Chapter 6 The Factors of Enterprise Growth
6.4 The statistical test models and estimation results
The coefficients from probit and logit model are not certain probability values of firms’ transformation. The coefficients must be translated into a mathematic function, and then we can get the i-th firm’s growth probability. In the probit model, the derivation of the probability with respect to a specific Xi in the set of variables
X is
i
Xi
y
E( ) ()
;
we define
z X , here )
2 exp( 1 2
) 1
(z z2
,which is the standard
normal density.
However, we are interested in the dimension of the sign and significance of the coefficients, because finding out which factors can influence a firm’s growth is the most important task in this chapter. In Table 6-1, we use probit and logit model and put all variables in the regression. Table 6-1 reports the results for all firms with all variables. The results show that the probability of a small firm’s growth increases
14 Stolper-samuelson effect means a rise in the relative price of a good will lead to a rise in the return to that factor which is used most intensively in the production of the good, and conversely, to a fall in
with the education level of employers, but it decreases with the average education level of employees. Apart from the two variables, the other variables are not significant.
Table 6-1 Estimation of a small firm’s growth factors (8 variables)
Dependent variable: The scale of firm (Large=1, Small=0)
Probit Logit
Variable Coefficient Prob.>t Coefficient Prob.>t
Type 2.79 0.139 5.07 0.15
(1.89) (3.55)
Subsidy -0.57 0.447 -1.04 0.43
(0.76) (1.34)
Year er 0.21 0.052** 0.36 0.06**
(0.11) (0.19)
Year ee -0.491 0.004* -0.87 0.001**
(0.17) (0.33)
Export -1.79 0.210 -0.30 0.21
(1.42) (2.45)
Rd 0.51 0.523 0.90 0.50
(0.80) (1.35)
Loan 0.32 0.731 0.81 0.64
(0.95) (1.35)
Area 0.84 0.205 1.41 0.20
(0.66) (1.12)
Obs. with Dep.=0 29 Total observations 41
Obs. with Dep.=1 12
* Significance level is 1 percent. ＊＊ Significance level is 10 percent.
Convergence achieved after 7 iterations
In Table 6-2, in order to observe and decrease the influence of multicollinearity in this regression, we eliminate three insignificant variables (Rd, Loan and Export) in the probit and logit model and get the results.
The results are slightly different. It shows that the probability of a small firm’s growth increases with the education level of employers and the type of the firm, but decreases with the average education level of employees. Except for the three variables, the other variables are insignificant.
Table 6-2 Estimation of small firm’s growth factors(5 variables)
Dependent variable: The scale of firm (Large=1, Small=0)
Probit Logit
Variable Coefficient Prob.>t Coefficient Prob.>t
Type 2.48 0.09** 4.21 0.10**
(1.48) (2.59)
Subsidy -0.51 0.41 -0.81 0.45
(0.63) (1.10)
Year er 0.22 0.04** 0.38 0.05**
(0.10) (0.20)
Year ee -0.47 0.002* -0.82 0.004*
(0.15) (0.29)
Area 0.70 0.24 1.22 0.24
(0.60) (1.04)
Obs. with Dep.=0 29 Total observations 41
Obs. with Dep.=1 12
* Significance level is 1 percent. ＊＊ Significance level is 10 percent.
Convergence achieved after 7 iterations
In Table 6-3, we change the eliminated insignificant variables (Subsidy, Export and Area) in these models and get the results. The results are different from table 6-2.
The coefficients of the education level of employer, the type of firm and the average education level of employee are still significant and the sign of the variables are the same as in Table 6-1. But the coefficient of the firm’s type is significant and the sign of the type is positive. Aside from that, the other variables are insignificant.
Table 6-3 Estimation of small firm’s growth factors (5 variables)
Dependent variable: The scale of firm (Large=1, Small=0)
Probit Logit
Variable Coefficient Prob.>t Coefficient Prob.>t
Type 2.30 0.07** 3.87 0.09**
(1.29) (2.29)
Rd -0.11 0.82 -0.19 0.83
(0.54) (0.92)
Year er 0.23 0.03** 0.42 0.04**
(0.11) (0.20)
Year ee -0.47 0.002* -0.82 0.004*
(0.15) (0.29)
Loan 0.13 0.86 0.37 0.78
(0.78) (1.35)
Obs. with Dep.=0 29 Total observations 41 Obs. with Dep.=1 12
* Significance level is 1 percent. ＊＊ 5 percent.＊＊＊ 10 percent.
Convergence achieved after 6 iterations
Table 6-4 Estimation of small firm’s growth factors (3 variables)
Dependent variable: The scale of firm (Large=1, Small=0)
Probit Logit
Variable Coefficient Prob.>t Coefficient Prob.>t
Type 2.29 0.06*** 3.80 0.08***
(1.25) (2.20)
Year er 0.23 0.02** 0.40 0.03**
(0.10) (0.19)
Year ee -0.46 0.001* -0.79 0.003*
(0.14) (0.26) Obs. with Dep.=0 29 Total observations 41 Obs. with Dep.=1 12
* Significance level is 1 percent. ＊＊ 5 percent.＊＊＊ 10 percent.
Convergence achieved after 6 iterations
In Table 6-4, we just take three variables (the education level of employers and employees, the type of the companies) in the probit and the logit model. The results in the both models are satisfying. All variables (the education level of employers and employees, the type of the firm) are significant. The education level of employers and the type of the firms are positively correlated to a firm’s growth, but the average education level of employees is negatively correlated to a firm’s growth.
The goal of this chapter is to investigate several econometric explanations that have been assumed to find a correlation between a firm’s growth and several other factors. The first key finding of this study is that the education level of employer is an important determinant of a firm’s growth. The correlation between a firm’s growth and the education level of employer is positive.
It may be due to the fact that a employer has a higher education level that helps
make intellectual decision to improve the firm and the firm can have a higher probability to transform into a large firm. Employers who have a higher education level also can perform tasks better in they own company.
The second key finding is that the type of the firms is also an important factor for a firm’s growth. If the firm is a corporation organization, there are more owners in a firm and they can make the policy decision together. Those policymakers can discuss and reach an optimal decision on the firm’s policy. It can decrease the occurrence of making the wrong policy and the firm could be more capable of taking on risks.
The third key finding is that the average education level of employees is a negative factor in a firm’s growth. If a firm has a higher academic level in the workforce at the start-up phase, it is not beneficial to the firm’s growth. It seems to be against conventional wisdom. Considering the special economic condition of Taiwan, the reason might be that small firms usually have a smaller amount of capital and possess lowly technology in Taiwan. It is difficult for a small firm to hire workers with a high education background and keep the workers staying in the same firm.
Inversely, it is not easy for workers with low education levels to find and get a new job in a large firm. When workers with lower academic education get a job from a small firm, they usually stick to the job for a long time and stay loyal to the firm.
They could have much experience and execute the production process with fewer mistakes. It could be beneficial to a small firm’s growth.
The situation may be different in other countries, because we just use the data from Taiwan’s firms. If we could collect the data from other countries, we may obtain different results and prove that different factors would also influence a firm’s growth.