I'm having trouble validating if following procedure to test for predeterminedness is plausible. Given the linear model:


Having $x_{2t} = y_{t+1|t}+v_t$ and $\epsilon_t$ uncorrelated with $x_{1t}, x_{2t}$. And $\epsilon_t$ i.i.d. with $E(\epsilon_t)=0, E(\epsilon_t^2)=0$. Given $v_t$ i.i.d. and also uncorrelated with $\epsilon_t$.

\begin{equation} \label{eq1} \begin{split} E[x_{1t}\epsilon_t] & = E[E[x_{1t}\epsilon_t|x_{1t}]] \\ & = E[x_{1t}\underbrace{E[\epsilon_t|x_{1t}]]}_{=0} = 0 \\ E[x_{2t}\epsilon_t] & = E[E[x_{2t}\epsilon_t|x_{2t}]] \\ & = E[x_{1t}\underbrace{E[\epsilon_t|x_{2t}]]}_{=0} = 0 \\ \end{split} \end{equation}

Can anyone confirm this?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.