Consider the following T-ARCH model:

\[\begin{aligned}& h_{t}=\delta+\alpha_{1} e_{t-1}^{2}+\gamma d_{t-1} e_{t-1}^{2} \\& d_{t}=\left\{\begin{array}{lll}1 & e_{t}<0 & \text { (bad news) } \\0 & e_{t} \geq 0 & \text { (good news) }\end{array}\right.\end{aligned}\]

a. If \(\gamma\) is zero, what are the values of \(h_{t}\) when \(e_{t-1}=-1\), when \(e_{t-1}=0\), and when \(e_{t-1}=1\) ?

b. If \(\gamma\) is not zero, what are the values of \(h_{t}\) when \(e_{t-1}=-1\), when \(e_{t-1}=0\), and when \(e_{t-1}=1\) ? What is the key difference between the case \(\gamma=0\) and \(\gamma eq 0\) ?