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In this Element and its accompanying second Element, A Practical Introduction to Regression Discontinuity Designs: Extensions, Matias Cattaneo, Nicolás Idrobo, and Rocıìo Titiunik provide an accessible and practical guide for the analysis and interpretation of regression discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. In this Element, the authors discuss the foundations of the canonical Sharp RD design, which has the following features: (i) the score is continuously distributed and has only one dimension, (ii) there is only one cutoff, and (iii) compliance with the treatment assignment is perfect. In the second Element, the authors discuss practical and conceptual extensions to this basic RD setup.

Regression analysis. --- Econometrics --- Discontinuous groups. --- Mathematical models. --- Combinatorial topology --- Functions of complex variables --- Group theory --- Economics, Mathematical --- Statistics --- Analysis, Regression --- Linear regression --- Regression modeling --- Multivariate analysis --- Structural equation modeling

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In this Element, which continues our discussion in Foundations, the authors provide an accessible and practical guide for the analysis and interpretation of Regression Discontinuity (RD) designs that encourages the use of a common set of practices and facilitates the accumulation of RD-based empirical evidence. The focus is on extensions to the canonical sharp RD setup that we discussed in Foundations. The discussion covers (i) the local randomization framework for RD analysis, (ii) the fuzzy RD design where compliance with treatment is imperfect, (iii) RD designs with discrete scores, and (iv) and multi-dimensional RD designs.

Regression analysis. --- Econometrics --- Discontinuous groups. --- Mathematical models.

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Despite the importance of housing for people's well-being, there has been little work done to assess the causal impact of housing and housing improvement programs on health and welfare. In this paper the authors help fill this gap by investigating the impact of a large-scale effort by the Mexican government to replace dirt floors with cement floors on child health and adult happiness. They find that replacing dirt floors with cement floors significantly reduces parasitic infestations in young children, reduces diarrhea, reduces anemia, and improves cognitive development. Finally, they also find that this program leave adults substantially better off, as measured by satisfaction with their housing and quality of life and by their significantly lower rates of depression and perceived stress.

Aged --- Child Development --- Children --- Depression --- Families --- Health --- Health Monitoring and Evaluation --- Health Outcomes --- Health, Nutrition and Population --- Implementation --- Injuries --- Intervention --- Iron --- Mental --- Mental Health --- Parasitic Diseases --- People --- Psychology --- Quality of Life --- Strategy --- Stress --- Ventilation