Table 2 Parameter estimates

\(\ln x_{2}\)

0.330***

(0.029)

0.0196***

(0.001)

\(\ln x_{3}\)

0.268***

(0.030)

− 0.082***

(0.001)

0.114***

(3.71)

\(\ln x_{4}\)

0.148***

(0.023)

− 0.005

(0.010)

− 0.063

(0.012)

− 0.047***

(7.95)

\(\ln y_{1}\)

− 0.211***

(0.036)

0.206***

(0.023)

− 0.041

(0.023)

0.042*

(0.021)

0.038

(0.012)

\(\ln b\)

− 0.438***

(0.038)

− 0.102***

(0.020)

0.055**

(0.021)

0.005*

(0.016)

− 0.096***

(0.024)

− 0.028

(0.033)

Year

− 0.018***

(0.003)

− 0.005***

(0.001)

0.004**

(0.001)

− 0.003**

(0.001)

− 0.014***

(0.002)

0.012

(0.002)

0.001***

(0.000)

Log likelihood = 7096*** \(\gamma = \frac{{\sigma_{u}^{2} }}{{\sigma_{u}^{2} + \sigma_{v}^{2} }} = 0.94\) N = 6229 (0.000)