             -0.004      0.001
            wood products,
            excluding furniture
21-22       Manufacture of paper and            -0.009      0.001
            paper products,
            printing, and publishing
23          Manufacture of coke,                 0.000      0.000
            refined petroleum
            products, and nuclear fuel
24          Manufacture of chemicals            -0.019      0.010
            and chemical
            products
25          Manufacture of rubber and           -0.008      0.002
            plastics products
26          Manufacture of other                -0.005      0.001
            nonmetallic mineral
            products
27-28       Manufacture of basic and            -0.021      0.008
            fabricated metals
29          Manufacture of machinery and        -0.013      0.000
            equipment not
            elsewhere classified
30-33       Manufacture of electrical           -0.038      0.009
            and optical
            equipment
34-35       Manufacture of motor                -0.016      0.000
            vehicles and
            transportation equipment
36-37       Manufacture of furniture and        -0.003      0.000
            manufacturing not
            elsewhere classified; recycling
E           Electricity, gas, and water supply  -0.010      0.009
F           Construction                        -0.006     -0.008
50          Sale, maintenance, and repair of    -0.002      0.000
            motor vehicles
            and fuel
51          Wholesale trade, excluding          -0.023      0.008
            motor vehicles
52          Retail trade, excluding motor       -0.018      0.002
            vehicles; repair of
            personal and household goods
H           Hotels and restaurants               0.003     -0.003
60-63       Transportation activities of        -0.018      0.005
            travel agencies
64          Post and telecommunications         -0.018      0.012
J           Financial intermediation            -0.017      0.009
70          Real estate activities               0.013     -0.086
71-74       Renting of machinery                 0.017     -0.008
            and equipment;
            computer and
            related activities; research and
            development; and
            other business activities
M           Education                            0.001     -0.002
N           Health and social work               0.001     -0.005
O           Other community, social, and         0.006     -0.004
            personal service
            activities
Total                                           -0.225     -0.046

Source: Authors' calculations, based on table 9.

Table 11. The Contribution of Total Factor Productivity Growth to the
Within-and Between-industry Components of the Change in Aggregate Labor
Share, by Decade, 1970-2007

         Actual annual change in         Predicted annual change in
         labor share in log points       labor share in log points
                  Between    Within             Between    Within
Decade   Total    industry   industry   Total   industry   industry

1970s     0.513   -0.187      0.700     -0.294  -0.124     -0.169
1980s    -0.459   -0.183     -0.276     -0.365  -0.005     -0.360
1990s    -0.263   -0.075     -0.188     -0.202   0.005     -0.207
2000s    -0.861   -0.425     -0.436     -0.231  -0.091     -0.140

Source: Authors' calculations, based on table 9.

Table 12. The Relationship between Productivity Growth and
Industry-Level Outcomes Allowing for Decade-Specific Direct Effectsa

                           Annual change in log outcome variable by
                           country-industry
                          Employment                           Hours
                          (1)             (2)            (3)

[SIGMA][DELTA]ln(own
-industry
TF[P.sub.i,c,t-k])
1970s (b)                 -0.834 (***)     0.042          -0.774 (***)
                          (0.194)         (0.148)         (0.205)
1980s-2000s (c)           -2.135 (***)    -1.182 (***)    -2.062 (***)
                          (0.170)         (0.148)         (0.183)

Model weights             Employment
                          Nominal value                  Real value
                          added                          added
                          (7)             IS)            (9)

[SIGMA][DELTA]ln(own
-industry
TF[P.sub.i,c,t-k])
  1970s (b)               -0.469 (*)      -0.089           0.627 (*)
                          (0.244)         (0.329)         (0.364)
  1980s-2000s (c)         -1.452 (***)    -0.685 (***)     0.640
                          (0.221)         (0.191)         (0.487)

Model weights                     Nominal value added

Fixed effects
  Country                 Yes             Yes            Yes
  Year                    Yes             Yes            Yes
  Sector                  No              Yes            No
  Country x               Yes             Yes            Yes
  time trend
  Country x               Yes             Yes            Yes
  business cycle
  Country x year          No              No             No

                            Annual change in log outcome variable by
                            country-industry
                           Hours                     Wage bill
                           (4)             (5)             (6)

[SIGMA][DELTA]ln(own
-industry
TF[P.sub.i,c,t-k])
1970s (b)                   0.071          -0.464           0.244
                           (0.154)         (0.283)         (0.259)
1980s-2000s (c)            -1.109 (***)    -1.855 (***)    -1.014 (***)
                           (0.166)         (0.261)         (0.208)

Model weights               Hours                   Hours
                                           Labor share

                           (10)            (11)            (12)
[SIGMA][DELTA]ln(own
-industry
TF[P.sub.i,c,t-k])
  1970s (b)                 1.126 (***)     0.146           0.289
                           (0.363)         (0.234)         (0.335)
  1980s-2000s (c)           1.224 (***)    -0.386 (***)    -0.423 (***)
                           (0.415)         (0.102)         (0.144)

Model weights              Nominal value added       Nominal value added

Fixed effects
  Country                   Yes             Yes             Yes
  Year                      Yes             Yes             Yes
  Sector                    Yes             No              Yes
  Country x                 Yes             Yes             Yes
  time trend
  Country x                 Yes             Yes             Yes
  business cycle
  Country x year            No              No              No

Sources: EU KLEMS; authors' calculations.
(a.) The models are estimated separately by subperiod. TFP is
other-country, within-industry TFP, and is rescaled to have a standard
deviation of 1. Standard errors clustered by country-industry are in
parentheses. Statistical significance is indicated at the (*) 10
percent, (**) 5 percent, and (***) 1 percent levels.
(b.) The estimates shown are the sum of coefficients for the
contemporaneous effect and two annually distributed lags. The number of
observations is 3,520.
(c.) The estimates shown are the sum of coefficients for the
contemporaneous effect and five annually distributed lags. The number
of observations is 13,341.

Table 13. The Contribution of Total Factor Productivity Growth to the
Within-and Between-industry Components of the Change in Aggregate Labor
Share, by Decade, 1970-2007

         Actucl annual change in labor     Predicted annual change in
         share in log points               labor share in log points
                  Between    Within             Between    Within
Decade   Total    industry   industry   Total   industry   industry

1970s     0.513   -0.187      0.700      0.030  -0.020      0.050
1980s    -0.459   -0.183     -0.276     -0.201  -0.022     -0.179
1990s    -0.263   -0.075     -0.188     -0.125  -0.016     -0.109
2000s    -0.861   -0.425     -0.436     -0.150  -0.085     -0.065

Source: Authors' calculations, based on table 12.
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Author:Alitor, David; Salomons, Anna
Publication:Brookings Papers on Economic Activity
Date:Mar 22, 2018
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