Set Theoretic Method

The field of corporate governance research has been identified as an opportunity for research using configuration analysis. For instance, Short et al. (2008) suggest that looking at the interaction of several characteristics of boards of directors simultaneously could help to solve equivocal issues such as the effect of CEO duality and independent directors on firm performance (Dalton, Daily, Ellstrand, & Johnson, 1998), which remain elusive when their effects are analyzed as competing determinants. Consequently, the set theoretic method (fsQCA) has increasingly been used in corporate governance studies as a way to empirically explore combinations of mechanisms as bundles and complementary factors rather than as isolated additive effects (Bell et al., 2013; Garcia-Castro et al., 2013; Misangyi & Acharya, 2014). It allows to study the interactions among multiple variables simultaneously, while interaction effects in statistical methods are difficult to interpret beyond three-way interactions. For these reasons, fsQCA lends itself to an analysis of the interplay between ownership structure, state/private control and commitment to best practices of corporate governance shaping the controlling shareholder’s behavior in terms of tunneling.

The appeal of set theoretic methods lies in the possibility of unraveling the complexity of causal relations. Greckhamer, Misangyi, Elms, and Lacey (2008: 697) explain that “(a) outcomes of interest rarely have any single cause, (b) causes rarely operate in isolation from each other, and (c) a specific causal attribute may have different and even opposite effects depending on context”. Of particular interest, configurational analysis allows for equifinality, causal asymmetry and the identification of core and peripheral causal conditions. Indeed, Fiss (2011: 410) summarizes the unique value of set theoretic methods, explaining that alternative statistical methods “offer only limited insight into the internal causal structure of the different types, the neutral permutations inherent to the types, and the asymmetric causal relationships present across the performance spectrum”. Firstly, equifinality involves a recognition that multiple causal paths can lead to a single outcome. Secondly, the identification of core conditions are useful to categorize different types of cases in which the causal relation to the outcome is supported by possibly interchangeable peripheral conditions (Fiss, 2011). Such second order equifinality may allow the identification of neutral permutations among peripheral conditions in a given configuration

and allow for a more subtle exploration of “intratype similarities and dissimilarities” (Fiss, 2011: 398). In other words, peripheral conditions are the factors that may vary across configurations that share the same main (core) causal factors. Thirdly, Fiss (2011) and Ragin (2008a) develop the concept of causal asymmetry, conveying that while some causal conditions can explain the presence of an outcome, their opposite might not explain the absence of the same outcome. A different set of conditions might instead be needed. For instance, Fiss (2011) finds that the causal conditions that explain high and very high firm performance are not the same as those that explain low and below average performance.

The operationalization of fsQCA rests the view that the outcome, the causal conditions and the relations between them are analyzed in terms of sets and subsets (Fiss, 2007; Greckhamer, Misangyi, & Fiss, 2013; Ragin, 2000, 2008a). A given case may have membership in more than one set, such as the set of large firms and the set of state-owned firms. The intersection of these sets, including the outcome set, provides evidence about the particular combinations of conditions that can produce the outcome. The set theoretic method allows studying causal mechanisms involving directional, one-way relations, but its value-added is where attributes and sets can be characterized by the concepts of necessity and sufficiency. An attribute is necessary if it is present in all combinations that produce the outcome. An attribute or combination of attributes is sufficient if it produces the outcome by itself. In the present chapter, the first part of the empirical study centers on the identification of configurations of attributes that are sufficient to produce the outcome of tunneling behavior. Following the insights on causal asymmetry, the second part aims to identify the configurations that are sufficient to produce the absence of tunneling.

Originally, fsQCA had been designed as a method that would allow systematic analysis of relatively small samples (N < 50). The present study is part of an emerging trend that uses the above-mentioned benefits of set theory on larger samples (Bell et al., 2013; Garcia- Castro et al., 2013; Park & El Sawy, 2013; Whittington, McKee, Goodwin, & Bell, 2013). For instance, Greckhamer et al. (2008) and Misangyi and Acharya (2014) have used QCA analysis on samples of 2841 and 1135 cases respectively. While the procedure remains largely the same as with small-N studies, some differences must be taken into account. Even

before starting the analysis, considerations must be given to the number of conditions included and to the calibration of variables into sets of causal conditions.

Firstly, especially in small N studies, the number of conditions has to be low to avoid that each case becomes its own configuration and to facilitate the search for commonalities. Limiting the number of conditions in large N studies is still important to reduce complexity and facilitate interpretation, but the volume of observations allows for greater flexibility. Generally, Ragin (2008a) suggests that interpretation beyond 8-10 conditions may become elusive. Greckhamer et al. (2013) contend that large-N QCA studies could potentially use up to 12 conditions. In a recent large-N study, Misangyi and Acharya (2014) include 10 explanatory conditions. The inclusion of 9 conditions in the present study is therefore in line with the dominant recommendations and strikes a balance between interpretability and the inclusion of the most important causal conditions identified in the literature.

Secondly, the approach to calibration with large samples might need adaptation from cannons originally designed for small samples. Calibration is the procedure by which variables are transformed into sets. In crisp sets, membership is coded as 1 while non- membership is coded as 0. Fuzzy sets allow for ordinal or interval scale variables to be calibrated along a spectrum between 0, full non-membership, and 1, full membership, where 0.5 is the cross-over point where set membership is at “maximum ambiguity” (Ragin, 2008a: 30). Because not all variance is meaningful (Crilly, 2011), the researcher is expected to use substantive knowledge during calibration to identify meaningful thresholds for full membership, full non-membership and the cross-over point (Fiss, 2011). However, Greckhamer et al. (2013) explain that in large-N studies, researchers are typically less familiar with each case. Using thresholds that are theory driven is preferable, but most recent studies that have used QCA on large samples used data-driven breakpoints to calibrate the variables that exhibit normal distributions. Greckhamer et al. (2008) centered most crossover points at the median. Fiss (2011) and Whittington et al. (2013) also use data driven breakpoints for all the conditions that were not based on Likert scales. This study uses a mix of theory-driven and data-driven calibration procedures depending on the nature of each condition. Five out of nine causal conditions were calibrated according to data-driven thresholds centered at the median. Yet, the fact that the breakpoints used in the data-driven

calibration rests on the distribution of the entire population of Chinese listed firms circumvents problems related to sample-specific biases.

After calibrating the sets of causal conditions and the outcome, the procedure in fsQCA involves three main steps. The first step is the construction of a truth table. The lines of the table list all the possible combinations of causal conditions. For 9 conditions, there are 92

lines for a total of 512 combinations. The columns of the table contain the causal conditions, the outcome variable, the frequency of firms that exhibit each combination and the consistency with which those firms are part of the outcome set. Roughly, the consistency represents the proportion of firms in each combination that display the outcome. Not all theoretically possible combinations are observed empirically. This phenomenon is referred to as limited diversity (Ragin, 1987, 2000).

The second step requires the researcher to reduce the table by choosing a minimum frequency level and determine a consistency cutoff. Only those combinations that display the minimum frequency are kept for the analysis. It is recommended that the frequency threshold must be set in order to include around 80% of the sample in the analysis (Greckhamer et al., 2013). In small-N studies the frequency is often set at 1, keeping all empirically observable combinations in the analysis to maximize the diversity and coverage (see for instance Meuer, 2014). In large-N studies, a common rule of thumb suggests that a minimum frequency of 3 shall preserve a reasonably large coverage while maintaining the width of the solution to a manageable level. While full coverage is often expected in small- N studies, a large coverage is desirable but not necessary in large N studies (Greckhamer et al., 2013).

In terms of consistency cutoff, while the recommendations vary from a minimum of .75 (Ragin, 2006) to .95 (Epstein, Duerr, Kenworthy, & Ragin, 2008), most studies consider .8 to be a reasonable threshold. Others suggest looking for a natural break in the data (Schneider, Schulze-Bentrop, & Paunescu, 2010). Determining the minimum frequency and the consistency cutoff has an influence on the coverage and overall consistency of the final solution. A higher frequency increases the coverage but complexifies the solution. A higher consistency cutoff reduces the coverage while increasing the overall consistency. This study uses a process of iteration to reduce the arbitrariness involved in choosing the frequency and

consistency cutoffs. Every possible combination of frequency and consistency cutoffs were tested, incrementally adding 1 unit to frequency and .01 of consistency. The resulting table displays the product of the coverage and overall consistency of each solution. Every solution with 10 or more configurations was eliminated for purposes of interpretability, as well as those displaying an overall consistency lower than .8. The cell with the highest product (overall consistency x overall coverage) set the cutoff points for the analysis.

The third step involves an algorithm that identifies the commonalities of the remaining combinations and reduces the solution into a single Boolean equation of sufficient configurations. The fsQCA software uses the truth table algorithm and produces a range of solutions (Rihoux & Ragin, 2009). The complex solution uses fewer simplifying assumptions, producing exhaustive Boolean equations that are difficult to interpret, while parsimonious solutions take into account all the possible counterfactuals based on hypothetical but empirically absent configurations. The intermediate solution, which uses existing knowledge to discern the plausible counterfactuals to be used as simplifying assumptions (Ragin, 2008a), offers a balanced output in that it provides some level of complexity by including both core and peripheral conditions but in a relatively concise equation (Fiss, 2011; Greckhamer, 2011). These easy counterfactuals “refer to situations in which a redundant causal condition is added to a set of causal conditions that by themselves already lead to the outcome in question.” (Fiss, 2011: 403)

The results are presented according to the notation suggested by Ragin and Fiss (2008). In a table, all the causal conditions are listed in the lines while the configurations appear in the columns. In each configuration, the core conditions are indicated with a big dot while peripheral conditions are indicated by a small one. Moreover, the conditions that must be present receive black dots while those that must be absent are displayed as crossed dots. (●: core present, ø: core absent, •: peripheral present, ø: peripheral absent).