Matthew effects in science and the serial diffusion of ideas: Testing old ideas with new methods

Abstract The Matthew effect has become a standard concept in science studies and beyond to describe processes of cumulative advantage. Despite its wide success, a rigorous quantitative analysis for Merton’s original case for Matthew effects—the Nobel Prize—is still missing. This paper aims to fill this gap by exploring the causal effect of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (hereafter the Nobel Prize in Economics). Furthermore, we test another of Merton’s ideas: successful papers can draw attention to cited references, leading to a serial diffusion of ideas. Based on the complete Web of Science 1900–2011, we estimate the causal effects of Nobel Prizes compared to a synthetic control group which we constructed by combining different matching techniques. We find clear evidence for a Matthew effect upon citation impacts, especially for papers published within 5 years before the award. Further, scholars from the focal field of the award are particularly receptive to the award signal. In contrast to that, we find no evidence that the Nobel Prize causes a serial diffusion of ideas. Papers cited by future Nobel laureates do not gain in citation impact after the award.


INTRODUCTION
In 1968, Robert K. Merton published a seminal paper in Science that has become one of the most cited references on the sociology of science and beyond. Based on previous research on the success of Nobel laureates after elevation, Merton coined the term Matthew effect 1 to describe "the accruing of greater increments of recognition for particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark " (1968; p. 58). While Merton was well aware of the very advantageous career opportunities of many Nobel laureates and the accumulation of various forms of peer recognition, such as the reception of other awards, outstanding citation impact, and external funding prior to being awarded the Nobel Prize, he emphasized that receiving the Nobel Prize elevated the research of laureates among other work of "prize-winning calibre" (p. 57).
1 While Merton's paper in Science has become the standard reference on Matthew effects, Merton himself acknowledged in the reprinting of the paper that the research of his wife Harriet Zuckerman (1977) was essential for developing the concept: "It is now [1973] belatedly evident to me that I drew upon the interview and other materials of the Zuckerman study to such an extent that, clearly, the paper should have appeared under joint authorship" (Merton, 1988, p. 607).
As a consequence, the "crowning" of scientific careers with a Nobel Prize leads to a further accumulation of scientific rewards such as assigning priorities in independent multiple discoveries and attributing individual contributions in collaborative research.
Merton's paper has not only become the core reference in the rich literature on cumulative advantages in academia (Allison, Long, & Krauze, 1982;Cole & Cole, 1973;de Solla Price, 1976), but also in the broader literature on rich-getting-richer phenomena in other areas of social life (DiPrete & Eirich, 2006;Salganik, Dodds, & Watts, 2006;van de Rijt, Kang et al., 2014). Thereby, the concept of Matthew effects has proven its explanatory value in a broad range of areas, including research on health inequalities, cultural markets, educational success, and labor market trajectories (for reviews see Rigney (2010) and Zuckerman (2011)).
Despite this wide use of the concept, a rigorous quantitative analysis for Merton's original case of the Nobel Prize is still missing. Indeed, the ideas of Merton and Zuckerman have inspired further scholarship on the Nobel Prizes (e.g., Bjork, Offer, & Söderberg, 2014;Boettke, Fink, & Smith, 2012;Cole, 1970;Diamond, 1988;Karier, 2010). For example, research has shown that the number of awards (Chan, Gleeson, & Torgler, 2014) as well as citation impacts steadily increases ahead of the event (Garfield & Welljams-Dorof, 1992;Mazloumian, Eom et al., 2011).
Similarly, Merton's and Zuckerman's pioneering work has marked the starting point for rigorous causal analyses of the effects of other positive status shocks in science. Analyzing decisions for early-career grant funding in the Netherlands as a sort of natural experiment, Bol, de Vaan, and van de Rijt (2018) find that grantees just above the funding threshold receive substantially more funding in the following years and are significantly more likely to become full professors than applicants just below the threshold. Focusing on prestigious midcareer awards in medicine and economics, Azoulay, Stuart, and Wang (2014) and Chan, Frey et al. (2013) find evidence for a citation boost caused by the honoring, although the studies disagree about how strong and lasting such an effect is. Moreover, numerous studies document that status markers such as author prestige (e.g., Wang, 2014), lead articles in journal volumes (e.g., Michayluk & Zurbregg, 2014), and designation of a paper by the editor as very important (Mutz, Wolbring, & Daniel, 2017) affect future citation impact 2 .
To sum up, the literature has clearly corroborated the idea that status affects future rewards and career opportunities. However, to the best of our knowledge, no study exists that provides a rigorous analysis of the causal effect of Nobel Prize reception on the accumulation of further citations for a group of laureates. An exception is our case study on the honoring of Robert J. Aumann with the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (hereafter the Nobel Prize in Economics) 3 which finds no Matthew effect at all on citation impact (see Farys & Wolbring, 2017). However, these results are unlikely to generalize to other Nobel laureates, because Aumann's work had been rarely cited before the award due to its high degree of mathematical abstraction. 2 A related literature also investigates the effects of negative status shocks. Taking the case of article retractions, Lu, Jin et al. (2013) report marked negative effects of non-self-reported retractions on citation impact of authors' recent and earlier papers. In addition, Azoulay, Zivin, and Wang (2010) highlight that negative status shocks can spill over: Collaborators in the "invisible college" suffer from the death of a superstar by markedly lower quality-adjusted publication rates. 3 We are aware of the cultural and political dimensions of the Nobel Prize and the widespread criticism of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel as being treated as a "Nobel Prize in Economics," legitimating economics as a "science" comparable to other Nobel fields (see Offer & Söderberg, 2017). It is further worth noting that only one woman, Elinor Ostrom, has received the award. These issues are beyond the scope of this study but certainly worth exploring.
Building on our previous work and based on the complete Web of Science (WoS) 1900-2011, we aim to fill this gap by exploring the causal effect of a Nobel Prize in Economics on citation impacts and its dynamic over time. Using a combination of different matching techniques and longitudinal modeling, we not only control for differences in intrinsic quality and unobserved variables affecting citation impact but also go beyond average effects in two ways. On the one hand, we explore potential heterogeneity for different Nobel Prize publications with respect to publication date, pre-Nobel citation impact, and journal reputation. On the other hand, we investigate audience-specific reactions to the awards by distinguishing citation impact among scholars of the focal field of the award (such as in business, economics, and management) and scholars of the neighboring social and behavioral sciences.
In addition, we want to explore whether another mechanism is at work that might cause spillover effects of the Nobel Prize on publications cited by the laureate. Merton (1995, p. 388) mentioned in later publications such a possibility, dubbing it the "serial diffusion of ideas" through "mediated references." The basic idea is that papers written by future Nobel laureates receive more attention after the reception of the prize (see also Frandsen & Nicolaisen, 2013). This might indirectly raise scholars' awareness of Nobel Prize winners' cited references (see Peterson, Press, and Dill (2010) for the distinction between direct and indirect mechanisms for citations) and in that sense the social status of a Nobel laureate might leak down the citation network; even publications cited by Nobel Prize winners' cited references might gain, to perhaps a lesser extent, in citation impact.

MATTHEW EFFECTS ON CITATION IMPACTS
Peer recognition for scientific achievements can come in various forms, ranging from more or less prestigious awards, memberships in scientific societies and external research grants to the possibly most elementary level of using and citing one's work (Merton, 1988, p. 620). In this paper, we focus on the effects of a Nobel Prize in Economics on citation impacts and the potential serial diffusion of ideas in the citation network. One reason for our focus on citations is that they are one of the most elementary forms of peer recognition in the science system. Another reason is that citations are "one of the micro-level stratifying mechanisms in science" (Baldi, 1998, p. 830), as citation impact can positively affect other forms of peer recognition. For example, bibliometric analyses have become an integral part of most research evaluations and can have consequences for hiring, tenure, and funding decisions.
Citations are the building blocks of knowledge claims in modern science. They are located at the level of publications and connect the argument in one publication with the content of another paper, creating a complex network of directed references among publications. Citations can thereby serve very different functions Leydesdorff, 1998;Nicolaisen, 2007;Tahamtan & Bornmann, 2019). Two positions have emerged in the literature which conflict in their interpretation of the role of citations in science: the normative view and the social constructivist view. Both views help to provide insights into the potential reasons why awards might affect citation impacts.
Proponents of the normative citation theory such as Merton (1988, p. 621) argue that "the institutionalized practice of citations and references in the sphere of learning is […] central to the incentive system and underlying sense of distributive justice" of modern science, because citations serve two functions. On the one hand, they have an instrumental cognitive function by making readers aware of the sources of knowledge and put them in a position to follow up on ideas and claims formulated in the literature. From this perspective, a Nobel Prize could increase citation impact, as it raises awareness of the existence of a laureate's knowledge claims. Such an attention boost caused by a Nobel Prize appears to be especially likely among less well informed scholars, such as those coming from a different, though related, field of inquiry. Similarly, cited references in a laureate's publications could indirectly profit from this attention boost, causing a serial diffusion of ideas.
On the other hand, citations also serve a symbolic institutional function according to the normative citation theory. Citations mark the origin of ideas, recognize authors' original contributions, and accrue social esteem. As such, they acknowledge property rights, signal intellectual debt, and reward scientific achievements. In short: They are supposed to give credit where credit is due (Kaplan, 1965). Thereby, in an ideal world of science, scholars should accrue peer recognition based solely on the worth of a contribution (e.g., the importance, content, and quality of a publication), and regardless of other nonmeritocratic criteria, such as authors' status or affiliation (Merton, 1973).
However, as the case of the Matthew effect shows, scientific practice sometimes deviates from this norm of universalism in systematic ways. In particular, authors might prefer to read and cite the publications of a Nobel laureate as compared to other equally relevant references due to different mechanisms. Merton (1968) himself already sketched one potential mechanism of why scholars might deviate from the norm of universalism: In the face of an increasing amount of scholarship as well as limited reading time-an argument nowadays even more important than back then (Falkinger, 2008;Franck, 2002)-scholars might rely on author status as a potential signal for the underlying quality of a publication. As Bothner, Podolny, and Smith (2011) show in a simulation study, employing such a strategy can be rational in the case of incomplete information as long as the association between status signal and intrinsic quality is sufficiently strong. However, such an approach becomes dysfunctional and leads to the neglect of other more relevant publications and ideas if status and quality are only weakly correlated.
Proponents of the social constructivist sociology of science (Callon, Law, & Rip, 1986;Knorr-Cetina, 1981;Latour, 1987) propose a different view of science and the role of citations therein. Instead of assuming that science is governed by a certain set of internal norms and a recognitiondriven reward system, they contend that science in practice is shaped by processes of social influence, political and financial interests, and power relationships. The constructivist view, hence, frames science as a "war of words" in which "publications are weapons in a struggle among scientists to persuade each other of the validity of knowledge claims, and thereby to establish dominant positions in the community" (Cozzens, 1989, p. 440). Therefore, scientific claims are not mere objective facts but socially constructed and deconstructed (Latour & Woolgar, 1979). To reach the status of objective facts, scholars need to convince readers, reviewers, and editors about the validity of their claims.
Against that background, proponents of social constructivist citation theory emphasize that citations often do not merely serve a cognitive instrumental or symbolic institutional function but are used as "tools of persuasion" (Gilbert, 1977;MacRoberts & MacRoberts, 1987). As rhetorical devices in the publication game, citations can mark the novelty and relevance of one's work, signal allegiance to certain intellectual traditions, or help to back up arguments. As scientific "defense lines," references might also be misquoted on purpose to strengthen one's position or be cited without actually being read (Latour, 1987;Luukkonen, 1997).
In contrast to the normative citation theory, the actual relevance and intrinsic quality of a publication should only matter for citation behavior to the extent that it can positively influence the credibility of one's claim. Hence, authors will try to draw on "codified" knowledge and cite "authoritative" references to create the impression of "facticity" (Gilbert, 1977;Moed & Garfield, 2004). It appears likely that Nobel Prize decisions trigger such strategic citation behavior 4 , as the award puts the laureate in a special position for convincing others about scientific claims (see also Strevens, 2006). While Nobel publications are likely to receive such "ceremonial" citations (see Adatto & Cole, 1981) according to the constructivist view, cited references do only matter for strategic behavior under certain conditions. For example, incentives for strategic citations might exist to cite references that were fundamental for the contribution of the Nobel laureate and hence also gain in authoritativeness by the award.
To sum up, citations can serve very different functions. Normative theories hightlight the role of citations as part of the scientific system of property rights and rewards, whereas social constructivist theories point out the often strategic nature of citations as a rhetorical device of persuasion. Both theoretical accounts have proven their heuristic and explanatory value in empirical research (e.g., Baldi, 1998;Collins, 1999;Cronin, 2005;Safer & Tang, 2009;Shadish, Tolliver et al., 1995;Thornley, Watkinson et al., 2015;White, 2004). Hence, in practice, a mixture of these and other processes is likely to be at work simultaneously (for a comprehensive framework see .
While it is undisputed that a Nobel Prize confers peer recognition and raises the professional standing of the laureate, it is not completely clear which mechanisms cause Matthew effects in citation impacts. According to the normative view, the work of the laureate might receive more attention due to the Nobel Prize especially by those less well informed prior to the honoring. Thereby, beyond a mere attention effect, the award might also work as a signal helping scholars to identify particular important high-quality research. Both mechanisms might also cause a serial diffusion of ideas. However, according to the social constructivist view, the Nobel Prize could also create incentives to cite a laureate's publications not because of their exceptional quality but due to their authoritative status. We would expect such strategic citation behavior especially among those from the focal field of the award, who should already be well informed about the laureate's research before the honoring. A serial diffusion of ideas would also be compatible with a social constructivist view of science, but such a prediction requires additional assumptions and likely only holds for a restricted set of publications among the references cited in Nobel publications.
While our analytical approach does not allow us to fully disentangle the mechanisms behind the observed citation pattern, the analyses will give at least some hints as to which processes are at work against the background of these theoretical considerations.

Database and Treatment Group
To dissect the effect of the Nobel Prize on the citation impacts of laureates' publications, we employ raw data from Clarivate Analytics' WoS 1900-2011, including the Science Citation Index Expanded, the Social Sciences Citation Index, and the Arts & Humanities Citation Index, but excluding other sources such as the Emerging Sources Citation Index and the Book Citation Index. The raw data comprise over 250 files amounting to over 150 Gbyte, originally managed by Clarivate Analytics in a databank system. We drew the necessary citation information directly from the raw data of the WoS Core Collection, which does not cover books and publications in edited volumes and conference proceedings, on the basis of unique article identifiers using Perl and R scripts. As the raw data also contain correction and gap files, which replace existing entries or which add new ones, we generated a tailor-made correction and doublet filter to reproduce citation counts one-to-one as reported in the web version of the WoS.
We focused on the 23 winners of the Nobel Prize in Economics for the years 2000-2010 (see Table 1). One important reason for choosing the Nobel Prize in Economics for the years [2000][2001][2002][2003][2004][2005][2006][2007][2008][2009][2010] was that coverage of publications in the WoS is much more comprehensive for Nobel laureates who received the award from 2000 onwards than for previous Nobel winners. Although going back in time would definitely be interesting from a substantive point of view, a more comprehensive coverage of publications improves the chances of detecting Nobel Prize effects and potential interactions should they actually exist. In addition, data for 184 publications of the 23 Nobel laureates yield a sufficient sample size for statistical analysis and stratification by publication characteristics and audience 5 .
Next, we referred to the "Scientific Background Reports" of the Royal Swedish Academy of Sciences (www.nobelprize.org) to identify the recipients' most important contributions. Using only those "Nobel publications" instead of all publications of the laureate offers the advantage of reducing the variance in quality judgments of works and helps to build a strong case for a context with relative quality certainty. We further restricted the sample to full articles, excluding other publications by the Nobel Prize winners listed in WoS, such as responses and corrections. Having defined the set of treated papers, we then searched for all 283 publications in the raw data of the WoS, collected yearly citation data for each of the 184 available Nobel publications (65%) in the raw data of the WoS, and linked further information regarding document, author, and publishing journal.

Construction of Synthetic Control Groups
Simple comparison of the numbers of annual citations for treated papers before and after the event is inadequate for estimating the causal effects of a Nobel Prize on citation impact Table 1. List of Nobel Laureates in Economics for the years [2000][2001][2002][2003][2004][2005][2006][2007][2008][2009][2010] Year Laureate Year Laureate Year Laureate because of a number of factors (for a detailed discussion see Farys & Wolbring, 2017). First, the number of citations in the WoS follows a strong positive time trend. Clarivate Analytics (and formerly Thomson Reuters) has substantially increased its coverage of journals over time and in 2005 added a new database, the Book Citation Index, to the WoS Core Collection (Testa, 2011). Second, modern science has expanded considerably. As a consequence, the number of publications and the average length of articles' reference lists is nowadays considerably larger than in the past (Bornmann & Mutz, 2015). Third, citation paths of articles usually follow fieldspecific citation life cycles. The citation rates of most articles (disregarding Sleeping Beauties or citation classics) typically peak depending on the field several years after publication and then steadily decline (Burton & Kebler, 1960;de Solla Price, 1970). Confounding due to such time trends and maturation effects problematizes any causal interpretation of changes in annual citations after Nobel Prize receipt.
Further strengthening these concerns for our current application is the fact that the set of Nobel Prize papers is a highly selective and highly cited subgroup which does not follow the typical citation life cycle and usually increases in citation impacts steadily ahead of the event (Garfield & Welljams-Dorof, 1992;Mazloumian et al., 2011). Hence, although a random sample of untreated papers from the WoS would probably suffice to control for general time trends in the citation frequency and for the growth of the global science system, this approach is not suited to adjust for biases due to selection on citation growth.
We therefore constructed tailor-made synthetic control groups which approximate the treated papers as regards publication date and yearly citations before the event (see Azoulay et al., 2014;Chan et al., 2013;Lu et al., 2013 for similar approaches) 6 . We proceeded in three steps: First step: We generated a full list of publications in the WoS 1900-2011. This provides over 100 million papers as potential controls. We excluded all treated papers from this donor pool for the control group.
Second step: We performed a coarsened exact matching (CEM) procedure Porro 2012, 2014). Unlike propensity score matching, CEM ensures that imbalances in covariates between matched observations from the treatment and control group do not exceed a certain threshold level defined ex ante by the specified coarsening of variables. CEM offers a good trade-off between bias reduction and the curse of dimensionality, provided that variables with numerous values are matched. In our case we use the (partially) coarsened publication year, a categorization of the cumulative number of citations and the WoS subject categories as matching criteria (for limitations of these categories see Leydesdorff and Bornmann (2016)). A match only occurs if a control paper has the treatment's exact same combination of field tags, publication year, and categorized number of cumulative citations prior to the Nobel Prize receipt. For all treated publications we matched on publication year dummies ranging from 1981 to the year of Nobel Prize receipt. For papers 6 Another approach to construct a control group would be to use shortlisted scholars. This design would exploit the positional nature of status and the sharp discontinuities in success (Frank & Cook, 1995;Goode, 1978;Hirsch, 1977). While such analyses of Matthew effects at the author level are interesting and important when focusing on scholarly careers (e.g., Bol et al., 2018;Chan et al., 2014), several reasons led us to decide against this approach. First, the nomination list has been top secret for many decades, meaning that we would have to rely on public rumors. Second, some of the candidates won the prize a few years later, limiting the use of this case as a control to the years between the first and second awards. Third, it is unlikely that shortlisted scholars are good controls for the pre-event citation path. However, approximating the citation path of Nobel publications for the counterfactual scenario that the laureate had not received the award is essential to avoid biased estimates of the causal effect.
published before 1981, we had to be less restrictive: For papers published between 1950 and 1980 we also matched papers that did not appear in exactly the same year but in the same decade. For papers published before 1950 we searched for matches that appeared during . Finding matches to papers with extraordinarily high citation numbers and sometimes steep citation paths is especially difficult. To categorize the citation numbers, 20 percentile groups of 5% each were formed. For example, if a Nobelist paper is among the 5% most cited, then the paper of the control group must also belong to the top 5%. From this CEM procedure we derive weights for the control group as follows: If a control paper is the only possible match, it gets weight 1; if there are n matches for a paper, each of these controls gets weight 1/n, thus forming a pool of controls for the treated paper. All unmatched papers get the weight 0 and do not appear in the further analysis.
Third step: Based on these weights, we used Entropy Balancing (Abadie, forthcoming;Abadie, Diamond, & Hainmueller, 2010;Hainmueller, 2012) to align the pre-Nobel citation life cycle of the control group with that of the treatment group. Entropy Balancing in general relies on a reweighting scheme that calibrates weights in a way that the reweighted control group satisfies a potentially large set of prespecified balance conditions (Hainmueller, 2012). In our case we balanced the means of citations for all the single years between 1991 and the year of Nobel Prize receipt, the four decades from 1950 to 1990, and the time window 1900-1949. We further included the scientific field and publication date (as before) to preserve the previous restrictions. The control group is therefore equivalent to the treatment group in terms of publication date, scientific field, and recent citation history up to the date of Nobel Prize receipt. Although our matching procedures do not use many variables, the strength of the approach lies in the fact that the pre-Nobel citation path controls a multitude of unobserved heterogeneity. As Abadie et al. (2010) and Abadie, Diamond and Hainmueller (2015) emphasize, such a synthetic control group can capture confounding unobserved characteristics, even allowing those influences to vary with time, such as the reception of other awards. Because the distribution of yearly citations skews strongly to the left, the logged number of annual citations will serve as the outcome variable in the following multivariate models. We thus repeated the entropy balancing procedure for means of logged citations instead of unlogged citations. In the following, we will use weights balancing unlogged citations for a graphical inspection and weights balancing logged citations for the estimation of statistical models. Both approaches lead to the same substantive conclusions.
For the sake of transparency and to enable replication, paper identifiers and code are publicly and permanently available at the Harvard Dataverse (Wolbring & Farys, 2021). Table 2 contains descriptive statistics on the composition of the treatment and control groups prior to award announcement. The statistics illustrate that the combination of CEM and Entropy Balancing achieves covariate balance among the included variables annual citations, publication year, and subject category. Moreover, the synthetic control group closely approximates the treatment group as regards citations in the years before Nobel Prize receipt.

Evaluation of Matching Quality
As can be seen in Figure 1, for some Nobel Prize laureates, balancing is not perfect for the period of 20 to 10 years prior to the event, indicating that, in a few instances, it is difficult to find exact matches for Nobel laureates' outstanding publications as regards pre-award citation impact. This especially holds for highly cited publications by Nobel Prize winners in the years 2000 ( James Heckman; Daniel McFadden) and 2004 (Finn E. Kydland; Edward C. Prescott). However, even though Nobel Prize winners' publications are already a very selective set of articles, entropy balancing ensures that the citation paths of the treatment and control groups overlap perfectly for the 10 years before the event. As a robustness check, we dropped Nobel years with insufficient balances, but all of our substantive findings remained unchanged.
Moreover, some readers might worry that balancing treatment and control groups with respect to only three variables is insufficient. For example, one could additionally adjust for article length, author number, and length of reference list (see Mutz et al., 2017), because these variables also affect citation impact . However, balancing for yearly citations in a large number of preintervention periods is a powerful tool to control for unobserved heterogeneity (Abadie et al., 2010(Abadie et al., , 2015 capturing those additional effects. In particular, including the flow of citations in the years before the award announcement in a rather fine-grained way helps to rule out reverse causality issues if a paper is "on the rise." Further, the chosen approach also takes into account field-specific differences in average citations (caused by the size and hotness of a field). Because of this, the use of synthetic control groups is closely related to the normalization of citation counts by field and publication year, which is common in bibliometrics (for overviews, see Bornmann & Marx, 2015;Waltman, 2016a). However, the former approach addresses additional methodological problems (such as reverse causality and selection on citation trends; see Leszczensky & Wolbring, 2019).

Statistical Analysis
To quantify the effects of the Nobel Prize treatment, to control for confounders, and to explore potential interactions of the treatment effect with publication characteristics, we estimate linear panel regression models with the logged number of yearly citations as outcomes 7 .
To take into account the possibility of autocorrelation and heteroscedasticity, we use robust standard errors clustered around Nobel laureate for statistical inference (Angrist & Pischke,7 Annual citations are count data with overdispersion. It is state of the art in bibliometrics to use negative binomial regression models (Ajiferuke & Famoye, 2015;Bornmann, Mutz et al., 2008;Schubert & Glänzel, 1983). In the negative binomial regression, a logarithmic function links model regressors and outcome, but in a more complicated way than simply taking the log of Y. Because of this, first matching on the log transformed variable and then running a negative binomial regression would still provide biased estimates, because the second step would impair the balancing achieved in the first step. Thus, for the current application, we decided to use linear regression models with logged Y + 1, which do not experience such problems. 2009). In addition to an idiosyncratic error term " it and a vector of covariates X it , we include paper fixed effects i in the model to control for time-constant influences of time-constant unobserved heterogeneity (Allison, 2009;Brüderl & Ludwig, 2015): Including paper fixed effects avoids confounding due to time-constant effects of article features, author characteristics, publication outlet, and discipline. Consequently, the fixed effects approach removes remaining differences in the average levels of citations between the treatment and synthetic control groups. We first estimate a baseline model that contains only paper fixed effects and a binary treatment indicator T, which changes from 0 to 1 for publications belonging to the treatment group if the current year is greater than the year of Nobel Prize receipt (model 1) 8 . Thus, although we include information on the control group in all models, we calculate point estimates and standard errors for the treatment effect in model 1 solely on the basis of the within change in annual citations in the treatment group. To take into account  8 We decided to classify the year after the Nobel announcement as the first year of treatment. Press releases about the Nobel Prize in economics appear in mid-October. Publication lag due to peer review makes it unlikely that many SSCI-listed publications in that year experienced influences due to the event. We decided to classify the Nobel year as a control case. Our robustness checks corroborate this decision (see especially model 4 in Table 2). maturation effects in the control group and overall time trends in citations, we include in the further regression models linear, quadratic, and cubic terms for demeaned publication age (model 2) and fixed effects for calendar year (model 3). To further explore the dynamics of Nobel Prize effects across time, model 4 contains a dummy impact function for the years after the event (see Allison, 1994). This approach, which is also known as distributed fixed effects, allows us to control for potential anticipation effects and to explore how the effects develop over time without imposing strong parametric restrictions on the exact functional form.
Despite the nonrandom nature of our sample of Nobel laureates and Nobel publications, we will provide results from signifance testing 9,10 .

RESULTS
In this section, we present results on the overall effect of a Nobel Prize in Economics on citation impact. Then we explore potential effect heterogeneity concerning publication characteristics and audience, and finally we test Merton's proposition of a serial diffusion of ideas. 9 While we are aware of the ongoing discussion in bibliometrics on the use of statistical inference in citation analysis and agree with some of the arguments pointing to conceptual difficulties (Schneider, 2016;Waltman, 2016b;Williams & Bornmann, 2016), we still believe that significance testing helps to quantify the degree of uncertainty and to get an idea how effects look in a hypothetical super population of Nobel publications from which our sample comes from (see Berk, Western, & Weiss, 1995;Cochran, 1953; see also Abadie, Athey et al., 2020 for an alternative design-based rationale). 10 Note also that while sample sizes in the following analyses might at first glance suggest substantial statistical power and might raise questions about the value added from reporting standard errors, p-values, and confidence intervals, the effective sample size is much lower than this first impression might suggest. First, the analyses contain a large number of reweighted controls as compared to a relatively small number of 184 Nobel publications. However, for statistical inference, the number of treated observations is an important determinant. Second, standard errors are clustered around Nobel laureates. This further reduces the effective sample size entering significance testing (see Snijders & Bosker, 2012). For that reasons, we decided to stick to standard thresholds of significance testing, but will keep in mind the difference between statistical and practical significance.

Matthew Effects for Nobel Laureates
The solid line in Figure 2 plots average yearly citations for Nobel Prize publications. As is apparent, the mean number of annual citations of these publications increases substantially over time and it appears that the growth in yearly citations accelerates after Nobel Prize receipt. Estimates from model 1 in Table 3, which contains only paper fixed effects and a binary treatment indicator, corroborate this conclusion. Average yearly citations increase by 89% (e 0.637 −1; p < 0.001) after Nobel Prize receipt. However, for the abovementioned reasons, simple pre-post comparisons are insufficient to identify causal effects in citation data and may be misleading (see also Farys & Wolbring, 2017).
It is thus necessary to compare the citation paths of the treatment and the tailor-made synthetic control group (dashed line). As becomes clear from visual inspection, the synthetic control group closely approximates the treatment group as regards citations in the years before Nobel Prize receipt. However, after Nobel Prize receipt, citation paths for the treatment group and the control group diverge: The average differences in citation impacts amount to 5.7 annual citations per publication 5 years after the announcement and 11.5 annual citations per publication 10 years after the announcement. Table 3 shed further light on the Matthew effect while taking into account maturation effects in the control group and overall time trends in citations by including the first, second, and third polynomials of publication age (model 2) and year fixed effects (model 3). In consequence of this covariate adjustment, the treatment effect estimate for treated publications decreases considerably, particularly when we control for both sources of confounding in model 3. However, with an increase of 29% in annual citations (model 3; e 0.255 −1; p < 0.001) the increase remains significant from both a statistical and a substantive point of view 11 .

Models 2 and 3 in
To further explore the dynamics of Nobel Prize effects across time, model 4 contains a dummy impact function for the years after the event. As can be seen, the annual number of citations of Nobel publications increases by 32% (e 0.278 −1; p < 0.001) in the year after receipt. This effect is remarkably stable across time and is still present 5 years after the event and later. With an increase of 35% (e 0.303 −1; p < 0.001), the effect is even slightly, although not significantly, stronger 5 or more years after Nobel Prize receipt, providing further suggestive evidence on the rich-getting-richer phenomenon in academia. In addition, model 4 serves as a robustness check for the correct specification of the timing of the event. The fact that the increase in annual citations is much smaller for the year of Nobel Prize receipt corroborates our assumption of a delayed treatment effect on citations due to publication lag.

Interaction with Publication Characteristics and Audience
Next, we ran three models containing interaction effects with dummies for publication age (published within 5 years before Nobel Prize receipt), journal impact (top 5% in the subject 11 This result is remarkably robust with respect to direction and strength if we drop the 2000 and 2004 laureates, for whom we could achieve only imperfect balance. As another sensitivity analysis, we estimated the triple and quadruple difference in differences model (Lee, 2016), which both demeans and (linearly or quadratically) detrends the data and hence provides another way to control for selection on citation impact and for selection on citation growth for Nobel Prize publications. The effects are remarkable similar to our results using a synthetic control group. Separate analyses for each Nobel Prize year further support our conclusions, but also illustrate heterogeneity with respect to average citation levels and strength of treatment effects (see Figure 1). Visual inspection indicates considerable treatment effects for publications of Nobel Prize winners in the years 2000,[2002][2003][2004]2006, and 2008, but not for laureates in the years 2001, 2005, and 2007. category according to journal impact factor), and pre-Nobel citation impact (top 5% according to the cumulative number of citations before Nobel Prize receipt). To test for variation in treatment effects by audience, we analyzed two different citation outcomes in separate models: logged yearly citations from "insiders" of the focal scientific field of economics (citations from publications in the WoS subject categories "economics," "business," "business, finance," and "management") and from "outsiders" (citations from publications in all other WoS subject categories covered by the Social Science Citation Index) (see Lynn (2014) for a similar approach; for a more fine-grained approach to measure within-field and out-of-field citations see Reschke, Azoulay, and Stuart (2018)) 12 .
Model 5 in Table 3 shows that considerable heterogeneity in the strength of treatment effects exists with regard to publication year. The treatment effect on citation impact for papers 12 As a robustness check, we restricted our analyses to publication years within 10 years before the event and publication years following Nobel Prize receipt. Sufficiently close balance between the treatment and the control group could be achieved for the publication years within 10 years before the event but not prior to that time period. The following results are robust to this sensitivity analysis. published up to 5 years before Nobel Prize receipt is much stronger as compared to less recent publications. The latter also receive a considerable attention boost but to a far lesser extent. Even after controlling for maturation effects using polynomials for publication age and calendar year fixed effects, more recent publications enjoy greater benefits from the Nobel Prize as regards citation impact. Annual citations of papers published up to 5 years before the event increased by 102% (e 0.701 −1; p < 0.001), whereas citations of publications appearing more than 5 years before the event only grew by 27% (e 0.236 −1; p < 0.001).
In contrast to the results by publication year, the other two interactions in models 6 and 7 turn out to be not relevant as regards both substantive and statistical significance. Both highly cited (30%; e 0.260 −1; p < 0.001) and non-highly cited papers (29%; e 0.252 −1; p < 0.01) experience similar growth in citations after the prize, as do publications in journals with very high field-specific impact factor (28%; e 0.250 −1; p < 0.001) and publications in all other journals (29%; e 0.254 −1; p < 0.001).
Finally, models 8a and 8b show that the Nobel Prize affects the citation behavior of both "insiders" and "outsiders," but has stronger effects on the former. Annual citations by publications in "economic" journals increase by 26% (e 0.233 −1; p < 0.001), whereas citations by publications in other SSCI-listed journals increase by only 12% (e 0.110 −1; p < 0.05) 13 . While the citation boost caused by outsiders might be due to their lower degree of familiarity with the work of the laureate before the award, we interpret the stronger effect for better informed 13 The effects for "insiders" and "outsiders" remain statistically significant and become slightly larger if we omit post-Nobel publications by the psychologist Daniel Kahneman from our analyses. The reason for this slight change in results is the different pattern of audience-specific reactions to his receiving the prize: Citations of his work in economics journals increased by 32%, while citations in other SSCI journals increased by 23%. The latter increase is not restricted to psychological publication outlets but reflects a more diverse growth in citations. Thus, due to the rather surprising decision of the Nobel Committee to honor a disciplinary "outsider," Kahneman's research program became more visible and gained in citation intensity both inside and outside economics.  12,070,423 58,660,654 11,410,798 58,008,944 11,235,676 57,440,026 AIC 24,140,848 117,321,309 22,821,604 116,017,896 22,471,579 114,880,282 BIC 24,140,863 117,321,325 22,821,661 116,017,960 22,473,204 114,882,116 Note: Fixed effects regression model with robust standard errors clustered around publications. Unstandardized coefficients; t statistics in parentheses. *p < 0.05, **p < 0.01, ***p < 0.001.
"insiders" from the focal field of research as an indication that citation impact does not only increase because awards raise awareness for the work of Nobel laureates. Instead, the social recognition of the scientific achievement seems to additionally cause scholars to increasingly cite Nobel Prize publications.

Is There a Serial Diffusion of Ideas?
For the sake of analytical clarity, we distinguish among works by Nobel laureates (publications of first degree in the citation network), works they cite (second degree), and further works cited by works in the Nobel laureates' cited references but not by the laureates themselves (third degree).
To test for a "serial diffusion of ideas," we extracted the reference lists of the Nobel Prize publications and searched for papers of second degree (59% found; 1,380 out of 2,349). We repeated the step for publications of third degree (74% found; 12,134 out of 16,483) and generated synthetic control groups in the same way as for the first degree, as described in Section 3. Figure 3 shows that treatment and control groups are almost perfectly balanced as regards pre-award citation paths.
Fixed effects models in Table 4 reveal that-after controlling for citation life cycles and general increases in citations-the Nobel Prize has no effect on citation impact of publications of second and third degree in the citation networks. Hence, we find no evidence of a serial diffusion of ideas: While publications of Nobel laureates receive more attention due to the award, cited references do not profit, but also do not suffer, from the honoring as regards citation impacts.

Summary and Discussion
Using the case of the reception of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, we investigated, on the basis of the complete WoS 1900-2011, Nobel Prize effects upon citation impacts. Thus, this study provides the first rigorous analysis of the Matthew effect in science using Merton's and Zuckerman's original example, Nobel Prize laureates. In a nutshell, we found clear evidence for a Matthew effect and hence for the existence of cumulative advantages in this supposedly meritocratic field. This finding is well in line with previous studies on the effects of other positive status shocks in the midcareer stage on citation impacts (Azoulay et al., 2014;Chan et al., 2013) as well as the likelihood of receiving research funding and becoming a full professor (Bol et al., 2018). Our study contributes to this literature by empirically showing that these processes are not restricted to the early and midcareer stages. The "crowning" of scientific careers with a Nobel Prize causes such Matthew effects with respect to citation impacts even among already well established and usually highly cited scholars.
Moreover, our analyses revealed that scholars from the focal field of the award are more receptive to decisions of the Nobel committee. While we can only speculate about the exact reasons for this finding, our results suggest that the substantial gain in legitimacy is the key mechanism for Nobel Prize effects upon citation impacts. In line with the social constructivist theory of citations, scholars in the focal field of the prize might try to exploit this increased credibility of the laureate to their advantage or feel compelled-due to expectations within the scientific community-by citing Nobel laureates to bolster their own arguments and to profit from the laureates' prestige. In the extreme scenario of "ceremonial" citations (see Adatto & Cole, 1981), scholars may cite Nobel Prize publications without personally believing in their high quality or without having actually read the papers in detail. Against this background, it seems likely that honoring a laureate with the Nobel Prize causes strategic citations in the focal field to some degree, while the mechanisms proposed by the normative theory of citations are likely simultaneously at work. These findings have broader implications for science. First, our findings corroborate previous research showing that science is a social system that is driven by not only meritocratic considerations (Cole & Cole, 1973;Merton, 1973) but also issues of persuasion, social expectations, and peer pressure (Callon et al., 1986;Knorr-Cetina, 1981;Latour, 1987). Such social influence creates strategic incentives for scholars to use symbolic acts of recognition, such as "ceremonial" citations and to float with the current instead of acting purely upon what they thinks is best from a scientific point of view. Second, awards and other forms of social recognition can cause concentration processes in science by providing focal points (Frank & Cook, 1995;Frey & Gallus, 2014;van Dalen & Henkens, 2005). This can have negative side effects for other scholars and can undermine the innovation potential of science (Bothner et al., 2011;Merton, 1968Merton, , 1988. Important contributions standing in the shadow of Nobel laureates might remain uncited and might be finally forgotten. Third, we have shown that reactions to awards can be audience specific and are often limited to certain fields (for related arguments on audience specificity see Ertug, Yogev et al., 2016;Keuschnigg, 2015;Lynn, 2014). An award does not uniformly raise the legitimacy of a scholar's research, but does so to different degrees among different audiences. Future research should further explore under what conditions awards cause a relevant status shift for an audience.

Limitations and Outlook for Future Research
These results and conclusions should be interpreted cautiously in light of a few limitations, which future research must address. First, citations are not only building blocks of scientific claims and markers of the origin of certain ideas, but they can also serve very different functions (Baldi, 1998;Leydesdorff, 1998). Our study suggests that considerations of legitimacy, persuasion, and peer pressure also drive citation. To provide a more direct test of these considerations, future research might extend our approach by distinguishing positive from negative citations or even use topic modeling techniques to enrich citations with context (see Ding, Zhang et al., 2014;Tahamtan & Bornmann, 2019;Yan, Chen, & Li, 2020;Zhu, Turney et al., 2015).
Second, using the raw data of WoS 1900-2011, we had to exclude other sources such as the Emerging Sources Citation Index and the Book Citation Index from our analysis. Our estimates might hence not map the average treatment effect for all relevant publications. However, the fact that only a few of the Nobel laureates in economics published their central insights and research findings in books or unlisted journals limits the potential impact of this pitfall upon our results. Another important consequence of the restriction to certain types of publications is that we have to assume that citation data are missing at random. A violation of this assumption would not affect the internal validity of our results, but would limit their generalizability.
Third, we balanced the treatment and control groups on observable covariates. Due to the large number of potential control cases, except for a few outstanding Nobel Prize winners' publications (which we excluded in sensitivity analyses), common support was not an issue. Still, publications might differ in terms of inherently difficult-to-measure aspects, such as "quality." However, matching on the pre-event citation impact, a fixed effects approach, and higher order difference in differences models capture a substantial portion of such unobserved heterogeneity (see also Abadie et al., 2010Abadie et al., , 2015. While this helps to minimize the uncertainty in our causal inferences, such models still rely on assumptions and only indirectly control for field-specific dynamics and the hotness of a field. An approach using keyword matching or topic modeling would get closer to this, though this invites the curse of dimensionality in matching (Abadie & Imbens, 2006).
Fourth, we decided to study Matthew effects upon citation impacts at the level of individual publications. Taking into account selection effects by matching Nobel publications with publications of similar citation impact, we estimated the increase in citation numbers caused by the honoring. While this approach recognizes the fact that cumulative advantages are already at play for future Nobel laureates before Nobel receipt by controlling for their often already exceptionally high pre-Nobel citation impact, we were not able to disentangle the direct effects of the Nobel Prize upon citation impacts from its indirect effects in the form of further cumulative advantages. However, access to generous research funding, additional awards, and prestigious memberships in scientific academies might further increase citation numbers.
Finally, it remains an open question whether the findings generalize to other Nobel Prize winners in economics and, more importantly, to Nobel laureates in other disciplines and to other awards. Future research should hence on the one hand concentrate on the question of how different disciplinary citation cultures moderate effects due to the Nobel Prize in different research areas. On the other hand, it might be well worth the effort to further investigate the effects of awards for younger, less-established scholars (see Azoulay et al., 2014;Bol et al., 2018;Chan et al., 2013). It appears likely that Matthew effects of early and mid career awards are stronger for two reasons. On the one hand, these scholars are much less well known than future Nobel laureates, increasing the importance of status signals. On the other hand, status advantages have more time to work and can accumulate over a longer period.

DATA AVAILABILITY
We acknowledge the use of ISI WoS data of Clarivate Analytics for our citation analysis. We thank the library of the Swiss Federal Institute of Technology Zurich for providing the WoS raw data. Data used in this manuscript are subject to strict requirements and cannot be made available in a data repository. To enable replication, paper identifiers and code are publicly and permanently available at the Harvard Dataverse (Wolbring & Farys, 2021).