Necessary conditions in international business research advancing the field with a new perspective on causality and data analysis

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Introduction
When theorizing about the relationships between two or more variables, researchers explicitly or implicitly refer to different causal logics.The most-used logic is additive logic.The aim of this logic is to explain an outcome by several determinants.Additive logic is implicit in different forms of regression or structural equation analyses.In these analyses the individual determinants are sufficient but not necessary for changing the outcome, and thus they can compensate each other.For example, in their study of the influence of institutions on foreign direct investment (FDI), Holmes, Miller, Hitt, and Salmador (2013) hypothesized, among others, that regulatory institutions promoting a friendly business environment, including democratic political institutions that provide stability and predictability, could attract FDI.They examined the relationships between these institutions and inward FDI by using a regression-based research method.This approach represents an additive logic since each of the institutional determinants is assumed to contribute to higher inward FDI.In this approach, since the absence of an institutional determinant can be compensated by another and will not prevent inward FDI, none of them are deemed necessary.
A second logic is configurational logic.This logic builds on the assumption that an outcome is usually not produced by a single determinant but by a combination of different determinants, which are called configurations.Within these configurations, the presence or absence of different determinants are decisive for the outcome.Thus, in contrast to regression analysis, the focus is not on individual determinants (and on the question which determinant has the highest impact), but on configurations of determinants (and on the question which conditions need to be present or absent to enable the outcome).Thereby, researchers assume that multiple configurations can lead to the same outcome (i.e., equifinality), which makes each configuration sufficient but not necessary for the outcome.Configurational logic is implicit in the different forms of qualitative comparative analyses (QCA).For example, in his study of the influence of institutions on FDI, Pajunen (2008) used this logic to argue that a country's ability to attract FDI depends on several different combinations of institutional conditions.Rather than assuming that several institutional conditions contribute to inward FDI (as done in Holmes et al., 2013), he proposed and analyzed whether combinations of institutional determinants, such as the combination of political stability, flexible labor regulation, and corruption, are jointly sufficient for a country to attract FDI.
A third logic is necessity logic.Necessity logic implies that a determinant is necessary but not sufficient for an outcome.If the necessary cause is not in place, the outcome will not materialize.Necessity logic differs from the previous logics in two key respects: First, it does not aim to explain how changes in a determinant change an outcome but aims to explain why an outcome does not occur if certain determinants are not in place (Goertz, 2017).For example, it does not aim to explain why more political stability may lead to higher FDI but aims to explain why there is no FDI when there is no political stability.Second, its focus is on single conditions that are necessary ('critical') for an outcome.Since a necessary condition cannot be compensated by other factors, its absence will guarantee failure.For example, if we assume that political stability is a necessary condition for FDI, there is no FDI without political stability, even if the country exhibits other strong configurations of institutional factors such as political rights and favorable taxation.
As we will show in this paper, necessary conditions and necessity logic are widely referred to in International Business (IB) research.Two prominent areas in which theoretical arguments follow a necessity logic are studies that discuss necessary conditions of (successful) internationalization processes (e.g., Filatotchev, Liu, Buck, & Wright, 2009;Johanson & Vahlne, 2009), and studies that discuss necessary conditions for successful knowledge transfer in IB (e.g., Minbaeva, Park, Vertinsky, & Cho, 2018;Noorderhaven & Harzing, 2009).Necessary condition analysis (NCA) is a technique to test this necessity logic and to identify necessary conditions in data sets (Dul, 2020b).NCA has been applied in a few management studies with an international flavor (e.g., global virtual teamwork, see Richter, Martin, Hansen, Taras, & Alon, 2021; expatriation intention, see Richter, Schlaegel, van Bakel, & Engle, 2020, innovation management in buyer-supplier relationships, see van der Valk, Sumo, Dul, & Schroeder, 2016) and in studies that refer to theoretical arguments that are likewise prominent in IB research (e.g., firm capabilities and performance, see Tho, 2018).Apart from these notable exceptions, it has not yet received much attention in IB research and its core outlets.However, NCA is a powerful approach that can benefit the IB field and its responses to specific challenges (Aguinis, Ramani, & Cascio, 2020;Fainshmidt, Witt, Aguilera, & Verbeke, 2020).
We argue that necessity logic and NCA, as the methodological toolset to test necessity arguments, can aid IB researchers in tackling the interdisciplinary and complex nature of IB phenomena, can lead to more rigor in theoretical thinking, can improve the theory-method fit in the field, and can produce results of high relevance to IB practitioners.Theory wise, additive, configurational and necessity logic offer different viewpoints on theoretical mechanisms.Being more attentive to these different logics can advance theorizing on associations and underlying mechanisms in the field and can assist in identifying theoretical explanations (stemming from different disciplines) that best fit IB phenomena in general and in specific contexts (e.g., in different countries, cultures, institutional environments, or periods).In addition, as we will demonstrate in our review of IB studies (that often apply regression-based procedures to test necessity arguments), disentangling logics and related research methods increases theoretical rigor and improves the theory-method fit in IB.Furthermore, NCA can reduce the complexity of IB challenges by identifying the critical factors that must be in place to prevent failure.Therewith, analyzing necessary conditions can advance the field by producing results of high practical value.Given these considerations, the aim of this paper is to familiarize IB scholars with necessity logic and NCA and to discuss how their application advances the field.

Fundamentals of necessity logic and NCA
Researchers use different phrases to express that condition X is a necessary cause for outcome Y. Common expression are "X is needed for Y", "Y requires X", "X is critical for Y", or "X must be present for Y to succeed".All these expressions refer to necessity logic and imply that outcome Y (e.g., FDI) can only be achieved if the specific condition X (e. g., political stability) is present (Dul, 2016(Dul, , 2020b)).Thus, a necessary condition constitutes a constraint, a bottleneck, or a critical factor that must be overcome or satisfied so that a desired outcome can exist.The absence of the necessary condition results in the absence of the desired outcome.Hence, the analysis of necessary conditions is useful to explain why a desired outcome did not materialize and, accordingly, to identify the required 'must-have' factors in order to avert guaranteed failure (Goertz, 2017).Notably, when talking about a necessary cause, we refer to a direct relation between X and Y. Thus, necessity logic should not be confused with moderating effects where the (average) effect of X on Y depends on a third variable (Hauff, Guerci, Dul, & van Rhee, 2021). 1  Analyzing necessary conditions should always start with theory.At the outset, authors (or researchers) need to develop a logical argument or a theoretical mechanism that explains why X is necessary for Y. Building on Goertz (2017) and Dul (2021), authors can develop this logic by following three steps (see Table 1): First, argue why the absence of X results in the absence of Y.For instance, develop a logic as to why there is no FDI to a country without political stability.Second, argue that in cases where Y is present X is also present.For instance, argue that there is FDI to politically stable countries.And third, discuss why there is no substitutability of X to enable Y.For instance, discuss why political stability cannot be substituted by other institutional factors (such as favorable taxes) when it comes to attracting FDI.
Necessity arguments can be translated into causal statements in the form of hypotheses.For instance, a necessity hypothesis can be formulated as "X is necessary for Y" or "A high level of X is necessary for a high level of Y".A necessity hypothesis can also be specified by adding a theoretical domain where it is supposed to hold true.For instance, if the hypothesis is that political stability is necessary for FDI, then the idea is that this applies to any country in the world.Adding a theoretical domain, such as a geographical or other delimiter, specifies that the causal statement is supposed to hold within the given domain (see Dul, 2020b).For example, an IB researcher could delimit the political stability hypotheses to specific economies (e.g., those of developed versus developing countries) or to firms that follow certain motives in their FDI.Further delimiters could relate to specific periods of time during which a certain necessity hypothesis holds.
Necessity logic can be applied to conditions and outcomes that are measured on different levels.Fig. 1 (left) illustrates the necessity logic for dichotomous conditions and outcomes.In this example, the presence of X (X = 1) is necessary for the presence of Y (Y = 1).If X is absent (X = 0), Y is also absent (Y = 0).The dichotomous case is the simplest form of a necessary condition and refers to necessity in kind where a condition is either necessary or not for an outcome (Vis & Dul, 2018).However, necessity statements can also refer to a certain level of the condition and a certain level of the outcome.For instance, instead of assuming that political stability is necessary for FDI (a binary statement), the presumption could be that a certain level of political stability (e.g., high political stability) is necessary for a certain level of FDI (e.g., high FDI).Thus, with variable scores with more than two levels (beyond

Table 1
Mechanisms to be explained in necessity logic theorizing.

Priority
Question to be answered Example 1 Why will Y be absent if X is absent?
Argue why there is no FDI to politically unstable countries 2 Why will X always be present if Y is present?
Argue why there is FDI to politically stable countries 3 Why can other concepts not compensate for the absence of X?
Argue why a country without political stability cannot compensate for this lack of stability by utilizing other (e.g., institutional) advantages to attract FDI dichotomous), necessary conditions in degree, i.e., more precise necessity statements, can be formulated.Fig. 1 (center) shows a discrete example where a medium level of X is necessary for a medium level of Y, and a high level of X is necessary for a high level of Y. Finally, Fig. 1 (right) shows a continuous example where a certain level of X (X C ) is necessary for a certain level of Y (Y C ).In all instances necessity is indicated by an empty space in the upper left corners of the tables or scatter plots.NCA identifies these empty spaces in scatter plots to determine the presence of a necessary condition.More specifically, NCA draws a ceiling line which separates the space without observations from the space with observations.This ceiling line determines the level of condition X that is necessary to reach a certain level of outcome Y. Two default ceiling lines are Ceiling Envelopment -Free Disposal Hull (CE-FDH) and Ceiling Regression -Free Disposal Hull (CR-FDH).The CE-FDH ceiling line is a step-wise linear line that is recommended for discrete data or when the pattern of observations near the ceiling line is irregular (Dul, 2020b).Since this ceiling line disallows points above it, it produces the largest empty space.The CR-FDH ceiling line is a trend line through the CE-FDH line.It is calculated by a linear regression using the upper-left points of the CE-FDH line and is recommended for continuous data or when the pattern of observations near the ceiling line is approximately linear.
Fig. 2 illustrates the CE-FDH and the CR-FDH ceiling lines.The ceiling lines are on top of the data.They do not represent an average trend (like the regression line shown in Fig. 2) but indicate which level of the condition is necessary for a specific level of the outcome.For example, outcome level Y C cannot be achieved at levels of X that are below X C .
Fig. 2 also shows the bottleneck table (for the CR-FDH line in the graph, left), which is a tabular representation of the ceiling line.The first column of a bottleneck table represents different levels of the outcome, and the next column represents (and additional columns represent) the corresponding required level(s) of the condition(s).These levels can be expressed as a percentage of the range, as actual values, or as percentiles.They indicate that higher levels of Y can only be achieved with higher levels of X.For example, to achieve a level of Y = 6, X must at least be 5.1.
NCA calculates several parameters to assess if a necessity hypothesis is supported.The main parameter is the necessity effect size d, which is calculated by dividing the empty space (called the ceiling zone) by the entire area that include observations (called the scope).Per definition, d can range between 0 and 1. Dul (2016) labels 0 < d < 0.1 as a small effect, 0.1 ≤ d < 0.3 as a medium effect, 0.3 ≤ d < 0.5 as a large effect, and d ≥ 0.5 as a very large effect.Previous studies used the threshold of d = 0.1 to consider an effect as practically meaningful (e.g., Karwowski et al., 2016;van der Valk et al., 2016).In addition, NCA allows an evaluation of the statistical significance of the effect size in terms of a p-value, indicating the probability that the effect size could be a random result of unrelated variables, which should also be considered when deciding whether or not to reject a necessity hypothesis (Dul et al., 2020).
There may be multiple necessary causes, but the necessity of a single X for Y does not depend on the absence or presence of other causes; other   determinants cannot compensate for the absence of a necessary condition.Thus, NCA is fundamentally a bivariate analysis.If researchers are interested in more than one necessary condition, a separate analysis is made for each of these conditions.This is possible because a necessary condition operates in isolation from the rest of the causal structure, i.e., the necessity of X 1 on Y does not depend on the necessity of X 2 on Y.This also implies that NCA models are parsimonious and do not need control variables (as do regression analyses) as there is no omitted variable bias (Dul, 2020b).

Necessity logic and the Use of NCA in IB research
To assess the relevance and usage of necessity logic and NCA in IB research, we searched the Journal of World Business and the Journal of International Business Studies since 2010 for commonly used keywords (including plurals and combinations) that express necessity (Dul, 2020b), among others 'necessary', 'but not sufficient', 'but insufficient', 'condition/ prerequisite/ requirement/ precondition', and 'sine qua non'.By focusing on these explicit formulations of necessity, we provide a rough estimate of the relevance of necessary conditions in IB research: admittedly, researchers may also implicitly follow a necessity logic without explicitly using these keywords.As the identification of the latter would involve a higher level of speculation about the implied logic, we concentrated on studies that used the more explicit formulations of the keywords.Furthermore, since some researchers might have used these keywords unintentionally, we carefully evaluated the context in which they were used to avoid an overestimation of the relevance of necessary conditions.Hence, our review underestimates rather than overestimates the relevance of necessity logic in IB research, which seems acceptable for our purposes.
We found 54 articles that refer to necessary conditions (see the overview in Appendix 1).Of these 54 articles, 41 refer to a necessity logic to develop their theoretical arguments.Therein, two noticeable sub-fields relate to these necessary conditions.The first concerns a core area in IB research: 16 articles refer to necessary conditions in the context of explaining internationalization (patterns) and the existence and performance of the multinational firm.For instance, Filatotchev et al. (2009) outline that R&D investment and network membership are necessary but insufficient conditions for internationalization; Henisz (2003) refers to effective cooperation with host governments and capital scarcity in the domestic market as necessary conditions for international activities; and Johanson and Vahlne (2009) refer to 'insidership' in relevant networks as a necessary but insufficient condition for successful internationalization. Second, 11 articles refer to necessary conditions in the context of knowledge sharing/ transfer and creation.For example, Minbaeva et al. (2018) assume that a foreign partner's ability to codify and articulate knowledge is a necessary but insufficient condition for successful knowledge acquisition by local partners; Noorderhaven and Harzing (2009) argue that social interaction is a necessary condition for knowledge exchange in the multinational enterprise (MNE); and Reiche, Harzing, and Pudelko (2015) refer to shared language among subsidiaries and headquarters as a necessary condition for identity construction and knowledge flows.Another four articles refer to foreign entry mode (success), and 10 articles relate to a diversity of topics that we did not cluster (such as brand identification, ecological sustainability).
Seven of the 13 remaining articles refer to necessary conditions when discussing their findings, but they do not actively engage in using necessity logic to develop a theoretical line of argument.Finally, six articles refer to necessity in the context of applying a configurational logic and a form of QCA (Crilly, 2011;Judge, Fainshmidt, & Lee Brown, 2014;Kim, 2013;Pajunen, 2008;Schneider, Schulze-Bentrop, & Paunescu, 2010;Witt & Jackson, 2016).These studies focus on combinations or configurations of different variables that are sufficient for an outcome.From the above, we conclude that necessity logic is of high relevance to IB research.
Based on our review, we identify two pressing aspects that IB researchers should pay more attention to in future.First, even if authors refer to certain causal mechanisms as necessary conditions, they are  (2018), for instance, who argued in favor of the necessity of a foreign partner's ability to codify and articulate knowledge as a necessary condition for knowledge exchange in a partnership, switched to a hypothesis that fits a sufficiency logic and contended that the "higher the foreign partner's ability to codify and articulate knowledge, the higher the extent of knowledge acquisition by the local partner" (Minbaeva et al., 2018: p. 715).Hence, the presented hypothesis does not reflect the necessity logic applied in theorizing (see Table 2 for further examples of hypotheses and research designs that do not correspond with the formulated necessary conditions).
Building on this finding, we argue that IB research can be advanced by incorporating more rigor in differentiating between additive, configurational and necessity logic.Specifically, when using expressions like "X is a condition for Y", "X is a prerequisite for Y", "X is a requirement for Y", researchers must ensure that they translate their theoretical arguments into hypotheses that reflect this necessity logic.It is crucial to consider the reasons why a specific condition is a necessary condition, namely why the absence of (a certain level of) the condition will prevent the existence of (a desired level of) the coveted outcome, why the outcome is present when the condition is present, and why no other determinant can compensate for the absence of the necessary condition (Goertz, 2017).Acknowledging the specifics of necessity logic will lead to greater precision and more theoretical clarity in IB research.
Second, researchers tend not to use empirical designs that appropriately consider the necessity logic of their theory.Following the unnoticed translation of necessity arguments into sufficiency logic hypotheses, authors typically refer to different variants of the general linear model (e.g., correlation, regression, or structural equation modeling) which are unable to identify necessary conditions.Thus, while the methodology might fit the hypotheses, it does not fit the theoretical argumentation behind it.Of the 41 articles that refer to a necessity logic, 26 are empirical studies (while 15 are conceptual articles).Of the 26 empirical studies, 22 use a regression-based method, one uses simple correlations (while the remaining three use a qualitative design, an experiment, and chi-square tests).None of them use NCA.Hence, we identify a misfit between theory and method that may be induced by the simple unavailability of NCA in the past.We believe that our study is a timely response to recommendations made on the use of NCA regarding IB-related questions (see Aguinis et al., 2020;Fainshmidt et al., 2020).For example, Fainshmidt et al. (2020) discussing the contributions of QCA to IB researchstate: "As a general recommendation, research seeking to identify necessity should also rely on alternative methods, such as Necessary Condition Analysis."We could not agree more since NCA is (currently) the best available methodology to analyze necessary conditions.

Illustrative case: Institutional environments and FDI
To illustrate the application and value of NCA in IB, we analyze whether institutional environmental factors are necessary conditions for FDI.Not only is the topic of ongoing relevance in this field (see Bailey, 2018;Nielsen, Geisler Asmussen, & Dohlmann Weatherall, 2017), but it also enables us to demonstrate the value of NCA in comparison to the past use of additive and configurational approaches.

Theoretical Foundations
The ownership, location, and internalization (OLI) framework (Dunning, 1988(Dunning, , 2001)), which builds on necessity thinking, is a main theoretical framework that explains FDI flows.Indeed, Dunning (1988) asserts that "a firm will engage in foreign value-adding activities if and when three conditions are satisfied" (Dunning, 1988: p. 45).These conditions are the possession of ownership-specific advantages, N.F.Richter and S. Hauff internalization advantages, and location advantages (see Fig. 3).
When it comes to explaining the location of firms' FDI, current research focuses on the influence of the L-factor and usually adopts an institutional perspective of location characteristics (e.g., Holmes et al., 2013).Following the necessity thinking of the OLI framework, an L-advantage, such as a beneficial regulatory and political environment, is considered as a necessary condition for firms to invest in a country.Other studies also refer to the notion of necessity.Bailey (2018), for instance, states that "governments most successful in attracting FDI will provide at a minimum a stable political environment where market-based institutions are reliable and predictable" (Bailey, 2018: p. 140).By introducing the notion of a minimum level, Bailey (2018) implicitly refers to necessity logic.Similarly, Pajunen (2008) focuses on the idea of necessity, indicating that a minimum level of an institutional factor is a prerequisite for FDI.
The idea that beneficial institutional environments are necessary location factors for FDI inflows are substantiated by our use of the framework outlined in Table 1.First, we contend that inward FDI will not materialize without beneficial institutional environments, as firms lack the incentive to use FDI instead of other modes to enter and serve the market.For example, it would be unrealistic to assume that firms will invest in a new manufacturing site in a country which is involved in a war (i.e., a country that lacks political stability), as this would pose considerable investment risks: thus, without political stability there is no FDI.Second, we argue that firms invest in countries with beneficial institutional environments as it is in their interest to exploit this favorable environment to their advantage.For example, in countries with a high level of political stability, firms profit from the stability in the environment without fear of expropriation or harm to their investments.Finally, in line with the OLI framework, a beneficial location cannot be compensated for by other advantages to the firm.Since we consider specific location factors, their substitutability is a matter of debate.We contend that they are not arbitrarily substitutable.That is, favorable taxation cannot compensate for the political instability of a country.Likewise, political stability cannot be a substitute if a country is imposing exorbitantly high tax burdens on foreign firms.Building on these arguments, we hypothesize that beneficial institutional environments are necessary location factors for FDI inflows (H1).

Research design
Similar to using other data analysis procedures, researchers need to devote attention to the testing of necessary conditions in relevant samples (Dul, 2020b).For instance, it would be misleading to derive practical implications for small, emerging countries if the focus is on large, developed economies.In our theorizing, we did not specify a domain to ensure that the hypothesis would only hold in specific subsamples of countries or within certain periods.Accordingly, we collected data on 55 countries, presenting a representative set of both developed and developing countries (thereby covering those listed in previous studies: Holmes et al., 2013;Pajunen, 2008).Our data covers the period from 2010 to 2017.
Moreover, research needs to ensure a reliable and valid measurement of the relevant research constructs.Our variables are single items that have proved to be useful in various previous studies in the same field (although NCA can also be applied to multi-item or latent constructs, see Richter, Schubring, Hauff, Ringle, & Sarstedt, 2020).Our dependent variable is the inward FDI performance index, i.e., the ratio of a country's share of global FDI inflows to its share of global GDP.Our independent variables are the institutional factors listed in Table 3 (building on the shortlist of Bailey, 2018 and the measurements that were implemented, among others, in Holmes et al., 2013and/or Pajunen, 2008).
We performed an outlier analysis prior to our analyses, following the procedures outlined in the literature (e.g., Aggarwal, 2017;Dul, 2021).None of our cases had to be removed from the dataset.We point out that NCA is sensitive to outliers since a single case can reduce or even eliminate the empty space and, thus, reduce the necessity effect size.Therefore, researchers should always check for influential cases on or close to the ceiling line (Dul, 2020b).If these outliers are due to measurement or sampling error, they should be excluded from the analysis.If there is no measurement or sampling error, researchers should carefully consider how to deal with these influential cases.More specifically, researchers can examine the sensitivity of findings on potential outliers.That is, they can examine the influence of a potential outlier case on the effect size and its p-value to evaluate if a found necessity (or a lack of necessity) remains approximately the same or not (see Dul, 2021).In terms of a deterministic view of necessity, any single case can falsify a necessity theory.Indeed, an influential case could even be a 'best case' where a highly desired outcome is achieved without (or with a minimum level of) the condition.Such an insight is of significant practical value and can trigger theory building as it defies expected cause-and-effect relationships (Gibbert, Nair, Weiss, & Hoegl, 2020).The probabilistic view of necessity allows a few exceptions above the ceiling line.Accordingly, necessity statements are more flexible and cloaked in terms like 'practically', 'virtually', and 'almost always' necessary to indicate that, in most cases, a condition poses a constraint to the desired outcome.

Table 3
Measurements of institutional factors.

Institutional Factor Measures and Sources (Non-)Corruption
Unethical and illegal activities such as bribery, patronage, and graft ( Pajunen, 2008).

Tax (burden)
The financial impact of government taxation policies on organizations and individuals (Holmes et al., 2013).
Tax burden measure of overall taxation (2010-2017) provided by The Heritage Foundation Ranging from 0 (high) to 100 (small) Following the procedure in Holmes et al., 2013.

Labor regulation
The extent to which governments interfere with free labor market transactions (Holmes et al., 2013).
Labor Note: There is no consistency in IB studies as regards the measurement of the institutional environmental factors.For some factors studies indicate no systematic difference in findings when using different measures (i.e., corruption, political rights), but for others there seems to be a difference caused by the measures used (i.e.taxation), while again for others this is not evident (e.g.political stability; see the discussion in Bailey, 2018).We opted for measures predominantly used in the field (see Aguilera & Grøgaard, 2019) or that were also used in Holmes et al. (2013) and/ or Pajunen (2008).These two studies address the same research questions from an additive logic and a configurational logic.
The data can be used in different formats.One approach is to average the annual data, following the line of argument that FDI entails a longterm relationship involving slow changes over time (e.g., Pajunen, 2008).Another approach is to use a time-lag perspective, namely to measure the institutional variables at time t and the outcome variable at time t+1 (e.g., Holmes et al., 2013).We included both formats in our analyses.Hence, we performed an NCA on both formats, i.e., on the averaged data and on the time-lagged data.2

Results
Fig. 4 shows the scatter plots for each institutional factor. 3The empty spaces in the upper left corners of the scatter plots show that several institutional factors may indeed present necessary conditions for FDI attractiveness.This is supported by the necessity effect sizes (Table 4).Since the pattern of observations near the ceiling line is irregular, we refer to effects sizes based on the CE-FDH ceiling lines (Dul, 2020b).
For non-corruption, favorable taxation, flexible labor regulations, and political stability we find large (d > 0.3) or very large (d > 0.5) effect sizes with low p-values.All these factors can be considered necessary conditions for FDI.By contrast, we conclude that political rights do not present a necessary condition as its necessity effect size is smaller and could be a random result (as indicated by the high pvalues). 4able 5 provides the bottleneck table for both percentage ranges and actual values of the FDI performance index (ranging from -4.663 to 28.844).The table is created along equidistant steps, along the whole value range.For instance, it shows that to achieve an outstanding FDI performance index of 25.494 (i.e., 90%), the following minimum levels (actual values) on the institutional factors need to be satisfied: noncorruption (74), favorable taxation (74), favorable labor regulations (80), and political stability (1.053).
The FDI performance of countries is unequally distributed.A few countries perform high on inward FDI, but most countries fall short of an outstanding FDI performance; hence, not all equidistant ranges in Table 5 are meaningful to policy makers.To offer interpretations of the FDI performance scores relevant to policy makers, we present a selection of specific FDI performance levels in a bottleneck table that is finegrained within this meaningful range (see Table 6).To find these levels, we used the mean value and standard deviation of FDI performance to create categories.That is, we posited that an FDI unattractive or attractive country is a country that is more than one standard deviation below or above the mean FDI performance.For those in between these ranges, we used equidistant intermediate levels.Accordingly, the bottleneck table indicates that in order for a country to achieve an FDI performance index of 3.714, which we deem mainly attractive, it needs to have a non-corruption perception index of 51, a favorable taxation index of 42, a flexible labor regulation index of 42, and a political stability index of 0.331 (all actual values).Policy makers must overcome these bottleneck, institutional index values to elevate their countries to a comparatively high level of attractiveness for FDI inflows.We will further discuss these results and their implications in the following.

Discussion
IB is a relatively young research field that faces complex and interdisciplinary research dilemmas.In addition, IB research is dynamic over time with constant change stemming from the dynamism of the international environments and business systems.This increases complexity (e.g., Eden & Nielsen, 2020).Understanding IB phenomena requires researchers to "combine theories, concepts, data and methods from multiple disciplines to explore the scope or boundary conditions of multiple disciplinary perspectives" (Cheng, Henisz, Roth, & Swaminathan, 2009: p. 1072).In the recent past several researchers have outlined a number of approaches and toolsets that fit the specific challenges posed by IB (e.g., Aguinis et al., 2020;Cuervo-Cazurra, Andersson, Brannen, Nielsen, & Reuber, 2016;Fainshmidt et al., 2020).In this paper we argue that necessity logic and NCA can contribute to coping with the challenges of specific relevance to IB.

Implications for IB Theorizing
First, IB researchers often face alternative explanations that fit the IB phenomenon under investigation (e.g., Cuervo-Cazurra et al., 2016).These explanations involve alternative theoretical frameworks (among others, borrowed from other management disciplines) and alternative logics that underly the theoretical mechanisms.Necessity logic is one of these alternatives.In this regard, the OLI framework presents an interesting case.Dunning (1988), in his summary of the OLI framework, outlines that a firm will only engage in international activities if three conditions are satisfied.First, the firm must have net ownership-specific advantages vis-à-vis other firms when serving markets.Second, it must be more beneficial for the firm to use these advantages itself, rather than to sell or lease them.Third, it must be in the firm's interest to use these advantages in conjunction with the locational advantages of countries (Dunning, 1988).The OLI framework is not only popular, but it also dominates the field.Many authors refer to its key arguments, among others that "the possession of firm-specific assets is a necessary condition for the successful internationalization of MNEs" (Kirca, Fernandez, & Kundu, 2016: 628).Hence, the prevailing wisdom in the field is that MNEs do not exist if these conditions are not satisfied, i.e., there is no Y (the MNE) if the O, L, and I conditions (X) are not satisfied.However, recent voices raise the issue whether the extant literature is correct in assuming that competitive advantages constitute a necessary condition for the emergence of MNEs.Among others, Hashai and Buckley (2014) discuss certain conditions under which MNEs exist without possessing such advantages and conclude that firms "do not need a competitive advantage to become MNEs" (Hashai & Buckley, 2014: p. 46).We believe that a further differentiation of O, L, and I arguments along additive, configurational and necessity logics would advance the field.Therefore, this serves as an example of alternative explanations that can be tested using NCA.The addition of NCA to existing toolsets creates the possibility of testing dominant against alternative theoretical viewpoints that include and challenge the necessity logic of popular paradigms. 5 Indeed, in addition to more traditional logics (i.e., additive and configurational logics), more attention to necessity logic can advance theorizing on associations and underlying mechanisms in the field.It can rule out some of the alternative explanations and provide more clarity on theories that fit specific IB-related issues (see also Aguinis et al., 2020).Second, most IB theorizing is contextual.So, an explanation that fits a particular country or cultural context does not necessarily fit other countries.In fact, several authors in IB call for the further contextualization of IB research (e.g., Meyer, 2013;Teagarden, Von Glinow, & Mellahi, 2018;Tsui, 2007).Necessity logic and NCA benefit this contextualization endeavor because they enhance our understanding of necessities that may be involved in some but not all country and/or cultural contexts.Hence, they advance the field by understanding the theoretical necessity mechanisms that, among others, apply to specific countries, sub-regions, cultural clusters, and institutional environments.
Third, IB researchand practiceis extremely complex.Research on IB phenomena is characterized by complex conceptual models that include many determinants influencing an outcome (e.g., Eden & Nielsen, 2020;Richter, Sinkovics, Ringle, & Schlaegel, 2016).This complexity can be overwhelming.Necessity logic and NCA address this complexity as they provide an understanding of the critical factors that must be present to prevent failure.This assists researchers in creating parsimonious models that not only reduce complexity, but that also provide results that are of value to researchers, business practitioners and policy makers (see also the subsequent discussion of practical implications).Notably, theorizing on necessity logic might be more difficult than expected.The reason is that we are familiar with dominant sufficiency logic thinking according to which an outcome usually depends on multiple determinants, where one determinant may complement another.Authors who want to engage in relevant theorizing can use the framework provided in Table 1.Importantly, NCA, like any other data analysis procedure, cannot conclusively prove causality.The requirements for causal interference are the same as for any other type of cause-effect relations, i.e., a necessary cause is more plausible if the cause precedes the outcome, the cause is related to the outcome, and no other variable is responsible for the observed relationship.Accordingly, it is important that the identified necessary conditions are theoretically justified, i.e., researchers must discuss the causal mechanisms that explain the necessity (Dul, 2020b).More intuitively formulated necessary conditions in IB (as outlined in our literature review) sometimes lack this specific theoretical thinking.

Implications for IB research
Our review revealed a mismatch between theory and method: while we found many indications of necessity logic in the theoretical arguments, researchers often applied a regression-based procedure which is misleading.Researchers should be aware of the different logics implied by the different methodologies, since ignoring them bears the risk of inappropriate conclusions.Thus, we strongly recommend that when researchers theoretically refer to necessity logic, they should translate this into necessity hypotheses and apply NCA to test for necessity.Pure necessity theories can be tested with NCA as a stand-alone method, allowing a clear narrative and a straightforward analysis (Dul, 2021).
Using NCA as a stand-alone method allows the addition of a necessity view to specific research questions (which previously might have been studied within a sufficiency perspective).However, in some instances the goal may be to test both necessity and sufficiency relations simultaneously.Whenever this is theoretically justified, in line with Nielsen et al. (2020) suggestion to make more use of triangulation in IB research, we recommend the use of NCA in combination with established methods like OLS, SEM, or QCA.Additive, configurational and necessity logics each address a specific perspective, which implies that each individual logic is ignorant of the perspectives of the others.For example, analyzing necessary conditions reveals the determinants that can prevent the existence of an outcome, but not the predictors that produce a desired outcome.Hence, the analyses of our illustrative example revealed that countries should ensure a minimum level of non-corruption, favorable taxation, flexible labor regulations, and political stability to make FDI possible.However, none of these factors can individually contribute to increasing FDI or ensure FDI if combined.Methodological triangulation "expands the scope of inquiry by allowing for a greater range of research questions to be addressed, and a more holistic understanding of the phenomenon obtained" (Nielsen et al., 2020(Nielsen et al., : p. 1494).Thus, using NCA along with other methodologies makes it possible to address a phenomenon in different ways that complement each other.
For example, the NCA results can complement the findings of regression-based approaches (and vice versa).Studies using additive sufficiency logic (e.g., Holmes et al., 2013; and the overview in Bailey, 2018) indicate that institutional factors are significantly related to FDI.For example, in his meta-analysis Bailey (2018) demonstrates that most studies find a positive relationship between political stability and inward FDI.Hence, the higher the level of political stability in a country the higher the inward FDI.We find that political stability is a necessary condition for FDI.Thus, for a country to attract inward FDI, political stability needs to surpass a certain level.As in this example, the analyzed factors can be both significant determinants from an additive logic and necessary conditions.In this situation, the findings confirm that a minimum level of the institutional factor must be surpassed and that increasing the institutional factor has the potential of increasing FDI.Likewise, other combinations of findings are possible: an institutional factor can be a non-significant determinant from an additive logic, but a necessary condition.In this case, although a minimum level of the institutional factor must be satisfied to achieve a certain level of FDI, any further increase in the institutional quality of this factor will not result in 5 When applying NCA to a field that presents both theoretical arguments for and against necessity, the detailed insights into the bottleneck levels could show that necessity depends on the level of the outcome and therewith may help to resolve the theoretical conflict.For instance, there may be a necessity relationship at high levels of an outcome, but not at lower levels of the outcome.
more FDI.If an institutional factor is neither a necessary condition nor a significant determinant, researchers combining these two logics would conclude that it is not relevant to FDI.Another example is the combination of NCA and QCA.Using fuzzyset QCA, Pajunen (2008) indicates that policy makers in central-eastern European countries, such as Bulgaria, concur that either "political stability, political rights, civil liberties, and [a] just judicial system" or "political stability, political rights, civil liberties, and property rights" will ensure FDI attractiveness.The NCA can complement these results by identifying the necessary levels of the individual components in these configurations.For instance, in our illustrative analysis the NCA demonstrated that a political stability score (actual value) of at least -1.537 is necessary for average FDI attractiveness.Hence, the NCA offers an added level of precision.It identifies the specific levels of the condition that are necessary for various levels of the outcome.In addition, it can complement the configurational logic by identifying necessary AND-configurations (i.e., multiple, single necessary conditions that are each individually necessary) (Vis & Dul, 2018).For instance, we find that there are four minimum levels of necessary conditions for average FDI attractiveness: non-corruption (31), favorable taxation (42), flexible labor regulation (35), and political stability (-1.537).There are first ideas worth exploring on how, technically best, to complement QCA with NCA (see Dul, 2020a).
In sum, we strongly recommend using NCA (as a stand-alone method) whenever researchers use necessity logic in their theoretical arguments, and we furthermore recommend a combination of NCA and other methodologies.The latter allows researchers to identify the factors and their respective levels that must be present for an outcome (i.e., necessity logic), and the factors or combinations of factors that contribute to achieving an outcome (i.e., additive and configurational logics).Nielsen et al. (2020) point out that it is easy to make claims about triangulation, but that it is difficult to implement triangulation.Indeed, not being feasible on account of time, resource, or manuscript length restrictions, it is unrealistic to expect that every study should use different methodologies.However, beyond the context of a single study, we believe that adding NCA to the toolset of IB research can advance the entire field.This application of a novel perspective on causality and data analysis adds to existing studies that use more traditional logics and analytical approaches.

Implications for IB practice
The IB community is increasingly concerned about research that has meaning beyond academia; IB research needs to be transferable to practice, policy and society (Aguzzoli, Gardner, & Newburry, 2021).Practitioners and policy makers typically focus on factors that are crucial for success instead of all the factors that can influence an outcome (represented in complex models).NCA delivers results that provide input on these 'must have' factors; factors that should be taken care of at the outset.Even if, according to traditional analyses, certain factors exert a significant influence on the outcome on average, this effect will not materialize without satisfying the necessary conditions.
The practical relevance of NCA is illustrated by the specific case of Bulgaria.If Bulgarian policy makers are interested in making their country a 'mainly attractive' market for inward FDI (according to our interpretation of specific FDI performance levels), they need to ensure the fulfillment of the must-have necessary levels.According to our analyses, Bulgaria presents a non-corruption perception index of 41 (41 < 51!), a favorable taxation index of 91 (91 > 42), a flexible labor regulation index of 72 (72 > 45), and a political stability index of 0.077 (0.077 < 0.331!; the numbers are from 2016).As a result, the Bulgarian policy makers face two critical bottlenecks, namely too much corruption and insufficient political stability.Thus, Bulgaria cannot improve its inward FDI by, for instance, granting further tax benefits.It first needs to improve the corruption perception of their country (to a level of noncorruption perception of 51) and their political stability (to a level above 0.331) to attract FDI.These results show that researchers, by including NCA in IB, can produce results which are of considerable practical value (in this case for policy makers).

Conclusion
Necessary conditions and necessity logic are extensively referred to in IB research.We encourage IB researchers to carefully position their theoretical arguments when they refer to necessity logic and to pay more attention to the translation of their theoretical arguments into necessity hypotheses, as this would advance conceptual thinking in IB.Moreover, we encourage researchers to apply NCA to support or falsify their necessity hypotheses and to ensure a theory-method fit.
We found numerous necessity statements in our review of the IB literature.Many of them were present in studies that aimed to explain internationalization.More specifically, the authors of these statements discussed the necessity of network advantages and 'insidership' in networks for internationalization, the necessity of location factors in internationalization, and the necessity of firm-specific assets, resources, and dynamic capabilities as conditions for the internationalization patterns and outcomes in IB.In addition, necessary conditions were often found in transaction cost-related theories that address internationalization processes or entry modes.Likewise, a more recent research topic that engages necessity arguments is knowledge sharing.The authors in this domain discussed necessity in the context of knowledge sharing related to innovation, headquarter and subsidiary relationships, and organizational learning.These are key topical areas that can significantly benefit from precision in the applied logic, as well as from more specificity in necessity thinking and the application of NCA.
Although IB researchers consider the 'determinants of success' in various subfields, thinking about the critical factors that induce failure could be a fruitful avenue to enrich our understanding of the mechanisms that explain the failure of, among others, institutions, MNEs, strategic alliances, and international teams.Finally, considering that necessity logic and NCA has the potential to benefit IB research more generally, especially by ruling out alternative, interdisciplinary explanations, by assisting the theorizing process on contextual domains in which certain explanations hold, and by reducing the complexity of IB research phenomena, we recommend their explicit use to confront future grand challenges of IB research.

Appendix 1
Necessary conditions in IB: Logic, hypotheses, analysis techniques, and interpretations.The article analyses the relationships between equity stakes in group-affiliated firms on FDI decisions.'To be successful, firms must have appropriate resources for international expansion.However, possession of such resources is a necessary but insufficient condition to achieve a competitive advantage.To achieve a competitive advantage, especially in international markets, such resources must also be managed effectively (…) The human capital of the firm's managers performs this managerial The article investigates the foreign activities in the banking sector, more specifically the motivation for foreign expansion and the determinants of foreign market choice.'The greater the imperfections in the markets for the exchange of [firm specific assets], the more likely it is that a firm that possesses these assets will use FDI to transfer the advantages embodied in these assets across national borders.We call advantages that come from the internalization of those products (…) Type 1 IB (internalization benefits).Type 1 IB constitute a necessary condition for crossborder internalization (…)' (p.233-234) And then, further on type 1 IB: '(…) multinational banks can secure revenues from its clients by matching its (…) products and (…) specific needs in their international operations.Information concerning a client's financial requirements (…), and other aspects of their operating status is an essential input into the development of the final products and services that a bank offers to its client.This intermediate product involves valuable knowledge (…).To build up client-specific information is a time-consuming process, which requires the bank to make detailed plans to acquire, develop and exploit the information.(…) Because the information is specific to the very relationship between that client and the bank, the external market fails; it is unable to mediate a price for the information, even if a bank wanted to sell that information to allow its clients to be serviced by a bank in its client's foreign markets (… The article presents a framework to understand the existence of international new ventures.'(…) a framework that describes four necessary and sufficient elements for the existence of international new ventures: (1) organizational formation through internalization of some transactions, (2) strong reliance on alternative governance structures to access resources, (3) establishment of foreign location advantages, and (4) control over unique resources.'(p.29) 'The first three elements define the necessary conditions for the existence of an international new venture (…).However, these are not sufficient conditions for sustainable competitive advantage.Sustainable competitive advantage (…) requires that its resources be unique.'(p.revealed that knowledge transfer is a two-way street involving learning by both multinational and indigenous firms (…).A necessary condition for such learning to create value is the possession by the two firms of knowledge-based complementary capabilities.However, this is not a sufficient condition: it does not guarantee that any joint effort to exploit the complementarity will yield a positive joint value for the two firms.Whether the potential value can be realized also depends on the efficiency of the mode that the two parties choose to exploit their complementary capabilities.'(p.365).
In a subsection the authors focus on an analysis of whether market failure is a necessary condition for joint venture formation.In their discussion of this subsection, they outline a set of jointly sufficient conditions for a joint venture, being the optimal mode of organization involving two parties that want to exploit their complementary assets.(p.377) answering specific questions using a simulation study] capabilities than existing theories; the new insight is due to an integration of the real options logic with the model to identify four factors that are expected to influence the choice of mode for exploiting synergy between complementary assets of two parties in the presence of uncertain learning.The article investigates the role of social interaction between managers for knowledge sharing in MNEs.'To the extent that knowledge is indeed socially constructed, social interaction should be seen not primarily as a means for transferring existing knowledge, but rather as a necessary condition for the social production of knowledge.'(p.725).
'Hypothesis 1: Social interaction between a subsidiary and other parts of the MNE will be positively related to knowledge exchange (inflows as well as outflows).'(p.725).
Regression-based 'Turning to the main effects of the explanatory variables, intensity of interaction has a consistent positive effect on all four types of knowledge flow.
N.F.Richter and S. Hauff
whether extant theories can explain the observed flows of FDI.It proposes some extensions that relate to investments in politically salient industries and in capital-scarce countries.'(…) I extend their discussion of effective cooperation with host governments so that this ability, like the n

Table 2
Examples of necessity statements in empirical IB research.

Necessity statements in theorizing section, analysis technique and discussion of findings
This confirms Hypothesis 1, our baseline hypothesis' (p.733).'Ouranalyseswereguided by the ideas developed in two different perspectives … Based on both perspectives we expected (as our baseline hypothesis) a positive effect of social interaction intensity on all intra-MNE knowledge flows.' (p.735) N.F.Richter and S. Hauffseldom translated into necessity research hypotheses.Minbaeva et al.

Table 4
Results of NCA.

Interpretation and/ or necessity arguments in the discussion AT fits logic Topic: Explaining internationalization (patterns) and the existence and performance of the MNE (total: 16)
The article presents a conceptual model of born global firm internationalization that is embedded in ideas on the role of market knowledge as an NCyet the conceptual framework itself focuses on the antecedent learning and knowledge building processes.'(…) market knowledge is a necessary but insufficient condition for the development of leading-edge knowledge evidenced as innovative products (…) which facilitates multiple market entry simultaneously in the firm's early stages of internationalization. (…) Following this analogy, we conjecture that (…) the firm must acquire knowledge from other sources to develop leading edge innovative products and services that will fulfill these needs.' (p.296-297) 'In sum, our conceptualization draws on a foundation of organizational learning theory in that we argue that for accelerated internationalization the firm must learn from multiple sources, and that knowledge results from this learning.'(p.298); '(…) there are three learning capabilities that are instrumental to early internationalization in born global firms: market-focused learning capability, internally focused learning capability, and networking capability.' (p.
These are: (1) absorptive capacities of the parties; (2) frictions in knowledge and asset markets and the associated incentive issues for knowledge sharing; (3) bargaining cost; and (4) switching cost.' (p.382) They conclude that the economic viability of a mode not only depends on the presence of complementarity between the capabilities of the parties but also on the efficiency of the chosen mode for combining the capabilities.(p.383) Reiche, Harzing, & Kraimer, 2009 (C) Knowledge sharing/ transfer/ creation; structural ties as NCs In the article the authors develop a cross-level model that explores how assignees' social capital translates into inter-unit intellectual capital.'(…) although social capital is based on a certain structural configuration of actors, its benefits can be realized only through the existence of relational and cognitive social capital.Structural ties are thus a necessary but insufficient conditionfor social capital effects to occur.Only once the assignee has connected the social networks at the home and host unit, thereby building structural inter-unit social capital, can employees use these cross-unit ties to develop relational and cognitiveinterunitsocial capital and, in turn, engage in knowledge-sharing.' (p.517) 'Proposition 2a: Structural inter-unit social capital will lead to the development of relational and cognitive inter-unit social capital.' (p.