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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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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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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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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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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Capital-Energy Substitution Revisted: New Evidence From Micro Data
April 1997
Working Paper Number:
CES-97-04
We use new micro data for 11,520 plants taken from the Census Bureau=s 1991 Manufacturing Energy Consumption Survey (MECS) and 1991 Annual Survey of Manufactures (ASM) to estimate elasticities of substitution between energy and capital. We found that energy and capital are substitutes. We also found that estimates of Allen elasticities of substitution -- which have been used as a standard measure of substitution -- are sensitive to varying data sets and levels of aggregation. In contrast, estimates of Morishima elasticities of substitution -- which are theoretically superior to the Allen elasticities -- are more robust (except when two-digit level data are used). The results support the views that (i) the Morishima elasticity is a better measure of factor substitution and (ii) micro data provide more accurate elasticity estimates than those obtained from aggregate data. Our findings appear to resolve the long-standing conflict among the estimates reported in the many previous studies regarding energy-capital substitution/complementarity.
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Capital Investment and Labor Demand
February 2022
Working Paper Number:
CES-22-04
We study how bonus depreciation, a policy designed to lower the cost of capital, impacted investment and labor demand in the US manufacturing sector. Difference-in-differences estimates using restricted-use US Census Data on manufacturing establishments show that this policy increased both investment and employment, but did not lead to wage or productivity gains. Using a structural model, we show that the primary effect of the policy was to increase the use of all inputs by lowering overall costs of production. The policy further stimulated production employment due to the complementarity of production labor and capital. Supporting this conclusion, we nd that investment is greater in plants with lower labor costs. Our results show that recent policies that incentivize capital investment do not lead manufacturing plants to replace workers with machines.
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Factor Substitution In U.S. Manufacturing: Does Plant Size Matter
April 1998
Working Paper Number:
CES-98-06
We use micro data for 10,412 U.S. manufacturing plants to estimate the degrees of factor substitution by industry and by plant size. We find that (1) capital, labor, energy and materials are substitutes in production, and (2) the degrees of substitution among inputs are quite similar across plant sizes in a majority of industries. Two important implications of these findings are that (1) small plants are typically as flexible as large plants in factor substitution; consequently, economic policies such energy conservation policies that result in rising energy prices would not cause negative effects on either large or small U.S. manufacturing plants; and (2) since energy and capital are found to be substitutes; the 1973 energy crisis is unlikely to be a significant factor contributing to the post 1973 productivity slowdown. of Substitution
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Business Dynamics Statistics of High Tech Industries
January 2016
Working Paper Number:
CES-16-55
Modern market economies are characterized by the reallocation of resources from less productive, less valuable activities to more productive, more valuable ones. Businesses in the High Technology sector play a particularly important role in this reallocation by introducing new products and services that impact the entire economy. Tracking the performance of this sector is therefore of primary importance, especially in light of recent evidence that suggests a slowdown in business dynamism in High Tech industries. The Census Bureau produces the Business Dynamics Statistics (BDS), a suite of data products that track job creation, job destruction, startups, and exits by firm and establishment characteristics including sector, firm age, and firm size. In this paper we describe the methodologies used to produce a new extension to the BDS focused on businesses in High Technology industries.
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