Nonparametric instrument model averaging

We present a new nonparametric model averaging approach to the instrumental variable (IV) regression where the effects of multiple instruments on the endogenous variable are modelled as nonparametric functions in the reduced form equations. Even if individual IVs may have weak and nonlinear relevance to the exposure, our proposed model averaging is able to ensemble their effects with optimal weights to produce valid inference. Our analysis covers both the case in which the number of IV is fixed and the case in which the dimension of IV is diverging with sample size. This novel framework can be especially beneficial to the practical situations involving weak IVs since in many recent observational studies we may encounter a large number of instruments and their quality could range from poor to strong. Numerical studies are carried out and comparisons are made between our proposed method and a wide range of existing alternative methods.