Table 1.

Comparison of different models

Model name	Model
1. Standard RE	$y_{ij}={\mathit{\beta }}_0+{\mathit{\beta }}_R{x}_{ij}+\left(u_j+e_{ij}\right)$
2. Within	$y_{ij}={\mathit{\beta }}_0+{\mathit{\beta }}_W\left(x_{ij}-{\overline{x}}_j\right)+\left(u_j+e_{ij}\right)$
3. Mundlak	$y_{ij}={\mathit{\beta }}_0+{\mathit{\beta }}_W{x}_{ij}+{\mathit{\beta }}_C{\overline{x}}_j+\left(u_j+e_{ij}\right)$
4. Within–between	$y_{ij}={\mathit{\beta }}_0+{\mathit{\beta }}_W\left(x_{ij}-{\overline{x}}_j\right)+{\mathit{\beta }}_B{\overline{x}}_j+\left(u_j+e_{ij}\right)$
5. Fixed effects	$\left(y_{ij}-{\overline{y}}_j\right)={\mathit{\beta }}_W\left(x_{ij}-{\overline{x}}_j\right)+\left(e_{ij}\right)$