In social sciences the measurement of performance is usually done giving the full credit of each paper to all its authors. Aiming to analyze the impact of the number of authors on the performance results, we propose an adjustment to the h-index that is flexible enough to allow the consideration of distinct co-authorship weighting schemes. We then evaluate the publication performance of the members of the departments of economics of the top 10 world universities (472 authors; 15,243 papers). Our results show that the number of authors per paper is rapidly increasing and that this dimension measurably affects the final ranking of authors even in a scientific area in which the average number of authors is lower than in physical and life sciences

Crespo, Nuno

Simoes, Nadia

Munich Personal RePEc Archive

MPRA
Munich Personal RePEc Archive
Publication Performance and Number of
Authors – Evidence for World Top
Economists
Nuno Crespo and Nadia Simoes
Instituto Universita´rio de Lisboa (ISCTE - IUL), ISCTE Business
School Economics Department, BRU - IUL (Business Research
Unit), Lisboa, Portugal.
2019
Online at https://mpra.ub.uni-muenchen.de/92581/
MPRA Paper No. 92581, posted 9 March 2019 09:43 UTC
Publication Performance and Number of Authors – Evidence for World Top 
Economists 
 
 
Nuno Crespo(a) and Nadia Simoes(a) 
 
 
(a) Instituto Universitário de Lisboa (ISCTE - IUL), ISCTE Business School Economics 
Department, BRU - IUL (Business Research Unit), Lisboa, Portugal.  
 
 
 
 
Abstract: In social sciences the measurement of performance is usually done giving the full 
credit of each paper to all its authors. Aiming to analyze the impact of the number of authors 
on the performance results, we propose an adjustment to the h-index that is flexible enough to 
allow the consideration of distinct co-authorship weighting schemes. We then evaluate the 
publication performance of the members of the departments of economics of the top 10 world 
universities (472 authors; 15,243 papers). Our results show that the number of authors per paper 
is rapidly increasing and that this dimension measurably affects the final ranking of authors 
even in a scientific area in which the average number of authors is lower than in physical and 
life sciences.   
 
Key words: publication performance, h-index, authors, credit.  
JEL Codes: A11, A14, C43, I23.  
 
Author for correspondence: Nuno Crespo. Av. das Forças Armadas, 1649-026 Lisboa, 
Portugal. Tel: + 351 21 790 34 77.  
  
2 
 
 
 
 “Possibly the greatest shortcoming of the h index is its inability to discriminate between 
authors that have very different coauthorship patterns”.   
(Hirsch, 2019, p. 2) 
 
1. Introduction 
Scientific collaboration is rapidly increasing, raising important challenges to the standard 
bibliometric approaches concerning the measuring of the effective contribution/merit of each 
author. Recognizing the importance of this aspect, several weighting schemes have been 
proposed (for a survey see Todeschini and Baccini, 2016). However, there are considerable 
differences between sciences regarding the importance given to this issue in performance 
evaluation exercises. Social sciences traditionally give lower attention to this aspect than 
physical and life sciences (Ossenblok et al., 2014; Henriksen, 2016).  
We argue that because of the importance of bibliometric measures for critical decisions 
concerning funding, hiring, promotions, and awards (Gao et al., 2016; Hamermesh, 2018; 
Osório, 2018) and the increasing average number of authors per paper (Wuchty et al., 2007; 
Frandsen and Nicolaisen, 2010; Larivière et al., 2015), ignoring this dimension is hard to accept 
as valid.   
This paper makes two main contributions. First, we propose an adjustment to the h-index to 
incorporate this dimension. Second, we evaluate the impact of the number and sequence of 
authors on publication performance considering a sample of 472 world top economists.     
 
2. Data 
In order to empirically discuss the importance of the number and sequence of authors on 
performance measures, we consider the authors with primary appointments at the departments 
3 
 
 
 
of economics of the top 10 world universities in the area of “Economics & Econometrics” 
according to the QS World University Ranking: Harvard University; Massachusetts Institute 
of Technology; Stanford University; University of California, Berkeley; Princeton University;  
University of Chicago; London School of Economics and Political Science; University of 
Oxford; Yale University; and Columbia University. Our sample includes the publications of 
472 authors, including 14 Nobel laureates, corresponding to the full list of tenure-track or 
tenured faculty members, as defined by departmental websites in October 2018. All data were 
gathered from the Web of Science (WoS) database (core collection) in October and November 
of 2018 using the following criteria: (i) type of paper: articles and reviews; (ii) language: 
English.  
To assure the validity of the data we conducted a detailed comparison for each of the 472 
authors included between the list of papers given by WoS and the information on individual 
publications retrieved from departmental and personal websites. When necessary 
complementary sources were also considered (e.g., Econlit). The final composition of the 
sample includes 15,243 papers (published between 1957 and 2018 in 709 different journals) 
and 1,288,803 citations.  
3. A New Index to Account for the Number and Sequence of Authors 
A scientific paper is the result of the effort and the merit of its authors. The reasons, advantages, 
and costs of scientific collaboration have been extensively discussed in the literature (see, for 
instance, Leahey, 2016; Fang, 2018; Henriksen, 2018). Our focus in the present study concerns 
the identification of the credit that should be given to each author. In fact, when there are two 
or more authors, a key question emerges: what is the real contribution of each author? The 
answer is subjective and in fact only the authors know it. However, recognizing the importance 
4 
 
 
 
of this issue, countless co-authorship weighting schemes have been suggested (Osório, 2018; 
Vavryčuk, 2018). They seek to infer the contribution of the author from his/her position in the 
author’s list of the paper. One exception is the standard counting scheme (full credit to all 
authors), in which the credit received by each author is independent of the number of authors 
and of their specific position. This is precisely the hypothesis inherent to the h-index, 
representing one of its most critical drawbacks (Hirsch, 2019). Other popular weighting 
schemes include uniform counting and proportional counting. Let us define the position of the 
author in the paper’s list of authors as   (  =  1, 2, … . ,  ) and the weight given to each author 
as  ( ). In the uniform counting,  ( )  =  1/ , "  while in the proportional counting  ( )  =
 1/ , therefore taking into account not only the number of authors but also their position. Other 
schemes follow a more extreme solution, giving the full credit of the paper to only one author. 
This is the case of the straight counting scheme, which gives the credit to the first author (Cole 
and Cole, 1973).   
Given the importance of this topic, some measures have been suggested aiming to adjust or to 
complement the h-index. Crispo (2015) proposes a complementary index – the AP-index – 
accounting for the average position of the author in the group of papers that compose the h-
core. Recently, Hirsch (2019) introduces the ℎ -index aiming to measure the degree of 
scientific leadership. Other measures opt to adjust the h-index. This can be done through a cut 
in the total number of papers (e.g., the paper fractional h-index, proposed by Egghe (2008)), a 
cut in the total number of citations (e.g., the weighted h-index suggested by Abbas (2011)), or 
through adjustments in the h-index after its calculation, such as those suggested by the pure h-
index (Wan et al., 2007) or the complementary h-index (Dorta-González and Dorta-González, 
2011).  
5 
 
 
 
We follow this last option but suggest an even simpler way to adjust the h-index. This new 
measure (ℎ∗-index) corresponds to the proportion of the total merit/performance of the author 
(defined by ℎ) that can be assigned to him/her, as defined by the weighting scheme used:  
ℎ∗ =    [ ∑  ( )]
  
                 (1) 
in which   represents papers and    are the last paper included in the h-core. ℎ
∗ is rounded to 
the lower value. When  ( ) = 1 for all papers, ℎ∗ = ℎ. In the remaining cases, ℎ∗ < ℎ.  
4. Evidence 
We start our empirical analysis with the issue of the author’s position in the list of authors. 
While in some cases it reflects a different role in the paper’s conception and production, in 
some sciences the common practice is to follow the alphabetical order of the names. When this 
occurs, a scheme that takes into account the sequence of authors should not be used. We test 
this aspect for the 15,243 papers of our sample and verify that alphabetical order is followed 
by 91.38% of the multi-authored papers, which is in line with previous evidence by Kadel and 
Walter (2015). Therefore, the uniform counting scheme will be adopted as reference.    
The 15,243 papers were produced by a total of 34,710 authors, corresponding to an average of 
2.28 authors per paper. The number of authors ranges between 1 (4,014 papers) and 255 (a 
paper by David Laibson published in Nature in 2016). Table 1 presents key evidence 
concerning the evolution of the number of authors per paper throughout the period considered.  
[Insert Table 1] 
The results clearly demonstrate a strong increase of scientific collaboration in economics, in 
which we highlight: (i) the increase of the average number of authors per paper, from 1.397 in 
6 
 
 
 
the period 1957-1970 to 2.893 in the current decade; (ii) the dramatic reduction of single-
authored papers, from 65.44% of the total in the first period to only 14.74% today.  
The impact on performance measures depends on the distribution of this variable (number of 
authors per paper). Figure 1 shows this evidence, highlighting the existence of remarkable 
differences among the authors.   
[Insert Figure 1] 
These results demonstrate that co-authorship is an important issue that must be addressed by 
the standard performance metrics since the lack of its consideration can lead to biased 
conclusions. Our evidence clearly illustrates this aspect. For example, we have 19 authors with 
ℎ∗ = 10 but their original h-index range between 12 and 35. The same happens for instance in 
the case of the authors with ℎ∗= 20. The seven authors with this adjusted score have values of 
the h-index between 29 and 43.  
Figure 2 presents the link between the average number of authors per paper (in the h-core), h, 
and ℎ∗. Authors represented more to the left in panel (2a) and more to the right in panel (2b) 
are those with the best scores in h and ℎ∗, respectively. 
[Insert Figure 2] 
Comparing the top 10 obtained with the two measures, we conclude that 7 authors belong to 
the top in both cases (Andrei Shleifer, Joseph Stiglitz, James Heckman, Peter Phillips, Robert 
Barro, Daron Acemoglu, and John Campbell) but significant modifications occur. Andrei 
Shleifer occupies the 1st position of the ranking based on the h-index, but due to his high number 
of co-authors per paper when compared to the average (the 2nd highest in the top 10), ranks 
only 6th according to ℎ∗. The first position in this measure belongs to Joseph Stiglitz (the author 
with most papers in the whole sample and the 3rd in the h-ranking). The most noticeable 
increases are seen for Amartya Sen (from 12th to 2nd) and Martin Feldstein (from 12th to 4th), 
which is explained by the fact that these authors register the lowest values of average number 
7 
 
 
 
of authors per paper (in the h-core) among all included in the top 30 of ℎ (1.12 and 1.31, 
respectively).  
 
5. Conclusion 
The stock of evidence presented in this study makes it clear that measuring performance using 
the most standard approach (ℎ-index) may produce biased conclusions since it lacks the 
consideration of one critical dimension – the number of authors – and that this problem is now 
much more important than in the past, even in social sciences, since scientific collaboration has 
increased rapidly throughout the last decades. This is also the case of economics. Therefore, 
obtaining fair decisions based on rankings of publication performance critically requires the 
use of performance measures that capture this dimension, such as the one suggested in this 
study (ℎ∗-index).   
 
 
References 
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8 
 
 
 
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Publication Performance and Number of Authors – Evidence for World Top Economists

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