Variables

Parameters

Estimated MLE coefficients

Model 1

Model 2

Model 3

Model 4

Constant

${\beta }_0$

2.011

(1.97)

7.024

(7.14)

3.875

(3.32)

5.902

(3.09)

ln(total number of employees)

${\beta }_1$

−1.711

(3.53)

−1.817

(2.87)

−2.252

(4.29)

−1.205

(1.30)

ln(total operating expenses)

${\beta }_2$

2.936

(5.79)

1.494

(1.74)

3.058

(5.49)

1.583

(2.11)

1/2 * [ln(total number of employees)]²

${\beta }_{11}$

0.566

(3.83)

0.289

(0.64)

0.652

(4.13)

0.242

(0.83)

1/2 * [ln(total operating expenses)]²

${\beta }_{22}$

0.323

(2.51)

0.006

(0.007)

0.336

(2.35)

0.050

(0.19)

[ln(total number of employees)]* [ln(total operating expenses)]

${\beta }_{12}$

−0.476

(3.38)

−0.081

(0.15)

−0.502

(3.28)

−0.139

(0.53)

Constant

${\delta }_0$

2.583

(5.75)

0.064

(0.07)

−2.881

(0.51)

1.262

(8.27)

Fleet utilization

${\delta }_1$

−0.0336

(4.34)

−0.0079

(0.44)

Profit

${\delta }_2$

−0.0000234

(2.27)

−0.0000797

(0.67)

Firm size

${\delta }_3$

0.0001

(0.14)

−0.0045

(6.72)

Sigma-squared

${\sigma }^2={\sigma }_U^2+{\sigma }_V^2$

0.093

(3.27)

0.254

(0.92)

0.939

(0.61)

0.060

(4.18)

Gamma

$\gamma =\frac{{\sigma }_U^2}{{\sigma }_U^2+{\sigma }_V^2}$

0.951

(33.62)

0.932

(1.05)

0.996

(143.99)

0.885

(5.58)

Log likelihood function

37.687

1.753

6.595

19.272