In the data I work with, it’s really common to come across data that’s measured as proportions: the percent of women in the public sector workforce, the amount of foreign aid a country receives as a percent of its GDP, the percent of religious organizations in a state’s nonprofit sector, and so on. When working with this kind of data as an outcome variable (or dependent variable) in a model, analysis gets tricky if you use standard models like

The world of econometrics has been roiled over the past couple years with a bunch of new papers showing how two-way fixed effects (TWFE; situations with nested levels of observations, like country-year, state-month, etc.) estimates of causal effects from difference-in-differences-based natural experiments can be biased when treatment is applied at different times.

Regression is the core of my statistics and program evaluation/causal inference courses. As I’ve taught different stats classes, I’ve found that one of the regression diagnostic statistics that students really glom onto is . Unlike lots of regression diagnostics like AIC, BIC, and the joint F-statistic, has a really intuitive interpretation—it’s the percent of variation in the outcome variable explained by all the explanatory variables.