If you’re in the observational study business, this, by Anirban Basu and Kwun Chan, looks potentially useful:
In the outcomes research and comparative effectiveness research literature, there are strong cautionary tales on the use of instrumental variables (IVs) that may influence the newly initiated to shun this premier tool for casual inference without properly weighing their advantages. It has been recommended that IV methods should be avoided if the instrument is not econometrically perfect. The fact that IVs can produce better results than naïve regression, even in nonideal circumstances, remains underappreciated. In this paper, we propose a diagnostic criterion and related software that can be used by an applied researcher to determine the plausible superiority of IV over an ordinary least squares (OLS) estimator, which does not address the endogeneity of a covariate in question. Given a reasonable lower bound for the bias arising out of an OLS estimator, the researcher can use our proposed diagnostic tool to confirm whether the IV at hand can produce a better estimate (i.e., with lower mean square error) of the true effect parameter than the OLS, without knowing the true level of contamination in the IV.
