INTRODUCTION
Management and Organization Review (MOR) was created ‘specifically for authors who study employees and firms in China’ as a place where authors did ‘not have to justify a Chinese sample’.[Footnote 1] To know what is Chinese, of course, one needs to know what is not Chinese, so comparative research is inherent in the mandate, and MOR has flourished as a source of quality comparative research on China (e.g., Batjargal, Reference Batjargal2007a). To paraphrase a conclusion from DiTomaso and Bian's (Reference DiTomaso and Bian2018) comparison of Chinese and US labor markets, the two countries come from different origins, and are steeped in different rhetoric, but have evolved to a similar condition of network connections providing competitive advantage for certain people and groups to secure more attractive positions and projects (cf. Boisot & Child, Reference Boisot and Child1996; Peng, Lebedev, Vlas, Wang, & Shay, Reference Peng, Lebedev, Vlas, Wang and Shay2019 on ‘network capitalism’ in emerging markets). In this article we apply Mill's ‘method of residues’ to specific examples of comparative network analysis, but the principles generalize across research topics. The message of this article will be new to some readers, a productive reminder to most readers, and quite familiar to a few readers, but even for the last, there is value in having succinct illustration available to share with colleagues and students. The article is in three parts: We introduce the method of residues with comparative evidence on the competitive advantage enjoyed by network brokers, then move to our main point about iterative residues – using comparative evidence on the connection between network closure and trust and other examples, then close with the use of data graphs to improve yield from iterative residues.
THE METHOD OF RESIDUES
Consider a familiar bit of network theory: People with networks rich in structural holes have information advantages of breadth, timing, and arbitrage that give them an advantage in detecting and developing opportunities. This bit of theory emerged from multiple sources in the late 1970s, becoming more articulate and established through the early 2000s (review in Burt, Kilduff, & Tasseli, Reference Burt, Kilduff and Tasselli2013).
The data in Figure 1 are illustrative supporting evidence from 4,137 business leaders and illustrative application of Mill's method of residues. The relative performance of individuals varies on the vertical axis. Network closure – the opposite of structural holes – varies across the horizontal. To the left are ‘network brokers’, people whose large, open networks reach across the structural holes separating social clusters (illustrated by the sociogram of a person's network below the left side of the horizontal axis). To the right are people embedded in a closed network of interconnected colleagues (illustrated by the sociogram at the bottom right of the horizontal axis). The metric across the horizontal is network constraint, which measures the extent to which a person's social contacts are limited to one group (Burt et al., Reference Burt, Kilduff and Tasselli2013). The data plotted in Figure 1 are average values of the horizontal and vertical axes within five-point intervals on the horizontal axis within each of several study populations. The solid dots describe a thousand managers from two study populations in Asia, primarily China. The hollow squares describe a thousand managers from three study populations in Europe. The hollow circles describe two thousand managers from seven study populations in the United States. As predicted by network theory, and reported in published studies of the populations, a manager's relative performance decreases as his or her network becomes more closed.[Footnote 2]
Figure 1. Returns to brokerage illustrate method of residues
Figure 1 is an illustration of what John Stuart Mill termed the ‘method of residues’, which in contemporary language involves taking out of data what is already understood to better see what remains to explain (the source reference is section 5, chapter 8, volume 1 of Mill's influential 1846 work, A System of Logic, but the method is familiar practice in formal modeling, e.g., Coleman, Reference Coleman1964: Chap. 15).
Comparison Facilitated by Residues
The network theory illustrated in Figure 1 predicts that people with more open networks have information advantages that manifest as performance higher than peers. Examples are higher compensation than peers, more positive job evaluations than peers, faster promotions than peers, and so on. But raw performance metrics covary with factors that can obscure the performance-network association. For example, the performance data in Figure 1 include annual compensation for investment bankers and supply chain managers. We know the bankers on average earn higher compensation than the managers, but the higher banker earnings have nothing to do with the network theory of advantage; that is an industry difference – so industry and job function differences are removed from the performance data. Among the bankers, we know that partners earn higher compensation, on average, than vice presidents, which is correlated with, but distinct from, the network theory of advantage – so differences due to job rank are removed from the performance data.
Adjusting raw performance for known confounding factors defines a residual measure of relative performance that can be compared across populations. The adjustment is as follows: Within a study population, typically the senior management in an organization, a measure of performance used for evaluation within the population is regressed across individual differences uninteresting for the study at hand but known to covary with performance. The performance measure and performance correlates are often different in different study populations (see footnote 2). The resulting regression model is illustrated by the diagonal line through the hypothetical data in the small graph to the upper left in Figure 1. Raw performance on the vertical axis is predicted within a study population by a set of performance-relevant variables. Note Bob and Jim marked with squares in the small graph. Bob and Jim have similar raw performance scores. If performance were measured by annual compensation, the two squares similarly located on the vertical axis would indicate that Bob and Jim earn similar levels of compensation. But Bob holds a job that is typically not well compensated, which makes his compensation high relative to peers. Jim holds a job that is typically well compensated, which makes his compensation low relative to peers. Z-score relative performance in Figure 1 is a person's raw performance score minus the performance score expected for the person in their study population, quantity divided by the standard deviation of expected performance scores in the study population. A z-score of zero indicates a person who is performing at a level typical for them in their study population (observations right on the regression line in the small graph to the upper left in Figure 1). The person's performance could be high or low on an absolute scale, but it is typical among the person's peers in the study population. Positive numbers indicate performance standard deviations ahead of peers. Negative numbers indicate performance standard deviations below peers. Performance variation between study populations is removed, and explicit controls for job rank, function, and other individual differences further clarifies how well an individual is performing relative to peers.
The definition of residual performance privileges the control variables over a network predictor since performance variation associated with the controls is removed before networks are allowed to predict performance. Since networks are associated with many of the controls (e.g., managers with large open networks tend to be promoted sooner to senior job rank), statistical tests of the network predictor are better conducted within a study population. What the residual measure of relative performance in Figure 1 does is display a strikingly consistent network association with performance in Asia (r = −0.79), Europe (r = −0.73), and the US (r = −0.75).
Comparison across three continents is explicit in Figure 1, but there are a great many other comparisons also in the evidence. Investment bankers from two continents are compared to engineering managers from the three continents – along with managers from a variety of other functions: HR, finance, human resources, operations, research, sales, and so on. More, the Asia data in Figure 1 include 258 managers in a large Asia-Pacific organization mixed with data from an area probability survey of 700 Chinese entrepreneurs (footnote 2). Thoughtful readers might be troubled by comparisons between entrepreneurs and managers.
Concern about the similarity of compared groups is valid, but not as severe an issue as it might seem. Ideally, one wants to draw comparison inferences from similar data on the populations being compared. An area probability sample of Chinese entrepreneurs should be compared to a similarly broad area probability sample of Western entrepreneurs, using the same kind of network data, with respect to the same measures of performance. The point holds as well for comparing two groups within the same society. For example, Holm, Opper, and Nee (Reference Holm, Opper and Nee2013) do a comparative analysis of trust behavior by a stratified random sample of Chinese entrepreneurs versus a matched random sample of Chinese household respondents to show that the entrepreneurs are more willing to trust within a competitive social situation (extended to guanxi in Opper, Nee, & Holm, Reference Opper, Nee and Holm2017). However, the comparisons in Figure 1 are not absent theory. They rest on a well-supported network theory of advantage. The theory predicts that complex projects are more successful when led by a person in a network rich in brokerage opportunities across structural holes. The theory is agnostic on the substance of the project, be it the arts, government, war, science, or business. The key to comparing different populations with respect to such a general theory is to have performance and network data appropriate to each population in order to compare how the theory works in connecting performance and network within each population. The managers in Figure 1 are measured for their work discussion networks and their relative pay, evaluation, or promotion. Those metrics are appropriate for managers. The entrepreneurs in Figure 1 are measured for their supportive contact networks and their relative success in growing their business. Adjusting performance for manager and entrepreneur differences reveals a consistent performance-network association across the diverse business activities in which the 4,137 people in Figure 1 are involved.
ITERATIVE METHOD OF RESIDUES
Figure 1 illustrates the method of residues used to show consistency across elements being compared, which can be useful in establishing the generality of a theoretical prediction. If we were to stop here, we would be supporting what Przeworski and Teune (Reference Przeworski and Teune1970: 25) famously termed the ‘postulate of substitutability’: ‘The bridge between historical observations and general theory is the substitution of variables for proper names of social systems in the course of comparative research’. For example, one can account for heart attacks being more likely in the US than Japan with a cultural story about social support mechanisms in Japan (Matsumoto, Reference Matsumoto1970). Or, one can replace the culture-laden proper names, Japan and US, with outcome-relevant variables: Relative to the Japanese, Americans eat a diet of sugar and certain fats that increases the risk of heart attack, so it follows that Americans are more likely victims of heart attack, and Japanese who eat an American diet should be at higher risk of heart attack than other Japanese (Keys, Reference Keys1957; Ueshima et al., Reference Ueshima, Sekikawa, Miura, Turin, Takashiam and Kita2008).[Footnote 3] In a similar vein, network closure replaces country in Figure 1. All we need to know to predict a manager's relative performance is how closed the social network is around the manager. The more closed the network, the weaker the manager's relative performance, whether the manager is American, Chinese, or European (or a banker, an entrepreneur, or other kind of manager). The evidence contradicts the occasional prior arguments, for example, that Chinese culture inhibits behavior so as to eliminate the advantages productive for network brokers in the West (see Burt & Burzynska, Reference Burt and Burzynska2017: 226–228, for discussion, Batjargal, Reference Batjargal2010).[Footnote 4]
We use the phrase ‘iterative method of residues’ to refer to the method of residues employed sequentially between contexts being compared – applying what is known in one context to highlight what is different in the other context, then taking what has been learned in the second context back to better understand the first, highlighting new details to be explained; and repeating the process back and forth as often as is productive in strengthening the power of general theory that cuts across both contexts.
Using the iterative back and forth between contexts, we steer a course through the research strategy gap Goldthorpe (Reference Goldthorpe and Goldthrope1997) summarizes by contrasting Przeworksi and Teune's variable-oriented comparative research against traditional case-oriented comparative research in which the social system is understood as indivisible elements, each made meaningful in its connection with one or more other elements (see Ragin, Reference Ragin1987, ch. 3–4 for rich description of case-oriented versus variable-oriented research strategies). The gap is analogous to the one spanned by the extremes of a ‘theory of Chinese management’ versus a ‘Chinese theory of management’ discussed by Barney and Zhang (Reference Barney and Zhang2009). We have in mind Goldthorpe's (Reference Goldthorpe and Goldthrope1997: 42) guidance for navigating the gap he describes (and see Levi Martin, Reference Levi Martin2017: ch. 7, for practical cautions): ‘What is required is that, in the process of comparison, cases should always remain identifiable as such, rather than being decomposed into variables that are then interpreted only in the course of the simultaneous analysis of the entire sample of cases under investigation’. We see our course as an operationalization of the combined emic-etic approach discussed by Leung (Reference Leung2009), as well as in the spirit of Whetten's (Reference Whetten2009: 49) efforts to make ‘theory borrowing more context sensitive’.[Footnote 5]
Network Closure and Trust
Consider a bit of network theory that has benefitted in the last few years from the proposed strategy: network closure's association with trust and reputation, which traces back to the golden age of social psychology (Festinger, Schachter, & Back, Reference Festinger, Schachter and Back1950). The closure-trust association was revitalized with the popularity of network metaphors (Coleman, Reference Coleman1988; Granovetter, Reference Granovetter1985), and enriched with research applications to organizations and markets (Acheson, Reference Acheson1988; Barker, Reference Barker1993; Bernstein, Reference Bernstein1992; Burt, Reference Burt2005: ch. 3–4; Ellickson, Reference Ellickson1991; Greif, Reference Greif1989; Uzzi, Reference Uzzi1997). The gist of the story is as follows: the more connected the people in a network, the higher the reputation cost for bad behavior, the more likely bad behavior will be detected and sanctioned, so the less likely bad behavior will occur, which lowers the risk of trust within the network, which thereby increases the probability of trust within the network. The closure-trust association is a central metaphor in Nee and Opper's (Reference Nee and Opper2012) story about the rise of entrepreneurial business in China. One of their survey respondents is quoted (Nee & Opper, Reference Nee and Opper2012: 105): ‘In my industry, there are fewer than 100 players. … We get together now and then at business meetings. … We all know each other. And hear about the other entrepreneurs at these meetings’. As if to continue the thought, another respondent is quoted on the next page: ‘Whoever dares to do something bad, everyone will know about it. Everyone will stop giving credit, and there will be no hope of making it in this business’. And another respondent chimes in on the same page with the opinion: ‘this is why people repay their loans. … To keep their reputation. We actually never had any default’. Given two people, ego and alter, the network prediction is that ego's trust in alter is higher as the network around ego and alter is closed by strong indirect connection between ego and alter through mutual colleagues as third parties to the ego-alter relationship.
The regression line marked A to the left in Figure 2 is illustrative evidence of the closure-trust association established in the West. The network data are from American and European investment bankers and analysts making annual evaluations of the colleagues with whom they worked this year. The horizontal axis varies from left to right with increasing closure around evaluator and colleague. To the left, the sociogram beneath the axis shows evaluator and colleague with no mutual colleagues this year (low closure). To the right, evaluator and colleague have many mutual colleagues (high closure). The vertical axis indicates the probability that the evaluator chooses to work with a colleague again next year and gives the colleague a top evaluation. Across 46,231 relationships, the dashed regression line marked A to the left in Figure 2 shows a strong tendency for the most positive colleague evaluations to occur next year within networks closed this year.
Figure 2. Network closure and trust
Burt and Burzynska (Reference Burt and Burzynska2017) use the network-trust association established in the West as a baseline for analyzing the trust Chinese entrepreneurs have in business contacts. The initial result is the dashed regression line marked B to the right in Figure 2. Trust from a Chinese entrepreneur increases with network closure in a nonlinear, upward sloping association similar to the association observed in the West. Like Figure 1, the associations in Figure 2 marked ‘A’ and ‘B’ are evidence of the same network mechanism operating in China and the West.
However, Burt and Burzynska also found outlier Chinese relations that did not fit the closure-trust model established in the West. Illustrated by the solid lines marked C to the right in Figure 2, the outlier relations involve a high level of trust with or without the reputational support of a closed network around the relations. These relations tend to be with contacts known for many years, sometimes family, but more often with people outside the family (Burt, Bian, & Opper, Reference Burt, Bian and Opper2018: 17; Burt & Burzynska, Reference Burt and Burzynska2017: 235). The characteristic that the outlier relations have in common is a contact cited as ‘most valued’ during a significant event in the history of the entrepreneur's business. Particularly deviant from the closure-trust model are the people cited as most valued in helping the entrepreneur to found the business. Test statistics in Figure 2 measure trust's dependence on network closure. The dependence is strongest for nonevent current contacts (25.79 t-test) and weakest for contacts most valued in founding the business (3.01 t-test) – the relationship between entrepreneur and the person who helped to found the business is sufficiently strong that trust is there least dependent on the safety of a closed network.
Burt and Burzynska (Reference Burt and Burzynska2017) note an analogy between the outlier relations and the Chinese image of guanxi. Guanxi ties are a subset of relationships in which a person feels toward another (1) familiarity, (2) trust, and (3) mutual obligation (Bian, Reference Bian1997, Reference Bian2018, Reference Bian2019; Chen, Chen, & Huang, Reference Chen, Chen and Huang2013; Farh, Tsui, Xin, & Cheng, Reference Farh, Tsui, Xin and Cheng1998). Burt and Burzynska (Reference Burt and Burzynska2017: 239–241) propose with the outlier relations in Figure 2 a network definition of guanxi: Guanxi are relations involving high trust relatively independent of network closure (typically built over time through acts of personal support).[Footnote 6] An example of guanxi is illustrated in the following interview quote with a Chinese venture capitalist: ‘Liu was my dorm-mate at Nankai University about 20 years ago. But we did not keep in touch for some reasons. Then, we met 2 years ago again at a conference on leveraged buy-out. Although my firm does not invest in new and small firms such as his, we started to talk about possible business opportunities. My partners and I have got to know well of what these guys are up to. Although we were not sure of their business model, we liked their product: a special device that serve as router between mobile and non-mobile communications equipment. Eventually, I linked this team to a university-funded venture capital firm that focuses on telecom and IT ventures’ (Batjargal, Reference Batjargal2007b: 1001).
Lin (Reference Lin, So, Lin and Poston2001) long ago suggested that that guanxi should be considered a subset of all relationships. Armed with high-quality data, Burt and Burzynska provide a concrete distinction between guanxi and not-guanxi relations analogous to Granovetter's (Reference Granovetter, Nohria and Eccles1992) conceptual distinction between relational and structural embedding. Not-guanxi relations are the usual business relations in which trust increases with network closure (structural embedding and the usual explanation of trust ensured by reputation cost for bad behavior). Guanxi relations are business relations in which trust is high and relatively independent of network closure (relational embedding). Guanxi relations by this network definition can occur in closed networks (e.g., within a family), but trust does not depend on closure. Once you know someone really well, you do not require the pressure of social opinion to ensure their good behavior; you know from experience that they will behave well, toward you at least. Independence from closure distinguishes guanxi relations from relations in a proverbial ‘old boys network’, wherein connected peers enforce reputation cost for bad behavior.
The contrast between guanxi and not-guanxi relationships holds up under closer scrutiny (Bian, Reference Bian2017; Burt et al., Reference Burt, Bian and Opper2018; Burt & Opper, Reference Burt and Opper2017), but our interest in this article is the next step. Given the network definition of ‘guanxi’ relations in China, why wouldn't a similar kind of strong connection exist in the West? Lin (Reference Lin, So, Lin and Poston2001) suggests that guanxi is a global phenomenon existing well beyond China. Shouldn't there be guanxi-like relations, for example, among the investment bankers and analysts in Figure 2?
There are. The regression line marked D to the left in Figure 2 goes through data that Burt and Burzynska (Reference Burt and Burzynska2017) took from an earlier unpublished analysis of decay in the investment banker and analyst relations. For relations that survived two years, the evaluator and colleague knew one another well enough such that trust no longer depended on mutual contacts. The flat regression line marked ‘D’ shows a high level of positive evaluation that is independent of network closure (0.81 negligible z-score logit test statistic). Thus, there are American guanxi that correspond by network definition to Chinese guanxi (though general American language doesn't have a word for them, perhaps because of their infrequency), so the theoretical association between trust and network closure has two tracks, the usual nonlinear positive trust association with closure among current contacts (lines A and B in Figure 2), and at a high level of trust, relatively independent of closure, around long-standing relations that have evolved into guanxi ties (lines C and D in Figure 2). At the same time that guanxi relations are defined by the upper lines D and C in Figure 2, not-guanxi relations are distinguished by the lower lines A and B: Not-guanxi is a relationship within which trust depends on an audience of observing third parties – which is the positive nonlinear trust association with closure so often observed in business relationships.
The iterative process giving rise to the new understanding is illustrated in Figure 3: (1) Social capital research in the US establishes a positive association between trust and network closure, which (2) is replicated in China, but (3) reveals outlier relations analogous to the Chinese image of guanxi ties, which (4) turn out to be similarly existent in the West. As displayed in Figure 3, the iterative method of residues involves determining what is similar in compared contexts, to highlight what is unique, to then discover the similar underlying the unique.
Figure 3. Illustrative comparative network analysis
To say with Figure 3 that the network association with trust is the same in China and the West does not mean that the business environments are identical. As illustrated in Figure 4, the number of relations that qualify to be guanxi ties is much lower among Western bankers and analysts. About one in ten cited colleague relations in the West are guanxi (9%), of which about half are current contacts (54%). In contrast, two thirds of business relations cited by the Chinese entrepreneurs are guanxi ties (65%), of which three fourths are current contacts (74%). In a phrase, there is more history in the networks around the Chinese entrepreneurs.
Figure 4. Same network mechanism, with different mixtures, can define different business environments
Now come the new research questions: Is the China difference a substantive difference between Chinese and Western culture, a substantive difference between the personal network around an entrepreneur versus the ‘what have you done for me lately’ network around an investment banker, or perhaps a methodological artifact of explicitly asking the Chinese entrepreneurs for contacts valued during the history of the business? How prevalent are guanxi ties in the West (now that we know what to look for), how often are they active as current contacts, and to what extent does success in the West depend on them as it does in China?
Other Examples
We use the Figure 2 illustration because it has developed largely in the pages of MOR. We discuss a selection of related examples here in four categories.[Footnote 7] The four categories refer to kinds of work, distinguished here to further clarify what we mean by iterative residues in comparative research.
Category 1: Non-comparative studies
The baseline category is research that describes social networks and correlates in a single context. Often-cited examples are Granovetter's (Reference Granovetter1973) ‘weak tie’ study of networks used in job searches by white-collar workers in Newton, MA, or Burt's (Reference Burt1992) ‘structural hole’ study of the networks associated with early manager promotion in a New England computer company. Chinese research in this category is often more comparative than corresponding research in the West, because the Chinese work so often uses work in the West as a foil to argue that China is different. For example, Bian (Reference Bian1997) uses Granovetter's study as a foil for his argument that ‘strong ties’ rather than weak ties are used in job search in China, and Xiao and Tsui (Reference Xiao and Tsui2007) use Burt's study as a foil for their argument that the structural holes valuable in the West deviate from the norm in China.
Category 2: Different networks
A next category of work involves comparing networks. Networks in two or more contexts can be different in size, density, composition, use, or anything else. For example, Bian and Ang (Reference Bian and Ang1997) compare Tianjin and Singapore for kinds of contacts used to find a new job. Job markets in Singapore were more developed than in Tianjin. Nevertheless, people job searching in both cities turn to strong ties significantly more often than weak ties, which Bian and Ang interpret in terms of both cities being densely Chinese Han, for whom guanxi ties are where one goes for help (cf., Lee, Ruan, & Lai, Reference Lee, Ruan and Lai2005). An exemplary piece of work in this category is Ruan's (Reference Ruan1998) comparison of the networks generated by Chinese versus Americans in response to the name generator used in the General Social Survey. Ruan (Reference Ruan1998: 261) concludes that the ‘GSS discussion question generated a range of social ties, which accounts, to a great extent, for an important part of the social world of a Chinese individual. … Thus, the current study has provided supporting evidence for the comparability of the discussion networks in urban China and America. That is, they are both “core discussion networks”’. The primary difference is that the Chinese networks are more anchored on co-workers than are the American networks (co-workers are 44% of the Chinese networks on average, versus 18% of the American networks; see Ruan, Zhou, Blau, & Walder, Reference Ruan, Zhou, Blau and Walder1990, for initial publication and explanation of the results; Chen, Reference Chen, Lin, Fu and Chen2014: 185, for similar results with national sample data on job-search networks: 50% co-workers in China, 40% in Taiwan, and 20% in the US). Throughout her analysis, Ruan is careful about methodological differences since network characteristics can be so greatly affected by how network data are gathered (e.g., a single name generator can be expected to generate smaller networks than multiple generators, and archival data such as email or peer evaluations can be expected to generate larger, less dense, networks than networks generated by survey interviews).
Comparing networks using the method of residues is most common in the form of network metrics that measure observed population network structure as a deviation from a baseline random structure. Substantively diverse populations can be compared for the extent to which observed structure contains some theoretically meaningful network characteristic more that would be expected by random chance. This is the early strategy that Holland and Leinhardt (Reference Holland and Leinhardt1970) used to measure the extent to which networks in a population contain more transitive triads that would be expected by random chance (beginning an evolution to contemporary p* and exponential random graph models, Robins et al., Reference Robins, Pattison, Kalish and Lusher2007; cf., Faust & Skvoretz, Reference Faust and Skvoretz2002, for p* comparisons across animal and human networks).
Freeman and Ruan (Reference Freeman and Ruan1997) compare networks in nine countries (Australia, China, the US, and six countries in Europe) for their pattern of associations between six kinds of exchanges (household help, borrowing money, personal advice, etc.) and nine kinds of roles (spouse, friend, co-worker, etc.). Do people in the different countries do the same kinds of exchanges with the same kinds of people? Freeman and Ruan define a baseline of associations between the kinds of exchanges and roles independent of differences in naming contacts for specific kinds of exchanges and roles (iterative proportional fitting), and report similar patterns in all of the countries except China. In China, friend, neighbor, and co-worker roles are clustered together as alternative partners for the same kinds of exchanges, and family roles are spread apart for specific kinds of exchanges with certain kinds of family roles. Freeman and Ruan (Reference Freeman and Ruan1997: 111) conclude: ‘The principal difference between the Chinese pattern and that of the other eight countries is that the Chinese make their primary distinction, not between financial matters and all others, but rather between family matters and all others’. (See Batjargal et al., Reference Batjargal, Hitt, Tsui, Arregle, Webb and Miller2013, for similar results on France and Russia.)
More relevant to the brokerage and closure predictions illustrated in Figures 1 and 2, and so often discussed with respect to business networks, residue from a random baseline is foundation for measuring the extent to which a population constitutes a ‘small world’. A population is a small world if it contains sparsely interconnected dense clusters (i.e., social clusters of closed networks occasionally connected across clusters by network brokers). Watts and Strogatz's (Reference Watts and Strogatz1998) widely-adopted metrics measure the extent to which (a) clustering in a population network is higher, and (b) indirect connections in the population network are shorter – than would be expected in a random network of the same size and density. The Watts and Strogatz metrics have been used to show the diversity of populations with a small world structure (e.g., film actor network, power grid network, a worm network in Watts & Strogatz, Reference Watts and Strogatz1998; and the comparative studies assembled in Kogut, Reference Kogut2012, in which countries are compared for the extent to which governance of their leading public corporations is structured as a small world, noting for MOR readers that China is among the countries showing low evidence of small world structure in the 1990s, Guthrie et al., Reference Guthrie, Okhmatovskiy, Schoenman, Xiao and Kogut2012: 125; the multiple-country network data are available for analysis).[Footnote 8]
Category 3: Different network correlates
A third category of work involves comparing network correlates. For example, Figure 1 generalizes earlier analyses by Burt, Hogarth, and Michaud (Reference Burt, Hogarth and Michaud2000), Merluzzi (Reference Merluzzi2013), and Burt and Burzynska (Reference Burt and Burzynska2017) showing similar performance returns to network brokerage in Asia, Europe, and the US. Substantive applications of the small-world metrics show the expected stability and performance correlates of clustering (e.g., Kogut & Walker, Reference Kogut and Walker2001, on corporate ownership, acquisitions, and stability in Germany), and bridges across clusters (e.g., Uzzi & Sprio, Reference Uzzi and Spiro2005, on production team networks and annual ticket sales for Broadway plays).
More often, the goal is to reject the null by showing different correlates in different contexts. For example, Bian, Hao, and Li (Reference Bian, Hao and Li2017) adjust responses to a ‘how happy are you’ question in national surveys in Australia, Britain, and China (so responses are comparable across the contexts) to reveal culture interacting with local networks: Expressions of well-being are higher in Britain and Australia than in China, especially among the rural Chinese, but contact with friends and family has significantly less positive effect in Britain and Australia, especially in Britain.
The most ambitious comparative network analysis to date was led by Nan Lin coordinating research efforts in China, Taiwan, and the US. Similar network data were gathered in national probability surveys in each country followed by a second wave of surveys two years later (rural areas excluded in China). The work was informed by separate analyses within more than the three study countries (Lin & Erickson, Reference Lin and Erikson2008; cf. David & Westerhuis, Reference David and Westerhuis2014, for a similar research strategy of juxtapositioning country-specific analyses). Reporting on the coordinated surveys, most chapters in Lin, Fu, and Chen (Reference Lin, Fu and Chen2014) are comparative analyses of the data from two or all three of the study countries (see Son, Reference Son2013, for a book-length comparative analysis of the first wave data, and Kogut, Reference Kogut2012, for a similar corporate-network research strategy in which most chapters are comparative analyses across countries).
For example, one of the chapters (Chen, Reference Chen, Lin, Fu and Chen2014) digs into a core proposition for the kind of network analysis used in the book: Job seekers find higher status jobs when they go through bridge relations to high-status contacts in other groups, and those bridge relations tend to be historical rather than current, making them ‘weak ties’ in a person's current network (Granovetter, Reference Granovetter1973; Lin, Ensel, & Vaughn, Reference Lin, Ensel and Vaughn1981). Using network data on the chain of contacts through whom respondents found their current job, Chen reports that the weak-tie proposition holds in China, Taiwan, and the US, but the proposition holds differently in the three societies. Americans are most likely to have found their job through personal contacts (180: 34% in China, 44% in Taiwan, 54% in the US), and they require the shortest chains of intermediaries to reach the final weak-tie contact in their search (180: 38% of Chinese had job-search chains of more than one person, versus 22% of the Taiwanese, and 20% of the Americans), largely because the Asians are more likely to begin with friends and family close to the searcher, who know little more than the searcher, before their search breaks out of their own group to reach the final weak-tie contact in another group (182–184: 11% of Chinese begin their search with someone less than close, as do 21% of Taiwanese, versus 38% of Americans).
Category 3 research requires more caution than the lower two categories because residues in category 3 can require level and slope adjustments to make the residues comparable. The Xiao and Tsui (Reference Xiao and Tsui2007) study cited above – an early comparative analysis of performance returns to network brokerage in China – illustrates the point. In contrast to Figure 1 showing lower performance from managers in more closed networks, Xiao and Tsui (Reference Xiao and Tsui2007) report negligible or opposite association in four Chinese organizations, and conclude their comparative network analysis on page 23: ‘Although structural holes may bring positive returns to individual actors in a market-like, low-commitment organizational culture, it is network closure that will bring advantages to the actors, by facilitating trust, reciprocity, and reputation, in a clan-like, high-commitment organization with a strong cohesive culture’. The conclusion is attractive for its fit to popular images of Chinese culture but seems unlikely given the clear association in Figure 1 showing Chinese managers in many organizations disadvantaged in proportion to network closure (the supportive evidence on Chinese entrepreneurs in Batjargal et al., Reference Batjargal, Hitt, Tsui, Arregle, Webb and Miller2013; Batjargal, Reference Batjargal2007c, is noteworthy here). If not Chinese culture, then what? One possibility is that Xiao and Tsui's organizations gave managers little discretion in their jobs, which would erode the advantages of network brokers, but job rank seems a likely explanation. The magnitude of the performance-network association in Figure 1 covaries with job rank. The more senior the job rank, the more a manager is the author of his or her job, obliged to figure out what to do, and from whom support is needed, which means network brokers are advantaged. The 4,137 managers in Figure 1 primarily hold middle and senior job ranks. At low levels of management in the West, there is often no performance association with open networks (Burt, Reference Burt1992: 133, 138; Reference Burt2005: 156–162). It is not surprising, therefore, to see the lack of a performance-brokerage association, or even a reversed association depending on what controls are in the prediction, in Xiao and Tsui's analysis because the study managers are young and disproportionately in low job ranks (see Burt, Reference Burt2010: 61n, for explicit comparison with another Asian technology organization). Among such managers, one would not expect in the West to see the usual brokerage association with performance. Still, the Xiao and Tsui article warrants serious attention because it shows that quality data are not enough. Their data are of exceptional quality, especially for such an early comparative study – full networks are measured around each study manager in four different organizations. The problem is that the quality data describe people doing jobs unlikely to show the performance benefits of an open network.[Footnote 9]
Category 4: Iterative exploration of different network correlates
The next level up is to expand network theory by digging into systematic deviations from baseline network correlates. This is the work we illustrate using the trust association with network closure in Figures 2, 3, and 4. This is the work for which we had difficulty finding examples, and expert opinion agreed is largely absent in comparative network research on China (footnote 9).
Here are a few illustrative bits of work: The network-broker solution to segregation in management populations was discovered by studying the networks around female managers in an organization in which women were outliers from the brokerage-performance association illustrated in Figure 1 (Burt, Reference Burt1992: ch. 4, Reference Burt1998). Kogut and Walker (Reference Kogut and Walker2001) move their small-world analysis to a next iteration when they subject the German social structure to variably severe exogenous shock to explore the stability implications of their initial analysis. The advantage in China of a ‘cocoon’ network around the launch of an entrepreneurial venture was discovered in residuals from the brokerage-performance association (Burt & Opper, Reference Burt and Opper2017), then re-affirmed upon returning to the West to find corresponding results in multiple unpublished research projects (Zhao & Burt, Reference Zhao and Burt2018).
DATA GRAPHS ENHANCE THE METHOD OF RESIDUES
Greve (Reference Greve2018) and Levine (Reference Levine2018) argue in MOR for authors to make more use of data graphs to improve the accuracy, reliability, and fecundity of empirical research (see Schwab, Reference Schwab2018 for related discussion, and Healy & Moody, 2014, for a lively, succinct, broad introduction to data visualization). In closing, we add to their good counsel that data graphs facilitate and enhance use of the method of residues.
Figure 5 is one of many possible examples. Graphs A and B correspond to the graphs that Burt and Burzynska (Reference Burt and Burzynska2017: 226) use to support their argument that closed networks are a disadvantage for Chinese entrepreneurs just as they are known to be a disadvantage for business leaders in the West. Graphs A and B show strong negative associations between network constraint and relative performance.
Figure 5. Performance returns to network Brokerage
Olav Sorenson, who generously agreed with MOR's editor to comment on Burt and Burzynska (Reference Burt and Burzynska2017), looked at the graphs A and B in Figure 5 and commented (Sorenson, Reference Sorenson2017: 275): ‘Although the relationships between success and structural holes appear similar, note that the two panels differ in the ranges of their horizontal axes. Managers in China appear far more constrained on average than their Western counterparts (i.e., they have fewer brokering relationships). Within the overlapping range of the data, moreover, the relationship between success and structural holes appears much steeper in China. Social capital, in the form of brokerage, therefore, appears both less common and far more valuable in the East’. He is quite correct in his reading of the graphs – and note that such inspection is made possible and facilitated when data graphs are presented rather than just presenting correlation/regression coefficients. Burt and Burzynska wanted to highlight the smooth clustering of the Chinese data along a negative performance association with network closure – clearly rejecting prior arguments that network brokerage offers no advantage in China – so they scaled the axes of graph B to the minimum and maximum of the Chinese data. In scaling the axes the way they did, however, Burt and Burzynska obscured the relative slope of association in the two graphs.
It is easier to visually compare the slope of association across the Chinese to the slope of association across the Americans and Europeans if the axes of graphs A and B are the same scale. Graph C in Figure 5 presents the data plotted in graph B, now plotted on the graph A axes.
Two points are made more obvious. First, the slope of association between success and network constraint in graph C is similar to the relatively flat slope at high levels of constraint on the American and European managers in graph A. The similarly flat slopes show there is no evidence of social capital, in the form of brokerage, being more valuable in China. Second, it is certainly true that networks around the Chinese entrepreneurs are more closed than the networks around the Western managers. The data distribution in graph C varies across the right half of the horizontal axis. There are no observations to the extreme left, where the largest networks, richest in structural holes, are found. However, we suspect the more closed networks around the Chinese entrepreneurs is not a characteristic of Chinese culture so much as a reflection of organization size. The observed Americans and Europeans work in organizations that number tens of thousands of employees. On average, the Chinese entrepreneurs work in much smaller organizations. The median number of employees is 67. More, Asian managers drawn from large organizations have the large, open networks to the extreme left on the horizontal axis (in Figure 1, there are solid dots to the left on the horizontal axis, and from the lack of data to the left in Figure 5C, none of the solid dots to the extreme left in Figure 1 are Chinese entrepreneurs).
We find the above a productive comparative discussion made possible by data graphs. Of course, the graphs are not statistical evidence. Statistical evidence is presented in the source articles in a table of regression results. The purpose of the graph is to provide an easily digested visual image of the data around the proposed association, while providing sufficient detail to reveal nonlinearities, outliers, or distinct clusters of observations (see Healy & Moody, 2014: 107; Levine, Reference Levine2018: 434). The purpose does not require sophisticated display; a simple two-dimensional graph will do. In our experience, the purpose is served by aggregating data up to a handful to a couple dozen average observations. Aggregation for Figure 2 is obvious since the network metric is an interval measure. Scores beyond the highest level displayed are combined because they are rare and pretty much consistent with the display. To create Figure 1, on the other hand, the continuous network index on the horizontal axis was divided into five-point intervals, and values of scores on the horizontal and vertical axis were averaged within each interval for each study population. The resulting 140 data points, summarizing 4,137 observations, is sufficiently detailed to lower the odds of data abnormalities, while communicating a smooth nonlinear association between performance and network closure consistent across the three continents. Similar graphs have been used to show the performance-network association increasing with job rank as the success of people in more senior ranks became more contingent on their social network (Burt, Reference Burt1992: 138), contradictory network associations with performance for men and women in sexist organizations (Burt, Reference Burt1998, Reference Burt2010: 196), good ideas less likely to come from people in closed networks (Burt, Reference Burt2004, Reference Burt2005: 92), and network closure in China more hierarchical than in the West (Burt, Reference Burt2019a).
CONCLUSION
We have argued for, and illustrated, the method of residues applied to comparative network research in the context of China. We introduced the method of residues with comparative evidence on the competitive advantage enjoyed by network brokers, then moved to our main point about iterative residues – using comparative evidence on the connection between network closure and trust and other examples, then closed with the use of data graphs to improve yield from iterative residues. We see our course as one operationalization of the combined emic-etic approach discussed by Leung (Reference Leung2009), and in the spirit of Whetten's (Reference Whetten2009: 49) efforts to make ‘theory borrowing more context sensitive’.
We close with illustrative questions for future research. Figures 1 and 5 display striking consistency for the performance association with network brokerage (−0.79 correlation in Asia, −0.73 correlation in Europe, -0.75 correlation in the US). To what extent are known exceptions also similar between East and West? We know that the performance association with network brokerage disappears for Western managers in low job ranks (Burt, Reference Burt1997, Reference Burt2004, Reference Burt2005: 159–162), and the same seems to be true for managers in China (Xiao & Tsui, Reference Xiao and Tsui2007). How widespread is the similarity?
Further, we know that the performance association with network brokerage disappears, and can even reverse, for Western managers who do not have the social standing to be accepted as brokers (Burt, Reference Burt1998; Burt & Merluzzi, Reference Burt, Merluzzi, Borgatti, Brass, Halgin, Labianca and Mehra2014; Rider, Reference Rider2009), and it has certainly been argued that reputation matters in Chinese business. Nee and Opper (Reference Nee and Opper2012: 211) describe Chinese entrepreneurs building reputation in the course of brokering connections: ‘Through personal introductions and fine-grained information passed through social networks, the “broker” typically signals trustworthiness and reputation of the prospective business partners. Moreover, it is in the broker's interest to make good recommendations, as most business partners will tend to reward their networking contacts in one way or another. Such introductions can span the social gaps, or “structural holes” between groups’. How widespread is the East-West similarity in the requirement for broker social standing, and is the cure in the West of being sponsored by a network broker (Burt, Reference Burt1998) similarly the cure in the East? In other words, does the performance of a women in a firm that typically focuses on men for senior leadership require the sponsorship of a well-connected man? Do would-be entrepreneurs from outside the city require the sponsorship of a well-connected insider? There are anecdotes and suspicions to answer ‘yes’ to these questions, but we await empirical comparative evidence.
And how precise can we, or should we, make the comparison of East and West? In our opening pages, we highlighted the legitimacy for the purposes here of comparing network results on Chinese entrepreneurs with network results on diverse kinds of managers in the West. East and West, entrepreneurs are different in many ways from managers, and investment banking managers are different in many ways from HR officers and engineers – but the network theory used here makes similar predictions for all, which is one of the theory's attractive features. At the same time, comparison could be more precise if comparison was between people in more similar kinds of work.
Given the strong accumulation of evidence on Western managers, a few strategic studies of senior Chinese management networks would have inferential power disproportionate to their numbers. Xiao and Tsui (Reference Xiao and Tsui2007) set the stage for such work, we just need to shift the research to more senior management. There is a long tradition of such work in the West, reflecting business interest in any research capability likely to help the business run more effectively or efficiently. With the rapid expansion of research-active business schools in China, we look forward to the results of similar university collaborations with large Chinese organizations.
Less network evidence has accumulated on entrepreneurs in East or West. A model is Batjargal et al.’s (Reference Batjargal, Hitt, Tsui, Arregle, Webb and Miller2013) comparative network analysis of entrepreneurs in China, France, Russia, and the United States. The data are not from area probability samples, and the network data collected are lean, but the article is exemplary for its effort to analyze comparable data across contexts. The time is ripe for a network study of American entrepreneurs using data comparable in quality to the Chinese data we had available here.
Shifting to the trust association with closure, how prevalent are guanxi ties in the West now that we know what to look for? In other words, how prevalent are ties that could be termed American and European guanxi? The Chinese have a word for guanxi ties, but the graphs in Figure 2 show that Americans have relationships that are similarly strong and independent of network structure, so how prevalent are such American and European guanxi? Is there a local rhetoric used in the West to distinguish such ties? For example, how does email language between people tied by guanxi compare with the language in not-guanxi ties – both not-guanxi ties in which trust is supported by a closed network, and not-guanxi bridge ties bereft of such support? When we observe current contacts, how often do we capture a person's guanxi ties? The Venn diagrams in Figure 4 show that guanxi ties are rare among the American analysts and bankers (9%) but about half of their guanxi ties are current (54%). Guanxi ties are more common in the networks of the Chinese entrepreneurs (65%), and three fourths of their guanxi ties are current (74%). Are these East-West differences a substantive difference between Chinese and Western culture, a substantive difference between the personal network around an entrepreneur versus the ‘what have you done for me lately’ network around an analyst or investment banker, or perhaps a methodological artifact of explicitly asking the Chinese entrepreneurs for contacts valued during the history of the business?
At the same time that the comparative analysis opens up new research questions about American and European guanxi, it opens up deeper research questions about the meaning of guanxi in the source society. The network distinction between guanxi versus not-guanxi relations provides a contrast variable with which we can dig into the meaning of guanxi (and hopefully take that back to the West at some point to better understand American and European guanxi). Why has no one asked Chinese business people to distinguish what they consider to be their guanxi relationships? There is a great deal of semantic acrobatics concerning the meaning of the word guanxi (citations deliberately not given), but no research to our knowledge in which a representative sample of business people inventory their key contacts and are asked to distinguish the subset of contacts who are guanxi: ‘Yang and Guo are guanxi, the others not so much’. This is a piece of research that cries out to be done. Armed with such data, new questions can be asked: (1) Do respondent distinctions between guanxi and not-guanxi match the network distinction in Figures 2 and 3? (2) How do individuals differ in their distinction between guanxi and not-guanxi relations? For example, are needy people more likely to interpret relations as guanxi in the hope of exploiting contact resources? Do resource-rich contacts react by avoiding such people? (3) How do guanxi relations differ in their origins from not-guanxi relations? The Chinese business people used here for illustration find some guanxi with family, but most originate outside the family (Burt et al., Reference Burt, Bian and Opper2018). (4) How do guanxi versus not-guanxi differ in the network structure around them? One could argue that guanxi relations are stable anchors for closed networks with friends of one's guanxi ties. On the other hand, not-guanxi ties might cluster into closed networks because trust in such relations is more likely within a closed network.
The above are only a few of the questions raised by comparative network research on China. We offer example questions not as specification, but merely as concrete illustration. Further, answers could come from diverse kinds of research – from archival big data on network structure and content, to survey-based network analyses, across to qualitatively rich ethnographic descriptions of context specific social ties – all of which are likely to be more productive with iterative use of Mill's method of residues to highlight promising new research results and frontiers.
