*3.5. Econometric Model*

We conducted a Hausman test to see whether the fixed effect or random effect model was suitable for regression. The test result yields a Chi-squared value of 391.42 with a 1% significance level and supports the use of the fixed-effect model. Accordingly, we ran the following fixed effect regression model.

$$\text{PERFORMAANCE} = \beta\_0 + \beta\_1 \text{SIZE} + \beta\_2 \text{AGE} + \beta\_3 \text{CFOP} + \beta\_4 \text{LEV} + \beta\_5 \text{FAM} + \beta\_6 \text{INS} + \epsilon$$

$$\beta\_7 \text{GOV} + \beta\_8 \text{FOR} + \beta\_9 \text{BO\\_SIZE} + \beta\_{10} \text{BO\\_MEET} + \beta\_{11} \text{BO\\_IND} + \beta\_{12} \text{FAM\\*IES} + \epsilon \tag{1}$$

$$\beta\_{13} \text{FAM\\*GOV} + \beta\_{14} \text{FAM\\*\ast FOR} + \beta\_{15} \text{BO\\_SIZESQ} + \beta\_{16} \text{BO\\_MEETSQ} + \epsilon$$

where PERFORMANCE represents the dependent variables: ROA and Tobin's Q. Variables such as SIZE, AGE, CFOP, and LEV are control variables defined in Table 2. Similarly, variables such as FAM, INS, GOV, FOR, BO-SIZE, BO\_MEET, and BO\_IND are the test variables defined in Table 2. We also include INS, GOV, and FOR as interaction with FAM to see their moderating effects on firm performance. Further, we square BO-SIZE and BO\_MEET to see the non-linear relationship. β<sup>0</sup> is the unknown intercept for each firm, and ε is the between-entity error.

To ensure the consistency of our estimates, we also invoked the following random effect regression model.

$$\text{PERFORMANCE} = \beta\_0 + \beta\_1 \text{SIZE} + \beta\_2 \text{AGE} + \beta\_3 \text{CFOP} + \beta\_4 \text{LEV} + \beta\_5 \text{FAM} + \beta\_6 \text{INS} + \epsilon$$

$$\beta\_7 \text{GOV} + \beta\_8 \text{FOR} + \beta\_9 \text{BO\\_SIZE} + \beta\_{10} \text{BO\\_MEET} + \beta\_{11} \text{BO\\_IND} + \beta\_{12} \text{FAM4'INS} + \epsilon \tag{2}$$

$$\beta\_{13} \text{FAM4'GOV} + \beta\_{14} \text{FAM4'FOR} + \beta\_{15} \text{BO\\_SIZESQ} + \beta\_{16} \text{BO\\_MEETSQ} + u + \varepsilon$$

where *u* is the between-entity error, and ε is the within-entity error. All other variables are the same as defined in Equation (1).

#### **4. Results and Discussion**
