The goal of most empirical projects is to draw causal inferences about how one or more independent variables affect some dependent variable of interest. As we saw Part I of this book, research design—not statistical methods—is what empowers the researcher to perform causal inference. To put it another way, with a deficient research design no statistical method will enable the researcher to perform causal inference.

For one type of study causal inference is relatively easy: experimental studies. But experiments are simply impossible for many projects relating to law. Especially when studying legal institutions, we can't experimentally manipulate lots of key variables: whether a judiciary is independent, whether a judge is male or female, or whether a constitution does or does not contain a particular provision. Instead, we're left with observational data produced by the world—not the researcher. What makes observational data more difficult to analyze is that we cannot control the independent variable of interest. The world controls it and so confounding factors may not balance themselves out between the treatment and control groups.

What should we do with observational data? First, we need to ensure that we have a research design that gives us enough leverage to answer the research question. Second, we require a statistical approach that will allow us to control for the potential effects of other factors. There are multiple ways to do this in practice, but the most common methods of statistical control are multiple regression models and their variants. Statistical control works by using a model—and, necessarily, its assumptions—to hold all other independent variables constant to isolate the effect of the key independent variable. Because these approaches are second-best to a true experiment, any causal inferences we draw from observational data require both faith in the research design and in the assumptions of the model. There is, alas, no silver bullet.

The purpose of this chapter is to review the various methods and show how we can use them to perform causal inference. We introduce the multiple regression model, tackle a number of important issues related to model specification, describe the logistic regression model, and conclude with a discussion of other methods for causal inference with observational data.

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