Invariance of covariance structures under groups of transformations

Summary The invariance of covariance structures under Lie groups of transformations is discussed. Implications for minimum discrepancy estimates of parameters are considered.     

The Performance Effects of Business Groups in Russia

This study analyses the impact of business group affiliation on firm performance during a time when business groups are newly formed, when the economic and institutional environment is changing, and when group survival is uncertain. Based primarily on a transaction cost approach, we develop two hypotheses, concerning profitability and risk sharing (redistribution) respectively. The positive profitability hypothesis proposes that company affiliation with a business group directly and positively affects the profitability of each affiliate. A positive direct effect emerges when each affiliate benefits from access to group resources. The redistribution hypothesis considers the simultaneous possibility that inter-affiliate transfers of resources through internal markets are designed to redistribute profits among group members. We argue that variance-reducing redistribution from strong to weak group members is linked to group survival in times of institutional change. Our empirical approach focuses on testing these two linked hypotheses (and their alternatives) using a relatively large, contemporary and time varying database of Russian firms. We also develop a framework that distinguishes among the four possible empirical outcomes associated with the hypotheses. Our results provide unambiguous support for the case where the impact of group membership on profitability is positive and redistribution is variance-reducing. We term this outcome Business Group Robustness, and contrast it with other possible empirical outcomes.