Instrumental Variable Regression via Kernel Maximum Moment Loss

Instrumental variables (IV) have become standard tools for economists, epidemiologists, and social scientists to uncover causal relationships from observational data [3, 46]. Randomization of treatments or policies has been perceived as the gold standard for such tasks, but is generally prohibitive in many real-world scenarios due to time constraints or ethical concerns. When treatment assignment is not randomized, it is generally impossible to discern between the causal effect of treatments and spurious correlations that are induced by unobserved factors. Instead, IVs enable the investigators to incorporate natural variation through an IV that is associated with the treatments, but not with the outcome variable, other than through its effect on the treatments. In economics, for instance, the season-of-birth was used as an IV to study the return from schooling, which measures causal effect of education on labor market earning [16]. In genetic epidemiology, the idea to use genetic variants as IVs, known as Mendelian randomization, has also gained increasing popularity [13, 14].