Calibration weighting can be used to adjust for unit nonresponse and/or coverage errors under appropriate quasi-randomization models. Alternative calibration adjustments that are asymptotically identical in a purely sampling context can diverge when used in this manner. Introducing instrumental variables into calibration weighting makes it possible for nonresponse (say) to be a function of a set of characteristics other than those in the calibration vector. When the calibration adjustment has a nonlinear form, a variant of the jackknife can remove the need for iteration in variance estimation.
