Case-Based Asymmetric Modeling of Firms with High Versus Low Outcomes in Implementing

Case-Based Asymmetric Modeling of Firms with High versus Low Outcomes in

Implementing Changes in Direction

Shengce Ren, Shanghai Maritime University

Huei-Ting Tsai, National Cheng-Kung University

Andreas B. Eisingerich, Imperial College London

The authors thank JBR Editor Arch Woodside for his continued support and constructive and very helpful comments. They thank Gerard George, Singapore Management University, and Matthias Seifert, IE Business School, for their critical feedback on an earlier version of this manuscript. The authors gratefully acknowledge funding from the National Science

Foundation of China (Project No. 70902074) and the Social and Humanity Foundation of

Ministry of Education of China (Project No. 09YJC790185). Send correspondence to Shengce

Ren, Shanghai Maritime University, School of Economics and Management, 1550 Haigang

Ave., Lingang New City, Shanghai, 201306, China, telephone/fax: +86 (0)21 3828 2480/+86

(0)21 3828 2409 (Email: [email protected]); Huei-ting Tsai, National Cheng-Kung

University, Department of Business Administration, 1 University Road, Tainan City, Taiwan, telephone/fax: +886 6 2757575/+886 6 2080179 (Email: [email protected]) ; Andreas

B. Eisingerich, Imperial College London, Imperial College Business School , London SW7

2AZ, United Kingdom, telephone/fax: +44 (0)20 7594 9763/+44 (0)2078237685 (Email: [email protected]).

1 Case-Based Asymmetric Modeling of Firms with High versus Low Outcomes in

Implementing Changes in Direction

ABSTRACT

The study builds on and extends prior work on the search scope and innovation performance of small and medium-sized enterprises. Specifically, this study explores combinational causes leading to high innovation performance for emerging market firms using fuzzy-set qualitative comparative analysis (fsQCA). By calibrating the data, constructing the truth table and producing the fsQCA results on the data of small and medium-sized enterprises from China, this study highlights the combination of several causes that the innovation performance of firms depends on. The findings of this study reveal that the strong presence of R&D capability and firm size are necessary, while upward search scope is a sufficient condition for strong innovation performance. The article closes with implications for theory and practice and avenues for future work.

Keywords: Innovation performance, search scope, SMEs, emerging market firms, fsQCA

2 1. Introduction

Several studies demonstrate direct effects of antecedents to innovation performance of firms (Ahuja, Lampert, & Tandon, 2008; Crossan & Apaydin, 2010; Damanpour & Aravind,

2006). Ren, Eisingerich, and Tsai (2015) for instance find that inter-organizational relationships, including connections with downstream customers and upstream suppliers have a significant impact on innovation performance. Although Ren et al. (2015) stress the significant effects of inter-firm relationships on innovation performance; their results inevitably suffer from the limitations of multiple regression analysis (MRA) (Amstrong,

2012; Woodside, 2013). For example, Soyer and Hogarth (2012) suggest the underestimation of uncertainty in forecasting regression analyses because of various misleading illusions, such as regressions providing the best linear but unbiased estimations and complexity illusion

(Amstrong, 2012). Furthermore, MRA is a net-effect estimation of research approach which deals with symmetrical relationships when the use of algorithms (recipes) more accurately estimates the realities of asymmetrical relationships (Woodside, 2013).

In light of these limitations, there are calls to move beyond MRA to craft and test theory by using algorithms (Fiss, 2011; McClelland, 1998; Ragin, 2008; Woodside, 2013, 2014).

Qualitative comparative analysis (QCA) is grounded in set theory and is useful for analyzing asymmetrical complex causal relationship versus the analysis of net effects (Ragin, 2008;

Woodside, 2013). This study responds to the calls for the use of fuzzy-set qualitative comparative analysis (fsQCA) as Fiss (2011) and Woodside (2013, 2014) propose. The study employs fsQCA using Ren et al.’s (2015) dataset and illustrates how this set-theory technique

3 can supplement correlational techniques by offering a more holistic, combinatorial view

(Skarmeas, Leonidou, & Saridakis, 2014) to this particular study of the causal relationship between search scope and innovation performance of firms. As Huff and Huff (2000) convincingly argue, this is of particular importance in business contexts that are characterized by strategic change. Importantly, the findings show that the fsQCA method offers a more detailed picture and allows for rich insights that increase understanding of the complex causal relationships and the effects of causal recipes of high innovation performance.

This study contributes to the literature in two critical ways. First, the findings show the importance of understanding the complex configurations regarding the relationship between search scope and innovation performance of firms. Second, in terms of method, the study offers additional support for Ragin (2008) and Woodside’s (2013, 2014) findings that fsQCA is relevant in providing and shedding light on combinational causal relationships. The paper proceeds as follows. The data, method, findings, and limitations of Ren et al.’s (2015) analyses are summarized in the next section. The third section explores and discusses fsQCA.

The fourth section reports a re-analysis of Ren et al.’s (2015) data using fsQCA. The final section offers a discussion of implications for theory and practice as well as future research.

2. The revisit of search scope and innovation performance

2.1. Ren et al.’s (2015) data, method and findings

Ren et al. (2015) examine the associations between search scope, R&D capability, and innovation performance for firms from emerging markets. They highlight the important roles of inter-organizational relationships (see also Freeman, 1991; Pittaway et al., 2004; Powell &

Grodal, 2005; Tsai & Eisingerich, 2010; Wu, 2011), including connections with downstream

4 customers (Greer & Lei, 2012; Ngo & O'Cass, 2013) and upstream suppliers (Johnsen, 2009;

Subroto & Sivakumar, 2010), in influencing firms’ innovation performance. Although a large body of prior work studied the effects of inter-firm connections on firm innovativeness and innovation performance, the results of prior studies on the links between search scope, R&D capability, and innovation performance were still inconclusive. Ren et al. (2015) therefore sought to shed additional light on the question as to whether firms from emerging markets such as China are more likely to benefit from greater innovation performance when they work with a selected few firms or a broader base of exchange partners, such as suppliers and customers. Put differently, does reliance on a limited number of customers and/or suppliers hinder or facilitate the innovation of emerging-market firms?

Ren et al. (2015) used a sample of 176 Chinese listed SMEs and longitudinal panel data. By employing MRA, they estimated the GEE models and the fixed effects of linear panel data regression models. The dependent variable is firm innovation performance measured by the firms’ yearly total patent application; the independent variables are R&D capability measured by the firms’ yearly research and development expenditure, upward search scope measured as the purchasing from top five suppliers as a proportion of the firms’ total purchasing cost, and downward search scope measured as sales to the top five customers as a proportion of the firms’ total sales. Finally, the control variables include firm size measured by firm total assets and profit. Ren et al.’s (2015) results show that upward and downward search scope along the supply chain strengthens the positive effect of R&D capability on the innovation performance of emerging-market firms (see Figure 1).

Furthermore, search scope along the supply chain has a positive moderating effect on

5 innovation performance. While Ren et al.’s (2015) contributes to the innovation literature by enhancing our understanding of the role of search scope along the supply chain on the relationship between R&D capability and innovation performance for SMEs in emerging markets, its findings also suffer from a number of limitations.

2.2. Ren et al.’s (2015) limitations

Ren et al. (2015) conducted a series of tests to examine the robustness of their findings. First, Ren et al. (2015) examine the sensitivity to changes in their models by estimating the random effect model and the pooled data models. They examine the possibility of reverse causality by reversing the models and examining the results thereof. In addition to this, Ren et al. (2015) performed a cross-validation test with holdout samples to address the previously noted limitations of regression analyses (Armstrong, 2012). However, even with these efforts and additional tests, the limitations of MRA cannot be avoided completely. Ragin

(2008) discusses and summarizes the critical problems of a net-effects approach as follows.

First, the net effects of MRA are dependent upon model specifications, which means results can be powerfully swayed by correlations between different variables, including competing variables (Ragin, 2008). Second, MRA aims to research symmetric relationships instead of asymmetric relationships. The objective of net-effects analysis is centered on the task of estimating context independent net-effects, whereas MRA is unable to assess the consequences of different combinations of causal effects effectively. Woodside (2013) eloquently underscored the importance of moving beyond studying simple symmetric relationships and moving towards shedding light on context independent occurring net- effects. As Woodside (2013) notes “… reality usually includes more than one combination of

6 conditions that lead to an outcome” and “many relationships among a dependent variable and independent variable are not linear and not well described by correlation coefficients.” Ragin

(2008, p. 182) concludes that the net-effects of MRA approach is particularly weak when used to study combinations of case characteristics, especially when dealing with overlapping inequalities. To avoid the above limitations of MRA, this study attempts to conduct an analysis by fsQCA on the associations that Ren et al. (2015) propose and show how this asymmetric analysis technique can provide more detailed results and deeper understanding of the effects of search scope on innovation performance.

Figure 1 about here.

3. Overview of the fsQCA technique

QCA was developed originally for the analysis of configurations of crisp set memberships (i.e., conventional Boolean sets) (Ragin, 1987, 2000, 2009a). Fuzzy sets extend crisp sets by permitting membership scores in the interval between 0 and 1 based on fuzzy-set theory (Zadeh, 1965). In general, fsQCA is an analysis of set relationships. A set can be a group of elements or a group of values (Skarmeas, Leonidou, & Saridakis, 2014). In a fuzzy- set analysis, both the outcome and the causal conditions are represented by using fuzzy sets

(Ragin, 2009a).

Researchers apply QCA primarily in political science and sociology researchers (e.g.,

Amenta, Carruthers, & Zylan, 1992; Amenta & Halfmann, 2000; Blake & Adolino, 2001;

Cress & Snow, 1996; Kiser, Drass, & Brustein, 1995; Redding & Viterna, 1999; Vis, 2011).

7 Management scholars call for the application of this methodology (Fiss, 2011; Woodside,

2013, 2014). Some researchers apply QCA in the fields of organization science

(Fiss,2007,2011; Greckhamer et al., 2008), marketing (Chang, Tseng, & Woodside, 2013;

Woodside, & Zhang, 2012, 2013; Woodside, 2013b), innovation (Cheng, Chang,& Li, 2013;

Ganter & Hecker, 2014; Meuer, 2014; Stanko & Olleros, 2013; Ordanini, Parasuraman, &

Rubera,2014) and corporate social responsibility (Crilly, Zollo, & Hansen, 2012; Skarmeas,

Leonidou,& Saridakis, 2014), among others. These studies show the usefulness of fsQCA.

Briefly, the standard procedure of fsQCA includes the following main steps (see for more details from Ragin, 2008). The first step is to create a data set with fuzzy-set membership scores. In this step of calibration of fuzzy membership scores, the key is to determine the three qualitative anchors: full membership, full non-membership, and the crossover point. The second step is to select a preliminary list of causal conditions. In general, the number of causal conditions should be modest, in the range of three to eight. The third step is to create a so-called truth table by specifying the outcome and the causal conditions.

Researchers then select a frequency threshold to apply to the data listed in the number column. This procedure is followed by selecting a consistency threshold for distinguishing causal combinations that are subsets of the outcome from those that are not. The next step is to input 1s and 0s into the empty outcome column, which is labeled with the name of the outcome and listed to the left of the consistency column. Using the threshold value selected in the previous step, researchers can enter a value of 1 when the consistency value meets or exceeds the consistency threshold and 0 otherwise. Finally, to produce the results, three solutions are offered: the complex, the parsimonious, and the intermediate solutions. Several

8 programs can execute this analysis: fs/QCA, Kirq, Tosmana, R packages QCA and QCA3,

Stata package fuzzy. This study uses fsQCA software (Ragin, 2009b) to re-analyze Ren et al.’s

(2015) data.

4. Applying fsQCA to Ren et al.’s (2015) data

The present study revisits the same data as in Ren et al. (2015), which is firm-level data collected from several sources. The sample is drawn from the Chinese stock market. The sample consists of 176 SMEs and the data consists of an unbalanced panel with 1074 firm- year observations. The panel data are transformed into cross-section data by using the average of the variables for each firm. Because of missing data some firms have to be dropped from the sample and the final dataset consists of observations for 166 firms.

4.1. Data calibration

Fuzzy-set theory is a well-developed mathematical tool for addressing partial membership in sets (Ragin,2008, 2009a; Zadeh, 1965).Well-constructed fuzzy sets, including the outcome and causal conditions represented in terms of membership scores, are the key to successful fuzzy set analysis (Ragin, 2008). Degree of set membership in a fuzzy-set can range from a score of 0.0 (full exclusion from a set) to 1.0 (full inclusion). This advantage makes fuzzy sets bridge quantitative and qualitative approaches to measurement because they are simultaneously qualitative and quantitative.

The calibration of fuzzy membership scores must be based on the knowledge of what constitutes full membership (1.0), full non-membership (0.0), and the point at which cases are

9 more in a given set than out (Ragin, 2000). An fsQCA without careful calibration of set membership is a futile exercise (Ragin, 2009a). The variables of this study are calibrated by direct method proposed by (Ragin, 2008) to specify the values of an interval scale that corresponds to the three qualitative breakpoints structuring a fuzzy set: full membership, full non-membership, and the crossover point. These three benchmarks are then used to transform the original interval-scale values to fuzzy membership scores (Ragin.2009a). Calibration values at 95%, 50% and 5% of the variables in this study are listed in the Table 1. The conventional variables are converted into fuzzy membership scores by using the calibrating function of fsQCA software and following the procedure detailed in Ragin (2008). Table 2 shows the summary of calibrated variables.

Tables 1 and 2 here.

4.2. Constructing the truth table

The advantage of fsQCA is its configurational thinking by focusing on causal complexity.

Causal complexity is defined as a situation in which a given outcome may follow from several different combinations of causal conditions—from various causal “recipes” (Ragin,

2008, p. 124). The key tool for analyzing causal complexity of using fsQCA is the truth table, which allows structured and focused comparisons (Ragin, 2008; George 1979). Truth tables list the logically possible combinations of causal conditions and the empirical outcome associated with each causal recipes (Ragin, 2008).

Constructing a truth table from continuous fuzzy set membership scores involves a

10 two-step analytic procedure (Ragin, 2008; also see for more detail in the fsQCA manual, p.

78). The first step consists of creating a truth table spreadsheet from fuzzy set data, which primarily involves specifying the outcome and causal conditions to include in the analysis

(fsQCA manual). In this step, the number of rows in the truth table equals to the number of possible configurations of causal conditions (Ragin, 2008b). It is a multidimensional property space with 2k corners, where k is the number of drivers of an outcome (Ragin, 2009a). In this study, we primarily investigate four causal conditions, which are firm size, R&D capability, a firm’s upward search scope and downward search scope, so the initial truth table has 24 (16) rows representing all possible combinations of causal conditions. The second step consists of preparing the truth table for analysis, by selecting both a frequency threshold and a consistency threshold (fsQCA manual, 2008, p. 78). A frequency threshold (i.e., a number-of- cases threshold) for estimating which configurations of conditions are relevant based on the number of cases with greater than 0.5 membership in each configuration (Ragin, 2009a).

Following the procedure detailed above, configurations of binary states of variables in this study are listed in the Table 3. Table 4 shows the truth table. This study specifies the frequency threshold as 3 for analysis of each group, capturing 100% of the cases in the study which is above Ragin's (Ragin, 2008). The consistency threshold employed in this study is

Tables 3 and 4 here.

4.3. Findings

11 The fsQCA program produces three solutions: complex solutions, parsimonious solutions and intermediate solutions. In general, intermediate solutions are superior to other solutions in that they do not allow removal of necessary conditions (Ragin, 2009a). Complex solutions are advised to be presented because this type of solution makes no simplified assumptions (Elliott, 2013; Skarmeas, Leonidou, & Saridakis, 2014).

The derived three types of solutions illustrating the alternative causal recipes (i.e., sufficient conditions) that lead to high membership in the outcome condition are summarized in the Table 5. In this case, when the frequency threshold is 3 cases (keep 100% cases) and the consistency cutoff is 0.8, the three types of solutions are identical. These three causal recipes are sufficient conditions leading to high innovation performance (Ragin, 2009a; Woodside,

2014). The XY-plot of the results can be seen in Figure 2.

The complex solutions suggest three configurations of antecedent conditions lead to high innovation performance: ~topsup_cal*lnta_cal, topcus_cal*~topsup_cal*lnrd_cal,

~topcus_cal*lnrd_cal*lnta_cal (where ~ represents the negation of the fuzzy set condition and the star * signs represent the operation of the logical AND on the fuzzy set). The coverage of the complex solutions is 0.692, and the consistency of the complex solutions, also solution consistency, is 0.754. The raw coverage and consistency of each causal recipe is also reported in the Table 5. This solution is fairly consistent, which explains a satisfactory amount of cases with high innovation performance.

The coverage and consistency indices for each configuration and for the solution as a whole show the significance of the solutions. Consistency measures the degree to which configurations are subsets of the outcome (Ragin, 2008). High consistency manifests that a

12 subset relation exists and favors a requirement of sufficiency (Ragin, 2008). In general, the consistency values exceed 0.75 is expected (Ragin, 2006). Table 5 shows that all consistency values in the solutions exceed 0.75, indicating that these configurations are sufficient conditions causing high product innovation performance.

Raw coverage and solution coverage measure the extent to which the configurations account for the outcome (Ragin, 2008). Calculating coverage only after ensuring that a set relation is consistent is reasonable (Ragin, 2006, 2008). All of the raw and solution coverage values in Table 5 are above 45% (except 37 percent of raw coverage of one solution), indicating that the configurations explain a large proportion of product innovation performance.

Table 5 here.

Figure 2 here.

5. Discussion and conclusion

5.1. Summary and contributions The primary results of the fsQCA solutions to Ren et al.’s (2015) data (~topsup_cal*lnta_cal, topcus_cal*~topsup_cal*lnrd_cal, ~topcus_cal*lnrd_cal*lnta_cal) are three causal recipes indicating high innovation performance of SMEs: (1) a firm’s wide upward search scope and large firm size; (2) a firm’s wide downward search scope, large firm size and strong R&D capability coinstantaneous; (3) a firm’s wide upward search scope, strong R&D capability, and narrow downward search scope simultaneous.

Except configuration (1), effects of the other two configurations are distinctive findings which run counter to a priori theory. These findings support Ren et al.’s (2015)

13 findings in part in that a firm’s wide upward search scope with large firm size, and a firms’ wide downward search scope with firm size and strong R&D capability associate positively to innovation performance. However, these results also show the surprising details of Ren et al.’s

(2015) that a firm’s wide upward search scope and narrow downward search scope associate positively to innovation performance when a firm’s R&D capability are strong.

This study furthers the investigation of high innovation performance by resetting the fsQCA frequency threshold as 11cases (keep 81% cases) and keeping the consistency cutoff as 0.80 in the truth table. The derived another three types of solutions are also identical (see

Table 6). The complex solutions suggest two configurations of antecedent conditions lead to high innovation performance: “~topsup_cal*lnrd_cal*lnta_cal” (consistency = 0.80; coverage

= 0.52), and “~topcus_cal*lnrd_cal*lnta_cal” (consistency = 0.78; coverage = 0.46). The coverage of the complex solutions is 0.606, and the consistency of the complex solutions is

0.776. Thus, these two combined antecedent conditions are necessary and their combination is sufficient for high innovation performance. These results show two paths lead to high innovation performance. One path is the combination of a firm’s wide upward search scope, strong R&D capability and large size. The other path is the combination of a firm’s wide downward search scope, strong R&D capability and large size.

Table 6 here.

This study also examines the fsQCA of the negation of innovation performance outcome (low innovation performance). By setting the frequency threshold as 3 cases (keep

14 100% cases) and the consistency cutoff as 0.8, three types of solutions are also reported identical (see Table 7 and Figure 3). In the complex solutions, there are three causal recipes which are regarded as sufficient conditions leading to low innovation performance: ~lnta_cal

(consistency = 0.79; coverage = 0.74), topcus_cal*~lnrd_cal (consistency = 0.86; coverage =

0.45), topsup_cal*~lnrd_cal (consistency = 0.91; coverage = 0.52). The coverage of the complex solutions is 0.796 and the consistency of the complex solutions is 0.790. Thus, these three combined antecedent conditions are necessary and their combination is sufficient for low innovation performance. These results show three paths leading to low innovation performance. One path is the firm with smaller size. The other path is the combination of a firm’s narrow upward search scope and weak R&D capability. The third path is the combination of a firm’s narrow downward search scope and weak R&D capability. These paths are mostly in accordance with the paths leading to high innovation performance.

Table 7 here and Figure 3 here.

5.2. Conclusion

This study re-examines Ren et al.’s (2015) research question about the association between search scope and innovation performance of SMEs by employing the fsQCA method.

In line with the findings of Ren et al. (2015), the findings here show that strong R&D capability, and firms size are necessary, and upward search scope is sufficient condition for the high presence of innovation performance. Beyond this, this study provides a more detailed picture of the combined antecedent conditions affecting the innovation performance of SMEs.

This study contributes to the literature in two noteworthy aspects. First, from a

15 methodological perspective, this study demonstrates the usefulness and importance of fsQCA in identifying casual configurations to achieve a specific outcome (Cheng et al., 2013;

Skarmeas et al., 2014). The study also shows that fsQCA is a valuable asymmetrical analytical method that researchers can use in conjunction with other symmetrical analytical techniques

(e.g., MRA). In doing so, researchers are able to develop thorough explanations of how cause recipes affect an outcome (Ragin, 2008; Stanko & Olleros, 2013). This is of particular importance in business contexts that are faced with change (Huff & Huff, 2000). Thus, fsQCA is an effective complementary analytical technique that advances the knowledge on the innovation performance.

Second, this study unearths additional explanations for Ren et al.’s (2015) findings.

The findings here reveal a few causal configurations for achieving high innovation performance. These explanations go beyond the traditional MRA net effects of exploration.

For example, R&D capability, which is taken as an antecedent of innovation performance independently for granted, needs to appear with wide downward or upward search scope together to unveil high innovation performance accurately.

The managerial implications of this study go beyond the implications that Ren et al.

(2015) offer. Ren et al. (2015) based their findings on multiple regression analysis and suggest that SMEs should never cease searching broadly along the supply chain. The study here supports the suggestion that SMEs should consider the joint effects of R&D, search scope, and firm size. For instance, to have high presence of innovation performance, wide upward search scope should be together with large firm size while wide downward search scope should be together with R&D capability and large firm size. The implication of this

16 study for innovation researchers is that, research on the antecedents of innovation performance should examine combinations of causes of the innovation performance by employing new algorithms (e.g., fsQCA) (Woodside, 2013). Fuzzy-set qualitative comparative analysis offers a powerful tool to test and craft theory. Researchers are often reluctant to acquire and employ new methodologies and ways of analyzing data that they are unfamiliar with. This study may encourage researchers to take advantages of some of the new research tools available. Moving beyond the sole reliance on multiple regression analysis helps to challenge some of the existing assumptions, shed additional light on observed effects, and offers new insights in effective management practice.

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22 Table 1. Summary of variables and calibration values

Variable Mean Std. Dev. Minimum Maximum N Cases Missing Median Calibration values at 95% 50% 5% rdint 0.06 0.03 0 0.24 166 0 0.05 0.09 0.05 0.02 totpat 12.57 23.85 0 213 166 0 5.3 30 5.3 1 topcus 0.38 0.20 0.02 0.99 166 0 0.36 0.6 0.36 0.15 topsup 0.43 0.18 0.14 0.89 166 0 0.40 0.7 0.40 0.2 lnrd 7.36 0.85 5.02 9.69 166 0 7.25 8.6 7.25 6.2 lnta 20.10 0.71 18.43 22.79 166 0 20.04 21.2 20.04 19.2 Note. Acronyms of variables mean as followings: rdint: R&D intensity; totpat: innovation performance; lnta: firm size; lnrd: R&D capability; topcus: downward search scope; topsup: upward search scope.

23 Table 2. Summary of variables (Fuzzy_set scores)

Variable Mean Std. Dev. Min Max rdint_cal totpat_cal topcus_cal topsup_cal lnrd_cal lnta_cal rdint_cal 0.51 0.31 0.01 1 1 totpat_cal 0.45 0.33 0.02 1 -0.06 1 topcus_cal 0.49 0.36 0.01 1 0.06 -0.07 1 topsup_cal 0.49 0.33 0.02 0.99 -0.00 -0.34* 0.08 1 lnrd_cal 0.51 0.32 0 1 0.25* 0.39* 0.01 -0.15 1 lnta_cal 0.49 0.32 0 1 -0.26* 0.47* -0.03 -0.18* 0.72* 1 Note. Number of observations=166. _cal is the variable name after calibrated.

24 Table 3. Configurations of binary states of variables

topcus_cal topsup_cal lnrd_cal lnta_cal Number of cases %     22 13%     20 26%     18 37%     18 48%     17 59%     12 66%     12 74%     11 81%     6 85%     4 87%     4 90%     4 92%     3 94%     3 96%     3 98%     3 100% 160 100% Note. =attribute absent, =attribute present.

25 Table 4. Truth table topcus_cal topsup_ca lnrd_c lnta_cal number totpat_ca raw consist. PRI consist. SYM l al l consist 0 0 1 1 22(13%) 0.815039 0.655765 0.666122 1 1 1 1 20(26%) 0.768313 0.495671 0.509266 1 0 0 0 18(37%) 0.726600 0.307818 0.318182 0 1 0 0 18(48%) 0.610812 0.153370 0.154006 1 1 0 0 17(59%) 0.592069 0.120610 0.123641 1 0 1 1 12(66%) 0.832468 0.620029 0.647792 0 1 1 1 12(74%) 0.803135 0.522264 0.531634 0 0 0 0 11(81%) 0.757355 0.389351 0.410526 0 0 0 1 6(85%) 0.857324 0.601415 0.619684 1 1 1 0 4(87%) 0.692307 0.175302 0.175302 1 0 1 0 4(90%) 0.803159 0.416567 0.416567 0 0 1 0 4(92%) 0.791651 0.454546 0.457819 1 1 0 1 3(94%) 0.776978 0.198275 0.198275 1 0 0 1 3(96%) 0.833632 0.395766 0.400329 0 1 1 0 3(98%) 0.767523 0.301047 0.302234 0 1 0 1 3(100%) 0.779037 0.328551 0.331403

26 Table 5. Three types of fsQCA solutions (1)

Table 5a Complex solution COMPLEX SOLUTION frequency cutoff: 3.00 consistency cutoff: 0.80 Raw Unique consisten coverage coverage cy ~topsup_cal*lnta_cal 0.58 0.06 0.79 topcus_cal*~topsup_cal*lnrd_c 0.37 0.03 0.79 al ~topcus_cal*lnrd_cal*lnta_cal 0.46 0.08 0.78 solution coverage: 0.69 solution consistency: 0.75

Table 5b Parsimonious solution PARSIMONIOUS SOLUTION frequency cutoff: 3.00 consistency cutoff: 0.80 Raw Unique consisten coverage coverage cy ~topsup_cal*lnta_cal 0.58 0.06 0.79 topcus_cal*~topsup_cal*lnrd_c 0.37 0.03 0.79 al ~topcus_cal*lnrd_cal*lnta_cal 0.46 0.08 0.78 solution coverage: 0.69 solution consistency: 0.75

Table 5c Intermediate solution INTERMEDIATE SOLUTION frequency cutoff: 3.00 consistency cutoff: 0.80 Assumptions: lnta_cal (present) lnrd_cal (present) topsup_cal (present) topcus_cal (present) Raw Unique consisten coverage coverage cy lnta_cal*~topsup_cal 0.58 0.06 0.79 lnta_cal*lnrd_cal*~topcus_cal 0.46 0.08 0.78 lnrd_cal*~topsup_cal*topcus_c 0.37 0.03 0.79 al

27 solution coverage: 0.69 solution consistency: 0.75

Note: Model: totpat_cal=f(topcus_cal, topsup_cal, lnrd_cal, lnta_cal). Frequency threshold=3, consistency cutoff=0.80.

28 Table 6. fsQCA solutions (2)

Table 6a Complex solution COMPLEX SOLUTION frequency cutoff: 11.00 consistency cutoff: 0.80 Raw coverage Unique coverage consistency ~topsup_cal*lnrd_cal*lnta_cal 0.52 0.14 0.80 ~topcus_cal*lnrd_cal*lnta_cal 0.46 0.08 0.78 solution coverage: 0.61 solution consistency: 0.78

Table 6b Intermediate solution INTERMEDIATE SOLUTION frequency cutoff: 11.00 consistency cutoff: 0.80 Assumptions: lnta_cal (present) lnrd_cal (present) topsup_cal (present) topcus_cal (present) Raw coverage Unique coverage consistency lnta_cal*lnrd_cal*~topcus_cal 0.46 0.08 0.78 lnta_cal*lnrd_cal*~topsup_cal 0.52 0.14 0.80 solution coverage: 0.61 solution consistency: 0.78

Note: Model: totpat_cal=f(topcus_cal, topsup_cal, lnrd_cal, lnta_cal). Frequency threshold=11, consistency cutoff=0.80.

29 Table 7 fsQCA solutions (3)

Table 7a Complex solution COMPLEX SOLUTION frequency cutoff: 3.00 consistency cutoff: 0.82 Raw coverage Unique coverage consistency ~lnta_cal 0.74 0.14 0.80 topcus_cal*~lnrd_cal 0.45 0.01 0.86 topsup_cal*~lnrd_cal 0.52 0.03 0.91 solution coverage: 0.80 solution consistency: 0.79

Table 7b Intermediate solution INTERMEDIATE SOLUTION frequency cutoff: 3.00 consistency cutoff: 0.80 Assumptions: lnta_cal (present) lnrd_cal (present) topsup_cal (present) topcus_cal (present) Raw coverage Unique coverage consistency ~lnta_cal 0.74 0.17 0.79 ~lnrd_cal*topsup_cal 0.52 0.03 0.91 ~lnrd_cal*topcus_cal 0.45 0.01 0.86 solution coverage: 0.80 solution consistency: 0.79

Note: Model: ~totpat_cal=f(topcus_cal, topsup_cal, lnrd_cal, lnta_cal) Frequency threshold=3, consistency cutoff=0.80

30 Figure 1 Asymmetric Modeling of the Influence of Complex Antecedent Conditions Notes. Key: “m” = modification. Arrows indicate highest consistency paths. Asymmetric modeling includes constructing usually 2+ unique models for both firms with high versus firms with low innovation performances

31 Figure 2a: High innovation performance by ~topsup_cal*lnta_cal

Figure 2 Fuzzy-set plots for fsQCA solutions (1)

32 Figure 2b: High innovation performance by topcus_cal*~topsup_cal*lnrd_cal

33 Figure 2c: High innovation performance by ~topcus_cal*lnrd_cal*lnta_cal

Figure 3a: Low innovation performance by ~lnta_cal

35 Figure 3b: Low innovation performance by ~lnrd_cal*topsup_cal

36 Figure 3c: Low innovation performance by ~lnrd_cal*topcus_cal