A randomization-consistent regression estimator (usually called a "generalized regression estimator" or GREG) for a population total is unbiased under a simple linear model and randomization consistent even when that model fails. It is often useful to put such an estimator in calibration form, that is, as a simple weighted sum of the sample quantities, where the weights satisfy the calibration equation and are each asymptotically indistinguishable from the inverse of the corresponding unit's selection probability.

This talk will describe a simple scenario where defining an instrumental variable is helpful for computing a set of calibration weights. The implicit model is simple regression with an intercept. The choice of instrumental variable can reduce the possibility that any of the set of calibration weights will be less than unity. A calibration weight less than unity means that a sample observation does not even fully represent itself in the estimator, which many find unsatisfactory.