Polygenic Scores as Proxies for Unobservables: An Instrumental Variables Approach and an Application to the Returns to Schooling (with Casper Burik and Philipp Koellinger)
In recent years, polygenic scores have become the favored tool for summarizing the influence of genetic predispositions on phenotypic characteristics and behavior when the genetic effect arises from the accumulation of small effects from a potentially very large number of genetic markers. In principle, such polygenic scores could be useful as proxies for unobserved characteristics in applied economics. Even though the explanatory power of polygenic scores continues to improve due to the combination of improved statistical techniques and larger sample sizes for genetic discovery, polygenic scores typically capture less variance than implied by the heritability of a trait. This attenuation of the predictive accuracy of polygenic scores creates well known problems in applied contexts; it biases downward the estimated effect of genetic markers on the outcome of interest, and it biases the effect of behavioral and environmental variables that are entered into the same specification as the genetic variables. Instrumental variables regression methods can correct for such bias under a set of assumptions, mostly notably the exclusion restriction, but the practical value of these strategies depends upon the strength of the instruments and the size of the sample used to carry out the estimation. This paper explores the potential use of polygenic scores as proxies for unobservables in the context of a returns to schooling estimation. Specifically, we approximate unobserved ability by a polygenic score for educational attainment. Using data from the Health and Retirement Survey, we employ a series of alternative plausible instrumental variables along with sensitivity analyses of the consequences of imperfect instruments to examine the potential improvement of model estimates.