Appendix 2.A Supplementary Outputs
4.6 Survey-Based Analysis
In summer 2011, I administered a survey to discriminate between the two theories presented in the previous section. I drew a random sample of the 1470 articles in my data set and asked the authors of these articles about their experiences in col-laborating with their co-authors. Each author was asked only about one publication and the questionnaire was always sent to both authors of an article.15 Details about the administration of the survey with additional descriptive statistics can be found in Appendix 4.A.
To quantify the conceptual and technical skills of the authors, I asked them how much they contributed to the underlying idea, how much of the technical tasks they performed, and about their share in writing the article. To test the theory of inter-personal relationships, I asked the authors whether they were already friends with their co-authors when they started working on the project, whether they became friends during that process or whether their relationship was purely professional. I also asked the two co-authors whether they ever applied for the same jobs. The answer to this question serves as a proxy for competition between the two collabora-tors. Note that the age difference is now defined as the age of the respondent minus the age of the co-author. It can, therefore, assume negative values.
Table 4.5 compares the arithmetic means for the survey responses of the two col-laborators. The difference is most pronounced for the share that the authors claim to have had in the technical execution of the project. Figure 4.4 visualizes these differences. Note the spike at 50%, which can also be observed in the distributions of the idea shares and writing shares.
I also calculated a measure of the shares in the three tasks relative to the average contribution. For this measure, I first computed the arithmetic mean of the three shares for every respondent and then divided each share by this arithmetic mean.
This measure accounts for the fact that an author may have had a higher or lower overall share in the realization of an article. In other words, even if an author said
15While the survey was being conducted, it turned out that it could not be sent to authors affiliated with institutions outside Germany Austria or Switzerland. Hence, if one of the respondents living in one of the three countries had a co-author outside these three countries, only he was asked about
different institution (<100 km) 0.0703(313) 0.0633(158) 0.0774(155) different institution (>100 km) 0.2684(313) 0.2785(158) 0.2581(155)
own share idea 50.75(308) 51.62(154) 49.87(154)
own share tech tasks 50.58(308) 44.74(154) 56.43(154) own share writing 51.07(308) 48.90(154) 53.25(154) idea rel. to av. contribution 1.0034(308) 1.0760(154) 0.9307(154) tech rel. to av. contribution 0.9900(308) 0.9152(154) 1.0648(154) writing rel. to av. contribution 1.0083(308) 1.0120(154) 1.0045(154) met >3y before collaboration 0.6804(316) 0.7063(160) 0.6535(156) met <3y before collaboration 0.3006(316) 0.2750(160) 0.3269(156) not met before collaboration 0.0190(316) 0.0188(160) 0.0192(156) colleagues / fellow students 0.4684(301) 0.5098(153) 0.4257(148) mentor-prot´eg´e relation 0.3389(301) 0.3203(153) 0.3581(148) met at a conference 0.1063(301) 0.0915(153) 0.1216(148) contacted to collaborate 0.0864(301) 0.0784(153) 0.0946(148) were friends before 0.6181(309) 0.6795(156) 0.5556(153)
became friends 0.1812(309) 0.1538(156) 0.2092(153)
purely professional 0.2006(309) 0.1667(156) 0.2353(153) ever applied for same jobs 0.1529(314) 0.1635(159) 0.1419(155) never applied for same jobs 0.7038(314) 0.6667(159) 0.7419(155)
do not know 0.1433(314) 0.1698(159) 0.1161(155)
Notes: Number of respondents in parentheses next to relative frequencies. 317 responses received in total (rate 54.75%).
0.1.2.3.4Fraction
0 20 40 60 80 100
Older co−authors’ share of tecnical tasks
0.1.2.3.4Fraction
0 20 40 60 80 100
Younger co−authors’ share of tecnical tasks
Figure 4.4: Older and younger co-authors’ claimed shares of the technical tasks.
contribution if he says he performed only 10% of the technical tasks and of writing the article.
Table 4.6 shows tests of the skill heterogeneity theory presented in Section 4.5.1.
The upper panel includes all respondents, whereas the middle panel only considers the older co-authors, and the lower panel considers younger co-authors. An author’s share of the underlying idea does not increase with the age difference. However, relative to the overall contribution, older scholars have a higher share of the idea, because older authors tend to contribute less overall relative to their younger col-laborators. The correlation between an author’s share of the technical execution and the difference between his and his co-author’s age is highly negative. The same applies to the share of writing the report. These findings provide some support for skill heterogeneity, but they do not exactly confirm it. In Section 4.5.1 it was argued that conceptual skills were increasing with an author’s age, whereas technical skills were decreasing with age. However, all coefficients on own age are virtually zero.16 Table 4.7 shows tests of the theory of personal relationships. In column (1), a dummy which indicates whether the respondent said that he and his co-author were friends when they started working on the project is regressed on the respondent’s age, the difference between his and his co-author’s age, and various covariates. The coefficient on own age is significantly negative and the coefficient on age difference is significantly positive when the whole sample is used. More informative are the mid-dle and lower panels, which divide the sample into older and younger authors. For older authors, age difference is a positive number, for younger authors, it is negative.
In both subsamples, the coefficients on age difference are significantly different from zero. When older authors are taken into consideration, the coefficient is negative, for younger authors it is positive. Even though the coefficients have different signs, the picture is the same: the smaller the age difference, the more likely the two authors were friends before they started their collaboration. In column (2), the dependent variable is equal to 1 if the authors were either friends before they started working on their joint project or if they became friends in the process. The findings are the same.
Columns (3) and (4) repeat this analysis, now with indicators for whether the respon-dent and his co-author have ever applied for the same job or whether the responrespon-dent
16Unreported results show that the coefficients on own age are different from zero at the 5% level of significance with the expected positive sign in column (2) and negative signs in columns (3) and
all respondents own age 0.2920 -0.0009 0.2913 0.0019 0.1928 -0.0013 (0.94) (-0.19) (1.00) (0.37) (0.74) (-0.33) age difference 0.0438 0.0098** -0.7437*** -0.0080* -0.4666** -0.0016 (0.17) (2.52) (-3.29) (-1.93) (-2.09) (-0.49)
controls yes yes yes yes yes yes
R2 0.1224 0.2160 0.2484 0.2266 0.1959 0.1744
observations 289 289 289 289 289 289
older authors own age -0.4298 -0.0175** 0.7226* 0.0128 0.4066 0.0046
(-0.85) (-1.99) (1.69) (1.35) (1.12) (0.89) age difference 1.0635* 0.0311*** -1.1071** -0.0206* -0.7521* -0.0117*
(1.88) (3.26) (-2.17) (-1.88) (-1.75) (-1.88)
controls yes yes yes yes yes yes
R2 0.3408 0.4461 0.4340 0.4545 0.3856 0.4125
observations 144 144 144 144 144 144
younger authors own age 0.6966 0.0075 0.1400 -0.0023 0.0141 -0.0052
(1.38) (1.09) (0.30) (-0.30) (0.03) (-0.69) age difference -0.5643 -0.0044 0.0130 0.0100 -0.7591* -0.0056 (-0.96) (-0.55) (0.03) (1.35) (-1.88) (-0.81)
controls yes yes yes yes yes yes
R2 0.2855 0.3783 0.3294 0.3404 0.2912 0.3083
observations 145 145 145 145 145 145
Notes: OLS regression; robust standard errors; t-statistics in parentheses; additional controls include indica-tors for respondent and co-author being female or economists, respectively, their human capital endowments, the article score CLm, indicators for distance during collaboration, how long the authors knew each other and how their collaboration started, as well as year and country dummies; *** p<0.01, ** p<0.05, * p<0.1.
107
all respondents own age -0.0583*** -0.0655*** -0.0484** -0.0464**
(-3.37) (-3.51) (-2.31) (-2.48)
age difference 0.0482*** 0.0468*** 0.0299** 0.0295**
(3.77) (3.32) (2.12) (2.25)
controls yes yes yes yes
Pseudo-R2 0.2204 0.2072 0.1179 0.1084
observations 289 289 294 294
older authors own age 0.0238 -0.0027 -0.0071 -0.0158
(0.79) (-0.09) (-0.25) (-0.58)
age difference -0.1156*** -0.0858** -0.1290*** -0.0938***
(-3.34) (-2.35) (-3.07) (-2.82)
controls yes yes yes yes
Pseudo-R2 0.3350 0.2931 0.2675 0.2389
observations 145 145 148 148
younger authors own age -0.0301 -0.0708* -0.0379 -0.0017
(-1.59) (-1.93) (-1.10) (-0.06)
age difference 0.0922*** 0.1143*** 0.1142*** 0.0945***
(3.10) (4.08) (3.10) (3.29)
controls yes yes yes yes
Pseudo-R2 0.2773 0.3151 0.2166 0.2044
observations 144 135 132 146
Notes: Probit estimates; robust standard errors; z-statistics in parentheses; additional controls in-clude indicators for respondent and co-author being female or economists, respectively, their human capital endowments, the article score CLm, indicators for distance during collaboration, how long the authors knew each other and how their collaboration started, as well as country dummies; other than before, year of publication was accounted for linearly; *** p<0.01, ** p<0.05, * p<0.1.
108
Again, I find that the smaller the age difference, the more likely it is that the two authors have ever competed on the job market. The survey, therefore, provides strong support for the hypothesis that personal relations matter for collaboration.
Common paradigms were not examined.
Table 4.B.1 in Appendix 4.B shows the coefficients on the covariates from the re-gressions of the shares in the three tasks when the entire sample was used (upper panel of columns (1), (3) and (5) in Table 4.6) and the dummies indicating whether the authors had already been friends before their collaboration when the entire sam-ple was used (upper panel of columns (1) and (3) in Table 4.7). One notable and intuitive result is that mentor-prot´eg´e relationships tend to reduce the probability that the two collaborators were friends before they started working together.
4.7 Conclusion
Jones (2010b) identifies two major trends in science: important innovations are made increasingly later in life and by teams rather than solo researchers. Age and team work are, therefore, of prime interest in the economics of science and this study demonstrates that the two must not be looked at in isolation. It investigates the relation between age composition of collaborators and the complementarity of their inputs. It suggests an optimal age difference between co-authors of about ten years.
This result is highly significant and robust to the way article output and human capital are measured.
To be sure, the assumptions underlying the analysis in this study are rather restric-tive. The production function is not estimated, it is simply assumed that it is of a CES type. Neither do I estimate the complementarity parameter ρ. Based on my assumptions about functional form, I obtain it through approximation. Further-more, my sample only includes collaborations that actually lead to published work.
Although most researchers submit their working papers until they eventually find an outlet, some papers may actually end up in the waste bin. It is, however, not clear whether and how such failure might be correlated with the age structure of the team which would induce bias. And collaboration between exactly two researchers is only a subset of all co-authorships in economics, although by far the most frequent
17In column (4) the dependent variable is equal to 1 if the respondent either checked that he and the co-author have ever applied for the same job or if he checked that he did not know.
potential source of bias, but it is not clear in which direction that bias would go.
Despite all these caveats, the findings presented in this paper may have implications for the way we think about collaboration in general. We do not live in a Robinson Crusoe economy. Virtually all instances of production involve some kind of human interaction.
I present two theoretical approaches which may explain my findings. The first is based on a framework with two different kinds of complementary skills, the second uses the theory of consumption benefits as a starting point and addresses inter-personal relationships. Survey-based analysis shows that the tasks performed in scientific production and personal relations are both related to the age difference between the collaborating authors.
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