This paper studies factor usage in the R&D sector. I show that the usage of non-labor inputs in R&D is significant, and that their usage has grown much more rapidly than the R&D workforce. Using a standard growth decomposition applied to the aggregate idea production function, I estimate that at least 77% of idea growth since the early 1960s can be attributed to the growth of non-labor inputs in R&D. I demonstrate that a similar pattern would hold on the balanced growth path of a standard semi-endogenous growth model, and thus that the decomposition is not simply a by-product of rising research intensity. I then show that combining long-running differences in factor growth rates with non-unitary elasticities of substitution in idea production leads to a slowdown in idea growth whenever labor and capital are complementary. I conclude by estimating this elasticity of substitution and demonstrate that the results favor complimentarities.
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Growth is Getting Harder to Find, Not Ideas
April 2025
Working Paper Number:
CES-25-21
Relatively flat US output growth versus rising numbers of US researchers is often interpreted as evidence that "ideas are getting harder to find." We build a new 46-year panel tracking the universe of U.S. firms' patenting to investigate the micro underpinnings of this claim, separately examining the relationships between research inputs and ideas (patents) versus ideas and growth. Over our sample period, we find that researchers' patenting productivity is increasing, there is little evidence of any secular decline in high-quality patenting common to all firms, and the link between patents and growth is present, differs by type of idea, and is fairly stable. On the other hand, we find strong evidence of secular decreases in output unrelated to patenting, suggesting an important role for other factors. Together, these results invite renewed empirical and theoretical attention to the impact of ideas on growth. To that end, our patent-firm bridge, which will be available to researchers with approved access, is used to produce new, public-use statistics on the Business Dynamics of Patenting Firms (BDS-PF).
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Academic Science, Industrial R&D, and the Growth of Inputs
January 1993
Working Paper Number:
CES-93-01
This paper is a theoretical and empirical investigation of the connection between science, R&D, and the growth of capital. Studies of high technology industries and recent labor studies agree in assigning a large role to science and technology in the growth of human and physical capital, although direct tests of these relationships have not been carried out. This paper builds on the search approach to R&D of Evenson and Kislev (1976) to unravel the complex interactions between science, R&D, and factor markets suggested by these studies. In our theory lagged science increases the returns to R&D, so that scientific advance later feeds into growth of R&D. In turn, product quality improvements and price declines lead to the growth of industry by shifting out new product demand, perhaps at the expense of traditional industries. All this tends to be in favor of the human and physical capital used intensively by high technology industries. This is the source of the factor bias which is implicit in the growth of capital per head. Our empirical work overwhelmingly supports the contention that growth of labor skills and physical capital are linked to science and R&D. It also supports the strong sequencing of events that is a crucial feature of our model, first from science to R&D, and later to output and factor markets.
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Science, R&D, And Invention Potential Recharge: U.S. Evidence
January 1993
Working Paper Number:
CES-93-02
The influence of academic science on industrial R&D seems to have increased in recent years compared with the pre-World War II period. This paper outlines an approach to tracing this influence using a panel of 14 R&D performing industries from 1961-1986. The results indicate an elasticity between real R&D and indicators of stocks of academic science of about 0.6. This elasticity is significant controlling for industry effects. However, the elasticity declines from its level during the 1961-1973 subperiod, when it was 2.2, to 0.5 during the 1974-1986 subperiod. Reasons for the decline include exogenous and endogenous exhaustion of invention potential, and declining incentives to do R&D stemming from a weakening of intellectual property rights. The growth of R&D since the mid-1980s suggests a restoration of R&D incentives in still more recent times.
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Outsourced R&D and GDP Growth
March 2016
Working Paper Number:
CES-16-19
Endogenous growth theory holds that growth should increase with R&D. However coarse comparison between R&D and US GDP growth over the past forty years indicates that inflation scientific labor increased 2.5 times, while GDP growth was at best stagnant. The leading explanation for the disconnect between theory and the empirical record is that R&D has gotten harder. I develop and test an alternative view that firms have become worse at it. I find no evidence R&D has gotten harder. Instead I find firms' R&D productivity declined 65%, and that the main culprit in the decline is outsourced R&D, which is unproductive for the funding firm. This offers hope firms' R&D productivity and economic growth may be fairly easily restored by bringing outsourced R&D back in-house.
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Property Rights, Firm Size and Investments in Innovation: Evidence from the America Invents Act
May 2025
Working Paper Number:
CES-25-31
I analyze whether a change in patent systems differentially affects firm-level innovation investments at patent-valuing firms of different sizes. Using legally required, economically representative, U.S. Census Bureau microdata, I separate firms into groups based on a firm's response to a question asking it to rank the degree of patent importance to its business and firm-size. I then measure how firms' innovation inputs/outputs respond to the America Invents Act (AIA). Results show the AIA reduced innovation investments at smaller, patent-valuing firms while increasing innovation investments at larger, patent-valuing firms, highlighting differential firm-size effects of patent policy and policy's importance to investments.
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Are firm-level idiosyncratic shocks important for U.S. aggregate volatility?
January 2016
Working Paper Number:
CES-16-47
This paper assesses the quantitative impact of firm-level idiosyncratic shocks on aggregate volatility in the U.S. economy and provides a microfoundation for the negative relationship between firm-level volatility and size. I argue that the role of firm-specific shocks through the granular channel plays a fairly limited role in the U.S. economy. Using a novel, comprehensive data set compiled from several sources of the U.S. Census Bureau, I find that the granular com-ponent accounts at most for 15.5% of the variation in aggregate sales growth which is about half found by previous studies. To bridge the gap between previous findings and mine, I show that my quantitative results require deviations from Gibrat's law in which firm-level volatility and size are negatively related. I find that firm-level volatility declines at a substantially higher rate in size than previously found. Hence, the largest firms in the economy cannot be driving a sub-stantial fraction of macroeconomic volatility. I show that the explanatory power of granularity gets cut by at least half whenever the size-variance relationship, as estimated in the micro-level data, is taken into account. To uncover the economic mechanism behind this phenomenon, I construct an analytically tractable framework featuring random growth and a Kimball aggrega-tor. Under this setup, larger firms respond less to productivity shocks as the elasticity of demand is decreasing in size. Additionally, the model predicts a positive (negative) relationship between firm-level mark-ups (growth) and size. I confirm the predictions of the model by estimating size-varying price elasticities on unique product-level data from the Census of Manufactures (CM) and structurally estimating mark-ups using plant-level information from the Annual Survey of Manufactures (ASM).
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The Rising Returns to R&D: Ideas Are Not Getting Harder to Find
May 2025
Working Paper Number:
CES-25-29
R&D investment has grown robustly, yet aggregate productivity growth has stagnated. Is this because 'ideas are getting harder to find'? This paper uses micro-data from the US Census Bureau to explore the relationship between R&D and productivity in the manufacturing sector from 1976 to 2018. We find that both the elasticity of output (TFP) with respect to R&D and the marginal returns to R&D have risen sharply. Exploring factors affecting returns, we conclude that R&D obsolescence rates must have risen. Using a novel estimation approach, we find consistent evidence of sharply rising technological rivalry. These findings suggest that R&D has become more effective at finding productivity-enhancing ideas but these ideas may also render rivals' technologies obsolete, making innovations more transient.
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The Intangible Divide: Why Do So Few Firms Invest in Innovation?
February 2025
Working Paper Number:
CES-25-15
Investments in software, R&D, and advertising have surged, nearing half of U.S. private nonresidential investment. Yet just a few hundred firms dominate this growth. Most firms, including large ones, regularly invest little in capitalized software and R&D, widening this 'intangible divide' despite falling intangible prices. Using comprehensive US Census microdata, we document these patterns and explore factors associated with intangible investment. We find that firms invest significantly less in innovation-related intangibles when their rivals invest more. One firm's investment can obsolesce rivals' investments, reducing returns. This negative pecuniary externality worsens the intangible divide, potentially leading to significant misallocation.
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The Rise of Specialized Firms
February 2024
Working Paper Number:
CES-24-06
This paper studies firm diversification over 6-digit NAICS industries in U.S. manufacturing. We find that firms specializing in fewer industries now account for a substantially greater share of production than 40 years ago. This reallocation is a key driver of rising industry concentration. Specialized firms have displaced diversified firms among industry leaders'absent this reallocation concentration would have decreased. We then provide evidence that specialized firms produce higher-quality goods: specialized firms tend to charge higher unit prices and are more insulated against Chinese import competition. Based on our empirical findings, we propose a theory in which growth shifts demand toward specialized, high-quality firms, which eventually increases concentration. We conclude that one should expect rising industry concentration in a growing economy.
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Corporate Share Repurchase Policies and Labor Share
February 2025
Working Paper Number:
CES-25-14
Using census data, we investigate whether share repurchases are responsible for the fall in labor share in U.S. corporations. Recent legislation imposes taxes on share repurchases, motivated by the assertion that share repurchases have led to reduced labor payments. Using several empirical approaches, we find no evidence that increases in share repurchases contribute to decreases in labor share. Top share repurchasing firms since 1982 did not decrease labor share. We also rely on exogenous changes in share repurchases around EPS announcements to pinpoint causality. Policies aimed at improving labor share by discouraging share repurchases will likely not achieve their objectives.
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