Patterns of interdisciplinary citations and asymmetry between economics and the neighboring social sciences from 1959 to 2018

This paper offers a quantitative study measuring, through citation analysis, the historical relationship between economics and the other social sciences (that is, anthropology, political science, psychology, and sociology). The exercise suggested here comprehends the period from 1959 to 2018 in order to understand both whether economics has opened more space for the other social sciences and, if so, the subtleties of this process


Introduction
Some time ago, commenting about the history of economics and the social sciences, Backhouse and Fontaine (2010, 3) stated that "whatever the period being considered, references to the relationships between economics and other social sciences are almost universally incidental in general histories of economics." In an attempt to contribute to this literature, this essay focuses on the evolution of the interdisciplinary relationships between economics and the social sciences.
Our research presents a descriptive quantitative analysis of the patterns of interaction among economics and other social sciences since 1959, an endeavor recently undertook by a handful of studies. In these accounts, knowledge exchange appears asymmetric, and economics is considered more insular than its neighboring disciplines. Fourcade et al. (2015, 94), for instance, evaluating the insularity -the absence of interdisciplinarity -of economics for the 2000s, identify economics as the least interdisciplinary 1 discipline in relation to other social sciences.
Notwithstanding, there are contemporary discussions on the topic indicating that economics has open-mindedly embraced other social sciences in the recent years, thereby increasing interdisciplinary interactions (Bögenhold, 2018(Bögenhold, , 1126Fontaine, 2015, 3;Mäki, 2017). These discussions fi nd support in a paper published by Angrist et al. (2020), which presents the growing tendency of economics to engage in interdisciplinary interaction with other social sciences.
The present study, though close to Angrist et al.'s (2020) exercise, offers a more comprehensive and focused discussion of the knowledge exchange between economics and the other social sciences. Our research is more comprehensive because it offers information on several fronts related to economics' social science interdisciplinarity, such as economics' evolution in citations to and from the fellow social sciences, the decennial growth rate of the interdisciplinary ties, and the rise in economics' signifi cance within the network of the social sciences. In these exercises, our results corroborate the idea that economics has indeed become a more interdisciplinary social science -even though it still has a lot ground to cover.
More important, however, is the coeffi cient for measuring asymmetry patterns in interdisciplinary exchange originally offered by this paper. Asymmetry in interdisciplinary citations is vaguely defi ned in Fourcade et al. (2015, 93), Pieters and Baumgartner (2002, 498), and Rigney and Barnes (1980, 119). These works loosely use this concept to represent an absolute mismatch between two disciplines' reciprocal interdisciplinary citations. Our Coeffi cient of Interdisciplinary Asymmetry, on the other hand, offers both a more thorough perception of economics' relative relevance before each social science and an evaluation of changes in the interdisciplinary structure of the social sciences in terms of reciprocal ties. Therefore, this coeffi cient indicates a direction for the interdisciplinary exchange between the social sciences and represents this paper's main contribution. Our results demonstrate that, as the attention devoted to economics by the social sciences grew much more than the other way around in the last decades, economics has moved to the center of the social sciences' network.
2 Methodology: citation analysis, empirical strategy, and the Coeffi cient of Interdisciplinary Asymmetry This section has three subsections. The fi rst explains what comprises a citation analysis and describes the four studies that, to our knowledge, measure social science interdisciplinarity. The second presents our empirical strategy, encompassing data, time span, and methodology. Finally, the third subsection lays out the estimation of the Coeffi cient of Interdisciplinary Asymmetry.

Citation Analysis
Citation analysis is a quantitative technique that answers for a bibliometric effort to understand how communication fl ows within a given scholarly network. Its aim is to describe the structure of the fl ow of ideas and understand the position journals, disciplines, and scholars occupy within a network (Edwards et al., 2018, 287;Jovanovic, 2018, 302;Pieters & Baumgartner 2002, 483-484). In this sense, we may understand the social sciences as a specifi c social network of scholars, journals, and academic departments, within which we are interested in the journal citation network. The disciplines commonly regarded as social sciences are anthropology, economics, political science, psychology, and sociology (Abbott, 2001, 123;Angrist et al., 2020, 4;Pieters & Baumgartner, 2002, 485;Rigney & Barnes, 1980, 114-115). To the best of our knowledge, four works aiming at understanding the structure of interdisciplinary journal citations within this network have been hitherto published. Rigney and Barnes' (1980) study consists of a comprehensive citation analysis to examine the interdisciplinary citations from 1936 to 1975 both a) within the social sciences network and b) between each individual social science and other groups of academic disciplines. Their conclusion about interdisciplinarity in economics is that, along with psychology, the discipline had the lowest rates of interdisciplinary borrowing, the highest levels of intradisciplinary citations, and an insignifi cant number of citations from fellow social sciences. Pieters and Baumgartner (2002) analyzed the communication fl ows from 1995 to 1997 both a) between economics journals and b) between economics journals and other social sciences and business. They worked with forty-two economics journals and divided them into seven clusters, organized by citation proximity. Again, economics exhibited high levels of intradisciplinarity, engaging in an allegedly asymmetric citation exchange with other social sciences. Fourcade et al. (2015) explored the relationship between economics and other social sciences in different measures, among which insularity is the most relevant to us. The authors considered the period 2000-2009, and the analysis was made vis-à-vis sociology and political science. The citing source adopted, as in Rigney and Barnes (1980), was the fl agship journal of each discipline, and the reference sources comprised the top 25 journals from each discipline. Their conclusion was that economics is more insular than the other social sciences and has more space in the neighboring disciplines than the neighboring disciplines in economics.
Finally, Angrist et al. (2020) evaluated, for the period 1970-2015, the impacts of extramural -that is, interdisciplinary -citations among the social sciences and many other fi elds of knowledge. The authors show that economics is among the most insular social sciences, but that this situation has been improved in the past few years. Their unit of analysis also comprises a fl agship journal for each discipline.
As such, these studies commonly regard economics as a discipline that relatively neglects its neighboring social sciences. To this extent, Angrist et al. (2020) differs from the other works insofar as it demonstrates the progressive improvement of economics in terms of interdisciplinarity. The most comprehensive discussion in Angrist et al. (2020), however, regards the fi elds of economics that have gained importance outside the discipline, not the interdisciplinary phenomena per se. Finally, this literature -once again, with the exception of Angrist et al. (2020), which does not make any reference to asymmetry patterns -employs the concept of asymmetry rather loosely, which, as we will see, may jeopardize an accurate comprehension of the asymmetry patterns.

Empirical Strategy and Methodology
Our empirical strategy is, to some extent, a hybrid effort. It combines features from the four aforementioned studies and some original elements. Above all, it is a quantitative evaluation of economics' relations with the neighboring social sciences as circumscribed to our time span.
Following Angrist et al. (2020), Fourcade et al. (2015), and Rigney and Barnes (1980), we will concentrate our analysis on one publication per discipline. This publication is each social science's fl agship journal of the main American learned society. This is meant to compare how each discipline's fl agship journal evolved in terms of interdisciplinary citations to the social sciences. From this comparison, as do Angrist et al. (2020) and Fourcade et al. (2015), we will extrapolate some general patterns to the social sciences as a whole, keeping in mind that this extrapolation must not be overstated.
In the literature, we fi nd four reasons to defend the selection of the fl agship journals as capable of indicating general patterns. First, it is reasonable to assume that the fl agship journal of the main American learned society for each discipline represents the central currents of research in their respective fi elds (Rigney & Barnes, 1980). Second, knowledge production is a socially and institutionally embedded act, and the learned societies play a crucial role in this process, creating stimuli and development conditions, sponsoring research agendas, and coordinating research activities (Almeida et al., 2017;Coats, 1985). Third, the choice for the learned societies' journals reduces the probability of publication biases emerging from the selection of journals maintained by single departments whose publication screening processes might follow particular internal logics (cf. Colussi, 2018;Heckman & Moktan, 2020). Finally, the American academy still holds the highest-ranked journals and faculty departments in economics (Coupé, 2003;Kalaitzidakis et al., 2003). Therefore, the journals analyzed are American Anthropologist (AA), American Political Science Review (APSR), American Sociological Review (ASR), Psychological Review (PR), and The American Economic Review (AER).
From these fl agship journals, we collect the bibliographic references in each original article to build our database. Subsequently, we search for references to the top 25 journals from each social discipline. Following this, our investigation seeks patterns of interdisciplinary journal citations fl owing from the fl agship journals to this group of representative publications. It does not consider sources outside the top 25 journals of each discipline. We perform our analysis using the statistical programming framework R, and most of our main functionalities pertain to the bibliometrix package (Aria & Cuccurullo, 2017). The citation database is compiled from the Elsevier Scopus and Web of Science (henceforth WoS) databases. 2 Our time span ranges from 1959 to 2018, which is different from the periods Rigney and Barnes (1980) and Angrist et al. (2020) analyzed. We chose the year 1959 as the starting point both because it marks the fi rst record of the word interdisciplinarity and its variations in economics, according to Scopus and WoS, and because the quality of citation data on WoS is signifi cantly worse before 1956 -which marks the creation of the Science Citation Index. In order to compare the interdisciplinarity of our fl agship journals and gain some insight on how economics' interdisciplinarity with the other social sciences evolved through time, we separated our time span in decades, from the 1960s (which includes 1959) to the 2010s (ending in 2018), and built a dynamic Top 25 Journal Ranking (henceforth T25) for each discipline. We qualify the T25 as dynamic because we constructed one ranking for each decade, with the objective of grasping each journal's infl uence in that specifi c period. Moreover, we built our rankings based exclusively on the inCites Journal Citation Reports (henceforth JCR), which orders journals according to their impact factors. There are, furthermore, three issues involving the construction of these dynamic rankings.
First, the dynamic rankings per decade comprise the arithmetic means of the year-by-year impact factors within each interval. We rely on the arithmetic mean of the simple journal impact factor because the 5-year impact factor was made available only from 2007 onward. Second, the Social Science Citation Index's JCR is only available from 1979 onward (Garfi eld, 2007, 65;Rice et al., 1988, 258). This means that social sciences' journal rankings do not have observations for the period 1959-1978. Hence, we adopted the same retrospective ranking for the 1960s and the 1970s. The reference for this ranking is the triennium 1979-1981. Moreover, there is a difference between the rankings for the 1960s and the 1970s related to journal coverage: journals that did not exist in the 1960s were kept solely for the 1970s ranking and were replaced by the next highest-ranked journal covering the 1960s. Finally, in cases where we had a coincidence of journals for two different sciences, we removed that journal from the discipline in which it occupied a lower average position; these journals were also replaced by the next highest-ranked publication. Rigney and Barnes (1980, 114) understand asymmetry as the situation in which "one fi eld cites another more often than it is cited in return." Pieters and Baumgartner (2002, 498-503), conversely, thinking of asymmetry as "reciprocal citation relationships," present asymmetry in relation to overall interdisciplinary citations of a discipline, but do not advance on this analysis. To amend the need for a more concrete approach to asymmetry in interdisciplinary exchange, we devised the Coeffi cient of Interdisciplinary Asymmetry (henceforth CIA). The CIA is designed to measure the relationship between two disciplines in terms of reciprocal proportion of citations; it quantifi es the importance of discipline A to discipline B in relation to discipline B's importance to discipline A. Its formula for a given point in time is . This equation measures the asymmetry

The Coeffi cient of Interdisciplinary Asymmetry
In this formula, gives the number of citations to discipline A in discipline B, gives the number of citations to discipline B in discipline A, and θ A and θ B yield the total number of interdisciplinary citations in disciplines A and B, respectively. Therefore, the CIA equation depicts the relationship between the proportion occupied by disciplines A and B in the interdisciplinary citation network of each other. We furthermore use a logarithmic function because, without it, since all variables are positive, our ratios would have an inferior bound (in the limit, zero), but no superior bound (the ratio might tend to infi nity). Once this is calculated, CIA B, A is simply CIA A, B 's inverse: CIA B, A = -CIA A, B . Therefore, since this is a coeffi cient regarding symmetry, the logarithmic function renders our results more symmetrically related.
If CIA A, B equals zero, then we have that A plays a role in B's network of interdisciplinary citations equivalent to the role played by B in A's. As such, values closer to zero represent higher symmetry than those farther away. Alternatively, a positive CIA A, B means that A is more representative to B than B to A, while a negative CIA A, B yields the opposite result.
We believe that the CIA offers a more accurate perspective on bilateral relations than the loose comparison between the absolute levels of interdisciplinary citations among disciplines, because the latter does not consider the fact that disciplines present different institutional and historical patterns of interdisciplinarity. Since this difference exists, such analyses almost inevitably present asymmetry toward the less interdisciplinary discipline, inasmuch as its propensity to cite the neighboring sciences is smaller. On the contrary, the CIA considers different degrees of interdisciplinarity among disciplines as given. In this sense, each discipline's weight in relation to each other is measured exclusively within the interdisciplinary citations to the network. Therefore, it is our claim that the CIA facilitates an effective understanding of the asymmetry patterns in terms of the relative relevance between two sciences within a given network, offering a direction for the analysis of interdisciplinarity.

Results: interdisciplinarity within the social sciences network across time
The main results to be detailed in this section are: a) the evolution of each fl agship journal's openness to the other social sciences' T25; b) the evolution of the citations in anthropology, political science, psychology, and sociology to the economics' T25 journals per decade; c) the aggregate relationships between the fl agship journals and a group of core journals for each science; d) the patterns of asymmetry in interdisciplinary citations; and e) the evolution of each fl agship journal's references to the T25 of its own discipline. Among these, a) and b) resemble the results presented by Angrist et al. (2020). Point e) is close to the conclusion of Fourcade et al.'s (2015, 94) concerning economics' regard for the top of its internal hierarchy. Despite these prior discussions, nevertheless, we believe our analyses offer new inputs and insights on the nature of these developments. Evaluations c) and d), furthermore, offer, to the best of our knowledge, original assessments on the structure of the interdisciplinary citations within the social sciences network.
That said, fi gures 1 to 5 illustrate the evolution of each fl agship journal's degree of interdisciplinarity in relation to the social sciences.
Figures 1 to 5 depict how each T25 was cited in particular fl agship journals. In these fi gures, each line denotes the citations to one single alien discipline. Accordingly, Figure 1 establishes the evolution of AA's citations to the T25 journals on each discipline, except anthropology; Figure 2 evaluates the progress of APSR's citations to the highest-ranked journals on each discipline, except political science; and so forth. The y-axis represents each T25's participation in the citations of the fl agship journals of the neighboring social sciences. If we take, for instance, the last observation of the black line in Figure 5, we have that 0.666% of all entries in the references of papers published by the AER belongs to political science's T25 in the 2010s. Angrist et al. (2020, 12) present similar fi gures, whose tendencies fi gures 1 to 5 corroborate. Figure 6, alternatively, aggregates each discipline's overall openness to the social sciences. Its lines represent how each individual fl agship journal evolved in its citations to each of the aggregate T25s. Again, citations to a discipline's own T25 were not taken into consideration, and the logic for the y-axis here is the same as detailed above for fi gures 1 to 5, except that now we deal with aggregate T25s. This fi gure also fi nds a similar representation in Angrist et al. (2020, 10).  Participation 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018    Participation 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018    Participation 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018  The coeffi cients behind fi gures 1 to 6 are summarized in Table 1, which presents the percentage of interdisciplinary citations by decade for each fl agship journal. The colored diagonals represent citations to a discipline's own T25. The last column, which supplies the observations presented in Figure 6, is a sum of all the coeffi cients in a given line -minus the colored diagonal. Collectively, fi gures 1 to 6 and Table 1 offer two insights. First, they reveal that the overall openness of the social sciences -if we take the fl agship journals as suffi ciently representative -to the neighboring disciplines has risen in the last 60 years, from 2.05 percent, in the 1960s, to 2.74 percent, in the 2010s -peaking throughout the six decades. This represents a growth of 33.74 percent in the average interdisciplinarity within the social sciences network (with an average growth rate of 5.99 percent per decade). The second perception is that we may divide the social sciences into three classes of disciplines by interdisciplinarity status. The class of high and growing interdisciplinarity, composed by political science and sociology, kept its degree of interdisciplinarity growing and above the average overall interdisciplinary openness throughout the entire series. In the class of low and growing interdisciplinarity, which comprises economics and psychology, interdisciplinarity levels grew along our time span but remained below the interdisciplinarity average of the social sciences. Anthropology is the only discipline in the class of decreasing interdisciplinarity, in which the interdisciplinarity levels fell below the average levels from a certain decade onward. These same groups could also be inferred from Angrist et al. (2020, 10)even though the authors do not follow the above classifi cation.

Participation
Political science's and sociology's fl agship journals present the highest degrees of interdisciplinarity. The disciplines' relatively high levels of interdisciplinarity are ratifi ed by the recognition that their lowest decennial percentages (3.47 percent and 2.88 percent, respectively), are greater than the highest decennial percentages of the other three disciplines. In fact, if it were not for these two disciplines, the social sciences' aggregate average of interdisciplinary openness would have decreased in the sample (from 1.22 percent in the 1960s to 1.12 percent in the 2010s). Additionally, in the 2010s, political science and sociology collectively represented more than three-quarters (75.46 percent) of the interdisciplinary citations within the network.
Economics' and psychology's fl agship journals show low but intertemporally growing degrees of interdisciplinarity. Economics departs from 0.37 percent in the 1960s to reach 1.42 percent in the 2010s, while psy-chology departs from 0.55 percent and reaches 1.06 percent. Economics departs from a lower degree of interdisciplinary openness and evolves prominently in relation to its fi rst observation, nearly quadrupling from this stage, while psychology's decennial percentages nearly double. Still, both economics and psychology remain below the average levels of interdisciplinary openness through all the decades.
Anthropology, at last, is the only discipline whose degree of interdisciplinary openness decreased throughout our period of analysis. In the 1960s, anthropology was above the average level of interdisciplinary openness, with 2.74 percent of its citations directed toward its fellow social sciences. From the 1970s onward, however, the tendency of anthropology to cite these disciplines decreased progressively, reaching 0.88 percent in the 2010s, which is anthropology's lowest degree of social science interdisciplinarity in our sample.
Based on these fi ndings, Table 2 compares the sampled points of departure and arrival of each fl agship journal. Political science, sociology, and psychology did not have their positions altered between the 1960s and the 2010s; they remained in the fi rst, second, and fourth positions, respectively. Economics, however, rose from the fi fth to the third place, superseding psychology and anthropology. Anthropology, given its progressively decreasing regard for the social sciences, descended from the third to the fi fth position. The fi rst four columns, regarding the starting and fi nal stages of interdisciplinary openness, are important to situate economics in relation to its fellow social sciences. Economics is much below political science and sociology in terms of interdisciplinarity citations to the other social sciences.
This was true in the 1960s, and it remains true in the 2010s. Economics, however, managed to improve its situation and became more mindful of the social sciences than psychology and anthropology. In the case of the latter, this can be partially attributed to anthropology's contraction of its own interdisciplinarity levels. However, the escalation of economics' degree of interdisciplinarity vis-à-vis those of psychology, political science, and sociology, surpassing the fi rst and reducing the gap with respect to the remaining two, must be credited to economics. These results comprise the fl agship journals, but, extrapolating them to the disciplines, we have reason to believe that economics, among all the fi ve disciplines, is the one that became more open in relation to its own former levels. This is depicted in the last two columns of Table 2. As already presented, anthropology is the only discipline whose degree of interdisciplinary openness decreased. It had a growth rate of -68.07 percent. Among those whose interdisciplinary citations increased, psychology nearly doubled, growing 95.33 percent, while sociology and political science also grew signifi cantly, recording growth rates of 77.31 percent and 41.32 percent, respectively. It must be noted that the latter two disciplines already departed from relatively high degrees of interdisciplinarity, which makes these numbers expressive. Economics, fi nally, even though it might be argued that its point of departure was -for reasons discussed in the next section -absurdly low, grew 279.65 percent. This means that, in the 2010s, within the universe of AER citations, articles originally published in the highly ranked journals of the alien social sciences occupied a space nearly four times bigger than in the 1960s. Therefore, when we compare economics in the 2010s with economics in the 1960s, we are compelled to conclude that our study does not fi nd enough substance to reject the hypothesis defended by Fontaine (2015, 3) and Mäki (2017) and measured by Angrist et al. (2020, 10-12): the attention of economics to other social sciences -as long as the AER as a proxy is concerned -has indeed become more prominent.
Furthermore, the increasing attention of economics to the neighboring social disciplines was answered by an active -and much more incisiveincrease in the attention of the alien social sciences to economics. Table  3 compares these rates of growth. The overall openness of the social sciences went up 33.74 percent, with an average growth rate of 5.99 percent per decade, as aforementioned. Meanwhile, the AER citations to the T25s of anthropology, political science, psychology, and sociology increased 279.65 percent, with an average growth rate of 30.58 percent. At the same time, the average number of citations of other fl agship journals to economics grew 333.52 percent, with an average growth rate of 34.09 percent per decade. This intertemporal evaluation further indicates that economics rose to the highest rank among the social sciences in terms of prestige in the 1980s, after an increase of 106.42 percent in citations directed toward its T25. From this decade onward, as displayed in fi gures 1 to 4, economics became the most cited social discipline in political science, psychology (both of which had sociology as most cited discipline in 1960s-1970s), and sociology (in psychology's stead) -the exception here is anthropology, in which sociology remained as the most cited discipline throughout the entire sample. This movement of economics towards the center of the social sciences network may be inferred from Table 4 and Figure 7. Table 4 contains information regarding the proportions of interdisciplinary (ID in the table) citations to and from economics. The fi rst three columns show that, among the fi ve disciplines and among all the interdisciplinary citations to social sciences (SS in the table) -accounted by the simple addition of the absolute number of interdisciplinary citations -the AER evolved from representing merely 2.19 percent in the 1960s to representing 19.23 percent in the 2010s. Additionally, the fi nal three columns illustrate that economics, which represented 15.90 percent of all the interdisciplinary citations of the fl agship journals of anthropology, political science, psychology, and sociology to the neighboring social sciences in the 1960s, accounted for 56.01 percent of these citations in the 2010s. Accordingly, these columns inform the reader that economics, from the 1990s onwards, became the target of more than half of the absolute number of interdisciplinary citations to the social sciences employed by AA, APSR, ASR, and PR. Furthermore, Figure 7 shows that this rise in attention toward economics was more conspicuous in political science and sociology, while anthropology actually contracted its utilization of citations to economics. A comparison between fi gures 5 and 7 facilitates the introduction of the asymmetric relationships between economics and other social sciences, as presented by Fourcade et al. (2015, 94). The comparison between these fi gures allows us to pair economics with each one of the other four disciplines per decade. This gives us twenty-four pairing observations, summarized in Table 5. The fi rst column in each box gives economics' citations to the paired discipline, while the second column gives the opposite relationship. The higher percentages in each comparison are in bold. In twentytwo out of the twenty-four observations, economics' space in the paired social science is bigger than the other way around. The only exception is psychology, both in the 1990s and 2000s.  This table indicates that economic knowledge fl ows into the other social sciences, more than contrariwise. In percentage terms, in the beginning of our sample, we fi nd that economics is more important to each alien discipline than each alien discipline to economics, and this relationship remained nearly untouched across the time period analyzed in our study.
In terms of growth rates, anthropology's citations to economics is the only one to have decreased, at an average rate of 31.43 percent per decade. Despite this, the AER never cited anthropology' T25 more than the AA cited economics' T25 in any given decade. Political science's and sociology's growth of citations to economics were much more prominent than Participation 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018  the opposite. Alternatively, psychology's citations to economics grew in signifi cance -more than economics' citations to psychology. Given that economics' representation in articles on psychology remained higher than psychology's representation in economics' articles (exception made to the 1990s-2000s observations), one might loosely infer that this movement actually represented a reduction of the asymmetry between economics and psychology or that the asymmetry took place towards psychology in 2000s-2010s. However, this result is unweighted for interdisciplinary citations within the social sciences network. In order to further our understanding of the asymmetry patterns, we must resort to the CIA. Accordingly, Figure 8 offers a visualization of how economics' asymmetry with the neighboring social sciences evolved between the 1960s and the 2010s. Table 6 presents the calculated CIAs.  The information displayed in Figure 8 is read as follows: the closer a point is to the dashed line in the center of each facet (which represents CIA = 0), the more symmetric is the relationship between economics and the indicated alien discipline. Points to the left of the line mean that economics is less representative for that science than otherwise -asymmetry contrary to economics. Points to the right of the symmetry line, on the other hand, mean that economics' weight in the interdisciplinary citations to social sciences in that specifi c discipline is greater than the opposite -asymmetry toward economics. The fi gure shows that economics weighted less on the social sciences' interdisciplinary citations in the 1960s than the opposite, with the exception of psychology. 3 In fact, psychology is the only discipline in which asymmetry was never contrary to economics. In the 1970s, economics grew in signifi cance within the network, and an asymmetry toward economics surfaced in political science. In the 1980s, only sociology maintained a pattern of asymmetry contrary to economics. From the 1990s onward, sociology joined the other disciplines; as a result, all the observations gave an asymmetry toward economics. There is another aspect regarding this fi gure that inspires caution. A difference exists between economics' relatively symmetric relationships with, for example, both sociology in the 1980s and anthropology in the 1970s. While the former is relatively symmetric because sociology was as important to economics as economics was to sociology in the 1980s, the latter is nearly symmetric because anthropology was as unimportant to economics as economics was to anthropology in the 1970s. Therefore, again, we must reiterate that these plots represent a reciprocal importance within the network, not absolute relevance of disciplines toward each other.
It also does not mean that a rise in asymmetry toward economics indicates that economics became more cited in that discipline in absolute terms. It means that economics rose in signifi cance. Accordingly, this can also be an outcome of the decline in a discipline's citations to other social sciences. This is the case, for example, in psychology, whose citations to political science and sociology decreased across time. We have seen that the number of AER citations to psychology have grown more than the number of PR citations to economics. Still, the asymmetry toward economics in relation to psychology became larger between the 1960s and the 2010s.
Furthermore, an additional and elucidating investigation arises from citations to the Core Journals. The results are summarized in Figure 9. The core journals of a discipline are taken to be those that appeared in the T25 of that discipline in all the decades analyzed, from the 1960s to the 2010s. All the disciplines have closely the same number of core journals, which range from four to six. 4 Figure 9 Unweighted references to core journals 4 Economics' core journals are AER, Econometrica, Economic Geography, Journal of Political Economy, Quarterly Journal of Economics, and Review of Economic Studies.  Figure 9 did not weigh the references for interdisciplinary citations to social sciences. This is intended to offer, beyond the recognition of the overall interdisciplinary citations to key journals, a point in case regarding the fl agship journals' citations to their own cores as well. From this fi gure, we may realize that, in regard to unweighted overall citations, economics' core is the most representative one for the APSR (1.52 percent), the PR (0.23 percent), and the ASR (1.03 percent). For the AER, on the other hand, the political science core is the most representative one (0.36 percent). These results endorse the weighted investigation, which places economics as the most relevant social science, citation-wise, within the network, and political science is revealed as the discipline to which the AER directs more attention. Moreover, again, we can easily identify political science  and sociology ahead of anthropology, economics, and psychology in terms of citations to their neighboring disciplines. It is worth highlighting, nonetheless, that anthropology and psychology are below economics in terms of social science interdisciplinarity. Figure 9 also corroborates Fourcade et al.'s (2015, 96) realization that economics, besides looking more inward than the other social sciences, also displays a much higher reliance on knowledge produced at the top of its internal hierarchy, a perception that shines through Figure 10 as well. This fi gure points to the fact that, in relation to the social sciences, the most prestigious economics journals occupy a much more central position in the network of intradisciplinary knowledge transmission. Accordingly, it should be noted that, even though knowledge produced in other sources had, by defi nition, less space to be preserved and replicated within the journal, the AER managed to become a more interdisciplinary social science in relation to itself and to the AA and the PR, and this might indicate, we argue, an overall opening of economics to the social sciences. Economics still has a 1959-1969 1970-1979 1980-1989 1990-1999 2000-2009 2010-2018  lot of ground to cover in order to become as open as political science and sociology to social science knowledge; however, it cannot be denied that the discipline's situation in this regard has undergone some improvement.

Discussion
A study of this nature is unlikely to be free of limitations, which go beyond the general ones pointed out by Cherrier and Svorencik (2018, 368-372). First, even though citations to periodical literature are a useful marketbased measure of research quality, they are imperfect measures of interdisciplinary infl uences 5 (Hamermesh, 2018, 125;Rigney & Barnes, 1980, 116). Second, we restricted our analysis to the fl agship journal of each social science. Third, the citation patterns analyzed comprise only journal articles. Other sources such as books, book reviews, and conference proceedings are entirely absent in our sample. Fourth, our ranking defi nitions for the T25 articles in each social science per decade had to extrapolate impact factors listed between 1979 and 1981 all the way back to the 1960s. The implicit assumption here is that the infl uence of the journals remained unaltered from the 1960s to the early-1980s. Finally, there are many factors that infl uence one discipline's citations to another, in addition to the infl uence of the cited discipline per se, such as observed scientifi c status of the cited discipline and the amount of literature available for citation (cf. Rigney & Barnes, 1980, 125). The results here, therefore, ought to be interpreted cautiously.
Still, the fi ndings of this essay are compelling especially in two senses. First, and more importantly, our results examine the asymmetry of knowledge transfer between economics and the social sciences, to which it provides a direction: anthropology, political science, psychology, and sociology resort more to economics than economics to each one of them. This pattern was intensifi ed in the last 60 years, especially from the 1980s onwards. This result is given both by the absolute number of citations and by economics' CIA with each one of the neighboring disciplines. Second, the results also point that three classes of disciplines may be singled out, which indicates that economics has space to intensify its interdisciplinary ventures, but also indicates that economics is not the most insular social science. Therefore, given the analysis laid down in this article, our estimates indicate that, between 1959 and 2018, economics became a) a more interdisciplinary social science -even though the openness toward economics in social sciences grew much more acutely than the openness toward social sciences in economics, and b) the most infl uential discipline within the social sciences interdisciplinary network. Nevertheless, the percentages of economics' openness to the social sciences remain below the average interdisciplinarity within the social sciences network all along our time span (from 0.37 percent vis-à-vis 2.05 percent, in the 1960s, to 1.42 percent visà-vis 2.74 percent, in the 2010s), and this should not be neglected. These conclusions encompass the perception that economics rose from the fi fth to the third position in terms of interdisciplinarity within the social sciences network, which is unlike the usual portrayal of economics as the least interdisciplinary social science.
At this point, some qualifi cation is necessary, because, even though economics has actually become a more interdisciplinary social science in the last decades of the twentieth century, this movement by no means represents a return to the levels of interdisciplinarity that prevailed from the fi rst decades of the twentieth century to the years around World War II. It must be noted that academia is undoubtedly much more compartmentalized in the twentieth-fi rst century than it was in the fi rst half of the 1900s (cf. Backhouse & Fontaine, 2018;Cavalieri, 2016;Morgan & Rutherford, 1998).
Nonetheless, we must recognize that economics reached a point of abnormally low interdisciplinarity in the decades comprising precisely the beginning of our time-span, as the years following World War II marked what Fontaine (2015, 6) labeled a cross-disciplinary age for the social sciences. In great part, this low point can be credited to the reversal of the problem-oriented ethos prevailing during and since the war effort. Economists, albeit not immune to the ethos prevailing around the time of World War II, became more and more hubristic and discipline-oriented (cf. Backhouse & Fontaine, 2018;Cohen-Cole, 2014;Crowther-Heyck, 2006). This cross-disciplinary age, furthermore, coincides with the transformation of economics into a highly mathematical discipline, with a compulsion toward logical rigor (cf. Backhouse, 1998;Debreu, 1991). This resulted in the narrowing of economics' search for insights within other social sciences, as the discipline came to defi ne itself more in terms of its methods than in terms of its subject matter. It is no coincidence, therefore, that the decades following World War II witnessed the simultaneous rise of a mainstream in economics and of economics imperialism. On the one hand, the upswing of a mainstream as strong as economics' generates a path dependence that hinders the search for alternative arguments both in the outskirts of economics itself and beyond its boundaries. On the other, economics imperialism gave vent to the belief, widespread among economists, that social phenomena located elsewhere in the disciplinary spectrum could not be fathomed unless through the tools of economics. Social disciplines, for economists, became competitive rather than complementary (cf. Backhouse & Fontaine, 2018;Becker, 1976;Mäki, 2009;Stigler, 1984). As a matter of fact, the CIA may serve as an illustration of the rise of economics imperialism, as the discipline became overwhelmingly infl uential within the social sciences network.
Economics imperialism imposes yet another compelling consideration: such a rise in economics' degree of social science interdisciplinarity may epitomize a sort of "recycled interdisciplinarity," insofar as the increment in economics' citations to other social sciences may express simply the restoration of economics' own arguments, previously reproduced outside its boundaries.
Therefore, quantitatively, the movement presented in this article does not amount to a return in V to the previous levels of integration between the social sciences. Likewise, it also does not necessarily represent a qualitative leap in interdisciplinary integration, as this rise in economics' citations to the neighboring social sciences may be of the recycled kind.
Alternatively, what the movement presented in this article does amount to is the upsurge in economics' relevance within the network of social sciences. Between 1936and 1975, Rigney and Barnes (1980 identifi ed that "[…] the only social science discipline that has cited economic literature to any important degree is political science, followed at a distant by sociology." Our results show that, from 1959 to 2018, there was a change in this landscape, especially from the 1980s onwards, when economics became the most cited discipline in the fl agship journals of political science, psychology, and sociology. Anthropology, as indicated earlier, is a particular case, and our results corroborate Pearson's (2010, 166) remark that "it would be hard to imagine two social sciences more mutually estranged than anthropology and economics." Still, the average level of citations to economics by the four neighboring social sciences grew from 0.40 percent in the 1960s to 1.74 percent in the 2010s, which marks a growth of 333.52 percent. This recognition, especially after employing the CIA, indicates a direction for the interdisciplinary exchange between the social sciences, as economics became the most signifi cant discipline within the network.
Furthermore, economics' gain of relevance before the social sciences coincides with what has been conventionally called the "empirical turn in economics," a phenomenon occurred in the last decades of the twentieth century (Backhouse & Cherrier, 2017, 2). Hamermesh's (2013, 168) bibliometric investigation shows that a shift toward more empirical work in economics actually took place between 1983 and 1993. Additionally, Angrist et al. (2020, 39) highlight a rise in the interest of the social sciences toward empirical studies in economics. Therefore, economics' effective rise as the most prestigious social science coincides precisely with the shift in its attention toward empirical research.
These conclusions are in line with part of the literature on the subject, which places economics precisely in this progressive state of interdisciplinarity. Fontaine (2015, 3), for example, defends that, even though economists usually misinterpret interdisciplinarity for economics imperialism, economics "has appeared more cross-disciplinary than expected" since World War II. Bögenhold (2018Bögenhold ( , 1126, in addition, concludes that, pari passu with the decline in sociology's public reputation, economics embraced the earlier discussions on the social dimension of economic behavior, moving toward other social sciences. Finally, in a 2017 American Economic Association discussion panel, 6 which examined publishing and promotion in economics, Angus Deaton asserted that economics, in relation to other fi elds, is a relatively open discipline. Our data show that economics is not among the most open social sciences, but that Deaton is not wrong: economics is not the most insular as well. George Akerlof, alternatively, in the same event, defended that there is almost a total disconnect between economics and sociology and that, perhaps, some combination of both would be more appropriate to deal with the type of situations economists tend to examine -an idea he recently reinforced (Akerlof, 2020). We believe this idea to be extendable to all the social sciences analyzed in this essay.
Strictly speaking, the data have shown that economics is paying more attention to the social disciplines, and therefore getting closer to Akerlof's ideal. As Angrist et al. (2020, 50) postulate in their conclusion, "economists are also increasingly likely to read other social sciences.
[…] economic scholarship has never been more exciting or useful than it is today." Excitement is a subjective mental state, for sure. Nonetheless, economics' usefulness, if the discipline aims at both honoring Akerlof's plea and following the examples set by political science and sociology in terms of interdisciplinarity, still has a long way to go.