This paper uses the data of China’s venture capital industry in the CVSource and Zero2IPO databases from 1999 to 2018 as a research sample. By using UCINET software to build the entire network of venture capital industry for social network analysis, I calculate the group tie density based on network interaction, status heterogeneity and faults based on network centrality, to analyse whether those group network characteristics affect the complementarity effect. Based on this, I use probit model regression test to carry on an examination.

#### Keywords

- complementarity
- network status heterogeneity
- network status-based faults
- group tie density

#### MSC 2010

- 03C30

In recent years, an increasing number of interorganisational networks have developed, from a simple bilateral relationship to multilateral consociations that involve many parties [1]. Since a multilateral alliance involves multiple organisations, it shows more complexity and differences in its dynamics than bilateral alliances [2], such as group differences and cooperation complexity [1, 3,4,5].

A multiparty alliance has a unique nature. First, a multilateral alliance includes other members outside the bilateral relationship, and the organisation considers cooperation with several partners at the same time and adjusts its behaviour accordingly. Second, unlike the bilateral perspective, the multilateral perspective includes group-level constructs, such as the overall density of the network tie among members and the structural differences among groups [5,6]. The industry network between members affects each other’s interactions, so that the complementarity effect between members is affected by the group-level network feature. Although different researchers have different perspectives on the division of social network dimensions, their division criteria are mainly based on the two aspects of structural and relational dimensions, according to Tichy et al. [7] Therefore, this paper attempts to consider how the group tie density (calculated by network interaction) and the network status-based difference (based on the structural centrality) enhance or weaken the impact of complementarity. Group tie density refers to the degree of repeated linkages among members of a multilateral alliance. Network tie leads to social capital, such as trust, reciprocity and social identity, affecting communication between members [8,9,10]. In addition, this paper examines the role of network structural difference for the complementarity effect based on network centrality. The status-based difference of members refers to whether there is a difference between members’ positions in the industry network, which is divided into status heterogeneity and status-based faults.

This paper uses China’s venture capital industry as a data sample to analyse the complementarity effect, as well as to calculate and analyse the boundary conditions of group tie density, network status heterogeneity and status-based faults. Improving on the shortcomings of previous studies, this paper attempts to solve two key research questions: first, how complementarity between members affects the performance of multilateral cooperation; second, on the group level, whether members’ tie density and network status-based difference enhance or undermine the positive impact of the complementarity effect.

I argue that greater complementarity increases the breadth of the knowledge and information pool of the entire group, which facilitates correct decision-making and improves the effectiveness of alliance management [11,12,13].

Group tie density refers to the number of duplicate connections in a group divided by all possible binary connections in the group [14]. The junction density aggregates the degree of association duplication in all bilateral relationships. Therefore, the group tie density improves the communication and coordination among members, which facilitates the flow and utilisation of complementary resources, as well as reduces the opportunistic behaviour.

Status represents an organisation’s position relative to other organisations throughout the industry network [15, 16]. In a multiparty alliance, there are two different types of status-based differences, which are status heterogeneity and status-based fault. Status heterogeneity refers to the different levels of network centrality among multiple members. Status-based fault refers to the degree of subgroups formed by multiple members based on their network centrality.

Network status heterogeneity leads to decreases in motivation and ability to share complementary resources among members, thereby reducing the advantages of the complementarity effect. Therefore, when there is network status heterogeneity, it weakens the advantage of complementarity.

The concept of faults is mostly seen in studies of the individual team level, which focus on the similarity within the team and the differences between groups. Network status-based faults lead to a lack of trust between subgroups and can weaken the interactions among subgroup members [6]. Therefore, due to the positional fault, the degree of sharing and utilisation of complementary resources between subgroups is reduced.

This paper uses China’s venture capital industry as an empirical scenario, using data from two major venture capital data providers, CVSource and Zero2IPO [17, 18]. Both CVSource and Zero2IPO are China’s leading research institutions, which contain the entire range of data from China’s venture capital industry. This paper combines the information from the two databases to obtain the most comprehensive data coverage and industry data for the period 1999–2018. Although the first international venture capital firm entered China in the early 1980s, China’s venture capital field did not develop until the late 1990s. Therefore, this paper uses 1 January 1999 as the starting point of the sample and 31 December 2014 as the end point, so that I can leave the 4-year window period up to 31 December 2018, to better evaluate performance. Since most Chinese venture capital firms were set up after 2000, left censoring is not a serious problem.

_{x} and _{y} are, respectively, the investment phase vectors of a pair of institutions _{k} is the number of all possible bilateral associations. Complementarity is a continuous variable between the values “0” and “1”; higher values indicate greater complementarity [19].

_{i,t} = ∑_{j}(_{ij})_{ijt} − 1, where _{i,t} is the centrality of member _{ijt} − 1 refers to the common investment matrix, _{ijt} − 1 [16,20]. Referring to Zhang et al. (2017) [5], I first calculate the similarity of each pair of bilateral positions, i.e., I divide the smaller party by the larger one and then calculate the group level by subtracting the mean of all bilateral similarities.

I control the group-level variables that affect group performance. First, I control the variables associated with the group’s activity; as the study sample is from the venture capital industry, the variables include factors such as investment activity uncertainty and whether there are multiple rounds of investment. Among them, the factor

Given the binary classification characteristics of the dependent variable, in this paper, I use the probit model to estimate the investment exit tendency, which refers to multilateral interorganisational performance: _{i} includes all control variables I mentioned above.

Table 1 is the descriptive statistics table, and Table 2 contains the correlation analysis of key variables in this paper. The sample of this paper is a multiparty investment alliance in the venture capital industry from 1999 to 2018. Since the network centrality needs to be calculated in the backward 5-year window, the performance of this paper needs to move forward 4 years. The number of observations is 651 multiparty groups from 2004 to 2014. Overall, the average performance of this group is 0.276, which means that about 27% of the investment has successfully exited through initial public offerings in 4 years [25]. The correlation coefficient between each variable is <0.65, which indicates that the multi-collinearity problem is not large, and the reliability of subsequent regression results can be basically guaranteed. In addition, the correlation coefficient between each control variable and Performance also shows that the control variables are effective.

Descriptive statistics

1 | Performance | 0.276 | 0.448 | 0 | 1 |

2 | Complementarity | 0.729 | 0.094 | 0.667 | 0.978 |

3 | Group tie density | 0.092 | 0.191 | 0 | 1 |

4 | Network status heterogeneity | 0.576 | 0.170 | 0 | 0.914 |

5 | Network status-based fault | 0.240 | 0.101 | 0 | 0.563 |

6 | Stage | 3.095 | 0.686 | 1 | 4 |

7 | Size | 3.641 | 1.109 | 3 | 10 |

8 | Unsingle | 0.656 | 0.475 | 0 | 1 |

9 | Resource | 10.40 | 11.34 | 0 | 70 |

10 | Age | 5.779 | 8.120 | 0 | 53 |

11 | Proportion of foreign members | 0.246 | 0.300 | 0 | 1 |

12 | Average geographical proximity | 0.279 | 0.300 | 0 | 1 |

Correlation analysis

1 | Performance | 1 | |||||||||||

2 | Complementarity | 0.132^{*} | 1 | ||||||||||

3 | Group tie density | 0.03 | 0.012 | 1 | |||||||||

4 | Network status heterogeneity | −0.010^{*} | 0.043 | 0.037 | 1 | ||||||||

5 | Network status-based fault | −0.186^{*} | −0.002 | 0.004 | 0.134^{*} | 1 | |||||||

6 | Stage | −0.011 | 0.091^{*} | −0.182^{*} | 0.028 | −0.054 | 1 | ||||||

7 | Size | 0.085^{*} | 0.524^{*} | −0.008 | 0.025 | −0.016 | 0.105^{*} | 1 | |||||

8 | Unsingle | −0.037 | 0.035 | 0.154^{*} | −0.033 | 0.076^{*} | −0.111^{*} | 0.074 | 1 | ||||

9 | Resource | −0.069 | 0.196^{*} | 0.115^{*} | 0.096^{*} | 0.019 | −0.03 | 0.190^{*} | −0.017 | 1 | |||

11 | Age | −0.092^{*} | −0.051 | 0.168^{*} | 0.089^{*} | −0.014 | −0.221^{*} | −0.089^{*} | 0.087^{*} | 0.538^{*} | 1 | ||

12 | Proportion of foreign members | −0.019 | −0.003 | 0.250^{*} | 0.025 | −0.03 | −0.268^{*} | −0.06 | 0.057 | −0.009 | 0.190^{*} | 1 | |

13 | Average geographical proximity | 0.023 | −0.083^{*} | −0.073 | −0.057 | 0.007 | 0.009 | −0.124^{*} | −0.009 | −0.062 | −0.046 | −0.232^{*} | 1 |

Indicates significant levels at 10%.

In order to ensure the consistency and validity of the model estimation, the data is processed as follows. First, to avoid the influence of outliers, the main continuous variables are subjected to tailing processing at the 1% level. Second, I standardise the main variables. Third, to overcome the effect of multi-collinearity, I centralise the interaction term variables. The variance inflation factor (VIF) diagnosis for all explanatory variables and control variables is <3, so I can eliminate the multi-collinearity problem.

Model 2 in Table 3 reports the results of testing for complementarity and joint investment performance. The coefficient of complementarity (

Probit regression results

Complementarity | 0.552^{***} (3.322) | 0.555^{***} (3.192) | 0.568^{***} (3.309) | 0.551^{***} (3.310) | 0.578^{***} (3.223) | |

Group tie density Complementarity | 0.476^{***} (4.215) | 0.513^{***} (4.496) | ||||

Network status heterogeneity Complementarity | −0.278^{***} (−2.824) | −0.331^{***} (−3.176) | ||||

Network status-based heterogeneity | −0.007 (−0.065) | −0.029 (−0.233) | ||||

Group tie density | 0.784 (1.501) | 0.753 (1.426) | 0.853 (1.372) | 0.707 (1.330) | 0.754 (1.427) | 0.880 (1.409) |

Network status heterogeneity | −0.756 (−1.417) | −0.835 (−1.537) | −0.806 (−1.466) | −0.871 (−1.567) | −0.836 (−1.538) | −0.936 (−1.637) |

Network status-based heterogeneity | −4.925^{***} (−4.623) | −5.215^{***} (−4.775) | −5.534^{***} (−4.966) | −5.394^{***} (−4.875) | −5.216^{***} (−4.777) | −5.820^{***} (−5.099) |

Stage | 0.482^{***} (4.053) | 0.722^{***} (4.025) | 0.801^{***} (4.021) | 0.792^{***} (4.019) | 0.759^{***} (4.006) | 0.901^{***} (4.009) |

Size | 0.210^{**} (2.371) | −0.187 (−1.221) | −0.209 (−1.261) | −0.207 (−1.284) | −0.188 (−1.222) | −0.239 (−1.409) |

Unsingle | −0.250 (−1.208) | −0.217 (−1.030) | −0.274 (−1.288) | −0.175 (−0.826) | −0.216 (−1.026) | −0.227 (−1.061) |

Resource | 0.000 (0.011) | −0.002 (−0.074) | −0.001 (−0.047) | −0.004 (−0.181) | −0.002 (−0.075) | −0.004 (−0.194) |

Age | −0.003 (−1.351) | −0.003 (−1.537) | −0.004^{*} (−1.669) | −0.003 (−1.595) | −0.003 (−1.537) | −0.004^{*} (−1.787) |

Proportion of foreign members | −0.572 (−1.449) | −0.720^{*} (−1.792) | −0.875^{**} (−2.102) | −0.727^{*} (−1.803) | −0.719^{*} (−1.790) | −0.883^{**} (−2.109) |

Average geographical proximity | 0.114 (0.345) | 0.034 (0.103) | 0.058 (0.171) | 0.029 (0.086) | 0.033 (0.099) | 0.057 (0.166) |

Industry | Yes | Yes | Yes | Yes | Yes | Yes |

Intercept | 1.970^{**} (2.335) | 3.753^{***} (3.667) | 3.971^{***} (3.756) | 3.942^{***} (3.729) | 3.755^{***} (3.665) | 4.291^{***} (3.926) |

N | 651 | 651 | 651 | 651 | 651 | 651 |

This paper constructs a theoretical analysis model of complementarity and performance of a multilateral alliance, and then puts forward a few research hypotheses. Based on the investment data of China’s venture capital institutions from 1999 to 2018, I analyse the complementarity effect between members in multilateral alliances. Based on the social network theory, I calculate the network ties and network centrality at the industry network level and then explore (a) the group tie density based on relational embedding and (b) the status-based difference based on structural embedding.

The main conclusions are as follows. First, in a multiparty cooperation, the complementarity of members is conducive to group-level performance. Second, the density of network tie between group members strengthens the positive impact of complementarity. Third, network status heterogeneity between partners can undermine the positive impact of complementarity. The heterogeneity of network status increases the preferences and cognitive conflicts of the different investment institutions in the alliance, in addition to weakening the positive effects brought about by complementarity, which is not conducive to the improvement of multiparty cooperation performance. Network status-based fault is not a significant boundary condition for the resource’s complementarity effect.

#### Probit regression results

Complementarity | 0.552^{***} | 0.555^{***} | 0.568^{***} | 0.551^{***} | 0.578^{***} | |

Group tie density Complementarity | 0.476^{***} | 0.513^{***} | ||||

Network status heterogeneity Complementarity | −0.278^{***} | −0.331^{***} | ||||

Network status-based heterogeneity | −0.007 (−0.065) | −0.029 (−0.233) | ||||

Group tie density | 0.784 (1.501) | 0.753 (1.426) | 0.853 (1.372) | 0.707 (1.330) | 0.754 (1.427) | 0.880 (1.409) |

Network status heterogeneity | −0.756 (−1.417) | −0.835 (−1.537) | −0.806 (−1.466) | −0.871 (−1.567) | −0.836 (−1.538) | −0.936 (−1.637) |

Network status-based heterogeneity | −4.925^{***} | −5.215^{***} | −5.534^{***} | −5.394^{***} | −5.216^{***} | −5.820^{***} |

Stage | 0.482^{***} | 0.722^{***} | 0.801^{***} | 0.792^{***} | 0.759^{***} | 0.901^{***} |

Size | 0.210^{**} | −0.187 (−1.221) | −0.209 (−1.261) | −0.207 (−1.284) | −0.188 (−1.222) | −0.239 (−1.409) |

Unsingle | −0.250 (−1.208) | −0.217 (−1.030) | −0.274 (−1.288) | −0.175 (−0.826) | −0.216 (−1.026) | −0.227 (−1.061) |

Resource | 0.000 (0.011) | −0.002 (−0.074) | −0.001 (−0.047) | −0.004 (−0.181) | −0.002 (−0.075) | −0.004 (−0.194) |

Age | −0.003 (−1.351) | −0.003 (−1.537) | −0.004^{*} | −0.003 (−1.595) | −0.003 (−1.537) | −0.004^{*} |

Proportion of foreign members | −0.572 (−1.449) | −0.720^{*} | −0.875^{**} | −0.727^{*} | −0.719^{*} | −0.883^{**} |

Average geographical proximity | 0.114 (0.345) | 0.034 (0.103) | 0.058 (0.171) | 0.029 (0.086) | 0.033 (0.099) | 0.057 (0.166) |

Industry | Yes | Yes | Yes | Yes | Yes | Yes |

Intercept | 1.970^{**} | 3.753^{***} | 3.971^{***} | 3.942^{***} | 3.755^{***} | 4.291^{***} |

N | 651 | 651 | 651 | 651 | 651 | 651 |

#### Correlation analysis

1 | Performance | 1 | |||||||||||

2 | Complementarity | 0.132^{*} | 1 | ||||||||||

3 | Group tie density | 0.03 | 0.012 | 1 | |||||||||

4 | Network status heterogeneity | −0.010^{*} | 0.043 | 0.037 | 1 | ||||||||

5 | Network status-based fault | −0.186^{*} | −0.002 | 0.004 | 0.134^{*} | 1 | |||||||

6 | Stage | −0.011 | 0.091^{*} | −0.182^{*} | 0.028 | −0.054 | 1 | ||||||

7 | Size | 0.085^{*} | 0.524^{*} | −0.008 | 0.025 | −0.016 | 0.105^{*} | 1 | |||||

8 | Unsingle | −0.037 | 0.035 | 0.154^{*} | −0.033 | 0.076^{*} | −0.111^{*} | 0.074 | 1 | ||||

9 | Resource | −0.069 | 0.196^{*} | 0.115^{*} | 0.096^{*} | 0.019 | −0.03 | 0.190^{*} | −0.017 | 1 | |||

11 | Age | −0.092^{*} | −0.051 | 0.168^{*} | 0.089^{*} | −0.014 | −0.221^{*} | −0.089^{*} | 0.087^{*} | 0.538^{*} | 1 | ||

12 | Proportion of foreign members | −0.019 | −0.003 | 0.250^{*} | 0.025 | −0.03 | −0.268^{*} | −0.06 | 0.057 | −0.009 | 0.190^{*} | 1 | |

13 | Average geographical proximity | 0.023 | −0.083^{*} | −0.073 | −0.057 | 0.007 | 0.009 | −0.124^{*} | −0.009 | −0.062 | −0.046 | −0.232^{*} | 1 |

#### Descriptive statistics

1 | Performance | 0.276 | 0.448 | 0 | 1 |

2 | Complementarity | 0.729 | 0.094 | 0.667 | 0.978 |

3 | Group tie density | 0.092 | 0.191 | 0 | 1 |

4 | Network status heterogeneity | 0.576 | 0.170 | 0 | 0.914 |

5 | Network status-based fault | 0.240 | 0.101 | 0 | 0.563 |

6 | Stage | 3.095 | 0.686 | 1 | 4 |

7 | Size | 3.641 | 1.109 | 3 | 10 |

8 | Unsingle | 0.656 | 0.475 | 0 | 1 |

9 | Resource | 10.40 | 11.34 | 0 | 70 |

10 | Age | 5.779 | 8.120 | 0 | 53 |

11 | Proportion of foreign members | 0.246 | 0.300 | 0 | 1 |

12 | Average geographical proximity | 0.279 | 0.300 | 0 | 1 |

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