*4.2. Stationary Test Results of Variables in the Model*

In fact, the threshold regression model of Hansen (1999) is an extension of the ordinary least squares (denoted by OLS) traditional estimation method. This method requires that all variables considered in the model must be stationary variables to avoid spurious regression. This study uses the Levin et al. (2002) and Im et al. (2003) standards to test the stationarity of variables in the model. By using STATA software with the dataset described in Section 4.1, the results of the unit root test and stationarity test of the variables are shown in Table 2 below.


**Table 2.** Unit root test results.

Note: LLC and IPS are unit root tests of Levin et al. (2002) and Im et al. (2003) respectively. \*\*\* and \*\* give 1% and 5% significance, respectively.

Table 2 shows that according to LLC and IPS accreditation standards, all variables representing profitability (ROA), cash holding (CASH), scale (SIZE), growth (MB), and leverage (LEV) are stationary sequence and statistically significant at 1% and 5%. Thus, the use of these variables in the threshold regression model is completely acceptable.

#### *4.3. Threshold Regression Results*

This study used GAUSS software and applied the bootstrap method to obtain an approximation of F-statistics and then calculated *p*-value. *F*-statistics include F1, F2 and F3, to evaluate H0 hypotheses for zero, one, and two thresholds, respectively. Table 3 provides results of single-threshold, double-threshold and triple-threshold tests.


**Table 3.** Test results of threshold effect of cash holding ratio on firm's performance.

Note: *F*-statistics and *p*-value were obtained by executing a repeating bootstrap procedure 500 times for each bootstrap test. \*\*\* indicates significance at 1%.

First of all, this study examined the existence of a single-threshold effect. By using bootstrap to perform 500 times, the obtained F1-statistics and *p*-value are 21.3377 and 0.004 (<1%), respectively. This suggested that the null hypothesis is rejected at the 1% significance level. Next, this study examined the existence of a double-threshold effect. Similarly, using bootstrap to perform 500 times, the obtained F2-statistics and *p*-value are 10.1255 and 0.156 (>10%), respectively. This suggested that the hypothesis that a double threshold is rejected. Finally, this study examined the existence of a triple-threshold effect. Similarly, by using bootstrap to perform 500 times, F3-statistics are 7.4726 and the *p*-value is 0.334 (>10%). This showed that the triple-threshold hypothesis is rejected.

Thus, the results of the threshold effect test showed that there is a single-threshold effect on cash holding and company efficiency. Figure 1 below shows the construction of confidence intervals for a single-threshold model.

Table 3 above presents the estimated values of the single threshold at 0.0993. The first-step threshold estimate is the point where the LR1(γ) equals zero, which occurs at γˆ <sup>1</sup>= 0.0993. All observations in the sample were divided into two sets by the CASH threshold variable (above and below the threshold value of γ = 0.0993). Accordingly, this study identified two modes formed by threshold values from 0 to 9.93% and above 9.93%.

Table 4 shows the estimated coefficients, standard deviations according to the OLS, and White Methods for two models mentioned above. When the cash holding ratio (CASH) is smaller than 9.93%, the estimated coefficient βˆ <sup>1</sup> is 0.4078 and statistically significant at 1%, indicating that ROA will increase by 0.4078% when the cash holding ratio increases by 1%. When CASH is higher than 9.93%, the estimated coefficient βˆ <sup>2</sup> is 0.1556 and statistically significant at 1%, indicating that ROA will increase by 0.1556% when CASH increases by 1%. The results showed that the ROA regression coefficient by CASH is not a fixed value but depends on each threshold of cash holding ratio. Thus, it is clear that the relationship between cash holding ratio and operational efficiency (slope values) varies according to different changes in cash holding ratio. This suggested the existence of a nonlinear relationship between cash holding ratio and company's performance.

**Figure 1.** Confidence interval for the single-threshold model.


**Table 4.** Estimated results of regression coefficient for the cash holding ratio.

Note: βˆ <sup>1</sup> and βˆ <sup>2</sup> are the coefficients of the cash holding ratio variable corresponding to each value of the threshold. \*\*\* indicate the meaning of 1% respectively.

Table 5 shows the estimated coefficients, the standard deviation according to the OLS, and White methods of three control variables, company size, growth, and leverage.


**Table 5.** Estimated results of coefficients for control variables.

Note: θˆ 1, θˆ 2, and θˆ <sup>3</sup> are the estimated coefficients of company's growth (MB), company's size (SIZE), and leverage (LEV). \*\*\* indicates significance at 1%.

Table 5 above shows the estimated coefficients, the standard deviation according to the OLS, and White methods of three control variables, company size, growth, and leverage.

Table 5 shows that the estimated coefficient of company's growth θˆ <sup>1</sup> is 0.0135 and has a positive relationship with ROA at the 1% level, implying that company's growth is a motivation to increase company efficiency. This result is consistent with empirical research by Abor (2005). Meanwhile, the estimated coefficient of company's size θˆ <sup>2</sup> is −0.0169 and is inversely related to ROA at the 1% level. This implied that scaling up the company is not an incentive to increase company efficiency. The empirical finding is consistent with Cheng et al. (2010), Martínez-Sola et al. (2013), and Nguyen

et al. (2016). At the same time, the estimated coefficient of company's leverage θˆ <sup>3</sup> is −0.1146 and is inversely related to ROA at the 1% level, suggesting that the use of more debt capital in the capital structure is harmful to firm's performance. This finding is consistent with the finding of Abor (2005), Nguyen et al. (2016), and Vijayakumaran and Atchyuthan (2017).

From Tables 4 and 5, the estimated model can be rewritten as follows:

$$\text{ROA}\_{\text{i,t}} = \begin{cases} \mu\_{\text{i}} + 0.0135 \text{MB}\_{\text{i,t}} - 0.0169 \text{SIZE}\_{\text{i,t}} - 0.1146 \text{LEV}\_{\text{i,t}} + 0.4078 \text{CASH}\_{\text{i,t}} + \varepsilon\_{\text{i,t}} \text{ if } \text{CASH}\_{\text{i,t}} \le 9.93\% \\\ \mu\_{\text{i}} + 0.0135 \text{MB}\_{\text{i,t}} - 0.0169 \text{SIZE}\_{\text{i,t}} - 0.1146 \text{LEV}\_{\text{i,t}} + 0.1556 \text{CASH}\_{\text{i,t}} + \varepsilon\_{\text{i,t}} \text{ if } \text{CASH}\_{\text{i,t}} > 9.93\% \end{cases}$$

Table 6 below shows the number of companies in each threshold by year.


**Table 6.** Number of companies in each threshold by year.

Table 6 shows that about 64% of companies fall into the category of having a cash holding ratio within the threshold of 9.93% (meaning that about 179 to 212 companies fall into this threshold each year), and about 36% companies fall into the threshold of having a cash holding ratio above 9.93% (meaning that about 94–127 companies fall into this threshold each year).
