The paper uses Formal Concept Analysis (FCA) to replicate the results of a study that employed fuzzy set Qualitative Comparative Analysis (fsQCA) to determine the con gurational conditions that are necessary or su cient to explain the participation of top banks in a multistakeholder agreement against money laundering. Using raw input data from a previous study, the same result regarding necessary conditions was reached using FCA, showing that FCA can be reliably used for this kind of analysis. However, di erences in scaling method resulted in the identi cation of su cient conditions that di ered from those of the original fsQCA study.
In the wake of money laundering scandals that dogged international banks at the
turn of the century, a few leading banks drew up a voluntary agreement in 1999
consisting of a number of standards aimed at preventing the use of the global
reach of the international banking system for criminal purposes. The initial
meetings took place at Ch^ateau Wolfsberg in Switzerland and accordingly the
signatories are known as the Wolfsberg Group and their agreed-upon principles as
the Wolfsberg Standards. The group, existing of 11 leading international banks,
meets quarterly to discuss issues around various nancial crimes that depend on
international banking services like money-laundering, corruption, nancing of
terrorism, and breaching internationally agreed-upon economic sanctions
Coordination is considered di cult in the context of international nance and it is therefore signi cant that more than a third of the top banks voluntarily joined this particular multi-stakeholder agreement. Bank participation is the outcome of complex causation of organizational, institutional and regulatory factors that cannot satisfactorily studied using statistical regressions, because the number of cases are too few. For this reason Maggetti (2014) brought settheoretic methods to bear on the problem of identifying the con guration of causal conditions for participation by top banks in such a multi-stakeholder agreement. He employed fuzzy set Qualitative Comparative Analysis (fsQCA) to investigate seven factors drawn from rm level, institutional context, and the regulatory framework. Each of these factors were backed up by a hypothesis derived from organizational and institutional theory.
Qualitative Comparative Analysis was speci cally developed by Ragin (2008) in the context of comparative politics and thus originally intended for comparative case studies with relatively few cases. Since Ragin developed fuzzy set QCA (fsQCA) the elds of application diversi ed. QCA and fsQCA are focused on including cases in sets of conditions and then making complex causal or descriptive inferences based on necessary and su cient conditions. It takes a causes of e ects approach that seek to explain why particular cases have certain outcomes by coming up with various con gurational recipes of causes which can be stated in a robust way and then logically minimized to parsimonious solutions. It is attractive for social scientists because it allows for complex causation and equi nality. This method is therefore well-suited to studying the organizational, macro-institutional and regulatory factors impacting on bank's participation in multi-stakeholder agreements in combination.
This paper uses Maggetti's input data to replicate his ndings, achieved with fsQCA, with a di erent method, namely Formal Concept Analysis (FCA). The two methods share set-theoretic roots, but whereas QCA was developed for speci cally for social research, FCA is a framework for data-analysis that is in principle domain-agnostic. Unlike QCA, FCA lacks an explicit focus on causality and is instead geared towards understanding the structure inherent in the data. However, by means of the notion of intent, FCA can be used to identify the necessary and su cient conditions for bank participation in the multi-stakeholder agreement.
The next sections rst describe Maggetti's dataset, explain how it was constructed in accordance with various choices regarding operationalization of the factors and scaling when coding them. Thereafter we describe the results of the fsQCA analysis and the conclusions reached. Second, the basic FCA de nitions are explained, choices about scaling of Maggetti's raw input data for FCA are described along with operations to obtain implications that support or contradict Maggetti's ndings.
Participation factors studied with fsQCA
The cases in Maggetti's dataset consist of the 26 banks that were on the list of the top 25 private banking institutions at the time.1 Ten of the 11 banks that make up the Wolfsberg Group are on this list. The eleventh bank in the Wolfsberg Group, Bank of Tokyo-Mitsubishi UFJ, was left out of on the grounds that it was not among the top 25 banks (Maggetti 2014, p.801). The rest of the cases are the further 16 banks on the top 25 list. Various causal conditions 2 that could explain participation in the Wolfsberg initiative were hypothesized and then coded for each case. The raw input data for each case and the various conditions and their relation to the output condition of participation are reproduced in Table 1. 1 Since two banks were tied, the top 25 list consists of 26 banks in total. 2 What is known as \conditions" in QCA, are known as \factors" in other methods. Case ABNAmro Barclays BNP Paribas Carnegie Citigroup Coutts & Co CS Deutsche Bank Goldman Sachs HSBC ING JPMorgan Julius Baer LCF LODH MeesPierson Merrill Lynch Morgan S Nordea Pictet & Cie RBC Rothschild Santander SG UBP UBS
NLD GBR FRA SWE USA GBR CHE GER USA GBR NLD USA CHE FRA CHE NLD USA USA SWE CHE CAN GBR ESP FRA CHE CHE
Universal Public No Commercial Public Explicit Universal Public Implicit Investment Public No Commercial Public Explicit Private Public Implicit Universal Public Explicit Universal Public Explicit Investment Public Explicit Commercial Public Implicit Universal Public Implicit Commercial Public Explicit Private Public No Private Private No Private Private No Private Public No Investment Public Implicit Investment Public Explicit Universal Public Implicit Private Private No Universal Public Explicit Investment Private No Universal Public Explicit Universal Public Explicit Private Private No Universal Public Explicit
The seven conditions that were hypothesized to in uence participation in the agreement are the type of bank, whether it is publicly owned, the existence of an internal code of conduct, the coordination of corporate relationships (an index that integrates shareholder power, dispersion of control, and size of the stock market), the extent of nancial liberalization, the stringency of regulations, and whether the target country is on an IMF blacklist. These factors were operationalized and coded by Maggetti as follows.
The type of bank (label: BankType). Maggetti hypothesized that banks focused on investment and private banking would have less incentive to join the agreement. Consequently he coded deposit or commercial banks 1 and investment and private banks 0.
Public ownership (label: Owner). Maggetti assumed that public ownership would increase the likelihood of joining the agreement and if the bank was publicly traded during the decade preceding the agreement it was coded 1 and 0 if it was not.
codes of conduct against money laundering was considered a driver for joining the agreement. Cases where the internal code of conduct explicitly mentions money laundering were assigned 1, cases where a code of conduct implies money laundering without explicitly mentioning it were assigned 0.5, and cases where such a code was absent were assigned 0.
Coordination of corporate relationships (label: CorpC). Here Maggetti
(2014) followed
relied on the average of a particular indicator regarding nancial reform for
the years 2000-2005 from database compiled by
intensity would lead to compliance with the agreements. Maggetti used a
7-point scale to capture variation on the regulatory intensity in the various
markets that the individual banks operate in. The data used to populate
this scale came from
Presence on IMF blacklist (label = BList). Maggetti used a 1999 blacklist published by the IMF of money laundering and tax haven countries. He hypothesised that presence on the blacklist exerts normative pressure on banks to participate in multistakeholder agreements and coded presence on the list as 1 and absence as 0.
Participation (label = Wolfs). The outcome condition was coded 1 when a bank participated in the Wolfsberg Initiative against money laundering and 0 if it did not. 2.3
The aim of the analysis was to discover various subset relationships where a condition (or a combination of conditions) are either a subset of the outcome set and thus can be considered su cient for an outcome, or where the outcome set is a subset of the condition set and thus can be considered necessary conditions for the outcome. This was done by Maggetti in two steps: rst, he determined the necessity by identifying all conditions with set membership scores equal or greater than the membership score of the outcome condition; second, he determined su ciency by comparing membership scores in the outcome condition with scores for all possible combinations of conditions (Maggetti 2014, p. 803). Thereafter he tested for consistency and coverage according to methods proposed by Ragin (2008, chapter 3) and derived complex, intermediate, and parsimonious solutions.
The results of the analysis were that public ownership (consistency 1.00; coverage 0.48) and the prior existence of a code of conduct (consistency 0.95; coverage 0.68) were necessary conditions for participation in the Wolfsberg Initiative (Maggetti 2014, p. 806). The results of the tests for su ciency for the complex solution (consistency 0.92; coverage 0.48) were that BankType BList
FinLib CorpC are su cient. In other words a universal, deposit, or commercial bank that were blacklisted and in a fully liberalized context in terms of nancial market and the coordination of corporate relations will de nitely participate in the Wolfsberg Initiative. The intermediate solution (consistency 0.77; coverage 0.57) holds that BankType BList FinLib are jointly su cient; in other words corporate coordination is left out. Finally, the parsimonious solution (consistency 0.75; coverage 0.60) holds that a combination of bank type and the presence on the blacklist are su cient to explain participation in the Wolfsberg Initiative (Maggetti 2014, p. 807). 3
Since the dataset used for the fsQCA is in table form, it can be structurally represented as a concept lattice and approached via FCA. Under FCA, the banks that made up the cases in the fsQCA study are properly considered to be `objects,' the factors that made up the conditions in the fsQCA study are considered to be `attributes.' Every formal concept in the lattice has `extent,' which is the corollary of set membership in fsQCA, but refers to the set of objects that falls under the formal concept, rather than the cases that belong to a particular con guration of conditions. Every formal concept also has `intent,' which is the corollary of necessary and su cient conditions in fsQCA, and refers to the set of all common attributes of objects from the extent. 3.1
Let us recall the basic de nitions of Formal Concept Analysis
A0 = fm 2 M j gIm for all g 2 Ag; B0 = fg 2 G j gIm for all m 2 Bg; we can de ne a formal concept of the context K to be a pair (A; B) satisfying A 2 G, B 2 M , A0 = B, B0 = A. A is called the extent, B is called the intent of the concept (A; B). These concepts, ordered by (A1; B1) (A2; B2) () A1 A2 form a complete lattice, called the concept lattice of K = (G; M; I). However, this paper depends more on the following de nition of (attribute) implication: For A; B M the implication A ! B holds if A0 B0, i.e., all objects having all attributes from A also have all attributes from B.
Using the de nition of implication we can model strict dependencies between the values of the target attribute, i.e., statements whether a bank has joined the agreement or not, with the values of other attributes of our dataset. 3.2
To show these dependencies in our dataset, let us rst scale the many-valued attributes of the original data, i.e., represent them as binary attributes, to produce the natural scaling in Table 2. BankType nominal universal, commercial, investment, private Owner nominal public, private Code nominal none, at least implicit, explicit CorpC ordinal 0.0, 0.14, 0.23, 0.44, 0.71, 0.74, 0.77, 0.82, 0.95 RegInt ordinal 45, 53, 75, 83, 144, 149, 277, 426 FinLib ordinal 0.9, 0.95, 0.98, 1.0 BList nominal yes, no
Wolfs nominal yes, no
We saw bank type as a nominal scale and binarized this attribute by creating a binary attribute for each of the four types of banks present in the raw data, namely universal deposit, commercial, investment, and private banks. Here we diverge from the prior study that coded bank type according to the hypothesis derived from theory, thereby creating two categories that lumped investment banks with private banks and commercial banks with universal deposit banks.
We binarized the three point fuzzy-scale for the prior existence of a code of conduct by making a category for each situation: no code of conduct, a code of conduct that at least implicitly discourages money laundering, and a code of conduct that explicitly mentions money laundering activities.
Whereas Maggetti relied on domain experts to code each bank onto a 6-point fuzzy scale for the coordination of corporate relationships (CorpC), we used the raw values from the corporate coordination index as reported by Maggetti. We treated this as an ordinal scale and used thresholds in our binarization on the actual values of 0.0, 0.14, 0.23, 0.44, 0.71, 0.74, 0.77, 0.82, and 0.95. In other words, all cases would be present at CorpC>= 0, and the number of cases would fall with each threshold of actual values of cases in the index until only six cases remain at CorpC>= 0:82 and only one at CorpC>= 0:95.
We treated the data for regulatory intensity (RegInt) in a similar fashion, by using the actual input data of the costs of nancial regulation per GDP to binarize using threshold values (at 45, 53, 75, 83, 144, 149, 277, and 426) to create an ordinal scale, rather than relying on the 7 point scale that Maggetti derived from that data. In other words, all cases were present at RegInt>= 45 and only 4 cases remain at RegInt>= 426.
For the extent of nancial liberalization (FinLib) we relied on Maggetti's fuzzy set for the values and scaled it similarly with thresholds on the values assigned of 0.9, 0.95, 0.98, and 1.0, so that all cases are present at FinLib>= 0:9 and 14 cases remain at FinLib>= 1:0. 3.3
In this short paper, we just wanted to replicate Maggetti's results using FCA instead of fsQCA. For this reason we focused on deriving attribute implications related to the outcome condition (namely participation in Wolfsberg Initiative). Using the natural scaling above, we could derive the following implications by navigating the resultant lattice:3 1. All commercial banks participated in the Wolfsberg Initiative. Formally,
BankType: Commercial ! Wolfsberg: Yes. 2. If the bank owner is private, then the bank does not participate in the
Wolfsberg Intitiative. Formally, Owner: Private ! Wolfsberg: No. 3. The absence of a prior code of conduct implies nonparticipation in the Wolfsberg Initiative. Formally, Code: No ! Wolfsberg: No. This negative implication is not mentioned by Maggetti, he just claims that the condition 3 This was done using FCART (Neznanov et al. 2013).
(attribute) can determine participation, but in fact attribute value is more accurate to determine the su cient condition (implication).
Although we set out to merely replicate the ndings about necessary and su cient conditions arrived at by Maggetti using fsQCA, we derived some implications that replicate his ndings, uncovered some implications not mentioned by him, and found a minor point of disagreement. Deriving the attribute implications by way of FCA show that Maggetti's solution that public ownership and the prior existence of a code of conduct are necessary conditions (Maggetti 2014, p. 806) and a combination of banktype and the presence on the blacklist are sufcient conditions to explain participation in the Wolfsberg Initiative (Maggetti 2014, p. 807) is not as nuanced as it could be. 4
In this short article we have considered a well-known dataset on banks from
Maggetti (2014) and proposed to analyze it from the perspective of Formal
Concept Analysis (FCA). From the results of the analysis it is clear that FCA
presents a simple and transparent way of treating this example. The FCA
analysis allowed us to obtain more ne-grained observations than proposed in Maggetti
(2014) and helped us to see some aws in the conclusions reached by the fsQCA
method that he used. We would like to focus our future research on
considering interesting association rules that can be obtained from the mentioned
dataset with the help of pattern structures on numerical and ordinal attributes