Propensity to Patent and Firm Size for Small R&D-Intensive Firms

Scott and Scott (2014) examine the Schumpeterian hypothesis about innovation rivalry in the context of Scherer’s foundational work.

Prominent examples include Link (1980), Bound et al. (1984), Pakes and Griliches (1984), and Acs and Audretsch (1988).

Here some prominent examples are Comanor (1967), Scherer (1983a, 1984b), Lunn and Martin (1986), Cohen and Klepper (1992, 1996a, b), and Cohen et al. (1987).

Schmookler (1966) advocates the use of patent statistics as a measure of research output. Griliches (1990) reviews patents as a measure of R&D output and observes (1990, pp. 1701–1702): “Among the major findings was the discovery of a strong relationship between patent numbers and R&D expenditures in the cross-sectional dimension, implying that patents are a good indicator of differences in inventive activity across different firms.” He also observes (1990, p. 1669): “The dream of getting hold of an output indicator of inventive activity is one of the strong motivating forces for economic research in this area…. One recognizes, of course, the presence of a whole host of problems: not all inventions are patentable, not all inventions are patented, and the inventions that are patented differ greatly in “quality,” in the magnitude of inventive output associated with them. The first two problems, one thinks, can be taken care of by industry dummy variables, or by limiting the analysis to a particular sector or industry. For the third, one tries to invoke the help of the “law of large numbers”: “The economic… significance of any sampled patent can also be interpreted as a random variable with some probability distribution” (Scherer 1965, p. 1098).” See also Comanor and Scherer (1969, p. 393) who observe that a patent’s “… underlying economic or technological significance can be interpreted as a random variable with some probability distribution” and use an examination of pharmaceutical manufacturing firms’ invention patents, R&D personnel, and the value of new product sales to ask “whether a simple count of the number of patents reflects only statistical noise or whether there is a meaningful message in the results”. They find support for a meaningful message in statistically significant correlations between patent counts and the employment of research personnel and the sales of new products.

In this paper, we study patents as a random count variable. Of importance for the issue of the quality of the counted patents is the distribution of the value of patents, where that value is a random variable. On the distribution of that value, see Harhoff et al. (1999), Scherer et al. (2000), and Harhoff et al. (2003); the ideas in these papers suggest that an interesting extension of the present paper would be to replace our patent counts for each R&D project with the use of quality-weighted patent counts, where quality is determined by the citations to the patents. We could then examine the effect of firm size on the elasticity of the quality of R&D output with respect to the R&D inputs.

That is fortunate, because, as William Comanor has emphasized to us in personal correspondence, what patent statistics actually measure is not at all clear, and rather than measuring research output, patenting may be an important intermediate step between R&D and innovation, and indeed may be a better measure of research input than of research output. In this paper we study the effect of firm size on R&D activity where the activity is measured by patenting. We think of patenting as an imperfect measure of research output, but the theory of how firm size affects R&D activity is valid whether or not patenting is thought of as a measure of innovative output or as an intermediate input in the innovation process.

Figure 1 in Kohn and Scott (1982, p. 247) shows R&D output on the horizontal axis, and thus depicts the marginal value and the marginal cost of the R&D output; in our empirical model, we measure that output with patents. However, as Kohn and Scott (1982, p. 246) explain, because the R&D output is an increasing function of the R&D input, the discussion can also be stated in terms of the R&D input, with R&D effort measured on the horizontal axis of Fig. 1. Thus, the Kohn and Scott theory that relates firm size to R&D activity applies equally well to R&D input as to R&D output. That is especially important because Comanor and Scherer (1969, p. 397) conclude that “it may be that patents are a better measure of research input than output.” Thus, although we interpret patents as a measure of R&D outputs, the theory by which we relate firm size to R&D activity holds equally well for explaining the relation of firm size to R&D inputs or to R&D outputs, and so our hypothesized relations hold if patents measure inputs rather than outputs.

Phase I awards are small and are intended to assist firms assess the feasibility of an idea’s scientific and commercial potential in response to the funding agency’s objectives and they generally last for 6-months. Phase II awards are focused on the initial steps toward commercialization, and they generally last for 2 years. Link and Scott (2012, pp. 19–32) provide a detailed description of the SBIR program and its Phase I and Phase II awards.

The scope of the NRC 2005 database was limited to Phase II SBIR awards by the largest five agencies that participated in the SBIR program. The other agencies are the Department of Defense (DoD), the National Institutes of Health (NIH), the National Aeronautics and Space Administration (NASA), and the National Science Foundation (NSF). Collectively, these five agencies funded 11,214 SBIR Phase II projects during the scope of the NRC study (1992 through 2001). Among those projects, DOE had 808 or 7.21% of the total number.

Link and Scott (2012, pp. 33–43, 128–130) provide detailed discussion and description of the NRC’s 2005 SBIR sampling strategy and the resulting samples and explain the data reduction process that resulted in the samples of projects from DoD, NIH, NASA, DOE, and NSF. Also Link and Scott (2012) estimate a Probit model of response to the NRC’s survey. The response model estimates well, with variables such as the project’s age and the number of Phase II awards that the firm had over the period from 1992 to 2001 being important for response.  However, for variables that describe the commercialization of the Phase II project’s results and for the patent variable that we use in the present paper, the correlation of the error in the model of response and in the model of substantive interest is low; consequently, response bias is not an issue. For an explanation of the absence of selection bias when the error in the equation that determines the sample selection is uncorrelated with the error in the equation of primary interest, see Greene (2012, pp. 872–876); for an example, see Link and Scott (2009, pp. 271, 274).

See note a of Table 1 in particular.

As with all agencies’ SBIR programs, DOE states (http://​science.​energy.​gov/​sbir/​about/​ accessed July 23, 2016) that it pursues the four legislated goals for the SBIR program: to stimulate technological innovation; use small business to meet Federal research and R&D needs; foster participation by small businesses that are socially and economically disadvantaged and those that are women-owned; and increase the commercialization of innovation that is derived from Federal support for R&D. For details of these legislated goals that all agencies’ SBIR programs address, see Link and Scott (2012, pp. 21–24); DOE’s particular emphasis is on technologies that address energy-related concerns such as environmental concerns of promoting clean, renewable energy. DOE emphasizes commercialization, which requires an evaluation of commercial potential in Phase I and Phase II applications. The Bayh-Dole Act (P. L. 96-517, Patent and Trademark Act Amendments of 1980) applies, and government grants then lead to privately held patents, although the DOE retains certain rights in those patents that allow it to license the technology. On the history, legislation, and implementation of Bayh-Dole, see Scherer (2009).

The Census assigns the primary category for many of these firms as “commercial physical research” (SIC 8731) or “research and development in the physical, engineering, and life sciences (except biotechnology)” (NAICS 541712). Others have portions of their firms that are devoted to such activity to expand their sales opportunities. The firms all use SBIR funding for their R&D project, but venture capital and other sources of capital are also used in some cases. Additional understanding of small, R&D-intensive, SBIR-supported firms, including their views about venture capital, is provided in case studies (e.g., see Wessner 2000, pp. 104–140, and the material there from discussions with the principals of the SBIR firms).

See the discussion in Kohn and Scott (1982, p. 248).

See Cohen (2010, pp. 183–185), and also see Henderson and Cockburn (1996, pp. 48–49) for a discussion and an illustration, in the context of their study of the pharmaceuticals industry, of the importance of controls for differences in technological opportunities when explaining patenting—in their case across different therapeutic classes (such as arthritis and related disorders as compared with anti-infectives). In Link and Scott (2013), we have shown that patents are important for the commercialization success (as measured by the firm’s employment growth that resulted because of the research project) of the small, research-intensive firms that participated in the SBIR program.

In addition to the Phase II SBIR award, the total investment funding for the R&D project includes non-SBIR federal funds, private investment funds (U.S. venture capital, foreign investment, other private equity, other domestic private company), other sources of funding including state or local governments and colleges or universities, any own company funding, including borrowed funds, and personal funds.

We follow the recommendation of Jankowski (1993, p. 204) and convert the nominal R&D expenditures for each sampled project to constant 2015 dollars by using the Gross National Product implicit price deflator (https://​fred.​stlouisfed.​org; accessed July 6, 2016).

We consider patent applications to be a better indication of the output developed in the projects of these small firms than patents received. Patent applications indicate results for which the firms considered intellectual property worthwhile and are not subject to the vagaries of the process of ultimately granting a patent. The two variables are similar in any case. For the 146 observations for which the data are available, the number of patents applications averaged 0.83 with standard deviation 1.62 and a range from 0 to 13; the number of patents received averaged 0.61 with a standard deviation of 1.19 and a range from 0 to 10.

Although the classification system is not good for defining meaningful industries, it is good for our purpose of assigning the projects to technology groups (see the discussion in footnote 4—we need to control for the differences in use and quality of patents across technologies). In addition to the technology area, Measuring and testing, left in the intercept, the technology areas to which the DOE SBIR projects have been assigned are listed in Table 4.

Of course, in some cases a firm will have founders with academic backgrounds and also founders with business backgrounds, and in such cases we anticipate the R&D projects would have characteristics that are associated with the human capital of each type of founder.

Of course, the variables PhI and PhII are highly correlated: Their correlation coefficient is 0.808. However, although all related Phase II projects are expected also to have Phase I projects that the firm would report as related, not all Phase I projects succeed and result in a Phase II project. Thus, using the two variables, we have the variance across projects in the number of related Phase I projects, given the number of related Phase II projects. The number of related Phase I projects can be much more for some of our observed R&D projects because of many failures of Phase I projects for each Phase II award won. In fact, as seen in the descriptive statistics of Table 3, for our sample’s R&D projects, the mean number of related Phase I projects is somewhat more than twice the mean number of related Phase II projects.

Instead of simply providing the descriptive statistics for only the 125 observations for which we have all of the variables needed for the estimation in Table 3, we have shown in Table 4 the descriptive statistics for the all of the observations for which the patent variable is available. The richness of the description of the sample thereby enabled comes with the cost of the intricate footnote to the table.

Note that the business founders—the owners—still have access and control in these small entrepreneurial firms. Indeed, in our experience interviewing the principals of SBIR firms, the founders often “wear all the hats” and are deeply involved of all aspects of the small firm’s operations.

There are many different ways that the small, SBIR firms use agreements with outside firms and financiers to exploit commercially their innovations. See Link and Scott (2012, pp. 91–102).

The technology effects as a whole are significant. The Wald test statistic against the null hypothesis that all of the effects are zero gives the Chi-squared statistic with 12 degrees of freedom = 1684.31 with the probability of a greater χ² = 0.0000.

In personal correspondence (July 22, 2016), F. M. Scherer observes that although—for our sample of small firms—this result is unlikely to have been caused by the presence of in-house lawyers (available in a sense at zero marginal cost), possibly the somewhat larger small firms have more experience with patent law and lawyers and hence bear a smaller psychological cost in applying for patents.

The literature has developed alternative ways to look at the count variable for patents in a model estimating elasticities, given that for many observations the number of patents is zero. For example, Bound et al. (1984, p. 39) observe that they want to include the zero observations in their estimation and will treat the issue in two ways.  One (p. 39) is to “set log patents to zero for all zero patent observations and allow those firms to have a separate intercept” in the regressions.  The other is (1984, p. 41): “Second, we model the patents properly as a counts (Poisson) variable, taking on values 1, 2, 3, etc…”  In our paper we use the negative binomial model, which is a generalization of the Poisson model. Bound et al. actually use the negative binomial because it is needed given the “overdispersion” present for the patent count variable.  Observe that with the formal treatment of the dependent variable as a count variable in the negative binomial (Poisson) context, there is no need to take the log of the zero observations.  Given the functional form of e ^x in a maximum likelihood estimation, the constant and the coefficients for the explanatory variables are chosen so that the “x” for the zero patent observations is sufficiently negative that the predicted patents can be close to zero and even essentially so if that outcome for the choice of the constant and other parameters maximizes the likelihood function. Scherer (1983a) provides another alternative—cubic equations, linear in the parameters estimated but nonlinear in the variables—that estimates the elasticities without the need to use the natural logarithms of the variables.

Recall from the discussion of the specification of Table 4 that the technology categories not included in the elasticity equation here did not have an effect on the relationship between firm size and the impact of R&D on patents.

Scherer (personal correspondence, July 22, 2016) has an insightful observation about the elasticities that we observe for our small firms: “I’m puzzled by the strong tendency toward diminishing R&D—patent returns, with elasticities in a range around 0.5.  I wonder if the following metaphor is plausible?  When one undertakes an SBIR project, one seems to be working on the technological and commercial working out of a particular idea. In a sense, one is doing R&D on a more or less bounded technological set, and when one applies more resources to a bounded objective, diminishing returns almost surely apply.  When on the other hand firms, large or small, decide what technological objectives they will pursue with their R&D, the set is virtually unbounded, and a tendency toward diminishing returns is much less compelling.   This could explain the difference between your results and my own earlier finding for samples of typically larger firms toward more or less constant returns.” We find the metaphor plausible, although we note also that Bound et al. (1984), discussed below, find essentially the same elasticities as ours for their small firm sample while observing their patenting and R&D at the level of the firm. Perhaps the R&D portfolios of their small firms are more like a focused R&D project than a collection of projects. See also the discussion in Griliches (1990, pp. 1674–1677) about the different elasticities for samples of small firms versus those for large firms. In particular, observe that we do not have the selection problem for our sample of small firms that Griliches discusses for the sample of small firms in Bound et al. (1984) where all of the small firms were successful in the sense that they were publicly traded firms, yet our elasticity estimates are essentially the same as the ones found there (and discussed by Griliches 1990, p. 1675) for the small firms.

This would be the case for R&D investments in process innovations if such innovations are more effectively used in-house by the firm—for example, because licensing or sale of the technology are less effective—and if smaller firms cannot grow to take advantage of a larger size when exploiting their innovations.

The inverted-U relationship here should not be confused with Scherer’s inverted-U in the relationship between R&D activity and seller concentration. For Scherer’s description—both the seminal theory and the seminal empirical observation—of that inverted-U, see Scherer (1967a, p. 530, b, pp. 391–392) and Scherer (1980, p. 437) with explicit reference to the “\( \cap \)-shaped relationship” at Scherer (1980, note 116, p. 437).

Scherer (1965, p. 1103) observes: “[T]he neo-Schumpeterian bigness contention receives greatest support when total employment is chosen as the scale measure and least when assets are chosen.” Scherer then uses the sales measure because of its more neutral characterization of firm size. As explained earlier, we use the employment measure of firm size because we can observe employment for our small R&D-intensive firms at the time of the proposal for the Phase II project—before any sales ultimately resulting from the project’s R&D output will be observed (and for many of our young entrepreneurial firms before they have established sales). The small firms in our sample are special in many ways (as discussed in Sect. 3), and certainly they are very different from the very large firms in Scherer’s seminal study.

Cohen and Klepper (1996a) use Scherer’s patent data linked to the FTC Line of Business Program’s data to develop support for “the basic idea that larger firms have an advantage in R&D because of the larger output over which they can apply the results and thus spread the costs of their R&D” (1996a, p. 241). Note this point is the one discussed above with caveats about the antitrust policy implications of the diminishing returns observed in the patenting to R&D relationship. Cohen et al. (1987) examine R&D expenditures as a function of a firm’s sales in a line of business and also firm-wide sales. They use the FTC Line of Business Program’s data and replicate the dominant result in Scherer (1984a, Table 11.3, p. 233, 1984b). Scherer controls for appropriability and technological opportunity conditions by estimating the elasticity of R&D with respect to line of business sales separately for each industry. He finds that the elasticity is unity for over 70% of the industries. Cohen et al. eliminate outliers from the FTC sample, examine the sample a whole, and find that controlling for industry effects, or instead controlling for the variance in conditions of appropriability and opportunity with their interesting industry-level variables, R&D intensity (the ratio of R&D to line of business sales) is not affected by the size of line of business sales. In other words, the elasticity of R&D to line of business sales is unity, which is what Scherer found for 71.4% of the industries. The outliers that Cohen et al. eliminate are reminiscent of the very large firms that were also outliers (Scherer 1965, p. 1110) in Scherer’s original study, discussed above, some 20 years before his studies that use the FTC data. Cohen et al. add that the probability of doing R&D is greater when lines of business have greater sales. They also report that total size (an aggregation of all of a firm’s lines of business) does not affect R&D intensity significantly either, given appropriate controls; in other words, R&D increases proportionately with firm size for the sample of very large firms absent the outliers, consistent with the finding of Bound et al. (1984) for their large firm sample, and moreover, consistent with Scherer’s (1965, p. 1110) “Scotch verdict.”