Schematic
Figure 1: Schematic presentation of valid and invalid instrumental variables X, Y, Z, and U denote the exposure, outcome, IV, and confounders (observed or unobserved), respectively. a) Z is associated with X and only related to Y through X (valid IV), b) Z is not associated with X (first IV assumption is violated), c) Z is not independent of confounders, i.e. Z has an indirect effect on Y (second IV assumption is violated), d) Z is not independent of Y given X and U, i.e. Z has a direct effect on Y (third IV assumption violated)