Christoph Rothe, National Science Foundation

Non-Standard Issues in Regression Discontinuity Designs, joint with Francois Gerard and Miikka Rokkanen

This project aims to develop new statistical methods for analyzing economic data. The goal is to expand the scope of the popular regression discontinuity (RD) design, which uses the presence of fixed eligibility cutoffs (e.g. Medicare eligibility at age 65) for estimating the effect of public and private policies on some outcome of interest (e.g. health care utilization, mortality) among individuals who are close to the cutoff. In particular, the research provides new methodological tools for dealing with two important and frequent practical challenges for RD designs: (i) how to deal with situations in which some individuals can manipulate their program eligibility, and (ii) how to infer the effect of the program on individuals who are far away from the cutoff. Because RD designs have become a popular method to evaluate many government policies, it is important to address these two challenges. This research, therefore, will improve the statistical methods we use to assess the effects of public policy, and it will allow economists and other social scientists to provide better information to policymakers.

This research project consists of two parts that each addresses an important limitation of standard RD designs. The first part of the project is motivated by the limitation that some units (i.e., individuals or families) may be able to manipulate their value of the so-called running variable used to determine eligibility (e.g., income, which could be misreported). Manipulation is problematic if it leads to units just to the left and right of the cutoff being no longer comparable due to self-selection, in which case treatment effects are no longer point-identified. The investigators show that interesting causal parameters can still be partially identified in RD designs when the running variable is manipulated. This research derives sharp bounds on treatment effects for the (unobserved) subgroups of units not engaging in a manipulation, and also derives new econometric methods to estimate these bounds and to conduct inference. The second part is motivated by the limitation that RD designs only allow for the identification of treatment effects for marginal units at the cutoff and are generally not informative about treatment effects for units away from the cutoff. This lack of external validity limits the usefulness of RD estimates in guiding policies that would change assignments of units away from the cutoff. The investigators develop a latent factor-based approach to the identification and estimation of treatment effects away from the cutoff. To the extent that the source of omitted variables bias in a RD design can be modeled using latent factors, the running variable is one of a number of noisy measures of these factors. Assuming other noisy measures are available, causal effects for all values of the running variable can be non-parametrically identified and estimated.