Methodological and empirical research on regression discontinuity (RD) designs typically employs, explicitly or implicitly, one of two alternative paradigms to interpret the findings and conclusions. In the "local randomization" paradigm, the RD design is interpreted as a local experiment near the cutoff; in the "continuity-based" paradigm, it is interpreted as an approximation to unknown functions that can be extrapolated. Unfortunately, the differences between these two paradigms are often unclear and researchers tend to confuse and convolve them, which generates some inconsistencies in the way empirical RD studies are analyzed. This observation motivated us to write this paper, where we discuss the differences between both paradigms, how each of them requires different strategies for empirical analysis, and the assumptions under which both paradigms can be related, illustrating our discussion with a well-known empirical application.
What is the main conclusion that becomes evident from your research? (Or, what is your main takeaway?)
The paradigm that one adopts for the interpretation of RD designs should also guide the empirical analysis; the assumptions invoked in each paradigm inform the type of statistical techniques that should be used for analysis. Moreover, for some cases, we can make a recommendation regarding which approach should be used. In general, the continuity-based approach relies on weaker assumptions than the local randomization approach, so it should be the default approach. However, this recommendation applies only to RD applications where the running variable is continuous and the sample size is large enough for the usual Normal approximations to be reliable. When the running variable is discrete or the sample size is small, the local randomization approach is the most natural. Empirical findings and conclusions naturally depend on which paradigm is adopted.
What are some of the more interesting or surprising findings/conclusions did you find in the process of bringing this together?
It was very reassuring to re-analyze an RD study whose conclusions are robust to both paradigms. In our re-examination of the impact of Head Start assistance on child mortality (initially studied by Ludwig and Miller, Quarterly Journal of Economics, 2007), we found that whether we use a local randomization approach or a continuity-based approach, the Head Start program assistance reduced child mortality. We have also seen robustness in other RD applications, for example the U.S. Senate study we analyzed in Cattaneo, Frandsen and Titiunik (Journal of Causal Inference, 2015). This shows that differentiating between the two paradigms has the added benefit of giving researchers tools to assess robustness to various types of assumptions, which is particularly valuable in the case of the RD design, a non-experimental design where the assumptions imposed are of course not guaranteed to hold.
is an Associate Professor of Economics and Statistics at the University of Michigan. He specializes in theoretical and applied econometrics, with emphasis on non-/semi-parametrics, treatment effects and policy evaluation methodology, and causal inference. Matias's work appears in various journals in the social sciences and statistics, including Econometrica, Journal of the American Statistical Association and Journal of Politics. He was born and raised in Buenos Aires, Argentina, where he completed his undergraduate education at the Universidad de Buenos Aires and Masters in Economics at the Universidad Torcuato Di Tella. He received his M.A. in Statistics and his Ph.D. in Economics from UC-Berkeley, and joined the Michigan faculty immediately thereafter.
Rocio Titiunik is James Orin Murfin Associate Professor of Political Science at the Unviersity of Michigan. She specializes in quantitative methodology for the social sciences, with emphasis on quasi-experimental methods for causal inference and political methodology. She is particularly interested in the development and application of experimental and non-experimental methods to the study of political institutions. Her substantive interests center on democratic accountability and the role of party systems in developing democracies. Rocio's work appears in various journals in the social sciences and statistics, including the American Political Science Review, American Journal of Political Science, Journal of Politics, Econometrica, Journal of the American Statistical Association and Journal of the Royal Statistical Society. In 2016, she received the Emerging Scholar Award from the Society for Political Methodology, which honors a young researcher who is making notable contributions to the field of political methodology. She was born and raised in Buenos Aires, Argentina, where she completed her undergraduate education at the Universidad de Buenos Aires. She received her Ph.D. in Agricultural and Resource Economics from UC-Berkeley in May 2009. She joined the Michigan faculty in the fall of 2010, after spending one year there as a postdoctoral fellow.
is a Ph.D. candidate in Economics and M.A. candidate in Statistics at the University of Michigan with interests in applied econometrics and econometric theory. His research focuses on the identification and estimation of treatment effects. His recent projects study finite-sample randomization inference methods in Regression Discontinuity Designs (RDDs) and identification and extrapolation in RDDs with multiple cutoffs. He is currently working on identification and estimation of treatment effects when units can interfere with each other and generate spillover effects. Prior to starting his Ph.D., Gonzalo received a B.A. in Economics from Universidad de San Andres in Buenos Aires, Argentina, and worked as a consultant for the Inter-American Development Bank and the World Bank in Washington DC.