4.3.4. Foreign Ownership and Firm Performance

We found a significant and positive connection between foreign ownership and the performance of family firms with ROA. A similar substantial and positive relationship was observed between foreign ownership and Tobin's Q for non-family firms. This result is consistent with the findings of Yoshikawa and Rasheed (2010), Sueyoshi et al. (2010), and Fukuda et al. (2018), which reveal that foreign ownership improves Tobin's Q for Japanese firms. Notably, we found that foreign ownership significantly enhances the performance of family firms (both ROA and Tobin's Q) when it interacts with family ownership. This means that foreign investors, because of their expertise in overseas market operations, can monitor the company's performance closely and provide necessary advice to improve the firm's profit in the short term (ROA). Furthermore, family firms can take advantage of new knowledge, innovation, and management expertise brought by foreign shareholders to enhance profits in the long term (Tobin's Q). In conclusion, there is evidence of a significant positive relationship between foreign ownership both for family and non-family firms (H4).

#### 4.3.5. Board Size and Firm Performance

We did not find any significant relationship between board size and firm performance for family firms, although it has been significant and positive for non-family firms. The result corresponds to previous studies by Hu and Izumida (2008) and Sueyoshi et al. (2010) for Japan. Looking at the case of all firms, we found that a non-linear negative relationship exists between board size and firm performance, indicating that the increase in board members can hurt firm performance. However, we note that it depends on the complexity of companies' structure, nature of the business, and economic goals. Finally, we do not accept H5 that a significant positive relationship exists between board size and performance of family firms (H5). However, H5 is accepted for non-family firms.

#### 4.3.6. Board Meeting and Firm Performance

We did not find any significant relationship between board meetings and firm performance either for family or for non-family firms. This could lie in the fact that the board of directors in Japanese firms usually consists of directors selected from employees who have been with the company under the life-time employment scheme, implying that there are little to no fresh ideas and perspectives on the board. Therefore, the traditional group thinking may dominate the entire discussion process, while innovation and breakthrough ideas may be sacrificed against conservatism. Our result does not approve the findings by Huse (2007), which document that frequency of board meetings enhances firm performance by improving monitoring activities and resolving corporate issues. Moreover, we did not find that a non-linear relationship runs between the frequency of board meetings and firm

performance. In conclusion, we reject H6 that a significant positive relationship runs between the number of board meetings and Tobin's Q for family firms in Japan.
