Is this a typo in this econometric exercise?

Question

I'm trying to solve an exercise in OLS estimator:

I'm not sure if $\mathrm{E}(u | \boldsymbol{x}, q)=0$ is a typo. Moreover, $\mathrm{E}(u | \boldsymbol{x})=0$ is used in the solution. Should it be $\mathrm{E}(u | \boldsymbol{x})=0$ rather than $\mathrm{E}(u | \boldsymbol{x}, q)=0$?

Thank you so much!

Answer 1

I don't think it's a typo. It seems natural to require $E(u\mid \mathbf x , q) = 0$ for your error term, and this is actually a stronger condition than $E(u\mid \mathbf x) = 0$.

To see this, recall that by the tower property of conditional expectations, we have that $$E(u\mid \mathbf x) = E(E(u\mid \mathbf x , q) \mid \mathbf x) = 0.$$