Measuring science: An exploration

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Abstract
This paper examines the available United States data on academic research and development (R&D) expenditures and the number of papers published and the number of citations to these papers as possible measures of "output" of this enterprise. We look at these numbers for science and engineering as a whole, for five selected major fields, and at the individual university field level. The published data in Science and Engineering Indicators imply sharply diminishing returns to academic R&D using published papers as an "output" measure. These data are quite problematic. Using a newer set of data on papers and citations, based on an "expanding" set of journals and the newly released Bureau of Economic Analysis R&D deflators, changes the picture drastically, eliminating the appearance of diminishing returns but raising the question of why the input prices of academic R&D are rising so much faster than either the gross domestic product deflator or the implicit R&D deflator in industry. A production function analysis of such data at the individual field level follows. It indicates significant diminishing returns to "own" R&D, with the R&D coefficients hovering around 0.5 for estimates with paper numbers as the dependent variable and around 0.6 if total citations are used as the dependent variable. When we substitute scientists and engineers in place of R&D as the right-hand side variables, the coefficient on papers rises from 0.5 to 0.8, and the coefficient on citations rises from 0.6 to 0.9, indicating systematic measurement problems with R&D as the sole input into the production of scientific output. But allowing for individual university field effects drives these numbers down significantly below unity. Because in the aggregate both paper numbers and citations are growing as fast or faster than R&D, this finding can be interpreted as leaving a major, yet unmeasured, role for the contribution of spillovers from other fields, other universities, and other countries.