Christophe Gaillac from Oxford will present " Linear Regressions with Combined Data"

Abstract: We provide new partial identification results and study inference for best linear predictors, in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Using tools from the optimal transport literature, we derive a constructive characterization of the sharp identified set. We then build on this characterization to develop an inference method, which is highly tractable and shown to perform well in finite samples. We apply our method to the question of racial inequality in the context of innovation, where data combination issues are pervasive. Using data on patent applications and granted patents in the United States over the period 2000 to 2019, our method yields bounds that are informative while allowing us to relax the exclusion restrictions that are commonly used in the literature on racial gaps in innovation.