Meaning of $\mathcal{I}_t$ in assumption $E[u_t\mid\mathcal{I}_t]$ of distributed-lag model

Question

When considering \begin{equation*} y_t = \beta_0 + \beta_1 x_t + \ldots + \beta_r x_{t-r} + u_t \end{equation*} an assumption made is \begin{equation*} E[u_t\mid\mathcal{I}_t] = 0 \end{equation*} What exactly does $\mathcal{I}_t$ stand for? I know it stands for "Information", but what is included in this information? Is it $x_{t-1}, \ldots, x_{t-r}$? Does it also include $y_{t-1}$ etc?

Answer 1

It includes everything you know (observe) at time $t$, that is, $x_t,x_{t-1}\ldots$ and $y_t,y_{t-1},\ldots$. It has to include the $y$'s as well, otherwise you could not compute the errors $u_t,u_{t-1}$ etc.

It does NOT include "future" variables, e.g., $x_{t+1},x_{t+2}$ etc.