Hi I am a beginner to econometrics!
I have been dealing with bivariate regression. We use the formula $y = \beta_0 + \beta_1 x$.
I am told that if $E(u\mid x) \ne 0$ then the estimate of the slope parameter $\beta_1$ will be biased.
My question is: if $E(u\mid x) = 1$ for all $x$'s, then why would the estimate of the slope parameter be biased? I thought this would mean that only the intercept estimate will be biased.
I thought that the slope parameter will only be biased if the expected value of the errors is different for each $x$. For example if $E(u\mid x_1) = 1$ and the $E(u\mid x_2) = 3$, etc. etc.
Any help will be immensely appreciated! Thank you!