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Comments and Discussion.

COMMENT BY

JOHN HALT1WANGER One of the oldest questions and concerns among economists is the impact of innovation and productivity growth on employment. Over the centuries, technological progress has raised productivity dramatically, enabling far greater output per unit of labor input. Moreover, accompanying product innovations have enabled associated rapid increases in the quality and range of products. Although this raises GDP per capita, concerns have frequently been raised about the workers left behind by technological advances. Recently, these concerns have arisen in the context of the impact on the workforce of perceived rapid changes in automation. Artificial intelligence, robotics, customized software, and specialized machinery have already become embedded in many production technologies, enabling the replacement of tasks once performed by workers.

Our understanding of these issues, even after much attention in the literature, remains relatively incomplete. Part of this reflects the fact that the type of data that is ideally needed to understand the labor-displacing nature of technology is not readily available. (1) Partly this reflects the view that each new wave of innovation is potentially different in both the nature and speed of any disruption and displacement that occurs. In addition, regardless of data limitations, it is challenging to sort through the complex mechanisms at the firm, industry, country, and global levels. Economic theory reminds us that technological improvements in one sector may yield a reallocation of labor to sectors with less rapid technological change (Ngai and Pissarides 2007), depending on the elasticity of substitution across sectors. The impact on aggregate employment also inherently depends on the elasticity of the labor supply. However, this latter perspective is in the long run, and there might be much disruption, displacement, and reallocation along the way.

This paper by David Autor and Anna Salomons weighs in on this ongoing debate by using pooled data, industry by country by time (mostly annual), on the relationship between outcomes such as employment growth, value-added growth, and the labor share with indicators of technological innovation. The primary focus in this paper is to use measures of total factor productivity (TFP) to capture the latter. The main findings in terms of employment growth are that there is an own-industry negative impact of rising TFP but offsetting indirect effects arising from the input-output linkages as well as the overall positive impact of rising TFP on aggregate value added and final demand. Taken at face value, the answer to the question posed in the paper's title is that though there may be sectoral reallocation induced by technological innovation, the aggregate effect on employment growth is positive. This answer is in principle reassuring to those who have continued to express concerns about the impact of innovation on employment outcomes.

Although I am sympathetic to the overall message of the paper and the careful analysis of rich industry-by-country data, I think there are several challenges in interpreting the paper's results. First, the empirical approach is entirely reduced form, which can be very useful for helping guide future analysis; but the nature of the reduced-form approach taken here does not provide much guidance about the mechanisms underlying the estimated results. (2) Second, there are many details about the measurement, specifications, and estimation that raise a host of questions about what we learn from using these industry-by-country-by-time data. Most of my remaining comment focuses on these latter issues.

A core concern is whether TFP growth at the industry level is a good proxy for innovation. In my figure 1, average annual TFP growth rates for the 28 industries used by Autor and Salomons from the U.S. KLEMS data are presented. Several remarks are warranted. First, the outsized role of information and communication technology (ICT) in productivity growth over this period is reflected in the electrical and optical equipment industry. Second, even during this period of rapid, ICT-induced productivity growth, 45 percent of industries have negative long-run productivity growth in the U.S. data. Autor and Salomons acknowledge the relatively high fraction of observations with negative productivity growth (and do some limited robustness analysis) but attribute much of this to high-frequency measurement error. (3) My figure 1 shows that this is a pervasive issue, even over long time intervals. Moreover, my figure 1 shows that it is not just the difficult-to-measure sectors, such as finance and services or the nonprofit sectors, that exhibit these patterns.

This pattern of pervasive industry-level negative productivity growth is also present at medium-run frequencies. My figure 2 presents a scatter plot of the employment growth rates and TFP growth rates at the industry level for the United States for these 28 industries using peak-to-peak variation (using the two-year average at each peak) based on reference cycles developed by the National Bureau of Economic Research. About 45 percent of the industry-by-time observations have negative productivity growth at this frequency. It is also evident that the negative own-industry effect estimated by Autor and Salomons is present in my figure 2. The elasticity of employment growth with respect to TFP growth using this medium-run variation is--0.207 (with a standard error of 0.090), which includes industry and time period controls, and the standard error is clustered at the industry level.

This pervasive finding of negative productivity growth at the industry level is not new. Dale Jorgenson, Mun Ho, and Jon Samuels (2018) summarize their views and the literature by highlighting four competing explanations: measurement error; resource depletion, relevant for sectors such as oil and gas extraction and mining; misallocation and regulation; and finally, sectors that especially deviate from private sector profit maximization (for example, health and education). All four of these explanations raise questions about the relevance of using TFP at the industry level as an indicator of innovation and technological progress. In addition, a few other factors also raise questions.

In particular, Michael Gort and Steven Klepper (1982) hypothesized long and variable lags between innovation and productivity growth. They argue that a surge in innovation in an industry is accompanied by a surge in the entry of new firms that engage in experimentation with new products and processes. During this period of experimentation, productivity growth might actually fall rather than rise. It is only later that productivity growth is observed, after successful entrants grow, while less successful entrants contract and exit. Gort and Klepper used relatively crude data on business formation and exits, but they did show patterns consistent with their hypothesis. Recent evidence from Lucia Foster and others (2018) provides more direct confirming evidence. We find that a surge in entry within an industry in one three-year period yields a decline in within-industry productivity growth and an accompanying rise in productivity dispersion across firms in the industry in the next three-year period. It is only in the subsequent years that productivity growth is observed, along with an accompanying decline in productivity dispersion. Gort and Klepper's firm dynamics are in some respects related to the misallocation hypothesis mentioned above, but in this case it is a more benign form of mis-allocation. Namely, Gort and Klepper argue that the firm dynamics and shakeout process inherent in innovation may lead to a decrease in productivity growth during the experimentation period, but this is part of the investment needed to eventually achieve successful innovations and productivity growth.

The firm dynamics hypothesized by Gort and Klepper (1982) also highlight another limitation of using industry-level as opposed to firm-level data to investigate the main questions of interest. Industry-level fluctuations in productivity reflect not only the within-firm innovations but also between-firm reallocation dynamics that may take some time to work through. A related issue is that many firm-level studies find a strong positive relationship between TFP and employment growth at the firm level (Decker and others 2018; Ilut, Kehrig, and Schneider, forthcoming). Reconciling the firm-level evidence with the industry-level evidence considered here likely requires distinguishing within-firm from between-firm innovations. That is, the successful innovators within an industry may be increasing employment but require less employment than unsuccessful firms that contract and exit. The overall impact at the industry level may be negative, but this may be entirely attributable to reallocation. Interestingly, Autor and others (2017) find that the decline in the within-industry labor share is primarily accounted for by reallocation, and not by within-firm declines in the labor share. In addition, even at the industry level, Daron Acemoglu, Ufuk Akcigit, and William Kerr (2016), using a similar specification to that used by Autor and Salomons, find a positive own-industry effect of TFP growth on employment growth (using a one-period lag of own-industry TFP growth).

All these issues raise questions about whether Autor and Salomons are providing much guidance about the impact of innovation on the potential displacement of labor. If nothing else, the timing and dynamics are complex, and a five-year lag specification is likely inadequate--especially from the perspective and findings of Gort and Klepper (1982) and of Foster and others (2018). In addition, there are interesting and complex issues in these dynamics. If productivity growth lags innovation substantially, at what point does any displacement of workers occur? Does it occur during the innovation or experimentation phase, or does it occur in the shakeout phase? The answer is likely all of the above.

These complex dynamics are important for more reasons than getting the frequency and lag structure of the empirical specification correct. At the core of concerns of the impact of automation on displacement is the speed of the transition dynamics. The Gort and Klepper firm dynamics suggest that implementation lags are long and variable. If implementation lags have shortened, then this has potentially important implications for the reallocation and displacement dynamics that might arise, even if there is no long-run adverse impact on employment.

There are other related concerns about the details of the implementation. The authors use a leave-out-mean approach for measuring within-industry-by-country TFP growth. This approach is intended to avoid the potential mechanical relationship between TFP and employment growth. The latter concern is potentially nontrivial, but does depend on the presence of measurement error in the labor input. The latter is likely among the best measured inputs in production. Moreover, others have overcome this concern using the relationship between contemporaneous employment growth and lagged TFP growth (Acemoglu, Akcigit, and Kerr 2016). I think using the leave-out-mean approach in this context also has other problems. For one, there is much evidence that innovation and productivity growth at the industry level is quite different across countries. The 1990s were a period when ICT innovation and productivity took off in the United States, relative to the rest of the world, including Europe. The approach taken by Autor and Salomons would distort this variation. The U.S. surge in productivity in the ICT sector in the 1990s would be left out of the U.S. measure, but it is so large that it would contribute substantially to the leave-out-mean of all other countries. Relatedly, I am skeptical that the leave-out-mean approach captures the technological frontier at the industry level.

Finally, I found the analysis of upstream and downstream industries interesting but difficult to interpret. Partly, it was difficult to interpret because of technical issues. The appropriate model and measurement methodology with input--output linkages is to use gross output production functions and explicit modeling and measurement of intermediate input usage. In addition, the results as presented are a bit of a black box. It would be interesting to explore and understand what types of supply chain links are especially important in this context. Acemoglu, Akcigit, and Kerr (2016) suggest some ways of exploring these issues.

REFERENCES FOR THE HALTIWANGER COMMENT

Acemoglu, Daron, Ufuk Akcigit, and William Kerr. 2016. "Networks and the Macroeconomy: An Empirical Exploration." NBER Macroeconomics Annual 31: 273-335.

Autor, David, David Dorn, Lawrence F. Katz, Christina Patterson, and John Van Reenen. 2017. "The Fall of the Labor Share and the Rise of Superstar Firms." Working Paper no. 23396. Cambridge, Mass.: National Bureau of Economic Research.

Decker, Ryan A., John C. Haltiwanger, Ron S. Jarmin, and Javier Miranda. 2018. "Changing Business Dynamism: Shocks vs. Responsiveness." Working Paper no. 24236. Cambridge, Mass.: National Bureau of Economic Research.

Foster, Lucia, Cheryl Grim, John C. Haltiwanger, and Zoltan Wolf. 2018. "Innovation, Productivity Dispersion, and Productivity Growth." Working Paper no. 24420. Cambridge, Mass.: National Bureau of Economic Research.

Gort, Michael, and Steven Klepper. 1982. "Time Paths in the Diffusion of Product Innovations." Economic Journal 92, no. 367: 630-53.

Hut, Cosmin, Matthias Kehrig, and Martin Schneider. Forthcoming. "Slow to Hire, Quick to Fire: Employment Dynamics with Asymmetric Responses to News." Journal of Political Economy.

Jorgenson, Dale W., Mun S. Ho, and Jon D. Samuels. 2018. "Educational Attainment and the Revival of U.S. Economic Growth." In Education, Skills, and Technical Change: Implications for Future US GDP Growth, edited by Charles R. Hulten and Valerie A. Ramey. University of Chicago Press.

Ngai, L. Rachel, and Christopher A. Pissarides. 2007. "Structural Change in a Multisector Model of Growth." American Economic Review 97, no. 1: 429-43.

(1.) For example, firm-level evidence on technology adoption accompanied by detailed information about the size and mix of the workforce in terms of skills is needed. Occasionally, modules have been added to firm-level surveys that provide very helpful information, such as the Survey of Manufacturing Technology in the 1980s and 1990s. We need a new wave of such modules for more recent advances in technology. In addition, we need to integrate such data with longitudinal matched employer-employee data to investigate the impact on the workforce.

(2.) Richard Rogerson's comment provides a detailed perspective on these issues.

(3.) I did not find the robustness analysis in the paper's table 6 compelling in terms of treating the negative TFP growth observations as zero. The discussion here highlights many different reasons that might underlie the observed negative TFP growth. Those same factors (such as reallocation dynamics) may be influencing the positive observations as well, and accordingly raise questions about the interpretation of the findings.

COMMENT BY

RICHARD ROGERSON Although the long-run effect of technological change on aggregate labor market outcomes has long been of interest to economists, concern about this issue has recently intensified, perhaps motivated in part by the decline in labor's share that has been observed in the United States and elsewhere in recent decades and by the sense that it might be due, at least in part, to increases in automation that reflect recent trends in technological change. This paper by David Autor and Anna Salomons seeks to assess the aggregate effects of automation on employment and labor's share since 1970 using sectoral data from a large set of developed economies. The paper provides much information that is useful in the effort to better explain the dynamics of employment and the labor share, complementing the earlier contribution to the Brookings Papers by Michael Elsby, Bart Hobijn, and Aysegul Sahin (2013), which focused entirely on the United States. However, though I think Autor and Salomons present a lot of interesting evidence, I nonetheless feel they are largely unsuccessful in their effort to offer compelling and credible evidence on the causal effects of automation on employment and the labor share at the aggregate level. The reduced-form methods employed by the authors essentially document conditional correlations. These correlations can serve as valuable diagnostics and provide suggestive evidence to help us distinguish between competing explanations. But these reduced-form methods are not well suited to delivering quantitative estimates of causal effects.

In the brief space that I have available here, I first describe why I think the empirical approach employed by the authors is unable to deliver reliable estimates of the causal effects of growth in total factor productivity (TFP) on employment and the labor share. I follow this with several shorter comments about details of the specification adopted by the authors.

USING SECTORAL DATA TO ESTIMATE AGGREGATE RESPONSES A key component of the paper's analysis is to recover the aggregate effects of TFP on employment and the labor share using reduced-form estimates of sectoral relationships. My main comment relates to the basis for interpreting these aggregate effects as the causal effects of TFP. As is well known, there is a long history of debate arguing the pros and cons of structural versus reduced-form approaches to uncovering causal effects, especially at the aggregate level. I do not want to get into this debate here, so I take as given that the goal is to learn what we can using reduced-form methods.

Before getting into specifics, I think it is important to first back up a bit to consider how the authors arrived at an analysis of sectoral data in their attempt to uncover aggregate effects. In particular, suppose we start with the premise that the goal is to use reduced-form methods to understand the effect of TFP growth on either employment or the labor share at the aggregate level in a particular country. Given this goal, it seems natural that one might first consider attempts to uncover these effects using reduced-form methods on aggregate data.

The simplest exercise that one might start with is to regress either of these aggregate outcome variables on aggregate TFP (perhaps including several lags, as the authors do). But if one simply ran the regression of either the employment--population ratio or the labor share on TFP for a single country, no one would view the coefficients as a reliable estimate of the causal effect of aggregate TFP on either outcome of interest. The reason is that potentially many other factors are at play that are also affecting these outcomes, these other factors may be correlated with TFP, and the regression is projecting all these effects onto changes in TFP.

One possible response is to try to include measures of the other potentially important factors on the right-hand side. Although there might be a few channels that we could capture this way, many of them are likely not easily measured, so there will always remain some concern that one is not isolating the effect of TFP. In such a situation, it is standard practice to include time effects as a way to control for unobserved factors; but using data for a single country, these time effects would explain all the variation in the left-hand-side variable.

If one thought that the key time effects were constant across countries, then expanding the analysis to include data from several countries would solve the problem. Note that one could of course also allow for country-level fixed effects in the analysis. But if one thought that the unobserved driving forces were specific to the country and year, expanding the analysis to many countries would not solve the basic problem of needing to isolate the effects of TFP from those of other factors, given that this would require a full set of interacted country and time effects.

A nice strategy adopted by Autor and Salomons is to use TFP from other countries as a proxy for TFP in the country being studied. This turns out to be a good proxy and, at least at first pass, would seem to eliminate the need for a fully interacted set of country and time fixed effects in the previous analysis. To the extent that global factors influence either labor share or employment across countries and are correlated with average movements in TFP, it would still be necessary to use time fixed effects to control for these other factors, but the use of other countries' TFP eliminates the effect of country-specific, non-TFP factors that might be correlated with country-specific TFP. But upon further reflection, it should be apparent that this strategy only solves the problem if it is assumed that the global non-TFP factors that are correlated with average TFP have identical effects on all countries. If not, we would still need a fully interacted set of country and time effects to control for these effects.

Why might one think that employment and labor share responses to a given shock might differ across countries? An old idea in the literature on cross-country differences in labor market evolutions--initially put forth by Michael Bruno and Jeffrey Sachs (1985), and later taken up by Paul Krugman (1994) and Olivier Blanchard and Justin Wolfers (2000)--is that country-specific factors (for example, labor market institutions) lead to differential responses across countries to a given shock. There seems every reason to think that this idea is relevant in the current context, when one seeks to estimate how output, employment, and wages respond to various driving forces. For example, the factors leading to increased global trade are plausibly correlated with TFP and plausibly have differential effects across economies, not only because of different labor market institutions, but also because different economies might have varying exposures to a given trade shock. (1)

To summarize, a key impediment to obtaining estimates of the aggregate effects of TFP on employment and the labor share from aggregate data using reduced-form methods is the need to include a set of fully interacted country and time fixed effects as a way to control for non-TFP factors.

Why might one turn to sector-level data in an attempt to uncover the aggregate effects? If one accepts that fully interacted country and time fixed effects are needed to properly control for non-TFP factors, then a sector-level analysis seems to offer a way around the issue, because one could now allow for a set of fully interacted country and time fixed effects and still have variation to consider. Two issues arise, however. First, why would we think that there are not important time and country effects at the sector level? The strategy of adding another layer of data to get around the need to have a full set of fixed effects presumes that we can rule out variation in driving forces or their impact at this new layer. But what is the rationale for this belief? My own view is that, in general, the more we disaggregate, the larger and more varied are the sources of idiosyncratic variation. Put differently, if one believes that interacted country and time fixed effects are important, why would it seem reasonable to assume that these effects do not vary at the sectoral level? Of course, these country-time-sector effects would not be a problem if they were uncorrected with TFP, but I see no basis for assuming this. The previous example of increased trade would certainly lead one to expect country-time-sector effects.

This issue aside, the second issue with moving to sector-level data is that each sector does not represent an economy. That is, even if we properly identify the effect of own-sector TFP changes on own-sector outcomes, we still need to determine how to aggregate the effects. This requires that we need to isolate not only the causal effect of TFP growth in sector i on outcomes in sector i, but also the causal effects of TFP growth in sector i on outcomes in all other sectors.

When one moves to sectoral data as a way to estimate aggregate effects, the implicit claim is that it is straightforward or easy to identify all these cross-sector, general equilibrium effects using reduced-form analyses. In fact, the authors characterize their analysis as building up the aggregate effects by quantifying each of several underlying effects, suggesting that it is easier to compute these individual underlying pieces than it is to directly compute the aggregate response. I argue below via a simple example that I believe this is not the case. That is, moving the analysis to the sectoral level does not get around any of the issues that led one to move from aggregate to sectoral data in the first place.

But before describing the simple example to make this point, I do want to emphasize that I nonetheless think sectoral analyses can be very useful. The reason is that they potentially provide additional information about driving forces and mechanisms. To be concrete, let us focus on the issue of the aggregate decline in the labor share. One may have various candidate driving forces or mechanisms in mind. The reason that sectoral data may be very useful is that there may be considerable variation across sectors, and this variation may prove to be a useful diagnostic to help us evaluate the promise of various driving forces. For example, in the current context, Autor and Salomons are interested in assessing the role of automation as a driving force. Variation in both investment in equipment (especially, perhaps, computing equipment), and the change in the labor share at the sectoral level might reveal something about the promise of a story that stresses automation. I say more about this below.

However, though I think sectoral-level data are therefore very valuable for qualitatively assessing different explanations, I do not think that moving to sectoral data provides any advantage in helping us to tease quantitative effects out of the data using reduced-form methods. And to think otherwise is basically wishful thinking. To see why, I consider the reduced-form methods employed by the authors in the context of a simple structural model.

In particular, consider an economy that captures the basic economics of William Baumol (1967). There is a representative household with preferences each period, given by

[C.sup.1-1/[sigma].sub.t] - B[H.sup.1+1/[gamma].sub.t].

There are N sectors, each with a constant-returns-to-scale production function:

[y.sub.i,t] = [A.sub.i,t][K.sup.[theta].sub.i,t][h.sup.1-[theta].sub.i,t].

Aggregate consumption and investment are produced by combining the outputs of the N sectors:

[C.sub.t]+[I.sub.t] = [([N.summation over (i=1)][a.sub.i][y.sup.1-1/[rho].sub.i,t]).sup.[rho]/[rho]-1]

Consider the competitive equilibrium for this economy. Even without doing any analysis, one might already sense something curious vis-a-vis the authors' analysis. The specification given above suggests that the two preference parameters [sigma] and [gamma] are surely going to be important for determining the response of aggregate employment to changes in the profile of sector TFPs. In particular, if we assume the limiting case of [sigma] = 1, then we have offsetting income and substitution effects, and it is easy to show that in the competitive equilibrium, aggregate employment is independent of the TFP profile across sectors. One may well ask how the empirical specification adopted by the authors is incorporating this key parameter and the associated labor supply effects, because the equations estimated by the authors all have the feel of being motivated by labor demand considerations, with no role for labor supply. Although it is common (even if not warranted) to abstract from labor supply considerations in the context of short-run fluctuations, there seems to be no basis for thinking that labor supply considerations do not factor into long-run labor market outcomes.

In what follows, I simply posit that aggregate employment is some unspecified function of the sector TFPs and capital stock, without imposing that equilibrium employment is consistent with desired labor supply of the household, taking all prices as given. Note, first, that if we normalize the wage to 1, then the sector i price is just the inverse of sector i TFP. Second, it is easy to show that maximization yields the following expressions:

[h.sub.i,t] = [[a.sup.[rho].sub.i][A.sup.[rho].sub.i,t]/[[summation].sub.j][a.sub.j][A.sup.[rho]-1.sub.j,t]][H.sub.t] [equivalent to] [a.sup.[rho].sub.i][A.sup.[rho].sub.i,t][D.sub.t][H.sub.t],

where [D.sub.t], is defined by

[D.sub.t] = [1/[summation over (j)][a.sub.j][A.sup.[rho]-1.sub.j,t]].

Taking the logs and first differences, we end up with

[DELTA] log [h.sub.i,t] = ([rho] - 1)[DELTA] log [A.sub.i,t] - A log [D.sub.t], + [DELTA] log [H.sub.t].

Recall that [H.sub.t], is implicitly a function of the profile of period t TFPs and the capital stock in the country being studied. The fact that it enters with a coefficient of 1 reflects the fact that preferences are homothetic, so that an increase in aggregate labor increases the output of each good proportionately. If one wanted to consider preferences that were nonhomothetic, then the coefficient on aggregate labor would vary across sectors, but the appropriate average of these effects would still be 1. A common coefficient of less than 1 would imply an inconsistency, given that aggregate labor must be the sum of the sectoral labors. The key point, however, is that the need to control for aggregate hours on the right-hand side surely suggests that one would need to include a fully interacted set of country and time effects to control both for the effects of TFP on total hours and for potential non-TFP factors. (2)

The approach taken by the authors is to replace [H.sub.t], with a measure of either nominal or real value added. Although this implicitly allows for a particular form of country-time fixed effect, this is appropriate only if aggregate hours and value added move one-for-one across all countries. But we know from growth accounting exercises that this is simply not the case. It also explains why they obtain the troubling result that a given percentage increase in aggregate value added at a single point in time, holding all else constant, leads to a smaller percentage increase in value added in all sectors.

The significance of the previous derivation is that even in a model with no driving forces beyond TFP, and no heterogeneity across countries other than TFP, one would need to include a fully interacted set of country and time fixed effects in order to properly estimate the sectoral relationship between TFP and employment. In reality, the time and country fixed effects will also pick up non-TFP effects. It follows that when one wants to use the estimates of this equation to compute the effect of TFP changes on employment, one needs to include the component of the country-time fixed effects that reflects TFP effects as opposed to non-TFP effects. That is, in order to trace out the causal effect of changes in TFP on employment using these estimates, one would need to be able to decompose the change in estimated country-time fixed effects into the parts that come from changes in TFP as opposed to non-TFP factors. But the whole reason for moving to sectoral data was because we did not know how to isolate the effect of TFP from non-TFP effects that were country and time varying. This sectoral approach ultimately requires that we have a solution to the problem that led us to the sectoral data in the first place!

Although my example is admittedly very simple, the key point derives from a very basic and robust property: In a multisector model, the allocation of labor to any sector will depend on the total amount of labor supplied in equilibrium, which will be a function of the profile of sector TFPs as well as any non-TFP factors that influence labor markets. The only way to credibly capture the evolution of this term over time and across countries in a linear regression model is to allow for a fully interacted set of country-time fixed effects. (3)

Let me summarize. I have raised two basic reasons for why the use of sectoral data should not be viewed as a path for obtaining credible estimates for causal aggregate effects using reduced-form methods. First, it presupposes that there are not important biases associated with country-time-sector effects that are correlated with the driving force of interest, in this case TFP. But second, this path requires that one be able to isolate TFP from non-TFP effects captured by country-time fixed effects. If one could do this credibly, then one would not need to go to sectoral data in the first place.

Although the discussion above explains what I view as the main limitation of the paper in terms of its ability to deliver credible estimates of the causal aggregate effects of TFP, in the remainder of my space I point out a few additional issues with the specification that the authors adopt.

TFP AS THE DRIVING FORCE The paper's title and some of its exposition suggest that the purpose of the analysis is to uncover the effects of automation on employment and labor's share. Automation reflects a particular type of technological progress. Because not all technological progress reflects automation, it would seem necessary for any study that seeks to isolate the effects of automation to first attempt to isolate the component of technological progress that might best be associated with automation. The authors instead choose to focus purely on the effects of an "omnibus" measure of technological progress--namely, TFP.

At one level, this is a simple issue of semantics--perhaps the authors' goals are really to assess the effects of TFP growth on labor market outcomes, rather than the effects of automation per se on labor market outcomes. But if we accept this alternative framing of the analysis, it seems that the analysis is implicitly abstracting from what surely must be the most important question. Two simple observations explain why I say this. First, until recently, there was a consensus that the so-called Kaldor facts (Kaldor 1961) provided a good description of aggregate economic outcomes in developed economies. Namely, both the employment--population ratio and the labor share were roughly constant. Second, we know from standard growth accounting exercises that changes in TFP are the dominant source of growth. Together, these observations tell us that for a long period in many economies, steady growth in TFP has been accompanied by stable values for both the employment--population ratio and the labor share.

It follows that if TFP growth is found to have significant effects on either the employment--population ratio or the labor share in the post-1970 period, this must surely reflect a change in the effects of TFP on these outcomes. The simplest explanation for why the effects of TFP might have changed surely lies in the possibility that the nature of technological progress has changed, and the authors clearly note this. But to my mind, this suggests that any study seeking to link changes in technology to recent changes in labor market outcomes must also make some effort to isolate the potentially different components of technological progress. Moreover, sectoral data would potentially be of particular importance in this regard, because we might think that there is heterogeneity both over time and across sectors in the composition of technological change and that this variation would prove to be important.

In fact, the EU KLEMS database that the authors use for their analysis does provide information on different categories of investment, and, to the extent that the authors wish to assess the effects of automation per se on labor market outcomes, a key limitation of the analysis is that they have not integrated this additional information into the analysis. On this point, I would again note the important earlier contribution to the Brookings Papers by Elsby, Hobijn, and Sahin (2013). Like the present paper, it sought to shed light on the causes behind the declining labor share by examining data at the sectoral level, though it focused solely on the United States. In their analysis, Elsby, Hobijn, and Sahin did consider the role of investment in equipment, and they found that it had little explanatory power for understanding the dynamics of the labor share over time and across sectors.

LEVELS VERSUS FIRST DIFFERENCES The basic premise in using sectoral data from several countries to estimate effects is that there is something common about how a given change in TFP affects outcomes across countries. Although this is a standard approach, the basis for it in the present context is not entirely clear. Two features of the data are notable. First, at any point in time, there are large differences in TFP across the countries in the authors' sample. Second, there are also large differences in labor share in a given sector across countries. If the labor share we observe is related to the technology being used, which is a basic premise of the analysis in this paper, then we might think that it is the level of TFP (that is, the technology being used) that is related to the labor share, and that one cannot assume that a given change in TFP has the same effect on employment and the labor share independent of the initial level of TFP.

To pursue this further, suppose that one country has TFP that is only 80 percent that of the leader in some sector. Suppose both this country and the leader experience an improvement in TFP of 5 percentage points. Assuming that this will have the same response in both countries is to assume that the effect of TFP on these variables is linear. But if we think that changes in the nature of technological progress are influencing these effects, it seems unclear that this is a reasonable assumption. Perhaps the trailing country should have effects that resemble those of the leading economy when it moved from 80 to 85 percent of its current level.

BENCHMARK SPECIFICATION Although not stated explicitly in the paper, I think it is understood that the goal of this analysis is to uncover the "long-run" effects of automation on employment and the labor share. This is a key point to note, given that there is good reason to believe that short-run effects might be very different. In particular, we know that individuals displaced from certain industries often experience long spells of nonemployment, including early retirement. The labor share is implicitly affected by the response of both prices and wages, and, to the extent that these variables respond very differently in the short and long runs, it is clearly important to distinguish between short- and long-run responses. Also, the dynamics of TFP changes may have varying serial correlation over time. Although I appreciate that the authors have taken some care to isolate the long-run effects of changes in TFP, I remain somewhat skeptical about the extent to which they have purged their results of short-run effects.

My own preference would have been for them to focus on consecutive long-period differences to generate their benchmark results. In the robustness section, they do present results for differences over consecutive five-year periods. The results for this case were only about two-thirds as large as for their benchmark specification, suggesting that this difference is potentially significant. Moreover, even in this setting they do not exclusively rely on five-year differences, because they retain observations for the period 2005-07 and they use observations for periods in which a country's data start in between the two endpoints. I suspect that about 20 percent of their observations in this exercise are not from five-year differences. This detail aside, my own preference would be to focus on ten-year differences. The authors' own calculations lead them to conclude that effects require about five years, and using five-year differences implies that any changes after the initial year will not have realized their full effect at the end of the interval. To retain data from the post-2000 period, they could define the three periods as 1975-85, 1985-95, and 1995-2005, or, alternatively, as 1977-87, 1987-97, and 1997-2007. I would find results from this specification to be both more transparent and more compelling.

VALUE-ADDED TFP VERSUS GROSS OUTPUT TFP In their initial specification, the authors run regressions of the outcome of interest on value-added TFP at the sector level. They later suggest that they want to incorporate sectoral input--output linkages into the analysis and use this to motivate the inclusion of value-added TFP terms from other sectors on the right-hand side, distinguishing them in terms of being upstream or downstream. When doing this, the authors continue to use value-added TFP measures as their TFP measure. I think it is problematic to continue to use value-added TFP measures in a context where one aims to measure effects propagated through input-output connections. Unfortunately, I think this is an issue that many researchers seem not to appreciate, so this is one of the reasons I raise it here.

The first point to realize is that value-added TFP and gross output TFP are two truly distinct objects. It is particularly important that value-added TFP already incorporates the effects of technological progress in supplier sectors. (4) Relatedly, when one chooses to represent the production side of the economy via value-added production functions, one is not assuming that there are no input-output relationships; rather, they are embedded in the value-added TFPs.

One reason for preferring a specification in which one starts with gross output production functions is that one might reasonably think that this provides a better description of how primitive technology shocks appear--that is, they affect the ability of a given sector to produce gross output. Propagation through the input--output network will imply that value-added TFP will change in other sectors, so that a representation using value-added production functions cannot easily be used to trace out the effect of a primitive technology shock to the gross output production function in one sector. However, for a given set of gross output TFP shocks, the valued-added representation will capture the same set of overall equilibrium responses, so there is no benefit to adopting one approach versus the other if one wants to study the overall effect of observed shocks. But using value-added TFP when explicitly studying input-output linkages makes it impossible to disentangle direct effects from effects operating through input-output linkages.

CONCLUDING COMMENTS One of the goals of Autor and Salomons's paper was to provide estimates of the effects of TFP on aggregate outcomes. To be sure, this is a challenging goal, and I do not think the profession is yet able to produce reliable estimates of these effects. In particular, for the reasons I have described, I do not feel that the approach taken in this paper is particularly promising in this regard. Nonetheless, the authors are to be commended for compiling a large amount of evidence about the relationships between key labor market outcomes at the sector level for a large set of countries. I think this information is valuable in the effort to learn more about the driving forces and mechanisms at work, and it will surely be useful to future researchers working on this important issue. But given the limitations of the methods used for uncovering quantitative causal relationships, I would have preferred if the authors had focused more on how the cross-country evidence shapes our priors about the plausibility of technological factors compared with other factors.

REFERENCES FOR THE ROGERSON COMMENT

Baumol, William J. 1967. "Macroeconomics of Unbalanced Growth: The Anatomy of Urban Crisis." American Economic Review 57, no. 3: 415-26.

Blanchard, Olivier, and Justin Wolfers. 2000. "The Role of Shocks and Institutions in the Rise of European Unemployment: The Aggregate Evidence." Economic Journal 110, no. 462: 1-33.

Bruno, Michael, and Jeffrey D. Sachs. 1985. The Economics of Worldwide Stagflation. Harvard University Press.

Elsby, Michael W. L., Bart Hobijn, and Aysegul Sahin. 2013. "The Decline of the U.S. Labor Share." Brookings Papers on Economic Activity, Fall: 1-52.

Kaldor, Nicholas. 1961. "Capital Accumulation and Economic Growth." In The Theory of Capital, edited by Friedrich Lutz and Douglas C. Hague. New York: St. Martin's Press.

Krugman. Paul. 1994. "Past and Prospective Causes of High Unemployment." Economic Review (Federal Reserve Bank of Kansas City) 79, no. 4: 23-43.

Moro, Alessio. 2012. "The Structural Transformation between Manufacturing and Services and the Decline in the US GDP Volatility." Review of Economic Dynamics 15, no. 3: 402-15.

(1.) This same logic, of course, suggests that it is not appropriate to impose a common response to TFP across countries.

(2.) The second term on the right-hand side also depends on the country-specific profiles of TFP, though readers familiar with these types of models will see that D is simply the model-implied aggregate price index. For present purposes, we can ignore this term.

(3.) My simple example does not include the linkages that Autor and Salomons include. Doing so would destroy the tractability of my simple example, but the basic point remains valid: A key determinant of hours in a given sector is the total amount of work being carried out.

(4.) See Moro (2012) for derivations that explicitly link value-added and gross output TFP in a simple setting.

GENERAL DISCUSSION Robert Gordon noted that a large number of industries in the Bureau of Labor Statistics data have negative total factor productivity (TFP) growth, as noted by commenter John Haltiwanger. One might be tempted to believe that negative TFP growth is a result of measurement error. But consider the example of the higher education industry, one in which negative TFP growth could actually be real, and a result of various processes unrelated to innovation. At a university, undergraduate students are the "output," which the university produces at a relatively fixed level and with a stable quality over time. "Inputs" include professors, administrative resources, and information technology. But other inputs include investments in expensive new buildings and sports facilities, which require maintenance over time. With the output of students fixed and with the value of inputs rising over time, TFP growth in higher education could indeed be negative. This framework could also apply to other industries. In retail, for example, e-commerce may not contribute enough to productivity growth to offset the decline in traditional bricks-and-mortar stores. In health care, hospitals have upgraded their facilities and hired additional staff, but without an increase in patient care. Taken together, such examples may explain why negative TFP growth could be a real phenomenon and not a product of measurement error.

Martin Baily made two comments. First, as commenter Richard Rogerson had suggested, labor supply is most likely the main determinant of employment at an aggregate level, not TFP growth. TFP growth might have effects on employment at a micro or industry level, but not at the aggregate level. Second, though the instrumental variables used by the authors as proxies for innovation--for example, patents and robot adoption--were interesting, Baily suggested they were probably poor instruments. Robot adoption, he reasoned, is still a recent phenomenon, and patent flows should probably only have a small effect on productivity. In his own research, Baily has found that many of the changes in productivity over the past few decades were not actually due to automation, but rather to scaling and business organization. In retail, for example, the transition from small mom-and-pop stores to big box--style department stores was a major driver of productivity growth. In the automobile industry, companies using similar technology and equipment were able to increase productivity mostly by organizing production more effectively. Research by the McKinsey Global Institute suggests that much of the decline in the labor share of income in the United States was due to changes in the manufacturing industry. (1)

Katharine Abraham disagreed with Gordon, arguing that there are significant parts of the economy for which mismeasurement of TFP and productivity growth are a real concern. The health care industry is an example of a major industry for which the difficulty of measuring output causes serious problems for measurement of productivity. She suggested that such measurement issues could pose major problems for the broad conclusions reached by the authors. Baily had suggested that mismeasurement might not be an issue as long as relative productivity growth--how the rate of productivity growth in any one industry compares to that in other industries--was not systematically affected by measurement bias. Instead, she suggested that measurement bias might shift the levels of TFP, productivity, and output by different amounts in different industries.

Valerie Ramey recommended that the authors revisit past research that showed a negative effect of productivity growth on employment and hours. Similar results were found in work by Olivier Blanchard and Danny Quah; Jordi Gali; Neville Francis and Ramey; and Susanto Basu, John Fernald, and Miles Kimball. (2) She recommended using the models developed in these papers to study the effect of technology on the labor share of income to see if they gave similar answers.

Robert Hall mentioned a few identification issues with the authors' empirical model. First, he noted that the authors assume there is no unobserved covariate simultaneously affecting both the labor share of income (the dependent variable) and TFP growth (the independent variable). If a covariate existed, it would bias the model's results. Second, the authors did not, in Hall's view, adequately demonstrate that the number of patent claims is a viable instrumental variable; specifically, it was not shown to be statistically independent of an unobserved covariate. Hall suggested one possible unobserved covariate might be the existence of market power in a given industry, which he suspected was of first-order importance.

Salomons first addressed data questions. She noted that although the authors present results for higher-frequency data, they also estimated models for long time intervals over decades, which yielded quantitatively and qualitatively similar results to those presented at higher frequencies. Second, she clarified the identification strategy used to estimate the aggregate effects of TFP growth across countries and industries. The authors did not look only at interactions between time and countries or take a set of country-year fixed effects in a regression to scale up the broad effects of automation on employment. Rather, they measured the effect of TFP growth on value added at the country, industry, and year levels, and then measured the total value-added effects across countries by using own-industry coefficient estimates on various macroeconomic outcomes, such as labor's share of income and employment. The empirical model could not include country-year fixed effects because doing so would absorb any variation in TFP growth across countries.

Salomons acknowledged that measurement issues associated with TFP growth could be a real concern with regard to the authors' conclusions. The reason the authors used TFP as a proxy for automation was because it is a broad measure, and does not erroneously focus on some very specific, idiosyncratic trend. Robotics, for example, might be an interesting measure of automation, but it has only a limited effect on select sectors of the economy. She acknowledged that a major drawback of using TFP growth is that it might be too broad, which is why they tried using robotics and patents as instrumental variables. Finally, Salomons commented on the possible drivers of the reallocation of resources between industries or firms, which lead to differing levels of productivity growth. The paper is silent on the causes of this reallocation, but Salomons noted that it could certainly be due to market power, as suggested by Hall and by Autor in previous work. (3)

Autor acknowledged that he and Salomons were sensitive to the issues of measurement and the omnibus definition of TFP as a measure of innovation and automation. He suggested that the instrumental variables used in their paper--robotics and patents--might be thought of as a "rescaling" of TFP. Patent flows, in particular, should be a good measure of innovation, and the data are highly correlated across countries. Although Autor acknowledged that these measures should probably not be treated as excludable instrumental variables, he suggested that they are still useful proxies for automation. In the final version of the paper, the authors use patents as a proxy for TFP--for which it has strong predictive power--but not as an instrument for TFP.

Blanchard and Rogerson had asked about identification, particularly related to the omission of country-year fixed effects. Echoing Salomons's comments, Autor noted that including country-year fixed effects would absorb the variation in the data required to provide a measure of the aggregate effects of TFP growth on macroeconomic outcomes across countries and over time. The authors do, however, measure the country-year effects more broadly by using the chain rule to get the effect of a particular industry on an entire country, and then they estimate the effect of the country on broad outcomes. Autor conceded that this still might not be the perfect identification method.

Autor agreed with Baily's comments about the problem of excluding the labor supply from the model. However, he argued that if the approach used in the paper was wrong, and the labor supply was in fact the main driver of employment, then one would expect productivity growth to be unrelated to employment, which is largely what they find. More surprising, however, is that they find that productivity growth is also negatively related to the change in labor's share of income, and that this effect changes over time.

Autor emphasized that the ultimate goal of the paper is not to exposit the driving forces behind TFP growth, a rather broad, omnibus measure of productivity, but rather to explore how productivity growth affects industry-level and aggregate employment, sectoral reallocation, and the evolution of labor's share of national income. Because TFP is difficult to measure, the nature of productivity growth is often unclear. One model of productivity growth, proposed by Daron Acemoglu and Pascual Restrepo, posits that productivity growth could be labor-intensive and capital-augmenting, thereby complementing the use of labor and expanding the number of available tasks, rather than reducing it. (4) Alternatively, productivity growth could be labor-displacing, meaning it reduces the share of output paid to labor. Autor emphasized that the exercise in the present paper is designed to tease out the nature of productivity growth by examining its effect on employment outcomes, which provides information about the nature of the productivity growth occurring. He also acknowledged the limitation of their cross-country, industry-level panel data set. Their main source of data, the EU KLEMS database, does allow for better analysis across countries than would be possible working with more detailed micro-level data specific to individual countries. He noted that the paper would likely be insufficient to satisfy macro or labor economists, but that the authors hoped to connect the two disciplines in an informative way--or at least to untie them in their shared disapproval of the methods and conclusions of the present paper.

(1.) Sree Ramaswamy, James Manyka. Gary Pinkus, Katy George, Jonathan Law, Tony Gambell. and Andrea Serafino, "Making It in America: Revitalizing US Manufacturing" (McKinsey Global Institute, 2017).

(2.) Olivier Jean Blanchard and Danny Quah, "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review 79, no. 4 (1989): 655-73; Jordi Gali, "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?" American Economic Review 89, no. 1 (1999): 249-71: Neville Francis and Valerie A. Ramey. "Measures of Per Capita Hours and Their Implications for the Technology-Hours Debate," Journal of Money, Credit and Banking 41, no. 6 (2009): 1071-97; Susanto Basu, John G. Fernald. and Miles S. Kimball, "Are Technology Improvements Contractionary?" American Economic Review 96, no. 5 (2006): 1418-48.

(3.) David Autor, David Dorn, Lawrence F. Katz, Christina Patterson, and John Van Reenen, "The Fall of the Labor Share and the Rise of Superstar Firms," Working Paper no. 23396 (Cambridge. Mass.: National Bureau of Economic Research. 2017).

(4.) Daron Acemoglu and Pascual Restrepo, "Artificial Intelligence, Automation and Work," Working Paper no. 24196 (Cambridge, Mass.: National Bureau of Economic Research, 2018).
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