Vice versa: The decoupling of content and topic heterogeneity in collusion research

Schmal, W. Benedikt Article — Published Version Vice versa: The decoupling of content and topic heterogeneity in collusion research Journal of Economic Surveys Provided in Cooperation with: John Wiley & Sons Suggested Citation: Schmal, W. Benedikt (2023) : Vice versa: The decoupling of content and topic heterogeneity in collusion research, Journal of Economic Surveys, ISSN 1467-6419, Wiley Periodicals, Inc., Hoboken, NJ, Vol. 38, Iss. 5, pp. 1686-1730, https://doi.org/10.1111/joes.12600 This Version is available at: https://hdl.handle.net/10419/313789 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/4.0/ DOI: 10.1111/joes.12600 ARTICLE Vice versa: The decoupling of content and topic heterogeneity in collusion research W. Benedikt Schmal Walter Eucken Institute, Freiburg (Br.) & DICE, Heinrich Heine University, Düsseldorf, Germany Correspondence W. Benedikt Schmal, Walter Eucken Institute, Goethestr. 10, 79100 Freiburg, Germany. Email: [email protected] Funding information Deutsche Forschungsgemeinschaft, Grant/Award Number: 235577387/GRK 1974 Abstract Collusive practices continue to be a significant threat to competition and consumer welfare. It should be of utmost importance for academic research to provide the theoretical and empirical foundations to antitrust authorities and enable them to develop proper tools to encounter new collusive practices. Utilizing topical natural language machine learning techniques allows me to analyze the evolution of economic research on collusion over the past two decades in a novel way. It enables me to review some 800 publications systematically. I extract the underlying topics from the papers and conduct a large set of uni- and multivariate time series and regression analyses on their individual prevalences. I detect a notable tendency towards monocultures in topics and an endogenous constriction of the topic variety. In contrast, the overall contents and issues addressed by these papers have grown remarkably. This caused a decoupling: Nowadays, more datasets and cartel cases are studied but with a smaller research scope. KEYWORDS antitrust, collusion, neural networks, systematic review, topic modeling This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. © 2023 The Authors. Journal of Economic Surveys published by John Wiley & Sons Ltd. 1686 wileyonlinelibrary.com/journal/joes JEconSurv.2024;38:1686–1730. SCHMAL 1687 JEL CLASSIFICATION D83, I23, L40, O33, Z13 1 INTRODUCTION In industrial economics and antitrust, cartels and collusive behavior seem to have gone off the radar somewhat. Even though the economic harm caused by it is non-negligible. Levenstein and Suslow (2006) report an 80% price increase caused by the international tea cartel and monopoly pricing of the US beer and the British ocean shipping cartel. Meta studies find an average price overcharge of 30%–50% and a median overcharge of 15%–25% by cartels in general (Bolotova, 2009; Boyer & Kotchoni, 2015; Connor, 2008). A proxy for the impact of collusion is the fines imposed: From 2000 to 2022, the European Union (EU) handed out penalties of some $31 billion.1Moreover, the EU plans to lose restrictions on anti-competitive behavior to promote the dissemination of environment-friendly technology (Schinkel & Treuren, 2021). Thus, collusion is and will continue to be a major issue for consumer welfare and antitrust policy. This paper investigates research on collusion during the past two decades applying topical artificial intelligence tools. It reveals crucial changes over time and hints at developments in the literature that will likely affect competition authorities. Methodologically, I provide a novel way of understanding how collusion is addressed and identify the centers of academic attention. I compute latent topics by applying a structural topic model, a state-of-the-art natural language processing technique that relies on unsupervised machine learning. Hence, the paper brings together the economics of science, the history of economics, and antitrust research by providing a novel quantitative comprehension of the development of research on cartels for economists as well as antitrust scholars. Since industrial organization research is a significant source of inspiration for policymakers, legislators, and antitrust authorities, understanding the patterns of collusion research may directly impact the evolution of related public policy.2 The core question the paper aims to answer is: How did economic research on collusion among firms change in the past two decades contentwise, and how is this entangled with publication and citation patterns? By using machine learning techniques, I cannot only excerpt the whole strand of this literature. I also quantify developments over time that could be captured only descriptively otherwise. The main idea of natural language processing is the quantification of text data. Figure 1illustrates this. This “word cloud” depicts frequent terms, where a larger font size implies a higher frequency. Here, I display words from topic 16 on leniency. It is important to note that I labeled the topic ex-post “leniency” as the unsupervised algorithm has “detected” it independently. Most words are shortened to their stems to account for inflections and variations between verbs and nouns. Unsurprisingly, terms such as leniency,effect,fine,orprogram form the center of collusion research on leniency schemes. I quantify these (and all other terms) using a “structural topic model.” While I explain the method in more detail later on, the core advantage is that it can incorporate explanatory variables to detect latent underlying topics in texts.I include time and place of publication as major determinants of which kinds of topics to expect. For every publication, I am able to compute the probability of each topic occurring. I utilize these topic probabilities to investigate topic prevalences over time using uni- and multivariate time series analyses. I amend my analysis with regressions investigating the relation between topics and citations. 1688 SCHMAL FIGURE 1 Wordcloud based on the computed latent topic on leniency. [Colour figure can be viewed at wileyonlinelibrary.com] To conduct the aforementioned text analysis, I build upon 777 publications in leading economics and antitrust journals addressing collusion. Among this arguably full body of research in this sub-discipline, I identify 21 latent topics, analyzing the content of the papers with a structural topic model. I cluster these topics and assign them to broader categories. Based on that, the first part of the subsequent analysis studies the evolution of topic categories over time. To achieve this, I extract the predicted probability for every topic to occur in a specific paper. It becomes visible that competition analyses studying the generalized behavior of firms are in retreat. Especially in recent years, empirical case studies of disclosed cartels and their court cases have seen a considerable boost. Furthermore, empirical evidence exists for specialization, that is, the focus of a paper seems to be narrowed to fewer topics. The case study-related topics are strongly correlated with the leading so-called “top 5” journals in economics. While other general interest and broader field outlets cover various topics, specific IO journals also seem to narrow their focus to a smaller set of topics. This may end up in an endogenous process of streamlining research. Conducting a repeated cross-section regression analysis on the relationship between citations and topics, I do not find any significant positive relationship but three topics to be negatively correlated with citations per year. Remarkably, these topics are in decline over time in terms of the predicted probability to occur in a paper. A subjectwise decrease does not match this content-wise decline: Applying the machine learning technique of neural networks, I can show that the superficial subjects of papers become more diverse over time while the underlying actual considerations are more closely tied together. In the last step, I conduct a multivariate time-series analysis to understand how the decline in competition analysis and the upswing in case studies are intertemporally related. The latter do not supersede the former but fill the gap the reduction in the latter leaves. The discipline tends to have lost some interest in the stylized models of markets and instead turned towards case studies. It serves as additional evidence for endogenous constriction of academic research on collusion, which may affect the ability of competition authorities to chase and disclose collusive structures. SCHMAL 1689 This paper is a systematic literature review based on natural language processing of industrial organization research. It contributes to the economic strand of the science of science literature that aims to understand how the process of creating and disseminating scientific progress works. Furthermore, it also reflects the rules and habits of the discipline of economic research. Earlier research by Einav and Levin (2010) discussed the developments in empirical IO, while Hovenkamp (2018,2021) recently criticized the current state of antitrust research. Lancieri et al. (2022) find evidence for a decline in antitrust enforcement in the United States but hardly any evidence for antitrust research playing a role in that. Shapiro (2020) raises the concern that antitrust economics has focused on technical aspects of markets but rather misses out on the broader economic issues affected by, for example, higher prices or less innovation. Jones and Kovacic (2020)discuss the problem of antitrust authorities dealing with the market power of digital platforms. This paper aims at contributing a detailed understanding of research on cartels. Methodologically, it follows Qasim (2017), who analyzes interdisciplinary sustainability research, and Ambrosino et al. (2018), who already clustered economic research in total via topic modeling. Natural language processing recently gained popularity in economic research (Gentzkow et al., 2019). Larsen (2021) uses it to understand market uncertainty. Much seminal economics research applying topic modeling investigates central bank communication and its macroeconomic effects (Hansen & McMahon, 2016; Hansen et al., 2018,2019). They use the latent Dirichlet allocation (LDA) algorithm. While easy to use, structural topic modeling (STM) allows for a more granular analysis with less restrictive model assumptions. Therefore, I choose the latter technique. The STM model begins to gain traction in economics and business research (see, e.g., Ebadi et al., 2021; Ferrara et al., 2022;Kumar&Srivastava,2022; Moschella et al., 2020; Nathan & Rosso, 2022; Schmal, 2022b) Last, Ash et al. (2022) have shown that economic ideas can have a high impact on practitioners as they show that economics classes for judges influenced their verdicts. An important recent example from antitrust is the OECD (2017) policy paper on algorithms and collusion, which draws from recently published economics and antitrust papers such as Ezrachi and Stucke (2016), Mehra (2015), Green et al. (2014), Potters and Suetens (2013)—even though such a topic almost naturally heavily relies on websites and online media. The remainder of the paper is structured as follows. Section 2describes the data and the machine-learning-based structural topic modeling methodology. Later on, it also describes the econometrics behind the analysis and how I cluster the computed topics. Section 3presents the paper’s findings, in particular, the time series and regression analyses. Section 4contextualizes and concludes. 2EMPIRICAL APPROACH 2.1 Data The foundation of the analysis is the data from the Scopus database, as shown in Figure 2,obtained with the Python API pybliometrics (version 3.3.0, Rose & Kitchin, 2019). I gather 34,564 publications in 35 journals from 2000 to 2021, downloaded from April 4–6, 2022. I identify papers that address collusion by choosing those with at least one of the operators “collusion,” “collusive,” “cartel,” “bidding ring,” or its declensions in its title, abstract, or keywords.3By that, the number of relevant papers collapses to 777.4 1690 SCHMAL Scopus data Structural Topic Model Topic Probabilities Quantitative Analysis FIGURE 2 Data used in the quantitative analysis. [Colour figure can be viewed at wileyonlinelibrary.com] I exploit the abstracts of papers published in leading IO and antitrust outlets and their related metadata. While a full-text analysis would encompass more information, abstracts are focused on the core techniques and messages a paper applies and wants to communicate to the reader. Due to its brevity, an abstract is usually not decorated with illustrative examples not used for deeper analysis, as often seen in introduction sections of full papers. This helps separate important from less important cases in the text analysis and follows the approach of Wu et al. (2019) and Gropp et al. (2016). Sybrandt et al. (2018) find that full texts may provide more information but, in turn, more “intruder” terms that obfuscate the topic modeling and subsequent interpretation.5 I preprocess the text data from the abstracts to ease the analysis. It includes the removal of punctuation, transforming all words into lowercase terms, and removing stopwords, for example, conjunctions or articles that have no real meaning but are necessary for humans to read and understand a text.6I manually remove so-called “boilerplate” words (see Lämmel & Jones, 2003) that are technically part of the abstracts but do not contain any useful information, such as copyrights of the publishers. Furthermore, I remove the operators “cartel” and “collusion” as these terms, by definition, should be part of virtually every abstract. Hence, they add no information on underlying topics within the subset of papers about cartels and collusion.7 Last, I stem the words, that is, plural forms or the past tense for verbs disappear. For example, “cooperation,” “cooperate,” and “cooperative” collapse to “coopera.” This bears the loss of some information, but it comes with a considerable gain in analytic power, as otherwise, every version of a word would be considered an independent term. 2.2 Structural topic modeling Based on the body of papers, I conduct natural language processing. I work with the papers’ abstracts to understand deeper relations and developments in collusion research over time. To do that, I apply the technique of topic modeling. This method was made popular by Blei et al. (2003). The core idea is as follows: A number of 𝐷text elements (usually called documents, in my case, paper abstracts) contain 𝐾“topics,” that is, clusters of words that belong together.8Each document 𝑑consists of a number of 𝑊words.9 The ultimate goal is identifying a pre-defined number of 𝐾latent topics without a prior which words belong to them. A data-generating process for each document is assumed in which every document consists of several topics, which themselves consist of a set of words that have their own probability of belonging to a particular topic. In the following, I sketch the mechanism of this unsupervised machine-learning algorithm based on the work of Blei et al. (2003) and Roberts et al. (2013). Note that I mostly follow the notation of the latter even though I adjust parts to address an economics readership better. SCHMAL 1691 I apply the structural topic model (STM, Roberts et al., 2013) using the R package stm of Roberts et al. (2019) because it allows for the incorporation of covariates as independent variables for the prevalence of topics. Based on that, I estimate regressions on relationships between specific topics and covariates 𝑋𝑑. Every document has a set of topics in it. The STM assumes that there is an individual prior for the particular set of topics for each document, which depends on a vector of covariates. Put differently, the covariates are assumed to determine which topics appear in a particular paper. Thinking of academic publications, a paper’s outlet is likely to be related to the topics as the Journal of Economic Theory may cover different topics than Empirical Economics. Second, a vector 𝜃𝑑∼𝑙𝑜𝑔𝑖𝑡(𝑋𝑑𝛾𝑘,𝜎) for each document contains the document-specific probability of each topic to occur there. 𝛾𝑘is a vector of covariates for 𝑋𝑑,with𝛾∼(0, 𝜎2 𝑘), such that one assumes as a prior the document-covariates to be uncorrelated with the topics and only deviate from this assumption for a strong correlation between the two. Each document has a document-specific probability for a word to occur. It depends on the overall distribution of words (𝑚) and the covariates (𝑋𝑑). It is captured by 𝛽(𝑋𝑑,𝑚)and describes the probability of a particular word occurring in a particular document, given that it contains some particular topic. 𝛽is a matrix of size 𝐾×𝑊, that is, it contains for every word (𝑤1…𝑤 𝑁) and every possible topic (𝑘1…𝑘 𝑁) the probability to occur. Based on 𝜃𝑑, one draws the topic (  𝑘𝑤) that is most likely for every word 𝑤in every document using a multinomial logit model, that is,  𝑘𝑤∼𝑀𝑢𝑙𝑡𝑖(𝜃 𝑑). Last, one draws an actual word  𝑤that has the highest probability to occur given  𝑘𝑤and 𝛽, that is,  𝑤=𝑚𝑎𝑥{𝑝(𝑤 𝑛| 𝑘𝑤,𝛽)} while the actual words are meant to be distributed 𝑤𝑑,𝑛 ∼𝑀𝑢𝑙𝑡𝑖(𝛽 𝑘=  𝑘𝑤 𝑑)). One can easily see that  𝑤should converge towards 𝑤. As the actual topics within each document are latent, structural topic modeling uses an expectation-maximization algorithm that iteratively tries to find a local maximum likelihood given the prevalence of latent topics. Determining the number of underlying topics 𝐾in a body of documents is a crucial task. There exists no “one size fits all” approach to elicit the optimal 𝐾∗(see, e.g., Grimmer & Stewart, 2013; Wehrheim, 2019). Nevertheless, several key measures contain important information on the quality of the topics dependent on the number of topics. One key measure is semantic coherence, which states that words that occur very frequently within topic 𝑘𝑖should also occur in a document, given this document contains 𝑘𝑖(Mimno et al., 2011). While this is a convincing concept, it suffers from the problem that for low 𝐾, semantic coherence is high by construction. As an antagonistic metric, I use exclusivity as proposed by Bischof and Airoldi (2012). The core idea behind that is that words that are only in one topic very frequently are “exclusive” while words with relatively equal frequencies across topics are somewhat non-exclusive. Consider the word “collusion” in the given context that should occur in many topics. As this is such a big keyword— it is part of nearly all abstracts by construction—I exclude it from the documents. Words that occur in many topics should lead to a higher semantic coherence because, in this case, the topics are more likely to cover many words in the actual abstracts. In contrast, these topics should have a low exclusivity, so the trade-off between these two measures should provide a sufficient choice of 𝐾. In Appendix B, I sketch in more detail the measures I compute to choose 𝐾. Overall, here I conclude to set 𝐾∗=21. 𝜃𝑑∼ 𝑦𝑒𝑎𝑟𝑑+𝑗𝑜𝑢𝑟𝑛𝑎𝑙 𝑑 I use a structural topic model, so I am able to add covariates to the topic regressions, which, in general, are fitted as linear models with the expected topic prevalence as the dependent variable. 1692 SCHMAL Accordingly, 𝜃𝑑represents the expected prevalence of the 21 topics. I include 𝑦𝑒𝑎𝑟 as a temporal variable to account for changes over time (linearly without any spline). I add the 𝑗𝑜𝑢𝑟𝑛𝑎𝑙 as a significant covariate that should be related to a paper’s particular content. To draw more general conclusions and increase statistical power, I group the journals into five categories, as shown in Table A.1 in the appendix, because clusters of journals with similarities in scope and methods exist.10 I later use these broader categories for the correlations between journal clusters and topics. Further variables could be added, but due to the model structure, only highly relevant covariates get assigned a value different from zero, which suggests a small set of important variables. Most parts of this paper rely on a structural topic model. I amend my analysis with a machine learning algorithm that relies on neural networks. Other than the statistical expectationmaximization approach taken in the STM, neural networks set up a plethora of interrelated nodes, to some extent equivalent to neurons in the human brain. By that, a neural network-based model draws relations between variables or topics from the relations between nodes and the particular weighting of these relations (see, e.g., Amari, 1995). In the present case of text analysis, I use the doc2vec neural network algorithm developed by Le and Mikolov (2014). The unsupervised algorithm autonomously learns relations between words in a text (here in academic publications) and converts it into a lower-dimensional vector for each document. Based on that, I compute the inner product of these vectors for each pair of publications within a year to measure the similarity of these papers. I average all similarities per paper and in a second step per year to compare changes over time. 2.3 Quantitative estimation The predicted topic prevalences drawn from the structural topic model and its unsupervised machine learning approach build the foundation of the analysis. As sketched in Figure 2, these probabilities are amended with additional publication data from the Scopus database. To analyze the dynamic dimension of topic prevalences, I construct multiple time series based on annual topic averages and conduct various stationarity tests, particularly the widely applied augmented Dickey-Fuller (ADF) test and the Phillips-Perron (PP) test. Both procedures share the weakness of non-stationarity being the null hypothesis. That is, no rejection of the null does not imply the existence of a unit root. Kwiatkowski et al. (1992) suggest the KPSS test that puts non-stationarity as the alternative hypothesis, such that a rejection of the null should be more unambiguous evidence for a unit root. I use all three test procedures to ensure valid findings. ADF and PP tests come in three different types, namely a linear model with no trend and no drift (type 1), one with no linear time trend but a drift (non-stationarity in the mean; type 2), and one with a linear trend and a drift (non-stationarity in mean and variance; type 3). Additionally, the number of lags in the auto-regressive process can be specified. While annual data usually apply one lag as it mostly relies on the previous year, I choose a lag of 𝑛=2. It has both an economic and a technical foundation that coincide: Economic publishing faces a notable lag between the submission of a paper and its publication.11 A two-year time lag is more reasonable, in which the topic prevalence of year 𝑡is a function of 𝑡−2.12 The range of my data implies 𝑚𝑎𝑥(𝑡)=22, which leads just as the theoretical considerations to 𝑛∗=2. For the unit root tests, I also rely on the test statistics of the second lag. Next, I conduct a repeated cross-sectional analysis of the relationship between latent topics and the reception of papers with these topics in the literature. My dataset allows me to look at the number of citations per paper (until 2022). I am able to study the relationship with the presence of specific topics. I use the number of citations per year of a specific paper 𝑖as the dependent SCHMAL 1693 variable and the expected topic probability 𝑇as an explanatory variable. This looks as follows: 𝑓(𝑐∕𝑦)𝑖=𝛽 𝑇𝑇𝑖𝑗 +𝛽 𝑂𝐴𝟙𝑂𝐴 +𝛽 𝐴𝐴𝑖+𝑌×𝐽+𝜖 𝑖,(1) whereby 𝛽captures the estimated coefficients of the covariates. Citations per year on the LHS are transformed to their logarithmic form. Figure A.5 in the appendix shows that this measure is approximately normally distributed. However, since there are papers without citations, some 13% of the observations get lost. Hence, I apply two transformations to avoid reducing the already rather small sample size. First, I use 𝑙𝑜𝑔(𝑐∕𝑦 + 1) to avoid the dropout of zero values. Second, I apply the widely used hyperbolic sine transformation, that is, 𝑙𝑜𝑔(𝑐∕𝑦 + √𝑐∕𝑦2+1). Solely relying on the “pure” logarithm would not be sufficient as papers with zero citations are an important part of the analysis, as not being cited is relevant information, too. On the right-hand side, I add the logarithm of topic 𝑗to understand how the prevalence of this particular topic corresponds to citations. I include two crucial control variables: First, the corresponding author (𝐴𝑖) to account for the fact that a paper’s visibility and reputation certainly depend on its author(s).13 Second, I use a binary dummy for open access (𝟙𝑂𝐴) to capture the fact that open access tends to affect citations, even though the evidence is mixed (McCabe & Snyder, 2021,2014; Gaule & Maystre, 2011). I also add a year×journal fixed effect to account for changes over time and journal reputation, as it is crucial for visibility, credibility, and citations. Last, I exploit the fact that we have several topics co-moving, such that one can set up a multivariate time series analysis, that is, a vector autoregression (VAR) model. I estimate a model including several groups of topics, which I name categories,14 and usually apply a lag length of two periods. It is reasoned by the publication lag in economics as well as econometric tests for the optimal VAR length. Details are specified and explained in the results section for each estimation. Based on all these computations, I obtain essential insights into the dispute and contention about collusive behavior within the scientific community, the evolution of approaches over time, and the appeal of particular topics captured by relationships between topics and journal types as well as by the “citability” of particular topics. 2.4 Clustering topics From a statistical and economic perspective, it is more useful to cluster and aggregate topics instead of studying them individually. However, doing so naturally raises the question of how to do that.15 I choose to adopt the Institutional Analysis and Development (IAD) framework, originally developed by Elinor Ostrom (see for an overview, e.g., McGinnis, 2011;Ostrom,2011)to structure and understand jointly used or managed common pool resources, it has found plentiful applications in political science but less so in economics. However, Schmal (2022a) indicates how far cartels can be understood to generate “common pool resources” on which the Ostromian IAD framework can be applied to understand their functioning better. Based on that, I argue that cartel research can be clustered in that way as the topics should reflect the actual structure of cartels. Nevertheless, alternative approaches and methods of clustering would be conceivable as well, just as mentioned beforehand. The framework is shown in Figure 3. It consists of three major blocks: On the left, there are topics that address issues outside of cartels themselves. Here, I go—equivalent to the original model—from broad to narrow, starting with topics on the overall economic environment to 1700 SCHMAL FIGURE 6 Topic probabilities of topics outside of the IAD framework. Red solid line: Sum of the three topics; Gray solid line: Topic 1—Antitrust Overview; Gray Dashed line: Topic 2—Court Cases; Gray dotted line: Topic 6—Collusion Cases. [Colour figure can be viewed at wileyonlinelibrary.com] To ensure that this decline is not misinterpreted, or put differently, to ensure there exists significant non-stationarity in the aggregated topics of the “competition analysis” subcluster within the “outside the cartel” block, I conduct stationarity tests as described in Subsection 2.3. The detailed results for all three tests can be found in Table A.4 in the appendix. The ADF test cannot reject the null hypothesis of non-stationarity for one or two lags for types 2 and 3. The PP test, however, rejects the null of non-stationarity for these two types. As Leybourne and Newbold (1999)have shown, the ADF and PP tests are susceptible to diverging, especially for AR(2) specifications. The KPSS test supports the economic hypothesis of non-stationarity by clearly rejecting the null of stationarity for a lag parameter of 2 (𝑝 = .0182). In contrast to the “competition analysis” topics, one can observe a remarkable surge in the prevalence of case-based topics outside the framework. It is shown in Figure 6. While there seems to be in the aggregate of these topics some major fluctuations in the early 2000s, one can observe a steady rise from 2009 on, which peaks in 2015 and stabilizes at a high level around 20% afterwards. Furthermore, up to 2009, the prevalence of the aggregated three topics was mainly driven by collusion cases (#6), that is, a topic that mainly addresses leaked-out or blown-up cartels by authorities and their economic implications. From 2008 on, both rather antitrust-focused topics began to rise in their respective aggregated prevalence. As Table A.5 in the appendix shows, no ADF test rejects the null for two lags but the PP test does, again. The KPSS test rejects the null of stationarity, such that a unit root seems to be present. Complimentary, the KPSS test rejects the null of stationarity. Chow tests on the 5% significance level for a structural break in the data suggest that there might be one in 2009 (𝐹 = 4.9398,𝑝 = .0195). Overall, I am sure this surge is statistically supported. It is likely to be driven by an intensive margin shift towards these topics and an extensive margin effect. Especially among antitrust journals, there are few publications addressing collusion in the early 2000s (see Table A.2 in the appendix). Second, both the number of cases and the number of fines awarded, for example, by the European Commission, only began to rise from 2005 and subsequent years on.20 Additionally, the EU put a substantially revised leniency regulation in place in 2006 (see, e.g., Wils, 2007). It might have triggered new academic inquiries after disclosed cartels employed this leniency scheme. Nevertheless, the extensive effect also affects the SCHMAL 1701 FIGURE 7 Topic densities of external topics prior- and post-2010. Density functions for the logged sum of external topics (1, 2, 6) up to 2010 (red solid) and from 2011 on (black solid). Upper panel: Probability density, lower panel: Cumulative density. [Colour figure can be viewed at wileyonlinelibrary.com] intensive margin as the focus on such topics naturally crowds out other topics from a researcher’s perspective. Also the attention of the discipline shifts if an increasing share of publications turns towards some specific topics. Figure 7looks at the density functions of the logarithmic sum of external topics as described above. One can observe the mean and the dispersion, that is, the second moment of the probability distribution. As Figure 6highlights, there was a major surge in 2010. I split the distribution at this point, separating the time range in half and leading to 𝑁≤2010 = 315 and 𝑁≤2010 = 462. The earlier years’ probability density function (PDF) is shaped close to a normally distributed PDF but with a fatter right tail. The PDF of the later years is bimodal with a second local maximum close to 𝑙𝑜𝑔[Σ(𝜏1+𝜏 2+𝜏 6)] = 0, which corresponds to a sum of probabilities ≈1in levels. Furthermore, one observes a shift to the right around the first local maximum. These characteristics of the PDFs correspond to a first-order stochastic dominance of the probability distribution of the earlier years over the later years, which can be drawn from the comparison of the cumulative density plots (CDF) in the lower panel of Figure 7. The corresponding one-sided Kolmogorov- Smirnov test confirms this as it rejects the null of no difference between the CDFs on every significance level (maximum difference 𝐷+= 0.34, 𝑝 = 0.000). It is further empirical evidence for a shift toward this set of topics. Furthermore, the bimodality in recent years also hints at 1702 SCHMAL FIGURE 8 Topic correlation with journal types. Upper panel: ‘Top 5’ journals, lower panel: General interest journals. [Colour figure can be viewed at wileyonlinelibrary.com] research “monocropping” in the sense that papers shift towards these topics and nearly solely focus on them, ignoring most of the other topics. 3.3 Topic correlations with journal types Until now, I have discussed topic prevalence without addressing where these topics are placed. In economics, however, the outlet of a paper has enormous importance (Fourcade et al., 2015; Schmal et al., 2023). This holds not only for a researcher’s reputation but also for the audience it reaches. The so-called “Top 5” and the leading general interest journals are widely read and guide young researchers on where to look and what to investigate (Heckman & Moktan, 2020). Figure 8shows the correlation between the leading general interest journals and the 21 computed topics. The upper panel focuses on the “Top 5” journals, while the lower panel encompasses the leading “non-Top 5” general interest outlets, for example, the Journal of the European Economic Association or the Economic Journal of the Royal Economic Society. Eight topics are significantly correlated with the top five journals, namely 1, 2, 6, 8, 9, 13, 16, and 17. Meaningful are the extraordinarily high correlations with the first two topics, that is, those that take a rather general approach and those that discuss specific competition infringement cases. Furthermore, topics 6 and 9 are additional topics that address collusion cases and law enforcement on cartels SCHMAL 1703 FIGURE 9 Relationship between topic prevalence and citations. Point estimates for the panel regression as described in Equation (1). Thick line: 90% confidence bands, thin line: 95% confidence band extensions. Left: topic 3, middle: topic 11, right: topic 19. [Colour figure can be viewed at wileyonlinelibrary.com] and anti-competitive institutions. Topics 16 and 17 tend to be case-related as well. Only topic 13 on vertical relations seems to diverge from this leading pattern. Among the general interest journals shown in the lower panel of Figure 8, one finds lower correlations with many topics. The three most prominent connections exist with topics 4, 5, and 7, that is, on auction theory, information mechanisms, and principal-agent issues, which are also likely to be information-driven. Among field journals, dedicated IO journals, and antitrust journals, many topics are significantly correlated (as shown in Figure A.3 in the appendix), but there is not such a clear pattern as for general interest and Top 5 journals. The pattern for the latter is especially striking. The correlation with the first two topics is significant and much higher than any correlation with another topic. Together with topics 6, 9, and 17, these journals seem to focus intensely on past disclosed cartels. Other than topics of the categories “competition analysis” or “inside the cartel,” those are rather case-study-based. see Figure A.4) 3.4 Topic correlation with citations Besides placing a paper in a highly-ranked journal, the number of citations of a paper is crucial in measuring academic impact and success. As my dataset allows me to look at the number of citations for each publication (up to early April 2022), I am able to study the relationship with the presence of certain topics. Conducting regression analyses for all 21 computed latent topics separately, I find significant relations for three topics. The results are shown in Figure 9. It shows two estimates for each topic. This stems from the fact that I report both transformations of the citations per year variable as described previously. All regression results, including those for 𝑙𝑜𝑔(𝑐∕𝑦), which suffer statistically from many missing values, are shown in the appendix in Table A.6. The affected topics are those on market shares (3), capacity constraints (11), and procurement auctions (19). The latter two topics are part of the category “competition analysis” which is generally in decline as shown throughout this study. All three topics are negatively related to the number of annual citations. And all three are not significantly correlated with the “Top 5” journals. The other topics show no significant relation at all. Given the logarithmic nature of the 1704 SCHMAL FIGURE 10 Mean topic prevalence of topics negatively correlated with citations. Black solid line: Topics correlated with citations (see Figure 9). Red dotted line: Fitted linear regression. [Colour figure can be viewed at wileyonlinelibrary.com] variables, a 1% increase in the expected probabilities of one of these topics is related to a decrease by around −0.1% up to −0.15%. One must remember that this is related to publications within the subdiscipline of collusion research. As lower citation rates are an inferior outcome for researchers, this raises the question of the time dimension of the prevalence of these topics. Figure 10 shows that the share of topics with a lower level of citations diminished over time—even though it is fluctuating. Overall, researchers seem to realize these topics’ relative unpopularity and shift their attention towards other topics. It is backed by the statistical tests for non-stationarity (see Table A.7 in the appendix). Again, the ADF test cannot reject the null of non-stationarity for two lags, while the PP test rejects it on the 5% level for types 2 and 3. As before, the KPSS test rejects its null of a unit root being absent, even on the 1% level. An alternative explanation might be that research on these particular topics has “ended” in the sense that there is (currently) nothing significantly new to contribute. Given that economics as a social science is never static and there is a continuous supply of new data, this seems less plausible. There is sufficient evidence for non-stationarity, such that researchers tend to shift away from topics for which they can observe lower citations. It aligns with an NBER working paper studying European Research Council (ERC) grants. The authors find for rejected funding applicants a cutback in risky research after their repudiation (Veugelers et al., 2022). It is further evidence that researchers quickly adjust their agenda after receiving signals that their current approach does not pay off. In contrast to the development of topics, the variety of subjects in papers has grown over time. I draw this from the neural network set up to understand similarities between papers year by year. I use the ‘doc2vec’ algorithm with 20 iterations of the training model and a 50 × 1 vector. As Mikolov et al. (2013) have shown, the dimension of the document vector matters. Figure A.6 in the appendix shows that variations (100 × 1,500 × 1) do not affect the result. Figure 11 plots the change over time. Unlike the previous analyses, the average similarity of papers of a particular year does not suggest an economically reasonable intertemporal relationship, suggesting a zero-lag specification. For a random walk without and with a drift (types 1 and 2), I cannot reject the null of SCHMAL 1705 FIGURE 11 Development of content similarity of publications over time. Black solid line: Mean similarity of papers of a specific year with all papers of the same year excluding a paper’s similarity with itself. Red dotted line: Fitted linear polynomial regression of order 3. Neural network specification: paragraph vector dimension: 50. Training iterations: 20. Method: paragraph vector with distributed memory (PV-DM, see Le & Mikolov, 2014, for details). [Colour figure can be viewed at wileyonlinelibrary.com] non-stationarity using ADF and PP. The KPSS test also suggests the presence of non-stationarity. The results are shown in the appendix in Table A.8. As I find a notable decline in similarity measured with a plain univariate linear regression of relative similarity on time (coefficient: −0.0199, 𝑝 = .0016), it implies that the variety of subjects actually increases. In particular, similarity within the body of research diminishes by some 2pp per year, which leads to a halving of the overall proximity of contents over time. Thus, the antitrust community faces two parallel developments: We see growing diversity in the subjects of papers, for example, different industries in which firms collude. However, at the same time, there is evidence for a sharp narrowing in underlying topics. Put differently, the scope of research diminishes while the scope of applications grows.21 3.5 Reciprocal topic prevalence over time While the preceding analyses already bear essential insights into how collusion research evolved during the early 21st century, a multivariate examination may provide a further understanding of the co-movement of topics discussed. Particularly meaningful is how the rise and fall of topic prevalence affect other topics. Causal inference in a microeconometric sense is difficult to obtain given the lack of a major shock that could serve as causal identification. There is some discontinuity for case study topics in 2009 (see Figure 6). The global financial crisis coincides with it. However, there is no apparent reason why this should have affected research on collusion, especially in light of the submission-publication lag. Therefore, I utilize the toolbox of macroeconomic multivariate time series analysis instead. Here, I look at the joint evolution of the “case-study topics” (topics 1, 2, and 6) and the “competition analysis” category (topics 4, 7, 11, 12, 18, 19). To do that, I set up a Vector Autoregressive (VAR) model.22 Even though there is evidence for cointegration, I utilize the Toda-Yamamoto (1995) approach (TY), which states that a VAR in base numbers instead of differences can be fully used even if there exists cointegration as long as one 1706 SCHMAL TABLE 3 Granger causality wald tests. Dependent variable Excluded 𝝌𝟐df Prob. >𝝌 𝟐 External topics competition analysis 21.653 3 .000*** Competition analysis external topics 2.729 3.435 Signif. codes: ***: 𝑝<.01, **: 𝑝<.05,*:𝑝<.1. adds the order of integration to the lag length of the VAR and the order of cointegration does not exceed the initial leg length. The selection criteria suggest two lags and cointegration of order 1 (see Tables A.9 and A.11 in the appendix). This leads to a specification with three lags (see Table A.10) The technical evaluation shows that this VAR (using logarithmic values) satisfies the common criteria for a reliable model (see Tables A.12 and A.13 in the appendix). All eigenvalues are inside the unit circle and satisfy the stability condition of VAR models (see Table A.14 in the appendix). The residuals are not auto-correlated and satisfy all conditions for a well-behaved normal distribution. A convenient feature of VAR models is the Granger causality analysis. Table 3shows the results for the very compact Granger causality Wald tests within the two-variable setting. Essentially, they test whether the past values of a variable influence another variable: If so, the excluded variable “Granger causes” the other one. Thus, it only satisfies a weak definition of causality.23 Past values of the “competition analysis” influence the prevalence of the “external topics” while the opposite does not hold because the test statistic cannot reject the null of no effect. It is reflected in the impulse response functions presented in the upper panels of Figure 12. One observes that a shock to the external topics (LHS) does not affect the “competition analysis.” In contrast, we observe a significant decrease for two periods in the external topics following a positive shock to the competition-related topics, as the right panel in the figure shows. The lower panels of Figure 12 show the forecast error variance decomposition (FEVD), which adds additional evidence for the previous finding. It measures the share a shock happening to one variable has on the forecast error of the other. The lower left panel shows that a shock to the external variables has no significant effect on the forecast error of the competition analysis. Hence, the latter evolves independently of the exogenous topics. The opposite is true for the right panel. It takes one period of inertia, but from the second lead on, a shock of the competition analysis category significantly and persistently affects the evolution of the external topic prevalence and effectively predicts a portion of slightly below 1/2 of it (see Table A.15 in the appendix for details). Hence, the external topics are at least partially endogenous because their evolution is driven by the changes in the prevalence of competition analysis in the literature but not vice versa. 4 CONTEXTUALIZATION AND CONCLUSION This systematic review of 777 academic publications on collusion identifies essential insights that may affect antitrust authorities and practitioners in their ability to detect cartels and collusive behavior. Using a structural topic model, I am able to identify the underlying latent topics that have driven collusion research in the past two decades. I obtain a hitherto non-existent research clustering in this subdiscipline by doing so. I have conducted various univariate time series analyses based on the computed topic probabilities. They reveal a substantial decline in competition analysis, often based on game-theoretical considerations and so-called toy models that study a particular feature of a market and its partial equilibrium effects. SCHMAL 1707 FIGURE 12 Impulse response functions and forecast error variance decomposition. LHS: Impulse variable: “External topics,” response variable: “competition analysis” RHS: vice versa. Upper panels: Impulse response functions, lower panels: forecast error variance decomposition. Further, I have computed panel regressions investigating the relation between latent topics and citation rates. While there are only a few significant correlations, all of them suggest a negative relationship. As shown in the time series plot on the expected mean topic prevalence, one sees a downward trend for the topics with a negative relation to citations. Hence, researchers select these topics, maybe noting that the receptions (captured by citations) are low in the discipline and might adjust their research foci over time. While researchers tend to narrow the number of topics addressed in their papers, they get more diverse as a neural network-based analysis on the similarity of the body of research can show. Last, I have conducted a multivariate analysis. It reveals that the decline in game theory is not triggered by the new dominance of data-heavy case studies but instead fills the gap the turn away from competition analysis has left. All of this happened parallel to a steady broadening of contents. While the core issues of the papers seem to be shrinking, the overall contents, such as cases discussed, grow. Hence, we have a two-level decoupling in research: Fewer topics get wider attention and coverage than two decades ago. It is a positive development that the quantitative rigor of these case studies has increased a lot since the “credibility revolution” (Angrist & Pischke, 2010) in empirical economics. For example, causal inference designs are nowadays widespread in such papers. Furthermore, structural approaches in empirical industrial organization may be helpful to avoid the reliance on ad hoc assumptions. 1708 SCHMAL The downside is that case studies, by definition, are backward-looking. Whether this will harm cartel detection remains an open question, as rule-based approaches may be more adoptable by competition authorities than granular but case-specific analyses of past cartels.24 It is notable, though, that case study topics have by far the highest correlation with the “Top 5” journals in economics. While one-third of the topics are significantly correlated with these prestigious outlets, the first two topics have the highest point estimates for correlation across all topics and journal categories. It implies that the leading figures of the economic discipline particularly value this kind of paper. Naturally, it should foster many follow-up papers of IO researchers on various cartels. Hence, it is likely that these cartel case studies remain a strong pillar of collusion research. Taking a closer look at IO field journals such as the Journal of Industrial Economics or the International Journal of Industrial Organization, which publish a lot of collusion research, it turns out that they still focus on competition analysis and market outcomes in terms of topics. The “game-theoretic oligopoly theory” (Budzinski, 2007, p. 301) pushed forward in the 1990s and considered a threat to competition economics and antitrust policy appears to be in retreat in collusion research. From the availability of large datasets and computing capacity emerge sophisticated and novel contributions—as predicted by Kovacic and Shapiro (2000). In contrast, the old Harvard school, predominant from the 1930s on and based mainly on industry case studies (Bresnahan & Schmalensee, 1987), seems to experience a revival. The high demand for validations of the core findings may require such detailed data that can be only drawn from case studies. When reviewing the large mobile-phone spectrum auctions at the turn of the millennium, Klemperer (2002) noted that it mostly needs “elementary economics” and what is usually understood as rule and incentive-based thinking, namely the avoidance of collusion and misbehavior of the auction participants. Already in 2007, Caves highlighted the benefits of the “old IO” approach based on crosssectional analyses. While I am far away from criticizing or questioning quantitative rigor, the developments in the IO literature outlined in this paper put in question to which extent competition authorities get equipped with the right tools to investigate markets and detect collusion.25 This paper also makes no claims on the usefulness of sophisticated empirical models such as structural estimations. Nevertheless, in the field of collusion, Ghosal and Sokol (2014) have shown that cartel enforcement in the US has shifted from a large number of cartels detected in the 1980s and 1990s towards an approach that detects a comparatively low number of cartels. Among them are very large cartels, and high fines were imposed. This shift from many (small) cartels towards a few “big fishes” might correspond to the shift in the literature. In the very last step, I want to provide some avenues for potential policy interventions. An important way of steering research foci is the creation of incentives. Hottenrott and Lawson (2014) and Schmal (2023) could show that external funding may affect researcher behavior. Hence, research organizations and competition authorities could foster research on topics that have lost attention by academics by handing out grants and research support. Furthermore, authorities could host or support academic conferences that address specific topics. It would raise attention to these topics and bring together dispersed researchers who might start new collaborations. More extensive approaches would be funding chairs or research centers at universities. While it is a rather costly exercise, hosting conferences would be a low-threshold measure with comparatively low costs (for a public body), which may still have the potential to evoke a sizable echo in the academic community, especially if such conferences become regular annual events. SCHMAL 1709 ACKNOWLEDGMENT I am very grateful for valuable feedback from the handling editor Les Oxley, two anonymous referees, Oliver Budzinski, Justus Haucap, Paul Hünermund, Ekkehard Köhler, Anselm Küsters, Maikel Pellens, and Chris Snyder, as well as feedback from participants at the 16th Biennal Conference of the International Network for Economic Method, the Annual Conference of the Royal Economic Society 2023, the MSI Research Group Meeting at KU Leuven, the DICE PhD Research Workshop, the 2022 NOUS Workshop at Albert Ludwigs University Freiburg, and the 56th Hohenheim colloquium. All errors are my own. Funding by the German Research Foundation (DFG) is gratefully acknowledged (Funding No. #235577387/GRK 1974). CONFLICT OF INTEREST STATEMENT The author declares that there exist no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The writing, spelling, and grammar of this research paper have been enhanced through the use of artificial intelligence (AI) tools. The AI technology was employed to aid in identifying and correcting errors in writing, spelling, and grammar, while human judgment was exercised in reviewing and approving the AI-generated suggestions, ensuring that the content accurately conveyed the intended meaning, and aligning it with the research findings. DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from Scopus. Restrictions apply to the availability of these data, which were used under license for this study. Data are available from the authors with the permission of Scopus. All code files as well as all data computed by the author are available on GitHub. ORCID W.BenediktSchmal https://orcid.org/0000-0003-2400-2468 ENDNOTES 1See https://competition-policy.ec.europa.eu/document/download/b19175c3-c693-410b-b669-27d4360d359c_en? filename=cartels_cases_statistics.pdf(up to November 2022). 2The exchange between academics and practitioners has been particularly established by the Chicago school of antitrust in the United States and the “more economic approach” for competition decisions in the EU. 3Using JEL codes to identify content-wise related papers would be an alternative, but antitrust journals often do not use them. Furthermore, researchers could be biased or strategically act when assigning specific codes to their papers (Wehrheim, 2019). Keywords would be another option, but latent topics go into much more detail and circumvent the subjective self-reporting by the authors. A different approach would be gathering a corpus of economics and antitrust journals, running a topic modeling on all papers, and extracting those with a prevalence of topics related to collusion. In the second step, a topic model could be constructed for this subset of publications. The core difference would be that the papers are not selected by a manual keyword identification. It would prevent papers from being falsely ignored if they discuss collusion without using the mentioned terms. While this is an advantage, the two-step process still requires a manual selection of topics that one may consider as collusion-related. Furthermore, especially in the abstracts, authors need to use common keywords to inform potential readers about the paper. Thus, abstracts are unlikely to miss out on the core keywords of the strand of literature they belong to. Thus, authors are unlikely to use uncommon and creative language in this part of a research article. 4I technically also exclude those papers without any abstract listed in Scopus. Table A.1 in the appendix lists the journals. 1716 SCHMAL TABLE A.2 Paper distribution by journal type and publication time. 2000 - 04 2005 - 09 2010 - 14 2015 - 19 ≥2020 Total Antitrust 1 3 33 72 35 144 Field 22 24 28 38 15 127 General Int. 17 19 19 19 6 80 Ind. Org. 69 105 65 92 45 376 Top 5 Journals 15 12 7 11 5 50 Total 124 163 152 232 106 777 TABLE A.3 Custom stopwords additional to the ‘SMART’ stopwords (Lewis et al., 2004). (1) (2) (3) (4) (5) blackwell journal academic editorial cartel rand institute among paper cartels springer ltd supervisor section collusion north-holland llc can literature cartels sciencebusiness iii due discuss collusive elsevier press may eu show mine will TABLE A.4 Unit root tests for non-stationarity in ‘competition analysis’ topics. 𝑵𝒐𝒏-𝒔𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒓𝒊𝒕𝒚 𝒕𝒚𝒑𝒆 𝒍𝒂𝒈 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 𝒑-𝒗𝒂𝒍𝒖𝒆 Augmented Dickey-Fuller Test type 1 0 −1.4285 .1607 type 1 1 −0.7044 .4170 type 1 2 −1.4713 .1456 type 2 0 −4.6124 .0100 type 2 1 −1.0280 .6731 type 2 2 −1.2545 .5950 type 3 0 −7.3787 .0100 type 3 1 −2.7905 .2634 type 3 2 −1.7740 .6464 Phillips-Perron Test type 1 2−1.7069 .4208 type 2 2−24.9596 .0100 type 3 2−34.4637 .0100 KPSS Test – 2 0.6486 .0182 SCHMAL 1717 TABLE A.5 Unit root tests for non-stationarity in external topics. 𝑵𝒐𝒏-𝒔𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒓𝒊𝒕𝒚 𝒕𝒚𝒑𝒆 𝒍𝒂𝒈 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 𝒑-𝒗𝒂𝒍𝒖𝒆 Augmented Dickey-Fuller Test type 1 0 −0.5879 .4583 type 1 1 0.1543 .6796 type 1 2 0.4255 .7577 type 2 0 −2.0858 .2997 type 2 1 −0.7813 .7582 type 2 2 −0.8569 .7321 type 3 0 −3.7039 .0426 type 3 1 −2.8528 .2408 type 3 2 −2.2273 .4682 Phillips-Perron Test type 1 2−0.2539 .6237 type 2 2−6.3929 .3547 type 3 2−18.9020 .0381 KPSS Test – 2 0.7030 .0133 TABLE A.6 Regression tables: topic prevalence and citations. 𝒍𝒐𝒈(𝒄∕𝒚) 𝒍𝒐𝒈[(𝒄∕𝒚) + 𝟏] 𝒉𝒔𝒊𝒏 𝒕𝒓𝒂𝒏𝒔𝒇. log(Topic 3) −0.209 (0.153) −0.113** (0.055) −0.146*(0.075) Observations 675 777 777 R20.522 0.690 0.663 Within R20.984 0.983 0.982 log(Topic 11) −0.069 (0.097) −0.081*(0.048) −0.107*(0.063) Observations 675 777 777 R20.464 0.644 0.618 Within R20.982 0.981 0.980 log(Topic 19) −0.190** (0.086) −0.129*(0.070) −0.170*(0.091) Observations 675 777 777 R20.494 0.650 0.625 Within R20.983 0.981 0.980 Signif. Codes:***:0.01, **:0.05, *:0.1. Standard errors clustered on year×journal level in parentheses. Further covariates: open access (Y/N), corresponding author, see eq. (1). If the corresponding author could not be identified using the Scopus database, the missing value has been replaced with a categorical value for the whole author team. Plot of the results in column 2 and 3 to be found in Figure 9. Separate regressions for each topic were conducted. 1718 SCHMAL TABLE A.7 Unit root tests for non-stationarity in topics with negative citation correlation. 𝑵𝒐𝒏-𝒔𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒓𝒊𝒕𝒚 𝒕𝒚𝒑𝒆 𝒍𝒂𝒈 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 𝒑-𝒗𝒂𝒍𝒖𝒆 Augmented Dickey-Fuller Test type 1 0 −1.2871 .2108 type 1 1 −1.1637 .2545 type 1 2 −1.8260 .0677 type 2 0 −3.1899 .0353 type 2 1 −1.6696 .4497 type 2 2 −1.2875 .5836 type 3 0 −7.0824 .0100 type 3 1 −5.1028 .0100 type 3 2 −3.2884 .0933 Phillips-Perron Test type 1 2−1.1818 .4677 type 2 2−13.2054 .0416 type 3 2−27.3217 .0100 KPSS Test –20.7659.0100 TABLE A.8 Unit root tests for non-stationarity of content similarity over time. 𝑵𝒐𝒏-𝒔𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒓𝒊𝒕𝒚 𝒕𝒚𝒑𝒆 𝒍𝒂𝒈 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 𝒑-𝒗𝒂𝒍𝒖𝒆 Augmented Dickey-Fuller Test type1 0 −0.9407 .3334 type1 1 −1.6127 .0982 type1 2 −2.0709 .0403 type2 0 −0.8835 .7229 type2 1 −0.9543 .6985 type2 2 −1.2101 .6103 type3 0 −3.7582 .0387 type3 1 −2.5902 .3363 type3 2 −2.2516 .4594 Phillips-Perron Test type 1 2−0.5815 .5521 type 2 2−1.7582 .7846 type 3 2−16.8967 .0718 KPSS Test –20.7185.0119 SCHMAL 1719 TABLE A.9 Tests for cointegration. Johansen test Coint. param. LL eigenvalue trace stat. 5% crit. value 06−29.0492 – 19.7907 15.41 1¶9−19.6268 0.6103 0.9459 3.76 210−19.1539 0.0462 Engle-Granger test Regression Results First Step Case Study Topics Competition Analysis −2.920*** (0.653) Constant −6.139*** (0.811) 𝑁22 𝐹(1, 20) 20.02 𝑅20.500 adj. 𝑅20.475 Standard errors in parentheses *𝑝<.05,**𝑝<.01, ***𝑝 < .001 Second Step: Dickey-Fuller test on residuals 𝑵𝒐𝒏-𝒔𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒓𝒊𝒕𝒚 𝒕𝒚𝒑𝒆 𝒍𝒂𝒈 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 𝒂𝒅𝒋𝒖𝒔𝒕𝒆𝒅 𝑫𝑭 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 1% 5% 10% type 1 1 −5.277 −4.29 −3.74 −3.45 Johansen Test: Constant trend; Lag length=2,𝑁=20, time: 2000-2021. Engle-Granger test: 𝑁=22, adjusted DF-statistic critical values based on (Davidson and MacKinnon, 1993, p. 722) since the standard DF-critical values cannot be used as the OLS estimation in the first step distorts the variance. ¶marks the cointegration level at which the critical value exceeds the trace statistic. TABLE A.10 Tests for cointegration for the two variable specification with three lags. Johansen Test Coint. param. LL eigenvalue trace stat. 5% crit. value 0¶10 −21.9278 – 14.6659 15.41 113 −15.5038 0.49146 1.8179 3.76 214−14.5949 0.09124 Johansen Test: Constant trend; Lag length=3,𝑁=19, time: 2000-2021. ¶marks the cointegration level at which the critical value exceeds the trace statistic. TABLE A.11 Selection-order criteria VAR. lag LL LR df pFPE AIC HQIC SBIC 0−32.2897 0.1058 3.42897 3.4484 3.52854 1−27.0995 10.38 4 .034 0.094303 3.30995 3.36826 3.60867 2−19.1539 15.891¶4 .003 0.064653¶2.91539¶3.01258¶3.41325¶ 0−29.1206 0.0907 3.27586 3.29268 3.3753 1−22.9299 12.381 4 .015 0.0724 3.0453 3.0957 3.3435 2−15.5564 14.747¶4.005 0.0518¶2.6902¶2.7743¶3.1872¶ 3−14.5949 1.9231 4 .750 0.0750 3.0100 3.1278 3.7059 ¶marks the best outcome in each column. For two lags: 𝑁=20, for three lags: 𝑁=19. 1720 SCHMAL TABLE A.12 Test for normally distributed residuals of the VAR model (3 lags). Jarque-Bera test Equation 𝜒2df Prob >𝜒2 Case studies 0.198 2.9058 Competition Analysis 0.361 2 .8346 All 0.559 4.9675 Skewness test Equation Skewness 𝜒2df Prob >𝜒2 Case studies −0.016 0.001 1 .9773 Competition Analysis −0.311 0.306 1.5799 All 0.307 2 .8576 Kurtosis test Equation Kurtosis 𝜒2df Prob >𝜒2 Case studies 2.501 0.197 1.6571 Competition Analysis 2.736 0.055 1 .8144 All 0.252 2.8815 TABLE A.13 Lagrange-multiplier test for autocorrelation of residuals in the VAR model. lag 𝝌𝟐df Prob >𝝌𝟐 1 8.6979 4 .069 26.8167 4.146 H0: no autocorrelation at lag order 𝑖. TABLE A.14 Eigenvalues for test of the Eigenvalue stability condition. Eigenvalue real part imaginary part Modulus 0.8198 0.8198 0.0465 +0.6665𝑖0.6681 0.0465 −0.6665𝑖0.6681 −0.6252 +0.1039𝑖0.6338 −0.6252 −0.1039𝑖0.6338 0.2160 0.2160 All eigenvalues have a modulus <1. The VAR with 3 lags fulfills the stability condition. See Figure A.7 below for the unit circle. SCHMAL 1721 TABLE A.15 Forecast error variance decomposition – table. Step FEVD Std. Err. 95% CI 00 0 0 0 1 0 0 0 0 2 0.3876 0.0556 0.7195 0.1694 30.5149 0.1789 0.8509 0.1714 4 0.5025 0.1545 0.8504 0.1775 50.4979 0.1536 0.8423 0.1757 6 0.4999 0.1520 0.8479 0.1775 7 0.5133 0.1604 0.8663 0.1801 8 0.5121 0.1551 0.8690 0.1821 Impulse variable: competition analysis, response variable: External topics. FEVD Computation for Figure 12. Exogenous Vars. Biophysical/ Material condition Attributes of the community Rules Evaluate Criteria Action Situation Actors Interactions Outcomes Action Arena FIGURE A.1 The main structure of the IAD framework. Taken from (Ostrom, 2005,p.15). 1722 SCHMAL FIGURE A.2 Frequency of paper types over time. A less granular alternative to the use of latent topics is clustering papers solely by their methodological focus. This is less detailed as latent topics can also capture the methodology used and the content of a publication – a level of granularity a classification by method cannot provide. I distinguish between the categories theoretical, empirical, experimental, and policy, which I manually assign, that is, I handcode based on the abstract and, if necessary, the introduction whether a paper can be considered mainly theoretical, empirical, or experimental in its methodology. If a paper applies two categories, for example, by developing a theoretical model and testing it empirically, I review the particular publication and weigh the contributions to come to a conclusion. I do not cluster the antitrust publications in this step. I also omit policy papers as they only account for a very small fraction of the publications. This leads to the frequencies over time, as shown here. One can see that there is a slight decline in theoretical papers in the years around 2010. However, reaching a minimum in 2014, the number of mainly theoretical contributions has begun to increase again. At the same time, one can observe a minor growth in empirical papers and a rather stable evolution of experimental ones. Even though there might be some changes over time, I mostly observe fluctuations, and changes in the topics’ prevalence may have other reasons than shifts in the methodology applied. [Colour figure can be viewed at wileyonlinelibrary.com] SCHMAL 1723 FIGURE A.3 Topic correlation with journal types. [Colour figure can be viewed at wileyonlinelibrary.com] 1724 SCHMAL FIGURE A.4 Histogram of citations ≤100. [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE A.5 Histogram of logarithmic citations per year. [Colour figure can be viewed at wileyonlinelibrary.com] SCHMAL 1725 FIGURE A.6 Publication Similarity over time using different neural network specifications. Upper plot: Paragraph Vector dimension: 100. Lower plot: Vector dimension: 500. Method: paragraph vector with distributed memory (PV-DM), iterations: 20. [Colour figure can be viewed at wileyonlinelibrary.com]