Sample Conditions Under Which Bias in IV Estimates can be Signed

The relative size of the treated and untreated groups, or the T/UT ratio, in an analysis sample often diverges from the T/UT ratio in the population (or original sample) because of choice-based sampling and missing values. While divergences of the sample from the population T/UT ratio do not generate bias for many estimators, instrumental variable (IV) estimates might be biased by such divergences even when (1) the IV is analytically valid for the population and (2) the sample-treated and -untreated groups are representative of the population-treated and -untreated groups, respectively. We survey published empirical manuscripts to show that this issue is prevalent across various fields. We also prove that the bias in IV estimates, generated by divergences of the sample from population T/UT ratio, is a monotonic function of the difference between the sample and population T/UT ratios when the above conditions (1 and 2) are met. Based on our findings, we suggest possible solutions and provide advice on how to interpret the bias in IV estimates even when the true T/UT ratio is not known.