Changing Business Dynamism and Productivity: Shocks vs. Responsiveness

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Changing Business Dynamism and Productivity: Shocks vs. Responsiveness Ryan A. Decker, John Haltiwanger, Ron S. Jarmin, and Javier Miranda 2018-007 Please cite this paper as: Decker,RyanA.,JohnHaltiwanger,RonS.Jarmin,andJavierMiranda(2018). “Changing BusinessDynamismandProductivity: Shocksvs. Responsiveness,”FinanceandEconomics DiscussionSeries2018-007. Washington: BoardofGovernorsoftheFederalReserveSystem, https://doi.org/10.17016/FEDS.2018.007. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Changing Business Dynamism and Productivity: Shocks vs. Responsiveness Ryan A. Decker, John Haltiwanger, Ron S. Jarmin, and Javier Miranda* January 2018 Abstract The pace of job reallocation has declined in all U.S. sectors since 2000. In standard models, aggregate job reallocation depends on (a) the dispersion of idiosyncratic productivity shocks faced by businesses and (b) the marginal responsiveness of businesses to those shocks. Using several novel empirical facts from business microdata, we infer that the pervasive post-2000 decline in reallocation reflects weaker responsiveness in a manner consistent with rising adjustment frictions and not lower dispersion of shocks. The within-industry dispersion of TFP and output per worker has risen, while the marginal responsiveness of employment growth to business-level productivity has weakened. The responsiveness in the post-2000 period for young firms in the high-tech sector is only about half (in manufacturing) to two thirds (economy wide) of the peak in the 1990s. Counterfactuals show that weakening productivity responsiveness since 2000 accounts for a significant drag on aggregate productivity. *Federal Reserve Board, University of Maryland and NBER, U.S. Census Bureau, and U.S. Census Bureau, respectively. John Haltiwanger is also a Schedule A part-time employee of the Census Bureau at the time of the writing of this paper. We gratefully acknowledge financial support from the Kauffman Foundation. Cody Tuttle provided excellent research assistance. We thank John Abowd, Rudi Bachmann, Martin Baily, Jonathan Baker, Dave Byrne, Chris Foote, Lucia Foster, Clément Gorin, Bronwyn Hall, Matthias Kehrig, Pete Klenow, Kristin McCue, and conference or seminar participants at the 2015 Atlanta Fed Conference on Secular Changes in Labor Markets, the ASSA 2016 meetings, the 2016 Brookings “productivity puzzle” conference, the 3rd International ZEW conference, the 2016 ICC conference, BYU, University of Chicago, Drexel University, the Federal Reserve Board, George Mason University, Georgetown University, Michigan State University, the New York Fed, Princeton University, the Richmond Fed, the spring 2017 Midwest Macro meetings, the 2017 UNC IDEA conference, and the 2017 NBER Summer Institute meetings for helpful comments. We are grateful for the use of the manufacturing productivity database developed in Foster, Grim and Haltiwanger (2016) as well as the revenue productivity database developed in Haltiwanger et al. (2017), and we thank Peter Schott for providing guidance and data for constructing import penetration data. Any opinions and conclusions expressed herein are those of the authors and do not necessarily represent the views of the U.S. Census Bureau or of the Board of Governors or its staff. All results have been reviewed to ensure that no confidential information is disclosed.

I. Introduction and motivation Business dynamics—the process of business birth, growth, decline and exit—is a critical driver of the productivity-enhancing reallocative process that characterizes market economies. But the pace of job reallocation in the U.S. has fallen in recent decades, and since 2000 this downward trend has accelerated and become pervasive across all sectors.1 We argue that the 0F post-2000 decline in job reallocation reflects increased frictions on adjustment facing U.S. businesses, potentially implying a drag on aggregate productivity. We present several novel facts from business-level data, and we study the changing pattern of reallocation by drawing inference from models of firm dynamics. In standard models, job reallocation arises from the growth and survival responses of businesses to their idiosyncratic productivity draws, so declining reallocation arises from either of two forces: First, a decline in the cross-sectional dispersion of business-level productivity “shocks” reduces reallocation by reducing idiosyncratic incentives for businesses to create or destroy jobs. Second, increased costs of, or frictions on, labor adjustment weaken the “responsiveness” of businesses to their conditions. This “shocks” versus “responsiveness” framework guides our analysis. We find support for the “responsiveness” hypothesis for the pervasive post-2000 reallocation decline by studying four key empirical moments implied by standard models.2 First, 1F within-industry dispersion of establishment TFP (which can be measured in manufacturing) has risen. Second, within-industry dispersion of firm labor productivity (which can be measured in all industries) has risen. Third, business growth and survival has become less responsive to idiosyncratic productivity (both TFP and labor productivity) with an especially large decline in responsiveness for young firms in the high-tech sector. Fourth, counterfactuals reflecting the reduced responsiveness imply a drag on industry-level productivity. These novel empirical moments, taken together with theories of firm dynamics and the fact of declining job reallocation, are consistent with an increase in adjustment frictions in the U.S. 1 See Davis et al. (2007), Haltiwanger, Jarmin, and Miranda (2011), Reedy and Litan (2011), Hyatt and Spletzer (2013), Davis and Haltiwanger (2014) and Decker et al. (2014). Job reallocation is defined as the sum of gross jobs created by expanding and entering establishments and gross jobs destroyed by downsizing and exiting establishments, expressed as a rate by dividing by average two-year employment as in Davis, Haltiwanger, and Schuh (1996). 2 See Berger and Vavra (2017) for an application of the “shocks vs. responsiveness” approach in a different context; that paper and others cited therein likewise find an important role for the responsiveness factor in explaining aggregate outcomes. 1

Consistent with our approach of focusing on multiple moments, we combine several data sources to shed light, from many angles, on the question of declining reallocation. We first study the manufacturing sector, with a particular focus on high-tech manufacturing given the role of high-tech in recent productivity dynamics. In a large sample of plant-level manufacturing data spanning 1980-2010, we can closely pair theory and empirics due to our ability to measure TFP (which we construct using multiple methods). We then extend our analysis to the entire private, non-farm sector using recently developed data on output per worker for all U.S. firms starting in the late 1990s. Our economy-wide exercises confirm that our manufacturing findings are not artifacts of sampling errors and that our substantive results are generalizable across industries. Hopenhayn and Rogerson (1993) show that an increase in dynamic frictions on factor (e.g., labor) adjustment reduces both job reallocation and productivity.3 Thus, a prima facie 2F concern is that declining reallocation may imply weaker aggregate productivity growth. At first glance, recent fluctuations in U.S. productivity growth do not match up with patterns of reallocation: productivity surged in the 1990s through the early 2000s before slowing after 2003, while aggregate job reallocation (and startup activity) fell throughout the 1980-2014 period. A careful review of theory and evidence resolves the inconsistency: prior to 2000, the decline in reallocation was dominated by the productivity-boosting consolidation of retail trade.4 Job 3F reallocation (and business formation) in high-tech actually rose during the 1980s and 1990s before declining after 2000 along with high-growth firm activity more generally (Haltiwanger, Hathaway, and Miranda (2014)), roughly coinciding with the ICT-driven surge in productivity from the late 1980s to early 2000s and subsequent decline after 2003 (Fernald (2014)). Our approach of using multiple moments to draw inference is strengthened by this crosssector variation in patterns of reallocation. In high-tech manufacturing, a hump-shaped pattern of reallocation is matched by a hump-shaped pattern of productivity responsiveness, consistent with theory linking responsiveness and reallocation. The implied covariance of business size and business productivity behaves similarly. Importantly, however, TFP dispersion in high-tech manufacturing rose gradually or was flat throughout recent decades. These patterns are 3 The Hopenhayn and Rogerson (1993) finding is about the effect of an increase in adjustment frictions on the level of productivity, which implies reduced productivity growth if adjustment frictions increase repeatedly over time and/or if the transition dynamics from an increase in adjustment frictions takes time. 4 Foster et al. (2006), Jarmin, Klimek, and Miranda (2009), and others document the shift away from single unit establishment firms (“mom and pop shops”) to national chains. Foster et al. (2006) and Foster et al. (2015) show that establishments of national chains are more productive and more stable. We discuss this evidence further below. 2

consistent with the strong role of “responsiveness” instead of “shocks” in accounting for the patterns of reallocation. We also find that changing responsiveness—not changing shocks— accounts for the patterns of reallocation in non-tech manufacturing. Our results have implications for aggregate productivity: Counterfactual exercises suggest that the increased responsiveness of the 1980s and 1990s yielded as much as half a log point annual boost in industry-level TFP in high-tech manufacturing by the second half of the 1990s, then the declining responsiveness of the 2000s yielded as much as a two-log-point drag on annual industry-level TFP by 2010. Moreover, evidence based on labor productivity suggests that the finding of declining responsiveness since 2000 generalizes beyond high-tech manufacturing to other high-tech businesses as well as other areas of the economy. The pre- 2000 rise and post-2000 fall of productivity responsiveness in the high-tech sector coincides with the ICT-driven rise and fall of aggregate productivity growth in the U.S. These findings on the changing contribution of reallocation to aggregate productivity comprise a novel contribution to the productivity slowdown literature. An alternative potential cause of changes in reallocation and the responsiveness of firms is the recent decline in startup rates (Decker et al. (2014)). If young firms are more responsive to productivity shocks, changes in the average age of U.S. firms would mechanically reduce overall responsiveness, and the question of declining responsiveness and reallocation would boil down to the question of why startup activity has declined. Consistent with earlier findings (Davis et al. (2007), Decker et al. (2014)), we show that the changing firm age structure induced by declining startup rates accounts for just one quarter of the overall decline in the job reallocation rate. We focus on changes in reallocation and responsiveness within firm age groups to mitigate the identification challenge posed by declining startup rates (while recognizing that the decline in startup rates is itself an important research area).5 4F We briefly explore other elements of changing responsiveness and productivity. The responsiveness decline in high-tech manufacturing is also evident when we measure responsiveness in terms of equipment investment instead of employment growth. We find mixed evidence linking falling responsiveness with import competition. Our finding of rising withinindustry labor productivity dispersion is not consistent with slowing innovation in a Gort and Klepper (1982) framework. 5 For example, see Alon et al. (2017), who quantify the productivity implications of declining entry. 3

Section II describes key facts about the declining pace of business dynamism. Section III describes the datasets we employ. In section IV, we use establishment-level data for manufacturing, with a particular focus on high-tech, to study whether the evidence implies “changing shocks” or “changing responsiveness,” and we analyze the implications of our findings for aggregate productivity growth. Section V looks beyond manufacturing and investigates the same questions using firm-level labor productivity and employment data for all U.S. sectors. Concluding remarks are in section VI. II. Business Dynamics: Basic facts A. Sectoral Patterns of Reallocation and Young Firm Activity Starting with Davis et al. (2007), many studies have documented a decline in the pace of aggregate job reallocation and other indicators of business dynamism in the last few decades. Decker et al. (2016) report wide cross-sector variation in patterns of reallocation: retail trade exhibits the strongest decline during the 1980s and 1990s, while information and high-tech saw rising reallocation over that period before falling sharply after 2000. These patterns are depicted on Figure 1 (using HP trends) for selected NAICS sectors as well as high-tech (as defined by Hecker (2005)).6 Figure 2 illustrates similar patterns in the share of employment accounted for 5F by young firms: retail trade saw declining startup activity throughout the 1980s-2010s, while information and high-tech saw rising startup activity prior to 2000.7 Figures 1 and 2 also single 6F out the high-tech component of manufacturing. Reallocation and startup activity behave similarly in high-tech manufacturing to the high-tech sector more generally. Information, which includes a heavy contingent of tech industries, behaves similarly to high-tech broadly. The changing prevalence of young firms—which have high reallocation rates—accounts for some of the reallocation patterns in Figure 1.8 Figure 3 reports annualized changes in 7F reallocation rates for select sectors (and economy wide) for three periods: the late 1980s to late 6 As noted above, high-tech is a particular focus of this paper due to its role in aggregate productivity dynamics (Fernald (2014)). Hecker (2005) defines industries as high-tech based on the 14 four-digit NAICS industries with the largest share of STEM workers. The high-tech sector thus defined includes industries in manufacturing (NAICS 3254, 3341, 3342, 3344, 3345, and 3364), information (5112, 5161, 5179, 5181, and 5182), and services (5413, 5415, and 5417). Notably, certain industries in the information sector are not high tech (e.g., book publishing). 7 Guzman and Stern (2016) focus on extreme high-potential startups and also find 2000 to be an important turning point, with fewer high-growth outcomes for startups identified as having high potential. 8 Young firms may be more volatile for a variety of reasons, such as the learning dynamics of Jovanovic (1982). 4

1990s (1987-1989 to 1997-1999), the late 1990s to mid-2000s (1997-1999 to 2004-2006), and the mid-2000s to early 2010s (2004-2006 to 2011-2013). We use three-year averages at business cycle peaks to abstract from cyclical concerns.9 Solid bars indicate the actual annualized change 8F in reallocation rates over the period. Patterned (non-solid) bars indicate annualized changes resulting from a shift-share exercise freezing the age composition of businesses at its initial state; that is, the non-solid bars describe within-age group changes in reallocation rates. We use seven age groups (firm age 0, 1, 2, 3, 4, 5, and 6+). During the 1990s (i.e., 1987-1989 to 1997-1999), the sharp decline in reallocation in retail trade and the increase in information are evident. The patterned bars show that falling young firm activity accounts for about a third of the reallocation decline in retail trade (i.e., two thirds of the decline occurred within age groups), and rising young firm activity accounts for about a tenth of the reallocation increase in information. Services saw a modest reallocation decline during the 1990s which is entirely accounted for by falling young firm activity. The pace of decline in several sectors accelerated after the late 1990s. This can be seen in services, which had a more modest decline during the early 1990s. More notably, though, reallocation rates in information fell markedly during the early 2000s after rising during the 1990s, with about a fifth of the early-2000s decline accounted for by falling young firm activity. Each sector continued declining during the late-2000s, and in each case the change in reallocation can be partially but not completely explained by falling young firm activity. This is the main inference we draw from Figure 3: while changing startup rates can account for a nontrivial portion of the overall change in job reallocation rates since the 1980s, most of the variation occurred within firm age groups. This finding encourages us to focus on changing patterns of responsiveness within firm age classes; focusing on patterns within firm age classes also permits us to abstract from factors that may underlie both the changing pace of startups and the change in the age structure of firms. B. Possible Sources of Changes in Young Firm Activity Though it is not our focus, it is worth noting that a number of competing hypotheses may account for the variation in startup rates and young firm activity seen in recent decades. Changes in startup rates may endogenously reflect changes in the pace of innovation in an industry for 9 2011-13 is not a cyclical peak but our sample ends in 2013. 5

reasons hypothesized by Gort and Klepper (1982): a period of rapid innovation leads to a surge in entry, reallocation and subsequent productivity growth.10 Moreover, Gordon (2016) has 9F argued that most of the 1980s-1990s high-tech innovations had already been implemented by the early 2000s, and the productivity slowdown since that time is due to slowed innovation and implementation. Taken together, these hypotheses suggest that the changing pace of both startup activity and reallocation in the high-tech sector in recent decades could have been caused by an exogenously changing pace of innovation.11 10F In retail trade, the share of sales and employment accounted for by single unit establishment firms fell from half to a third from 1977 to 2007 (see Foster et al. (2006), Jarmin et al. (2009), and Foster et al. (2015)). This dramatic transition is almost entirely accounted for by the rise of large, national “big box” retailers, which are more productive (by about 30 log points) and have lower entry and exit rates (by a factor of 15) than single-unit operations. Retail consolidations were likely facilitated by globalization and advances in information technology that permitted the development of large and efficient supply chains and distribution networks. Retail trade is an example of a sector in which declining reallocation and entrepreneurship has been productivity enhancing, a change that is reflected in the age structure of firms (from which we abstract in our analyses). Yet another factor contributing to variation in the pace of startups is demographics-driven changes in labor force growth. Karahan, Pugsley, and Sahin (2015) show that variation in labor force growth driven by exogenous changes in population growth is positively associated with startup activity, an insight consistent with Hopenhayn (1992)-type models in which labor force growth is accommodated by adjustment in the number of firms. Each of these factors underlying the changing share of young firm activity likely has some merit, and we seek to abstract from them to focus on the shocks vs. responsiveness hypotheses. We therefore study changes in the pace of reallocation within firm age groups. By abstracting from the changing age distribution, we may be understating the contribution of declining responsiveness to the post-2000 decline in productivity growth since the hypothesis that is the main focus of this paper—rising frictions inducing lower responsiveness of 10 Foster et al. (2017) provide supportive empirical evidence for these dynamics for the 1990s U.S. high-tech sector. 11 In the Gort and Klepper (1982) framework, declining innovation should be accompanied by declining dispersion of productivity within industries. While certainly not dispositive for the hypothesis of slowing innovation, we find the opposite below. 6

businesses—may be contributing to the pervasive, all-sector decline in startup rates since 2000. An increase in adjustment frictions raises the cost of business activity and reduces the expected discounted value of profits for entrants, a key quantity governing entry in standard models. III. Data and Measurement The backbone dataset for our analysis is the Longitudinal Business Database (LBD), to which we attach other data as detailed below. The LBD includes annual location, employment, and industry for the universe of private non-farm establishments, with firm identifiers based on operational control (not an arbitrary tax identifier).12 We use the LBD for 1979-2013 (during 11F which consistent establishment NAICS codes are available from Fort and Klimek (2016)). As in previous literature, we construct firm age as the age of the firm’s oldest establishment when the firm identifier first appears in the data, after which the firm ages naturally. A. Manufacturing and TFP We construct TFP measures for 2 million plant-year observations (1981-2010) using data from Foster, Grim, and Haltiwanger (2016) (hereafter FGH) combining the Annual Survey of Manufacturers (ASM) with the quinquennial Census of Manufacturers (CM). The ASM-CM is representative of the manufacturing sector in any given year, but it is based on a rotating sample and thus lacks the complete longitudinal coverage of the LBD. To compensate, we integrate the ASM/CM TFP data into the LBD to obtain establishment-level employment growth.13 12F We construct two alternative empirical measures of TFP for our analysis. The first, which has been commonly used in the literature (see, e.g., Baily, Hulten and Campbell (2001), Foster, Haltiwanger and Krizan (2001), Syverson (2011), Ilut, Kehrig and Schneider forthcoming), is a cost share-based index given by: (1) where QR is r 𝑙𝑙 e 𝑙𝑙 a 𝑙𝑙 l 𝑙𝑙 ou 𝑙𝑙 t𝑒𝑒p𝑒𝑒u = t, K 𝑙𝑙𝑙𝑙 i 𝑄𝑄 s 𝑒𝑒r 𝑅𝑅 e𝑒𝑒a − l c 𝛼𝛼 ap𝐾𝐾i 𝑙𝑙 t 𝑙𝑙 al 𝐾𝐾 , 𝑒𝑒L𝑒𝑒 i − s l a 𝛼𝛼 b𝐿𝐿o 𝑙𝑙 r 𝑙𝑙 , 𝐿𝐿 M𝑒𝑒𝑒𝑒 i − s m 𝛼𝛼 a𝑀𝑀te 𝑙𝑙 r 𝑙𝑙 ia 𝑀𝑀 ls𝑒𝑒,𝑒𝑒 E − is 𝛼𝛼 e𝐸𝐸n 𝑙𝑙𝑙𝑙 er 𝑙𝑙 g𝑒𝑒y𝑒𝑒, α denotes factor elasticities, e denotes individual establishments, and t denotes time. Output is total value of shipments plus total change in the value of inventories, deflated by industry deflators from the 12 See Jarmin and Miranda (2002) for a full description of the LBD. 13 We use propensity score weights (based on a logit model on industry, firm size, and firm age) to adjust the ASM/CM/LBD sample to represent the LBD (in the cross section) in each year (see FGH for details). These weights are cross-sectionally representative in any given year but are not ideal for using samples of ASM/CM that are present in both t and t+1. We discuss this further below. 7

NBER-CES Manufacturing Industry Database. Capital is measured separately for structures and equipment using a perpetual inventory method. Labor is total hours of production and nonproduction workers. Materials are measured separately for physical materials and energy (each is deflated by an industry-level deflator). Outputs and inputs are measured in constant 1997 dollars. Factor elasticities are estimated using industry cost shares (of total factor costs) with a Divisia index that allows cost shares to vary over time.14 More details are in FGH. 13F This measure of TFP is a revenue-based measure and is increasingly referred to as TFPR. TFPR is defined by Foster, Haltiwanger, and Syverson (2008) as P*TFPQ, where P is the plantlevel price and TFPQ is the typical measure of plant-level technical efficiency in economic models such as the model we consider below. If plants are price takers, within-industry variation in TFPR only reflects TFPQ.15 If plant-level prices are endogenous, TFPR still will be highly 14F correlated with TFPQ in the adjustment cost framework we specify below. Moreover, as we show below, TFPR-based inferences about changing responsiveness are still valid in such a framework. However, with endogenous prices, variation in dispersion of TFPR will reflect not only shocks to fundamentals such as TFPQ but also adjustment costs. Given possibly endogenous plant-level prices, we also consider an alternative measure of TFP that has been increasingly used in recent literature (e.g., Gopinath et al. (2017) and Foster et al. (2017)). Consider a simple plant-level demand function (where is an 𝜑𝜑−1 idiosyncratic demand shock and is the inverse deman 𝑙𝑙 d𝑒𝑒 𝑒𝑒el = as 𝐷𝐷 tic𝑒𝑒i𝑒𝑒t 𝑄𝑄 y𝑒𝑒),𝑒𝑒 a plant pro 𝐷𝐷 d𝑒𝑒u𝑒𝑒ction function that is Cobb-Douglas with factor elasticity for factor i equal to , and TFPQ equal to 𝜑𝜑−1 . Then plant revenue is given by (lower case variables are in logs): 𝛼𝛼𝑖𝑖 𝐴𝐴𝑒𝑒𝑒𝑒 (2) where 𝑝𝑝 fo𝑒𝑒𝑒𝑒r + fac 𝑞𝑞 t𝑒𝑒o𝑒𝑒r = i. 𝛽𝛽 T𝑘𝑘h 𝑘𝑘 a𝑒𝑒t 𝑒𝑒is + , t 𝛽𝛽 h𝑙𝑙e 𝑙𝑙 𝑒𝑒𝑒𝑒 + co 𝛽𝛽 e𝑚𝑚ff 𝑚𝑚 ici𝑒𝑒e𝑒𝑒n + ts 𝛽𝛽 ar𝑒𝑒e 𝑒𝑒 𝑒𝑒t𝑒𝑒he + re 𝜑𝜑 v 𝑎𝑎 e𝑒𝑒n𝑒𝑒u + e e 𝑑𝑑 la𝑒𝑒𝑒𝑒sticities that reflect both de 𝛽𝛽 m𝑖𝑖 a = nd 𝜑𝜑 p 𝛼𝛼 a𝑖𝑖rameters and the producti 𝛽𝛽 o𝑖𝑖n function factor elasticities. Given revenue elasticity estimates, the “revenue productivity residual” (RPR) is given by: 14 Cost shares yield factor elasticities under the assumptions of cost minimization and full adjustment of factors. We are not assuming full adjustment for each plant at each unit of time but rather that this holds approximately when pooling across all plants in the same industry over time. 15 Assuming price taking behavior is not equivalent to assuming homogenous goods and a single price in an industry. If plants in an industry have different product segments but are price takers within product segments then TFPR still only reflects fundamentals reflecting the quality differentials accounted for by price heterogeneity within an industry. TFPR is a referable measure to TFPQ in this case since it captures quality differentials. 8

(3) that is, RPR is solely a function of i 𝑅𝑅 di 𝑙𝑙 o 𝑅𝑅 sy𝑒𝑒𝑒𝑒nc = ra 𝜑𝜑 tic 𝑎𝑎 𝑒𝑒T𝑒𝑒F + PQ 𝑑𝑑 𝑒𝑒a𝑒𝑒n , d demand. This implies that (as discussed in detail in Foster et al. (2017)) RPR can exhibit positive dispersion regardless of frictions and distortions. We estimate RPR by estimating the revenue function in (2) using the GMM approach in Wooldrige (2009) (see Appendix C for more details).16 15F For each of these measures of productivity (which we denote as TFP for convenience), we take the log of TFP and deviate it from its detailed industry-by-year mean. These alternative measures are therefore within-industry measures that abstract from aggregate and industryspecific shocks and are unaffected by mismeasurement of industry-level prices (Byrne and Corrado (2015, 2016)). We model TFP as an AR(1) process. The current-period realization of the idiosyncratic component of TFP is the shock, and we also consider innovations to these shocks by estimating the AR(1) process below. In practice, we find that TFPR and RPR are highly correlated (about 0.8), consistent with the findings in Foster et al. (2017). Moreover, Foster, Haltiwanger, and Syverson (2008, 2016) find that TFPR and TFPQ are highly correlated (about 0.75) for the selected set of products where P and Q data are available to construct direct measures of TFPQ. Unsurprisingly, then, the main results of our empirical analysis on changing responsiveness and changing shocks are robust to using TFPR or RPR. For the sake of brevity, we focus on the TFPR results in the main text, but we discuss the results for RPR throughout. In addition, the details of the results for RPR are provided in Appendix C. B. Economywide Labor Productivity In Section IV we extend our analysis to nearly the entire economy by constructing measures of firm-level labor productivity. Combining LBD employment (collapsed from the establishment to the firm level) with revenue measures in the Census Bureau’s Business Register (BR) (aggregated across EIN reporting units to the firm level) yields an enhanced LBD that we refer to below as the RE-LBD. Revenue data are available from 1996 to 2013; see Haltiwanger et al. (2017) for more details.17 Consistent with previous literature, we construct annual firm 16F 16 Gandhi et al. (2016) argue that if some factors are completely variable then the Wooldridge (2009) method may not be identified. As noted in Appendix C, our results are robust to an alternative estimation method that addresses this identification concern. 17 About 20-percent of LBD firm-year observations cannot be matched to BR revenue data because firms can report income under EINs that may fall outside of the set of EINs that the Census considers part of that firm for 9

employment growth rates on an “organic” basis to represent changes in establishment-level employment rather than artificial growth caused by mergers and acquisitions. Similar to our TFP construction, we use (log) revenue per worker deviated from detailed (6-digit NAICS) industry-by-year means as a measure of firm labor productivity. We thereby control for price differences across industries such that our labor productivity measure is a within-industry relative gross output per worker measure; Foster, Haltiwanger, and Krizan (2001, 2006) show that within-industry relative gross output per worker is highly correlated with within-industry relative value added per worker and strongly correlated with within-industry relative TFP (suggesting that materials and capital shares are similar across firms within industries). We omit firms in the Finance, Insurance and Real Estate sectors (NAICS 52-53) from all analysis due to the difficulty of measuring output and productivity in those sectors. As we show below, in our adjustment cost framework inferences regarding changing responsiveness can also be made using revenue per worker. IV. Change in shocks vs. change in responsiveness A. Theoretical motivation Models of firm18 dynamics suggest that a within-sector decline in the pace of reallocation 17F is due to either a change in the dispersion of shocks faced by firms or a change in firms’ responses to those shocks. In appendix B we consider a standard model in the tradition of Hopenhayn and Rogerson (1993). Firms face idiosyncratic productivity shocks, where the realization of productivity in the current period, , is drawn from a persistent AR1 process. Net hiring and downsizing are subject to non-con 𝐴𝐴 v𝑒𝑒e𝑒𝑒x (kinked) adjustment costs. The resulting decision rule for firms’ net hiring rates implicitly reflects adjustment costs and is given by , where the state variables are the productivity realization and initial 𝑔𝑔𝑒𝑒,𝑒𝑒 = e 𝑓𝑓𝑒𝑒m (𝐴𝐴 pl𝑒𝑒o𝑒𝑒y ,𝑙𝑙 m𝑒𝑒e𝑒𝑒n−t1 ) , both of which are observed prior to the growth decis 𝐴𝐴 io𝑒𝑒n𝑒𝑒. 18F 19 We do not model entry or exit b 𝑙𝑙 u𝑒𝑒t𝑒𝑒 −d1iscuss these margins below. For purposes of discussion in this section and employment purposes. We address potential match-driven selection bias by constructing inverse propensity score weights (separately for births, deaths, and continuers) such that the RE-LBD is representative of the LBD universe in terms of the size, age, employment growth rate, broad industry, and single/multi-unit structure of firms. 18 We use the term “firms” loosely in this subsection for expositional ease. 19 A similar rule would exist for investment in a model with capital. For net hiring rate dynamics, see, e.g., Cooper, Haltiwanger, and Willis (2007, 2015) and Elsby and Michaels (2013). For investment dynamics, see, e.g. Cooper and Haltiwanger (2006). 10

appendix B, is referred to as TFP or TFPQ. If there are demand shocks, this measure should be interpreted 𝐴𝐴 𝑒𝑒a𝑒𝑒s a composite shock measure reflecting both TFPQ and demand shocks. We calibrate the model and report numerical analysis to motivate the empirical specifications and moments we consider below (see appendix B for calibration details). Our model and calibration allow for endogenous plant-level prices. Importantly for our empirical approach, revenue productivity measures with endogenous plant-level prices —TFPR or revenue labor productivity—are highly correlated with TFPQ (pairwise correlations of about 0.90) in a calibration with a plausible level of adjustment costs, though we do not target this moment in the calibration. Foster, Haltiwanger, and Syverson (2008) find an empirical correlation of 0.75 for a subset of industries. In our empirical analysis below, we find a correlation of 0.80 between TFPR and RPR (where, from equation (3), RPR reflects TFPQ and demand shocks). While we leave model details to the appendix, here we summarize the model’s rich empirical predictions for two experiments: a decline in the dispersion of TFP and an increase in labor adjustment frictions. We can easily generate changes in the rate of job reallocation with these experiments; our interest is in observing implications for other moments that would allow us empirically to distinguish between the “shocks” hypothesis and the “responsiveness” hypothesis (with the latter corresponding to changing adjustment frictions). We study the experiments’ effect on “responsiveness” by using a regression estimate (on simulated data) of the employment growth policy function ; we simply regress employment growth on lagged productivity and employm 𝑔𝑔 en𝑒𝑒𝑒𝑒t t = he 𝑓𝑓 n ( o 𝐴𝐴 b𝑒𝑒s𝑒𝑒e , r 𝑙𝑙 v𝑒𝑒e𝑒𝑒 −th1) e coefficient on productivity. 19F 20 The other moments of study are the standard deviation of labor productivity and the Olley-Pakes covariance between employment and productivity (Olley and Pakes 1996). As will become clear in our empirical analysis below, the OP covariance needs to be interpreted with caution empirically but it is still an instructive moment for identifying structural changes. First, we hold adjustment frictions constant at the baseline calibration and vary the dispersion of TFPQ. A decline in TFPQ dispersion yields: (1) lower job reallocation (as intended); (2) weaker responses of firm-level growth ( to ) to the realization of both TFP 𝑡𝑡 𝑡𝑡+1 20 That is, we focus on from . This timing convention is designed to match our empirical work; the qualitative results are robust to other timing conventions. 𝛽𝛽 𝑔𝑔𝑒𝑒𝑒𝑒+1 =𝜂𝜂+𝛽𝛽ln𝐴𝐴𝑒𝑒𝑒𝑒+𝛿𝛿ln𝑙𝑙𝑒𝑒𝑒𝑒+𝜀𝜀𝑒𝑒𝑒𝑒+1 11

and labor productivity in (conditional on employment in ); 21 (3) lower standard deviation of 20F labor productivity; and (4) lower Olley-Pakes covariance between size and productivity. 𝑡𝑡 𝑡𝑡 Second, we hold TFPQ dispersion constant at its baseline calibration and vary the magnitude of adjustment frictions. An increase in adjustment frictions yields: (1) lower job reallocation (as intended); (2) weaker responses of firm-level growth ( to ) to the realizations of both TFP and labor productivity in (conditional on employment in ); (3) higher 𝑡𝑡 𝑡𝑡 +1 standard deviation of labor productivity; and (4) lower Olley-Pakes (OP) covariance (i.e., the 𝑡𝑡 𝑡𝑡 covariance between firm size and productivity) for both TFPQ and labor productivity, implying a decline in aggregate productivity consistent with a greater extent of misallocation. These empirical predictions are sufficient to distinguish between the “shocks” and “responsiveness” hypotheses even in the absence of observable TFP dispersion. The key distinguishing moment is labor productivity dispersion. For example, in the presence of declining reallocation, responsiveness, and Olley-Pakes covariance, rising labor productivity dispersion would imply that adjustment costs have increased while falling labor productivity dispersion would imply that TFP dispersion is declining. Conveniently, we also observe TFP dispersion (in manufacturing), enhancing our ability to draw empirical inference. This focus on multiple empirical moments is a key strength of our approach. We have in mind a potentially broad interpretation of the “responsiveness” hypothesis. For example, recent literature shows that an increase in the dispersion of static distortions will have some similar qualitative effects to an increase in frictions: lower productivity due to a weaker relationship of firm growth (and survival) with fundamentals.22 Moreover, while our 21F simple model has only employment dynamics, we have in mind any type of increased friction that may impede adjusting the scale of operations at a firm. Additional forces may be at work—beyond changes in shocks and frictions—that are not apparent from our illustrative model. In particular, the model neglects firm entry and exit, and as noted above there have been striking changes in entry in recent decades. Hopenhayn and 21 Kinked adjustment costs give rise to inaction ranges. As TFP dispersion falls there is a decrease in the fraction of firms that make zero adjustment (i.e., the “real options” effect). But declining TFP dispersion also implies smaller adjustments among those firms that do adjust (i.e., the “volatility” effect). Vavra (2014) argues that the volatility effect dominants the real options effect in the steady state, a general result extending back to Barro (1972). Bloom et al. (2016) and others use a similar model to study the effects of uncertainty on business cycles; even in their model, the volatility effect dominates at annual frequency. 22 See, e.g., Restuccia and Rogerson (2008), Hsieh and Klenow (2009) and Bartelsman et al. (2013). 12

Rogerson (1993) find that a rise in adjustment frictions reduces entry and exit. In their model, the lower bound of productivity necessary for survival declines as frictions increase. The empirical prediction, then, is that not only will firm growth for continuers become less responsive to productivity, but so will exit. We explore this prediction in the empirical analysis below. Moreover, since the firm dynamics of young firms differ from those of mature firms, we control for potentially exogenous changes in entry rates by studying empirical moments within firm age groups. We draw inference from theory by characterizing the evolution of key moments and reduced form relationships in the data. We do not identify a structural model of adjustment frictions, but we think this is a rich area for future research. For example, we do not take a stand on the exact form of adjustment costs (e.g., convex vs. non-convex), an area of interest in the literature. One potential use of our empirical findings, as suggested above, would be as moments to discipline such analysis.23 A benefit of our reduced form approach is that it readily permits 22F controlling for many different factors in a panel regression environment and allowing estimates to vary systematically by key firm characteristics such as detailed industry and firm age. In addition, we can use this reduced form approach to explore potential explanations for changes in the responsiveness to shocks that we detect. B. Empirical Analysis of U.S. Manufacturing In this section, we investigate these issues with establishment-level data for U.S. manufacturing with a particular focus on high-tech manufacturing.24 We first study the “shocks” 23F hypothesis by directly exploring the evolution of TFP dispersion (i.e., the dispersion of establishment productivity draws), quantified as the standard deviation of (log) within-industry TFP (see Section III for TFP measurement details). Figure 4 reports TFP dispersion separately for plants of young and mature firms, in high-tech and non-tech manufacturing.25 We focus on 24F low-frequency variation by reporting HP trends. Figure 4 shows that TFP dispersion has risen gradually or been flat in high-tech 23 See Cooper and Haltiwanger (2000, 2006). 24 These include NAICS codes 3341 (computer and peripheral equipment), 3342 (communications equipment), 3344 (semiconductor and other electronic components), 3345 (navigational, measuring, electromedical, and control instruments), 3254 (pharmaceutical and medicine), and 3364 (aerospace product and parts). 25 Our unit of analysis in this section is the establishment (plant), but the LBD permits us to classify plants based on the age of the firm to which they belong. 13

manufacturing since the early 1980s and in non-tech manufacturing since the early 1990s.26 25F Within-industry TFP dispersion is large (consistent with, e.g., Syverson (2004, 2011)); for example, a level of 0.4 (40 log points) on Figure 4 implies that a plant one standard deviation above the mean for its industry is about times as productive as the mean. Within- 0.4 industry TFP dispersion is about the same for plants of young and mature firms. Figure C1 in 𝑒𝑒 ≈ 1.5 appendix C shows very similar results for the alternative RPR productivity measure based on Wooldridge (2009). Bils, Klenow and Ruane (2017) suggest that the observed rising withinindustry TFP dispersion may be due to rising survey-based measurement error in the ASM, but as we discuss below (and show on Figure A6 in appendix A) we find rising revenue productivity dispersion even in administrative data. Plant dynamics depend not only on dispersion but also on persistence of idiosyncratic TFP: plants facing adjustment costs are more likely to respond to TFP shocks if TFP is more persistent (Cooper and Haltiwanger (2006); Cooper, Haltiwanger, and Willis (2007)). Our data are not ideally suited for estimating TFP persistence and innovations, but Figure A4 in appendix A suggests that persistence is reasonably stable with an estimated AR(1) coefficient of about 0.6 to 0.7, and trends of TFP innovation dispersion (Figure A5) mimic trends of TFP dispersion. Figures 4 and A4 suggest that changing reallocation is not driven by changing TFP dispersion or persistence. Consider high-tech: Figure 1 shows reallocation rising during the 1990s then falling after 2000. For dispersion and persistence of TFP to account for the reallocation trend we would expect dispersion and/or persistence to mimic these patterns; or, conversely, given the patterns of TFP dispersion and persistence, we should see flat or rising reallocation in the manufacturing sector in the post-2000 period. That we see the opposite is evidence against the “shocks” hypothesis for declining reallocation during that period. Moreover, as we note below in our investigation of firm labor productivity, labor productivity dispersion has also risen in manufacturing (see Figure A6 in appendix A). Consistent with our multiple moments approach, we next estimate the relationship between productivity and growth (and survival) at the establishment level. Our main dependent variable of interest is establishment employment growth from year to using the Davis, 𝑡𝑡 𝑡𝑡+1 26 Bloom et al. (2016) report dispersion of a different measure of productivity shocks; while we study the withinindustry dispersion of TFP draws for the manufacturing sector generally, those authors study overall dispersion of innovations to TFP among a selected subset of plants that appear in manufacturing samples for 25 years or more. 14

Haltiwanger, and Schuh (1996) (hereafter DHS) concept that accommodates exit (by using the two-year average of employment as the denominator). We estimate the following: (4) 𝑔𝑔𝑒𝑒,𝑒𝑒+1 = � [𝛽𝛽𝑎𝑎𝑎𝑎𝑒𝑒𝑙𝑙𝑙𝑙𝑙𝑙𝑒𝑒𝑒𝑒 +𝛿𝛿1𝑎𝑎𝑎𝑎𝑒𝑒𝑙𝑙𝑙𝑙𝑙𝑙𝑒𝑒𝑒𝑒 ∗𝑙𝑙𝑇𝑇𝑒𝑒𝑙𝑙𝑑𝑑𝑒𝑒 𝑎𝑎𝑎𝑎𝑒𝑒=𝑦𝑦,𝑚𝑚 2 ′ where is t + he 𝛿𝛿 D2𝑎𝑎H𝑎𝑎S𝑒𝑒𝑙𝑙 e 𝑙𝑙 m 𝑙𝑙 p𝑒𝑒l𝑒𝑒o ∗ ym 𝑙𝑙𝑇𝑇 en 𝑒𝑒𝑙𝑙 t g 𝑑𝑑 r𝑒𝑒o ] w ∗ th 𝐼𝐼 𝑎𝑎r𝑎𝑎a𝑒𝑒te,𝑒𝑒 𝑒𝑒fo r + es 𝑋𝑋 ta𝑒𝑒b𝑒𝑒l Θ is + hm ε een,t+t 1e f r o m t i m e to , 𝑔𝑔 is𝑒𝑒 ,(𝑒𝑒l+o1g) industry-deviated TFP for establishment at time , and i 𝑡𝑡 s a s 𝑡𝑡 im + p 1 le linear 𝑙𝑙 tim 𝑙𝑙𝑙𝑙 e𝑒𝑒 t𝑒𝑒rend. 26F 27 The responsiveness to TFP in terms of the 𝑒𝑒 main and 𝑡𝑡 trend 𝑙𝑙 e 𝑇𝑇 f 𝑒𝑒 fe 𝑙𝑙 c 𝑑𝑑 ts𝑒𝑒 can vary by firm age with an indicator for young (age<5, subscript ) and mature (subscript ) plants (these dum𝐼𝐼𝑎𝑎m𝑎𝑎𝑒𝑒y,𝑒𝑒 𝑒𝑒variables are denoted Young and Mature in𝑦𝑦 the discussion below). 𝑚𝑚 includes year effects, establishment size, firm size, state effects and a state-level business cy 𝑋𝑋 c𝑒𝑒l𝑒𝑒e measure (the change in state unemployment rates). We also interact the state cyclical measure with TFP and the young and mature dummies; our liberal inclusion of cyclical indicators is intended in part to avoid result contamination from the Great Recession. We estimate equation (4) for 1981-2010 using propensity score weights relating the ASM/CM to the LBD. This reduced form specification is broadly consistent with the specifications of selection and growth dynamics from the literature discussed above, and it is consistent with our modelbased exercises (which estimate the equivalent of equation (4) on simulated data). Moreover, by using DHS growth rates we can incorporate both the intensive margin and the extensive margin (exit) of plant-level growth; as noted above, adjustment cost models of employment growth predict that growth (and exit) from to is related to the realization of TFP in period and state variables, and standard empirical specifications of exit (e.g., Syverson (2011)) likewise find 𝑡𝑡 𝑡𝑡+1 𝑡𝑡 that exit is related to TFP realizations. In this sense, equation (4) produces a reduced-form yet direct estimate of policy functions generated by standard models.28 27F Our question is whether the response to idiosyncratic productivity shocks has changed over time. The inclusion of the variable allows us to estimate a time-varying 𝑙𝑙𝑇𝑇𝑒𝑒𝑙𝑙𝑑𝑑𝑒𝑒 27 Ilut, Kehrig and Schneider (forthcoming) estimate broadly similar reduced-form policy functions with a focus on asymmetric responsiveness, finding that businesses respond more strongly to negative than to positive shocks. These authors do not study changes in this asymmetry over time, a potentially interesting question given our findings. 28 TFP in period t is measured for calendar year t while establishment growth is measured from March of t to March of t+1. Thus, the empirical timing of the data is closer to the timing in the theoretical specifications in Appendix B than might first appear. In Appendix B, we show declining responsiveness of firm-growth to current or lagged realizations in productivity from an increase in adjustment frictions. 15

relationship between productivity and growth. In unreported results we have considered alternative ways to capture a changing trend (e.g., interacting a linear trend with decade dummies), and results are robust to considering such alternatives. On Table 1, we report the main effects for TFP by firm age group and the interactions with the trend terms. Columns 1 and 2 show the growth regressions of equation (4); columns 3 and 4 show a linear probability model with exit as the dependent variable (but otherwise identical to equation (4)). The estimates for and are given by the “TFP*Young” and “TFP*Mature” rows. These positive (negativ 𝛽𝛽 e𝑦𝑦) coef 𝛽𝛽 fi𝑚𝑚cients show that, consistent with previous literature, productivity and growth (exit) are positively (negatively) related.29 The growth 28F coefficients are stronger for establishments of young firms, consistent with intense selection working on recently started businesses; the exit coefficients follow the same pattern in non-tech manufacturing, though interestingly this is not the case in high-tech. The significant establishment-level relationship of productivity with growth and exit implies a positive contribution of reallocation to aggregate productivity growth. The estimates of and are given by the “TFP*Young*Trend” and “TFP*Mature*Trend” ro 𝛿𝛿 w1s𝑦𝑦 of Ta 𝛿𝛿 b1l𝑚𝑚e 1, respectively. These coefficients show how the marginal responsiveness of establishments to their idiosyncratic productivity has changed with time. Notably, in high-tech manufacturing and are positive (negative) and significant for the growth (exit) of plants of both young 𝛿𝛿 a1n𝑦𝑦d mat 𝛿𝛿 u1r𝑚𝑚e firms, with the exception of the exit coefficient for mature firms, suggesting that productivity responsiveness generally strengthened in the early years of the sample (which begins in 1980), while the coefficients are close to zero among nontech establishments. Both inside and outside of high-tech, however, the growth (exit) coefficients on the quadratic term ( and ) are negative (positive). We next graphically illustra 𝛿𝛿 te2 𝑦𝑦the im 𝛿𝛿 p2l𝑚𝑚ications of the combined linear and quadratic trend terms. Since TFP is measured relative to industry-year means, we can calculate the growth differential between a “productive” plant—the plant with TFP one standard deviation above its industry mean—and the average plant in an industry by multiplying the total regression coefficient (including trend effects) by the within-industry TFP standard deviation.30 To abstract 29F 29 The coefficients relating productivity with growth or exit are statistically significant at the 1 percent level in all but one case: the coefficient for exit among young high-tech establishments is significant at the 10 percent level. 30 We set the cyclical indicator (state change in unemployment) to zero to evaluate effects at a neutral cyclical state. 16

from changing TFP dispersion, we fix the standard deviation at 0.40 for high-tech and 0.37 for non-tech (roughly the respective averages across time). Figure 5 shows the resulting growth differentials averaged by decade. First note that young firm plants are more responsive to productivity than are mature firm plants, especially in high-tech. In the 1980s (black bars), the growth differential among young high-tech plants was 13 percentage points: the plant with productivity one standard deviation above its industry mean grew 13 percentage points faster, over a one-year period, than the plant with industry mean productivity, compared with 6 percentage points among mature high-tech plants. This and Figure 4 imply that the high pace of reallocation of young-firm plants is not driven by a high variance of TFP but rather by a high responsiveness to TFP differences consistent with, for example, a learning model. The difference in responsiveness between plants in young and mature firms implies that overall responsiveness depends in part on the age distribution—hence our within-age group approach. Our main focus is the variation in responsiveness over time. First, consider high-tech manufacturing. For plants in young firms, the growth differential rises from 13 to 16 percentage points from the 1980s to the 1990s then declines to 9 percentage points in the 2000s. For plants in mature firms, responsiveness initially declines modestly from the 1980s to the 1990s then accelerates into the 2000s, with the growth differential stepping down from 6 to 5 percentage points then dropping to 3 percentage points. These declines in responsiveness are large in magnitude. High-tech plants responsiveness in the post 2000 period is only about half that in the 1990s for plants of both young and mature firms. Next, consider the non-tech results. Again, plants in younger firms are more responsive to TFP. Among young firms, the growth rate differential was about 10 percentage points in the 1980s, 9 percentage points in the 1990s, and 6 percentage points in the 2000s. Among mature firms, the growth differential was just above 5 percentage points in the 1980s and 1990s and fell by about half a percentage point in the 2000s. On Figure C3 of appendix C, we report exercises using the Wooldridge (2009) RPR as our TFP measure.31 In high-tech manufacturing, young-firm RPR responsiveness rises then falls 30F as with TFPR, and mature-firm RPR responsiveness falls sharply in the post-2000 period in a 31 The decline from the 1990s to the 2000s among young high-tech businesses is not as notable in the RPR-based regressions as it is for TFPR, but it is still substantial as we show below in aggregate productivity counterfactuals. 17

manner similar to the TFPR results. For non-tech plants, the overall drop in responsiveness from the 1980s to the 2000s is similar with RPR compared to TFPR, though more of the drop in responsiveness happens during the early part of the period (versus the later part for TFPR). The RPR results tell broadly the same story as the TFPR results, with reasonable similarity both quantitatively and qualitatively. As can be seen from column 3 of Table 1, part of the growth responsiveness pattern is driven by selection dynamics associated with changing exit responsiveness (Figure A1 in appendix A shows exit charts analogous to Figure 5). Among young firm high-tech establishments, exit selection intensified from the 1980s to the 1990s then weakened in the 2000s; young non-tech establishments saw steadily weakening selection throughout the period. Among mature firm plants, selection intensity did not vary notably until it weakened somewhat in the 2000s. The findings on exit are interesting in their own right as they imply that in the post-2000 period low-productivity plants are more likely to survive, constraining aggregate productivity (and potentially raising TFP dispersion). An alternative story is that rising dispersion of TFP (and its innovations) in the post-2000 period not only could be partially endogenous to changing selection but also could independently contribute to weakening growth responsiveness: in the presence of non-convex adjustment costs, higher TFP dispersion widens inaction bands and reduces the frequency of adjustment, a mechanism that has inspired a large literature on uncertainty and business cycles.32 But these 31F concerns are not likely to be playing a dominant role: during the 1990s, we find increased responsiveness of exit in high-tech despite mild increases in TFP dispersion, a finding that also holds for RPR (Figure C1 in appendix C). More broadly, the combined 30-year patterns of dispersion and responsiveness, across age and industry groups, cannot tell the alternative story coherently. As noted above, our model and a broader literature theorize that the “frequency” effect of widening inaction bands is not likely to dominate the “volatility” effect of larger adjustment-conditional changes in employment due to higher TFP dispersion.33 32F Taken together, these results have important implications for the evolution of firm dynamics in recent decades. The way in which individual businesses respond to their 32 See Bloom (2009), Bachmann and Bayer (2013). 33 Bloom et al. (2016) construct a model similar to ours in which the real options effect dominates the volatility effect in the short term (less than four quarters) at high frequency. We study annual responses in a steady state setting, consistent with our long-term (rather than cyclical) focus. 18

idiosyncratic realizations of productivity has changed. The positive relationship between realized productivity and subsequent employment growth remains robust, but it has weakened, particularly since 2000. Through the lens of firm dynamics models, our results are evidence that establishment-level policy functions have changed over time, particularly for young firms but also for older ones.34 In the post-2000 period, these changes are consistent with an increase in 33F adjustment costs or other frictions that reduce marginal responsiveness to productivity in these models. The changes are most striking among high-tech businesses, where we observe a pattern of rising and falling productivity responsiveness that coincides with the ICT-driven acceleration and deceleration of aggregate productivity growth documented by Fernald (2014) and others. C. Implications for aggregate (industry-level) productivity How important are the changes in responsiveness for aggregate fluctuations in productivity? For this purpose, we compute the following diff-in-diff counterfactual that is inspired by, but distinct from, the Olley-Pakes covariance: (5) 𝑒𝑒+1 𝑇𝑇 𝑁𝑁𝑇𝑇 Δ𝑒𝑒 = �(𝜃𝜃𝑒𝑒,𝑒𝑒+1 −𝜃𝜃𝑒𝑒,𝑒𝑒+1)𝑎𝑎𝑒𝑒𝑒𝑒 where is the predicted employmen𝑒𝑒t share for establishment in period based upon 𝑇𝑇 the full 𝜃𝜃 e𝑒𝑒m𝑒𝑒+p1irical model that includes trend patterns in responsiven 𝑒𝑒 ess (the s 𝑡𝑡 u + pe 1 rscript refers to “trend”), and is the predicted employment share for establishment in period 𝑙𝑙 𝑁𝑁𝑇𝑇 predicted by t 𝜃𝜃 h𝑒𝑒e𝑒𝑒 e+s1timated model with parameters reflecting responsivene 𝑒𝑒 ss at the be 𝑡𝑡 g + inn 1 ing of the sample period (that is, we set the trend terms equal to zero, so means “no trend”).35 34F The employment share prediction for an establish 𝛿𝛿 m𝑖𝑖𝑖𝑖ent in a given perio 𝑁𝑁 d 𝑙𝑙 ( ) is based on the 𝑇𝑇 actual realizations of productivity and initial employment for that establish 𝜃𝜃 m𝑒𝑒,𝑒𝑒e+n1t in the previous period, fed through the estimated growth rate model.36 35F This diff-in-diff object is distinct from the OP covariance because it reflects the changing 34 Karahan, Pugsley, and Sahin (2016) argue that the dynamics of incumbent firms have not changed over this time period based on average growth rates for various age classes. We differ from their approach by directly estimating policy functions at the establishment level. Viewed through their framework, our results suggest that factors in addition to changes in the growth of the labor force are likely relevant for understanding the decline in startup rates. 35 We set the cyclical effects to zero by setting the state-level change in unemployment to zero. 36 This approach is related to other accounting productivity decompositions in the literature (see, e.g., Foster, Haltiwanger, and Krizan (2001) for a review). Our present approach focuses only on model-driven reallocation arising from variation in productivity across businesses, holding constant the productivity distribution. Decker et al. (2017) use the Dynamic Olley-Pakes (DOP) decomposition developed by Melitz and Polanec (2015) to show that these accounting decompositions also imply a decline in the contribution of the change in the covariance terms after 2000. Alon et al. (2017) use the DOP decomposition to study the cumulative contribution of changes in entry rates. 19

marginal responsiveness from our estimated empirical model. The standard Olley-Pakes decomposition approach is based on the weighted average of establishment- (or firm-) level productivity. As shown in Appendix B, this latter weighted index is equivalent to standard industry measures of productivity, defined as industry output per unit (composite) input, only under constant returns to scale and perfect competition. Under these assumptions, the marginal revenue product of the composite input at the establishment level does not change with the level of inputs. An implication is that, in the absence of frictions, all inputs should be allocated to the most productive establishment. In contrast, under revenue function curvature from decreasing returns to scale and/or imperfect competition, the weighted average of establishment level productivity is not equivalent to industry productivity. A corollary is that under revenue function curvature it is generally not optimal to allocate all inputs to the most productive establishment, even in the absence of frictions. Instead, inputs should be reallocated to establishments with higher marginal productivity. These properties imply that, for any increase in frictions, the standard OP covariance declines more quickly than true aggregate productivity in the presence of revenue curvature. We show in Appendix B (Figure B6) that the diff-in-diff counterfactual in (5), on the other hand, closely tracks the true aggregate productivity effects of changing adjustment costs and responsiveness in our benchmark model. The reason for the superior performance of our diff-indiff counterfactual versus the standard OP covariance is intuitive: unlike the standard OP covariance, our diff-in-diff approach uses (estimated) optimal policy functions that reflect the impact of revenue function curvature on marginal revenue products. It is easily shown in the model that the responsiveness of establishment-level growth to realizations of productivity declines with greater curvature in the revenue function. Another attractive feature of this diff-in-diff counterfactual is that it only captures the effect of time-varying responsiveness within firm age groups. Differences in responsiveness between young and mature firms will be present in both the counterfactual with and the counterfactual without the trend, as will the changing age structure of firms overall. Moreover, this diff-in-diff design mechanically abstracts from potential effects of changing TFP dispersion. We report for each year on Figure 6. For example, the observation for 𝑒𝑒+1 has ∆ 𝑒𝑒because the trend variable begins then, and for high-tech the yea 𝑡𝑡 r + 20 1 01 = again 1981 1 gi 9 v 8 e 1 s ∆1980. = B 0 ut the 2004 observation for high-tech shows that, given the productivity and 2001 ∆2000= 0 20

size distributions of 2003, if responsiveness from 2003 to 2004 had been at the 1981 pace instead of the actual pace (as estimated by our model) then the productivity index in 2004 would have been about half a log point higher ( ). For high-tech manufacturing plants, the 2004 increasing responsiveness over the ∆ 19208003s = an − d 0 1 .0 99 0 0 5 s yields an implied counterfactual increase in the index that peaks at about half a log point per year in the 1990s. The sharp decline in responsiveness during the post-2000 period implies a decline in the productivity index of as much as 2 log points per year by 2010. Some caution needs to be used in interpreting the magnitude at the end points—and certainly extrapolating out of sample—since the pattern in Figure 6 is driven by fitting a quadratic trend. But the drag on this index of industry level productivity due to the decline in responsiveness may be quite substantial. Figure C4 in appendix C reports the same exercise but using the RPR productivity concept; in high-tech, the RPR results are quite similar—qualitatively and quantitatively—to the TFPR results from Figure 6, while outside of high-tech the productivity drag implied by the RPR regressions starts somewhat sooner. The basic message of the TFPR and RPR results is the same, however, particularly in high-tech: changing responsiveness has quantitatively large implications for aggregate productivity. In high-tech, changing responsiveness starts to be a drag on productivity around 2003, about the time that Fernald (2014) finds a trend break in productivity growth in the IT sector. Outside of high-tech, both the TFPR and RPR results show a decline in aggregate productivity from the 1980s to the 2000s from declining responsiveness. Some caution should be used in interpreting our counterfactual results as yielding patterns that mimic actual aggregate (industry-level) productivity growth since there may be changes in the within-plant productivity components of aggregate (industry-level) growth that we have not estimated in this context. Fernald (2014), Byrne et al. (2016) and Gordon (2016) highlight many factors that are likely contributing to within-plant (and within-firm) declines in productivity growth in the post-2000 period. In addition to the factors they emphasize, there may be a role for declining entrepreneurship in declining within-firm productivity growth given the contribution of young firms to innovative activity (Acemoglu et al. (2013) and Alon et al. (2017)). We examine the within-firm productivity growth patterns later in the paper. D. Changing Business Models It is possible that changing responsiveness reflects changes in business models that are benign for productivity. For example, perhaps businesses increasingly respond to shocks by 21

adjusting their capital stock instead of labor (a sort of capital/labor substitution). We repeat the regressions from equation (4), replacing the employment growth rate with the investment rate (investment divided by initial capital) and adding initial capital as an additional control.37 This 36F regression therefore includes the key state variables: productivity, employment, and capital. Table 2 reports the regression results for high-tech manufacturing, and Figure 7 shows results analogously to Figure 5. As with employment, young firms’ investment is more responsive than is mature firms’. Investment responsiveness in high-tech manufacturing displays a qualitatively similar pattern to employment responsiveness, with a significant decline in the 2000s among young firms: In the 1990s, a young-firm plant with TFP one standard deviation above its industry-year mean had an equipment investment rate 8 percentage points higher than the plant at the mean; this differential is about 3 percentage points in the post-2000 period. The decline in employment responsiveness was not accompanied by stronger investment responsiveness in high-tech manufacturing. Among non-tech manufacturing businesses, however, there is rising investment responsiveness from the 1980s to the 1990s, with responsiveness remaining elevated in the 2000s, suggesting that capital-labor substitution may play some role outside of the high-tech sector. More broadly, we cannot rule out other forms of capital investment—like intangibles—as substitute adjustment mechanisms. In appendix D, we describe two other exercises exploring changes in business model. First, we find mixed evidence that industries facing increased import competition saw bigger declines in responsiveness, suggesting that globalization may be an interesting avenue for future work. Second, we find no evidence that industry composition shifts within high-tech manufacturing explain declining responsiveness. V. Beyond Manufacturing Thus far we have focused on the manufacturing sector for which we have high-quality TFP data. An important question is whether the patterns of productivity dispersion and responsiveness we have described are present outside manufacturing. For example, the information sector has been a key contributor to U.S. innovation in recent years. Moreover, 37 See appendix D for more detail. Note that the theory linking adjustment costs to employment growth applies equally to investment in models of firm dynamics (Cooper and Haltiwanger (2006)). 22

changes in startup rates and in the dispersion and skewness of firm growth rates are even more dramatic in non-manufacturing components of the high-tech sector (Decker et al. (2016)). We next conduct the same exercises as in section IV, but with firm-level gross output per worker as our productivity concept and with the full private nonfarm sector as our sample.38 37F Output per worker cannot be used to directly track the pattern of shocks, but our adjustment cost framework in appendix B shows that moments based on output per worker move systematically with changes in adjustment frictions. We employ RE-LBD data (described in Section III), which permit the measurement of revenue per worker at the firm level for the entire U.S. private, nonfarm sector from the mid-1990s to 2013. A contribution of this section is new evidence on the relationship between productivity and reallocation dynamics outside manufacturing.39 38F The inferences we draw in this section recognize that output per worker endogenously reflects not only TFP but also changes in adjustment frictions. However, as our benchmark adjustment cost model illustrates, several empirical moments based on output per worker are informative for changing adjustment frictions. First, recall from section IV that an increase in adjustment frictions implies an increase in the within-industry dispersion of labor productivity: adjustment frictions dampen the tendency for marginal revenue products to be equalized, implying higher labor productivity dispersion. Second, an increase in adjustment frictions also reduces the responsiveness of firm-level employment growth from to to the realization of revenue labor productivity in (controlling for employment in ). Finally, an increase in 𝑡𝑡 𝑡𝑡+1 adjustment frictions reduces the diff-in-diff counterfactual using labor productivity in a manner 𝑡𝑡 𝑡𝑡 that tracks the implications for aggregate productivity. Our multiple moments approach, then, is still well suited to a study of labor productivity. A. Productivity and growth at the firm level Figure 8 reports the standard deviation of within-industry labor productivity for young and mature firms, in and out of high-tech; labor productivity dispersion has risen for each of these groups (note that our definition of high-tech now includes certain industry groups in 38 We omit finance, insurance, and real estate (NAICS 52-53) from our sample. This exercise requires that we assign each firm an industry code; we do this by choosing the industry that accounts for the largest share of the firm’s employment. An alternative approach is to construct firm-level within-industry labor productivity as the deviation of firm output per worker from a full set of relevant industry fixed effects. Our results are robust to this alternative approach to controlling for firm industry activity. 39 Relatively little is known about these issues outside manufacturing. Exceptions include several retail trade studies (Foster, Haltiwanger, and Krizan (2006), Jarmin, Klimek, and Miranda (2009) and Foster et al. (2015)). 23

services and information as well as manufacturing). Notably, unlike TFP, labor productivity is more dispersed among young than mature firms; younger firms likely face greater learning or other frictions and may also be more heterogeneous in capital intensity. To provide perspective on the relationship between the findings in this section using firm-level data for the private, non-farm sector and the earlier analysis using establishment-level manufacturing data, Figure A6 in Appendix A reports within-industry revenue labor productivity dispersion for manufacturing in both the RE-LBD and the ASM. Labor productivity dispersion has risen in both the firm-level administrative data and the establishment-level survey data, contrary to the Bils et al. (2017) hypothesis of rising measurement error in the ASM.40 39F Our finding of rising within-industry productivity dispersion is consistent with other work documenting increased differences between firms. For example, Andrews, Criscuolo, and Gal (2015) find a widening productivity gap between “frontier firms” and others, arguing that the pace of technological diffusion has slowed. While the diffusion hypothesis could play a role, our estimates of TFP persistence (Appendix A Figure A4) suggest that the group of “frontier firms” is sufficiently fluid to somewhat limit the diffusion story’s explanatory power. Increased adjustment frictions is an alternative, but not mutually exclusive, explanation. Both explanations allow for a decoupling of technological progress and aggregate productivity growth.41 40F Rising labor productivity dispersion is evidence against the “shocks” hypothesis for falling reallocation in various U.S. sectors. We next estimate equation (4)—the regression we used to measure changing TFP responsiveness in manufacturing—except that we now use firmlevel data (vs. establishment), labor productivity in place of TFP, all U.S. sectors (except finance, insurance and real estate), and only the years 1997-2013.42 41F Table 3 reports results of these regressions. The first two columns report regressions using the DHS growth rate denominator inclusive of exit; the last two columns report results using only a binary exit outcome as the dependent variable. Figure 9 graphically shows the time 40 Figure A6 shows that these findings are robust to employment weighting industries. Interestingly, rising revenue labor productivity dispersion is more apparent in the administrative data than the survey data. 41 Andrews, Criscuolo, and Gal (2015) (ACG) provide evidence of rising productivity dispersion within broad sectors using ORBIS data on both labor productivity (similar to our approach here) and multifactor productivity (similar to our analysis in Section IV). ACG measure the difference between “frontier firms” and average firms, where the frontier firms are usually defined as the top 50 or 100 firms within a broad (2-digit) sector, and in the case of the U.S. their unit of analysis is actually the establishment (Pinto Ribeiro, Menghinello and De Backer (2010)). 42 We also apply propensity score weights; see Section III for RE-LBD details. 24

series pattern of the growth coefficients; as with TFP results, we report the growth rate differential between the firm one standard deviation above its industry mean and the mean. Growth is indeed related to revenue labor productivity, as theorized; that is, firms with higher output per worker are more likely to grow.43 Figure A2 in Appendix A shows a strong 42F relationship between labor productivity and exit as well. Young firms are particularly sensitive to labor productivity, including on the exit margin, indicating that labor productivity is correlated with selection mechanisms. Moreover, the relationship of labor productivity with growth and survival has weakened over time, particularly among young high-tech firms (where the growth differential has fallen by 10 percentage points), consistent with the TFP-based evidence from Section IV. This decline implies that responsiveness of young high-tech firms in 2013 is only about two thirds of what it was in the late 1990s. Broadly speaking, the evidence suggests that the survival and growth differential between high- and low-productivity firms is declining over time, particularly in high-tech. The data on both labor productivity dispersion and the relationship linking labor productivity with growth and survival indicate that the TFP-based patterns we found in manufacturing are likely to hold in other sectors. Again, the framework of our model, applied to multiple moments of evidence, suggests slowing reallocation is a symptom of increased frictions rather than changes in the distribution of idiosyncratic productivity shocks. B. Reallocation and aggregate labor productivity Following the approach from Section IV, we quantify the labor productivity regression results by relating them to aggregate productivity growth using the OP covariance-related diff-indiff counterfactual approach from equation (5). As shown in Figure B6 in Appendix B, in the calibrated model the diff-in-diff counterfactual using labor productivity tracks the impact of increased adjustment frictions on true aggregate (industry-level) productivity quite well.44 43F The diff-in-diff counterfactual for the high-tech (not just manufacturing) and non-tech sectors is presented in Figure 10. By 2013, the weakening responsiveness of growth and survival to productivity accounts for more than 5 log points in the diff-in-diff counterfactual. This 43 Growth differentials for labor productivity may seem large compared with TFP-based differentials from the previous section; this is partly because labor productivity dispersion is higher than TFP dispersion. 44 Though we are using the diff-in-diff counterfactual, it is useful to note that for gross output per worker the weighted mean of micro productivity tracks gross output per worker at the industry level quite well (see Figure A3 in Appendix A) 25

implies that if responsiveness during 2012-2013 had been as strong as in 1996, aggregate productivity in 2013 would be 5 log points higher (given the firm distribution of 2012). In contrast to the TFP-based results from manufacturing, our labor productivity-based calculations for the entire economy show a similar pattern for firms inside and outside high-tech. In unreported results we find that this is driven by particularly strong declines in the sensitivity of exit to productivity among firms outside high-tech; moreover, within manufacturing specifically, we do find stronger results in high-tech than outside of it in the labor productivity counterfactuals, as in the TFP counterfactuals. C. Changing Patterns of Within-Firm Productivity Growth Has a falling productivity contribution from reallocation been offset by stronger withinfirm productivity growth? We use the firm labor productivity database to construct two related but distinct measures of within-firm productivity growth. The first measure is the simple unweighted mean of annual within-firm productivity growth. The second is the employmentweighted mean of annual within-firm productivity growth using time- employment weights for productivity growth from to . We compute these measures at the 6-digit industry level 𝑡𝑡 then aggregate using time-invariant employment weights for each industry.45 𝑡𝑡 𝑡𝑡+1 44F Figure 11 shows trends in within-firm productivity growth, both weighted and unweighted, for the average industry, separately for high-tech and non-tech. For high-tech, within-firm productivity growth declines using both measures; for non-tech, weighted withinfirm productivity growth declines, but the unweighted measure exhibits less systematic variation. The weighted measure is much larger than the unweighted measure for both tech and non-tech, and the unweighted measure is always negative for non-tech and turns negative for high-tech early in the sample; this might be surprising since it implies negative productivity growth for the average firm. However, as discussed by Decker et al. (2017), the unweighted measure overwhelmingly describes very small firms (more than 90 percent of firms have fewer than 20 45 Importantly, these measures of within-firm productivity growth exploit the RE-LBD’s longitudinal links and are therefore distinct from exercises that measure average productivity growth among specific groups of firms. 26

employees).46 In sum, within-firm improvements (e.g., innovation by incumbents) have not 45F quickened to compensate for weaker reallocation.47 46F VI. Conclusion Reallocation has declined in all sectors—particularly the high-tech sector—since the early 2000s. In the 1980s and 1990s, the declining overall pace of reallocation was dominated by sectors such as retail trade, while innovative high-tech sectors (including high-tech manufacturing) exhibited rising reallocation. Within-industry TFP dispersion has risen gradually in recent decades, both in and out of high-tech manufacturing, as has within-industry labor productivity dispersion throughout U.S. industries. The marginal employment growth response of businesses to idiosyncratic productivity draws has mimicked the pattern of aggregate reallocation over time, particularly among young firms, as has the relationship between productivity and exit. The decline in responsiveness is especially large in the high-tech sector with the responsiveness of young firms in the post-2000 period only about half (manufacturing) to two thirds (economy-wide) of the peak responsiveness in the 1990s. Counterfactual exercises imply that the decline in responsiveness yields a significant drag on aggregate (industry-level) productivity, as much as 2 log points in high-tech manufacturing and more than 5 log points economy-wide in recent years. These novel facts, taken together and studied through the lens of standard models of firm dynamics, imply that changing reallocation is the result not of changes in the dispersion or intensity of idiosyncratic shocks but rather of changes in the responsiveness to those shocks arising from an increase in adjustment frictions. Moreover, the timing of reallocation and responsiveness patterns in high-tech is consistent with the timing of the productivity slowdown, which evidence indicates was driven by ICT-producing and using industries. Importantly, our evidence abstracts from the confounding effect of declining startup rates since we study responsiveness within firm age groups. Our main results are based on plant-level TFP in high- 46 Decker et al. (2017) further show that the positive difference between the weighted and the unweighted means reflects a positive relationship between within-firm productivity growth and initial shares (i.e., larger firms have higher within-firm productivity growth). 47 Alon et al. (2017) also use the Dynamic Olley Pakes decomposition method described by Melitz and Polanec (2015) to study the productivity slowdown. The authors show that declining entry has had a significant cumulative negative effect on aggregate productivity growth, consistent with our emphasis on the contribution of changing firm dynamics. 27

tech manufacturing, but the results extend to manufacturing broadly and, when focusing on firmlevel labor productivity, to other U.S. industries more generally. In addition to shedding light on the drivers of declining business dynamism, these findings comprise a novel contribution to the literature on the U.S. productivity slowdown in the post-2000 period. The cross-sector and time series dimensions of reallocation and responsiveness are consistent with the timing of aggregate productivity fluctuations, and our counterfactuals demonstrate the quantitative importance of this relationship. Notably, productivity dispersion within industries has risen in the post-2000 period, while a slowing pace of innovation would produce falling dispersion in a Gort and Klepper (1982) framework. Slowing reallocation and business-level responsiveness is, at least, complementary to innovationbased explanations for the productivity slowdown such as Gordon (2016) (and is consistent with Byrne, Fernald and Reinsdorf (2016) and Syverson (2016), who find that the productivity slowdown is not an artifact of mismeasurement). We document several other interesting patterns. The responsiveness of equipment investment to TFP in high-tech manufacturing follows a similar pattern to employment responsiveness, rising during the 1980s and 1990s then falling sharply after 2000, while investment responsiveness in non-tech manufacturing was flat throughout the 1990s and 2000s after rising in the 1980s. The strong relationship between growth and productivity that has previously been documented for TFP in manufacturing also holds for labor productivity in other sectors. The decline in productivity-enhancing reallocation has not been offset by stronger within-firm labor productivity growth. We do not study specific policy or other factors that may be contributing to declining responsiveness, a large task that we leave for future work. Our theoretical framework focuses on increased adjustment costs, but broader interpretations may be plausible. Globalization may have played a role in subdued business-level growth responsiveness by facilitating cross-border factor adjustment (see Appendix D). Other explanations could include any forces that raise the cost of, or reduce the incentive for, factor adjustment; possibilities include unlawful discharge regulations, occupational licensing rules, scope of intellectual property protection, land use regulations, rules or norms that increase job match specificity, or various other state or federal 28

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Figure 1: Job reallocation patterns vary by sector 45 40 35 30 25 20 Information Manufacturing Retail Services 15 High-tech High-tech manufacturing Economywide 10 Note: Y axis does not start at zero. HP trends using parameter set to 100. Industries defined on a consistent NAICS basis; high-tech is defined as in Hecker (2005). Data include all firms (new entrants, continuers, and exiters). Author calculations from the Longitudinal Business Database (LBD). Figure 2: Young firm share patterns vary by sector 30 Information Manufacturing Retail Services High-tech High-tech manufacturing 25 Economywide 20 15 10 5 0 Note: Young firms have age less than 5. Industries are defined on a consistent NAICS basis; high-tech is defined as in Hecker (2005). Data include all firms (new entrants, exiters, and continuers). Author calculations from the LBD. 36

Figure 3: Most variation in job reallocation is not explained by changing startup rates Note: Sectors are defined on a consistent NAICS basis. Author calculations from the LBD. Figure 4: Within-industry TFP dispersion has risen (manufacturing) 0.50 0.40 0.30 0.20 High-tech young High-tech mature 0.10 Non-tech young Non-tech mature 0.00 Note: Y axis does not start at zero. Young firms have age less than 5. Standard deviation of within-detailed industry log TFPR. High-tech defined as in Hecker (2005). Author calculations from the LBD, the Annual Survey of Manufacturers (ASM), and the Census of Manufacturers (CM). HP Trends. Figure 5: Establishment job growth has become less responsive to TFP (manufacturing) 0.20 1980s 0.15 1990s 0.10 2000s 0.05 0.00 High-tech young High-tech mature Non-tech young Non-tech mature Note: Young firms have age less than 5. High-tech is defined as in Hecker (2005). Growth rate of plant with TFPR one std. dev. above industry mean vs. industry mean. Author calculations from the LBD, the ASM, and the CM. 37

Figure 6: Changing contribution of reallocation to aggregate TFP (manufacturing) 0.010 0.005 0.000 -0.005 -0.010 -0.015 -0.020 -0.025 Note: Figure depicts diff-in-diff counterfactual as described in the text from TFPR concept. High-tech is defined as in Hecker (2005). Author calculations from the LBD, the ASM, and the CM. Figure 7: Establishment investment rates have become less responsive to TFP (manufacturing) Note: Young firms have age less than 5. High-tech is defined as in Hecker (2005). Investment rate of plant with TFPR one std. dev. above industry mean vs. mean. Author calculations from the LBD, the ASM, and the CM. Figure 8: Within-industry labor productivity dispersion has risen (economywide) Note: Y axes do not begin at zero. Standard deviation of log labor productivity deviated from industry by year means. Young firms have age less than five. High-tech is defined as in Hecker (2005). Author calculations from the RE-LBD. Finance, Insurance and Real Estate (NAICS 52-53) omitted. 38 1891 3891 5891 7891 9891 1991 3991 5991 7991 9991 1002 3002 5002 7002 9002 High-tech Non-tech 0.08 1980s 0.06 1990s 2000s 0.04 0.02 0.00 High-tech young High-tech mature Non-tech young Non-tech mature 1.20 High-tech young High-tech mature Non-tech young Non-tech mature 1.10 1.00 0.90 0.80 0.70

Figure 9: Firm growth has become less responsive to labor productivity (economywide) 0.40 High-tech young High-tech mature 0.35 0.30 0.25 0.20 0.15 0.10 Note: Y axis does not start at zero. Growth rate of firm with labor productivity one std. dev. above industry mean vs. industry mean. Young firms have age less than five. High-tech defined as in Hecker (2005). Author calculations from the RE-LBD. Finance, Insurance and Real Estate (NAICS 52-53) omitted. Figure 10: Changing contribution of reallocation to aggregate labor productivity (economywide) 0 -0.01 -0.02 -0.03 -0.04 -0.05 -0.06 High-tech Non-tech -0.07 Note: Figure depicts diff-in-diff counterfactual as described in the text. High-tech is defined as in Hecker (2005). Author calculations from the RE-LBD. Finance, Insurance, and Real Estate (NAICS 52-53) omitted. Figure 11: Within-firm productivity growth in the average industry (economywide) 0.10 0.05 0.00 -0.05 Unweighted within, high-tech Weighted within, high-tech -0.10 Unweighted within, non-tech Weighted within, non-tech Note: Average within-firm productivity growth, with and without employment weights. Author calculations from the RE-LBD. 39

Table 1: Effect of Lagged Productivity on Plant-Level Employment Growth and Exit Growth including exit Exit High-tech Non-tech High-tech Non-tech TFP*Young 0.2025*** 0.2732*** -0.0292* -0.0905*** (0.0390) (0.0090) (0.0162) (0.0037) TFP*Young*Trend 0.0317*** 0.0016 -0.0160*** -0.0005 (0.0061) (0.0014) (0.0025) (0.0006) TFP*Young*Trend2 -0.0012*** -0.0002*** 0.0005*** 0.0001*** (0.0002) (0.00005) (0.0001) (0.00002) TFP*Mature 0.1228*** 0.1394*** -0.0403*** -0.0464*** (0.0174) (0.0043) (0.0072) (0.0018) TFP*Mature*Trend 0.0054** 0.0016 -0.0016 -0.0012 (0.0026) (0.0007) (0.0011) (0.0003) TFP*Mature*Trend2 -0.0003*** -0.0001* 0.0001*** 0.00005*** (0.0001) (0.00002) (0.00003) (0.00001) N 125000 2055000 125000 2055000 R2 0.059 0.032 0.098 0.054 Notes: Standard Errors in Parentheses. Dependent variable in Growth columns is DHS growth rate. Dependent variable in Exit columns is indicator=1 if exit, 0 Young firms have age less than 5. Unreported are estimates of controls including year effects, state effects, firm age dummies, firm size dummies, log plant level employment in period t, state cyclical indicators (change in state level unemployment rate), state cyclical indicators interacted with TFP. All variables that use TFP including all interactions are fully interacted with firm age dummies. Sample size rounded to nearest 5000 observations. * p < 0.1, ** p < 0.05, *** p < 0.01. Table 2: Estimated Effect of Productivity on Plant-Level Equipment Investment Rate High-tech Non-tech TFP*Young 0.0826*** -0.0125** (0.0236) (0.0052) TFP*Young*Trend 0.0189*** 0.0156*** (0.0037) (0.0008) TFP*Young*Trend2 -0.0008*** -0.0004*** (0.0001) (0.0000) TFP*Mature 0.0232** 0.0039 (0.0105) (0.0025) TFP*Mature*Trend 0.0024 0.0067*** (0.0016) (0.0004) TFP*Mature*Trend2 -0.0001* -0.0002*** (0.00005) (0.0000) N 125000 20055000 R2 0.068 0.047 Notes: Standard errors in parentheses. Young firms have age less than 5. Unreported are estimates of controls including year effects, state effects, firm age dummies, firm employment size dummies, log plant level employment in period t, dummies for initial capital, state cyclical indicators (change in state level unemployment rate), state cyclical indicators interacted with TFP. All variables that use TFP including all interactions are fully interacted with firm age dummies. * p < 0.1, ** p < 0.05, *** p < 0.01. 40

Table 3: Lagged Labor Productivity and Firm-Level Employment Growth and Exit Growth including exit Exit High-tech Non-tech High-tech Non-tech LP*Young 0.3845*** 0.3467*** -0.1258*** -0.1224*** 0.0020 0.0005 0.0009 0.0002 LP*Young*Trend -0.0141*** -0.0043*** 0.0026*** 0.0014*** 0.0006 0.0001 0.0002 0.0001 LP*Young*Trend2 0.0004*** 0.0000*** -0.0001*** 0.0000*** 0.0000 0.0000 0.0000 0.0000 LP*Mature 0.2755*** 0.2522*** -0.0710*** -0.0758*** 0.0021 0.0004 0.0009 0.0002 LP*Mature*Trend -0.0042*** -0.0056*** -0.0008*** 0.0020*** 0.0006 0.0001 0.0002 0.0000 LP*Mature*Trend2 0.0000 0.0001*** 0.0001*** -0.0001*** 0.0000 0.0000 0.0000 0.0000 N 55385000 55385000 55385000 55385000 R2 0.126 0.108 0.105 0.093 Dependent variable in all regressions is firm-level employment growth rate (DHS). All regressions include controls for state business cycle (change in state unemployment rate) and firm employment size in period t-1. Labor productivity is measured as the log difference from 6-digit NAICS industry mean. High-tech is defined as in Hecker (2005). Observations rounded to nearest five thousand. *** p<0.01; ** p<0.05; * p<0.10 41

Appendix A. Figures and tables to supplement the main text Figure A1: Exit selection on TFP has weakened (manufacturing) High-tech young High-tech mature Non-tech young Non-tech mature 0.00 -0.02 -0.04 1980s -0.06 1990s 2000s -0.08 Note: Young firms have age less than 5. High-tech is defined as in Hecker (2005). Exit probability of plant with TFPR one std. dev. above industry mean vs. industry mean. Author calculations from the Longitudinal Business Database, the Annual Survey of Manufacturers, and the Census of Manufacturers. Figure A2: Exit selection on labor productivity has weakened (economywide) 0.00 High-tech young High-tech mature -0.02 Non-tech young Non-tech mature -0.04 -0.06 -0.08 -0.10 -0.12 -0.14 Note: Annual coefficients constructed from Table 3. Young firms have age less than five. High-tech defined as in Hecker (2005). Exit probability of plant with labor productivity one std. dev. above industry mean vs. industry mean. Author calculations from the RE-LBD. Finance, Insurance and Real Estate (NAICS 52-53) omitted. Figure A3: Average industry-level productivity growth, BLS and aggregated microdata 0.14 Micro-based high-tech 0.12 Micro-based non-tech 0.1 BLS non-tech 0.08 BLS high-tech 0.06 0.04 0.02 0 Source: BLS and author calculations from RE-LBD. 42

Figure A4: Little change in persistence of TFP (manufacturing) 0.80 High Tech Non Tech 0.60 0.40 0.20 0.00 1980s 1990s 2000s Note: High-tech is defined as in Hecker (2005). AR(1) coefficients for establishment TFPR, averaged by decade. The LBD-ASM-CM database is not ideally suited for estimating persistence since this requires relying on the longitudinal nature of the ASM/CM, which is less robust than the longitudinal properties of the LBD. That is, estimating productivity persistence parameters requires pairwise continuing plants in t and t+1 to be measured in the ASM/CM. The panel rotation of the ASM as well as Census years make this a challenge. That is, in the first years of a new ASM panel and in Census years we have a much smaller and less representative set of continuing plants than other years. For this exercise we exclude those years; even for other years, though, our propensity score weights are not ideally suited for making the sample of continuers representative. In principle, we can develop separate propensity score weights for this restricted sample of continuing plants. Doing so is more of a challenge, given the rotating nature of the ASM sample. See Figure B2 in appendix B for the same exercise on RPR productivity. Figure A5: Standard deviation of innovations to plant-level TFPR 0.40 High Tech Non Tech 0.30 0.20 0.10 0.00 1980s 1990s 2000s Note: High-tech is defined as in Hecker (2005). For the set of years where we can estimate the AR(1) process (see note for Figure A4), we can also recover the distribution of innovations to plant-level TFP for continuing plants. Since this is for selected years we report averages of standard deviation of innovations to TFP by decade as we did with persistence. 43

Figure A6: Rising labor productivity dispersion in survey and administrative data (manufacturing) 1.00 Survey (ASM) Survey (ASM), weighted Admin (RE-LBD) 0.95 Admin (RE-LBD), weighted 0.90 0.85 0.80 0.75 0.70 Note: Revenue labor productivity is measured as real revenue per employee. For the ASM, revenue and employment are from survey data. For the RE-LBD, revenue and employment are from administrative data. Dashed lines for each series depict HP-Filtered series. Two alternative types of weighting are used. For the employment-weighted series, the within industry dispersion at the 6-digit NAICS level are computed for each industry and year cell using the propensity score weights as described in the text. Then the employment shares for each industry are computed from the RE-LBD and the reported dispersion at the total manufacturing level uses such industry-level employment weights. Both the ASM and RE-LBD series use the RE-LBD industry-level employment weights. Results are similar using ASM-based employment weights. For the non-employment-weighted measures, the reported measure is based on first sweeping out 6-digit NAICS-by-year effects from the micro data and then computing the pooled dispersion measure using the propensity score weights. This is equivalent to a 2-step method weighting industries by the number of producers in the data. One source of discrepancy between the ASM and RE- LBD is the former is at the establishment level while the latter is at the firm level. 44

Appendix B. Illustrative Model of Adjustment Costs A. Model environment Consider the following model of firm-level adjustment costs.49 A firm maximizes the 48F present discounted value of profits. The firm’s value function and its components are specified as follows: 𝜑𝜑 with: 𝑉𝑉(𝑙𝑙𝑒𝑒𝑒𝑒−1;𝐴𝐴𝑒𝑒𝑒𝑒) = 𝐴𝐴𝑒𝑒𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒 −𝑤𝑤𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒 −𝐶𝐶(𝐻𝐻𝑒𝑒𝑒𝑒)+𝛽𝛽𝑉𝑉(𝑙𝑙𝑒𝑒𝑒𝑒+1;𝐴𝐴𝑒𝑒𝑒𝑒+1) 2 𝛾𝛾 𝐻𝐻𝑒𝑒𝑒𝑒 � � 𝐶𝐶(𝐻𝐻𝑒𝑒𝑒𝑒) = � 2 𝑙𝑙𝑒𝑒𝑒𝑒 +𝑙𝑙+max (𝐻𝐻𝑒𝑒𝑒𝑒,0)+𝑙𝑙−max (−𝐻𝐻𝑒𝑒𝑒𝑒,0) 𝑒𝑒𝑓𝑓 𝐻𝐻𝑒𝑒𝑒𝑒 ≠ 0 0, 𝑜𝑜𝑡𝑡ℎ𝑒𝑒𝑇𝑇𝑤𝑤𝑒𝑒𝑒𝑒𝑒𝑒 𝑎𝑎𝑒𝑒𝑒𝑒 = 𝜌𝜌𝑎𝑎𝑒𝑒𝑒𝑒 +𝜂𝜂𝑒𝑒𝑒𝑒 𝑙𝑙𝑒𝑒𝑒𝑒 = 𝑙𝑙𝑒𝑒𝑒𝑒−1+𝐻𝐻𝑒𝑒𝑒𝑒 where due to product differentiation so that is the revenue function, is 𝜑𝜑 employ 𝜑𝜑 m ≤ en 1 t for time , is net hires made at the 𝐴𝐴 b𝑒𝑒𝑒𝑒e 𝑙𝑙 g𝑒𝑒in𝑒𝑒ning of time , or 𝑙𝑙𝑒𝑒𝑒𝑒 (this can be positive o 𝑡𝑡 r n 𝐻𝐻 eg𝑒𝑒a𝑒𝑒tive), is the wage, and i 𝑡𝑡 s a re 𝐻𝐻 v𝑒𝑒e𝑒𝑒nu = e 𝑙𝑙 sh𝑒𝑒𝑒𝑒o − ck 𝑙𝑙𝑒𝑒,𝑒𝑒−1 potentially reflecting TFPQ and de 𝑤𝑤 m𝑒𝑒and shocks (for ex 𝑎𝑎 p𝑒𝑒o𝑒𝑒s = itio lo n g al ( 𝐴𝐴 co𝑒𝑒𝑒𝑒n ) venience we focus on TFPQ). We interpret the revenue function curvature as reflecting product differentiation rather than decreasing returns to help draw out relations between revenue productivity and technical efficiency. That is, let firm-level prices be given by where is firm- 𝜑𝜑−1 level output subject to a CRTS technology. This imp 𝑙𝑙 li𝑒𝑒e𝑒𝑒s = tha 𝑄𝑄 t 𝑒𝑒𝑒𝑒 . 𝑄𝑄 I𝑒𝑒n𝑒𝑒 t = erm 𝐴𝐴̃𝑒𝑒s𝑒𝑒 o 𝑙𝑙 f𝑒𝑒 𝑒𝑒t h e 𝜑𝜑 terminology of the literature and the main text, is TFPQ; a 𝐴𝐴 n𝑒𝑒d𝑒𝑒 s = inc 𝐴𝐴̃e𝑒𝑒 𝑒𝑒labor is the only factor of production, both TFPR and revenue labor produ 𝐴𝐴̃c𝑒𝑒ti𝑒𝑒vity (RLP) are given by . Note that this specification nests the price-taking version of the model with . In tha 𝑙𝑙 t𝑒𝑒 c𝑒𝑒𝐴𝐴 ãs𝑒𝑒e𝑒𝑒, TFPQ, TFPR and RLP are equivalent. We focus on the case in our calibration but discuss some aspects 𝜑𝜑 = 1 of the price-taking case below. 𝜑𝜑 < 1 49 We use the term “firm” for expositional purposes; for modeling purposes we do not distinguish between firms and establishments. Our main empirical results focus on establishments. 45

This simple adjustment cost model is similar to Cooper, Haltiwanger, and Willis (2007, 2016), Elsby and Michaels (2013), and Bloom et al. (2016) and, in principle, accommodates both convex and non-convex costs. Under non-convex costs the solution has the following form: 𝐼𝐼 𝐻𝐻 where 𝑉𝑉 = max (𝑉𝑉 ,𝑉𝑉 ) 𝐼𝐼 𝜑𝜑 𝑉𝑉 = 𝐴𝐴𝑒𝑒𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒−1 −𝑤𝑤𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒−1 +𝛽𝛽𝑉𝑉(𝑙𝑙𝑒𝑒𝑒𝑒;𝐴𝐴𝑒𝑒𝑒𝑒+1) 𝑒𝑒𝑓𝑓 𝐻𝐻𝑒𝑒𝑒𝑒 = 0 𝐻𝐻 𝜑𝜑 𝑉𝑉 = 𝐴𝐴𝑒𝑒𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒 −𝑤𝑤𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒 −𝐶𝐶(𝐻𝐻𝑒𝑒𝑒𝑒)+𝛽𝛽𝑉𝑉(𝑙𝑙𝑒𝑒𝑒𝑒;𝐴𝐴𝑒𝑒𝑒𝑒+1) 𝑒𝑒𝑓𝑓 𝐻𝐻𝑒𝑒𝑒𝑒 ≠ 0 with the notation indicating that is the value of inaction (i.e., zero net hiring), and is the 𝐼𝐼 𝐻𝐻 value of nonzero net hiring (in either positive or negative amounts). 𝑉𝑉 𝑉𝑉 We view this model as primarily illustrative but we seek to use a reasonable baseline calibration that matches many of the features of the data and the parameters of the existing literature. Appropriate caution is needed since we do not model entry or exit, and we do not have any lifecycle learning dynamics or frictions that make young firms different from more mature firms. We regard the calibration as mostly providing guidance about the qualitative predictions for the key data moments we study but within a reasonable range of the parameter space. Our main calibration exercise implements “general equilibrium” in the sense that the wage adjusts to clear the labor market; however, we fix the labor supply, so this calibration may be thought of as an extreme scenario. In unreported exercises, we also consider the opposite extreme in which labor supply is perfectly elastic and the wage is fixed (i.e., partial equilibrium). A limitation of the partial equilibrium exercise is that when the wage is fixed, adjustment frictions can have large effects on average firm size and therefore productivity via channels that are unrelated to reallocation. However, our key results on how adjustment costs affect reallocation rates, firm-level productivity responsiveness, and the OP covariance do not substantively depend on general vs. partial equilibrium. We report the more realistic (yet still extreme) general equilibrium (inelastic labor supply) results here. B. Calibration We set , consistent with annual data. We specify that , consistent with a markup of 25 percent. For the shock process, we specify , which is roughly the 𝛽𝛽 = 0.96 𝜑𝜑 = 0.8 𝜎𝜎𝑎𝑎 = 0.35 46

standard deviation of TFPR or RPR in U.S. manufacturing during the 1980s; and we set , broadly consistent with the AR(1) coefficient on TFPR and RPR that we find among 𝜌𝜌 = manufacturing establishments in the 1980s (see Figure A4 and Appendix C). These values of 0.65 and imply that innovations to TFP have a standard deviation of . Strictly speaking 𝜎𝜎 , 𝑎𝑎 if pla 𝜌𝜌 nt-level prices are endogenous (which this model permits) th 𝜎𝜎 e 𝜂𝜂ap = pr 0 o . p 2 r 6 iate empirical moments are those from RPR. We calibrate the adjustment cost parameter(s) to target a job reallocation rate of 25 percent, roughly the rate for the U.S. manufacturing sector in the 1980s. Focusing only on kinked (non-convex) adjustment costs (i.e., setting ), we find that the target reallocation rate implies when . For quadratic adjustment costs (i.e., ) 𝛾𝛾 = 0 matching the 𝑙𝑙 j+ob = r 0 ea .8 ll 5 ocation 𝑙𝑙 r−ate = o 0 f 0.25 requires . We make no at 𝑙𝑙 t+em = pt 𝑙𝑙 t−o = joi 0 ntly calibrate convex and non-convex adjustment costs for our illustrative purposes. For the key 𝛾𝛾 = 1.3 moments we study empirically, the model produces broadly similar predictions regardless of cost type. The literature suggests that non-convex costs are important for certain properties of microdata, so we focus on this cost type here and leave convex cost exercises unreported. However, the qualitative patterns we present are robust to consideration of variation of alternative adjustment cost parameters. The model produces a (non-targeted) correlation between TFPQ and TFPR (which is the same as RLP in this one-factor setting) of 0.90, qualitatively similar to the 0.75 found by Foster, Haltiwanger, and Syverson. This strong correlation implies that the responsiveness of growth to realizations of productivity is essentially the same whether we use TFPQ or TFPR/RLP as the measure of productivity. We consider two types of experiments in the simulation. The first is an increase in adjustment frictions starting from , our baseline non-convex cost calibration described above. 49F 50 We increase 𝑙𝑙 +fr = om 0 . z 8 e 5 ro ,𝑙𝑙 t−o = stu 0 dy rising adjustment costs from a starting point that matches the patterns o f 𝑙𝑙 T−FP and reallocation in the 1980s. In the second experiment, we fix adjustment costs at the baseline ( ) but vary TFP dispersion around the 𝑙𝑙+ = 0.85,𝑙𝑙− = 0 50 We also find similar patterns if we consider a case with F>0 and F =0 and then begin increasing F Cooper, - + + Haltiwanger, and Willis (2007) found that including a kinked adjustment cost to be important to match the shape of the growth rate distribution of employment but found similar results using either F or F to generate the kink. - + 47

baseline to study the relation between TFP dispersion and responsiveness, RLP dispersion, and the OP covariance. C. Changing adjustment costs Here we describe results from the general equilibrium (i.e., flexible wage with inelastic labor supply) model. We consider several moments calculated on model-simulated data;51 these 50F moments are the job reallocation rate; the standard deviation of labor productivity (or, equivalently in this model, TFPR); the TFP coefficient from a regression of firm-level employment growth from time to on TFP in time and (log) employment in time (that is, we run a regression analogous to equation (4) in the paper; hereafter we call this moment the 𝑡𝑡 𝑡𝑡+1 𝑡𝑡 𝑡𝑡 “productivity coefficient”); the Olley-Pakes covariance for TFP (hereafter “OP covariance”); and the OP covariance for labor productivity. Figures B1 and B2 show the effect of increasing adjustment frictions (i.e., raising the downsizing cost while holding fixed ). An increase in adjustment frictions yields: (i) a decline in th 𝑙𝑙 e− job reallocation rate; 𝑙𝑙 (i+i) = a d 0 e .8 cl 5 ine in the productivity coefficient; (iii) an increase in the dispersion of RLP; and (iv) a decline in the OP covariance for both TFP and RLP (where employment serves as weights). Each of these relationships is monotonic in adjustment costs except the Olley-Pakes covariance for RLP (which we discuss below). There are many possible moments relating growth to TFP that are similarly sensitive to adjustment costs. For example, in unreported regression results (in which we always control for period- log employment), increasing adjustment costs yield (i) a decline in the estimated coefficient of a regression of firm-level growth between and on TFP in period 𝑡𝑡 (rather than ); (ii) a decline in the estimated coefficient of a regression of firm-level growth 𝑡𝑡 𝑡𝑡+1 𝑡𝑡+1 between and on the change in TFP from period to ; and (iii) a decline in the 𝑡𝑡 estimated coefficient of a regression of firm-level growth between and on the innovation 𝑡𝑡 𝑡𝑡 +1 𝑡𝑡 𝑡𝑡+1 of TFP ). In principle, we could use any of these moments to detect a change in adjustment 𝑡𝑡 𝑡𝑡+1 frictions ( . 𝜂𝜂 W𝑒𝑒𝑒𝑒e use the specification reported in Figure B1 for measurement and econometric reasons discussed in the main text. The exact timing in the model vs. the data are different, so it is reassuring that the predictions on responsiveness hold equally well qualitatively in the numerical analysis using current or lagged productivity. 51 We simulate 2000 firms for 1000 periods then discard the first 100 periods. 48

The model-based predictions in B1 and B2 are the primary moments that we explore empirically in the main text. In the empirical analysis we also consider the estimated coefficient of firm-level growth between and on revenue labor productivity in (with log periodemployment as a control as usual). Given the simple revenue functions in the model, this 𝑡𝑡 𝑡𝑡+1 𝑡𝑡 𝑡𝑡 estimated coefficient is identical to the coefficient on TFP shown on Figure B1 (this is because the only production factor is labor, and initial employment is explicitly included in all regressions). This precise equivalence is model dependent, but the general inference is not. That is, in response to an increase in adjustment frictions, there should be a decline in the covariance between firm-level growth and realizations of labor productivity as firms find it more costly to equalize their marginal products. D. Changing TFP dispersion Figure B3 shows how key moments vary with TFP dispersion. Increased TFP dispersion yields: (i) an increase in the job reallocation rate; (ii) an increase in the productivity coefficient; and (iii) an increase in the dispersion of labor productivity. As before, the finding for the productivity coefficient also holds using real labor productivity as the regressor. While the results in Figure B3 are generally intuitive, one finding merits further discussion—specifically, the finding that responsiveness increases in TFP dispersion. The net effect of TFP dispersion on responsiveness reflects two competing mechanisms (as discussed in the main text). The first is the “real options” effect: Non-convex costs create “inaction bands” or regions of the TFP innovation range in which firms prefer inaction (i.e., zero hiring) to action. Inaction bands widen as shock dispersion or volatility rises (consistent with an “uncertainty” interpretation), which, ceteris paribus, reduces responsiveness. We observe this effect in our simulated data when we examine only the extensive margin: a given absolute change in TFP is more likely to induce action when TFP dispersion is smaller (holding initial employment constant). However, in the model this effect is dominated by the “volatility effect” in which adjustments—when they actually do occur—are larger when TFP is more widely dispersed. The dominance of the “volatility effect” is consistent with Barro (1972); Bloom et al. (2016) find, in a business cycle-focused model that is otherwise similar to ours, that the real options effect dominates for a few quarters at high frequency, but the volatility effect dominates after a year or more. Given our long-run focus, the steady-state result that the “volatility effect” dominates is the relevant intuition. 49

E. The frictionless case The patterns in Figures B1-B3 are, for the most part, robust to changes in the curvature of the revenue function, the shock space and the adjustment cost parameters. One exception highlights the importance of using multiple moments in our empirical exercises. Specifically, in a frictionless benchmark with zero adjustment costs (in contrast to our baseline above, in which hiring costs are set to , there is zero labor productivity dispersion and, therefore, zero OP covariance for labo 𝑙𝑙 r+ p = ro 0 du .8 c 5 ti ) vity (though still positive OP covariance for TFP). At first glance, this implies that the OP covariance for labor productivity may not be an informative moment, but we show here that the frictionless benchmark yields patterns that are very far from empirical plausibility. Figure B4 shows the effects of increasing adjustment costs from zero, the frictionless case. As adjustment frictions rise above zero, labor productivity dispersion rises (Figure B4) and, consistent with the discussion above, reallocation and the productivity coefficient decline. But Figure B5 shows that the OP covariance for labor productivity initially rises as labor productivity begins to be dispersed, continuing to rise over the range of adjustment frictions that produce reallocation rates above 30 percent (compare Figure B5 to Figure B4). But since productivity responsiveness declines monotonically as adjustment costs rise, the OP covariance eventually declines as labor is increasingly “trapped” in unproductive firms while productive firms are starved of resources (i.e., employment weight). Thus, the OP covariance for labor productivity is decreasing in adjustment costs (and increasing in misallocation) across the plausible range of costs. This pattern is related to that found in Bartelsman, Haltiwanger, and Scarpetta (2013), in whose model distortions reduce the OP covariance for labor productivity as long as the benchmark is characterized by sufficient frictions; we explore the OP covariance in more detail below. As can be seen on Figure B4, the frictionless benchmark produces implausibly large rates of reallocation—above 100 percent, while empirical reallocation in the manufacturing sector was around 25 percent in the 1980s and has since declined. Here we demonstrate basic analytical intuition underlying the empirical implausibility of the frictionless case. In the frictionless case ( ), the first-order condition for labor is given by: 𝛾𝛾 = 𝑙𝑙+ = 𝑙𝑙− = 0 1 1−𝜑𝜑 φAet 𝑙𝑙𝑒𝑒𝑒𝑒 = � � 𝑤𝑤𝑒𝑒 50

Taking logs (indicated by lower case) and differences (indicated by ) and sweeping out year and industry effects yields: ∆ 1 which implies ∆𝑒𝑒𝑒𝑒𝑒𝑒 = ∆𝑎𝑎𝑒𝑒𝑒𝑒 1−𝜑𝜑 1 where indicates standard de𝑒𝑒v𝑡𝑡i𝑑𝑑a ( ti∆o𝑒𝑒n 𝑒𝑒 . 𝑒𝑒 ) Th=at is, in 𝑒𝑒th𝑡𝑡e𝑑𝑑 (fr∆ic𝑎𝑎t 𝑒𝑒 i 𝑒𝑒 o)nless model, the dispersion of 1−𝜑𝜑 employment growth rates (i.e., log differences) is proportional to the dispersion of TFP with the 𝑒𝑒𝑡𝑡𝑑𝑑() factor of proportionality greater than one. The among continuing manufacturing plants is about 0.33 (this is from RPR – similar 𝑒𝑒 s 𝑡𝑡 t 𝑑𝑑 at ( is ∆ t 𝑎𝑎 ic𝑒𝑒s𝑒𝑒 ) emerge from TFPR). For , corresponding to a markup of 25 percent, we should expect ; for a 33 percent 𝜑𝜑 = 0.8 markup we should expect . Yet in U.S. m 𝑒𝑒 a 𝑡𝑡 n 𝑑𝑑 u ( fa ∆ c 𝑒𝑒 t𝑒𝑒u𝑒𝑒r ) in = g d 1 a .6 ta 5 . This relatively low dispers 𝑒𝑒 io 𝑡𝑡𝑑𝑑 n ( o ∆ f 𝑒𝑒 p𝑒𝑒l𝑒𝑒a ) n = t-le 1 v .3 e 2 l employment growth rates compare 𝑒𝑒 d 𝑡𝑡𝑑𝑑 to (∆ th 𝑒𝑒 e𝑒𝑒𝑒𝑒 ) = 0.35 dispersion in shocks illustrates that the frictionless model yields implausible empirical patterns. Given the empirical implausibility of the frictionless model, then, we are comfortable drawing inference from key moments—including the OP covariance for labor productivity— along the plausible range of adjustment costs. We elaborate further on strengths and limitations of the OP decomposition below. F. The Olley-Pakes decomposition and covariance While we show above that the OP covariance is declining in adjustment costs over plausible parameterizations, additional doubts about its usefulness may arise from limitations of the accounting-based decomposition on which it is based (Levinsohn and Petrin (2003); Petrin, White, and Reiter (2011); Hsieh and Klenow (2017)). We do not formally use the OP covariance in any of our empirical analysis but instead use diff-in-diff counterfactuals. However, it is instructive to compare and contrast our diff-in-diff counterfactuals with the OP covariance. The OP productivity decomposition is given by:52 51F 52 In empirical work, it is common to use a weighted average of log firm-level productivity to avoid index number problems. We use the weighted average of firm-level productivity here to highlight that under CRTS and pricetaking behavior that this weighted average is equal to aggregate productivity. Empirical implementation still requires addressing the index number problems. 51

𝑂𝑂𝑂𝑂 𝐴𝐴𝑒𝑒 = �𝜃𝜃𝑒𝑒𝑒𝑒𝐴𝐴𝑒𝑒𝑒𝑒 = 𝐴𝐴̅𝑒𝑒 +𝑐𝑐𝑜𝑜𝑐𝑐(𝜃𝜃𝑒𝑒𝑒𝑒,𝐴𝐴𝑒𝑒𝑒𝑒) where is the Olley-Pakes concep𝑓𝑓t of industry aggregate productivity, is the employment 𝑂𝑂𝑂𝑂 share o 𝐴𝐴 f 𝑒𝑒firm , is productivity of firm , is (unweighted) average p 𝜃𝜃 r𝑒𝑒o𝑒𝑒ductivity for the industry, and 𝑓𝑓 𝐴𝐴𝑒𝑒𝑒𝑒 is the OP covar 𝑓𝑓 ian 𝐴𝐴 c̅e𝑒𝑒 (which is proportional to true covariance). Defin 𝑐𝑐 e 𝑜𝑜 a 𝑐𝑐 g ( g 𝜃𝜃 r𝑒𝑒e𝑒𝑒g , a 𝐴𝐴 te𝑒𝑒 𝑒𝑒p ) roductivity as , that is, aggregate output divided by aggregate employment. A critical questio 𝐴𝐴 n𝑒𝑒 is = h 𝑄𝑄 ow𝑒𝑒/ 𝑙𝑙 w𝑒𝑒ell matches ; a related question is 𝑂𝑂𝑂𝑂 how to interpret the quantitative variation in the OP cova 𝐴𝐴 r𝑒𝑒iance term. 𝐴𝐴 C𝑒𝑒ontinuing with our model, characterized by constant returns to scale but potentially imperfect competition,53 note 52F that aggregate output is given by: 1 𝜑𝜑 𝜑𝜑 𝑄𝑄𝑒𝑒 = ��𝑄𝑄𝑓𝑓𝑒𝑒� where . Aggregate productivity is as follo𝑓𝑓ws: 𝜑𝜑 ≤ 1 1 𝜑𝜑 𝜑𝜑 𝑄𝑄𝑒𝑒 �∑𝑓𝑓𝐴𝐴𝑒𝑒𝑒𝑒𝑙𝑙𝑒𝑒𝑒𝑒� It is straightforward to see that if 𝐴𝐴𝑒𝑒 =, th 𝑙𝑙 a𝑒𝑒t =is, perfe 𝑙𝑙 ct𝑒𝑒 competition, aggregate output of the final good is simply the sum of firm-level output, and the OP decomposition measures aggregate 𝜑𝜑 = 1 productivity exactly: 𝑄𝑄𝑒𝑒 ∑𝑓𝑓𝐴𝐴𝑓𝑓𝑒𝑒𝑙𝑙𝑓𝑓𝑒𝑒 𝑂𝑂𝑂𝑂 𝐴𝐴𝑒𝑒 = = = �𝐴𝐴𝑓𝑓𝑒𝑒𝜃𝜃𝑓𝑓𝑒𝑒 = 𝐴𝐴𝑒𝑒 In this case the size distribution ca𝑙𝑙n 𝑒𝑒 only be𝑙𝑙 𝑒𝑒 determine𝑓𝑓d in the presence of frictions; but the OP covariance term’s effect on aggregate productivity is intuitive since the firm with the highest average productivity also has the highest marginal productivity. Moving resources to the most productive firm will always increase aggregate productivity (this inference is robust to a model with multiple inputs). The key is that with CRTS and perfect competition, the marginal revenue product of a firm does not change with scale but only varies with TFPQ. 53 A broader interpretation of our simple model is that the revenue function curvature reflects either (or both) imperfect competition or decreasing returns to scale. The effects of either on the accuracy of the OP decomposition are similar, so we proceed in this subsection with a focus on the imperfect competition. 52

For , however, aggregate productivity is no longer equal to the OP weighted average of firm productivity. Moreover, it is no longer the case that continually moving 𝜑𝜑 < 1 resources to the most-productive firm (in terms of average productivity) will increase aggregate productivity. This is because with , as resources are moved to the most productive firms marginal revenue products rise for the least productive firms and fall for the most productive 𝜑𝜑 < 1 firms. This implies that with the OP weighted average of firm productivity declines more rapidly with an increase in adjustment costs than does aggregate productivity. Intuitively, 𝜑𝜑 < 1 revenue function curvature (i.e., low or declining ) dampens the marginal responsiveness of firms to their TFP realizations relative to linear revenue, or (which, in unreported results, 𝜑𝜑 we verify in our model); the OP covariance declines too quickly as adjustment costs rise because 𝜑𝜑 = 1 it implicitly assumes extremely high optimal TFP responsiveness To overcome this limitation of the OP covariance measure, in our empirical analysis we rely instead on a diff-in-diff counterfactual (equation (5) in the text) given by: 𝑒𝑒+1 𝑇𝑇 𝑁𝑁𝑇𝑇 Δ𝑒𝑒 = �(𝜃𝜃𝑒𝑒,𝑒𝑒+1 −𝜃𝜃𝑒𝑒,𝑒𝑒+1)𝑎𝑎𝑒𝑒𝑒𝑒 This diff-in-diff counterfactual isolates the𝑓𝑓 impact of changing responsiveness on the weighted mean holding everything else constant. In particular, this diff-in-diff object implicitly relies on estimated policy functions that reflect optimal growth responses of firms to their productivity draws and initial size, taking the degree of revenue curvature as given and therefore implicitly acknowledging that equalization of marginal products is the driving force behind labor adjustment. As such, the diff-in-diff object more accurately tracks changes in aggregate productivity than does the raw OP covariance, which relies on linear revenue function assumptions and therefore sees all movement of labor toward high-productivity firms as productivity enhancing. Conveniently, this diff-in-diff object can be easily constructed empirically, with the main source of error being estimation error inherent in the process of using OLS to estimate nonlinear policy functions. Figure B6 illustrates how aggregate productivity, the OP covariance using TFPQ and the diff-in-diff counterfactuals using either TFPQ or RLP (equivalent to TFPR in the one-factor model) evolve as adjustment costs rise. Consistent with the discussion above, as adjustment costs rise, aggregate productivity declines less rapidly than the OP covariance. In contrast, the diff-in-diff counterfactuals track aggregate productivity very closely. In unreported results, we 53

have shown that the properties of Figure B6 are robust to alternative values of . In particular, the close quantitative correspondence between changes in aggregate productivity and the diff-in- 𝜑𝜑 diff counterfactuals is robust to alternative values of One might ask why we do not simply quantify changes in aggregate (industry) 𝜑𝜑 < 1. productivity in our empirical analysis. The reason is that simple comparisons cannot isolate the change in aggregate productivity that is due specifically to changing adjustment frictions and slowing reallocation. Our diff-in-diff counterfactual achieves this objective and, since it relies on actual (estimated) firm policy functions, is reasonably robust to the parameters of the economic environment. 54

Figure B1: Responses of key moments to changes in adjustment costs Note: The x axis reflects values of , or the cost of reducing employment, holding the hiring cost fixed at . General equilibrium model with flexible wage and inelastic labor supply. 𝑙𝑙− 𝑙𝑙+ 𝑙𝑙+ = F 0. i 8 g 5 ure B2: Responses of OP covariances to changes in adjustment costs Note: The x axis reflects values of , or the cost of reducing employment, holding the hiring cost fixed at . General equilibrium model with flexible wage and inelastic labor supply. 𝑙𝑙− 𝑙𝑙+ 𝑙𝑙+ = F 0. i 8 g 5 ure B3: Responses of key moments to changes in TFP dispersion Note: Model with kinked adjustment costs ( ). General equilibrium model with flexible wage and inelastic labor supply. 𝑙𝑙+ =0.85,𝑙𝑙− =0 55

Figure B4: Responses of key moments to changes in adjustment costs from frictionless benchmark Note: Model with no upward or downward adjustment costs ( ) with varying downward adjustment costs ( ) indicated on the x axis. General equilibrium model with flexible wage and inelastic labor supply. 𝑙𝑙+ =0 𝑙𝑙− Figure B5: Responses of OP covariances to changes in adjustment costs from frictionless benchmark Note: Model with no upward adjustment costs ( ) with varying downward adjustment costs ( ) indicated on the x axis. General equilibrium model with flexible wage and inelastic labor supply. 𝑙𝑙+ =0 𝑙𝑙− Figure B6: Response of Diff-in-Diff Counterfactuals to Increase in Adjustment Costs 1 0.9 0.8 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Downsizing Cost F_ Aggregate Productivty OP Covariance (TFP) Diff-in-Diff TFP Diff-in-Diff RLP Note: The x axis reflects values of , or the cost of reducing employment, holding the hiring cost fixed at . General equilibrium model with flexible wage and inelastic labor supply. 𝑙𝑙 − 𝑙𝑙+ 𝑙𝑙+ = 0.85 56

Appendix C. Alternative TFP calculation While our TFPR measure as a measure of TFP is common in related literature, as we discus in the main text we also consider an estimate of RPR using the proxy method of Wooldridge (2009). As we show in equation (3), RPR is only a function of exogenous TFPQ and demand shocks (even if plant-level prices are endogenous) because the elasticities recovered by revenue function estimation are revenue elasticities (not factor elasticities) capturing both production and demand parameters (Foster et al. (2017)). In this appendix, we discuss the estimation of RPR and the results using the RPR measure of TFP. Given the possible presence of demand shocks, RPR should be interpreted as reflecting both TFPQ and demand shocks. Foster et al. (2017) find that the Woolridge residuals are sensitive to outliers; pooling across a large number of observations mitigates this sensitivity, so we estimate revenue elasticities that vary at the 3-digit NAICS level.54 After estimating the elasticities, we compute 53F the revenue productivity residuals and deviate the latter from 6-digit NAICS industry by year means. We find that has a correlation of 0.76 with . We replicate o 𝑅𝑅 u 𝑙𝑙 r 𝑅𝑅 m𝑒𝑒a𝑒𝑒in empirical exercises replacing 𝑙𝑙 𝑙𝑙 T 𝑙𝑙 F 𝑅𝑅 PR𝑒𝑒𝑒𝑒 with RPR. Figure C1 shows the evolution of within-industry dispersion in for manufacturing plants. Consistent with Figure 4, we observe gradually rising RPR dis 𝑅𝑅 pe 𝑙𝑙 r 𝑅𝑅 si𝑒𝑒o𝑒𝑒n throughout the time period, with higher dispersion in high-tech than elsewhere. Figure C2 reports AR(1) coefficients for plant-level RPR (see note to Figure A4 in appendix A for a discussion of this measure and its limitations in our dataset). Again, RPR results are consistent with TFPR results, confirming that changes in the TFP distribution cannot explain aggregate job reallocation patterns. We estimate equation (4) using RPR in place of TFP. Figure C3 reports growth differentials (between the plant with productivity one standard deviation above its industry mean and the mean) as discussed in the main text. The results are generally consistent with those reported for TFP on Figure 5, with young firm productivity responsiveness in high-tech that rises from the 1980s to the 1990s then falls in the 2000s. Among mature firms in high-tech, 54 The cost share-based TFPR measure we use in the main text is constructed with cost shares that vary at the 4-digit SIC level prior to 1997 and the 6-digit NAICS level thereafter. The instability and outlier sensitivity of the RPR elasticity estimates precludes this level of detail. The cost share-based TFPR method therefore allows for more flexibility in elasticity values implying a better fit in detailed industries, while the RPR method avoids problems of price endogeneity and isolates exogenous TFPQ and demand shocks. This tradeoff is the reason we ensure robustness of our exercises to both productivity concepts. 57

responsiveness is somewhat flat from the 1980s to the 1990s before falling markedly in the 2000s. Finally, Figure C4 reports the diff-in-diff counterfactual described by equation (5). Among high-tech plants, declining responsiveness produces a counterfactual that is broadly similar—both qualitatively and quantitatively—with the TFPR-based results from Figure 6, with a productivity “drag” that is only slightly smaller under RPR than under TFPR. Among non-tech plants, the counterfactual produces somewhat different results from those reported in Figure 6, with a gap opening up early in the sample then remaining stable (and negative) after the late 1990s. In general the RPR results confirm the TFP-based findings suggesting a quantitatively significant change in the contribution of reallocation to aggregate productivity growth. We conduct an additional robustness check addressing the concerns of Gandhi et al. (2016), who argue that if some factors are completely variable then the Wooldridge (2009) and related proxy methods may not be not identified. Ackerberg, Caves, and Frasier (2015) offer guidance about when their (and the equivalent Wooldridge (2009)) method is identified;55 54F however, as a robustness check we consider a hybrid method that estimates revenue elasticities for materials and energy (the factors most likely to be completely variable) using non-parametric methods in a first step. In practice, this amounts to using the means of the revenue cost shares of materials and energy to estimate the revenue elasticities. Then the Wooldridge (2009) method is used to estimate the revenue elasticities for labor and capital in a second step. We do not report this robustness exercise for the sake of brevity, but the results are quite similar to those we report for RPR. This is not surprising since this hybrid measure yields an RPR measure with a correlation of 0.94 with the RPR measure estimated using the Wooldridge (2009) procedure that we describe above. The standard deviation of the two alternative RPR measures (sweeping out industry-by-year effects) are both about 0.41. 55 If input prices of variable factors are serially correlated then this is one way that the ACF and Wooldridge estimators are still identified. 58

Figure C1: Within-industry dispersion in RPR (standard deviation), manufacturing Note: The standard deviation is the based on within-detailed industry log revenue productivity residual. High-tech is defined as in Hecker (2005). Manufacturing is defined on a consistent NAICS basis. Author calculations from the Longitudinal Business Database, the Annual Survey of Manufacturers, and the Census of Manufacturers. HP trends. Figure C2: Persistence of plant-level RPR: High-tech vs. non-tech 1 High tech Non-tech 0.8 0.6 0.4 0.2 0 1980s 1990s 2000s Note: High-tech is defined as in Hecker (2005). Author calculations from the Longitudinal Business Database, the Annual Survey of Manufacturers, and the Census of Manufacturers. Figure C3: Relative employment growth rates, high-productivity vs. average-productivity plant (RPR) 0.12 1980s 0.10 1990s 0.08 2000s 0.06 0.04 0.02 0.00 Tech young Tech mature Non-tech young Non-tech mature Note: Young firms have age less than 5. High-tech is defined as in Hecker (2005). Author calculations from the Longitudinal Business Database, the Annual Survey of Manufacturers, and the Census of Manufacturers. 59

Figure C4: Diff-in-diff counterfactual (RPR productivity), manufacturing Note: Figure depicts diff-in-diff counterfactual as described in the text. High-tech is defined as in Hecker (2005). Author calculations from the Longitudinal Business Database, the Annual Survey of Manufacturers, and the Census of Manufacturers. 60

Appendix D. Changing Business Models in Manufacturing A. Investment As noted in the text, Table 2 and Figure 5 report our standard responsiveness regression using establishment investment rates as the dependent variable in place of employment growth. We include the capital stock as an additional state variable in these regressions; we do not include the capital stock in our main employment growth regressions, but in unreported exercises we find our main results are robust to its inclusion. The timing is slightly different for equipment investment as opposed to the employment growth specifications: in the employment growth specifications, we measure growth from March of t to March of t+1 as a function of size in March t and productivity for year t. In the investment specification, we measure investment throughout year t as a function of size in March t, productivity for year t, and capital stock at the beginning of year t. Consistent with standard models, we have in mind a time-to-build assumption that investment during period t contributes to capital used during period t+1, which means the difference in timing from the employment growth regressions is not large. Moreover, our model exercises in Appendix B suggest that our theoretical framework is not heavily dependent on specific timing concerns. B. Globalization Globalization may be playing a role in declining responsiveness since increased exposure to foreign trade facilitates adjustment by scaling international operations. That is, it may be that rather than growing domestically, productive firms are more likely to expand and produce in other countries, a dynamic that could eliminate or even reverse the standard positive correlation between growth and productivity (since we do not observe employment outside the U.S.). There is substantial evidence already that the decline in US manufacturing employment is closely linked to rising import penetration of production activity from low wage countries (see, e.g., Bernard, Jensen, and Schott (2006), Schott (2008) and Pierce and Schott (2016)). Bernard, Jensen and Schott (2006) and Schott (2008) develop measures of import penetration ratios from low wage countries. Their measures vary by 4-digit SIC industry from 1972-2005 and by 6-digit NAICS industry from 1989-2005; we extend the time series using the public domain information from Census on imports by country and industry.56 We integrate 55F 56 To construct low-wage import penetration data by year and industry, Bernard, Jensen and Schott first construct domestic absorption for each industry. Next, they construct total imports of goods produced by each industry that are 61

these public domain data into our data infrastructure from 1981-2010. Our ability to integrate this is facilitated by our having 4-digit SIC codes in the micro level data from 1981-1996 and 6digit NAICS codes from 1981-2010; hence, we need not rely on aggregate SIC/NAICS concordances.57 Figure D1 shows aggregate import penetration ratios in and out of high-tech 56F manufacturing. Table D1 presents results of a modified version of our main regressions in equation (3). The additional regressors added are the 6-digit NAICS import penetration ratio for each year and the interaction of this ratio with lagged TFP. We permit the coefficients on this interaction effect to differ between plants belonging to young and mature firms. The main effect of the import penetration (not reported) is negative and significant: Consistent with Bernard, Jensen, and Schott (2006), plants in industries with especially large increases in import penetration have lower net employment growth. The last two rows of Table D1 show that the interaction effect for young plants of lagged TFP and the import penetration ratio is estimated to be negative and significant. This implies that young-firm plants in industries with especially large increases in import penetration ratios have larger decreases in responsiveness. In Figure D2, we quantify the effect of changing import penetration ratios using the estimated effects from Table D1. The overall effects show, consistent with Table 1, that the marginal effect of productivity on employment growth among young high-tech firms increased from the 1980s to 1990s then declined in the post-2000 period. We compute the fraction of these patterns accounted for by the changing import penetration ratios by using the coefficients from Table D1 along with the aggregate pattern of import penetration ratios for high-tech manufacturing. The role of rising penetration is very modest in the 1980s to 1990s. However, the rapid rise in import penetration during the 2000s accounts for a substantial share (about 16 percent) of the overall decline in responsiveness over that period. We also perform these analyses using the Wooldridge (2009) RPR productivity measure (unreported), finding no significant role for import penetration, so we consider this evidence mixed. More research on globalization and dynamism is needed; promising avenues include sourced in a low-wage country, which are defined as countries whose GDP per capita is less than 5 percent of the U.S. Import penetration is the ratio of low-wage imports to total domestic absorption, by industry and year. We thank Peter Schott for providing the import data and guidance necessary for extending the dataset. 57 We integrate the SIC-based import penetration ratios from 1981-88 and the NAICS-based ratios from 1989-2010 into the micro data. We use the internally consistent NAICS codes in the micro data from 1981-2010 to conduct our analysis. (see Fort and Klimek (2016)). 62

specific policy variation, distinction between intermediate and final goods competition, and differences between TFP concepts. C. Composition Effects In the high-tech manufacturing sector, another possible cause of declining productivity responsiveness after 2000 is the transition from “general-purpose” to “special-purpose” equipment manufacturing in the U.S documented by Byrne (2015).58 Perhaps manufacturers of 57F special-purpose products are less responsive to productivity shocks due to demand constraints or uncompetitive environments that reduce adjustment imperatives. Figure D3 shows that during the 1990s the share of employment in among general purpose technology producers grew rapidly but, consistent with Byrne (2015) (who examined revenue shares), the general purpose share has fallen substantially since the late 1990s. Given these compositional changes, it is possible that changing average responsiveness reflects differential responsiveness across industries. We estimate equation (4) separately for each 6-digit industry in high-tech manufacturing but, importantly, we omit time trend interactions from the specification. With the estimated responsiveness coefficients for each 6-digit industry, we compute the employment-weighted aggregate responsiveness in each year using the actual annual 6-digit employment weights.59 If 58F any industry composition effect—including the shift between general and special purpose electronics—is driving our results, we should see these aggregated responsiveness patterns mimicking the result from Figure 5. Figure D4 shows the implied changing responsiveness over time due to composition effects within high-tech manufacturing. There is no implied increase in responsiveness due to composition effects from the 1980s to the 1990s (which would have been expected if generalpurpose producers were more responsive on average), and there is actually a modest increase in responsiveness from the 1990s to the 2000s rather than a decline. Declining responsiveness must therefore be a within-category phenomenon with respect to the general-purpose/special-purpose taxonomy and other industry characteristics. 58 We thank Christopher Foote for this insight. 59 We use employment weights given our interest in the implications of changing responsiveness for job reallocation. 63

Figure D1: Import penetration ratios from low-wage countries Source: Extended versions of Import Penetration Ratios from Bernard, Jensen and Schott (2006) and Schott (2008). Reported statistics are averages across 6-digit NAICS industries for high-tech and non-tech industries. Figure D2: The role of globalization in changing responsiveness (high-tech Manufacturing) Note: “Overall” bars for young and mature are the change in marginal responsiveness of employment growth to productivity across decades. Globalization reflects implied change in marginal responsiveness accounted for by changes in import penetration ratios from low wage countries. Figure D3: General purpose technology share of high-tech Manufacturing 0.50 0.40 0.30 0.20 0.10 0.00 Note: Tabulations from the LBD by authors. General purpose high-tech 4-digit industries are NAICS 3341 (Computers), NAICS 3342 (Communication Equipment) and NAICS 3344 (Semiconductors). 64

Figure D4: Change in responsiveness due to industry composition changes (high-tech) 0.40 1980s 0.35 1990s 0.30 0.25 2000s 0.20 0.15 0.10 0.05 0.00 Young Mature Note: Specification (2) as in Table 1 estimated for every 6-digit NAICS industry but without any trend effects. Reported coefficients are employment-weighted averages of the 6-digit NAICS industry estimated coefficients. Employment-weights vary by year. Table D1: Employment growth, lagged productivity, and import penetration TFP*Young 0.2085*** (0.0390) TFP*Young*Trend 0.0298*** (0.0061) TFP*Young*Trend2 -0.0011*** (0.0002) TFP*Mature 0.1246*** (0.0174) TFP*Mature*Trend 0.0052** (0.0026) TFP*Mature*Trend2 -0.0003*** (0.0001) TFP*Young*Import Penetration -0.0037*** (0.0011) TFP*Mature*Import Penetration 0.0002 (0.0004) Notes: Standard Errors in Parentheses. High-tech sample used. See notes to Table 1. Young firms have age less than 5. Unreported are estimates of controls including year effects, state effects, firm age dummies, firm size dummies, log plant level employment in period t, state cyclical indicators (change in state level unemployment rate), state cyclical indicators interacted with TFP, and a main effect for the 6-digit import penetration ratio. All variables that use TFP including all interactions are fully interacted with firm age dummies. * p < 0.1, ** p < 0.05, *** p < 0.01. 65