Data Science for Business and Decision Making

${\mathit{performance}}_{\mathit{tjk}}={\pi }_{0\mathit{jk}}+{\pi }_{1\mathit{jk}}\cdot {\mathit{year}}_{\mathit{jk}}+e_{\mathit{tjk}}$

${\pi }_{0\mathit{jk}}=b_{00k}+b_{01k}\cdot {\mathit{gender}}_{\mathit{jk}}+r_{0\mathit{jk}}$

${\pi }_{1\mathit{jk}}=b_{10k}+b_{11k}\cdot {\mathit{gender}}_{\mathit{jk}}+r_{1\mathit{jk}}$

$b_{00k}={\gamma }_{000}+{\gamma }_{001}\cdot {\mathit{texp}}_k+u_{00k}$

$b_{01k}={\gamma }_{010}$

$b_{10k}={\gamma }_{100}+{\gamma }_{101}\cdot {\mathit{texp}}_k+u_{10k}$

$b_{11k}={\gamma }_{110},$

which results in the following expression:

$\begin{array}{l}{\mathit{performance}}_{\mathit{tjk}}={\gamma }_{000}+{\gamma }_{100}\end{array}$