It is a standard practice in regression analyses to allow for clustering in the error covariance matrix if the explanatory variable of interest varies at a more aggregate level (e.g., the state level) than the units of observation (e.g., individuals). Often, however, the structure of the error...

We analyze linear models with a single endogenous regressor in the presence of many instrumental variables. We weaken a key assumption typically made in this literature by allowing all the instruments to have direct effects on the outcome. We consider restrictions on these direct effects that...