The method of comparative-historical analysis: a tailor-made approach to public diplomacy research

In view of the major methodological challenges which confront researchers in public diplomacy (PD), the paper recognizes the method of comparative-historical analysis (CHA) as an eminently suitable approach for robust empirical studies. The paper starts by exploring different conceptualizations and operationalizations of public diplomacy. Subsequently, four defining characteristics of CHA are identified: (1) CHA starts from a positivist epistemological perspective; (2) CHA-based research usually is concerned with “big questions;” (3) comparative methods are applied in CHA, either across different cases or within cases across time, allowing for in-depth analyses; (4) by considering respective starting points, specific historical developments, and cultural particulars, CHA is committed to methods drawn from historical research, including process tracing and causal narrative. The paper demonstrates that CHA, in view of these characteristics and with its highly interdisciplinary pedigree and methodological eclecticism, is eminently suited for studies exploring PD practices and outcomes. To provide a tailor-made approach for such endeavors, CHA is innovatively combined with the method of structured, focused comparison. Finally, drawing on both the different operationalizations of PD and the requirements of CHA, a comprehensive matrix for CHA-based PD research is presented, offering a tangible framework for future empirical analyses.


Introduction
In the information age of the twenty-first century, public diplomacy (PD) has become one of the most promising fields of research and its importance in international relations today is widely shared among practitioners and scholars alike. 1 Classically defined by Hans N. Tuch in 1990 "as a government's process of communicating with foreign publics in an attempt to bring about understanding for its nation's ideas and ideals, its institutions and culture, as well as its national goals and current policies," 2 public diplomacy has received increasing attention especially since the turn of the millennium.
Different developments have contributed to this trend: First, advances in information and communication technologies have made the access to and exchange of information both faster and cheaper than ever before. In view of these technological advances, and coupled with trends of increasing globalization, interdependence, and democratization, Pierre Pahlavi even heralded the entry into a "global information society." 3 Consequently, new avenues of international communication and exchange have been opened up, giving rise to an unprecedented surge in public diplomacy, both qualitatively and quantitatively, despite the fact that its practice as a tool of diplomacy and statecraft can be traced back millennia. Second, as recognized by many scholars, the terrorist attacks of September 11, 2001, and the subsequent "War on Terror" by the George W. Bush administration have put public diplomacy at the very top of the political agenda. 4 Today, this increasing interest in and practice of public diplomacy is hardly restricted to the United States alone, as countless international actors-from nation states to international organizations to non-state and non-governmental actors and networks-have stepped up their efforts to engage with publics abroad by means of public diplomacy. In fact, regardless of size and regime type of respective states, governments around the world have recognized and included public diplomacy as a crucial instrument in their foreignpolicy tool box, 5 not least in the context of their soft power strategies.
However, despite this increasing interest in and an evergrowing body of literature on public diplomacy, fundamental methodological questions concerning the rigorous study of its premises, its modes of operation as well as its outcomes remain largely unanswered. In particular, the latter the identification of palpable outcomes brought about by public diplomacy, has become as much as the philosopher's stone in PD research. Against this very background, the paper explores a promising methodological approach in order to study public diplomacy and its outcomes more rigorously: the method of comparative-historical analysis (CHA). It will be demonstrated in the following that CHA, combining comparative methods with the in-depth historical analysis of selected processes and the identification of causal relationships, pays tribute to major methodological challenges in public diplomacy research.
To substantiate this assessment, the paper first briefly explores the role of public diplomacy today, especially when understood as a tool for wielding soft power and in view of the major research challenges posed by its study. Subsequently, starting from its ontological and epistemological premises, the method of comparative-historical analysis will be presented. Identifying its key characteristics, it will be shown that CHA, with its highly interdisciplinary pedigree and methodological eclecticism, is eminently suited for studies exploring the operation and outcomes of PD in practice. Aided and innovatively supplemented by the method of structured, focused comparison, CHA thus offers an auspicious approach indeed to the robust study of public diplomacy practices and outcomes today. Springing from these insights, a research agenda for the application of CHA in public diplomacy research will be outlined, providing starting points for empirical analyses. In this context, a matrix for CHA-based research in public diplomacy is proposed, offering a tool box for researchers to draw upon.

Public diplomacy: definitions, characteristics, and operationalizations
Public diplomacy has become a key component in the practice of international affairs today. Still, the concept itself remains heavily contested and controversial. 6 Geoffrey Cowan and Nicholas J. Cull have in this vein noted that "few fields are as relevant, compelling, or ready for serious study. Few reveal so much neglect and past folly, but few contain so much hope for the future." 7 This widely-shared estimate begins with the very definition and understanding of public diplomacy itself, giving rise to a "litany of attempts" 8 over the decades. Besides the one by Tuch quoted above, Edmund A. Gullion's definition from the mid-1960s remains influential today, defining public diplomacy as "the means by which governments, private groups and individuals influence the attitudes and opinions of other peoples and governments in such a way as to exercise influence on their foreign policy decisions." 9 More recent proposals to define public diplomacy, including the ones by Paul Sharp ("the process by which direct relations are pursued with a country's people to advance the interests and extend the values of those being represented" 10 ) and Bruce Gregory ("ways and means by which states, associations of states, and nonstate actors understand cultures, attitudes, and behavior; build and manage relationships; and influence opinions and actions to advance their interests and values" 11 ), continue to stress the importance of realizing one's interests on the part of the wielder of public diplomacy. Efe Sevin accordingly noted that "public diplomacy is a foreign policy tool with the ultimate objective of contributing to the advancement of national interests." 12 Beside this understanding of PD as an interest-driven instrument of an actor's foreign policy, the definitions referred to above increasingly highlight the significance of the receiver in (successfully) wielding public diplomacy. These developments have given rise to what Jan Melissen called the "new public diplomacy." 13 By "shifting from one-way informational diplomatic objectives to two-way interpretative public exchanges," 14 the focus in public diplomacy practice and research hence increasingly rests upon its relational character today. Jan Melissen hence stated, "The new public diplomacy moves away from-to put it crudely-peddling information to foreigners and keeping the foreign press at bay, towards engaging with foreign audiences." 15 As with its basic definition, public diplomacy has equally defied easy operationalization. Eytan Gilboa noted on this account, Despite growing significance of public diplomacy in contemporary international relations, scholars have not yet pursued or even sufficiently promoted systematic theoretical research in this field. They have developed models and tools for analysis in several relevant disciplines but have not proposed a comprehensive and integrated framework. 16 Sharing these observations, different attempts can be found in literature for such frameworks. R. S. Zaharna, for example, distinguished between "level of participation," "degree of coordination," "scope," "time duration," and "policy objective." 17 In order to discern different aspects of PD, the factor of time is frequently applied as a discerning criterion. 18 Joseph Nye, for instance, draws on the work of Mark Leonard, Catherine Stead, and Conrad Smewing when he distinguishes between "daily communications," "strategic communication," and "lasting relationships." 19 Despite their principal usefulness, such distinctions are not necessarily sustainable in practice (as practices tend to overlap), especially when regarded as the single separating criterion, and therefore their sole value for empirical analysis of PD is limited. Rather, a supplementary separation along different forms of public diplomacy offers more promising theoretical starting points. In this regard, the identification of five distinct components of public diplomacy by Nicholas J. Cull-(1) listening, (2) advocacy, (3) cultural diplomacy, (4) exchange diplomacy, and (5) international broadcasting-offers resilient starting points for empirical analyses. 20 As shall be demonstrated in the following, a combination of these different operationalizations proofs particularly helpful for CHA-based public diplomacy research.
The highly interdisciplinary character of public diplomacy contributes to observed difficulties in conceptualization. At the same time, however, it allows for innovative approaches drawn from different disciplines in order to assess its practices and outcomes. 21 Gilboa, for example, identified as many as thirteen disciplines which have contributed to public diplomacy, including public opinion, cultural studies, and public relations branding. 22 Research in these neighboring fields not least provides auspicious starting points for methodologically robust studies in public diplomacy. In fact, there is a rich tradition in PD research to draw on the insights and practices of "sister disciplines" such as public relations. 23 Another field contributing significantly to PD as identified by Gilboa is International Relations. 24 In this discipline in particular, PD has frequently-and increasingly-been tied to power, especially to the concept of soft power. 25 In this context, public diplomacy is regularly conceptualized as an instrument for the wielding of attractive soft power in international affairs. 26 Public diplomacy, in this understanding, is applied in order to obtain information on foreign receptions of "the self" and increase one's attractiveness towards "the other" by means of different programs and initiatives. As with public diplomacy, soft power is known for the methodological pitfalls it presents when seeking to empirically assess its sources, instruments, reception, and especially its outcomes. 27 Sound methodological approaches to identify concrete outcomes in particular have been notoriously elusive in soft power and public diplomacy research alike, despite the fact that the importance of this aspect is widely shared. Benjamin E. Goldsmith and Yusaku Horiuchi, for example, aptly noted while alluding to the importance of changed behavior, "Without some effect on international outcomes, the term soft power would, of course, be a misnomer." 28 And Joseph Nye agreed that ultimately "it is outcomes, not resources, that we care about." 29 How, however, can outcomes be traced and compared empirically? To present an example for this conundrum in line with the above-mentioned taxonomy: How can the success of a scholarship program-a classic example of exchange diplomacy-be determined? Can (foreign-policy) changes in behavior, in line with corresponding national interests, be observed and can they in turn be 21 Szondi (2009, p. 293). 22 Gilboa (2008, p. 74). 23 Fitzpatrick et al. (2013, pp. 1-21). 24 Gilboa (2008, p. 57). 25 See, for example, Auer et al. (2015, p. 39), Hocking (2005, pp. 28-29). 26 For example, Nye (2008, p. 95), Nye (2004, pp. 107-125), Melissen (2005b, p. 3), Cull (2011, p. 15). 27 For the distinction between these four "subunits" of soft power, see ; the author also explores the method of CHA as a promising approach to the empirical study of soft power. 28 Goldsmith and Horiuchi (2012, p. 560); authors' emphasis. 29 Nye (2013, p. 568). attributed to such programs in a concrete empirical case? In fact, (academic) exchanges, despite their wide scope in terms of numbers, are ultimately a decisively individual experience. Consequently, respective contexts and personal experiences on part of the receiver may do as much-or as littleto contribute to their success-or failure-as any well-meant effort on part of the wielder. Besides, they may take years or even decades to bear fruit, and even if changed behavior can ultimately be attested, questions of attribution remain, especially if decades have passed. In view of this example, at least three major-and interconnected-methodological difficulties in substantive public diplomacy research can be established: (1) the recognition of respective (cultural, temporal, or even individual) contexts, (2) the host of potentially intervening variables over a long period of time, and (3) the issue of attribution of (observable) outcomes and (changed) behavior. The method of comparative-historical analysis, as shall be shown in the following, provides a remedy to these difficulties.

Comparative-historical analysis: a royal road for PD research?
Like public diplomacy itself, the method of comparativehistorical analysis exhibits a highly interdisciplinary pedigree as it draws on and combines approaches from historical research and political science alike. With its combination of historical methods and comparative tools, it in fact bridges the (often overstated) divides between both disciplines. While such differences have long been recognized and are often repeated, sinking even to the level of caricatures at times, 30 they certainly should not be exaggerated. 31 Rather, on closer consideration, as Andrew Bennett and Alexander L. George have rightly noted, "researchers in history and political science have more in common with one another than they do with some schools of thought within their own disciplines." 32 Consequently, especially in the fields of international studies or diplomatic history, considerable overlaps and promising starting-points for "cross-fertilization" can be detected. 33 As Stephen Pelz has noted, "[H]istorians and political scientists can learn a great deal from each other." 34 This reciprocal process of learning from each other has picked up pace considerably after the end of the Cold War, 35 with methods drawn from historical research (re-)entering into political science on a significant scale. 36 As a consequence, the notion that methods originating in historical science may be applied profitably within the social sciences is widely shared today. 37 In fact, with an eye to the intricacies of public diplomacy noted above, the (comparative) study of past practices has recently been identified as specifically auspicious in public diplomacy research. 38 One particularly promising approach in that respect-combining, in a sense, the best of both worlds-is the method of comparative-historical analysis.

The origins of comparative-historical analysis
Generally speaking, comparative-historical analyses encompass "any and all studies that juxtapose historical patterns across cases." 39 More precisely, with its combination of in-depth case studies and comparative methods, CHA "is defined by a concern with causal analysis, an emphasis on processes over time, and the use of systematic and contextualized comparison." 40 Consequently, "it helps limit the Scylla of overly general explanations in the absence of knowledge about actual causal processes and the Charybdis of getting lost in the details of a single case and overlooking commonalities across cases." 41 Looking back on a long and illustrious tradition, 42 it has increasingly been applied within the social sciences in recent times. 43 Today, its practitioners "remain resolutely committed to methodological and theoretical eclecticism as the best way for social science to proceed toward genuinely cumulative 'substantive enlightenment.'" 44 As Theda Skocpol has noted on this account, CHA is "splendidly open to synergy and innovation." 45 After identifying its key characteristics, this very advantage will be drawn upon in order to provide a tailor-made methodological approach to the study of public diplomacy.
(1) Underlying epistemology Comparative-historical analysis starts from a fundamentally positive (or realist) epistemological stance, holding that scientific knowledge about its (social) subjects of study can in fact be gained. 48 Its proponents accordingly agree that "social scientists can gain knowledge about social relations by using social scientific methods." 49 While rather a matter of the philosophy of science, this basic outlook can be regarded as much as a prerequisite to allow for substantiated analyses of the practice of public diplomacy and its outcomes in international relations. In fact, this epistemological starting point is widely shared in PD research, which frequently starts from the premise that (1) public diplomacy, in principle, works, (2) that it might be intricate but nonetheless open for operationalization and empirical examination, (3) that the major challenge lies in the question of how PD takes effect. 50 (2) Units of analysis Comparative-historical analysis frequently focuses on what has been called "big questions" 51 or "first-order questions." 52 Consequently, those engaging in comparative-historical research tend to focus on "aggregate cases," including nation states, social movements, empires, et cetera. 53 CHA regularly engages, in short, in "questions about large-scale outcomes that are regarded as substantively and normatively important by both specialists and nonspecialists." 54 Again, this orientation renders CHA eminently suited for PD research, frequently dealing with complex social relationships and intricate international networks involving a variety of different actors. While more "traditional" studies in PD may focus on select nation states and their respective programs, other (potential) analyses include non-state actors, international (non-governmental) organizations, sub-national actors or select components of a given actor's PD practices. CHA, in this regard, is exceedingly open to such trends and permits flexible adaptations depending on respective research objectives. For example, while by tendency still focusing on "big questions," it nonetheless allows researchers to " [zoom] in to inspect specific crucial episodes or patterns at closer range." 55 In sum, for PD research, CHA opens up an "essentially boundless spectrum of imaginable comparative configurations." 56 (3) Comparative methods Third, and given its very name an almost trite observation, comparative-historical analysis requires the application of comparative methods in order to draw inferences across different units of comparison. In general, comparative studies allow for the identification of similarities and differences (across cases) as well as the documentation of traditions and changes (over time). In fact, just as studies increasingly tend to "zoom in" to the macro-level as well, "[c]omparative-historical studies have also long since outgrown the phase of static comparative frameworks. The point is no longer to search only for commonalities and differences within a chronologically 'frozen' configuration, but rather to track changes and their causes over longer periods." 57 Consequently, comparative-historical studies allow for synchronic (i.e., comparisons across distinct units at a given time) as well as diachronic (i.e., comparisons of a given unit across distinct time sequences) comparisons. 58 The decision between the two ultimately rests with the researcher and their respective research interests. 59 For PD research, both paths provide viable alternatives which shall be picked up and elaborated upon below.
In particular, the importance of context is widely agreed upon in comparative research, as is the role of the researcher in reflecting upon how their own epistemological, disciplinary, and cultural backgrounds influence the construction and conduct of their research. 64 The insights of cultural transfer studies and histoire croisée acknowledge such challenges in comparative-historical research, 65 and PD research should take note of them. In fact, as argued above, the "new public diplomacy" pays tribute to the receiver as much as the wielder of PD. Consequently, comparative studies in PD should take into account respective contexts as well as cultural, societal, and transnational connections and entanglements between their objects of comparison. A diachronic study of U.S. public diplomacy towards Germany over the course of the past decades, for example, would have to include other actors' efforts and their respective (self-)perceptions at least to some degree-including, for example, the Soviet Union's/Russia's and China's. Accordingly, not only do actors reciprocally influence their perceptions, also do third parties play an important role in the success or failure of PD.
In view of these intricacies, comparative studies, even those focusing on a limited number of cases, are in need of further concretization, sequencing, and filtering since they cannot possibly address cases in their entirety. 66 Gilboa, noting the merits of comparative case studies in PD research, in this regard argued that "[c]omparative research on public diplomacy should follow what Alexander  called 'structured focused comparison.'" 67 In view of the methodological flexibility of CHA addressed above, the integration of structured, focused comparison into CHA is highly promising, indeed. As observed by Gilboa, the approach was introduced by Alexander L. George in 1979. 68 In his later writings, George defined its eponymous components, The method is 'structured' in that the researcher writes general questions that reflect the research objective and that these questions are asked of each case under study to guide and standardize data collection, thereby making systematic comparison and cumulation of the findings on the case possible. The method is 'focused' in that it deals only with certain aspect of the historical case examined. 69 It might be added, of course, that it is comparative in nature in that it applies its structured and focused questions across (a small number of) cases. Jack Levy hence noted that it constitutes a method "in which each case is structured by a single set of questions and focused on those aspects of each case that the theory defines as relevant." 70 To be sure, all historical case studies tend to be inherently focused on some aspects of interest to the researcher: A comparativehistorical study of the Founding Fathers and their formative influence upon the American Revolution, for example, might very well be interested in the upbringing, education, or political philosophy shared among them, but readily neglect their diets, heights, or eye colors. It is in this vein that David de Vaus argued, "A case study deals with the whole case but this cannot possibly mean that the case study consists of everything about the case." 71 While hence as much as a truism in comparative case-studies, the method of structured, focused comparison nonetheless offers a powerful tool to conduct such comparisons more rigorously as well as explicitly theory-driven, both important requirements of comparative research. 72 As Alexander L. George and Andrew Bennett stipulate, "The important device of formulating a set of standardized, general questions to ask of each case will be of value only if those questions are grounded in-and adequately reflect-the theoretical perspective and research objectives of the study." 73 Consequently, with an eye to public diplomacy research, the integration of the method of structured, focused comparison into comparative-historical analysis can provide meaningful techniques of collecting, sampling, and comparing materials based on respective conceptualizations. The classification of public diplomacy by Cull along its five defining components, for example, provides a first pattern of comparison in this regard to be elaborated upon below.
(4) Within-case methods Finally, different historical within-case methods are available to comparative-historical methods that provide "techniques for gathering, analyzing, and synthesizing diverse evidence in order to gain insight into the research question." 74 By means of such within-case methods, "the investigator situates the study within the relevant contexts, takes a sophisticated approach to historiography, thinks seriously about issues of process, timing, and historical trajectories, and gains a deep understanding of the cases." 75 With these characteristics, within-case methods put the "H" into CHA, "that is, they are temporal and analyze processes over time." 76 Again, this component is particularly well-suited for PD research. In fact, research in public diplomacy has a long tradition of including insights from past practices, 77 and examples of historically informed studies are legion, paying tribute not least to the persistent practice of public diplomacy throughout history.
In CHA, different within-case methods are available which allow for such historically and contextually informed inquiries that are required in PD research. In this regard, Matthew Lange distinguishes between three varieties: pattern matching, process tracing, and causal narrative. 78 The first among these methods-pattern matching-allows for theory testing. 79 Its value for the empirical study of public diplomacy, consequently, is rather limited. 80 The second and third within-case methods, however, are more auspicious: First, process tracing encompasses "the attempt to trace empirically the temporal and possibly causal sequences of events within a case that intervene between independent variables and observed outcomes." 81 James Mahoney has noted the value of such approaches for detecting causation, especially when combined with comparative methods. 82 Sevin, in this sense, has explicitly argued with respect to public diplomacy that "[a] process-based approach makes it possible to argue for the causality between the projects and the outcomes," 83 and elsewhere advocated the method of process tracing in PD research. 84 In addition, causal narrative "describes processes and explores causal determinants. Narrative analysis usually takes the form of a detective-style analysis which seeks to highlight causal impact of particular factors within particular cases." 85 Drawing on the means of historical narrative, 86 it "explores the causes of a particular social phenomenon through a narrative analysis, that is a narrative that explores what caused something." 87 Lawrence Stone has defined such narratives as "the organization of material in a chronologically sequential order, and the focusing of the content into a single coherent story, albeit with subplots." 88 Again, these within-case methods available to CHA are highly promising for PD research. The withincase method of causal narrative in particular, allowing for the telling of historical narratives and the identification of causal connections, promises resilient results regarding the workings and outcomes of PD as it accounts for respective (temporal or cultural) contexts, distinct starting points, and actor-related peculiarities. To offer an example: One could, by means of causal narrative, "tell the story" of U.S. cultural centers (Amerika Häuser) created in West Germany in the early Cold War by means of causal narrative. Such an approach would include not only an investigation into the development, goals, and programs of the Amerika Häuser, which were to become focal points in U.S.-German cultural interaction, but also an analysis of outcomes attributable to their establishment and practices, i.e., their impact on the U.S. image in Germany as well as tangible (foreign) policy changes.
All things considered, the method of comparative-historical analysis, especially when innovatively combined with the tool of structured, focused comparison, provides an auspicious basis for the robust empirical study of public diplomacy practices and outcomes. As has been demonstrated, its key characteristics are in fact as much as cut out for PD research. Building on these insights, the final part of this paper identifies a CHA-based research agenda and for that purpose introduces a comprehensive matrix for future PD research.

Introducing a matrix for CHA-based public diplomacy research
How can the method of comparative-historical analysis be applied practically to facilitate meaningful public diplomacy research? In line with the abovementioned characteristics of CHA, two interconnected aspects (paying tribute to the "H" and the "C" in CHA, respectively) are of particular importance in this endeavor: sequencing and selecting points of comparison. 89 First, while recognized as crucially important in the social sciences in general, the issue of selecting time periods and sequences for analysis is all the more important in comparative-historical analysis. 90 In public diplomacy research, such a selection is complicated by the fact that its key components operate on vastly differing time tables, ranging, as noted above, from daily or even real-time communication to the establishment of long-standing relationships. With an eye to the five components identified by Cull, these differences become readily apparent: While listening and advocacy tend to run on a short-term schedule, international broadcasting has a medium-term time table, and cultural and especially exchange diplomacy are decidedly long-term endeavors. 91 Just as a successful public diplomacy strategy arguably encompasses all aspects to get desired outcomes, a substantiated, holistic analysis has to pay tribute to these different time frames. At the same time, these different schedules allow for the selection of a closer emphasis by focusing, for example, merely on short-term objectives in one actor's public diplomacy.
Second, and intimately connected with the issue of sequencing, cases for comparison have to be established in order to facilitate substantive CHA-based research in public diplomacy. This selection can be contrived in two directions: first with respect to the cases to be compared in general; second with respect to the concrete points of comparison within these cases, as different modes of comparison as well as the method of structured, focused comparison outlined above facilitate.
As argued, comparative case selection in public diplomacy research is still usually done along national boundaries, i.e., different public diplomacy strategies by (or towards) selected nation states at a given time are juxtaposed. One could, for example, compare the PD efforts of the United States and China towards a select Europe country, say Germany, since the turn of the twenty-first century. Today, non-state actors pursuing their own PD strategies (including international organizations, non-governmental organizations, or multinational enterprises), however, contribute to an increasingly crowded stage and further increase the number of possible cases. Besides classic-synchronic-crossactor comparisons, another-diachronic-option accounts for the selection of different stages of the public diplomacy practices by just one actor, oriented for example along the lines of changes of government or other (internal or external) political variances. Especially the change of administrations, paying tribute to the considerable significance of individuals in public diplomacy and soft power, 92 provides a meaningful starting point. For example, the Biden administration, which has already taken first steps to reengage with the world by means of soft power, is likely to dramatically change its public diplomacy outlook as compared to the previous administration. Both of these (ideal-typical) possibilities-crosscase as well as within-case comparisons-provide promising frameworks for CHA-based public diplomacy research. At the same time, they may be combined to draw upon the best of both worlds: Consequently, to return to the example just introduced, one could compare PD efforts of the United States and China towards Germany in, say, the three time periods of 1949-1990, 1990-2001, and 2001-present days. Regardless of the road taken, the selection of concrete points of comparison within these cases is equally important.
That is to say that within these larger questions of one's research design, indicators for comparison, in terms of the structured, focused comparison, have to be identified as well. Conceivable indicators to draw upon, and in a sense constituting the foundation for CHA-based public diplomacy research, include (1) the overall organizational structure in one actor's public diplomacy, (2) personnel, (3) budget, (4) particular programs and their position in the overall strategy, (5) numbers of participants/perceivers, (6) perceptions, and (7) policy changes/outcomes. 93 Depending on individual research objectives, the list may of course be amended or adapted. Like cross-case or within-case comparisons, these indicators may be combined with temporal sequencing, as both synchronic and diachronic comparisons are conceivable, according to respective research interests. Additionally, both synchronic or diachronic comparisons along the lines of the taxonomy proposed by Cull are feasible as well: Different components of the overarching public diplomacy strategy-say, international broadcasting programs-can thus be compared-again across actors or across time-with recourse to the indicators identified.
Seeking to amalgamate these reflections, and bearing in mind the methodological requirements and pitfalls of comparative-historical analysis in general and PD-related research in particular, the following matrix for CHA-based public diplomacy research can be established (Table 1). It seeks to innovatively combine different operationalizations of public diplomacy, including temporal, conceptual, or indicator-based classifications, and provide the researcher with a variety of combination possibilities. 94 From these different elements, ideal-typically discerned and juxtaposed here, the researcher may assemble their own, tailor-made research framework, fitted to respective research objectives and targeted research outputs. Of course, a variety of different combinations is possible, even advisable, to diversify, counter-check, and confirm results. The matrix, however, depicts what can be regarded the most auspicious option of combining different rationales of comparison. In this context, for example, it may not be precluded per se to conduct long-term examinations across actors (as the matrix might suggest at first glance). As a rule of thumb, however, longer periods of time under observation traditionally warrant fewer cases of comparison in order to ensure the in-depth analysis which PD research, and CHA itself, for that matter, requires. In view of the importance of context and the difficulties of attribution in extended time frames in particular, such studies would pose considerable challenges. By contrast, diachronic studies dealing with one actor and its aggregate public diplomacy strategy over a lengthy time frame, sequenced into different periods, may be the most promising approach in order to yield substantiated and holistic evidence concerning the (changing) practice, perceptions, and outcomes of one actor's public diplomacy efforts. 95 Still, the proposed matrix need not be seen as a methodological straightjacket. Rather, it provides a tool box for the researcher to draw upon according to their respective needs in CHA-based public diplomacy research.

Conclusions
With deep roots in the practice of diplomacy and statecraft, public diplomacy has become a key component in the conduct of foreign affairs in the interconnected world of the twenty-first century. Despite its increasing application and study, however, precise definitions, operationalizations, and particularly robust methodological approaches towards its empirical examination are still lacking. This holds true especially since vastly different actors engage and in fact compete in public diplomacy today. Given also the interdisciplinary and intricate nature of PD, its different-albeit traditionally long-modes of operation, its functioning in complex interdependent actor networks, and its considerable context dependence, its outcomes are notoriously hard to grasp.
Starting from these observations, the paper explored different definitions and operationalizations of public diplomacy. Concerning the former, the paper subscribed to a highly relational character of public diplomacy, prevalent in literature and practice today, especially in the wake of Jan Melissen's work on the "new public diplomacy." Concerning the latter, different attempts of operationalization, including the classification of different PD practices along temporal (e.g., Joseph S. Nye) as well as conceptual (e.g., Nicholas J. Cull) criteria, were discussed. As argued, a combination of these approaches offers the most auspicious starting points for meaningful empirical analyses. In order to facilitate such analyses and to provide resilient foundations and frameworks, the method of comparative-historical analysis was introduced and its constituent characteristics-its epistemological starting points, its potential units of analysis, its comparative methods, and its within-case methods-were explored. In view of these characteristics, and especially when combined with the method of structured, focused comparison, CHA can indeed be regarded as an eminently suited approach towards more rigorous studies of public diplomacy practices and outcomes. As has been shown, CHA is in fact as much as tailor-made for PD research and, consequently, it should be applied in empirical analyses. Combining the conceptual observations of PD and the methodological requirements of CHA, the introduced matrix for CHA-based public diplomacy research provides directions that researchers may follow in this endeavor. Not to be understood as an immutable itinerary, but rather a flexible roadmap pointing towards promising avenues for research, its resilience will have to be tested empirically in future studies. (1) Overall organizational structure, (2) Personnel, (3) Budget, (4) Particular programs and their position in the overall strategy, (5) Numbers of participants/receivers, (6) Perceptions, (7) Policy changes/outcomes