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Change of ownership networks in Japan

Wataru Souma, Yoshi Fujiwara, Hideaki Aoyama

arXiv:physics/0504045v1physics.soc-ph

TL;DR

The paper asks how Japanese shareholding networks change across years and how their degree distributions relate to ownership patterns. It models these networks as directed graphs using shareholder data and analyzes outgoing-degree distributions. The distributions retain a power-law form with an exponential tail, while the exponent varies and is strongly negatively correlated with long-term and cross-shareholding rates.

  • Problem

    The paper examines the structure of Japanese shareholding networks across years and its relationship to long-term and cross-shareholding rates.

    Source: §1 · pp. 1–2

  • Method

    The study represents shareholder relationships as directed graphs and analyzes top-20 shareholder data for Japanese companies across six years.

    Source: §1 · p. 2

  • Results

    The outgoing degree distributions follow a power law except in the tail, with year-dependent exponents; comparable reported exponents include γMIB = 1.97, γNYSE = 1.37, and γNASDAQ = 1.22.

    Source: §2 · p. 3

  • Takeaways & Limitations

    The power-law shape is maintained across years, while the exponent is strongly and negatively correlated with long-term and cross-shareholding rates.

    Source: §2 · p. 4, §3 · p. 5

    The interpretation assumes that changes in the exponent can be attributed to changes in shareholding patterns.

    Source: §2 · p. 4

Abstract

from arXiv · show

As complex networks in economics, we consider Japanese shareholding networks as they existed in 1985, 1990, 1995, 2000, 2002, and 2003. In this study, we use as data lists of shareholders for companies listed on the stock market or on the over-the-counter market. The lengths of the shareholder lists vary with the companies, and we use lists for the top 20 shareholders. We represent these shareholding networks as a directed graph by drawing arrows from shareholders to stock corporations. Consequently, the distribution of incoming edges has an upper bound, while that of outgoing edges has no bound. This representation shows that for all years the distributions of outgoing degrees can be well explained by the power law function with an exponential tail. The exponent depends on the year and the country, while the power law shape is maintained universally. We show that the exponent strongly correlates with the long-term shareholding rate and the cross-shareholding rate.

1 Introduction

The paper defines Japanese shareholding networks as directed ownership graphs and analyzes their structure across multiple years. It uses shareholder data to examine degree distributions and their relation to long-term and cross-shareholding.

Network definition

  • Japanese shareholding networks treat companies as nodes and shareholding relationships as directed edges between them.Source: §1 · p. 1

Data and scope

  • The analysis covers Japanese networks in 1985, 1990, 1995, 2000, 2002, and 2003 using shareholder lists.The data cover companies listed on stock or over-the-counter markets, with the top 20 shareholders used uniformly.Source: §1 · p. 2
  • The network construction includes listed companies and non-listed financial institutions but excludes officers and other individuals.The resulting node and edge counts vary by year and are summarized in Table 1.Source: §1 · p. 2, Table 1 · p. 2

Research objectives

  • The paper shows that outgoing degree distributions follow a power law with an exponential cutoff, while the exponent varies by year and country.It also examines correlations between the exponent and long-term and cross-shareholding rates.Source: §1 · p. 2

2 Change of outgoing degree distribution

Japanese shareholding networks exhibit outgoing-degree distributions with a power-law body and an approximately exponential tail, while the exponent varies across years and correlates negatively with ownership-rate measures.

2 Change of outgoing degree distribution

  • The network representation draws arrows from shareholders to stock corporations, leaving incoming degree bounded by 20 while outgoing degree has no bound.The top-20 shareholder lists impose the incoming-degree bound used for consistency across companies.Source: §2 · p. 2
  • The outgoing-degree distribution follows a power law except in the tail, where it is approximately exponential.The power-law portion is mainly associated with non-financial institutions, whereas the exponential tail is mainly constructed from financial institutions.Source: §2 · pp. 3–4
  • The exponent γ varies by year, and comparable power-law exponents were reported for Japanese, MIB, NYSE, and NASDAQ shareholding networks.Reported comparison values are γ_MIB = 1.97 in 2002, γ_NYSE = 1.37 in 2000, and γ_NASDAQ = 1.22 in 2000.Source: §2 · p. 3
  • Both long-term and cross-shareholding rates decrease after 1990.Figure 2 tracks these rates over time and relates them to the exponent γ.Source: §2 · p. 4, Figure 2 · p. 4
  • The exponent γ has strong negative correlations with both the long-term shareholding rate and the cross-shareholding rate.The correlation analysis is shown in the right panel of Fig. 2, with γ on the horizontal axis.Source: §2 · p. 4, Figure 2 · p. 4

3 Summary

Across Japanese shareholding networks from 1985 to 2003, outgoing-degree distributions retain a power-law form with a tail, while their exponents vary and correlate negatively with long-term and cross-shareholding rates.

3 Summary

  • Across all examined years, outgoing-degree distributions are explained by a power law except in the tail, and the exponent depends on year and country.The study examines Japanese networks from 1985, 1990, 1995, 2000, 2002, and 2003.Source: §3 · p. 5
  • The exponent has strong negative correlations with both long-term shareholding and cross-shareholding rates.The summary states that dissolution of these forms of shareholding causes the exponent to increase.Source: §3 · p. 5
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