In this Element and its accompanying Element, Matias D. Cattaneo, Nicolás Idrobo, and Rocío 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 accompanying Element, the authors discuss practical and conceptual extensions to the basic RD setup.

The increase in the international price of commodities after the international financial crisis in 2008 produced a gold rush in the Colombian economy, making legal and illegal mining a very profitable and attractive business. The increase in the illegal exploitation of metals like gold has exacerbated violence in municipalities with an abundance of such minerals. Gold is believed to be a new engine in the Colombian conflict. This paper documents the phenomenon and quantifies the causal impact that the gold boom has had on indicators of violence such as homicides, forced displacement and massacres. We use the location of national parks, indigenous reserves and geochemical anomalies associated with the presence of gold mines as instruments for illegal mining in order to disentangle the causal effect of illegal mining on violence. By law, it is very difficult to get licenses for the extraction of gold in parks and indigenous reserves, and this might be a factor increasing the prevalence of illegal mining activities in municipalities with these features. In order to have time variation in our instruments, we interact geographical features associated with the presence of gold and illegal gold mining (which vary only at the municipal level) with the international price of gold. Our estimates indicate that the rise of illegal gold mining has caused a statistically significant increase in violence, as measured with the homicide rate and the victims of massacres. However, we do not find a significant causal effect of illegal gold mining on forced displacement. Our interpretation is that the increase in the profitability of illegal mining activities has sparked a dispute over territorial control between illegal armed groups in order to monopolize the extraction of the precious minerals. Nevertheless, illegal mining is a labor intensive activity, and this may have counteracted the incentives of illegal armed groups to displace local populations from their land.

Surprising trends in late-counted votes can spark conflict. When late-counted votes led to a narrow incumbent victory in Bolivia last year, fraud accusations followedwith dramatic political consequences. We study the pro-incumbent shift in vote share as the tally progressed, finding that we can explain it without invoking fraud. Two observable characteristics, rurality and region, account for most of the trend. And what looked like a late-breaking surge in the incumbent's vote share-which electoral observers presented as evidence of foul play-was actually an artifact of methodological and coding errors. Our findings underscore the importance of documenting innocuous explanations for differences between early-and late-counted votes.

Surprising trends in late-counted votes can spark conflict. When late-counted votes led to a narrow incumbent victory in Bolivia last year, fraud accusations followedwith dramatic political consequences. We study the pro-incumbent shift in vote share as the tally progressed, finding that we can explain it without invoking fraud. Two observable characteristics, rurality and region, account for most of the trend. And what looked like a late-breaking surge in the incumbent's vote share-which electoral observers presented as evidence of foul play-was actually an artifact of methodological and coding errors. Our findings underscore the importance of documenting innocuous explanations for differences between early-and late-counted votes.

This monograph, together with its accompanying first part (Cattaneo, Idrobo, and Titiunik, 2020), collects and expands the instructional materials we prepared for more than 40 short courses and workshops on Regression Discontinuity (RD) methodology that we taught between 2014 and 2022. These teaching materials were used at various institutions and pro-