Designing Discontinuities
This work addresses the design of discontinuities for causal inference, offering a method to optimize effects in domains like social capital and health, though it is incremental as it builds on existing regression discontinuity techniques.
The paper tackles the problem of designing optimal partitions for discontinuous variables to maximize causal effects, proposing a quantization-theoretic approach with dynamic programming and reinforcement learning, and demonstrates it by optimizing time zone borders for social and health outcomes using novel data.
Discontinuities can be fairly arbitrary but also cause a significant impact on outcomes in larger systems. Indeed, their arbitrariness is why they have been used to infer causal relationships among variables in numerous settings. Regression discontinuity from econometrics assumes the existence of a discontinuous variable that splits the population into distinct partitions to estimate the causal effects of a given phenomenon. Here we consider the design of partitions for a given discontinuous variable to optimize a certain effect previously studied using regression discontinuity. To do so, we propose a quantization-theoretic approach to optimize the effect of interest, first learning the causal effect size of a given discontinuous variable and then applying dynamic programming for optimal quantization design of discontinuities to balance the gain and loss in that effect size. We also develop a computationally-efficient reinforcement learning algorithm for the dynamic programming formulation of optimal quantization. We demonstrate our approach by designing optimal time zone borders for counterfactuals of social capital, social mobility, and health. This is based on regression discontinuity analyses we perform on novel data, which may be of independent empirical interest.