Econometrics: why the i.i.d assumption and weak exogeneity assumption imply strict exogeneity?
\begin{align*}
\mathbb{E}\left[ \epsilon_t \vert X \right] &amp;= \mathbb{E}\left[\epsilon_t \vert X_1, \dots, X_t, \dots, X_n \right]\\
&amp;= \mathbb{E} [Y_t - X_t'\beta^0 \, \vert X_1, \dots, X_t, \dots, X_n] \\
&amp;= \mathbb{E} [Y_t - X_t'\beta^0 \, \vert X_t] \quad \text{since $\{Y_t,X_t\}$ is iid.} \\
&amp;=\mathbb{E}\left[ \epsilon_t \vert X_t \right] \\
&amp;= 0 \quad \text{by Assumption A2.}
\end{align*}