Association for Public Policy Analysis & Management

Political scientists are often interested in the effect of a high dimensional intervention, such as a text, an image, or a politician's record while in office. The usual approach to dealing with a high dimensional intervention is for the researcher to determine a rule to code a low-dimensional treatment from that high-dimensional intervention. We provide a different approach where we discover a set of low-dimensional treatments from the high-dimensional intervention. We prove that even though we do not explicitly randomize the low-dimensional treatments we are able to identify their effect. We then provide a procedure that enables us to simultaneously estimate the low-dimensional treatments and credibly estimate their causal effect with valid confidence intervals. We apply our procedure to data from an experiment on the effects of Chinese propaganda, the determinants of response time at the the Consumer Financial Protection Bureau, and from a popular online discussion forum.