Synergies or trade-offs in university life sciences research.

Using citations requires attending to the time and subject dependency of the counts, namely, the truncation problem associated with more recent articles or patents that may not have had time to generate many citations as well as different citation rates across disciplines (Sampat, Mowery, and Ziedonis 2003). The citation adjustment measure constructed here for each life science article/patent is the deviation from the average citation rate of an article/patent in the same broad patent class or disciplinary category published in the same year. For example, a 1995 biochemistry article with ten citations is compared to the average level of citations of all biochemistry articles produced in 1995. For a given year, the average article within a disciplinary category has a citation rate of 1, with higher-quality articles then having a measure greater than 1 and lower-quality articles receiving a measure between zero and 1. This relative citation approach minimizes a truncation bias that would be introduced using an absolute citation count. Further details on the citation measure are in the appendix.

Empirical Results

Descriptive Statistics

A useful starting point for considering the issue of trade-offs or synergies between university life science article, patent, and doctorate production is an aggregate view of the recent trends in those outputs. Table 1 demonstrates the tremendous takeoff in life science patent production at U.S. universities in the 1990s, with the number of accepted patents in 1998 at sixteen times the level of 1981. Table 1 also shows the approximately 50% growth in published life sciences articles from 1981 to 1998 and the 33% growth in life science doctorates at a time in which life science R&D expenditures grew 88% in real terms. These growth rates in life science production are quite remarkable when contrasted with Foltz et al.'s (2005) estimates of only a 1% yearly rate of technical change in the university production process. (11)

The growth in life science article production shows steady growth over the entire period averaging about 2.4% per year, with the most rapid growth period being between 1984 and 1992. Patents show short growth spurts in the 1980s and then stable growth until 1995 when three years of exponential growth occurred. Doctorates, meanwhile, grew most in the early 1990s. While the boom in life science patenting in the late 1990s may have been fueled by the growth in life science article production in the earlier period, the leveling off of all three research outputs at much higher levels at the end of the 1990s suggests that at least strict tradeoffs among articles, doctorates, and patents during the boom era of life science patenting did not occur. It is possible, nonetheless, that the explosion in patent activity in the latter part of the decade may have dampened the other forms of research production.

Cost Surfaces

While table 1 demonstrates the growth of university life science outputs, it does not give evidence on potential complementarities between outputs. Descriptive evidence of economies of scale and scope can be seen in the realized cost surfaces of university production choices. A cost surface (or region) with cost complementarities will be convex with respect to costs across the two outputs, higher along the edges where more of a single product is produced and lower in the middle where both products are produced. A cost surface exhibiting returns to scale in a single product will be concave to the origin along one output axis.

Descriptive evidence on the shapes of university life sciences research cost surfaces is presented in figures 1 and 2 using a nonparametric Lowess smoothing estimation procedure and the pooled data set. (12) The relationship between articles and patents in quantity space is shown in figure 1. With its strong concavity along the article axis, it suggests significant returns to scale in article production, and with both convex and concave regions in the article-patent plane it also appears to show some regions of cost complementarities along with some regions of trade-offs. For example, one major convex region appears between thirteen and twenty-two patents and 660 to 1,080 articles. Also noteworthy is the plateau at the upper end of the article distribution, above 1,700 articles per year, where increases in either articles or patents appear relatively costless. This provides some suggestion that returns to scale and economies of scope may exist for the most productive/largest universities.

[FIGURES 1-2 OMITTED]

The second nonparametric cost surface (figure 2) depicts the citation-adjusted cost relationship between articles and patents. Along the article axis, the initial slope of this surface shows much steeper costs than did the quantity version, suggesting that quality research articles do not come cheaply. At higher levels of quality-adjusted article output, however, economies of scale do appear and persist. The cost surface also shows approximately the same inflection points for the region of convexity between articles and patents, but overall this surface is less suggestive of cost complementarities than was the surface in quantity space.

Econometric Estimates

The nonparametric cost surfaces obviously do not control for other factors and therefore only provide suggestive evidence about scale and scope economies. The next step in the analysis is to estimate for both quantity and citation-adjusted outputs the life science research cost function using panel data methods. Estimates are presented in tables 2 and 3 using a panel of 1,563 data points from eighty-seven universities over eighteen years (1981-1998). Each table presents two regression models: a fixed effects and a random effects regression. The tables also show the chi-square ([chi square]) statistic from the Hausman test of random versus fixed effects, the Breusch Pagan test that the random effects parameter [v.sub.i] is different than zero and two t-tests for the most likely types of heterskedasticity, that the estimated variance is different (a) by university and (b) by year.

The dependent variable is university life science research and development expenditures measured in thousands of dollars. In addition to the quadratic formulation for the three research outputs and the two input costs we include a number of regressors to control for possible unmeasured differences. We include the university-wide undergraduate student-to-faculty ratio in order to control for potentially higher research costs for places with higher undergraduate teaching responsibilities. The regression also includes an indicator variable for whether the university is a land grant (LGU) institution, a medical school dummy variable, and the two technology transfer variables described above.

Table 2 presents fixed effects and random effects parameter estimates for the quantity model, while table 3 presents the citation-adjusted parameters. The tables also show the results of the tests of the error terms, while table 4 presents the estimates of scale and scope that are derived from inserting the parameters into equations (2) and (3) from the regression estimates. In terms of regression diagnostics, all equations have reasonably high [R.sup.2]'s. For the random effects models, we cannot reject the null hypothesis of homoskedasticity, while the Breusch Pagan test shows that we can reject the null hypothesis that [v.sub.i] = 0. For the quantity regressions, the insignificant Hausman test implies that we cannot reject the random-effects model as the correct model, while we can reject the random-effects model specification for the citation-adjusted results.

All of our model specifications provide similar and highly significant results for most of the regressors. The coefficient estimates for articles and patents in all regressions show that their production increases costs, but at a decreasing rate. These significant estimates provide supportive evidence of the necessary conditions for scale economies in those outputs. The parameter estimates on graduate student production have more ambiguous but statistically insignificant effects. The interaction terms between outputs show significant trade-offs between PhD's and both articles and patents, although in the citation-adjusted regressions the significance of the PhD/article trade-off disappears. The negative, though insignificant, coefficient on the article/patent interaction term suggests some possibility of synergies between these outputs.