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Team production in economics: A comment and extension
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ELSEVIER
T,ABOUR ECONOMICS Labour Economics4 (1997) 185-191
Team production in economics: A comment and extension F r a n k l i n G. M i x o n Jr. * Department of Economics and International Business, The University of Southern Mississippi, Box 5072, USM Station, Hattiesburg, MS 39406-5072, USA
Received 15 January 1996; accepted 10 September 1996
JEL classification: A1 Keywords: Mentoring; Co-authoring; Division of labor; Scholarship
1. Introduction In an interesting article in a recent issue of this journal, Laband and Piette (1995) note (as have others before them, such as McDowell and Melvin, 1983; Barnett et al., 1988; Laband, 1993) that there has been a significant rise in the incidence of co-authorship in economic science over time. As pointed out and developed by Barnett et al. (1988), there are two popular hypotheses concerning this rise: (1) increased co-authorship reflects capture by authors of gains from division of labor and specialization, and (2) an increasingly random component to the review process induces authors to engage in academic conglomerate merger as a means of diversifying against risk. The Laband and Piette (1995) study proposes to investigate empirically the nature of the relationship between co-authors in economics. Specifically, they aim to answer two basic questions: (1) does joint production involve same-age/experienced scholars who bring equal, yet complementary skills to the productive process (the specialization hypothesis)? Or, (2) is
* Tel.: (+ 1) 601-266.5083; fax: (+ 1) 601-266.4920; e-mail: [email protected]. 0927-5371/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0927-5371 (96)00028-0
186
F.G. Mixon Jr. / Labour Economics 4 (1997) 185-191
the typical collaborative effort characterized more by a 'mentor-protege' relationship in which senior scholars lead junior scholars through the maze of scientific advancement (the mentor-prot~g6 hypothesis)? The second hypothesis above suggests that inputs in the productive process are unequal (Laband and Piette, 1995, pp. 33-34). They investigate these hypotheses by analyzing the distribution of the dispersion in ages and productive capacities brought to the merger by the contributing parties. They find that co-authorship is not randomly distributed throughout the population of economics scholars, which means that co-authorship is not motivated by any randomness in the review process. They also, however, find no significant evidence of a mentor-prot6g6 relationship. Their findings suggest that over 50 percent of co-authored research is done by similar-age, complementary-skilled contributors. The present comment suggests altematives for measuring the mentor-prot6g6 relationship, and offers an extension of the Laband-Piette analysis by examining the determinants of the 'types' of co-authored articles in economics. The evidence suggests that the number of co-authors is significantly related to the reason for co-authorship, as there are clear group economies (economies of scale) for mentoring by senior scholars within the scientific community. 2. The model and statistical results
Laband and Piette (1995) collect data from 415 co-authored articles published in the top 27 economics journals in 1984 (see Liebowitz and Palmer (1984) for rankings). They identified citations to each article from the Social Science Citation Index for the five following years, as a proxy for article quality. Several article characteristics (length, lead article), author characteristics (age, affiliation, gender, cumulative citation stock for five years before 1984), and journal and editor characteristics were included in the Laband-Piette model. They also include dispersion in authors' ages and dispersion in authors' citation stocks as regressors against the dependent variable (citations to the 1984 published articles) in order to test the above hypotheses. If the mentor-prot6g6 hypothesis is dominant, then one would expect the coefficients for cite-dispersions and age-dispersions to be positive and significant. If, however, the division/specialization of labor hypothesis is dominant, one would expect these coefficients to be negative and significant. The regression results produce negative but insignificant coefficients for these dispersions (Laband and Piette, 1995, pp. 36-37). They conclude that the mentor-prot6g6 form of intellectual contribution is no more, or less, productive, in terms of impact of specific papers produced on other scholars' thinking than collaboration between equally skilled, comparably-aged scholars (Laband and Piette, 1995, p. 37). The present note argues that the age-dispersion measure used by Laband and Piette may not work to properly capture mentor-prot6g6 relationships; this note also produces a model which examines the statistical determinants of the choice of
F.G. Mixon Jr. /Labour Economics 4 (1997) 185-19l
187
co-authors, without regard to other scholars' thinking about the productivity of the merger. Data for the model come from co-authored articles published in volumes 83-84 (years 1993-1994) of the American Economic Review, and volumes 107-108 (years 1992-1993) of the Quarterly Journal of Economics, two top journals in economic science. These two journals were chosen because they consistently rank at or near the top in significant scholarly research on journal rankings in economics (see the work of Liebowitz and Palmer (1984), and Laband and Piette (1994)), and because one, the American Economic Review, holds an association affiliation (American Economic Association) and the other (Quarterly Journal of Economics) is independent. The latter qualification should allow for any possible differences with regard to scholarly/editorial practices at various types of journals and test the robustness of the theory presented here. The specific years for each journal were chosen because they represent the most recent two-year period for each journal where the complete volumes were available (at the time this research note was being completed). Specifically, the present note proposes the following model: EconLitdisper = ~0 + 6a Length + 6 2 Gender + ~3 Theoretical + ~4 Auts + e~
(1)
where the dependent variable, EconLitdisper, is a measure of author reputation: specifically EconLitdisper is calculated from entries in the ECONLIT on-line data base of scholarly work in economics (maintained by the American Economic Association), and it is equal to the dispersion in the number of entries for authors of co-authored articles in the AER and QJE. For papers with two authors only, EconLitdisper (the dependent variable) is equal to the difference in the ECONLIT scores or entries (for scholarly work by economists) for the two authors. For articles written by more than two economists, the dependent variable is equal to the difference in the ECONLIT scores or entries for the authors with the highest and lowest ECONLIT count among the group of co-authors. For example, if Stigler's count (on ECONLIT) is 150 and Johnson's count is 25, then the dependent variable for an article co-authored by Stigler and Johnson is 125, or 150 minus 25. However, if Stigler and Johnson write an article with Becker, whose ECONLIT entries total 180, then the dependent variable for this article or observation is 155, or 180 (Becker's, the highest) minus 25 (Johnson's, the lowest). If this value is small, one expects the co-authorship merger to be of the division of labor/specialization form; if large, the mentor-prottg6 type of merger is exhibited. This measure is perhaps a better proxy for these types of scholarly mergers than age-dispersion because the age of many new PhD graduates in economics (and other disciplines) is high, and small age differences do not always signify equally-skilled scholars. For instance, ECONLIT entries for Laband total 48, while Piette's entries total 20; when their joint output is omitted, Laband has 44 entries and Piette has 16. With 20 percent of Piette's work produced in conjunction with the inputs offered by Laband, one could argue that a mentorprottg~ type of relationship between the two exists (in fact, Laband's total is 2.75
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F. G. Mixon Jr. / Labour Economics 4 (1997) 1 8 5 - 1 9 1
times that of Piette's when their co-authored work is omitted). However, according to the '1993 Survey of Members' by the American Economic Association (American Economic Review, December 1993), the dispersion in their ages is only 9 - 1 0 years (a division of labor relationship?), with Piette being the 'senior' scholar among the two. Piette, however, completed his PhD only three years before Laband. The ECONLIT numbers could also reflect the fact that Piette has spent significant time outside of the academic world, and thus offers a better measure of these relationships. The Laband-Piette measure of cite-dispersion also does a better job of capturing the same ideas than does age-dispersion. The present note offers no a priori prediction concerning the values of the parameters attached to the first three regressors. These are length (in number of pages) of the article (Length), a dummy variable equal to one for articles with at least one female author, and zero otherwise (Gender), and a dummy variable equal to one for theoretical articles, and zero otherwise (Theoretical). The final regressor, Auts, is a dummy variable equal to one for articles with three or more authors, and zero otherwise (two authors only). One expects that mentor-prot6g6 mergers are more likely as the number of authors rises, so that senior scholars can take advantage of group economies inherent in such relationships. The economics literature is replete with studies pointing out scale and scope economies inherent in educational processes, including evidence regarding class(room) size and the size and scope of educational and research activities at major research universities in the United States (see Nelson and Hevert, 1992; Ratcliffe et al., 1990; de Groot et al., 1991). Using a translog cost function (with data from 147 Colleges/Universities in the U.S.), de Groot et al. (1991) point out that the cost of operating PhD programs in economics falls as class-sizes rise, and that there are significant economies of scale left to be achieved by the average school in the sample. To the mentor, the average cost of mentoring - by way of co-authoring articles in economics as a form of teaching research methods - falls as the number of co-author/proteges rises, up to some threshold. One could consider these relationships informal classroom settings where the subject is implementing scientific research agendas. Like doctors who escort medical interns on their 'rounds', senior scholars can guide groups of junior scholars through the scientific process at lower cost. On the other hand, as the number of scholars falls, one expects that the division of labor is the prevalent motivation behind the scholarly merger. Therefore, I expect that the coefficient attaching to Auts will be OSitive. Below, in Eqs. (2) and (3), results from the AER and the QJE espectively) regressions (OLS) are reported: EconLitdisper = 35.74 -
(1.59)
0.61 Length + 8.14 Theoretical + 2.32 Gender + 36.01Auts * * *, (-0.62) (0.74) (0.17) (2.91)
(2)
n o b s = 70, F = 2.30, R-square = 0.12, Adj. R-square --- 0.07; E c o n L i t d i s p e r = 31.78 + O.32 Length -
(0.87)
(0.30)
2.77 T h e o r e t i c a l - 1 7 . 9 8 Gender + 58.57 Auts* * * , (-0.14) (-0.63) (2.83)
n o b s = 49, F = 2.32, R-square = 0.17, Adj. R-square --- 0.10.
(3)
F. G. Mixon Jr./Labour Economics 4 (1997) 185-191
189
Based on the t-statistics in parentheses, the only significant regressor in explaining the different types of academic mergers offered by the dependent variable is Auts. This is consistent with the presence of group economies in the mentor-protfg6 production process, and that no more than two complementary inputs are usually employed within mergers that are motivated by the division of labor/specialization concept. Even though the parameter for Auts in the QJE regression is much larger, there is no statistical difference between the two regressions (t-value for the difference in parameters is 0.94). It is also possible, however, that the parameter for Auts depicts the statistical expectation that as the number of authors grows, the greater the expected ECONLIT dispersion for that group of authors, regardless of the motive for the merger. 1 In light of such a possibility, the robustness of these findings is subjected to logit regressions (below) where a binary dependent variable for Auts is included with EconLitdisper as a right-hand-side variable. Next, as a further test, Eqs. (4) and (5) and Eqs. (6) and (7) offer simultaneous estimations (2SLS) for the AER and QJE regressions (respectively), where article length is a second dependent variable. EconLitdisper= 1 5 5 . 5 2 - 6.36 L e n g t h - 13.03 Gender+38.81Auts***, (0.82) ( - 0.67) ( - 0.42) (2.39)
(4)
nobs = 70, R-square = 0.08; Length = 36.53 - 0.68 EconLitdisper + 4.69 Theoretical + 24.73Auts, (0.65) (-0.29) (0.21) (0.30)
(5)
n o b s = 70, R-square = 0.00; EconLitdisper = 15.69 + 0.83 Length - 16.20 Gender + 60.36 Auts * * *, (0.16) (0.24) (0.55) (2.83)
(6)
nobs= 49, R-square = 0.17; Length = 23.84* + 0.18 EconLitdisper- 4.60 Theoretical - 13.94 auts, (1.80) (0.55) ( - 1.08) (0.71)
(7)
nobs = 49, R-square = 0.05. Again, the results are consistent with the hypothesis (as well as the alternative statistical expectation) - there are significant group economies to the mentoring process of scholarly production. For both journals, the dispersion in ECONLIT counts will be significantly larger as the number of authors (of each co-authored paper) increases. Again, the parameter difference for Auts between the two regressions is not significant (based on a t-value of 0.80). These results suggest that the variable Auts could be used to test the robustness of the Laband-Piette results. The 'length' regressions do, however, perform rather poorly, as noted by
I I am grateful to an anonymous referee for reminding me of this expectation. Although there are two possible interpretations for the variable Auts in these regressions, further statistical exploration is also consistent with the hypothesis developed here. I do regret, however, that these concerns are not completely alleviated.
F.G. Mixon Jr.~Labour Economics 4 (1997) 185-191
190
the lack of significant regressors and the R-square statistic in Eq. (5) above. As a result, a final test of the robustness of the theory (as noted above) is detailed below. As a final test, Eqs. (8) and (9) examine the probability that the co-authored articles in the AER and QJE (respectively) will have three or more authors, using EconLitdisper, Gender, and Theoretical as regressors within logit models. It is expected that, because of group economies of scale, EconLitdisper will be positively related to the probability that Auts = 1. The results are presented below: auts = - 1 . 4 3 ' * * ( - 2.79)
+ 0 . 0 2 EconLitdisper** - 0.51 Theoretical- 0 . 3 4 Gender, (2.29) ( - 0.88) ( - 0.45)
(8)
n = 70, Model X 2 = 8.03, % of cases Auts predicted correctly = 75.9%; auts = - 1 . 6 6 " * * ( - 2.92)
+ 0.01 EconLitdisper** - 1.13 Theoretical + 0.01 Gender, (2.26) ( - 1.19) (0.01)
(9)
n = 49, Model X 2 = 9.12, % of cases Auts predicted correctly = 72.7%. The dispersion in ECONLIT entries among co-authors is positively related to the probability that there will be three or more authors of the output; this relationship is significant at the 5% level and suggests that senior scholars will guide young scholars through the scientific process in groups, so that output (journal articles) and the external economic benefits (mentoring) can be produced in a low-cost manner. Eqs. (8) and (9) above do not completely alleviate the concerns about the alternative statistical expectation, but they do add some weight to the hypothesis developed in this study. Perhaps it would be interesting to insert a dummy variable (equal to one for articles with three or more authors) like 'Auts' into the Laband-Piette regressions as a further test of the type of scholarly merger in an effort to re-address the two questions posed above and in their own study.
3. Concluding comments The present comment captures an idea not tested in the Laband and Piette (1995) study - namely that there are significant group economies in the mentoring process and that the number of authors merging to produce scientific knowledge is related to these costs. It seems that when two economists merge to produce scholarly output, the primary factor relating to the merger is specialization and trade of complementary productive skills. When there are three or more authors however, a mentor-protrg6 relationship is exhibited in an attempt by senior scholars to lead junior scholars on the 'rounds' of scientific advancement.
Acknowledgements The author is grateful to an anonymous referee for many helpful suggestions. Any remaining errors are my own.
F. G. Mixon Jr./Labour Economics 4 (1997) 185-191
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References Barnett, Andy H., Richard W. Ault and David L. Kaserrnan, 1988, The rising incidence of co-authorship in economics, Further evidence, Review of Economics and Statistics 70, 539-543. de Groot, Hans, Walter McMahon and J. Fredericks Volkwein, 1991, The cost structure of American research universities, Review of Economics and Statistics 73, 424-431. Laband, David N, 1993, The production and dissemination of scientific knowledge, Unpublished book manuscript (Auburn University, AL). Laband, David N. and Michael J. Piette, 1994, The relative impacts of economics journals, 1970-1990, Journal of Economic Literature 32, 640-666. Laband, David N. and Michael J. Piette, 1995, Team production in economics, Division of labor or mentoring? Labour Economics 2, 33-40. Liebowitz, Stanley J. and John C. Palmer, 1984, Assessing the relative impacts of economics journals. Journal of Economic Literature 22, 77-88. McDowell, John and Michael Melvin, 1983, The determinants of co-authorship: An analysis of the economics literature, Review of Economics and Statistics 65, 155-160. Nelson, Randy and Kathleen Hevert, 1992, Effect of class size on economies of scale and marginal costs in education, Applied Economics 24, 473-482. Ratcliffe, Kerri, Bruce Riddle and John Yinger, 1990, The fiscal condition of school districts in Nebraska: Is small beautiful? Economics of Education Review 9, 81-99.
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ELSEVIER
T,ABOUR ECONOMICS Labour Economics4 (1997) 185-191
Team production in economics: A comment and extension F r a n k l i n G. M i x o n Jr. * Department of Economics and International Business, The University of Southern Mississippi, Box 5072, USM Station, Hattiesburg, MS 39406-5072, USA
Received 15 January 1996; accepted 10 September 1996
JEL classification: A1 Keywords: Mentoring; Co-authoring; Division of labor; Scholarship
1. Introduction In an interesting article in a recent issue of this journal, Laband and Piette (1995) note (as have others before them, such as McDowell and Melvin, 1983; Barnett et al., 1988; Laband, 1993) that there has been a significant rise in the incidence of co-authorship in economic science over time. As pointed out and developed by Barnett et al. (1988), there are two popular hypotheses concerning this rise: (1) increased co-authorship reflects capture by authors of gains from division of labor and specialization, and (2) an increasingly random component to the review process induces authors to engage in academic conglomerate merger as a means of diversifying against risk. The Laband and Piette (1995) study proposes to investigate empirically the nature of the relationship between co-authors in economics. Specifically, they aim to answer two basic questions: (1) does joint production involve same-age/experienced scholars who bring equal, yet complementary skills to the productive process (the specialization hypothesis)? Or, (2) is
* Tel.: (+ 1) 601-266.5083; fax: (+ 1) 601-266.4920; e-mail: [email protected]. 0927-5371/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0927-5371 (96)00028-0
186
F.G. Mixon Jr. / Labour Economics 4 (1997) 185-191
the typical collaborative effort characterized more by a 'mentor-protege' relationship in which senior scholars lead junior scholars through the maze of scientific advancement (the mentor-prot~g6 hypothesis)? The second hypothesis above suggests that inputs in the productive process are unequal (Laband and Piette, 1995, pp. 33-34). They investigate these hypotheses by analyzing the distribution of the dispersion in ages and productive capacities brought to the merger by the contributing parties. They find that co-authorship is not randomly distributed throughout the population of economics scholars, which means that co-authorship is not motivated by any randomness in the review process. They also, however, find no significant evidence of a mentor-prot6g6 relationship. Their findings suggest that over 50 percent of co-authored research is done by similar-age, complementary-skilled contributors. The present comment suggests altematives for measuring the mentor-prot6g6 relationship, and offers an extension of the Laband-Piette analysis by examining the determinants of the 'types' of co-authored articles in economics. The evidence suggests that the number of co-authors is significantly related to the reason for co-authorship, as there are clear group economies (economies of scale) for mentoring by senior scholars within the scientific community. 2. The model and statistical results
Laband and Piette (1995) collect data from 415 co-authored articles published in the top 27 economics journals in 1984 (see Liebowitz and Palmer (1984) for rankings). They identified citations to each article from the Social Science Citation Index for the five following years, as a proxy for article quality. Several article characteristics (length, lead article), author characteristics (age, affiliation, gender, cumulative citation stock for five years before 1984), and journal and editor characteristics were included in the Laband-Piette model. They also include dispersion in authors' ages and dispersion in authors' citation stocks as regressors against the dependent variable (citations to the 1984 published articles) in order to test the above hypotheses. If the mentor-prot6g6 hypothesis is dominant, then one would expect the coefficients for cite-dispersions and age-dispersions to be positive and significant. If, however, the division/specialization of labor hypothesis is dominant, one would expect these coefficients to be negative and significant. The regression results produce negative but insignificant coefficients for these dispersions (Laband and Piette, 1995, pp. 36-37). They conclude that the mentor-prot6g6 form of intellectual contribution is no more, or less, productive, in terms of impact of specific papers produced on other scholars' thinking than collaboration between equally skilled, comparably-aged scholars (Laband and Piette, 1995, p. 37). The present note argues that the age-dispersion measure used by Laband and Piette may not work to properly capture mentor-prot6g6 relationships; this note also produces a model which examines the statistical determinants of the choice of
F.G. Mixon Jr. /Labour Economics 4 (1997) 185-19l
187
co-authors, without regard to other scholars' thinking about the productivity of the merger. Data for the model come from co-authored articles published in volumes 83-84 (years 1993-1994) of the American Economic Review, and volumes 107-108 (years 1992-1993) of the Quarterly Journal of Economics, two top journals in economic science. These two journals were chosen because they consistently rank at or near the top in significant scholarly research on journal rankings in economics (see the work of Liebowitz and Palmer (1984), and Laband and Piette (1994)), and because one, the American Economic Review, holds an association affiliation (American Economic Association) and the other (Quarterly Journal of Economics) is independent. The latter qualification should allow for any possible differences with regard to scholarly/editorial practices at various types of journals and test the robustness of the theory presented here. The specific years for each journal were chosen because they represent the most recent two-year period for each journal where the complete volumes were available (at the time this research note was being completed). Specifically, the present note proposes the following model: EconLitdisper = ~0 + 6a Length + 6 2 Gender + ~3 Theoretical + ~4 Auts + e~
(1)
where the dependent variable, EconLitdisper, is a measure of author reputation: specifically EconLitdisper is calculated from entries in the ECONLIT on-line data base of scholarly work in economics (maintained by the American Economic Association), and it is equal to the dispersion in the number of entries for authors of co-authored articles in the AER and QJE. For papers with two authors only, EconLitdisper (the dependent variable) is equal to the difference in the ECONLIT scores or entries (for scholarly work by economists) for the two authors. For articles written by more than two economists, the dependent variable is equal to the difference in the ECONLIT scores or entries for the authors with the highest and lowest ECONLIT count among the group of co-authors. For example, if Stigler's count (on ECONLIT) is 150 and Johnson's count is 25, then the dependent variable for an article co-authored by Stigler and Johnson is 125, or 150 minus 25. However, if Stigler and Johnson write an article with Becker, whose ECONLIT entries total 180, then the dependent variable for this article or observation is 155, or 180 (Becker's, the highest) minus 25 (Johnson's, the lowest). If this value is small, one expects the co-authorship merger to be of the division of labor/specialization form; if large, the mentor-prottg6 type of merger is exhibited. This measure is perhaps a better proxy for these types of scholarly mergers than age-dispersion because the age of many new PhD graduates in economics (and other disciplines) is high, and small age differences do not always signify equally-skilled scholars. For instance, ECONLIT entries for Laband total 48, while Piette's entries total 20; when their joint output is omitted, Laband has 44 entries and Piette has 16. With 20 percent of Piette's work produced in conjunction with the inputs offered by Laband, one could argue that a mentorprottg~ type of relationship between the two exists (in fact, Laband's total is 2.75
188
F. G. Mixon Jr. / Labour Economics 4 (1997) 1 8 5 - 1 9 1
times that of Piette's when their co-authored work is omitted). However, according to the '1993 Survey of Members' by the American Economic Association (American Economic Review, December 1993), the dispersion in their ages is only 9 - 1 0 years (a division of labor relationship?), with Piette being the 'senior' scholar among the two. Piette, however, completed his PhD only three years before Laband. The ECONLIT numbers could also reflect the fact that Piette has spent significant time outside of the academic world, and thus offers a better measure of these relationships. The Laband-Piette measure of cite-dispersion also does a better job of capturing the same ideas than does age-dispersion. The present note offers no a priori prediction concerning the values of the parameters attached to the first three regressors. These are length (in number of pages) of the article (Length), a dummy variable equal to one for articles with at least one female author, and zero otherwise (Gender), and a dummy variable equal to one for theoretical articles, and zero otherwise (Theoretical). The final regressor, Auts, is a dummy variable equal to one for articles with three or more authors, and zero otherwise (two authors only). One expects that mentor-prot6g6 mergers are more likely as the number of authors rises, so that senior scholars can take advantage of group economies inherent in such relationships. The economics literature is replete with studies pointing out scale and scope economies inherent in educational processes, including evidence regarding class(room) size and the size and scope of educational and research activities at major research universities in the United States (see Nelson and Hevert, 1992; Ratcliffe et al., 1990; de Groot et al., 1991). Using a translog cost function (with data from 147 Colleges/Universities in the U.S.), de Groot et al. (1991) point out that the cost of operating PhD programs in economics falls as class-sizes rise, and that there are significant economies of scale left to be achieved by the average school in the sample. To the mentor, the average cost of mentoring - by way of co-authoring articles in economics as a form of teaching research methods - falls as the number of co-author/proteges rises, up to some threshold. One could consider these relationships informal classroom settings where the subject is implementing scientific research agendas. Like doctors who escort medical interns on their 'rounds', senior scholars can guide groups of junior scholars through the scientific process at lower cost. On the other hand, as the number of scholars falls, one expects that the division of labor is the prevalent motivation behind the scholarly merger. Therefore, I expect that the coefficient attaching to Auts will be OSitive. Below, in Eqs. (2) and (3), results from the AER and the QJE espectively) regressions (OLS) are reported: EconLitdisper = 35.74 -
(1.59)
0.61 Length + 8.14 Theoretical + 2.32 Gender + 36.01Auts * * *, (-0.62) (0.74) (0.17) (2.91)
(2)
n o b s = 70, F = 2.30, R-square = 0.12, Adj. R-square --- 0.07; E c o n L i t d i s p e r = 31.78 + O.32 Length -
(0.87)
(0.30)
2.77 T h e o r e t i c a l - 1 7 . 9 8 Gender + 58.57 Auts* * * , (-0.14) (-0.63) (2.83)
n o b s = 49, F = 2.32, R-square = 0.17, Adj. R-square --- 0.10.
(3)
F. G. Mixon Jr./Labour Economics 4 (1997) 185-191
189
Based on the t-statistics in parentheses, the only significant regressor in explaining the different types of academic mergers offered by the dependent variable is Auts. This is consistent with the presence of group economies in the mentor-protfg6 production process, and that no more than two complementary inputs are usually employed within mergers that are motivated by the division of labor/specialization concept. Even though the parameter for Auts in the QJE regression is much larger, there is no statistical difference between the two regressions (t-value for the difference in parameters is 0.94). It is also possible, however, that the parameter for Auts depicts the statistical expectation that as the number of authors grows, the greater the expected ECONLIT dispersion for that group of authors, regardless of the motive for the merger. 1 In light of such a possibility, the robustness of these findings is subjected to logit regressions (below) where a binary dependent variable for Auts is included with EconLitdisper as a right-hand-side variable. Next, as a further test, Eqs. (4) and (5) and Eqs. (6) and (7) offer simultaneous estimations (2SLS) for the AER and QJE regressions (respectively), where article length is a second dependent variable. EconLitdisper= 1 5 5 . 5 2 - 6.36 L e n g t h - 13.03 Gender+38.81Auts***, (0.82) ( - 0.67) ( - 0.42) (2.39)
(4)
nobs = 70, R-square = 0.08; Length = 36.53 - 0.68 EconLitdisper + 4.69 Theoretical + 24.73Auts, (0.65) (-0.29) (0.21) (0.30)
(5)
n o b s = 70, R-square = 0.00; EconLitdisper = 15.69 + 0.83 Length - 16.20 Gender + 60.36 Auts * * *, (0.16) (0.24) (0.55) (2.83)
(6)
nobs= 49, R-square = 0.17; Length = 23.84* + 0.18 EconLitdisper- 4.60 Theoretical - 13.94 auts, (1.80) (0.55) ( - 1.08) (0.71)
(7)
nobs = 49, R-square = 0.05. Again, the results are consistent with the hypothesis (as well as the alternative statistical expectation) - there are significant group economies to the mentoring process of scholarly production. For both journals, the dispersion in ECONLIT counts will be significantly larger as the number of authors (of each co-authored paper) increases. Again, the parameter difference for Auts between the two regressions is not significant (based on a t-value of 0.80). These results suggest that the variable Auts could be used to test the robustness of the Laband-Piette results. The 'length' regressions do, however, perform rather poorly, as noted by
I I am grateful to an anonymous referee for reminding me of this expectation. Although there are two possible interpretations for the variable Auts in these regressions, further statistical exploration is also consistent with the hypothesis developed here. I do regret, however, that these concerns are not completely alleviated.
F.G. Mixon Jr.~Labour Economics 4 (1997) 185-191
190
the lack of significant regressors and the R-square statistic in Eq. (5) above. As a result, a final test of the robustness of the theory (as noted above) is detailed below. As a final test, Eqs. (8) and (9) examine the probability that the co-authored articles in the AER and QJE (respectively) will have three or more authors, using EconLitdisper, Gender, and Theoretical as regressors within logit models. It is expected that, because of group economies of scale, EconLitdisper will be positively related to the probability that Auts = 1. The results are presented below: auts = - 1 . 4 3 ' * * ( - 2.79)
+ 0 . 0 2 EconLitdisper** - 0.51 Theoretical- 0 . 3 4 Gender, (2.29) ( - 0.88) ( - 0.45)
(8)
n = 70, Model X 2 = 8.03, % of cases Auts predicted correctly = 75.9%; auts = - 1 . 6 6 " * * ( - 2.92)
+ 0.01 EconLitdisper** - 1.13 Theoretical + 0.01 Gender, (2.26) ( - 1.19) (0.01)
(9)
n = 49, Model X 2 = 9.12, % of cases Auts predicted correctly = 72.7%. The dispersion in ECONLIT entries among co-authors is positively related to the probability that there will be three or more authors of the output; this relationship is significant at the 5% level and suggests that senior scholars will guide young scholars through the scientific process in groups, so that output (journal articles) and the external economic benefits (mentoring) can be produced in a low-cost manner. Eqs. (8) and (9) above do not completely alleviate the concerns about the alternative statistical expectation, but they do add some weight to the hypothesis developed in this study. Perhaps it would be interesting to insert a dummy variable (equal to one for articles with three or more authors) like 'Auts' into the Laband-Piette regressions as a further test of the type of scholarly merger in an effort to re-address the two questions posed above and in their own study.
3. Concluding comments The present comment captures an idea not tested in the Laband and Piette (1995) study - namely that there are significant group economies in the mentoring process and that the number of authors merging to produce scientific knowledge is related to these costs. It seems that when two economists merge to produce scholarly output, the primary factor relating to the merger is specialization and trade of complementary productive skills. When there are three or more authors however, a mentor-protrg6 relationship is exhibited in an attempt by senior scholars to lead junior scholars on the 'rounds' of scientific advancement.
Acknowledgements The author is grateful to an anonymous referee for many helpful suggestions. Any remaining errors are my own.
F. G. Mixon Jr./Labour Economics 4 (1997) 185-191
191
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