Research Scientist Productivity and Firm Size: Evidence from Panel Data on Inventors

It has long been recognized that worker wages and possibly productivity are higher in large firms. Moreover, at least since Schumpeter (1942) economists have been interested in the relative efficiency of large firms in the research and development enterprise. This paper uses longitudinal worker-firm-matched data to examine the relationship between the productivity of workers specifically engaged in innovation and firm size in the pharmaceutical and semiconductor industries. In both industries, we find that inventors’ productivity increases with firm size. This result holds across different specifications and even after controlling for inventors’ experience, past productivity, the quality of other inventors in the firm, and other firm characteristicsPatents; Innovation; Labor productivity; Research; Firm size

Research Scientist Productivity and Firm Size: Evidence from Panel Data on Investors

It has long been recognized that worker wages and possibly productivity are higher in large firms. Moreover, at least since Schumpeter (1942) economists have been interested in the relative efficiency of large firms in the research and development enterprise. This paper uses longitudinal worker-firm-matched data to examine the relationship between the productivity of workers specifically engaged in innovation and firm size in the pharmaceutical and semiconductor industries. In both industries, we find that inventors' productivity increases with firm size. This result holds across different specifications and even after controlling for inventors' experience, education, the quality of other inventors in the firm, and other firm characteristics. We find evidence in the pharmaceutical industry that this is partly accounted for by differences between how large and small firms organize R&D activities.Patents; Innovation; Labor productivity; Research; Firm size

International Knowledge Flows: Evidence from an Inventor-Firm Matched Data Set

We describe the construction of a panel data set from the U.S. patent data that contains measures of inventors' life-cycle R&D productivity--patents and patent citations. We match the data set to information on the U.S. pharmaceutical and semiconductor firms for whom they work. In this paper we use these data to examine the role of research personnel as a pathway for the diffusion of ideas from foreign countries to U.S. innovators. In particular, we find in recent years an increase in the extent that U.S. innovating firms collaborate with or employ researchers with foreign experience. This increase appears to work primarily through an increase in U.S. firms' employment of foreign-residing researchers; the fraction of research-active U.S. residents with foreign research experience appears to be falling, suggesting that U.S. pharmaceutical and semiconductor firms are increasingly locating operations in foreign countries to employ such researchers, as opposed to such researchers immigrating to the U.S. to work. In addition, we investigate which U.S. firms conducting R&D build upon innovations originating abroad. We find that employing or collaborating with researchers who have research experience abroad seems to facilitate the use of output of non-U.S. R&D. We also find that in the semiconductor industry smaller and older firms, and in the pharmaceutical industry, younger firms are more likely to access foreign R&D output.

The Influence of University Research on Industrial Innovation

We use U.S. patent records to examine the role of research personnel as a pathway for the diffusion of ideas from university to industry. Appearing on a patent assigned to a university is evidence that an inventor has been exposed to university research, either directly as a university researcher or through some form of collaboration with university researchers. Having an advanced degree is another indicator of an inventor's exposure to university research. We find a steady increase in industry's use of inventors with university research experience over the period 1985-97, economy wide and in the pharmaceutical and semiconductor industries in particular. We interpret this as evidence of growth in the influence of university research on industrial innovation. Moreover, during this period we find that firms with large research operations in both industries, and young and highly capitalized firms in the pharmaceutical industry, are disproportionately active in the diffusion of ideas from the university sector. Finally, we find that the patents of firms that employ inventors with university research experience are more likely to cite university patents as prior art, suggesting that this experience better enables firms to tap academic research.

Quasi-Limiting Behavior of Drifted Brownian Motion

A Quasi-Stationary Distribution (QSD)for a Markov process with an almost surely hit absorbing state is a time-invariant initial distribution for the process conditioned on not being absorbed by any given time. An initial distribution for the process is in the domain of attraction of some QSD $\nu$ if the distribution of the process a time $t$, conditioned not to be absorbed by time $t$ converges to $\nu$. In this work study mostly Brownian motion with constant drift on the half line $[0,\infty)$ absorbed at $0$. Previous work by Martinez et al. identifies all QSDs and provides a nearly complete characterization for their domain of attraction. Specifically, it was shown that if the distribution a well-defined exponential tail (including the case of lighter than any exponential tail), then it is in the domain of attraction of a QSD determined by the exponent. In this work we 1. Obtain a new approach to existing results, explaining the direct relation between a QSD and an initial distribution in its domain of attraction. 2. Study the behavior under a wide class of initial distributions whose tail is heavier than exponential, and obtain no-trivial limits under appropriate scaling.Comment: 32 pages, 4 figures, 2 tables. Updated Nov 18 2020 under the recommendation of anonymous referee (correcting errors, omitted references, etc.

Linear stability analysis of wake vortices by a spectral method using mapped Legendre functions

A spectral method using associated Legendre functions with algebraic mapping is developed for a linear stability analysis of wake vortices. These functions serve as Galerkin basis functions, capturing correct analyticity and boundary conditions for vortices in an unbounded domain. The incompressible Euler or Navier-Stokes equations linearised on a swirling flow are transformed into a standard matrix eigenvalue problem of toroidal and poloidal streamfunctions, solving perturbation velocity eigenmodes with their complex growth rate as eigenvalues. This reduces the problem size for computation and distributes collocation points adjustably clustered around the vortex core. Based on this method, strong swirling $q$-vortices with linear perturbation wavenumbers of order unity are examined. Without viscosity, neutrally stable eigenmodes associated with the continuous eigenvalue spectrum having critical-layer singularities are successfully resolved. The inviscid critical-layer eigenmodes numerically tend to appear in pairs, implying their singular degeneracy. With viscosity, the spectra pertaining to physical regularisation of critical layers stretch out toward an area, referring to potential eigenmodes with wavepackets found by Mao & Sherwin (2011). However, the potential eigenmodes exhibit no spatial similarity to the inviscid critical-layer eigenmodes, doubting that they truly represent the viscous remnants of the inviscid critical-layer eigenmodes. Instead, two distinct continuous curves in the numerical spectra are identified for the first time, named the viscous critical-layer spectrum, where the similarity is noticeable. Moreover, the viscous critical-layer eigenmodes are resolved in conformity with the $Re^{-1/3}$ scaling law. The onset of the two curves is believed to be caused by viscosity breaking the singular degeneracy.Comment: 53 pages, 21 figure

Airfoil Optimization using Design-by-Morphing

We present Design-by-Morphing (DbM), a novel design methodology applicable to creating a search space for topology optimization of 2D airfoils. Most design techniques impose geometric constraints and sometimes designers' bias on the design space itself, thus restricting the novelty of the designs created, and only allowing for small local changes. We show that DbM methodology does not impose any such restrictions on the design space and allows for extrapolation from the search space, thus granting truly radical and large search space with a few design parameters. In comparison to other shape design methodologies, we apply DbM to create a search space for 2D airfoils. We optimize this airfoil shape design space for maximizing the lift-over-drag ratio, $CLD_{max}$, and stall angle tolerance, $\Delta \alpha$. Using a bi-objective genetic algorithm to optimize the DbM space, it is found that we create a Pareto-front of radical airfoils exhibiting remarkable properties for both objectives