Synergies or trade-offs in university life sciences research.

2. Economies of scope: The economies of scope for a product set t relative to the product set of all other n products not including t: (n - t), can be computed from following function:

(3) [SC.sub.t](Y) = [C([Y.sub.t]) + C([Y.sub.n-t])

- C(Y)]/C(Y),

where C([Y.sub.t]) is the cost of producing only the product set t and C([Y.sub.n-t]) is the cost of producing the other n products except those in set t. Economies of scope exist when [SC.sub.t](Y) > 0.

In this application, we analyze economies of scope that compare producing patents as a separate operation from articles and doctorates and producing all three together as a single operation.

Econometric Specification

In the case of university research output in the life sciences, the vector of outputs Y is measured by journal publications, patents, and doctorates, while the costs are measured by the total expenditures on life sciences research in a given year. To control for the presence of university-specific effects in the error structure, panel data are used to estimate a panel data model, such as that presented in equation (4).

(4) [C.sub.it] = [alpha] + [x.sub.it][beta] + [u.sub.it], where [u.sub.it] = [v.sub.i] + [[epsilon].sub.it],

where [C.sub.it] are costs, [x.sub.it] represent the independent variables (Y, w), [beta] is a vector of parameters to be estimated, [v.sub.i] is a university-specific residual estimated as either a fixed or random effect, while [[epsilon].sub.it] is the "usual" residual which contains both a time-specific element and a standard equation residual (Wooldbridge 2002).

We estimate two versions of the econometric specification under different assumptions on the two error terms. A fixed effects model, which estimates [v.sub.i] separately for each university, is presented first. A random effects specification is then estimated to accommodate a number of regressors that change infrequently and to include a number of indicator variables that parameterize the differences between universities in ways that we predict will affect the cost of research production, e.g., presence of a longstanding tech transfer office and medical school, and land grant status. The random effects estimator imposes the assumption that [x.sub.it] and the random effects, [v.sub.i], are uncorrelated. The results of a Hausman test of this assumption along with tests for significance of the random effects and for heteroskedasticity are described in the results section.

In terms of the functional form of the multiple-output cost framework, the literature presents a number of variants, including the generalized quadratic and the translog forms. Since a key independent variable, patents, is zero for nearly a quarter of the university-year combinations the translog formulation would be undefined for a large part of our sample unless we added an ad hoc small number to each of these data points. Given that the literature provides no specific guidance on the optimality of one functional form over another; we therefore have chosen the generalized quadratic because it minimizes the number of ad hoc assumptions necessary for implementation. None of the key results about economies of scale or scope presented in this article are sensitive to our choice of functional form. (6)

In order to meet the theoretical requirements of a cost function, we impose homogeneity in input prices in the manner suggested by Chambers (1988):

(5) C = [w.sub.l] f (y, [w.sub.m]/w.sub.l]),

where [w.sub.l] and [w.sub.m] are two different input prices. The interpretation and estimation are facilitated if one divides through by [w.sub.l] to get the equation to be estimated as:

(6) C/[w.sub.l] = f (y, [w.sub.m]/[w.sub.l]).

The choice of normalizing input price is discussed below in the data section.

Finally, the econometric models estimated below use both strict quantity measures for research output and quality measures in which citations of articles and patents are used to control for quality of those two research outputs. The specifics of this citation adjustment are discussed next in the data section.

Data on University Life Science Research, 1981-1998

The data set combines information on life science research inputs and outputs for ninety-six U.S. universities over an eighteen-year period, spanning an era of remarkable growth in the role of life sciences in universities and the global economy. We focus on the segment of life sciences--biological and agricultural sciences--that has been most affected by recent court rulings in the United States that allow patenting of life forms. Following the National Science Foundation's (NSF) definition of "life sciences," these categories include departments that produce most biotechnologies and agricultural science research, but exclude departments that are primarily engaged in clinical medicine (see Appendix for a complete listing). This choice is consistent with a historical division within most universities, where biological and agricultural life sciences are contained in distinct administrative units from medical and pharmaceutical schools. The ninety-six U.S. universities roughly correspond to the Carnegie classification of "Research I" universities, and they are responsible for the vast majority of U.S. university production of articles and patents in life sciences. (7) The exact choice was driven in large part by the availability of accurate article and cost data.

For the dependent variable in our estimation, [C.sub.it], we use university life science research costs as measured by the NSE The university's outputs, the elements of the vector [Y.sub.it], are measured as life sciences patents, articles, and doctorates. (8) Life science patent assignee and citation information were extracted from the NBER patent database (Hall, Jaffe, and Trajtenberg 2003), while the Science Citation Index (ISI Web of Science 2002) provided the life science article and citation counts by year for each university. Patents are credited by application year rather than by grant date in order to measure them as close as possible to the date research costs were involved. In addition, although our cost measure does not include teaching costs, we include the university's undergraduate student to faculty ratio as a method of controlling for differences in teaching loads that might influence the costs of research.

We use three input costs, [w.sub.it], in the cost function estimation: average faculty salary, average wage rate in the university's town as a measure of the cost of support personnel, and an index of overall costs in agricultural research compiled by Huffman and Evenson (2005). In order to preserve homogeneity of degree 1 in prices we divide all input prices and our dependent variable, research costs, by the research cost index. Since this also has the effect of deflating our cost variables, we otherwise use nominal values of the variables.

Also to capture the university's level of technology transfer infrastructure we include two indicator variables: one captures whether the university has a technology transfer office, while the other captures whether a university had a technology transfer office before the promulgation of the Bayh-Dole act in 1980. Finally, in the random effects models, we include three variables to control for missions of universities that may be poorly measured in the outputs variables we use. They are (a) LGU an indicator variable for whether a university has land grant status, (b) "Extension FTE" a measure of the number of extension personnel (measured in FTE) in the state (Ahearn, Lee, and Bottom 2002), and (c) "Med School" for whether a university has a medical school. We expect that land grant universities will have higher base costs (positive coefficient) because of their multiple outreach missions of providing public goods to the state. These outreach missions may be poorly measured by the research outputs we are including. We therefore include the extension FTE measure, which we expect to be positive since it represents a major component of the outreach mission and we expect that servicing a larger set of extension personnel could raise the costs of research. (9) The medical school dummy variable should be negative if we have counted outputs from medical programs without accounting for their costs, or insignificant otherwise.

We estimate two sets of regressions, one using quantity output measures and another adjusting the quantity of articles and patents by their citation counts as a measure of quality. (10) Citation adjustments were sought because in the case of research output, quality is likely to matter significantly to the implicit value of the research and also to the potential synergies between patents and articles. In the first case, highly cited articles and patents are likely to generate flows of additional research or licensing funds to the author or assignee, while in the latter research that gives rise, for example, to an article that is highly cited may also be more likely to generate a patent than would a larger number of uncited articles. Empirically, studies of patent citations have shown that they provide a proxy for both the quality of a patent and knowledge spillovers from patents, because each time a new patent uses a piece of research from another patent it is obligated to cite the previous patent (Henderson, Jaffe, and Trajtenberg 1998). Article citations are also commonly used as measures of quality in studies of departmental or university quality, e.g., Adams (1998).