This post combines two of my long-standing interests: causal inference and Bayesian statistics. I’ve been teaching a course on program evaluation and causal inference for a couple years now and it has become one of my favorite classes ever.

In most of my research, I work with country-level panel data where each row is a country in a specific year (Afghanistan in 2010, Afghanistan in 2011, and so on), also known as time-series cross-sectional (TSCS) data.

At the end of my previous post on beta and zero-inflated-beta regression, I included an example of a multilevel model that predicted the proportion of women members of parliament based on whether a country implements gender-based quotas for their legislatures, along with a few different control variables. I also included random effects for year and region in order to capture time- and geography-specific trends.

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

I’ve been teaching a course on program evaluation since Fall 2019, and while part of the class is focused on logic models and the more managerial aspects of evaluation, the bulk of the class is focused on causal inference. Ever since reading Judea Pearl’s The Book of Why in 2019, I’ve thrown myself into the world of DAGs, econometrics, and general causal inference, and I’ve been both teaching it and using it in research ever since.

Update #1 An update to knitr has made it a ton easier to embed fonts in SVG files from R. Jump to the update to see how. Update #2 Also, it’s possible to change TikZ fonts and not use Computer Modern for everything! Jump to the second update to see how.

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.

Since my last two blog posts on binary and continuous inverse probability weights (IPWs) and marginal structural models (MSMs) for time-series cross-sectional (TSCS) panel data, I’ve spent a ton of time trying to figure out why I couldn’t recover the exact causal effect I had built in to those examples when using panel data. It was a mystery, and it took weeks to figure out what was happening.

In my post on generating inverse probability weights for both binary and continuous treatments, I mentioned that I’d eventually need to figure out how to deal with more complex data structures and causal models where treatments, outcomes, and confounders vary over time.