Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.

Relational dimensions of corporate governance in translation: networked governance in China and India

The effectiveness of corporate governance mechanisms has been a subject of academic research for many decades. Although the large majority of corporate governance studies prior to mid 1990s were based on data from developed market economies such as the U.S., U.K. and Japan, in recent years researchers have begun examining corporate governance in transition economies. A comparison of China and India offers a unique environment for analyzing the effectiveness of corporate governance. First, both countries state-owned enterprise (SOE) reform strategies hinges on the Modern Enterprise System characterized by the separation of ownership and control. Ownership of an SOE’s assets is distributed among the government, institutional investors, managers, employees, and private investors. Effective control rights are assigned to management, which generally has a very small, or even nonexistent ownership stake. This distinctive shareholding structure creates conflict of interest not only between management (insiders) and outside investors but also between large shareholders and minority investors. Moreover, because both governments desire to retain some control—in part through partial retained ownership of commercialized SOEs, further conflicts arise between politicians and firms. Second, directors in publicly listed firms in both countries are predominantly drawn from institutions with significant non-market objectives: the government and other state enterprises, particularly in China, and extended families, particularly in India. As a result, the effectiveness of internal governance mechanisms, such as the number of independent directors on the board and the number of independent supervisors on the supervisory committee, are likely to be quiet limited, although this has yet to be fully evaluated. Third, because of the political nature of the privatization process itself, typical external governance mechanisms, such as debt (in conjunction with appropriate bankruptcy procedures), takeover threats, legal protection of investors, product market competition, etc., have not been effective. Bank loans have traditionally been viewed as grants from the state designed to bail out failing firms. State-owned banks retain monopoly or quasi-monopoly positions in the banking sector and profit is not their overriding objective. If political favor is deemed appropriate, subsidized loans, rescheduling of overdue debt or even outright transfer of funds can be arranged with SOEs (soft budget constraints). In addition, a market for private, non-bank debt is limited in India and has yet to be established China. There is no active merger or takeover activity in Chinese stock markets to discipline management. Information available in the capital markets is insufficient to keep at arm’s length of the corporate decisions. In light of the above peculiarities, China and India share many of the typical institutional characteristics as a transition economy, including poor legal protection of creditors and investors, the absence of an effective takeover market, an underdeveloped capital market, a relative inefficient banking system and significant interference of politicians in firm management. Su (2005) finds that the extent of political interference, managerial entrenchment and institutional control can help explain corporate dividend policies and post-IPO financing choices in this situation. Allen et al. (2005) demonstrate that standard corporate governance mechanisms are weak and ineffective for publicly listed firms while alternative governance mechanisms based on reputation and relationship have been remarkably effective in the private sector. Because the peculiarities are significant in this context, the differences in the political-economies of the two countries are likely to be evident in such relational terms. In this paper we explore the peculiarities of corporate governance in this transitional environment through a systematic examination of certain aspects of these reputational and relationship dimensions. Utilising the methods of social network analysis we identify the inter-organisational relationships at board level formed by equity holdings and by shared directors. Using data drawn from the Orbis database we map these relations among the 3700 largest firms in India and China respectively and identify the roles played in these relational networks by the particularly characteristic institutions in each case. We find greatly different social network structures in each case with some support in these relational dimensions for their distinctive features of governance. Further, the social network metrics allow us to considerably refine proxies for political interference, managerial entrenchment and institutional control used in earlier econometric analysis.