Salvaging Falsified Instrumental Variable Models
What should researchers do when their baseline model is falsified? We recommend reporting the set of parameters that are consistent with minimally nonfalsified models. We call this the falsification adaptive set (FAS). This set generalizes the standard baseline estimand to account for possible falsification. Importantly, it does not require the researcher to select or calibrate sensitivity parameters. In the classical linear IV model with multiple instruments, we show that the FAS has a simple closed-form expression that only depends on a few 2SLS coefficients. We apply our results to an empirical study of roads and trade. We show how the FAS complements traditional overidentification tests by summarizing the variation in estimates obtained from alternative nonfalsified models.