Motif analysis of the establishing, sustaining, and unwinding of cross-shareholdings in Japan

Cross-shareholdings or mutual aid shareholdings (Kabushiki mochiai) represent a distinctive feature of Japan’s corporate governance system. Cross-shareholding arrangements originated in the post-war period, and operated as tacit mutual pacts designed to secure a stable source of funding and insulate the management of both sides from hostile takeover. However, such arrangements have been largely criticized for promoting unfair trading practices and stagnating the economy. Companies have been under intensive pressure by the government and foreign companies to dissolve them. Although the merits/demerits of the unwinding of cross-share-holdings have been well discussed, the process and mechanism have been insufficiently addressed. Existing network research on shareholding relationships has mostly focused on the structural properties of overall networks, not investigating local patterns of inter-company relationships and their temporal changes. In this study, we constructed the time-varying shareholding network, in which nodes and edges represent listed companies in Japan and their shareholding relationships, respectively, for the period of 1956 – 2019. Firstly, we conducted a motif analysis of the cumulative network (i.e., ignoring temporal changes). Null-models we used for comparison are networks generated by reshuffling edges in the original network while retaining in- and out-degrees of each node. The results (shown in Figure 1) suggest that cross-shareholdings are significantly overrepresented in the network (see Patterns 1 – 8). The cyclic cross-shareholding pattern (i.e., Pattern 9) is often featured in existing literature and yet not found to be significant. Instead, we found that cyclic relationships do occur in the form of Patterns 5, 7 and 8 – i.e., patterns that include a cycle and mutual edge(s). We further conducted a temporal motif analysis to see how these patterns have emerged over time. There was not even a single case where any of the Patterns 5, 7 or 8 triads occurred by adding one or two edge(s) to a Pattern 9 cyclic triad. These patterns seem to occur when two companies have a cross-shareholding relationship first, then establish further connections involving another company. By applying temporal motif analysis, we also investigated the temporal ordering in which companies dissolve relationships, and the duration of cross-shareholding relationships being sustained. Our findings include that cross-shareholding relationships are more persistent than one-way relationships, and that companies tend to find a new partner and form a shareholding relationship before they dissolve an old cross-shareholding. We believe that our study provides useful insight into corporate strategies for shareholding, leading us to a deeper understanding of the emerging mechanism of economic stagnation and why cross- shareholdings remain in existence.